The slope of the function 5x − 3y = −3 is 5/3 and the y-intercept of the function 5x − 3y = −3 is 1.
First, let us understand the slope intercept form;
The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.
We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.
We are given;
5x − 3y = −3
- 3y = -5x - 3
3y = 5x + 3
y = 5/3 x + 1
Compare with y = mx + c, we will get;
m = 5/3
b = 1
So, the slope is 5/3 and the y-intercept is 1.
Thus, the slope of the function y = 2 + 34x is 5/3 and the y-intercept of the function y = 2 + 34x is 1.
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IXL Please Help Fast!
In the given rectangular prism vector line IM and LM intersect each other. Option B is correct.
What is a rectangular prism?It is defined as a six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.
Six faces, twelve sides, and eight vertices make up a rectangular prism (corners). Three of the 12 edges meet to create right angles at each vertex.
Since from all 12 edges vector line IM and LM meet to form right angles at each vertex.
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Thus, in the given rectangular prism vector line IM and LM intersect each other. Option B is correct.
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NO LINKS!! Please help me with the Segment Proofs Part 1
Answers in bold
GivenGivenDefinition of midpointTransitive property of equalityAddition property of equalitySimplificationSubstitutionSegment addition postulateTransitive property of equalityDivision property of equality====================================================
Explanation:
Always start the proof with what you are given. It seems silly to repeat the given information, but it's just how all proofs are formed. This is to build from those given statements to lead to what we want to prove on the last line.
The term "midpoint" refers to splitting a segment into two equal smaller pieces. So for instance, if Q is the midpoint of PR, then the pieces PQ and QR are equal. Each smaller piece is half as long as PR.
The transitive property is the idea if A = B and B = C, then A = C. Think of it like substitution. Or you can think of a set of dominoes: A knocks down B, which knocks down C. Therefore A knocks down C.
The addition property of equality is where we go from A = B to A+C = B+C. I've added C to both sides. Adding the same thing to both sides will not change the equation. It keeps things balanced. When going from line 4 to line 5, we added PQ to both sides.
In line 6, we've gone from PQ+PQ to 2PQ.
In line 7, we replace PQ with QR on the right hand side. We use the substitution property here (refer to line 3 where we found PQ = QR)
Line 8 uses the segment addition postulate. If A,B,C are collinear, then AB+BC = AC. The point B doesn't necessarily need to be the midpoint.
Line 9 uses the transitive property again (we combine lines 7 and 8 to lead to line 9).
The final line has us divide both sides by 2 to get what is shown in the table. This is the division property of equality.
------------------------
Shortcut using informal logic:
PQ = QR
QR is half as long as QS
Therefore, PQ is also half as long as QS
Answer:
The last reason for [tex]PQ=\frac{1}{2}QS[/tex] is division property of equality
Step-by-step explanation:
The reason for [tex]PQ=\frac{1}{2}QS[/tex] can be evaluated as follows
For the statement [tex]Q[/tex] is the midpoint of [tex]\overline{PR}[/tex], the reason is given
For the statement [tex]R[/tex] is the midpoint of [tex]\overline{QS}[/tex], the reason is given
For the statement [tex]PQ=QR, QR=RS[/tex] , the reason is definition of midpoint
The midpoint of a line segment is the point that separates the line segment into two congruent parts.
For the statement [tex]PQ=RS[/tex] , the reason is transitive property
Transitive property says that if [tex]a=b[/tex], and [tex]b=c[/tex], then [tex]a=c[/tex]
In this statement [tex]PQ=QR, QR=RS[/tex], then [tex]PQ=RS[/tex]
For the statement [tex]PQ+PQ=PQ+RS[/tex] , the reason is addition property of equality
Addition property of equality says that if [tex]a=b[/tex], then [tex]a+c=b+c[/tex]
For the statement [tex]2PQ=PQ+RS[/tex] , the reason is combining of like terms of algebraic expression
Combining like terms is the process to add or to substract the coefficient of the terms
In this statement combining like terms is at the left side of the equation, [tex]PQ+PQ=2PQ[/tex]
For the statement [tex]2PQ=QR+RS[/tex] , the reason is substitution property
Substitution property of equality says that if [tex]a=b[/tex], then [tex]a[/tex] replaces [tex]b[/tex] in any equation, in this statement [tex]QR[/tex] replaces [tex]PQ[/tex]
For the statement [tex]QR+RS=QS[/tex] , the reason is substitution property and definition of midpoint
In this statement [tex]QR+RS[/tex] replaces [tex]2PQ[/tex], and [tex]QS[/tex] is the sum of two congruent parts [tex]QR+RS[/tex]
For the statement [tex]2PQ=QS[/tex] , the reason is substitution property
In this statement [tex]2PQ[/tex] replaces [tex]QR+RS[/tex]
For the statement [tex]PQ=\frac{1}{2}QS[/tex] , the reason is division property of equality
Division property of equality says that if [tex]a=b[/tex], and [tex]c\neq 0[/tex], then [tex]\frac{a}{c} =\frac{b}{c}[/tex]
In this statement [tex]\frac{2PQ}{2} =\frac{QS}{2}[/tex] or can be reduced into [tex]PQ=\frac{1}{2}QS[/tex]
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what is 3 5/8 adding 1 2/8
Answer:
The solution is 4 7/8 or 39/8
Step-by-step explanation:
[tex] \sf 3 \frac{5}{8} + 1 \frac{2}{8} \\ \\ = \sf (3 + 1) + ( \frac{5}{8} + \frac{2}{8} ) \\ \\ = \sf 4 + \frac{7}{8} \\ \\ = \sf 4 \frac{7}{8} [/tex]
Or
[tex]\sf 3 \frac{5}{8} + 1 \frac{2}{8} \\ \\ = \frac{29}{8} + \frac{10}{8} \\ \\ = \sf \frac{39}{8} [/tex]
11. This table shows the items sold by an ice cream ship in the first hour after opening.
Cup 6
Cone 4
Milkshake 3
Sundae 1
What is the experimental probability that the next customer will order a cone?
Answer:
2:7 or [tex]\frac{2}{7}[/tex]
Step-by-step explanation:
The cone total is 4 and the total orders is 14
[tex]\frac{4}{14}[/tex] = [tex]\frac{2}{7}[/tex]
Solve for x. Round to the nearest tenth, if necessary.
Answer:
27.64
Step-by-step explanation:
As the triangle is right-angle triangle,take another 29° and take sin29°You will get sin29°=x/57-- as(p/h)then x=57*sin29°=27.64Find the value of x.
( please help! Dude today!)
Answer: tell me the soulation like how do you solve it then I can help
Step-by-step explanation:
Using slope-intercept, standard form, or point slope -
An arrow released from a bow, traveling towards a target 200 yards away,
reaches a max height of 42.6 ft in only 1.5 seconds. What is the height of the
arrow at 2.5 seconds?
Thank you so much!
The height of the arrow at 2.5 seconds is 71 feet.
Given:
An arrow released from a bow, traveling towards a target 200 yards away,reaches a max height of 42.6 ft in only 1.5 seconds.
1.5 seconds = 42.6 feet
divide by 1.5 on both sides.
1 sec = 28.4 feet
0.5 sec = 28.4/2
0.5 sec = 14.2 feet
2.5 sec = 1.5 sec + 1 sec
= 42.6 + 28.4
= 71 feet
Therefore The height of the arrow at 2.5 seconds is 71 feet.
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Which number line represents the solutions to |–2x| = 4?
(I want a clear explanation)
Answer:
third option
Step-by-step explanation:
| - 2x | = 4
the absolute value function always gives a positive value, however, the expression inside can be positive or negative , that is
- 2x = 4 ( divide both sides by - 2 )
x = - 2
or
- (- 2x) = 4
2x = 4 ( divide both sides by 2 )
x = 2
solutions are x = - 2 , x = 2
these are illustrated on the number line by solid circles at - 2 and 2
this is indicated on the third number line
Number line represents the solutions to |–2x| = 4 is third number line (x1 = -2, x2= 2).
Solving steps :
1. Calculate
Calculate the absolute value.
|-2x| = 4
Use |ab| = |a| * |b| to transform the expression.
|-2x|
|-2| * |x|
The absolute value of any number is always positive.
2 * |x|
We did it!
|-2x| = 4
2 * |x| = 4
2. Divide both sides
Divide both sides of the equation by 2.
2 * |x| = 4
2 * |x| ÷ 2 = 4 ÷ 2
Any expression divided by itself equals 1.
|x| = 4 ÷ 2
Calculate the quotient.
|x| = 2
3. Separate into possible cases
Use the absolute value definition to rewrite the absolute value equation as two separate equations.
|x| = 2
x = 2
x = -2
4. The equation has 2 solutions.
x1 = -2, x2= 2
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A rectangular garden has an area of 72 square yards. The dimensions of the
garden are not prime numbers. What are the possible dimensions of the
garden
The possible dimensions of the rectangular garden with an area of 72 square yards are (4,18), (8,9), (6,12), (2,36)
What is meant by an area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
Given,
The area of a rectangular garden is 72 square yards.
And also given that the dimensions of the garden are not prime numbers.
LCM of 72 is,
=2×2×2×3×3
Therefore, the possible dimensions of the garden are:
(4,18)
(8,9)
(6,12)
(2,36)
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An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1050 feet apart. As the
airplane passes over the line joining them, each observer takes a sighting of the angle
elevation to the plane, as indicated in the figure. If A = 30 degrees and B = 40 degrees how high is the
airplane?
If the angle elevation to the plane A = 30 degrees and B = 40 degrees , then the Airplane is 359.11 feet high .
In the question ,
it is given that
the distance between the two observer = 1050 feet
the measure of angle A is = 30°
the measure of angle B is = 40°
By angle sum property angle C is = 180 - (30 + 40)
= 180 - (70)
= 110
By Sine Law .
Sin(110)/1050 = Sin(30)/a = Sin(40)/b
Using , Sin(110)/1050 = Sin(30)/a ,
we get ,
Sin(110)/1050 = 0.5/a
a = 558.69
Using Sin(110)/1050 = Sin(40)/b
b = 718.24
By using Sine Law
Sin(40)/h = Sin(90)/558.69
h = 359.11
Therefore , If A = 30 degrees and B = 40 degrees , then the Airplane is 359.11 feet high .
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What is the equation of the line that passes through the point
(
6
,
2
)
(6,2) and has a slope of
−
1
2
−
2
1
?
The equation of the line that passes through the point (-6, 2) and has slope of -1/2 is y = (-1/2)x - 1
The slope of the line = -1/2
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope intercept form
y = mx + b
Where m is the slope of the line
b is the y intercept form
The coordinates of the point = (-6, 2)
Substitute the values in the equation
2 = (-1/2)(-6) + b
2 = 3 +b
b = 2 -3
b = -1
The equation will be
y = (-1/2)x - 1
Hence, the equation of the line that passes through the point (-6, 2) and has slope of -1/2 is y = (-1/2)x - 1
The complete question is :
What is the equation of a line that passes through (-6, 2) and has a slope of -1/2 ?
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deposited $8500 into a savings account 3 years ago. The simple interest rate is 2%. How much money did marsha earn in interest?
Answer:Marsha earned interest = $850
Step-by-step explanation:
Amount deposited = $8500
Time = 2 years
Interest rate = 5% = 0.05
We need to find how much did Marsha earn in interest
The formula use is:
Where I is interest earned, P is amount deposited, r is interest rate and t is time.
Putting values and finding interest.
So, Marsha earned interest = $850
Determine whether the figure is a parallelogram using the distance formula.
Q\left(-10,-2\right),R\left(1,-1\right),S\left(1,-7\right),T\left(-11,-8\right)Q(−10,−2),R(1,−1),S(1,−7),T(−11,−8)
The distance formula used to determine if the figure is a parallelogram indicates;
The length of QR ≈ 11.0 and the length of ST ≈ 12.0. The length of QS ≈ 12.1, and the length of RT ≈ 13.9. Therefore, QRST is not a parallelogramWhat is a parallelogram?A parallelogram is a quadrilateral that have two pairs of facing sides that are parallel and of the same length.
The length of the sides can be found by using the formula for finding the distance between two points on the coordinate plane as follows;
The distance between the points (x₁, y₁) and (x₂, y₂) is d = √(x₂ - x₁)² + (y₂ - y₁)²
The length of QR = √((1 - (-10))² + (-1 - (-2))²) = √(122) ≈ 11.0
Length of ST = √((1 - (-11))² + (-7 - (-8))²) = √(145) ≈ 12.0
Length of QS = √((1 - (-10))² + (-7 - (-2))²) = √(146) ≈ 12.1
Length of RT = √((1 - (-11))² + (-1 - (-8))²) = √(193) ≈ 13.9
The lengths of the opposite sides of a parallelogram are the same. The lengths of the sides of the quadrilateral QRST are different, therefore, quadrilateral QRST is not a parallelogram.
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You have 4,592 grams of a radioactive kind of scandium. How much will be left after 168 days if its half-life is 84 days?
Answer:
1,148
Step-by-step explanation:
NO LINKS!! Describe the set of all points P(x, y) in a coordinate plane that satisfy the given condition. Part 2
Part (d)
If xy > 0, then the two items x and y must have the same sign.
Examples where x,y are both positive
x = 2 and y = 5 leads to xy = 2*5 = 10x = 7 and y = 4 leads to xy = 7*4 = 28Examples where x,y are both negative
x = -1 and y = -9 leads to xy = -1*(-9) = 9x = -12 and y = -3 leads to xy = -12*(-3) = 36This places us in either the first quadrant or third quadrant (Q1 and Q3)
Q1 is where x > 0 and y > 0 (northeast corner)Q3 is where x < 0 and y < 0 (southwest corner)Answer: The set of all points in quadrants I and III (x and y have the same sign)======================================================
Part (e)
If y < 0, then we have points like (2,-5) and (1,-7). The x coordinate doesn't matter as long as the y coordinate is negative.
Visually speaking we are below the x axis. This places the point in Q3, Q4, or on the negative y axis. The point cannot be on the x axis. You can think of this point as being underground or underwater.
Answer: The set of all points below the x axis======================================================
Part (f)
If x = 0, then the point is on the vertical y axis. Recall that y intercepts always occur when x = 0. Two examples would be (0,4) and (0,12).
Answer: The set of all points on the y axis.Answer:
(d) The set of all points in quadrants I and III (x and y have the same sign).
(e) The set of all points below the x-axis.
(f) The set of all points on the y-axis.
Step-by-step explanation:
The Cartesian plane is divided into four quadrants.
Quadrant I is the upper right quadrant and the rest follow in a counterclockwise direction.
Quadrant I: x > 0 and y > 0 → (x, y)Quadrant II: x < 0 and y > 0 → (-x, y)Quadrant III: x < 0 and y < 0 → (-x, -y)Quadrant IV: x > 0 and y < 0 → (x, -y)Part (d)
For xy > 0, x and y should either both be positive or both be negative, i.e. have the same sign.
x and y are both positive in quadrant I.x and y are both negative in quadrant III.Therefore, the description that satisfies the given condition is:
The set of all points in quadrants I and III (x and y have the same sign).Part (e)
For y < 0, y is always negative.
y is negative in quadrant III.y is negative in quadrant IV.Quadrants III and IV are below the x-axis.
Therefore, the description that satisfies the given condition is:
The set of all points below the x-axis.Part (f)
The only place where x = 0 is the y-axis.
Therefore, the description that satisfies the given condition is:
The set of all points on the y-axis.A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 13 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places.
The probability that exactly 4 insects will survive is 0.8975
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, 0 indicates impossibility of the event and 1 indicates certainty.
probability= sample space/total possible outcome
the total possible outcome for the insecticide to kill insect is 60%
If 4 will survive out of 13, it means 7 will be killed by the insecticide, the percentage is now 7/13×100 = 53.85%
Therefore the probability for 4 insect to survive is 53.85/60= 0.8975
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Members of the drama club are selling tickets on the night of the their show. Some money is placed in the cashbox before any tickets are sold. As drama club members sell their tickets, they record the number of tickets sold and the total amount of money in the cash box
Number of Tickets sold
20
43
108
Money is the Cashbox (dollars) :
320
492.50
980
a. Assuming all of the tickets are the same price, write an equation. that describes the relationship between the number of tickets sold and the total amount of money in the cashbox
b. How much money is in the cashbox before any tickets are sold? Explain how you found your answer by using the equation from part a
c. What is the price of each ticket? Explain how you found your answer by using the equation from part a
From the question, we could give annotations for the number of tickets sold and the amount of money in the cashbox. We also find that there is 2 other elements related to the relationship between the tickets sold and the amount of money in the cashbox; the price of each ticket and the amount of money in the cashbox before any tickets are sold. Hence we could make some annotations:
m = money in the cashbox (after tickets are sold)
p = price of each tickets
x = number of tickets sold
c = money in the cashbox (before tickets are sold)
Based on the question, we know that the amount of money in the cashbox is dependeding on the number of tickets sold and the original amount of money in the cashbox before any tickets are sold. The relationship between the money in the cashbox and the number of tickets sold is depending on the price of each ticket. Based on this understanding, we could rewrite the relationship into such equation:
m = px + c ... (i)
Using data from the question, we could input the datas into equation (i):
m = px + c
320 = 20p + c ... (ii)
492.50 = 43 p + c ... (iii)
980 = 108 p + c ... (iv)
By using equation (ii) and (iv) we could find the value of p
320 = 20p + c
980 = 108p + c -
660 = 88p
p = 7.5 ... (v)
Using the finding value of p, we could find the value of c by using subtitution of equation (v) into equation (ii):
320 = 20p + c
320 = 20(7.5) + c
320 = 150 + c
c = 170 ... (vi)
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7x²(2x - 3) 3z3 + 4 in word form?
Answer:
seven multiplied by x to the second power multiplied by the difference of two multiplied by x subtract 3 multiplied by the product of three multiplied by z multiplied by 3 add four.
Step-by-step explanation:
This is a useless question, word form isn't in any sort of ACTUAL GLOBAL TEST. So don't stress over this.
(3x + 5y)^5
Rewrite the following expression in expanded form and simplify completely.
Answer: 243x^5 + 2025x^4y + 6750x^3y^2 + 11250x^2y^3 + 9375xy^4 + 3125y^5
Step-by-step explanation:
1. To find each term, use BINOMIAL EXPANSION THEOREM (best to look up theorem on your own).
2. Expand the summation (after finding each term).
3. Simplify the exponents for each term.
> 1 • (3x)^5 • (5y)^0 + 5 • (3x)^4 • (5y)^1 + . . . + 1 • (3x)^0 • (5y)^5
4. Simplify.
At Monroe College, 1/2 of the students are enrolled in an art class. Of the students enrolled in an art class, 3/10 are enrolled in a painting class. What fraction of the students at Monroe College are enrolled in a painting class?
Answer:7/10
Step-by-step explanation:
You buy two tickets for a school raffle. If 358 tickets are sold, what is the probability that you will win the
raffle? Write your answer as a percent rounded to the nearest thousandth of a percent.
Answer:
0.559%
Step-by-step explanation:
The chance of winning equals the number of tickets bought divided by the total number of tickets
2 tickets are bought by the person, and 358 tickets are sold in total
2/358 would equal 0.00558659218..., and the percentage would be 0.558659...%
Rounding 0.558659 to the nearest thousandth's place would yield
0.559, so 0.559% would be the final answer
Triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E'. Side D'E' measures 3.5. What is the measure of Side DE?
If triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E' , then measure of the side DE is 14.
In the question ,
it is given that ,
The triangle CDE is dilated by scale factor of 1/4
and the new triangle formed after dilation is C'D'E' .
it is given that the measure of the side D'E' = 3.5 .
let the measure of the the side DE = x
So , according to the question ,
x *(1/4) = 3.5
On cross multiplication,
we get ,
x = 4* 3.5
x = 14
Therefore , If triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E' , then measure of the side DE is 14.
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Express the trig ratio as fractions in simplest terms
The trigonometric ratio (trig ratio) for the angle in this right-angled triangle should be expressed as fractions in simplest terms as follows:
Sin(M) = 21/121
Cos(L) = 10/11
Tan(K) = 21/100
How to express the trig ratio as fractions?In Mathematics, a trigonometric ratio (trig ratio) can be calculated by using this mnemonic SOHCAHTOA:
Sinθ = Opposite/Hypotenuse
Sin(M) = KM/ML
Sin(M) = √21/11
Taking the square of both the numerator and denominator, we have:
Sin(M) = (√21)²/11²
Sin(M) = 21/121
For the cosine of an angle in a right-angled triangle, we have:
Cosθ = Adjacent/Hypotenuse
Cos(L) = KL/ML
Cos(L) = 10/11
For the tangent of an angle in a right-angled triangle, we have:
Tanθ = Opposite/Adjacent
Tan(K) = KM/KL
Tan(K) = √21/10
Taking the square of both the numerator and denominator, we have:
Tan(K) = (√21)²/10²
Tan(K) = 21/100
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A rectangle's length is 5.1 more than 2 times its width. Its perimeter is 165.6. Write and solve a system of equations to find the dimensions of the rectangle.
Type the area of the rectangle, rounded to the nearest tenth.
The length of the rectangle is 56.9 unit and the breadth of the rectangle is 25.9 unit.
Area of the rectangle is 1473.7 sq. unit.
Given, a rectangle's length is 5.1 more than 2 times its width.
Its perimeter is 165.6.
Let the length of the rectangle be l,
breadth of the rectangle be b.
According to the question,
l = 5.1 + 2b
Using the formula of Perimeter,
Perimeter = 2(l + b)
165.6 = 2(5.1 + 2b + b)
165.6 = 2(5.1 + 3b)
82.8 = 5.1 + 3b
3b = 77.7
b = 25.9
Now, l = 5.1 + 2(25.9)
l = 5.1 + 51.8
l = 56.9
So, the length of the rectangle is 56.9 unit
and the breadth of the rectangle is 25.9 unit
Now, the area of the rectangle be,
Area = l×b
Area = 56.9×25.9
Area = 1,473.71
Area of the rectangle = 1473.7 sq. unit
Hence, the length of the rectangle is 56.9 unit and the breadth of the rectangle is 25.9 unit.
Area of the rectangle is 1473.7 sq. unit.
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Need help with this problem please help
The error is that the student used the formula for a reflection in the x-axis, and the correct endpoints are: C'(1, 1) and D'(3, -2)
What is the error in finding the coordinates of the image after a rotation of 270?Rotation simply means turning.
In a cartesian plane, if a point P, whose position vector is (x,y), is rotated through 270° about the origin, the position of the image P' is (y, -x)
But the reflection in the x-axis is defined as (x,y) => (x, -y) i.e. if a position vector of a point is (x,y), the position vector of its image in the x-axis is (x, -y)
Given: C(-1, 1) and D'(2, 3)
Therefore, the student used the formula for a reflection in the x-axis. The 2nd option is the answer.
The correct endpoints are: C'(1, 1) and D'(3, -2)
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Is anyone able to solve this?
Answer:
2.4
Step-by-step explanation:
The bottom is a right triangle. You know the 2 legs, you need the hypotenuse.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]1^{2}[/tex] + [tex]1^{2}[/tex] = [tex]c^{2}[/tex]
1 + 1 = [tex]c^{2}[/tex]
2 = [tex]c^{2}[/tex]
[tex]\sqrt{2}[/tex] = [tex]\sqrt{c^{2} }[/tex]
[tex]\sqrt2[/tex] = c
Now we know the 2 legs for the larger triangle on top.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]\sqrt{2} ^{2}[/tex] + [tex]2^{2}[/tex] = [tex]c^{2}[/tex]
2 + 4 = [tex]c^{2}[/tex]
6 = [tex]c^{2}[/tex]
[tex]\sqrt{6}[/tex] = [tex]\sqrt{c^{2} }[/tex]
[tex]\sqrt{6}[/tex] = c
[tex]\sqrt{6}[/tex] rounded to the tenths place is 2.4
Find the y-intercept and x-intercept of the following linear equation.
−32x−3y=3
Plot 2 sets of coordinates
The y-intercept and x-intercept of the following linear equation is
x intercept = -0.094y intercept = -1How to find the interceptsx intercept
x intercept refers to the value of x when y is zero
−32x−3y=3
at y = 0
-32x - 3 * 0 = 3
-32x = 3
x = -3/32 = -0.09375
the coordinate is (-0.094, 0)
y intercept
y intercept refers to the value of y when x is zero
−32x −3y=3
at x = 0
0 - 3y = 3
y = -1
the coordinate is (0, -1)
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You have 72 square feet of material to build a rectangular box.
The length is twice the width and there is no top.
What values for W and L and H will create a box that encloses the maximum volume using the material you have?
W = ?
L = ?
H = ?
For the given conditions, the length of box=6.92 feet, width of box=3.46 feet and height of box=2.31 feet.
What is volume?Each object in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's capacity.
Here,
area of material=72 feet²
V=lbh
l=2b
72=lb+2lh+2bh
substitute l as 2b,
72=2b²+4bh+2bh
36=b²+3bh
3bh=36-b²
h=(36-b²)/3b
v=lbh
v=2b*b*(36-b²)/3b
v=2b*(36-b²)/3
=(72b-2b³)/3
differentiate the v,
v'=1/3(72-6b²)
v'=0
72-6b²=0
6b²=72
b²=12
b=√12
b=3.46 feet
l=2b=6.92 feet
h=(36-b²)/3b
=(36-12)/3*3.46
h=2.31 feet
The box measures 6.92 feet long, 3.46 feet wide, and 2.31 feet tall under the specified circumstances.
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Answer:
[tex]W=2\sqrt{3}=3.46\; \sf ft\;(2\;d.p.)[/tex]
[tex]L=4\sqrt{3}=6.93\; \sf ft\;(2\;d.p.)[/tex]
[tex]H = \dfrac{4\sqrt{3}}{3}=2.31\; \sf ft\;(2\;d.p.)[/tex]
Step-by-step explanation:
If the length is twice the width:
W = widthL = 2W = lengthH = heightSurface area of the box
[tex]\implies SA = WL + 2WH + 2LH[/tex]
[tex]\implies SA = W(2W) + 2WH + 2(2W)H[/tex]
[tex]\implies SA = 2W^2 + 2WH + 4WH[/tex]
[tex]\implies SA = 2W^2 + 6WH[/tex]
If the surface area is 72 ft²:
[tex]\implies 2W^2 + 6WH = 72[/tex]
[tex]\implies 6WH = 72 - 2W^2[/tex]
[tex]\implies H = \dfrac{72 - 2W^2}{6W}[/tex]
[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]
Volume of the box
[tex]\implies V = LWH[/tex]
[tex]\implies V = (2W)WH[/tex]
[tex]\implies V = 2W^2H[/tex]
Substitute the found expression for H into the formula for volume:
[tex]\implies V = 2W^2\left(\dfrac{36 - W^2}{3W}\right)[/tex]
[tex]\implies V = \dfrac{2W^2(36 - W^2)}{3W}[/tex]
[tex]\implies V = \dfrac{2W(36 - W^2)}{3}[/tex]
[tex]\implies V = \dfrac{72W - 2W^3}{3}[/tex]
[tex]\implies V =24W-\dfrac{2}{3}W^3}[/tex]
To find the value of W when the volume is at its maximum, first differentiate the equation for volume with respect to W:
[tex]\implies \dfrac{\text{d}V}{\text{d}W}=24-2W^2[/tex]
Now set the derivative to zero and solve for W:
[tex]\implies 24-2W^2=0[/tex]
[tex]\implies 2W^2=24[/tex]
[tex]\implies W^2=12[/tex]
[tex]\implies W=\sqrt{12}[/tex]
[tex]\implies W=2\sqrt{3}[/tex]
As length is twice the width:
[tex]\implies L=2 \cdot 2\sqrt{3}[/tex]
[tex]\implies L=4\sqrt{3}[/tex]
To find H, substitute the found value of W into the expression for H:
[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]
[tex]\implies H = \dfrac{36 - (2\sqrt{3})^2}{3(2\sqrt{3})}[/tex]
[tex]\implies H = \dfrac{36 - 12}{6\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{24}{6\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{4}{\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{4\sqrt{3}}{3}[/tex]
Bob's Gift Shop sold 500 cards for Mother's Day. One salesman, Camila, sold 10% of the cards sold for Mother's Day. How many cards did Camila sell? answer: 50
The number of cards Camila sold is 50cards
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”. For example if 10% of 200 students in a school are boys, the the number of boys in the school is 10/100× 200= 20students
Similarly Camila sold 10% of the card sold on mother's day. The number of cards sold on mother's day is 500.
Therefore Camila sold 10/100×500= 50cards
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Answer:
Step-by-step explanation:
A small welding shop employs four welders and one secretary. A workers' compensation insurance policy charges a
premium of $10.51 per $100 of gross wages for the welders and $1.33 per $100 of gross wages for the secretary. If each welder earns $33,000 per year, and the secretary earns $26,000 per year, what is the total annual premium for this insurance?
The total annual premium for this insurance will be $14,219.
Define premium.
An amount that the insured pays on a regular basis to the insurer to cover his risk is known as a premium. In terms of finance, a premium is the sum of the costs associated with an option or the distinction between the higher price paid for a fixed-income instrument and the relevant face amount. For many different insurance policies, including health, homeowner's, and rental insurance, premiums are typically paid. Automobile insurance is a typical example of an insurance premium.
Solution explained:
A/Q, as we calculate,
Annual Premium for one worker is = [tex]33000 X \frac{10.51}{100}[/tex] = $3468.3
Annual Premium for four workers is = 4 X 3468.3 = $13873.2
Annual Premium for the secretary is = 26000 X [tex]\frac{1.33}{100}[/tex] = 345.8
Therefore, the total annual premium for this insurance will be
= 13873.2 + 345.8 = 14219
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