Answer:
[tex]y-8=-\dfrac{6}{5}(x-5)[/tex]
Step-by-step explanation:
Define the given points:
(x₁, y₁) = (5, 8)(x₂, y₂) = (10, 2)First find the slope of the line by substituting the given points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-8}{10-5}=-\dfrac{6}{5}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-8=-\dfrac{6}{5}(x-5)[/tex]
An artist is building a pedestal out of wood that
will be used to display a piece of sculpture. She
plans to cover the pedestal with tile.
10 cm
6 cm
10 cm
16 cm
30 cm
How much tile will it take to cover the pedestal,
including the bottom?
The area of tiles taken to cover the pedestal, including the bottom is 1176 cm².
What is the Total Surface Area of a Triangular Prism?A triangular prism's surface area is also referred to as its total surface area. A triangular prism's total surface area is the sum of the areas of all its faces. A triangular prism consists of two triangular faces and three rectangular faces.
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 +S2 + S3)L + bh
where,
b is the base triangle's bottom edge, h is its height, L is its length, and S1, S2, and S3 are the three edges (sides) of the base triangle (bh).
[2 (1/2 bh)] = bh is the area of the two triangular faces
Given:
From the figure, we can say that the pedestal is in form of a triangular prism.
To find the area of the tile that it takes to cover the pedestal, including the bottom we have to determine the surface area of the pedestal.
So from the figure,
The side lengths of the triangular base are:
S1 = S2 = 10 cm
S3 = 16 cm
Base of prism = 16 cm
Height of prism = 6 cm
Length of prism = 30 cm
Surface area = (S1 +S2 + S3)L + bh
= (10+10+16)30 + 16×6
= 1176 cm²
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Write the equation of the line in point-slope form that has a slope of 2/3 and a y-intercept of (0,-2)
y-2= 2/3 (x-0)
y-0= 2/3 (x-2)
y-0=2/3 (x+2)
y+2=2/3 (x-0)
Answer:
y + 2 = 2/3(x - 0)
Step-by-step explanation:
The general form of an equation of line with slope m, passing through point (x1, y1) is:
y - y1 = m(x - x1)
substituting values:
y - (-2) = 2/3(x - 0)
simplify
y + 2 = 2/3(x - 0)
Answer:
where
m(Gradient or slope) =2/3
y1=-2
x1=0
Suppose f(x) = 3x² – 48. Solve f(x) = 0
ANSWER:
x = 4 and x = -4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)\: =\: 3x^{2}\: -\: 48[/tex]We solve the values of x for when the function is equal to 0, as follows:
[tex]\begin{gathered} \: 3x^{2}\: -\: 48=0 \\ \: 3x^{2}\: -=48 \\ x^2=\frac{48}{3} \\ x=\sqrt[]{16} \\ x=\pm4 \end{gathered}[/tex]Is 24x equivalent to 3(2x + 6x)?YesNo
Answer
Yes
Step-by-step explanation
Given the expression:
[tex]3(2x+6x)[/tex]Combining similar terms:
[tex]3(8x)[/tex]Multiplying:
[tex](3\cdot8)x=24x[/tex]A rectangular auditorium seats 1749 people the number of seats in each row exceed the number of rows by 20 find the number of seats in each row
Let x = the number of seats
Let y = the number of rows.
Since the auditorium is rectangular and it has 1,749 people, then we can say that:
[tex]x\times y=1749[/tex]Then, if the number of seats "x" exceeds the number of rows "y" by 20, then we can say that:
[tex]\begin{gathered} seat=row+20 \\ x=y+20 \end{gathered}[/tex]Now we have two equations. To solve for x, let's use the substitution method.
1. Rewrite the equation 2 x = y + 20 into y = x - 20.
2. Replace the value of "y" in equation 1 by x - 20.
[tex]\begin{gathered} xy=1749 \\ x(x-20)=1749 \end{gathered}[/tex]2. Multiply x and x - 20.
[tex]x^2-20x=1749[/tex]3. Transfer the constant term 1749 on the left side of the equation. When transferring over the equal sign, the operation will change. From +1749, it becomes -1749.
[tex]x^2-20x-1749=0[/tex]4. To solve this quadratic equation, let's find the factors of -1749 that sums to -20.
a. 3 and -583 = -580
b. 11 and -159 = -148
c. 33 and -53 = -20
As we can see above, the factors of -1749 that sums to -20 are 33 and -53. Hence, the quadratic equation above can be factored to:
[tex](x+33)(x-53)=0[/tex]5. Equate each factor to zero and solve for x.
[tex]\begin{gathered} x+33=0 \\ x=-33 \end{gathered}[/tex][tex]\begin{gathered} x-53=0 \\ x=53 \end{gathered}[/tex]Since the value of x cannot be negative, then the value of x is 53.
Therefore, the number of seats in each row is 53. In addition, there are 33 rows in the auditorium.
Select the correct answer. Which graph represents the solutions to this equation? x2 + 8x = -20 A. Linear-quadratic system graph shows upward parabola with vertex at (minus 2, 4) and passing through x and y-axis (minus 8, 0), and (0, 0) B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8) C. Linear-quadratic system graph shows upward parabola with vertex at (4, 0) and passing through (1, 4), and (6, 4) D. Linear-quadratic system graph shows a downward parabola with vertex at (0, 8) which intercepts the x-axis at 3 and minus 3 units. Reset Next
A graph which represents the solutions to this quadratic equation (x² + 8x = -20) is: B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8).
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve.
In conclusion, we can reasonably infer and logically deduce that the given quadratic equation is modeled by an upward parabola with its vertex at (-4, 4) as shown in the graph attached below.
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if EB=7, find the value of CD
Both lines AB and CD are secant lines beacuse in two points they are touching the circunference. There is a Theorem which says the following
[tex]PB\cdot PA=PD\cdot PC[/tex]Since the distance from the center of the circle to each secant line is the same (5 units), we could assume that the both secant lines are similar. saying:
[tex]PB=PD;\text{ }PA=PC\Rightarrow AB=CD[/tex]Then the lenght of CD is:
[tex]CD=2\cdot EB=2(7)=14[/tex]Every rhombus is a square 
Answer: False!
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
Rhombus as a quadrilateral with equal sides. The angles may or may not be right-angled.
However, a square is a quadrilateral with equal sides and all angles are right angles.
Hence, every square is a rhombus but the opposite is not true.
4. (01.02 LC)
Brandi earned $59.00 in interest after one and one half years on an account that paid 5.5% simple interest annually. Use the formula / -Prt to find Brand's principal balance. Round to the nearest hundredth. (1
point)
O $486.75
$535.23
$617.98
O $715.15
Simple interest is a clear and simple method for computing financial interest. Simple Interest is the amount returned for using the borrowed funds over a predetermined amount of time.
What is meant by simple interest?Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
Simple Interest is the amount returned for using the borrowed funds over a predetermined amount of time.
A = P(1 + rt)
Simple interest is a method for figuring out how much interest was paid on a sum of money during a specific time period at a specific rate. Simple interest has a constant principle amount. Simple interest is a clear and simple method for computing financial interest.
Therefore, the correct answer is option D. $715.15.
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DUE IN 30 MINUTES PLEASE HELP!!!!
WITH WORK PLEASE
1. Write a piecewise defined rule from a graph
2. Write three equations and show all your steps to get full credit
For the given question,
The coordinates of the three lines are given with the end points.
Part a: The slope piece wise rule for defined graph is-
[2, 1) - as (1 - 1) is at the open interval.[1,5] - both ends with closed interval.[5,8] - both ends with the closed interval.Part b: calculate the three equations-
First find the slope for the three given lines;
slope (blue line);
coordinates - (0, -4) and (1, -1)
m = (-1 + 4)/(-1 - 0)
m = -3
Equation of line;
y + 4 = -3(x -0)
y = -3x - 4
slope (red line);
coordinates - (1, 4) and (5, 8)
m = (8 - 4)/(5 - 1)
m = 4/4
m = 1
Equation of line;
y - 4 = 1(x - 1)
y = x + 3
slope (green line);
coordinates - (5, 8) and (8, 8)
m = (8 - 8)/(8 - 5)
m = 0
Equation of line;
y - 8 = 0(x - 5)
y = 8
Thus, the three equation of line are found.
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If (-1, y) is a solution to the equation y = x + 5, determine the value of y.
HELP I WILL MARK BRAINLIEST
Answer:
4
Step-by-step explanation:
The solution to the equation means that the coordinate satisfy the equation. Given that the equation is y= x +5, we know the relationship between the y-coordinate (y) and the x-coordinate (-1) of the point.
y= x +5
Substitute the coordinates into the equation:
When x= -1, y= y,
y= -1 +5
y= 4
Thus, the value of y is 4.
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The pair of values below is form an inverse variation find the missing value (3,16) (10,y)
An inverse variation is represented as:
[tex]y=\frac{k}{x}[/tex]To find the missing value we need to find k first. Using the first pair we have:
[tex]\begin{gathered} 16=\frac{k}{3} \\ k=3\cdot16 \\ k=48 \end{gathered}[/tex]Now, we plug the value of k and use the second pair to find y:
[tex]\begin{gathered} y=\frac{48}{10} \\ y=\frac{24}{5} \end{gathered}[/tex]Therefore, y=24/5.
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Exponents and powers are terms that occasionally get used interchangeably, which can be confusing.
Mathematics uses expressions called powers, where n is the exponent and x is the base. When a number or variable is multiplied repeatedly, it is referred to as a power. The exponent of power tells us how many times to multiply the base by itself.
You can interpret the term as "x to the power." The exponent (n) is written smaller and at the head of the line using superscript, whereas the base (x) is printed in full size (if you are typing it on a computer). For instance, it is written as x squared or x to the second power, which in reality means that the value of x is multiplied by an amount equal to the exponent's value.
If the base is a number: In this situation, all you have to do to discover the solution is multiply the base by itself as many times as the exponent's value.
If the base is a variable, you must first replace the variable with a value before continuing.
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What is the answer to this math problem which isn4/5+3/5=7/5=
Answer:
14/5 or, 2 4/5.
Step-by-step explanation:
4/5 + 3/5 = 7/5, 7/5 + 7/5 = 14/5
14/5 as a mixed number is 2 4/5.
I think you're talking about fractions so.
Solve:x + 2y + z = 82x + y - z = 1x + y – 2z = - 3
We are given the following system of equations:
[tex]\begin{gathered} x+2y+z=8,(1) \\ 2x+y-z=1,(2) \\ x+y-2z=-3,(3) \end{gathered}[/tex]To solve the system we will add equations (1) and (2):
[tex]x+2y+z+2x+y-z=8+1[/tex]Adding like terms:
[tex]\begin{gathered} 3x+3y=9 \\ x+y=3,(4) \end{gathered}[/tex]Now we multiply equation (2) by -2:
[tex]-4x-2y+2z=-2[/tex]Now we add this equation to equation (3):
[tex]x+y-2z-4x-2y+2z=-3-2[/tex]Adding like terms:
[tex]-3x-y=-5,(5)[/tex]Now we add equations (4) and (5):
[tex]x+y-3x-y=3-5[/tex]Adding like terms:
[tex]-2x=-2[/tex]Dividing both sides by -2:
[tex]x=-\frac{2}{-2}=1[/tex]Now we replace this value of "x" in equation (4):
[tex]\begin{gathered} x+y=3 \\ 1+y=3 \end{gathered}[/tex]Subtracting 1 to both sides:
[tex]\begin{gathered} 1-1+y=3-1 \\ y=2 \end{gathered}[/tex]Now we replace the values of "x" and "y" in equation (1):
[tex]\begin{gathered} x+2y+z=8 \\ 1+2(2)+z=8 \end{gathered}[/tex]Adding like terms:
[tex]\begin{gathered} 1+4+z=8 \\ 5+z=8 \end{gathered}[/tex]Subtracting 5 to both sides:
[tex]\begin{gathered} 5-5+z=8-5 \\ z=3 \end{gathered}[/tex]Therefore, the solution of the system is:
[tex]x=1,\text{ y=2, z=3}[/tex]HELPPPPPPPPP PLEASEEEEEEEEEE
-6 x 1.5 ______ 50 ÷ (-8) which is greater
Answer: The answer is that 50 ÷ (-8) is greater
Answer:
-6 x 1.5 < 50 ÷ (-8)
-6 x 1.5 = -9
50 / -8 = -6.25
50 divided by -8 is greater than -6 times 1.5p
Step-by-step Explanation:
=D
I think one is 10 I am just not sure though
Right Triangles
A right triangle is identified because it has an interior angle of 90° (right angle). The other two angles must be acute and add up to 90°.
In the special case that both acute angles have a measure of 45°, then we have an isosceles triangle, that is, both legs have the same length.
We can see one of the legs measures
[tex]L=5\sqrt[]{2}[/tex]Being this an isosceles triangle, the other leg (the base of the triangle) also measures L, thus you should drag
[tex]5\sqrt[]{2}[/tex]To the box at the bottom.
The other unknown length is the hypotenuse H. According to the Pythagorean's Theorem:
[tex]H^2=L^2+L^2=2L^2[/tex]Substituting:
[tex]\begin{gathered} H^2=2(5\sqrt[]{2}^{})^2 \\ \text{Operating:} \\ H^2=2\cdot50=10 \\ \text{Thus:} \\ H=\sqrt[]{100} \\ H=10 \end{gathered}[/tex]You should drag the length 10 to the hypotenuse.
Which expression is equivalent to (-3t - x) - (5y - 8x)?
which transformations had to occur for the blue triangle to become the purple triangle? [note: all rotations are about origin]
Let:
A = (-4,3)
B = (-1,3)
C = (-1,1)
after a 90 clockwise rotation:
A = (-4,3)--------->(y,-x)------->(3,4)
B = (-1,3)----------->(y,-x)------>(3,1)
C = (-1,1)------------>(y,-x)------>(1,1)
After a translation 3 units down and 2 units left:
(3,4)------>(x-2,y-3)------->(1,1)
(3,1)------>(x-2,y-3)------->(1,-2)
(1,1)------>(x-2,y-3)------->(-1,-2)
---------------------------
Therefore, the answer is D
I need help with this!! 4. Ms. Ruggiero is rewarding her best class for doing outstanding on the final exam with a virtual pizza party. The pizzas are $8.75 each. On top of buying the pizza, she buys herself an order of wings for $4.25, pays 9.25% sales tax, and tips the clerk 15% after tax. How many pizzas can she buy with $50?
Let's use the variable x to represent the number of pizzas Ms. Ruggiero can buy.
If each pizza is $8.75, the wings are $4.25, the tax is 9.25% and the tip is 15%, and all this needs to be lesser than or equal 50, we have the inequality:
[tex]\begin{gathered} (8.75x+4.25)\cdot1.0925\cdot1.15\le50 \\ 10.99x+5.34\le50 \\ 10.99x\le50-5.34 \\ 10.99x\le44.66 \\ x\le\frac{44.66}{10.99} \\ x\le4.06 \end{gathered}[/tex]So Ms. Ruggiero can buy 4 pizzas with $50.
A food company sells its corn flakes in two different sizes: the regular box and the family value box. For the family value box, the length of the box has been increased by 30%, the height has been increased by 25%, and the width remains the same.By what percentage does the volume of the box increase from the regular box to the value box? Round your answer to the nearest percent.
Hay, this is the solution:
Length of the box = increased 30%
Height = Increased 25%
Width = Remains the same
Volume of the value box = 1.3 * 1.25 * 1
Volume of the value box = 1.625
Volume of the regular box = 1 * 1 * 1
Volume of the regular box = 1
Percentage of increase = 1.625/1 - 1
Percentage of increase = 0.625
Percentage of increase = 62.5 = 63% (Rounded to the nearest p
The triangle is translated. B' is the translated position of B.
Draw the new triangle, then verify that they are congruent with the distance formula.
The new triangle A'B'C' shown in the attached graph has the coordinates of B' are (2, 8), A' are (1, 6), and C' (4, 6).
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
The given triangle ABC shown in the graph has:
The coordinates of B are (-7, 6),
The coordinates of A are (-8,4),
The coordinates of C are (-5, 4)
If B' is the translated position of B.
The new triangle A'B'C' shown in the attached graph has:
The coordinates of B' are (2, 8)
The coordinates of A' are (1, 6)
The coordinates of C' are (4, 6)
Length of AB = A'B' = √5
Length of BC = B'C' = 2√2
Length of CA = C'A' = 3
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The students in my class watch less than 2 hours television at night. how can I decide what data to collect to test this statement, How can I design a suitable data collection instrument?
Solution
For this case we need to select a sample of students from the class
We can ask to each student how much time spend on average watching tv at night
From the results we can take the average and the standard deviation and we can use a t-test to test the statement
I need help trying to find side c and to see if my other answers are correct?
we have that
B=5 degrees
C=125 degrees
b=200 units
step 1
Find out the measure of angle A
Remember that
the sum of the interior angles in any triangle must be equal to 180 degrees
so
A+B+C=180
substitute given values
A+5+125=180
A=180-130
A=50 degrees
step 2
Applying the law of sines
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]Find out the value of a
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]substitute given values
[tex]\frac{\sin 50^o}{a}=\frac{\sin 5^o}{200}[/tex]solve for a
[tex]a=\frac{200\cdot\sin 50^o}{\sin 5^o}[/tex]a=1,757.9 units
step 3
Find out the value of c
[tex]\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]substitute given values
[tex]\frac{\sin 5^o}{200}=\frac{\sin 125^o}{c}[/tex][tex]c=\frac{200\cdot\sin 125^o}{\sin 5^o}[/tex]c=1,879.7 unitsMischa dives from a platform that is 5 meters above water. Her dive takes her 1.7 meters below the surface of the water. How
far does Mischa's dive take her?
Conditional equations - Mischa's dives take her 6.5 meter
What are conditional equations?
An equation that holds true for one or more values of the variable but holds false for other values of the variable is known as a conditional equation.
Explain the airthematic mathematical operations.
it deals with the study and use of numbers in all other branches of mathematics. Basic operations include +,-, x, and /.
We frequently employ these fundamental mathematical operations in our daily lives: +, -,x, and, /. For every such area of our lives, we apply mathematical operations, whether it be to figure out the annual budget or distribute things evenly to a lot of people.
Mischa dives from a platform that is 5 meters above the water.
Her dive take her 1.7 meters below the surface of the water.
The total distance of Mischa's dive take her will be,
5+1.7meters
=6.7 meter
thus Mischa's dives take her 6.5 meters far.
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make a 2 column proofplease make it simple like JK is parallel to NM(given)
Explanation:
Since L is the midpoint of JM, then JL = LM.
Therefore,
Statement: JL = LM
Reason: L is the midpoint of JM
The lines JK and NM are parrallel; therefore, by the alternate interior angles theorem,
[tex]\angle LJK=\angle LMN[/tex]Furthermore, since ∠JLK and ∠MLN are vertical angles,
[tex]∠JLK=∠MLN[/tex]Now since ∠JLK = ∠MLN, ∠LJK = ∠LMN, and JL = LM, then by ASA postulate
[tex]\boxed{△JKL=△MNL.}[/tex]Hence, our proof is complete!
An expresion is shown. - 2 3 /4 + 3 2/3 What is the value of the expression?
,By following these steps, we can find the value of this expression:
[tex]-2\times\frac{3}{4}+3\times\frac{2}{3}[/tex]first we multiply both -2 and 3 by their corresponding fractions, we do this by just multiplying the numbers with the numerator of the fraction, like this:
[tex]\frac{-2\times3}{4}+\frac{3\times2}{3}=\frac{-6}{4}+\frac{6}{3}=-\frac{6}{4}+\frac{6}{3}[/tex]Now simplify the fractions:
[tex]-\frac{6}{4}+\frac{6}{3}=-\frac{3}{2}+2[/tex]To sum fractions, we have to make sure that the denominators are the same, this is not the case, we can make their denominators the same by dividing and multiplying the two by two, like this:
[tex]-\frac{3}{2}+2=-\frac{3}{2}+\frac{2\times2}{2}=-\frac{3}{2}+\frac{4}{2}[/tex]Now, we just have to sum up the numerators, like this:
[tex]-\frac{3}{2}+\frac{4}{2}=\frac{-3+4}{2}=\frac{1}{2}[/tex]Then, the value of this expression is:
[tex]\frac{1}{2}[/tex]Students were trying to use the sample standard deviation formula for the given
data: (8,1,3,0,3). Determine what they did wrong for each case and calculate the
correct value.
S=
Σ(x − x)2
n-1
The sample standard deviation formula is
square root {(Σ(X - mean)²) / (N - 1)}
What the student did wrong?
The square root sign was not included in their calculation
The correct value of the sample standard deviation is = 3.08
What is standard deviation?Standard deviation shows the by how much the values differs from the mean.
How to calculate the sample standard deviationThe calculation is done by forming the table and calculating the required variables as below:
X (X - mean)²
8 25
1 4
3 0
0 9
3 0
ΣX = 15
mean = ΣX/N = 15/5 = 3
Σ(X - mean)² = 38
Σ(X - mean)² / (N-1)
= 38 / 4
= 9.5
Sample standard deviation = √9.5
= 3.08
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Answer the questions below.