To find the slope of a line that passes through two points, you can use the formula:
slope = (y2 - y1)/(x2 - x1)
In this case, the two points are (0,0) and (1/3, 7/3). Substituting these values into the formula, we get:
slope = (7/3 - 0)/(1/3 - 0)
slope = 7/3
Therefore, the slope of the line that passes through (0,0) and (1/3, 7/3) is 7/3.
John and his friends are dining at a restaurant. The bill comes to $334.43. John tips the waiter 16.5% of the total bill amount. He estimates that the total amount they need to pay is about $390. Is this a reasonable estimate?
Answer:
Yes
Step-by-step explanation:
Given the discussion in Example 9.4.4, what is the maximum possible length of the repeating section of the decimal representation of 941 and 1,549 ?
On solving the question as said we get to know that the maximum possible length of the repeating section of the decimal representation of the given number is 10.
As 941 and 1549 are already in whole number lets assume that the question says to find the decimal repetition is 941 and 15 divided by 41 and 59 respectively.
9 divided by 41 is equal to 0.2195121951
15 divided by 49 is equal to 0.306122449.
Therefore, the maximum possible length for their repeating section is 10.
The preferred method for representing both integer and non-integer numbers is the decimal numeral system, often known as the base-ten positional numeral system and denary.
It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers using the decimal system.
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A rectangle has a length of 3x and a width of x . If the perimeter of the rectangle is 48 cm, what are the dimensions of the rectangle? *
Answer:
perimeter of a triangle is the total
Step-by-step explanation:
p=48cm
Length=3x
width=x
Now P= 2(L+W)
48 =2(3x+x)
48=2(4x)
48=8x
dividing both sides by 8
we have x=6
and so length=18 and width =6
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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Jack needs to earn $1000 for a cart. He earns $12 an hour and already has $112 saved. write an equation to find out how many hours needs to work to save for his car
Answer: $1000 = 12x + 112
Step-by-step explanation:
let x be the amount of hours worked
A regular hexagon has a perimeter of 120 m. Find its area. Express your answer in the simplest radical form.A) 1800√3m2B) 5 √3 m2C) 600 √3 m2D) 3600 √3 m2
The area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².
There are many different types of hexagons. The most common type is a regular hexagon, which is a hexagon that has sides of equal length and angles of equal measure. The perimeter is the total length or distance around a two dimensional shape. In the figure below, the perimeter of each shape is the sum of the lengths of each side, shown in red. The perimeter of a circle or ellipse is called the circumference. For a polygon, the perimeter is the sum of its side lengths.
The given polygon is a regular hexagon with perimeter 120 m.
Thus, the length of each side,
s = 120/6 = 20 m.
The area, A, of a regular hexagon can be found given only its side length, s, with the formula:
[tex]A = \frac{3\sqrt{3} }{2} s^{2}[/tex]
Substitute s = 120 m in above formula:
[tex]A = \frac{3\sqrt{3} }{2} (20)^{2} \\A = \frac{3\sqrt{3} }{2}(400)\\A = 600 \sqrt{3}[/tex]
Thus, the area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².
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Triangles ABC and DEF are shown.
B
25 cm
A
35 cm
Choose
20 cm
D
C
E
28 cm
16 cm
F
20 cm
Select the correct transformations from the drop-down menus to complete the statement below.
Doug shows that ADEF is similar to triangle AABC by using a series of transformations.
First, he Choose....
begin Math ToWeb (your LaTeX) S\triangleDEFS ADEF end
MathToWeb Choose...
✓Then, he Choose...
ADEF
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
What is congruent triangle?The SSS congruence theorem tells us that the triangles are congruent because there are three pairs of congruent sides. The corresponding triangle sides are also in proportion, so they are similar according to the SSS similarity theorem.The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.If two triangles have the same size and shape they are called congruent triangles. If we flip, turn or rotate one of two congruent triangles they are still congruent. If the sides of two triangles are the same then the triangles must have the same angles and therefore must be congruent.The measurement of side DF is 4cm.If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.Here in the figure attached below,
Given two triangles ΔABC and ΔDEF
Also given that,
ΔABC and ΔDEF are congruent to each other.
Given AC = 4cm
Since both triangles are congruent ,
Side AC is congruent to DF
Therefore DF = 4cm (based on SSS theorem).
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Solve the system, using the method of your choice. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. Express answers as integers or simplified fractions if necessary.
-8x+8y=-80
8x-4y=68
Determine the solution to the Quadratic Linear System
y = x² - 10x +30
y = 4x - 3
The solutions to the quadratic linear system equations are (11, 41) and (3, 9).
The given equations are y=x²-10x+30 and y=4x-3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, y=x²-10x+30 -------(I) and y=4x-3 -------(II)
Substitute equation (II) in the equation (I), we get
4x-3=x²-10x+30
⇒ x²-10x+30-4x+3=0
⇒ x²-14x+33=0
⇒ x²-11x-3x+33=0
⇒ x(x-11)-3(x-11)=0
⇒ (x-11)(x-3)=0
⇒ x=11 and x=3
So, y=4(11)-3=41 and y=4(3)-3=9
Therefore, the solutions to the quadratic linear system equations are (11, 41) and (3, 9).
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Divide the polynomials.
Your answer should be in the form p(x)+{k}/{x+3} where p is a polynomial and k is an integer.
{x^2-7}/{x+3}=
The given division will give the result as (x-3) + [2/(x+3)].
What is a polynomial?Polynomial are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
The given division of the two of the polynomial can be carried out as shown below,
[tex]\dfrac{x^2-7}{x+3}\\\\=x+\dfrac{-3x-7}{x+3}\\\\=x-3+\dfrac{2}{x+3}\\\\=(x-3)+\dfrac{2}{x+3}[/tex]
Hence, [tex]\dfrac{x^2-7}{x+3}=(x-3)+\dfrac{2}{x+3}[/tex].
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3.8 divided by 34.2 the quotient is..
The required quotient is 34.2 ÷ 3.8 = 9.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
We have been given 3.8 divided by 34.2
According to the given question, we can write the quotient as:
⇒ 34.2 ÷ 3.8
⇒ 34.2 / 3.8
⇒ 342 / 38
Apply the division operation, and we get
⇒ 9
Therefore, the required quotient is 34.2 ÷ 3.8 = 9.
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Triangle EFG is formed by connecting the midpoints of the side of triangle BCD. The lengths of the sides of triangle EFG are shown. What is the length of CD? Figures not necessarily drawn to scale.
Applying the triangle midsegment theorem, the length of CD is: 8 units.
What is the Midsegment of a Triangle?If the midpoints of two sides of a triangle are joined together by a line segment, that line segment is called the midsegment of the triangle. Every triangle has three of these.
What is the Triangle Midsegment Theorem?According to the triangle midsegment theorem, the third side of a triangle is parallel to its midsegment, and also has a length that is twice of the length of the midsegment.
Given the image above, where points G, E, and F are the midpoints of the sides of the given triangle, thus:
EG is a midsegment that is parallel to a third side CD.
Therefore:
Length of CD = 2(EG)
Substitute
CD = 2(4)
CD = 8 units.
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What is the remainder when 2^70 + 3^70 is divided by 13?
Answer: hope it helps
Step-by-step explanation:
2^6=64≡ -1 ( mod 13)
So 2^70=16*(2^6)^11=16*(-)^11(mod 13)
2^70 ≡-16 ( mod 13)
2^70 ≡10 ( mod 13)
Now 3^3=27≡1 ( mod 13)
So 3^70= 3*(3^3)^23≡ 3*(1)^23 ( mod 13)
≡ 3 ( mod 13)
Thus 2^70+3^70 ≡ 10+3 (mod 13)
≡ 0 ( mod 13)
Is 2 fourths greater than 2 thirds?
Answer:
NO
Step-by-step explanation:
Two fourths =
[tex] \frac{2}{4} = 0.5[/tex]
Two thirds =
[tex] \frac{2}{3} = 0.66667[/tex]
Therefore
0.66667 > 0.5
[tex] \frac{2}{3} > \frac{2}{4} [/tex]
or
0.5 < 0.66667
[tex] \frac{2}{4} < \frac{2}{3} [/tex]
i hope this helped
Answer: No, 2/4 is not greater than 2/3
Step-by-step explanation: To find an easy way to calculate their values we have 2 options. So, the 1st option is to turn them into a decimal. I already calculated their values which are:
2/4 = 0.5
2/3 = 0.667
Then, we compare the two decimal numbers to get the answer.
0.5 is not greater than 0.667.
The 2nd way is to find a common denominator, which would look like this:
2/4 = 6/12
2/3 = 8/12
8/12 is greater than 6/12, so that also proves that 2/4 is not greater than 2/3.
claire boarded the airplane in richmond, va, and flew 414 miles directly to Charleston, sc. The total flight time was 3/4 hours. How fast did Claire's airplane fly, in mile per hour
Answer:
552 mph
Step-by-step explanation:
414 / 3/4 = 414 * 4/3 = 1656/3 = 552
Ashley used the method shown below to add 3/5 and 1/4
Step 1 3/5 + 1/4 = 0.6 + 0.25
Step 2 0.85 = 85/100
Step 3 17/20
Is Ashley's work correct? If not, which is the first incorrect step?
All steps are correct.
The first incorrect step is Step 1.
The first incorrect step is Step 2.
The first incorrect step is Step 3.
the answer will be "all steps are correct"
Determine the domain of the rational function h (z) =
4/4z^2 +4
The domain of the given function is z<0 or z>0
What is a domain?The entire range of independent variable values is the domain of a function.
According to this definition, it means:
The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.
Keep these things in mind when locating the domain:
A fraction's denominator (bottom) cannot be 0.
In this section, the integer following a square root symbol must be positive.
Calculation:The domain of a function is a set of input of argument values for which the function is real or defined.
1) Finding the singularity point:
Taking the denominator 4×[tex]z^{2}[/tex] = 0 ⇒ z = 0
∴The following function will not be defined if z = 0
So the function domain is z>0 or z<0
The domain of the given function is z<0 or z>0
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Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years.
It takes 11.55 years for money to double if invested at 6% compound interest.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.Calculating the answer exactly: P⁰°⁰⁶ⁿ=A .
We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.
P⁰°⁰⁶ⁿ = 2P
We divide both sides by P
e⁰°⁰⁶ⁿ = 2
Using natural logarithm:
0.06 n = ln(2)
n = ln(2)/0.06
n = 11.55 years
Hence, It takes 11.55 years for money to double if invested at 6% compound interest.
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Find sin2x,cos2x, and tan2x if sin x=-3 and x terminates in quadrant IV.
sin2x=
cos2x=
tan2x=
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
tan x= -3/1
So, H = √1 + 9 = √10
sin x= -3/ √10 and cos x= 1/ √10
So, sin 2x= 2 sin x cos x =2 ( -3/ √10 )(1/ √10) = -3/10
and, cos 2x= 1- 2 sin²x
= 1- 2( 9/10)
= -8/10
and, tan 2x = sin 2x/ cos 2x = -3/10 / ( -8/10) = 3/8
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help meeeeeeeeeee pleaseee
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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Irena has 20 apples she has a apple juice what times that is a apple juice? poopie
Answer: about 4:30
Step-by-step explanation:
he used the restroom starting at 4:15, he sat on the toilet and watched tt for exactly 14 minutes, He then whiped himself which took about 50 seconds. Flushing the toilet took 10 seconds and when he flushed it was 4:30.
Given: θ = 20° opposite = 45 Find: hypotenuse
The value of hypotenuse will be;
⇒ Hypotenuse = 132.35
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ θ = 20° opposite = 45
Now,
Since, The values are,
⇒ θ = 20° opposite = 45
We know that;
⇒ sin θ = Opposite / Hypotenuse
⇒ sin 20° = 45 / Hypotenuse
⇒ Hypotenuse = 45 / sin 20°
⇒ Hypotenuse = 45 / 0.34
⇒ Hypotenuse = 132.35
Thus, The value of hypotenuse will be;
⇒ Hypotenuse = 132.35
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Dan invests £13000 into his bank account. He receives 2.3% per year simple interest. How much will Dan have after 4 years? Give your answer to the nearest penny where appropriate
Answer
150000 after 4 years
Step-by-step explanation:
Please help me I can’t finger it out and I am failing math
An inequality that expresses the mean number of steps that Diego needs to walk during the last 3 days of this week to more than 70,000 steps is 32076+3x>70000.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Diego's goal is to walk more than 70,000 steps this week.
a) The mean number of steps that Diego walked during the first 4 days of this week is 8019.
So, the number of steps =4×8019
= 32076
Let x be the mean number of steps that Diego needs to walk during the last 3 days of this week to walk more than 70,000 steps.
Now, the inequality is 32076+3x>70000
b) The mean number of steps that Diego needs to walk during the last 3 days of this week is 12642
Substitute x=12642 in the inequality 32076+3x>70000, we get
32076+37926>70000
70002>70000
Yes, Diego will reach his goal of walking more than 70,000 steps this week.
Therefore, the inequality to represent the given situation is 32076+3x>70000.
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Given the equation P=S₁t-S₂t, which equation is solved for t?
Ot=p(S₁-S₂)
Ot=p-S₁+S₂
Answer:
Step-by-step explanation:
Therefore, C is the correct option.
Step-by-step explanation:
We have been given the equation
The GCF of the right hand side of the equation is t. Hence, factored out the GCF.
Now, is in multiplication with 't'. So in order to isolate t, we can divide both sides by
Therefore, C is the correct option.
A rectangular dog pen is constructed using a barn wall as one side and 80 meters of fencing for the other three sides. Find the dimensions of the pen that give the greatest area.(example to write an answer: 20m×15m).
Let the dimensions of the pen be L for the length and W for the width. The area of the pen is L*W.
We are given that the width of the pen is 80 meters and that the length of the pen is greater than the width. Therefore, the length of the pen must be greater than 80 meters.
Since the area of the pen is L*W, the area will be greatest when L is as large as possible and W is as large as possible. Therefore, we can set L equal to 80 and W equal to 80 to find the dimensions of the pen that give the greatest area:
L = 80
W = 80
The dimensions of the pen that give the greatest area are 80 meters by 80 meters. Therefore, the answer is 80m x 80m.
The dimensions of the pen are 20 m × 40 m and the area will be 600 m².
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given data in the question,
Let the length of the rectangle is x and,
Let the width of the rectangle is y.
So, the equation will be,
2x + y = 80 (1)
y = 80 - 2x (2)
Use the formula of the area of a rectangle,
A = x × y
Substitute y = 80 - 2x in the above formula,
A = x × (80 - 2x)
= 80x - 2(x)²
= -2x² + 80x
dA/dx = -2x² + 80x
A' = -4x + 80
-4x = -80
x = 80/4
x = 20 m
Substitute x = 20 in equation (2)
y = 80 - 2(20)
y = 40 m
So, the area should be,
A = 20 × 40
A = 600 m².
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Adam has 18 counters. He gives 10 of the counters to Lesley. what fraction of the 18 counters does Adam have now
Adam have 4 / 9 fraction of the 18 counters. A fraction is a number that is stated as a quotient by dividing the numerator and the denominator.
What is a fraction ?Fraction a number that is stated as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. A fractional equation is one that contains one or more terms that are fractions. The first step in solving a fractional equation is to eliminate the fractions by multiplying both sides of the equation by the LCD of each term.
Adam has 18 counters
Lesley get 10 counters
Adam have 18 - 10 = 8
8 / 18 = 4 /9
Adam have 4 /9 fraction of the counters.
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MODELING REAL LIFE Oak Street intersects Walnut
Street and Maple Street at their midpoints. A parade float
starts at point S, travels up Walnut Street to Oak Street, up
Oak Street to Maple Street, over Maple Street to Spruce
Street, and then down Spruce Street to the starting point.
About how far does the float travel? Round your answer to
the nearest hundredth place.
Answer:4.05
Step-by-step explanation: Walnut divided by 2 is 0.9 and Oak is 0.9. Maple is 0.45 and Spruce. All that is added up to 4.05
please show work on this, I need help
A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.
How do you type a horizontal line symbol?The fastest way to add a horizontal line or rule is to use the AutoFormat feature. When you type certain characters three times in their own paragraph and then press Enter, those characters instantly become a full-width horizontal line.How to insert a horizontal line in Word using the keyboardPolynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials.The polynomials can be identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The non-polynomial expressions will be the expressions which contain other operations.Place your cursor on a blank line where you want to insert a horizontal line. ...To insert a basic line, type three or more hyphens (---) in a row.Hit "Enter" on your keyboard. ...Move this line by pressing "Enter" on your keyboard on a line of text above the line.
6. x = 28 degrees
7. z = 1.6 cm
6. Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:
50 + 69 + (2 x +5) = 180
combine like terms:
119 + 2 x + 5 = 180
124 + 2 x = 180
subtract 124 from both sides:
2 x = 56
divide by 2 both sides:
x = 56 / 2
x = 28 degrees
Problem 7.
If the two triangles are congruent, then the side MN must equal side RS.
Since MN measure 1,8 cm, then RS must also measure 1.8 cm
and we can write the equation:
1.8 = 3 z - 3
adding 3 to both sides:
1.8 + 3 = 3 z
4.8 = 3 z
dividing both sides by 3:
z = 4.8 / 3
z = 1.6 cm
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5.A firm sells a product for Rs. 750. Variable costs per unit are Rs. 200 for materials and Rs. 300 for labor whereas annual fixed cost is Rs.100000. a.Construct the profit function in terms of x, the number of unitsproduced and sold. b.What profit is earned if annual sales are 1500 units? c.What level of output is required in order to earn zero profit?
The profit function is 250x and the profit earned is 375000.
What is cost?
In production, research, retail, and accounting, a cost is that the value of cash that has been spent to provide one thing or deliver a service, and thence isn't obtainable to be used any longer.
Main body:
A) Profit function = R() – TC()
= 750 – (300+200)x
= 750 – 500x
= 250 x
b) total profit = 250 x
= 250 *1500
= 375000
c) The zero-profit condition is that the condition that happens once AN business or kind of business has a very low (near-zero) value of entry to or exit from the business. during this scenario, some companies not already within the business tend to hitch the business if they calculate that they're going to create a positive economic profit (profit in more than the price of effort investible funds). a lot of and a lot of companies can enter till the economic profit per firm has been driven all the way down to zero by competition.
hence the profit function is 250x
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