a pair of vertical angles has measures (2z 43)° and (−10z 25)°. what is the value of z? responses −32 negative 3 over 2 −114 , negative 11 over 4, −14 , negative 14 −31

Answer:

Slope of the line DV = -1

Step-by-step explanation:

Let point D (-5, 1) be \((x_{1}, y_{1})\)

Let point V (-1, -3) be \((x_{2}, y_{2})\)

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Plug in the appropriate values,

\(m = \frac{-3-1}{-1-(-5)} = \frac{-4}{4} = -1\)

slope equals -1

Answer: 30 7/40

Step-by-step explanation:

Answer:

4 23/40 miles

Step-by-step explanation:

\(17\dfrac{3}{8}-12\dfrac{4}{5}=\dfrac{139}{8}-\dfrac{64}{5}\\\\=\dfrac{139*5}{8*5}-\dfrac{64*8}{5*8}\\\\=\dfrac{695}{40}-\dfrac{512}{40}\\\\=\dfrac{183}{40}\\\\=4\dfrac{23}{40}\)

Answer:

\( y = x \).

Step-by-step explanation:

Equation to represent the proportional relationship between years (x) and megawatts (y) is represented as \( y = kx \).

Where k = constant of proportionality, which is y/x.

To find k, we can use the coordinates of any point on the line. Let's use (4, 4).

k = y/x = ⁴/4 = 1

Substitute k = 1 into \( y = kx \).

✅Equation representing the relationship would be:

\( y = (1)x \).

\( y = x \).

Answer:

first of all we don't know the exact lift they took but here's your answer:

if they took the plane then that's easy

600×5=3000

105×5=525. 3000-525=2475

while for the bus

3000-60=2940

The number of fruits that he sold is given as follows:

For a total of 178 fruits.

The amount of fruits sold is obtained solving a system of equations, for which the variables are given as follows:

Mr Chan has 154 more apples than pears, hence:

x = 154 + y.

After selling 4/7 of the apples(3/7 remaining) and 1/2 of the pears, he had 144 fruits left, hence:

3x/7 + y/2 = 144.

Replacing the first equation into the second, the value of y is given as follows:

3(154 + y)/7 + y/2 = 144

6(154 + y) + 7y = 2016.

y = 84.

Then the value of x is given as follows:

x = 154 + 84

x = 238.

The amounts sold are given as follows:

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The probability of spinning a multiple of 2 on Josefina's spinner is 1/5 or 0.2.

The spinner has 15 equal sectors labeled 1 through 15, of which 7 sectors are even numbers (2, 4, 6, 8, 10, 12, 14).

There are three multiples of 2 on the spinner, which are 2, 4, and 6. Since there are a total of 15 sectors on the spinner, the probability of landing on a multiple of 2 is 3/15 or 1/5.

The probability of landing on an even number is the number of favorable outcomes (7) divided by the total number of possible outcomes (15):

P(multiple of 2) = 7/15

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The equation for the radius of the ball, treated as a sphere, in terms of its surface area is given by r = √(A/4π). For a measured surface area of A = 65 cm², the radius can be calculated as r ≈ 2.028 cm. The density of the ball is calculated by dividing its mass by its volume. With a measured mass of M = 75 g, the density is approximately p ≈ 0.86 g/cm³. To convert this density to Pkg/m³, we need to multiply by 1000, resulting in P ≈ 860 kg/m³.

(a) The surface area of a sphere is given by the formula A = 4πr², where r is the radius of the sphere. Rearranging the formula to solve for the radius, we get r = √(A/4π). Plugging in the measured surface area A = 65 cm², we can calculate the radius as r ≈ √(65/4π) ≈ 2.028 cm.

(b) The density of an object is calculated by dividing its mass by its volume. In this case, the measured mass is M = 75 g. The volume of a sphere is given by V = (4/3)πr³, where r is the radius. Using the previously calculated radius r ≈ 2.028 cm, we can find the volume V ≈ (4/3)π(2.028)³ cm³. Dividing the mass M by the volume V, we get the density as p ≈ 75 g / [(4/3)π(2.028)³ cm³] ≈ 0.86 g/cm³.

(c) To convert the density from g/cm³ to kg/m³, we need to multiply by a conversion factor of 1000 since there are 1000 g in 1 kg and 1 m³ is equal to 1,000,000 cm³. Therefore, the density in kg/m³ is P ≈ 0.86 g/cm³ * 1000 ≈ 860 kg/m³.

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Answer:

The percentage increased by approximately 5%.

Step-by-step explanation:

52.10 - 49.62 = 2.48

2.48/49.62 x 100 = 4.998%

The percentage increase in the price is approximately 5%. Hope this helps! :)

Answer:

Step-by-step explanation:

From the information given, we need to get the rate of change of distance which is the velocity (slope.)

velocity = Δd/Δt

v = d2-d1/t2-t1

from the table;

when t = 2, d = 700

when t  = 3, d = 1050

v = 1050/750/3-2

v = 350/1

v = 350

Since v = d/t

350 = d/t

cross multiply

350t = d

Rearrange:

d = 350t

Hence the equation that represents the information is d = 350t

Answer:

D

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

45/0.5 can also be written as 45*2.

So, 45/0.5 is 90.

-hope it helps

Answer:

A. 12 miles

B. 9 miles

C. 2 hours

D. 5 hours

E. Max did not move

F. 9 hours

G. 5 hours

hope this helps :)

Step-by-step explanation:

Answer:

y =- x+5

Step-by-step explanation:

hello :

note :

Use the point-slope formula.

y - y_1 = m(x - x_1)   when : x_1= 1   y_1= 4

     m is the slope  m=(y_1 - y_2)/( x_1 -  x_2)  and  x_2=6   y_2= -1

m = (4+1)/(1-6)= 5/-5 = -1  

an equation  is : y-4 =-1(x - 1)   means : y =- x+5

The given expression is a simplified algebraic equation: (1/2) * a^2 - 3b + 2c. It represents a combination of variables a, b, and c with their respective coefficients.

Utilizing symbols and operations, an algebraic equation illustrates the equivalence or inequivalence of two expressions. These generated expressions may hold variables that have varying values.

The premise centered around calculus is to arrive at a solution by acquiring the correct value(s) of these variable(s), ultimately fulfilling the outlined specification in the problem. Algebraic equations can range from uncomplicated linear problems to elaborate polynomials and trigonometric functions.

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Answer:

4

Step-by-step explanation:

4^2 is 4x4 aka squared

Quantity: 1,000 items

Price: $80 per item

Fixed cost: $20,000

Variable cost: $40 per item

The fixed cost stays the same, the total variable cost is:

Total variable cost (TVC) = variable cost * quantity

TVC = $40 * 1,000 = $40,000

Total costs = TVC + Fixed costs = $40,000 + $20,000 = $60,000

Te income is:

Income = price * quantity = $80 * 1,000 = $80,000

The profit is income minus total costs:

Profit = income - total costs = $80,000 - $60,000 = $20,000

Profit = $20,000

Answer:

125 people

Step-by-step explanation:

P( green) = number of green / total

                = 25/120

                 =5/24

Multiply this probability by 600

5/24 * 600 =125

Answer:

out of 120 people 25 people has chosen green

out of 1 people green will be chosen by 25/120 people

out of 600 people green colour will be chosen by( 25/120)×600 people =25×5=people

Answer: 16.8 m - 5m - 84 m area

Step-by-step explanation:

Answer:

0.036cm

Step-by-step explanation:

Curve Surface Area of Cone =

\(curve \: surface \: area \: of \: = \\\pi \: rl \\ \)

\(\pi = 3.142 \: \: radius \: = unknown \: \: \: l = 5cm \\ r = \frac{\pi \: l}{csa} = \: \frac{3.142 \times 5}{140 \times 3.142} = 0.036cm\)

The radius of the base of the cone is 28 cm

For a right circular cone of radius 'r', height 'h', and slant height 'l', we have; Curved surface area of the right circular cone = π r l. The total surface area of a right circular cone = π(r + l) r. The volume of a right circular cone = 1/3π r²h.

Given here CSA=140π cm² and slant height  l=5

thus using the formula for curved surface area we get

π×r×l =140π

 r = 140/5

 r=28 cm

Hence The radius of the base of the cone is 28 cm

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The difference quotient and simplify the result for the function h(x) = x^2 + 4x + 5 can be evaluated result of the difference quotient is 2x + Δx + 4

Step 1: Start with h(x + Δx) = (x + Δx)^2 + 4(x + Δx) + 5 = x^2 + 2xΔx + Δx^2 + 4x + 4Δx + 5.

Step 2: Subtract h(x) from h(x + Δx) to get the numerator:(h(x + Δx) - h(x)) = [(x^2 + 2xΔx + Δx^2 + 4x + 4Δx + 5) - (x^2 + 4x + 5)]

Step 3: Simplify the numerator by cancelling out the common terms: (h(x + Δx) - h(x)) /Δx= (x^2 + 2xΔx + Δx^2 + 4x + 4Δx + 5) - (x^2 + 4x + 5) = (2xΔx + Δx^2 + 4Δx)/(Δx)

Step 4: Factor the numerator:(2xΔx + Δx^2 + 4Δx) = Δx(2x + Δx + 4)

Step 5: Substitute this into the difference quotient to get: (h(x + Δx) - h(x)) / Δx = Δx(2x + Δx + 4) / Δx = 2x + Δx + 4.

Therefore, the simplified result of the difference quotient is 2x + Δx + 4.

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Answer:

Step-by-step explanation:

1) x+27=1

 -27  -27

x = -26

2) x-2y=5 (solving for x)

     +2y  +2y

x = 5 + 2y

2) x-2y=5 (solving for y)

  -x       -x

2y = 5 -x

2y/2    5/2   -x/2

y = 5 - x

   _____

        2         (5-x over 2)  

Following are the calculation to the linear combination method:

Given:

\(\to \bold{x+2y=1}\\\\ \to \bold{x-2y=5}\)

To find:

Solve the equation by linear combination method

Solution:

\(\to \bold{x+2y=1}........(a)\\\\ \to \bold{x-2y=5}........(b)\)

Adding both the equation (a) and (b):

\(\to\bold{x+2y=1}\\\\ \to \bold{x-2y=5}\\\\+\ \ - \ \ \ \ +\\\\ \to \bold{2x=6}\\\\ \to\bold{x=\frac{6}{2}}\\\\ \to\bold{x=3}\\\\\)

Putting the value of x into the equation (b):

\(\\ \to \bold{3-2y=5}\\\\\to \bold{-2y=5-3}\\\\\to \bold{-2y=2}\\\\\to \bold{y=- \frac{2}{2}}\\\\\to \bold{y=- 1}\\\\\)

Therefore, the final answer is "(3,-1)"

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Hello !

Answer:

\(\Large \boxed{\sf r=\frac{3}{2} }\)

Step-by-step explanation:

Let's remember :

We know that the volume of the sphere is equal to half its surface area.

\(\sf V_{sphere}=\frac{1}{2} A_{sphere}\\\\\sf \frac{4}{3}\pi r^3=\frac{1}{2} 4\pi r^2\\\\\sf \frac{4}{3}\pi r^3=2\pi r^2\)

Let's solve this equation for r.

First, substract \(\sf 2\pi r^2\)  from both sides :

\(\sf \frac{4}{3} \pi r^3-2\pi r^2=0\)

We can now factorize by taking out the highest common factor: 2r²

\(\sf 2r^2(\frac{2}{3} \pi r-\pi )=0\)

We can use the zero-product property.

There are two solutions :

The first solution is absurd : The radius of a sphere cannot be 0.

We conclude that we must keep the second solution.

Have a nice day ;)

The greatest number of average students that could be in each row is 8. This is because there are an equal number of girls and boys, so the teacher can arrange them in equal rows with 4 girls and 4 boys in each row.

48 girls/8 students per row = 6 rows

32 boys/8 students per row = 4 rows

Total number of rows = 10

The teacher has 48 girls and 32 boys in the choir and wants to arrange them in equal rows. To accomplish this, the teacher needs to ensure that the same number of boys and girls are in each row. The greatest number of students that can be in each row is 8. This is because if 4 girls and 4 boys are in each row, then the total number of rows will be 6 for the girls and 4 for the boys, totaling 10 rows. This arrangement will allow the teacher to keep an equal number of boys and girls in each row, and will also ensure that the same number of students is in each row. Having 8 students in each row is the most efficient way to arrange the choir, as it will require the least amount of rows and will still keep the number of boys and girls even.

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The time taken to completely fill the pool is 5/4 hour

From the question, the given parameters are:

Time =3/4 hour

Size of the pool = 3/5

The time to fill the pool is then calculated as

Time = Given time/Proportion of the pool

Substitute the known values in the above equation

So, we have the following equation

Time = 3/4 hour ÷ 3/5

Express the quotient as product

So, we have the following equation

Time = 3/4 hour x 5/3

Evaluate the products

Time = 5/4 hour

Hence, the time taken is 5/4 hour

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Answer:

the correct answer is option C

Answer:

254.34 inches²

Step-by-step explanation:

The formula for area of a circle is: pi x r². The radius is half of the diameter (18) which in this case would be 9. Square it to get: 81. Multiply by pi: 81 x 3.14 = 254.34.

Hope it helps!

Answer:

I believe it is around 56.52

Step-by-step explanation:

3.14

x

 18

--------

56.52

Answer:

b. 10

Step-by-step explanation:

3 (x 2) = 6

5 (x 2) = 10

Answer:

Helen scores 10 points.

Step-by-step explanation:

We are given that for every 3 points Glenn scores, Helen scores 5 points. Glenn now scores 6 points and Helen's score is unknown. We can write this as a ratio.

Glenn - 3 : 5 - Helen

Glenn - 6 : ? - Helen

We can divide 6 by 3 to get the rate of change, which is 2. Then multiply 5 and 2 and we get 10! Helen scores 10 points for every 6 points Glenn scores. I hope this helps! :D

Answer:

those are the right answers

Step-by-step explanation:

for sin90 you have to put sin(90) which is 1, all the other answers r correct (same with my calculator)

\(\dfrac{x-2}3 +\dfrac 16 = \dfrac 56 \\\\\implies \dfrac{x-2}3 = \dfrac 56 - \dfrac 16\\\\\implies \dfrac{x-2}3= \dfrac 46\\ \\\implies \dfrac{x-2}3 = \dfrac 23\\\\\implies x -2=2\\\\\implies x =2+2 = 4\\\\\text{Hence, the value of x is 4.}\)

Answer:

Somoeone knows the answer?

Step-by-step explanation:

In spherical geometry the based on (two dimensional) geometric objects that are located on a spherical surface

The statement that is true in plane geometry but not true in spherical geometry is statement option D.

D. Any two lines intersect in exactly one point

The reason why the statement is correct is given as follows;

Spherical geometry is the geometry that has basic concepts being the point and great circles where the basic concepts in plane geometry is the point and the line

Therefore, while in plane geometry, a unique line is determined by two points, in  spherical geometry, a unique great circle is determined by two non polar points (points not at the poles)

However, we have;

Therefore, the correct option is option D.

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