Question 3: A car travels 1 6 of the distance between two cities in 3 5 of an hour. At this rate, what fraction of the distance between the two cities can the car travel in 1 hour?

➷ First find the angle on the opposite side of x.

We can find this using the rule that angles on a straight line equal 180 degrees

180 - (90 + 47) = 43

Vertically opposite angles are equal

Therefore, x would also be 43 degrees.

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Answer:

x=43

Step-by-step explanation:

The angle between x and 47 is a right angle because it is a vertical angle to the right angle and vertical angles are equal.

Starting with x, we add x + the right angle +47 and we have a straight line.  We know straight lines are 180 degrees

x + 90 + 47 = straight line

x+ 137 = 180

Subtract 137 from each side

x+137-137 = 180-137

x = 43

Answer:

The answer is C 5/4

Step-by-step explanation:

When lines are parallel and you know there is a scalar factor, make the ratio by putting the original over the dilation 15:12 or 15/12 this is the ratio and after you need to reduce by dividing by the greatest common factor. 15 and 12's GCF is 3 so (15/3)/(12/3) = 5/4.

Answer:

C. both student 1 and student 2

Step-by-step explanation:

Dilation does not change any angles, so the triangles are similar and the trig functions of corresponding angles will be identical.

The slope of CB is -1/3 and the slope of BA is 3, so they multiply together to give -1. That means the segments are at right angles and the triangle is a right triangle.

Both the premise and the conclusion of each student is correct.

It’s the first one t(10t-29)=-10

Answer:

(2t - 5)(5t - 2) = 0

Step-by-step explanation:

I got it right!

Answer:

  3 cm

Step-by-step explanation:

The volume of a cube is the cube of the side dimension, hence the side dimension is the cube root of the volume.

  ∛(27 cm³) = 3 cm

_____

Problems like this are worked readily if you memorize the cubes of small integers. I suggest 1–5 at least, perhaps 1–10.

Answer: 90 pounds.

Step-by-step explanation:

Let's call:

A: pounds of type A coffee.

B: pounds of type B coffee.

Based on the information given in the problem you can set up the following system of equations:

[tex]\left \{ {{A+B=153} \atop {4.25A+5.45B=758.25}} \right.[/tex]

You can use the Elimination method:

- Multiply the first equation by -4.25.

- Add both equations.

- Solve for B.

Then, you obtain:

[tex]\left \{ {{-4.25A-4.25B=-650.25} \atop {4.25A+5.45B=758.25}} \right.\\----------\\1.2B=108\\B=90[/tex]

He used 90 pounds of type B coffee.

Answer:

B = 90 pounds

Step-by-step explanation:

We know that Han's Coffee shop uses coffee A at $4225 per pound and coffee B at $5.45 per pound and this month it made 153 pounds of blend for a total cost of $758.25.

We are find the number of pounds for coffee B used.

[tex]A+B=153[/tex]

[tex]A=153-B[/tex] --- (1)

[tex]4.25A+5.45B =758.25[/tex] --- (2)

Substituting equation (1) in (2) to get:

[tex]4.25(153-B)+5.45B=758.25[/tex]

[tex]650.25-4.25B+5.45B=758.25[/tex]

[tex]1.2B=758.25-650.25[/tex]

[tex]1.2B=108[/tex]

B = 90 pounds

The total payback for a $2500 loan at 9% annual interest for two years is $2,864.64.

To calculate the total payback for a $2500 loan at 9% annual interest for two years, we can use the formula M = P * [(1 + m)^na] / [(1 + m)^na - 1].

M represents the monthly payment, P is the principal (loan amount), m is the monthly interest rate (9% / 12), and na is the total number of payments (2 years * 12 months).

Substituting the values, the monthly payment becomes $119.32.

Multiplying this by the total number of payments gives us the total payback of $2,864.64.

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Answer:

  D.  √((2 +4)² +(5 -8)²)

Step-by-step explanation:

The distance is found using the formula ...

  d = √((x1 -x2)² +(y1 -y2)²)

Selection D has this formula properly filled in with the values ...

  (x1, y1) = (2, 5)

  (x2, y2) = (-4, 8)

the answer is D because 6 and 10 aren't multiples of 8 and 12

To find the fraction that is not equivalent to 8/12, simplify each given fraction and check for equivalence.

To find which fraction is not equivalent to 8/12, we need to simplify or reduce each of the given fractions. If the simplified form of a fraction is not equal to 8/12, then it is not equivalent. Let's simplify each option:

A) 2/3 - already in simplest form, not equivalent to 8/12

B) 24/36 - can be simplified to 2/3, equivalent to 8/12

C) 4/6 - can be simplified to 2/3, equivalent to 8/12

D) 6/10 - can be simplified to 3/5, not equivalent to 8/12

Therefore, option D is NOT equivalent to 8/12.

Answer:

  B: quadratic model, 0.997

  Yes, 0.997 is very close to 1.

Step-by-step explanation:

In general, the better the model, the closer the R²-value is to 1. A graph shows the quadratic model to be a good fit.

_____

Comment on "better models"

A 4th-degree polynomial can be written that will fit each of the 5 points exactly and give an R²-value of 1. However, the model does not appear to interpolate or extrapolate well. The quadratic offers a reasonable fit that is better than that of the linear model and seems to have reasonable behavior between and beyond the given data points.

Answer:

a circle with a circumference of 34π

Step-by-step explanation:

The circumference is given by ...

C = 2πr

so the circle with a radius of 16 has a circumference of ...

C = 2π·16 = 32π

The area is proportional to the square of the circumference, so the circle with a larger circumference will have a larger area.

The circle with the circumference of 34π has the largest area.

Answer:

Part 1) The volume of the cylinder is [tex]V=108\ units^{3}[/tex]

part 2) The volume of the sphere is [tex]V=144\ units^{3}[/tex]

Step-by-step explanation:

step 1

Find the radius of the cone

we know that

the volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]V=36\ units^{3}[/tex]

[tex]h=r\ units[/tex]

substitute and solve for r

[tex]36=\frac{1}{3}\pi r^{2} (r)[/tex]

[tex]108=\pi r^{3}[/tex]

[tex]r^{3}=108/ \pi[/tex] ------> equation A

step 2

Find the volume of the cylinder

we know that

the volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=r\ units[/tex]

substitute

[tex]V=\pi r^{2} (r)[/tex]

[tex]V=\pi r^{3}\ units^{3}[/tex]

substitute the equation A in the formula above

[tex]r^{3}=108/ \pi[/tex] ----> equation A

[tex]V=\pi (108/ \pi)\ units^{3}[/tex]

[tex]V=108\ units^{3}[/tex]

step 3

Find the volume of the sphere

we know that

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}\ units^{3}[/tex]

substitute the equation A in the formula above

[tex]r^{3}=108/ \pi[/tex] ----> equation A

[tex]V=\frac{4}{3}\pi (108/ \pi)[/tex]

[tex]V=144\ units^{3}[/tex]

Answer:

Domain: (-∞ , 8) ∪ (8, +∞)

Step-by-step explanation:

Since denominator is x - 8 so x ≠ 8

If x = 8 then y = 8/0  : undefined.

Hence, the domain is all real numbers except  8

So

Domain: (-∞ , 8) ∪ (8, +∞)

Answer:

The correct answer is A) x does not equal 8

Step-by-step explanation:

In order to find gaps in the domain, we look for two things. The first we look for is negatives under square roots (which are not an issue here since there are none) and then we look for 0, denominators. So to find the gap, we set the denominator equal to 0 and see what the x value cannot be.

x - 8 = 0

x = 8

Hope this helps , use SOHCAHTOA

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To remember, hope this helps !

The correct answer:

B. 6 - 2

Answer:

B. 6-2

Step-by-step explanation:

We have been given expression : [tex]\left(+6\right)-\left(+2\right)[/tex]

Now we need to rewrite that expression [tex]\left(+6\right)-\left(+2\right)[/tex], without parenthesis then select which of the given choices are correct.

[tex]\left(+6\right)-\left(+2\right)[/tex]

We know that product of opposite sign is always negative sign.

Then product of - and +2 gives -2

So we can rewrite the problem as:

[tex]=6-2[/tex]

Hence choice B. 6-2 is the final answer.

Final answer:

To find the missing height of a cone with a given diameter of 6 cm and volume of 84.78 cm³, the volume formula for a cone is used, and after plugging in the known values, solving for the height gives an approximate value of 3.0 cm when rounded to the nearest tenth.

Explanation:

The student is asking for the missing height of a cone given the diameter and the volume. The formula to calculate the volume of a cone is V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone. Since the diameter is given as 6 cm, the radius is half of that, which is 3 cm. The known volume of the cone is 84.78 cm³. Plugging these values into the formula gives:

84.78 cm³ = (1/3)π(3 cm)²h

After solving for h, we get:

h = ³ × 84.78 cm³ / (π × (3 cm)²)

h = 84.78 cm³ / (9π cm²)

h = 84.78 / (9 × 3.14159)

Now calculating h and rounding to the nearest tenth:

h = 84.78 / 28.27431

h ≈ 3.0 cm

Therefore, the height of the cone is approximately 3.0 cm.

B'(0,-7)

C'(0,-9)

D'(-4,-7

E'(-4.-2)

Answer:

see the attachment for a graph

4.53 thousand square yards remain after 6 years

Step-by-step explanation:

The area can be described by an exponential equation that multiplies the area by 0.85 when the time variable increases by 1 year. Such an equation might be ...

a(t) = 10.2·0.85^(t-1)

The graph of this is attached.

After 6 years, the equation predicts

a(6) = 10.2·0.85^(6-1) ≈ 4.53 thousand square yards

of island will remain.

Answer:

o

Step-by-step explanation:

the median is obvi zero

Answer:

0

Step-by-step explanation:

Answer:

  p < 5

Step-by-step explanation:

We want to find p for ...

  1.5p -1 < 1 +1.1p

  0.4p < 2 . . . . add 1-1.1p

  p < 5 . . . . . . . multiply by 2.5

The desired relationship will be the case for values of p less than 5.

The first one. Start at origin. Move 6 units to the right and up 2 units

Answer:

Option 1 - Start at the origin. Move 6 units to the right, then move 2 units up.

Step-by-step explanation:                  

To find : Which set of directions correctly describes how to plot the point (6,2) on the coordinate plane?

Solution :

The point (6,2) means the x-coordinate is 6 and y-coordinate is 2.

According to graphing,

As the x-coordinate is positive it moves to right side.

So, From origin there is a shift of 6 units right.

As the y-coordinate is positive it moves to upward side.

So, From origin there is a shift of 2 units up.

Therefore, 'Start at the origin. Move 6 units to the right, then move 2 units up'.

Hence, Option 1 is correct.

Answer:

  The solids are similar.

Step-by-step explanation:

Each linear dimension of the larger solid is 3 times the corresponding linear dimension of the smaller one. Since the scale factor is the same in every direction, the solids are similar.

Answer:

46.20 square units

Step-by-step explanation:

The area of a regular polygon can be found from the side length and apothem as ...

A = (1/2)ap . . . . . where a = apothem, p = perimeter (# of sides times side length)

The total area of the pentagon is then ...

A = (1/2)(5.51)(5·8) = 110.20 . . . . . square units

__

The shaded area is the difference between the area of the pentagon and the area of a square with side length 8. The square's area is ...

A = s^2 = 8^2 = 64 . . . . . . square units

__

Then the shaded area is ...

A = (pentagon area) - (square area) = 110.20 -64.00 = 46.20 . . . . . square units

Answer:

$0.55

Step-by-step explanation:

2x36= 72

39.60/ 72

Answer:

14. 5log3(x) -2log3(y)

18. ln(x+1) -2ln(x)

Step-by-step explanation:

The relevant rules of logarithms are ...

log(ab) = log(a) +log(b)

log(a^b) = b·log(a)

___

14. Applying the first rule gives ...

log3(x^5) +log3(y^-2)

Applying the second rule gives ...

5·log3(x) -2·log3(y)

___

18. The log of a sum cannot be simplified. We can make this be a simpler expression so that the log of it will be fairly simple.

ln(1/x +1/x^2) = ln(x/x^2 +1/x^2) = ln((x+1)/x^2)

Now, we can apply rule 1 to get ...

ln(x+1) +ln(1/x^2)

and applying rule 2 gives ...

ln(x+1) -2ln(x)

Answer:

B. Square root

Step-by-step explanation:

using distance formula:

x = √z^2 - y^2

y = √z^2 - x^2

=> z = √x^2 + y^2

Answer:

Option B. square root

Step-by-step explanation:

An incoming airplane is x miles due North at A from the control tower and a second airplane is y miles East at B of the same control tower.

The shortest distance between the two airplanes is z miles.

By Pythagoras Theorem

z² = x² + y²

z = √(x² + y²)

So function which models the situation best is "square root".

Therefore, option B. square root is the answer.

Answer:

  |x -23| = 0

Step-by-step explanation:

In order for there to be one x-intercept, the x-intercept must be the vertex. The vertex of your form will be (b, c), and you want that to be (23, 0). Hence your equation is ...

  |x -23| = 0

An absolute value equation with the single solution set x=23 can be expressed as |x-23|=0, where b=23 and c=0 in the formula |x-b|=c.

To write an absolute value equation with the solution set x=23, we need to express this in the form |x-b|=c. The value of c must be positive, as the absolute value is always non-negative, and b will be the number that x is being compared to within the absolute value.

In this case, since we only have a single solution, this means that b=23 and c=0 because we want the equation to be true only when x is exactly 23. Thus, the absolute value equation that has only the solution set x=23 is |x-23|=0.

Answer: 14 centimeters.

Step-by-step explanation:

You need to use the formula for calculate the volume of a sphere:

[tex]V=\frac{4}{3}(3.14r^3)[/tex]

Where the radius of the sphere is "r".

As you know the volume of the ball, you can susbtitute it into the formula [tex]V=\frac{4}{3}(3.14r^3)[/tex], and solve for the radius "r":

[tex]1437=\frac{4}{3}(3.14r^3)\\\\3( 1437)=4(3.14r^3)\\\\4311=12.56r^3\\\\r=\sqrt[3]{\frac{4311}{12.56}}\\\\r=7.0cm[/tex]

The diameter of the ball can be calculated with:

[tex]D=2r[/tex]

Where r is the radius of the ball.

Substituting the radius of the ball into  [tex]D=2r[/tex], you get that the diameter of the ball that she should purchase, rounded to the nearest whole number, is:

[tex]D=2(7.0cm)\\D=14.0cm\\D=14cm[/tex]

Final answer:

To solve for the diameter of the ball, the volume of a sphere formula is used. The calculated diameter is rounded to the nearest whole number, and Martha should purchase a treat ball with a diameter of approximately 14 centimeters.

Explanation:

To find the diameter of the ball that can hold 1437 cubic centimeters of treats, we need to use the formula for the volume of a sphere: V = (4/3) π r^3, where V is the volume and r is the radius. We will solve for r and then multiply by 2 to find the diameter. Given that the volume, V, is 1437 cubic centimeters, the formula becomes:

1437 = (4/3) × 3.14 × r^3

To isolate r, we first divide both sides of the equation by (4/3) × 3.14:

r^3 = 1437 / ((4/3) × 3.14)

Calculating the right side gives us the approximate value of r^3. Then, we take the cube root of both sides to solve for r:

r = ∛(1437 / ((4/3) × 3.14))

Once we find r, we can calculate the diameter, D, by:
D = 2 × r

Calculating the above with the given volume, we find:

r ≈ ∛(1437 / ((4/3) × 3.14)) ≈ 6.83 cm

D ≈ 2 × 6.83 cm ≈ 13.66 cm

So, rounding the diameter to the nearest whole number, Martha should purchase a treat ball with a diameter of approximately 14 centimeters.

Values that do not satisfy the inequality -2x - 6 ≤ 1 are those which are less than -3.5. This is found by isolating x and solving the inequality.

The question asks which values do not satisfy the inequality -2x - 6 ≤ 1. To solve this, first, let's isolate x on one side of the inequality. We follow these steps:

This means that all values of x that are greater than or equal to -3.5 satisfy the inequality. Thus, values that do not satisfy the inequality are those less than -3.5.