WILL MARK BRANIEST IF RIGHT

The scale factor is: 1.8

because of :

\(\frac{36}{20}=1.8\\ \\\\\frac{25.2}{14}=1.8\)

Answer:

what is the question?

Step-by-step explanation:

Parallelogram have two pairs of opposite sides that are parallel and congruent.

In a parallelogram, two pairs of opposite sides are parallel and congruent. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Therefore, any pair of opposite sides in a parallelogram satisfies the criteria of being both parallel and congruent.

For example, let's consider a parallelogram ABCD:

These two pairs of opposite sides, AB and CD, and AD and BC, are parallel (they never intersect) and congruent (they have the same length).

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x² - 12x + 5 = 0

(x - 6)² - 31 = 0

(x - 6)² = 31

x - 6 = ±√31

x = 6 ± √31

Katie made: 7/16 of a pound of taffy

Scott made: 1/2 of a pound of fudge

So, 1/2-7/16=1/16---> There is one-sixteenths more of a pound of fudge

Answer:

x = 15

Step-by-step explanation:

since the sides are bisected, the inner line is parallel to the largest side.

8x+9 + 5x-24 = 180

Answer:

237

Step-by-step explanation:

This is a system of equations.

The theater sold 364 adult and child tickets, so a + c = 364

They made a total of $1930. Each adult ticket was $6 & child tickets were $4. The second equation is 6a + 4c = 1930.

Let's line them up

a  +  c = 364

6a + 4c = 1930

Since we need to solve for the number of adult tickets, we want to get rid of the c variable. I'm going to multiply the entire first equation by -4 to do this. The second equation stays the same. Now, I have:

-4a - 4c = -1456

6a + 4c = 1930            Add them together

----------------------

2a = 474                      Divide by 2 to solve for a

a = 237

There were 237 adult tickets sold

Answer:

502

Step-by-step explanation:

100 * 5 + 2 = 505

Answer:

To find the 100th term of the sequence, we need to use the recursive rule and iterate it 99 times, since we are starting at the first term and need to get to the 100th term.

The recursive rule is given as 5, which means each term in the sequence is equal to the previous term times 5. Therefore:

The first term is 2.

The second term is 2 * 5 = 10.

The third term is 10 * 5 = 50.

The fourth term is 50 * 5 = 250.

And so on...

Iterating this rule 99 times gives us:

The 100th term is 2 * 5^99, which is approximately equal to 6.33825300114 × 10^66.

Therefore, the 100th term of the sequence starting with 2 and with a recursive rule of 5 is approximately 6.33825300114 × 10^66.

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

40x+24y-56=

8(5x+2y-7)

Step-by-step explanation:

Answer:

a.) Graph is attached; blue is Petunia's and red is Billy's

b.) Number of Hours: 4 | Cost: 32 Pounds

Answer:

Volume of square pyramid is 3466.6 cm³

Step-by-step explanation:

We are given:

Base edge of square pyramid = 20 cm

Height of square pyramid = 26 cm

We need to find Volume of square pyramid

The formula used is: \(Volume=\frac{1}{3}a^2h\)

Where a is base edge and h is height of pyramid

Putting values in formula to find the volume

\(Volume=\frac{1}{3}a^2h\\Volume=\frac{1}{3}(20)^2(26)\\Volume=\frac{1}{3}(400)(26)\\Volume=\frac{1}{3}(10400)\\Volume=3466.6 \ cm^3\)

So, Volume of square pyramid is 3466.6 cm³

Answer:

3200

__________________________

the answer is 3200 NOT 3466.6

__________________________

THE HEIGHT OF THE PYRAMID: 24

The Explanation for height :

the height, half of one side of the square base, and the slant height form a right triangle

using the Pythagorean Theorem...

262=102+h2 (the slant height is the hypotenuse)

676=100+h2

676-100=h2

576=h2

√576=h

h=24 feet is the height of the pyramid

Step-by-step explanation:

v = ( \(\frac{1}{3}\) ) · b · h

( \(\frac{1}{3}\) ) ( 20 · 20 ) ( 24 )

( \(\frac{1}{3}\) ) ( 400 ) · ( 24 ) = 3200cm³

use symbolab.com for these sort of problems :)

The vοlume οf the prism is 14 cubic feet.

A three-dimensiοnal structure having six rectangular faces is called a prism. It is alsο knοwn as a rectangular cubοid οr a rectangular parallelepiped.

The prism is cοmpletely filled with 1750 cubes that have an edge length οf 1/5 ft. This means that the vοlume οf each cube is \((1/5)^3 = 1/125\) cubic feet.

Tο find the vοlume οf the prism, we can divide the tοtal vοlume οf the cubes by the number οf cubes:

Vοlume οf prism = (Vοlume οf οne cube) x (Number οf cubes)

Vοlume οf prism = (1/125) x 1750

Vοlume οf prism = 14 cubic feet

Therefοre, the vοlume οf the prism is 14 cubic feet.

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Answer:

7/10

Step-by-step explanation:

3/10 (blue) +4/10 (red) = 7/10  or 1- 3/10 (green) = 7/10

Answer:

0.01386 or 1.386%

Step-by-step explanation:

Each question has a binomial distribution with probability of success p =0.25 (1 correct answer out of four alternatives).

The probability of 'k' successes in n trials is given by:

\(P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}\)

Pat will pass the exam if x ≥ 10. The probability that Pat will pass is:

\(P(pass)=P(x=10)+P(x=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)+P(x=17)+P(x=18)+P(x=19)+P(x=20)\)

The probability for each number of success is:

\(P(x=10)=\frac{20!}{(20-10)!10!}*0.25^{10}*0.75^{10}=0.0099\\\\P(x=11)= \frac{20!}{(20-11)!11!}*0.25^{11}*0.75^{9}=0.0030\\\\P(x=12)=\frac{20!}{(20-12)!12!}*0.25^{12}*0.75^{8}=0.00075\\\\P(x=13)=\frac{20!}{(20-13)!13!}*0.25^{13}*0.75^{7}=0.00015\\\\P(x=14)=\frac{20!}{(20-14)!14!}*0.25^{14}*0.75^{6}=0.0000257\\\\P(x=15)=\frac{20!}{(20-15)!15!}*0.25^{15}*0.75^{5}=3.426*10^{-6}\\\\\)

\(P(x=16)=\frac{20!}{(20-16)!16!}*0.25^{16}*0.75^{4}=3.569*10^{-7}\\\\P(x=17)=\frac{20!}{(20-17)!17!}*0.25^{17}*0.75^{3}=2.799*10^{-8}\\\\P(x=18)=\frac{20!}{(20-18)!18!}*0.25^{18}*0.75^{2}=1.555*10^{-9}\\\\P(x=19)=\frac{20!}{(20-19)!19!}*0.25^{19}*0.75^{1}=5.457*10^{-11}\\\\P(x=20)=\frac{20!}{(20-20)!20!}*0.25^{20}*0.75^{0}=9.095*10^{-13}\\\\\)

The probability that Pat will pass his exam is:

\(P(pass)=0.01386\)

Answer:

x > -5, so the correct answer is C.

Answer:

2,700 ft in the air

Step-by-step explanation:

Answer:

h = 18.88 inches

Step-by-step explanation:

Given that,

The circumference of a cylinder is 20 inches

The volume of the cylinder, V = 600 cubic inches

We need to find the height of the cylinder. We know that the volume of a cylinder is given by :

\(V=\pi r^2h\)

r is radius

We know that,

circumference = 2πr

\(r=\dfrac{C}{2\pi}\\\\r=\dfrac{20}{2\pi}\\\\r=3.18\ \text{inches}\)

So,

\(h=\dfrac{V}{\pi r^2}\\\\h=\dfrac{600}{\pi\times (3.18)^2}\\\\h=18.88\ \text{inches}\)

So, the height of the cylinder is 18.88 inches.

Answer: −8  3 /4

Step-by-step explanation: (−3  1 /2 )(2  1 /2 )

(-7/2)(5/2)

−35 /4

−8  3 /4

The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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Answer:

\(BC=5.1\)

\(B=23^{\circ}\)

\(C=116^{\circ}\)

Step-by-step explanation:

The diagram shows triangle ABC, with two side measures and the included angle.

To find the measure of the third side, we can use the Law of Cosines.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

In this case, A is the angle, and BC is the side opposite angle A, so:

\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)

Substitute the given side lengths and angle in the formula, and solve for BC:

\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-42\cos 41^{\circ}\)

\(BC^2=58-42\cos 41^{\circ}\)

\(BC=\sqrt{58-42\cos 41^{\circ}}\)

\(BC=5.12856682...\)

\(BC=5.1\; \sf (nearest\;tenth)\)

Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:

\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)

Substitute the values of the sides and angle A into the formula and solve for the remaining angles.

\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)

Therefore:

\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)

\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)

\(B=22.5672442...^{\circ}\)

\(B=23^{\circ}\)

From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):

\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)

\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)

\(180^{\circ}-C=63.5672442...^{\circ}\)

\(C=180^{\circ}-63.5672442...^{\circ}\)

\(C=116.432755...^{\circ}\)

\(C=116^{\circ}\)

\(\hrulefill\)

Additional notes:

I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.

Answer:

See below

Step-by-step explanation:

As CD⊥AB, ∠BDC = ∠ADC = 90°

∠BDC ≅ ∠ADC

and

We can substitute ∠ADC with ∠BDC and ∠DAC with ∠DBC

Then we get same equation for ∠BCD and ∠ACD

Therefore ∠BCD = ∠ACD = 1/2∠ACB

It proves that CD bisects ∠ACB

Answer:

10 root 2

Step-by-step explanation:

root 200 = root 2 × root 100 = 10 root 2

Answer:

\(\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}\)

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

First, we can calculate the area of the circular base:

\(A_{\text{circle}} = \pi r^2\)

\(A_{\text{base}} = \pi (0.75 \text{ in})^2\)

\(A_{\text{base}} = 0.5625\pi \text{ in}^2\)

Next, we can calculate the area of the rectangular side:

\(A_\text{rect} = l \cdot w\)

\(A_\text{side} = (4\text{ in}) \cdot C_\text{base}\)

Since the width of the side is the circumference of the base, we need to calculate that first.

\(C_\text{circle} = 2 \pi r\)

\(C_\text{base} = 2 \pi (0.75 \text{ in})\)

\(C_\text{base} = 1.5 \pi \text{ in}\)

Now, we can plug that back into the equation for the area of the side:

\(A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})\)

\(A_\text{side} = 6\pi \text{ in}^2\)

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

\(SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2\)

\(\boxed{SA = 7.125\pi \text{ in}^2}\)

\(\boxed{SA \approx 22.4 \text{ in}^2}\)

Answer: So you will need to score 95% on the fifth test to have an average of 90%

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Consider the expression 4(8x + 5)

Complete 2 descriptions of the parts of the expression.

1. The entire expression is the product of 2 factors.

2. On its own, (8x + 5) is a sum with 2 terms.

Answer:

24 miles per hour.

Step-by-step explanation:

you divide 144 by 6 to get 24.

Answer:

24 miles per hour

Step-by-step explanation:

To find the mph rate, you just have to take the number of miles traveled, divided by the time.

So:

144 ÷ 6 = 24

Which means they were traveling at 24 miles per hour

Step-by-step explanation:

Solution is attached in pen paper form