Angle rst is a right angle

Answer:

Step-by-step explanation:

Along with the angle of elevation, the initial velocity of the ball will determine how far and how high it goes.

Also, the initial height that the ball is hit from, as well as the horizontal distance from the fence, will affect whether the ball clears the fence.

There's also the acceleration of gravity, but here on Earth, that doesn't change much near the surface.

Answer:

equal angles and vertical angles

Step-by-step explanation:

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always equal

In this problem

∠14=∠16 -----> by vertical angles

therefore

The answer is

equal angles and vertical angles

Answer:

Vertical angles, equal angles

Step-by-step explanation:

when a transversal passes through two lines, then,

Angles formed in the same side and inside the two lines are same side interior angles.

Angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles.

Angles formed on opposite sides of the transversal and outside the two lines are alternate exterior angles.

Angles with the same relative position at each intersection are corresponding angles,

While, when two lines intersect each other then the opposite angles formed called vertical angles,

supplementary angles : When the sum of two angles are 180°,

Right angles : angle that has the measurement of 90°,

Equal angles : angles with the same measurement.

Now, vertical angles are always equal angles,

Also, when two parallel lines are cut by the same transversal then the pair of alternate interior angles, alternate exterior angles, corresponding angles are always equal.

Hence, by above definitions it is clear that,

∠16 and ∠14 are vertical and equal angles.

Answer: Hey i am single and ready to mingle

Step-by-step explanation:

I need someone

The 18-inch wrench will generate more torque and make it easier for Marge to loosen the lug nuts because torque is the product of the force applied and the lever arm, and the longer wrench provides a larger lever arm.

The wrench that Marge should use to generate more torque and make her job easier when changing a flat tire is the one that is 18 inches long. This is because torque (au) is calculated as the product of the force (F) applied and the distance (r) from the pivot point, with the equation torque (au) = force (F) × lever arm (r). Since the wrenches provide the lever arm and assuming the same force is applied to both, the longer wrench will provide greater torque due to a larger r.

For example, if Marge exerts a force of 100 newtons, the torque generated by each wrench would be:

12-inch wrench: au = 100 N × 0.305 m = 30.5 N.m (since 12 inches is approximately 0.305 meters)

18-inch wrench: au = 100 N × 0.457 m = 45.7 N.m (since 18 inches is approximately 0.457 meters)

The 18-inch wrench generates 45.7 N.m of torque, compared to 30.5 N.m with the 12-inch wrench, thus the 18-inch wrench will make loosening the lug nuts easier.

Answer:

Dependent

Step-by-step explanation:

The given system of equations is inconsistent.

The given system of equations is:

-35x + 40y = 55

7x = 8y - 11

To determine if the system is consistent and independent, consistent and dependent, or inconsistent, we need to solve the system of equations and analyze the solution.

We can start by rearranging the second equation to solve for x:

7x - 8y = -11

Next, we can multiply the first equation by 7:

-245x + 280y = 385

Now, we can add the two equations together:

-245x + 280y + 7x - 8y = 385 - 11

-238x + 272y = 374

Simplifying this equation:

-119x + 136y = 187

We can see that the coefficients of x and y in this equation are not equal to the coefficients in the original equations. Hence, the lines represented by the equations do not intersect and the system is inconsistent.

Therefore, the answer is: The system is inconsistent.

Answer:

160

Step-by-step explanation:

e.g. 5×8 --> 10×16 =160

4×10 --> 8×20 =160

2×20 --> 4×40 =160

160

When you double both the length and width, you are multiplying by 2 twice. Whatever you do to one side of an equation, you have to repeat on the other.

l * w = 40; This is the original equation.

2l * 2w = 40 * 2 * 2; This is when you double the length and the width.

The 2 * 2 on the end can be simplified.

2l * 2w = 40 * 4

Now, simplify 40 * 4.

2l * 2w = 160

So, when you double both the length and the width, you multiply the area by 4, making the area 160.

Answer:

x=1

y=2

Step-by-step explanation:

Hope this helps (3

Answer:

A: [tex](x-0)^{2} +(y-0)^{2} = 2^{2}[/tex]

or [tex]x^{2} +y^{2} =4[/tex]

B: [tex](x-5)^{2} +(y+4)^{2} =9[/tex]

Check the picture below.

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{small}{circle}~~ \begin{cases} r=2\\ h=0\\ k=0 \end{cases}\implies (x-0)^2+(y-0)^2=2^2\implies x^2+y^2=4 \\\\\\ \stackrel{large}{circle}~~ \begin{cases} r=3\\ h=5\\ k=-4 \end{cases} \\[3em] [x-5]^2+[y-(-4)]^2=3^2\implies (x-5)^2+(y+4)^2=9[/tex]

Answer:

1650

Step-by-step explanation

1320/12=110

110x15=1650

Answer:

24

Step-by-step explanation:

Write a proportion.  1 serving is to ¼ apples as x servings is to 6 apples.

1 / ¼ = x / 6

Cross multiply:

¼ x = 6

Multiply both sides by 4:

x = 24

She can prepare 24 servings with 6 apples.

The probability of a new financial establishment succeeding and making profits in either the $25,000-$50,000 range or the $50,000-$75,000 range is 18.59 percentage points higher than the probability of a new food establishment succeeding and earning up to $25,000. None of the given options (A-D) are correct.

To answer Perry’s question, we first need to calculate the success rate for the different types of businesses. The success rate can be calculated by subtracting the number of closed businesses from the number opened, and this result is divided by the number opened initially.

For food businesses, the success rate = (3193 - 1977)/3193 = 38.06%. Next, from those successful new food businesses, 945 out of 1216 make up to $25,000, hence the probability is 945/1216 * 100 = 77.67%.

For financial businesses, the success rate = (1898 - 1443)/1898 = 23.97%. Among those successful new financial businesses, 244 out of 455 are making profits in the range of $25,000 - $50,000 and 195 out of 455 are in the range of $50,000 - $75,000. The combined probability is (244+195)/455 * 100 = 96.26%.

This demonstrates that the probability of a new financial establishment succeeding and making profits in either the $25,000-$50,000 range or the $50,000-$75,000 range (96.26%) is higher than the probability of a new food establishment succeeding and making up to $25,000 (77.67%), by 18.59 percentage points.

Therefore, none of the given options (A-D) are correct.

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Answer:

x=3

Step-by-step explanation:

25x+57+x=45x

26x+57=45x

57=19x

x=57/19

x=3

ANSWER

x=3

EXPLANATION

Use the exterior angle theorem:

25x°+(57+x)°=45x°

Group similar terms,

57=45x-25x-x

19x=57

Divide both sides by 19.

x=3

Just solve.

[tex](17-k)^3\\k=12 \\ \\ (17-12)^3 \\ \\ (5)^3 \\ \\ 125\\[/tex]

[tex]\\\\(5+2n)^5 \\ n=-2 \\ \\ (5+2(-2))^5 \\ \\ (5-4)^5 \\ \\ (1)^5 \\ \\ 1[/tex]

Answer:

±(√35 i)

Step-by-step explanation:

[tex]\pm\sqrt{-35}[/tex]

We need to solve the above equation using the imaginary unit i.

We know i= √-1

Solving

±√-35 =±( √-1 √35)

         = ±(√35 i)Since 35 = 5*7 or 35*1 it cannot be further simplified

So our answer is ±(√35 i).

Answer:

B.

Step-by-step explanation:

If you look at the graph carefully, the graph/line is starting to fall at (0,45) which is the starting point or dropping point.

I hope this helped =)

Answer:

The team needs to win 15 races today.

Step-by-step explanation:

The team has completed 45 races so far and has won 30 so far.

The current success rate is

[tex]r = \frac{30}{45} * 100\% = 66.7\%[/tex]

We need this success rate to be 75%

Then the team must win a number x of races such that

[tex]r = \frac{30 + x}{45 + x} = 0.75[/tex]

Now we solve the equation for x.

[tex]\frac{30 + x}{45 + x} = 0.75\\\\30 + x=0.75(45 +x)\\\\30 + x=0.75(45) +0.75x\\\\x- 0.75x = 33.75-30\\\\0.25x = 3.75\\\\x= \frac{3.75}{0.25}\\\\x=15[/tex]

Finally the team need to win  15 carreras today

Answer: 15 races

Proof of validity is shown below.

Answer:

≈ 2.1 m

Step-by-step explanation:

Given

v = [tex]\sqrt{9.8d}[/tex] ← substitute v = 4.5

4.5 = [tex]\sqrt{9.8d}[/tex] ← square both sides

4.5² = 9.8d

20.25 = 9.8d ← divide both sides by 9.8

d = 2.0663 ≈ 2.1 m ( nearest tenth )

Answer:

28 biscuits.

Step-by-step explanation:

Belinda has 10 cups of flour

She uses 3 cups to make a loaf of bread

She uses [tex]\frac{1}{4}[/tex] cup of the remaining flour for each biscuit she wants to make.

There are 10 - 3 = 7 cups of flour remaining

[tex]\frac{1}{4}[/tex] cup of flour makes -> 1 biscuit

7 cups of flour will make;

7 × 1 ÷  [tex]\frac{1}{4}[/tex]  = 7 × 4 = 28 biscuits

Answer:

11,520

Step-by-step explanation:

The reserve rate simply refers to the amount the bank sets aside as reserves. In this case, the bank sets aside 4% of deposits made by its customers implying the bank would loan out 96%  of all deposits made; so we have  

12000x 0.96 = 11,520 is free to loan out

Answer:

volume of sphere if radius is divided by 2 is 1/8 of volume of sphere with r radius.

Step-by-step explanation:

The formula to find volume of sphere is:

Volume of sphere  = 4/3 π r^3

if radius is divided by 2 i.e r/2

Volume of sphere if r/2 = 4/3 π (r/2)^3

                                      = 4/3 π r^3/8

                                      =  (4/3 π r^3) / 8

                                      = (Volume of sphere 1)/8

So, volume of sphere if radius is divided by 2 is 1/8 of volume of sphere with r radius.

Answer:

The volume become 1/8 th of the initial volume

Step-by-step explanation:

Points to remember

Volume of sphere V = 4/3(πr³)

Where r is the radius of sphere

It is given that radius of sphere is r/2

To find the effect in volume

Here r = r/2

V = 4/3(πr³)

V = 4/3(π(r/2)³)

  = 4/3(πr³/8)

  = 1/8( 4/3(πr³)

New volume = 1/8(V)

Answer:

Step-by-step explanation:

The formula of a midpoint:

[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have (2, 3) and (12, 3).

Substitute:

[tex]x=\dfrac{2+12}{2}=\dfrac{14}{2}=7\\\\y=\dfrac{3+3}{2}=\dfrac{6}{2}=3[/tex]

Answer: (7,3)

Step-by-step explanation:

See the paper attached. (:

N = 3 - Y

- You isolate the variable by dividing each side by factors that don't contain any variables what so ever.

- Ouma

Answer:

n = 3 - p

Step-by-step explanation:

Given

14n + 6p - 8n = 18 ← simplify left side

6n + 6p = 18 ( subtract 6p from both sides )

6n = 18 - 6p ( divide both sides by 6 )

n = [tex]\frac{18-6p}{6}[/tex] = [tex]\frac{18}{6}[/tex] - [tex]\frac{6p}{6}[/tex] = 3 - p

Answer:

The dot will land on red 74.8% of the time

Step-by-step explanation:

To start off we need to find the Area of the whole circle. We can calculate this by using the Area of a Circle Formula on the larger circle measurement.

[tex]A = \pi r^{2}[/tex]  .... A is Area, and r is radius.

[tex]A = \pi 8.01^{2}[/tex]

[tex]A = \pi *64.1601[/tex]

[tex]Aw = 201.56in^{2}[/tex] .... rounded to the nearest hundredth

So now we know that the area of the WHOLE circle is [tex]201in^{2}[/tex]. Now we need to find the area of the inner white circle.

[tex]Aw = \pi 4.02^{2}[/tex]

[tex]Aw = \pi *16.1604[/tex]

[tex]Aw = 50.77in^{2}[/tex] .... rounded to the nearest hundredth

Now that we have the area of the whole circle and the area of the smaller inner circle we subtract them to find the area in red.

[tex]Ar = 201.56in^{2} - 50.77in^{2}[/tex]

[tex]Ar = 150.79in^{2}[/tex]

Lastly, we divide the Area in Red by the total Area to get the percentage of time the dot will land on red.

[tex]d = \frac{150.79in^{2} }{201.56in^{2} }[/tex]

[tex]d = 0.748 * 100[/tex] .... multiply by 100 to turn decimal into a percent.

[tex]d = 74.8[/tex]

Finally, we can see that the dot will land on red 74.8% of the time.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

To find the percent of the time that the point will be in the shaded region of the larger circle, we need to find the ratio of the area of the shaded region to the area of the larger circle and convert it to a percentage.

To find the percent of the time that the point will be in the shaded region, we need to find the ratio of the area of the shaded region to the area of the larger circle. Let's say the radius of the larger circle is R, and the radius of the smaller shaded circle is r. The area of the larger circle is πR2 and the area of the shaded circle is πr2. So the ratio is πr2 / πR2 = r2 / R2. The percentage is then (r2 / R2) * 100. Round this to the nearest tenth of a percent to get the final answer.

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Answer: x = 75.7 cm

Step-by-step explanation:

In the given picture, we are given a right triangle.

The length of hypotenuse = 85 cm

Angle opposite to x= [tex]63^{\circ}[/tex]

Using trigonometry,

[tex]\sin\theta=\dfrac{\text{Side opposite to }\theta}{\text{Hypotenuse}}\\\\\Rightarrow\ \sin63^{\circ}=\dfrac{x}{85}\\\\\Rightarrow\ x=85\times\sin63^{\circ}\\\\\Rightarrow\ x=85\times0.89100652418\\\\\Rightarrow\ x=75.7355545553\approx75.7\ cm[/tex]

Hence, the value of x = 75.7 cm

Answer:

m = 6.57 and n = -2

Step-by-step explanation:

To answer this question you will covert the thickness of a dollar to standard notation and then compare the two values.

0.07 =compared to 0.0043 = 0.0657

0.0657 = 6.57 x 10^-2

A quarter is thicker than a dollar by 6.57 x 10^-2.

m = 6.57 and n = -2

m = 6.57 and n = -2

Step-by-step explanation:

To answer this question you will covert the thickness of a dollar to standard notation and then compare the two values.

0.07 =compared to 0.0043 = 0.0657

0.0657 = 6.57 x 10^-2

A quarter is thicker than a dollar by 6.57 x 10^-2.

m = 6.57 and n = -2

Answer:

  - 52/15 your welcome

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sigma notation is:

n

∑ ak

k=1

The n on top is the number of terms.  ak is the expression for the kth term.

Let's look at the first one.  The series is:

-2+4+-8+...+64+-128

There's two things to notice.  One, the sign changes back and forth between + and -.  Two, the magnitude doubles with each next term.  Therefore:

ak = (-2)ᵏ

Next we need to find the number of terms.  -128 is the last term, so:

128 = 2ⁿ

n = 7

So the answer is:

7

∑ (-2)^k

k=1

Now the second one.  Notice the numerators are all 1 and the denominators are all perfect squares.  Therefore:

ak = (1/k)²

The last term is 1/100, so n = 10.

So the answer is:

10

∑ (1/k)²

k=1

Now the last one.  Notice that each term is 5 plus the previous term.  This is an arithmetic series.  So we can say:

ak = 4 + 5(k-1)

ak = 4 + 5k - 5

ak = 5k - 1

The last term is 49, so:

49 = 5n - 1

n = 10

So the answer is:

10

∑ (5n-1)

k=1

Hey there! :)

Given the coordinates (1, 4) & (3, 10), we must find the slope, y-intercept, and standard form.

Keep in mind that in order to find the slope, we must use the slope formula, which is : [tex]m = \frac{y_{2-y_{1} } }{x_{2}-x_{1}  }[/tex]

(1, 4) is our first set of coordinates while (3, 10) is our second set. Meaning that for 1 = x1, 4 = y1 while 3=x2, 10 = y2

Using this information, simply plug into our slope formula.

m = (10-4) / (3-1)

Simplify/

m = 6/2 --> 3

Therefore, our slope is 3.

Now, use the point-slope form to figure out what the y-intercept is.

y - y1 = m(x - x1)

Plug in using the above coordinates and our slope, which is 3.

y - 4 = 3(x - 1)

Simplify!

y - 4 = 3x - 3

Add 4 to both sides.

y = 3x + 1

This means that 1 is our y-intercept.

This is also our equation in standard form.

Hope this helped! :)

Answer:

Step-by-step explanation:

m=marta's rope

d=dilbert's rope

3d-10=m

m+d=120

Then you can substitute equation 1 into the second one

(3d-10)+d=120

3d-10+d=120

4d-10=120

4d=130

d=32.5

m+d=120

m+32.5=120

m=120-32.5

Answer:

25

Step-by-step explanation:

The absolute value function always returns a positive result which represents the magnitude of the input.

The magnitude of -25 is 25.  The magnitude of 25 is 25.

Thus, |−25| = 25.

ANSWER: 25

Every time you see that sign ( | | )is the number without a sign example: |-56|= 56 ; |-37282|=37282.

Answer:

She'll need 8143 cubic inches of foam and 1,809.6  square inches of fabric.

Step-by-step explanation:

Assuming you want to know how much foam and fabric she will need...

First the foam... so we need to determine the volume of that footstool.  The Volume of a cylinder is given by:

V = π * r² * h

So, we plug in the numbers:

V = π * 12² * 18 = π * 144 * 18

V = 2,592 π  = 8143 cubic inches.

Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.

The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool.  The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.

So the lateral surface of the cylinder is:

LS = 18 * 75.14 = 1,357.2 sq inches.

Then we need to calculate the area of the top... which is easy:

A = π * r²  = π * 12²  = 144 π = 452.4 sq inches

So, to cover the lateral side of the footstool and its top, she needs to use:

TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.