Type the correct answer in the box. Use numerals instead of words. The height of a baseball, in feet, is represented by this expression, where t is time in seconds. -16t squared+64t+3 The height of the baseball after 3.5 seconds is BLANK feet.

Answer:

m∠U = 103° and m∠TRS = 6°

Step-by-step explanation:

In the given circle O,

Since, RS║VU, and VR is a transverse,

Therefor, m∠V + m∠R = 180° [Consecutive interior angles]

m∠R + 103° = 180° [m∠R = 103° given]

m∠R = 180° - 103°

m∠R = 77°

Since m∠R = m∠VRT + m∠TRS

77° = 71° + m∠TRS

m∠TRS = 77° - 71° = 6°

Quadrilateral RTUV is a cyclic quadrilateral.

Therefore, m∠U + m∠R = 180°

m∠U + 77° = 180°

m∠U = 180° - 77° = 103°

Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.

We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.

We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.

Answer:

Theres more than one answer so b and a

Step-by-step explanation:

The missing probability P(A∪B) will be 37/50.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Given information;

P(A)= 7/20,

P(B)=3/5,

P(A∩B) =21/100 ,

We need to find the missing probability P(A∪B).

We know that

P(A∪B)= P(A) + P(B) + P(A∩B)

P(A∪B) = 7/20 + 3/5 + 21/100

P (A U B) = 37/50

Therefore, the missing probability P(A∪B) will be 37/50.

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Answer:

[tex] IJ = 2(KL) [/tex]

Step-by-step explanation:

From the information given, the smaller figure was dilated on a scale factor of 2, to produce the bigger figure. In essence, the bigger figure is times 2 of the smaller figure.

Therefore, line IJ would be twice the length of KL.

The relationship that both lines have can be represented as: [tex] IJ = 2(KL) [/tex]

Answer:

By using The Pythagorean Theorem:

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex]

/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]

Step-by-step explanation:

The Pythagorean theorem states that: Given a Right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides ( Here, being the length of the altitude and length of leg). That is,

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex] and hence,

/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]

For example, If the length of the altitude is 4m and the length of leg is 3m. Using The Pythagorean theorem, the length of the hypotenuse will be

[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \\\/Hypotenuse/ = \sqrt{/Length of altitude/^{2} + /Length of leg/^{2}} \\/Hypotenuse/ = \sqrt{4^{2} + 3^{2} }[/tex]

[tex]/Hypotenuse/ = \sqrt{16+9} \\/Hypotenuse/ = \sqrt{25} \\/Hypotenuse/ = 5m[/tex]

The length of the hypotenuse for the given example will be 5m.

This is how to find the length of an hypotenuse.

Answer:

156.6 square yards

Step-by-step explanation:

To find the surface area of the pyramid, find the area of each surface and add them together.

formula for area of a triangle = 1/2(b·h)

1. There are three triangles with a base of 9 and a height of 9

1/2(9·9) = 40.5

Multiply by the three triangles

40.5 · 3 = 121.5

2. There is one triangle with a base of 9 and a height of 7.8

1/2(9·7.8) = 35.1

3. Add the areas of all surfaces

121.5 + 35.1 = 156.6

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids.

A sphere is a solid shape.

Given data

radius of sphere = 17 units

The volume of a sphere can be expressed as below

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

Substituting our data into the expression we have

[tex]volume = \frac{4}{3}*3.142*17^3[/tex]

[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]

The volume of the sphere is given as

20582.195 units

Answer:

D. zero

Step-by-step explanation:

Since the graphs do not intersect, there are zero solutions.

The number of solutions on the graph is zero

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

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Answer:

The age of Noi is 13.333 Years and the age of Noy is 12.67 years

Step-by-step explanation:

The given  information are;

The sum of the ages of Noi and Noy = 26 years

Four times Noi's age - Two times Noy's age = 28

Let the age of Noi = X and let the age of Noy = Y

We have;

X + Y = 26 years.................(1)

4X - 2Y = 28 years.............(2)

Divide equation (2) by 2 to get;

(4X - 2Y)/2 = (28 years)/2 which gives;

2X - Y = 14 years.................(3)

Add equation (3) to equation (1), to get;

X + Y +  2X - Y = 26 years + 14  years

3X = 40 years

X = 40/3 = 13.333 Years

From equation (1), X + Y = 26 years, therefore;

Y = 26 - X = 26 - 13.33 = 12.67 years

Therefore, the age of Noi = 13.333 Years and the age of Noy = 12.67 years.

Answer:

(D) There are [tex]5 \frac{1}{2}[/tex]  three-fourths in [tex]4 \frac{1}{8}[/tex]

Step-by-step explanation:

We can see that in this model, the student tried to put [tex]\frac{3}{4}[/tex] into  [tex]4 \frac{1}{8}[/tex]. We know this because the top of Step 2 is  [tex]4 \frac{1}{8}[/tex] and he is counting how many fourths in the bottom.

So this becomes the division statement:

[tex]4 \frac{1}{8} \div \frac{3}{4}[/tex].

We can convert  [tex]4 \frac{1}{8}[/tex] into a mixed number by multiplying 8 and 4, then adding 1.

[tex]\frac{33}{8} \div \frac{3}{4}[/tex].

Multiply by the reciprocal:

[tex]\frac{33}{8} \cdot \frac{4}{3} = \frac{132}{24}[/tex]

Which simplifies down to

[tex]\frac{11}{2}[/tex], which is just [tex]5 \frac{1}{2}[/tex] in improper form.

Hope this helped!

Answer:

D

Step-by-step explanation:

Answer:

(3x-1) (x+1)

Step-by-step explanation:

3x^2 + 2x − 1

3x^2 factors into 3x and x

-1 factors into -1 and 1

We want a postive 2x

(3x-1) (x+1)

Answer:

(3x-1)(x+1)

Step-by-step explanation:

3x² + 2x − 1

when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.

(3x        )(x      )     first step : 3x*x=3x^2

(3x-      ) (x+   )      the sign for the constant is minus so the factoring has to be minus and plus on each side

(3x-1)(x+1)   look at the 2x it has positive sign, means the sign is plus:

3x-1

x+1

                        regular standard multiplication

3x(x)-1(x)+1(3x)-1

3x²+2x-1

Answer: (-1, -2)

Step-by-step explanation:

so at first you have (1, 2)

then you were asked to reflect about y=x which is (x, y) = (y, -x)

(1, 2) = (2, -1)

then followed by y=-x which is (x, y) = (-y, -x)

(2, -1) = (-1, -2)

I hope this helps!

Answer:

A.) median; 1.5

Step-by-step explanation:

Hello!

The median is the number that is in the middle when the numbers are listed from least to greatest

0, 0, 1, 1, 2, 2, 2, 14

We can take one from both sides till there are one or two numbers left

0, 1, 1, 2, 2, 2

1, 1, 2, 2

1, 2

If there are two numbers left we add them then divide by 2 to get the median

1 + 2 = 3

3 / 2 = 1.5

The answer is A.) median; 1.5

Hope this helps!

Step-by-step explanation:

It is given that,

The height of the sail on a boat is 7 feet less than 3 times the length of its base.

Let the length of the base is x.

ATQ,

Height = (3x-7)

Area of the sail is 68 square feet.

Formula for area is given by :

[tex]A=lb\\\\68=x(3x-7)\\\\3x^2-7x=68\\\\3x^2-7x-68=0[/tex]

x = 8 feet and x = -3.73 feet

So, length is 8 feet

Height is 3(8)-7 = 17 feet.

So, its height and the length of the base is 17 feet and 8 feet respectively.

Answer:

a⁴b⁴ - c⁴

Step-by-step explanation:

The difference of squares formula states that (a - b)(a + b) = a² - b². In this case, a = a²b² and b = c² so a² - b² = (a²b²)² - (c²)² = a⁴b⁴ - c⁴.

Answer:

a^4b^4 - c^4.

Step-by-step explanation:

(a²b²-c²)(a²b²+c²)

Difference of 2 squares:

= (a²b²)^2 - (c²)^2

= a^4b^4 - c^4.

Answer:

[tex]\Huge \boxed{3}[/tex]

Step-by-step explanation:

The function is given :

f(x) = 4x + 15

For f(-3), the input for the function f(x) is -3.

Replace the x variable with -3.

f(-3) = 4(-3) + 15

Evaluate.

f(-3) = -12 + 15

f(-3) = 3

The output for f(-3) is 3.

Answer: f(-3) = 3

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(-3).

We find f(-3) by plugging -3 in for x,

everywhere that x appears in the function.

So we have 4(-3) + 15.

4(-3) is -12 so we have -12 + 15 which is 3.

So f(-3) is 3.

Answer:

21

Step-by-step explanation:

4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]

5 × [tex]\frac{21}{5}[/tex] = (5×21)/5

[tex]\frac{105}{5}[/tex] = 21

Answer:

elimination method

x+2y=4     1

5x-2y=8     2

1+2

6x=12

x=2

plug into x+2y=4

2+2y=4

2y=4-2

2y=2

y=1

(2,1)

so graph 1

Answer:

See below.

Step-by-step explanation:

[tex]\frac{u-x}{v-x}=\frac{u}{v^2} \\[/tex]

Cross multiply and distribute.

[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]

Move all the u to the left side:

[tex]uv-ux-uv^2=-xv^2[/tex]

Factor out a u:

[tex]u(v-x-v^2)=-xv^2[/tex]

Divide:

[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]

(I factored out a negative in the second term.)

Answer:

Here's what I get  

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)  

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500

Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)  

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007

A = (-7,-6)

B = (8,-9)

Find the slope of line AB

m = (y2-y1)/(x2-x1)

m = (-9-(-6))/(8-(-7))

m = (-9+6)/(8+7)

m = -3/15

m = -1/5

The slope of line AB is -1/5.

Flip the fraction and the sign to go from -1/5 to +5/1 = 5. The perpendicular slope is 5.

Let m = 5.

Use the coordinates of point C (2,12) along with the perpendicular slope to get

y - y1 = m(x - x1)

y - 12 = 5(x - 2)

y - 12 = 5x - 10

y = 5x - 10+12

y = 5x + 2

Lastly, convert this to standard form

y = 5x + 2

5x+2 = y

5x+2-y = 0

5x-y = -2

Choice A is the closest match, but the -56 should be -2 instead. It seems like your teacher made a typo somewhere.

Answer:

5x - y = -2.

Step-by-step explanation:

The equation of this altitude line has a slope = -1/m where m is the slope of line AB . It will also pass through the point C.

The slope of line AB = (-9 - (-6)) / (8 - (-7))

= -3/15

= -1/5

So the slope  of the required line = -1 / -1/5 = 5.

Using the point C and the point-slope form of a line:

y - y1 = m(x - x1)

y - 12 =  5(x - 2)

y - 5x = -10 + 12

y - 5x = 2

5x - y = -2.

Answer:

d) More than 3.

Step-by-step explanation:

The polynomial (x - 5)(x + 2)  ( = x^2  - 3x + 10) has zeros of -2 and 5 but so have the polynomials formed by multiplying this by any integer:

- for example 2(x - 5)(x + 2) , 4(x - 5)(x + 2) and so on.

Answer:

SI=PRT/100

=10000*5*42/12*100

=1750

SI=1750

TOTAL AMOUNT=PRINCIPLE+SI

=10000+1750

=101750

Answer:

9:45 A.M.

Step-by-step explanation:

First, add the time that took him to hike:

6:30 + 2 hours and 15 minutes = 8:45 A.M.

Next, add the 1 hour that he played volleyball for:

8:45 + 1 hour = 9:45 A.M.

So, he finished playing volleyball at 9:45 A.M.

Answer:

9:45 am

Step-by-step explanation:

He went at 6:30 am to a hike.

It took him 2 hours 15 minutes

=> 6 : 30

+  2    15

=> 8 : 45

He came back from the Hike at 8:45 am

He played volleyball for 1 hour.

=> 8 : 45

+  1

=> 9 : 45

He finished playing volleyball at 9:45 am

Hey There!!

Your best choice is 76%

Because, 19/25 = x/100

25x = 1900

x = 76

°He got 76% correct!!°

By °Itsbrazts°

Answer:

76%

Step-by-step explanation:

Thomas got 19/25 marks.

** Note: Percents are always out of 100.

We don't know how many marks he got out of 100.

=> 19/25 = x/100

There are two ways to solve it from now.

=> Multiply 19 and 100; 25 and x

=> 25x = 1900

Next, Divide 25 on each side.

=> 25x/25 = 1900/25

=> x = 76

He got 76% on the quiz.

Another way is:

=> 19/25 = x/100

=> We need to divide 25 from 100.

=> We get 4.

So, 25 x 4 = 100

=> 19 x 4 = x

=> x = 76

He got 76% on the quiz.

Both ways are correct.

The measure of angle Q in the triangle QMN is 52.83°

An equation is an expression that shows the relationship between two or more variables and numbers.

For a triangle with sides a, b, c and respective opposite angles A, B, C, cosine rule is:

a² = b² + c² - 2bc * cos(A)

In triangle QMN, QM = 18, MN = 17, QN = 20, hence:

17² = 18² + 20² - 2(18)(20) * cos(Q)

Q = 52.83°

The measure of angle Q in the triangle QMN is 52.83°

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Answer:

53

Step-by-step explanation:

its rounded

Answer:

a or b

Step-by-step explanation:

it just looks like b or a

H(t) = -4.9t^2 + 25t + 2

Height is a function of time

plug in 0, 1,2,3,4, and 5 to find the height at 0, 1,2,3,4, and 5 seconds.

at t = 0

H(0) = -4.9(0)^2+25(0) + 2 = 2 meters

Repeat for T=1,2,3,4 and 5

Notice the ball peaks around t = 3 seconds and starts to descend.  

H(1) = (-4.9)(1^2) + 25(1) + 2 = 22.1 meters

H(2) = (-4.9)(2^2)+25(2)+2=32.4 meters

H(3) = 32.9 meters

H(4) = 23.6 meters

H(5) = 4.5 meters

Answer:

-16, 0 real solutions. (Complex Roots)

Step-by-step explanation:

[tex]5x^2-2x=-1\\5x^2-2x+1\\A=5\\B=-2\\C=1\\(-b±√(b^2-4ac))/2a\\=\\=-2^2-4(5)(1)\\=4-20\\=-16[/tex]

Answer:

  2n+2 ways to win

Step-by-step explanation:

You generalize by observing patterns in the way you solve the smaller problems.

The number of winning moves is 2n+2: the total of the number of diagonals, columns, and rows.

For an n×n board, there are 2 full-length diagonals, n columns, and n rows, hence 2+n+n = 2n+2 ways to win.