A roller coaster starts out at a height of 100 feet. It
then drops 43 feet, loops around, drops another 29
feet and finally increases 10 feet to the exit platform.
a. Write an expression to represent this.
b. Then determine the altitude of the exit platform.

Answer:

11 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]           (Pythagorean Theorem)

[tex]a^{2}[/tex] + [tex]4^{2}[/tex] = [tex](12\frac{1}{3})^{2}[/tex]  (square numbers)

[tex]a^{2}[/tex] + 16 = 152 [tex]\frac{1}{9}[/tex]  (subtract 16, both sides

[tex]a^{2}[/tex] = 136 [tex]\frac{1}{9}[/tex]        (square root both sides)

a = 11 [tex]\frac{2}{3}[/tex] or 11.66 repeating

Answer:

1/16

Step-by-step explanation:

plug in -4 instead of the x.

if the exponent is negative it can be written as 1/2^4

so the answer is 1/16

Answer:

r = ⅙

⅙ × ⅙ = 0.03

0.03 × 3 = 0.09

Answer:

if c=1

then,

28-1×1×1+6=33

if c=2

then,

28-2×2×2+6=26

if c=3

then,

28-3×3×3+6=7

Expression: 28 - c^3 + 6

If c = 1...

28 - (1)^3 + 6

28 - 1 + 6

27 + 6

33

If c = 2...

28 - (2)^3 + 6

28 - 8 + 6

20 + 6

26

If c = 3...

28 - (3)^3 + 6

28 - 27 + 6

1 + 6

7

Hope this helps!

The perimeter of the triangle described in statement has a measure of 56 units long.

After a quick though careful reading, we construct a triangle based on all information given in the statement, based on the fact that the longest segment is adjacent to the longest missing side. Since both sides have two angles with the same magnitude, then we have the following ratios:

[tex]\frac{x}{7} = \frac{x+5}{9}[/tex]   (1)

Now we solve the expression for x:

9 · x = 7 · x + 35

2 · x = 35

x = 17.5

And the perimeter of the triangle is determine by summing the three sides:

p = 9 + 7 + (17.5) + (17.5 + 5)

p = 56

The perimeter of the triangle described in statement has a measure of 56 units long. [tex]\blacksquare[/tex]

To learn more on triangles, we kindly invite to check this verified question: https://brainly.com/question/2773823

Answer:

see explanation

Step-by-step explanation:

look at the explanation& answer photo

Answer:

Value of X: X=2

Length of One Side: 31

Area: 961u^2

Perimeter: perimeter = 124

Step-by-step explanation:

Set the sides equal to each other, simplify and then use quadratic equation. One result is positive and the other is negative, shape's sides have to be positive so use the positive value for X.

Answer:

See below, please

Step-by-step explanation:

This square

[tex]3 {x}^{2} + 6x + 7 = 2 {x}^{2} - 2x + 27[/tex]

[tex](3 {x}^{2} - 2 {x}^{2} ) + (6x + 2x) + (7 - 27) = 0[/tex]

[tex] {x}^{2} + 8x - 20 = 0[/tex]

[tex](x + 10) \times (x - 2) = 0[/tex]

Hence,

[tex]x1 = 2[/tex]

[tex]x2 = - 10[/tex]

Because x is positive, So,

[tex]x = 2[/tex]

Then we know

The length of one of the sides

[tex] = 3 {x}^{2} + 6x + 7 = (3 \times {2}^{2}) + (6 \times 2) + 7 = (3 \times 4) + 12 + 7 = 31[/tex]

The area of the square

[tex] = {31}^{2} = 961[/tex]

The perimeter of the square

[tex] = 31 \times 4 = 124[/tex]

Answer:

The last one

Step-by-step explanation:

Look at A and A'

It moved 4 units to the right and 1 unit down

The same with B, B' and C, C'

Answer:

25

if j 25 L is going to be 25

Answer:

x = 3, y = - 2

Step-by-step explanation:

By substitution method,

4x + y = 10 -------> equation 1.

7x + 2y = 17 -------> equation 2.

From equation 1,

y = 10 - 4x ------> equation 3.

Substitute equation 3 in 2,

7x + 2 ( 10 - 4x ) = 17

7x + 20 - 8x = 17

7x - 8x = 17 - 20

- x = - 3

x = 3

Substitute x = 3 in equation 1,

4 ( 3 ) + y = 10

12 + y = 10

y = 10 - 12

y = - 2

Hence,

x = 3

y = - 2

✿————✦————✿————✦————✿

:

=

=−

✿————✦————✿————✦————✿

:

* , . .

* ℂ - .

* .

* .

* / − +.

* − / + / , +=.

* - / + /

* /

* /

*

* − = -/ + /. , .

* -/ -

* / / . .

✿————✦————✿————✦————✿

pa brainliest kung ayaw, edi wag** char

Answer:

8

Step-by-step explanation:

y^2=-16

y= -16/1 % 2/1

y=-16/1 % 1/2

y = 8

Answer:

y=4

Step-by-step explanation:

its -y^2=-16. square root both sides to get rid of the exponent and it gives you -y=-4 which is the same as y=4

Answer:

197.92

Step-by-step explanation:

radius of bigger circle is 12 (9 + 3). Area of cirlce is Pi(R²)

12² is 144 so 144Pi

9² is 81 (for the inner circle) so 81Pi

144 - 8 is 63Pi which in decimal form is 197.92.

Answer:

90

Step-by-step explanation:

supplementary angles equal 180 degrees and 90+90=180

Answer:

90°

Step-by-step explanation:

     Supplementary angles are angles that add up to 180°.

     Congruent means the angles are equal to each other.

     Since there are two angles, and they have to be equal to each other, we can divide 180° by 2 to find the measure of each angle.

180° / 2 = 90°

            Both angles have a measure of 90°.

The value of the third angle that can be found in the information given about the congruent triangles will be 45°.

From the complete information, the angles that are given in the triangle are 76° and 59°.

It should be noted that the value of the total angles that are in a triangle is 180°. Therefore, the value of the last angle will be:

= 180° - (76° + 59°)

= 180° - 135°

= 45°

Learn more about triangles on:

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Total surface area includes the area of the 2 bases and the area of the curve surface area this was found to be 289.064 square inches for all four mugs

Given Data

Total surface area of cylinder = 2πr(r + h)

TSA of 1 mug = 2*3.142*2(2+3.75)

TSA of 1 mug = 12.568(5.75)

TSA of 1 mug = 72.266 square inches

if the total surface area of one mug is 72.266 square inches

hence the total surface area of 4 mugs will be

= 72.266*4

= 289.064 square inches

Learn more about cylinders here:

https://brainly.com/question/9554871

Answer:

this is easy the a sewer is 12

Answer:

A difference of squares has the following form . Any two perfect squares connected by subtraction can be factored.

It factors to (a+b)(a-b).

Step-by-step explanation:

A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.

A difference of squares has the following form . Any two perfect squares connected by subtraction can be factored.

It factors to (a+b)(a-b).

Answer:

Step-by-step explanation:

An example is a^2 - b^2.

Also 64 - 49   (as 64 are both perfect squares).

The way to factor is by using the identity:

a^2 - b^2 = (a - b)(a + b)      ( a + in one parentheses and - in the other)

Examples:

x^2 - 4y^2 = (x - 2y)(x + 2y)     [ x is the square root of x^2 and 2y is square root of 4y^2)

144 - 16 = (12 - 4)(12 + 4)

9x^2 - 36y^2 = (3x - 6y)(3x + 6y)

Answer:

58

Step-by-step explanation:

x=9

3(9) + 1 + 4(9) -8 + (9) - 7 = 58

Hello!

[(4πr³)/3]/2

r = 7,5yd

[4 *3,14*7,5³/3]/2

=> 883, 125yds ³

Answer:

p = r-8

Step-by-step explanation:

40-8=32
45-8=37
50-8=42
47-8=47
each step goes down by the same amount, so anika gives an 8 dollar discount to the local restaurants

Answer:

The value of n = 7

Step-by-step explanation:

=> 3n-4=17

=> 3n = 17+4

=> 3n = 21

=> n = 21/3

=> n = 7

Answer:

n=7

Step-by-step explanation:

1. Solve

3n-4=17

3n-4+4=17+4

3n=21

3n/3=21/3

n=7

2. Check

3x7-4=17

21-4=17

17=17

Correct!
3. Answer

n=7

A ratio shows the relation between two numbers. The amount of more material that is needed by Jake is 42.5 cm³.

A ratio shows us the number of times a number contains another number.

Given that the volume of the first prism is 14.5cm³, while the scale factor is 4. Since the scale factor is applicable to dimension, and volume is always the cube of three-dimension.

Therefore, the volume of the scaled prism will be the cube the of the volume of the first prism, which can be written as,

[tex]\rm \text{Volume of the Scaled prism}= (Scale\ factor)^3 \times \text{Volume of the first prism}[/tex]

Substitute the values,

[tex]\rm \text{Volume of the Scaled prism}= 4^3 \times 14.5 = 928\ cm^3[/tex]

Since, the volume of material with Jake is 900 cm³, while the material he has already used is 14.5 cm³, thus the volume of the material that is left with Jake is 885.5 cm³(900cm³-14.5cm³).

Now, since the material needed to make the scaled prism is 928 cm³, the amount of material that is with Jake is 885.5 cm³, therefore, the amount of the material that is needed by Jake to complete the scaled prism can be written as,

The Amount of more material Needed by Jake = Amount of material needed to make the scaled prism - Amount of material left with Jake

The Amount of more material Needed by Jake = 928 cm³ - 885.5 cm³

                                                                               = 42.5 cm³

Hence, the amount of more material that is needed by Jake is 42.5 cm³.

Learn more about Ratios:

https://brainly.com/question/1504221

Answer:

UM make a graph if you want so yea

Step-by-step explanation:

[tex]\\ \rm\rightarrowtail x^2-4x+3[/tex]

Use quadratic formula

[tex]\\ \rm\rightarrowtail x=\dfrac{4\pm\sqrt{16-12}}{2}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{4\pm 2}{2}[/tex]

[tex]\\ \rm\rightarrowtail x=2\pm 1[/tex]

[tex]\\ \rm\rightarrowtail x=3,1[/tex]

Answer:

-3.274

Step-by-step explanation:

attached

Hopes this helps

{please mark me brainiest}

Answer:

1= 40, 25, 10

2= 9,375, 46,875, 234,375

3= 234, 729, 2,187

4= 192, 384, 768

Answer:

its a cause you divide 6 on both sides and 48 divided by 6 is 8 and since its a greater than symbol and the numbers werent negative its gonna be a

Step-by-step explanation:

Answer:

A ) the Value of t is greater than 8

Step-by-step explanation:

6t>48

t>48/6

t>8

Answer:

[tex]\sf \dfrac{x}{8}-22[/tex]

Explanation:

[tex]\rightarrow \sf \left(\dfrac{7}{8}x-4\right)-3\left(\dfrac{1}{4}x+6\right)[/tex]

remove parenthesis

[tex]\sf \rightarrow \dfrac{7}{8}x-4-\dfrac{3x}{4}-18[/tex]

expand

[tex]\rightarrow \sf \dfrac{7x}{8}-\dfrac{3x}{4}-22[/tex]

simplify

[tex]\rightarrow \sf \dfrac{x}{8}-22[/tex]

Answer:

[tex]\frac18x-22[/tex]

Step-by-step explanation:

Given expression:

[tex](\frac78x-4)-3(\frac14x+6)[/tex]

Expand:

[tex]\implies \frac78x-4-\frac34x-18[/tex]

Gather like terms:

[tex]\implies \frac78x-\frac34x-4-18[/tex]

Change 3/4 into eighths:

[tex]\implies \frac78x-\frac68x-4-18[/tex]

Combine like terms:

[tex]\implies \frac18x-22[/tex]