A scale model of a building is 3 inches tall. If the building is 90 feet tall, find the scale of the model.

         There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.

[1] using the quadratic formula

     When the equation is in the form of ax² + bx + c = 0.

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

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[2] factoring

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[3] completing the square

     To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c

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Explanation:

Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.

The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.

Multiply this floor area with the height of the room (22 m) to get the volume of the room.

volume = (floor area)*(height) = 84*22 = 1848 cubic meters

Answer:

D)

Step-by-step explanation:

[tex]\sf f(x) = \sqrt{x+1}\\\\\\g(x) = 7x\\\\ g(f(x)) = g(\sqrt{x+1}) = 7*\sqrt{x+1}[/tex]

The two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a quadrilateral ABCD which is reflected over a line and formed a mirror image A'B'C'D' of the quadrilateral.

From the graph:

The two points are (-4, -2) and (4, 5)

The line equation passing through two points:

[y - 5] = (5+2)/(4+4)[x - 4]

y - 5 = 7/8[x - 4]

8y - 40 = 7x - 28

8y = 7x + 12

Thus, the two points are (-4, -2) and (4, 5) and the equation of the line is 8y = 7x + 12 passing through the two points.

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Answer:

n² blocks are needed to build a staircase with n steps.

Step-by-step explanation:

Answer:

[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]6x^2+5x-6=0[/tex]

First, factor the left side of the given equation.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=6\cdot-6=-36[/tex]

[tex]\implies b=5[/tex]

So the two numbers are: 9 and -4

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 6x^2+9x-4x-6=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 3x(2x+3)-2(2x+3)=0[/tex]

Factor out the common term [tex](2x+3)[/tex]:

[tex]\implies (3x-2)(2x+3)=0[/tex]

To solve for x:

[tex]\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}[/tex]

Therefore:

[tex]x=\dfrac{2}{3},-\dfrac{3}{2}[/tex]

Answer:

15.71 m

Step-by-step explanation:

C = πd

d= diameter

C = π (3.14) * 5

= about 15.71 m

A. 15.71 m

Answer:[tex]5\pi[/tex]

Step-by-step explanation:The circumference is pi times the diameter. If you want a proof you can find it online with a quick search. This applied here means that since the diameter is 5, the circumference is 5*pi or rather 5pi.

[tex]|2x+1|=10\\2x+1=10 \vee 2x+1=-10\\2x=9 \vee 2x=-11\\x=4.5 \vee x=-5.5[/tex]

Answer:

[tex]x= \dfrac 92~~\textbf{or}~~x = -\dfrac{11}2\\\\[/tex]

Step-by-step explanation:

[tex]\underline {\textbf{Absolute value rule: }}\\\\\textbf{If}~ |a| = b~ \textbf{then} ~a =b~ \textbf{or}~ a =-b \\\\\underline{\textbf{Solution;}}\\\\\textbf{Given that,}\\\\~~~~~~~|2x+1| = 10\\\\\implies 2x +1 = 10~~~~~~\textbf{or} ~~~~~~~~~~~2x+1 = -10\\\\\implies 2x = 10-1~~~~~~\textbf{or}~~~~~~~~~~~2x = -10-1\\\\\implies 2x = 9~~~~~~~~~~~~~\textbf{or}~~~~~~~~~~~2x = -11\\\\\implies x= \dfrac 92~~~~~~~~~~~~~~\textbf{or}~~~~~~~~~~~x = -\dfrac{11}2\\\\[/tex]

Answer:

A) x = 113°

Explanation:

Given three sides: 6.4 cm, 5.8 cm, 10.2 cm

Use the cosine rule:

c² = a² + b² - 2ab cos(C)

Insert/put variables:

[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]

[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]

[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]

[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]

[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex]   = 113.36°  ≈ 113°  (rounded to nearest degree)

Graph is in attached image.

Answer:

5.6 is the mean

Step-by-step explanation:

add up everything and then divide it over how many numbers are in the set to find the mean.

give brainliest, please!
hope this helps :)

Complete the square:

x² - 4x + 6 = 0

x² - 4x = -6

x² - 4x + 4 = -6 + 4

(x - 2)² = -2

But the left side is positive for any real number x, so there are no real solutions.

If you're solving over the complex numbers, we can go on to say

x - 2 = ± √(-2)

x - 2 = ± 2i

x = 2 ± 2i

where i = √(-1).

[tex]\begin{cases} v=5i-7j\\\\ w=3i+2j \end{cases}\qquad \begin{cases} < \stackrel{a}{5}~~,~~\stackrel{b}{-7} > \\\\ < \stackrel{a}{3}~~,~~\stackrel{b}{2} > \end{cases}\qquad \qquad \stackrel{magnitude}{\sqrt{a^2 + b^2}} \\\\[-0.35em] ~\dotfill\\\\ ||v||~~ - ~~||w||\implies \sqrt{5^2+(-7)^2}~~ - ~~\sqrt{3^2 + 2^2}\implies \sqrt{74}-\sqrt{13} ~~ \approx ~~ 5[/tex]

Answer:

56/64 simplified is 0.875 or 7/8 as a fraction

Answer:

about 127.28 feet

Step-by-step explanation:

The length of the hypotenuse of a right triangle with a base and a height of 90 feet each.

root (90)^2 + (90)^2

Answer:

i am not sure about your question but if it is 3 divided by y-3 =12 divide by y+3 you can use this

Step-by-step explanation:

3÷y-3=12÷y+3

cross multiply

12(y-3)=3(y+3)............brackets off

12y-36=3y+9..............group the same

12y-3y=9+36

9y=45.......duved by 9 both sides

y=5

Answer:

r = - 18/5

I hope this helps! ^^

( This problem has 13 steps, so it would take a lot of time to type them in ^^)

The answer of the following options are as 50, 64, 36, 40, 100, 9, 12, 12 100, 27, 150 42, 50 72, 28.3.

Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be

[tex]\dfrac{a}{b}[/tex]

Then, we can interpret it as:

a parts out of b parts of a thing.

[tex]1. \dfrac{2}{5} t = 20\\\\t = 20 \times \dfrac{5}{2}\\\\t= 50[/tex]

[tex]2. \frac{7}{8} p = 56\\\\p = 56 \times \frac{8}{7} \\\\ p= 64[/tex]

[tex]3. \frac{5}{6} x = 30 \\\\x = 30 \times \frac{6}{5} = 36[/tex]

[tex]4. \frac{1}{2} x = 20\\\\x = 20 \times 2 = 40[/tex]

[tex]5. \frac{3}{5} s = 60\\\\s = 60 \times \frac{5}{3} = 100[/tex]

[tex]6. \frac{1}{3} t = 3 \\\\t = 3\times 3 = 9[/tex]

[tex]7. \frac{3}{4} x = 9\\\\x = 12[/tex]

[tex]8. \frac{11}{12} x = 11\\\\x = 11 \times 12/11 = 12[/tex]

[tex]9. \frac{8}{10} t = 80\\\\t = 80 \times 10/8 = 100[/tex]

[tex]10. \frac{p}{3} = 9 \\\\p = 9 \times 3 = 27[/tex]

[tex]11. \frac{n}{5} = 30\\\\n = 30 \times 5 = 150[/tex]

[tex]12. \frac{6a}{7} = 36 \\\\a = 36 \times 7/6 = 42[/tex]

[tex]13. \frac{1}{2} t + 3 = 28\\\\t = (28 - 3)2 = 50[/tex]

[tex]14. \frac{1}{6} r = 12\\\\r = 12\times 6 = 72[/tex]

[tex]15. \frac{11}{12} b = 32\\ \\b = 32 \times 11/12 = 29.33[/tex]

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The graph of the two given system of inequalities y > 2x - 5

y < -3x is; Attached below

We are given two inequalities;

y > 2x - 5

y < -3x

The graph that represents the 2 inequalities has been attached and from the graph, we see that;

The solution of the system of inequalities is the shaded pink area between the two dotted lines.

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Answer:

whats nine + 10

Step-by-step explanation:

21

pencil is .10

pen is .90

Step-by-step explanation:

x = pencil y = pen

3x + y = 1.20

7x + 2y = 2.50

try make x or y cancelable

-2 times (3x + y = 1.20) = -6x - 2y = - 2.40

7x + 2y = 2.50

-6x - 2y = - 2.40

x = .10

plug .10 back into one of the equations

3(.10) + y = 1.20

.30 + y = 1.20

y = .90

[tex]\displaystyle\\|\Omega|=\binom{72}{4}=\dfrac{72!}{4!68!}=\dfrac{69\cdot70\cdot71\cdot72}{2\cdot3\cdot4}=1028790\\|A|=\binom{46}{4}=\dfrac{46!}{4!42!}=\dfrac{43\cdot44\cdot45\cdot46}{2\cdot3\cdot4}=163185\\\\P(A)=\dfrac{163185}{1028790}=\dfrac{473}{2982}\approx0.1586[/tex]

Answer:

a = 63

b = 117

c = 63

Step-by-step explanation:

The sum of interior angles in a triangle is = 180

so the measure of a:

85 + 32 + a = 180 add like terms

117 + a = 180 subtract 117 from both sides

a = 63

a and be are supplementary angles so their sum is equal to 180

180 - 63 = 117 is the b's value

since a and c are on a pair of parallel lines, their value must be equal therefore the value of c is also 63

Answer:

i think the answer is 25q - 5 / 4

Answer:

Simplifying

-9 + 4 = 40

Combine like terms: -9 + 4 = -5

-5 = 40

Solving

-5 = 40

Couldn't find a variable to solve for.

This equation is a the left and right sides are not equal, therefore there is no solution.

Hope This Helped

Answer:

x=5

Step-by-step explanation:

The two lines are the same length

2x+7 = 5x-8

15 = 3x

x = 5

Answer:

12345678910

Step-by-step explanation:

TANQR

The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]

The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]

It is the way of writing a large number between 1 to 10 with a power of 10.

We have,

7,250,000

To write this number in standard notation, we can use powers of 10.

We start by counting the number of digits to the left of the decimal point.

In this case, there are 7 digits to the left of the decimal point.

We can then express this number in scientific notation as:

[tex]7.25 \times 10^6[/tex]

This means that we have 7.25 times 10 raised to the power of 6.

Now,

0.000045

To write this number in standard notation, we can again use powers of 10. We start by counting the number of digits to the right of the decimal point. In this case, there are 5 digits to the right of the decimal point.

We can then express this number in scientific notation as:

[tex]4.5 \times 10^{-5}[/tex]

This means that we have 4.5 times 10 raised to the power of -5.

Thus,

The standard notation of 7,250,000 is [tex]7.25 \times 10^6[/tex]

The standard notation of 0.000045 is [tex]4.5 \times 10^{-5}[/tex]

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The complete question.

Write this number in standard notation.

7,250,000

0.000045

Answer: The correct answer is A.

Step-by-step explanation: A line with a positive slope always increases and goes up.

Answer:

1) Ans; C .

2) Ans; D.

3) Ans; A.

4) Ans; C.