In the figure below, m1=3x° and m2 = (x+18)°.
Find the angle measures.
L
2
m 21 =
m2 2 =

Answer:

Step-by-step explanation:

The equation of the perpendicular line is y = x + 15.

In this problem we need to determine the equation of the line perpendicular to another line, that intersects at the point (x, y) = (- 5, 10). The explicit form of the equation of the line is defined by the following first order polynomial:

y = m · x + b      

Where:

The first line has a slope - 1 and the slope of the second line is:

m' = - 1 / m

m' = 1

Then, the intercept of the second line is:

b = y - m · x

b = 10 - (- 5)

b = 15

The equation of the perpendicular line is y = x + 15.

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Answer:

Density=13g/45cm cubed

Step-by-step explanation:

D=M/V

D=65g/225cmcubed

D=13g/45cm cubed

The domain at which the function f(x) = x² - 4•x + 2, and the inverse of the function, f(x), is given by the option;

The given function is f(x) = x² - 4•x + 2.

The points through which the parabola passes are;

The inverse of the function is found as follows;

f(x) = x² - 4•x + 2

The standard form of a quadratic equation is f(x) = a•(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

a = The coefficient of x²

Comparing, we have;

(h, k) = (2, -2)

a = 1

Which gives;

f(x) = x² - 4•x + 2 = (x - 2)² - 2

f(x) = (x - 2)² - 2

Let f(x) = y

y = (x - 2)² - 2

y + 2 = (x - 2)²

x - 2 = √(y + 2)

x = √(y + 2) + 2 = 2 + √(y + 2)

x = 2 + √(y + 2)

Therefore, f(x) has an inverse when y > -2, which gives;

The domain where f(x) has an inverse is x > 2, given that the expression, 2 + √(y + 2), is always positive.

The inverse of the function is obtained by changing x to [tex] f^{-1}(x) [/tex] and y to x in the equation, x = 2 + √(y + 2), to give;

The correct option is therefore;

x > 2, f superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot

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Answer:

Its D.x > 2; f Superscript negative 1 Baseline (x) = 2 + StartRoot x + 2 EndRoot

Step-by-step explanation:

Answer:

-63, -90, -1924. -|63|, etc

Step-by-step explanation:

Answer:4.6 miles for 5 days

Step-by-step explanation:

37 - 14 = 23

23 divided by 5 = 4.6

Answer:4.6 miles

Step-by-step explanation: she has already ridden 14 miles so 5 mroe days is 4.6 miles

Answer:

No one can answer this

Step-by-step explanation:

You need to add a picture or something because we need more information. This could be a graph, a number line, etc.

Answer:

(Image 1)

d(A,C)=10d(C,B)=8

d(A,B)=d(A,C)+d(C,B)=10+8=18

(Image 2)

AB=AC−BC

=10−8=2

Step-by-step explanation:

The coordinates of the new triangle are P' = (5, 3), K' = (3, 1) and Y' = (1, 4)

The coordinates of the triangle in the figure are

P = (-5, -3)

K = (-3, -1)

Y = (-1, -4)

The transformation is given as 180 degrees rotation

The rule of this transformation is

(x, y) = (-x, -y)

When this is applied on the triangle, we have the coordinates of the new triangle to be

P' = (5, 3)

K' = (3, 1)

Y' = (1, 4)

Hence, the coordinates of the new triangle are P' = (5, 3), K' = (3, 1) and Y' = (1, 4)

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Answer:

8 quarters equal 2 dollars 11 dimes is a dollar and 10 cents so 3 dollars and 10 cents

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

[tex]AB \cong BC \implies AB=BC \\ \\ 3x+6=15x-2 \\ \\ 6=12x-2 \\ \\ 8=12x \\ \\ x=\frac{2}{3}[/tex]

[tex] \: \Large \mathbb{SOLUTION:}[/tex]

[tex] \: \: \rm{ {7x}^{2} + 4x - {x}^{2}}[/tex]

[tex] \: \: \text{Reorder and gather like terms}[/tex]

[tex] \: \: \rm{( {7x}^{2} - {x}^{2} ) + 4x}[/tex]

[tex] \: \: \text{Collect coeffiecients of like terms}[/tex]

[tex] \: \: \rm{(7 - 1) {x}^{2} + 4x}[/tex]

[tex] \: \: \text{Calculate the sum or difference}[/tex]

[tex] \: \: \rm{ \underline{ \underline{ {6x}^{2} + 4x}}}[/tex]

[tex] \rm{6x {}^{2} + 4x}[/tex]

Collect like terms

[tex] \red{7x {}^{2} } + 4x \red{ - x {}^{2} }[/tex]

[tex] \red{6x {}^{2} } + 4x [/tex]

Answer:

37

Step-by-step explanation:

Evaluate 40-15/t for t=5 step by step

first, remember PEMDAS

substitute in 5 for t

40-15/5

since division (D) comes before subtraction (S) in PEMDAS, we divide first

15/5 is 3

we are left with

40-3

if we subtract, we are left with

37

Answer:

37

Step-by-step explanation:

PEMDAS

Parenthesis

Exponents

Multiply          

Divide

Add

Subtract

^

This is the order you should complete your problem in...

Answer:

Please see the picture below.  You were on the right track.  You were just off in letter A.

Step-by-step explanation:

If two side lengths of a fence are 9 and 12 inches and the sum of the three lengths ranges from 31 to 40 inches, then the length of the third side, x,  can be presented by the compound inequality 10 < x < 19.

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

Given that the sum of the three lengths of a fence ranges from 31 to 40 inches, the inequality can be written as:

31 < sum < 40

If two side lengths are 9 and 12 inches, and let x be the third length, the inequality becomes:

31 < 9 + 12 + x < 40

31 < 21 + x < 40

Subtracting 21 at all sides,

31 - 21 < 21 + x - 21 < 40 - 21

10 < x < 19

Hence, the compound inequality to show the length of the third side can be written as 10 < x < 19.

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Answer:

81

Step-by-step explanation:

81 is a perfect square, and also ends with 1.

The light must be at a height of 7.07m from the floor for the maximum illumination at P.

How  Distance  is that?

Let I be the illumination at P then according to given conditions,

I =  k cosθ/r²

Where k is constant of proportionality: since

r² = h² + 10²

cosθ = [tex]\frac{h}{\sqrt{h^{2} + 10^{2} } }[/tex]

then

I = k [tex]\frac{h}{( h^{2} + 100)^{3/2} }[/tex]

on differentiating

[tex]\frac{dI}{dh} = k \frac{h^{2} + 100)^{3/2} - 3h^{2 ( h^{2} + 100)^{1/2} } }{( h^{2} + 100)^{3} }[/tex]

[tex]= k \frac{( 100 - 2h^{2}) }{( h^{2} + 100)^{5/2} }[/tex]

[tex]\frac{dI}{dh} = 0[/tex]

gives

that is

h = √50 = 7.07

now

[tex]\frac{d^{2I} }{dh^{2} } = k \frac{( 6h^{3} - 900h }{( h^{2} +100)^{7/2} }[/tex]

for h = 7.07

[tex]\frac{d^{2}I }{dh^{2} } = - 10267.6[/tex]

then by second derivative test,I has a maximum ath=7.07

Hence the light must be at a height of 7.07m from the floor for the maximum illumination at P.

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Answer:

26%

Step-by-step explanation:

Number of seats by 6th graders / Number of seats in total × 100% = Percentage of seats by 6th graders

442/1700 × 100% = 26%

Hope this helps! ^^

Answer:

5:45

...................................

Answer:

the time is 5:45 PM according to that watch

Peyton needs to buy at least 45 sets for the restaurant to have enough forks.

Let the number of sets of forks be represented by 'x'. according to the question there are 10 forks in each set.

Since there are currently 287 forks available in the restaurant, and the restaurant needs at least 732 forks.

The inequality used to represent the given scenario is given by:

10x + 287 ≥ 732

10x ≥ 445

x ≥ 44.5

As Peyton cannot buy 44.5 sets of forks so we round it off to 45.

Therefore, he requires 45 sets in total.

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Answer:

0

Step-by-step explanation:

Answer:

0.02

Step-by-step explanation:

Answer:

Step-by-step explanation: i bet your ray r stands for g

Answer:  [tex]\text{y} = \frac{7}{3}\text{x}-\frac{2}{3}[/tex]

This is the same as writing y = (7/3)x - 2/3

=======================================================

Explanation:

The given equation is in y = mx+b form

m = -3/7 = slope

b = 4 = y intercept

Flip the fraction for the slope to get -7/3, and flip the sign from negative to positive to get 7/3

The original slope is -3/7 and the perpendicular slope is 7/3. These two slopes multiply to -1.

We want the perpendicular line to go through [tex](\text{x}_1,\text{y}_1) = (2,4)\\\\[/tex]

We'll use the point-slope form to get...

[tex]\text{y} - \text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y} - 4 = \frac{7}{3}(\text{x}-2)\\\\\text{y} - 4 = \frac{7}{3}\text{x}+\frac{7}{3}(-2)\\\\\text{y} - 4 = \frac{7}{3}\text{x}-\frac{14}{3}\\\\\text{y} = \frac{7}{3}\text{x}-\frac{14}{3}+ 4 \\\\\text{y} = \frac{7}{3}\text{x}-\frac{14}{3}+ \frac{12}{3} \\\\\text{y} = \frac{7}{3}\text{x}+\frac{-14+12}{3} \\\\\text{y} = \frac{7}{3}\text{x}-\frac{2}{3} \\\\[/tex]

This equation has a slope of 7/3 and y intercept of -2/3.

Answer:

[tex]\sqrt{17}[/tex]

Answer:

Question? where is a question...that is a statement

Answer: 14/15

Step-by-step explanation:

[tex]9x=10x-x[/tex]

Divide both parts of the equation by 9:

[tex]\displaystyle\\x=\frac{10x-x}{9}\\\\x=0,9333333...\\\\Hence,\\\\x=\frac{10*0,933333...-0,9333333...}{9} \\\\x=\frac{9,333333...-0,933333...}{9} \\\\x=\frac{8,4}{9} \\\\x=\frac{8,4*10}{9*10} \\\\ x=\frac{84}{90}\\\\x=\frac{14*6}{15*6} \\\\ x=\frac{14}{15}[/tex]

Answer: 0.75km

Step-by-step explanation:

Answer:

320

Step-by-step explanation:

Plug the 4 into x and go from left to right:

4 times 4 is 16 times 20 is 320