Find mZHFG if mZEFG = 2x + 52, mZEFH = 21°, and mZHFG = 1 + 31

Given:

The function is:

[tex]f(x)=2x^2-14x+10[/tex]

The function g(x), the image of f(x) after a [tex]r_{y=x}[/tex] (reflection over the line y=x).

To find:

The function g(x).

Solution:

We have,

[tex]f(x)=2x^2-14x+10[/tex]

Substitute [tex]f(x)=y[/tex] in the given function.

[tex]y=2x^2-14x+10[/tex]

The function g(x), the image of f(x) after a [tex]r_{y=x}[/tex] (reflection over the line y=x). So, interchange x and y.

[tex]x=2y^2-14y+10[/tex]

Now, we need to find the value of y.

[tex]x=2(y^2-7y+5)[/tex]

[tex]\dfrac{x}{2}=y^2-7y+5[/tex]             [Divide both sides by 2]

[tex]\dfrac{x}{2}-5=y^2-7y[/tex]             [Subtract 5 from both sides]

Add both sides half of square of coefficient of y, i.e. [tex](\dfrac{-7}{2})^2[/tex], to make it perfect square.

[tex]\dfrac{x}{2}-5+(\dfrac{-7}{2})^2=y^2-7y+(\dfrac{-7}{2})^2[/tex]

[tex]\dfrac{x}{2}-5+\dfrac{49}{4}=y^2-7y+(\dfrac{7}{2})^2[/tex]

[tex]\dfrac{x}{2}-5+\dfrac{49}{4}=\left(y-\dfrac{7}{2}\right)^2[/tex]          [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]

[tex]\dfrac{x}{2}+\dfrac{49-20}{4}=\left(y-\dfrac{7}{2}\right)^2[/tex]

Taking square root on both sides, we get

[tex]\pm\sqrt{\dfrac{x}{2}+\dfrac{29}{4}}=y-\dfrac{7}{2}[/tex]

[tex]\dfrac{7}{2}\pm\sqrt{\dfrac{2x+29}{4}}=y[/tex]

[tex]\dfrac{7}{2}\pm\dfrac{\sqrt{2x+29}}{2}=y[/tex]

[tex]\dfrac{7\pm \sqrt{2x+29}}{2}=y[/tex]

Substituting [tex]y=g(x)[/tex], we get

[tex]\dfrac{7\pm \sqrt{2x+29}}{2}=g(x)[/tex]

Therefore, the required function is [tex]g(x)=\dfrac{7\pm \sqrt{2x+29}}{2}[/tex].

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

=> Factor.

When an algebraic expression can be written as the product of two or more expressions, then each of these expressions is called a factor of the given expression.

[tex] \sf \: It's \: called \: a \: \boxed{\underline{\bf \: factor}}[/tex]

When an algebraic expression can be written as the product of two or more expressions, then each of these expressions is called a [tex]\boxed{\underline{\bf \: factor}}[/tex]of the given expression.

Answer:

y = |x - (-2)| -3

Step-by-step explanation:

Answer:

P(AUB)'=2/15

Step-by-step explanation:

According to the Question,

So, P(B)=1-P(B') ⇒ P(B)=1-(1/3) ⇔ P(B)=2/3

P(A∩B)=3/5 × 2/3 ⇒ P(A∩B)=2/5

Thus, P(AUB)= 3/5 + 2/3 - 2/5

P(AUB)=1/5 + 2/3

P(AUB)=(3+10)/15 ⇔P(AUB)=13/15

Answer:

y=-2/7x-2

Step-by-step explanation:

Just move the 2x to the other side, then divide both sides by 7.

Answer:

2 grams

Step-by-step explanation:

a = 145 * (1/2)⁶

a = 2.265625

Rounded

2 grams

Answer:

The choose (a)

2x+1

Step-by-step explanation:

f(g(x)) = 2(x-3)+7

=2x-6+7

=2x+1

Answer:

2x+1

Step-by-step explanation:

We know that g(x)= x-3

So f(g(x))= f(x-3)  

We put it in the equation :

f(x-3)= 2(x-3) +7 = 2x-6+7 = 2x +1

[tex]\longrightarrow{\blue{ C. \: 2 {x}^{2} + 4x - 30 = 0 }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \frac{6}{x} = \frac{2x + 4}{5} [/tex]

[tex] \: 6 \times 5 = x \: (2x + 4)[/tex]

➺ [tex] \: 30 = 2 {x}^{2} + 4x[/tex]

➺ [tex] \: 2 {x}^{2} + 4x - 30 = 0[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

Step-by-step explanation:

An algebraic expression with non.zero coefficients and variables having non-negative integers as exponents is called a polynomial.

Yes, It is a polynomial. The highest power of the variable is the degree of the polynomial.

So, Degree = 2

Answer:

yes

because the descent of the ball is 32m per second

Step-by-step explanation:

To determine if the relationship is proportional, determine the descent of the ball per second

after 2 seconds = 64 / 2 = 32

after3 seconds = 96/3 = 32

after 4 seconds = 128 / 4 = 32

the relationship is proportional

Answer: 340

Step-by-step explanation: It would follow the basic volume formula w*l*h so filling in the values gets us (10)*(17)*(2) and multiplying them out gets us 340.

Answer:

25%

Step-by-step explanation:

increase by = 150 - 120

=30

increase percent = 30/120 * 100%

=3000/120

=25 %

Answer:

25%

Step-by-step explanation:

Percentage increase=(new value-original value)/(original value) x 100%

Percentage increase=(150-120)/120 x 100%

Percentage increase=30/120 x 100%

Percentage increase=1/4 x 100%

Percentage increase=25%

Answer:

D

Step-by-step explanation:

Given

5 - [tex]\sqrt{c+5}[/tex] = 1 ( subtract 5 from both sides )

- [tex]\sqrt{c+5}[/tex] = - 4 ( multiply both sides by - 1 )

[tex]\sqrt{c+5}[/tex] = 4 ( square both sides )

c + 5 = 4² = 16 ( subtract 5 from both sides )

c = 11

The value of c is 11 when n = 5.To find the value of c in the equation [tex]n - \sqrt(c + 5) = 1[/tex] when n = 5, you can simply substitute n with 5 and then solve for c.

Given equation: [tex]n - \sqrt(c + 5) = 1[/tex]

Now, replace n with 5:

[tex]5 - \sqrt(c + 5) = 1[/tex]

Next, isolate the square root term by moving the constant term to the other side:

[tex]sqrt(c + 5) = 5 - 1\\sqrt(c + 5) = 4\\[/tex]

Now, square both sides of the equation to eliminate the square root:

[tex](c + 5) = 4^2\\c + 5 = 16[/tex]

Finally, isolate c:

c = 16 - 5

c = 11

So, the value of c is 11 when n = 5.

To know more about equation:

https://brainly.com/question/10724260

#SPJ2

Answer:

2 words

Step-by-step explanation:

Scalene (D)

Obtuse-angled (E)

Answer:

1/15

Step-by-step explanation:

Step 1 find probability of pulling 1 pink marble

Like stated previously probability = # of favorable outcomes / # of possible outcomes

The favorable outcomes is what we want to happen

We want to pull a pink marble and there are a total of 3 pink marbles

So # of favorable outcomes = 3

To find the # of possible outcomes we simply find the number of marbles. There are a total of ten marbles

So probability of pulling one pink marble = 3/10

Step 2 find the probability of pulling another pink marble ( IMPORTANT NOTE: It says to find the probability of pulling 2 pink marbles if the first one is NOT put back before the second pull. this meaning that we must subtract 1 from the total # of marbles and 1 from the total # of pink marbles )

3 - 1 = 2

10 - 1 = 9

So after the first pull there would be 2 pink marbles out of 9 total marbles

So the probability of pulling a pink marble on the second pull is 2/9

Finally we multiply the two probabilities together to find our answer

3/10 * 2/9 = 1/15

Responder:

4.400.000

Explicação passo a passo:

A quantidade total de ingressos vendidos = 7,9 milhões = 7.900.000

Desse total, o valor vendido ao espectador estrangeiro = 3,5 milhões, = 3,5 milhões

O valor dos ingressos vendidos ao espectador brasileiro será a diferença entre o valor total do ingresso vendido e o total vendido ao espectador estrangeiro.

7.900.000 - 3.500.000 = 4.400.000

Answer: the root of 145 so b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Use the Pythagorean theorem:

a^2 + b^2 = c^2

9^2 + 8^2 = c^2

81 + 64 = c^2

144 = c^2

[tex]\sqrt{144}[/tex] = c

Remember, C is always the hypotenuse, or the longest side. A and B can be either base.

Answer:

150 cm

Step-by-step explanation:

The information in the question includes;

The length of rope P = 3 × The length of rope Q

The length of rope P - 10 cm  = 4 × (The length of rope Q - 10 cm)

Let p represent the original length of rope P and let q represent the original length of rope Q, we have;

p = 3·q...(1)

p - 10 = 4·(q - 10)...(2)

Expanding equation (2) gives;

p - 10 = 4·q - 40

∴ p = 4·q - 40 + 10 = 4·q - 50

p = 4·q - 50...(3)

Equating the values of p in equation (1) and equation (3) gives;

p = 3·q, and p = 4·q - 50, therefore, by the substitution property of equality, we have;

3·q = 4·q - 50

50 = 4·q - 3·q = q

q = 50

p = 3·q

∴ p = 3 × 50 = 150

The original length of P before it was cut, p = 150 cm.

Answer:

You would do the change in y over the change in x.  

That means you subtract your y values and that's the numerator.  Subtract your x values and that is your denominator.  Then simplify.

(4 - 4)

______

(-2 - 2)

Step-by-step explanation:

Answer: y=4

Step-by-step explanation:

4 is the y-intercept. The slope is 0

Answer:

(10,-2) x=10 y=-2

Step-by-step explanation: I used substitution

Answer:

x = 4.17

Step-by-step explanation:

We can use a ratio to solve

4.2 k                  2 k

---------------- = ---------------

8.76                     x

Using cross products

4.2 * x = 2 * 8.76

4.2x =17.52

Divide by 4.2

x=4.17

Answer:

2kg cost £4.18

Step-by-step explanation:

4.2 kg of oranges cost £8.76

:. 1 kg of orange cost £8.76/4.2 = £2.09

2kg cost 2 × £2.09 = £4.18

Answer:

I think it's C. cause I multipled 16 by 7

Answer:

they might be since they could be like 16 and if it was raised they couldn't drive any more

Answer:

Yes, there is a high chance that this sample is biased since our pool of participants is not random.

Step-by-step explanation:

The population from which the talk show host drew is not representative of the entire country's population. Being a part of the live studio audience, these viewers are not considered a random sample and may be influenced by the opinions of the talk show due to response bias, specifically a desire to please bias.

Answer:

-4/5

Step-by-step explanation:

If you use the number line, after adding 3/5 you can see that it still doesn't make it positive but brings it up to -4/5 (Hope this helps)

Answer:

You subtract them:

3/5-7/5 (the plus disappears when faced with a minus)

-4/5

Answer:

36 degrees

Step-by-step explanation:

Angles on a line equal 180

180-117=63

a=63

Angles in a triangle equal 180

180-(63+81)=36

b=36 degrees

Answer:

a=117(being straight line angle)

a=180-117

a=63ans

a+b+81=180(being the sum of the angle of triangle)

b+63+81=180

b+144=180

b=180-144

b=36ans

Answer:

[tex](f/g)(4)=8[/tex]

Interpretation: 4 elephants traveled at a speed of 8 miles per hour

Step-by-step explanation:

Given

[tex]f(x) = 4x + 8[/tex]

[tex]g(x) = x -1[/tex]

Required

[tex](f/g)(4)[/tex]

This is calculated as:

[tex](f/g)(4)=\frac{f(4)}{g(4)}[/tex]

We have:

[tex]f(x) = 4x + 8[/tex]

[tex]f(4) = 4 * 4 + 8 =24[/tex]

[tex]g(x) = x -1[/tex]

[tex]g(4) = 4 - 1 = 3[/tex]

So:

[tex](f/g)(4)=\frac{f(4)}{g(4)}[/tex]

[tex](f/g)(4)=\frac{24}{3}[/tex]

[tex](f/g)(4)=8[/tex]

Answer:

Answer:C) 8; The elephants’ rate in miles per hour

Step-by-step explanation:

First write the question as an equation that can be solved to give you a numerical answer.

[f(4)=4(4)+8] / [g(4)=(4)-1]

Then solve the equation.

24/3=8

Finally use background information to give you the context.

Since the problem gives you the function for distance and the function for time then it can be concluded that the context will be the elephants’ rate in miles per hour

Step-by-step explanation:

Answer:

hlw its jess

your answer is here

Step-by-step explanation:

hope it may help you

Answer:

1.4, 1 1/8, 0.7

Step-by-step explanation:

1 1/8 is equal to 1.125 which it makes it less than 1.4 but more than 0.7.

Answer:

[tex]0.7, \frac{11}{8},1.4[/tex]

Step-by-step explanation:

In order to understand what numbers are greater and what numbers are smaller, we need to make them have the same common denominator. So firstly, we turn all of these numbers into fractions, and we get...

[tex]0.7 = \frac{7}{10}\\\\1.4 = \frac{14}{10}\\\\\frac{11}{8 }= \frac{11}{8 }[/tex]

Now we, need to find the least possible number divisible by 10 and 8, to find the least common denominator. And we get, that the least common denominator is 40, and knowing this, now we have to take each fraction and turn it into an equivalent fraction with the denominator of 40. So we do...

[tex]\frac{11}{8}= \frac{(11)(5)}{(8)(5)}= \frac{55}{40}\\\\\frac{7}{10} = \frac{(7)(4)}{(10)(4)} = \frac{28}{40} \\\\\frac{14}{10} = \frac{(14)(4)}{(10)(4)} = \frac{56}{40}[/tex]

Now we can put these fractions in order from least to greatest...

[tex]\frac{28}{40} < \frac{55}{40}<\frac{56}{40}[/tex]

Therefore, we know that...

[tex]0.7 < \frac{11}{8} < 1.4[/tex]

Answer:

what-

Step-by-step explanation: