If the measure of FGH IS 64º and the measure of EGD is (4x+8), what is the value of x?
E
D
F
H

f(x) = 5x^2 + 25x + 30

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Explanation:

The roots, aka x intercepts, of this curve are x = -3 and x =  -2. This is where the graph crosses the x axis.

Since x = -3 is a root, this makes x+3 a factor of the quadratic. Similarly, x = -2 leads to x+2 as another factor. I'm using the zero product property.

So far we have found that the polynomial is (x+3)(x+2). This isn't the full factorization because if we plugged x = -1 into that expression, then we would get

y = (x+3)(x+2)

y = (-1+3)(-1+2)

y = (2)(1)

y = 2

But we want y = 10 instead. So we must multiply that factorization by 5 to jump from 2 to 10 (i.e. 5*2 = 10)

Therefore, the full factorization of this parabola is y = 5(x+3)(x+2)

Now let's expand everything out and simplify

y = 5(x+3)(x+2)

y = 5(x^2+2x+3x+6)

y = 5(x^2+5x+6)

y = 5x^2+5*5x+5*6

y = 5x^2 + 25x + 30

Choice C is the final answer

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To check this, we can plug in x = -3 and we should get 0

y = 5x^2 + 25x + 30

y = 5(-3)^2 + 25(-3) + 30

y = 5(9) + 25(-3) + 30

y = 45 - 75 + 30

y = -30 + 30

y = 0

This proves that x = -3 is a root of y = 5x^2 + 25x + 30

I'll let you check x = -2. You should also get y = 0 when plugging this x value in.

Plugging x = -1 should lead to y = 10 as the last bit of confirmation. I'll let you check this one as well.

This value is approximate.

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Work Shown:

First we need to find angle C

A+B+C = 180

46+73+C = 180

119+C = 180

C = 180 - 119

C = 61

This is not the final answer, so answer choice B is likely a trick/trap answer.

We'll use this angle value to help find side c. Use the law of sines

c/sin(C) = b/sin(B)

c/sin(61) = (32.3)/sin(73)

c = sin(61)*(32.3)/sin(73)

c = 29.5410185554849 which is approximate

c = 29.5 which points us to choice A as the final answer.

Answer:

x=6

Step-by-step explanation:

(0.6)(x-1.5)=2.7

(x-1.5)=4.5

x=6

Answer:

The value of y = -1 , if x is -5.

Step-by-step explanation:

y = |x| – 6

y = |-5| – 6

|-x| = x ---> this is the rule of absolute value, so let's apply this to our equation.

y = 5 – 6 -------------->  -5 becomes 5

y = -1

there are x boys and y girls at the camp.how many children are at the camp altogether?

(EXPRESS YOUR ANSWER IN TERMS OF X AND Y )

Answer;

no.of boys = x

no.of girls = y

total no.of children in camp = no.of boys + no.of girls

= x + y..........

Answer:

total children = x+y

Explanation:

The total numper of children at the camp would be the sum of the total number of boys and the total number of girls.

Answer:

[tex] P = 6E - 4M - O [/tex]

Step-by-step explanation:

[tex] E = \dfrac{O + 4M + P}{6} [/tex]

Multiply both sides by 6.

[tex] 6E = O + 4M + P [/tex]

Subtract O and 4M from both sides.

[tex] 6E - 4M - O = P [/tex]

Switch sides.

[tex] P = 6E - 4M - O [/tex]

Answer:

An octagon has eight interior angles.

Interior angle total sum = (n-2) x 180, where n = number of sides.

Since an octagon has 8 sides, we have:

6 x 180 / 8, which is 135.

The answer is 135.

Let me know if this helps!

Answer:

profit of 3.33%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve the system by substitution:

Find p:

Total profit or loss:

Profit percent:

Answer:

1533

Step-by-step explanation:

73x21= 1533

Answer:

73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73

=73x21=1533

Step-by-step explanation:

Answer:

556

Step-by-step explanation:

Surface area of the cuboid = 2*(lb+bh+lh)

Surface area = 2*(80+88+110)=556

Answer:

3/8

Step-by-step explanation:

first year's work is 1/6

second year's work is 1/8

third year's work is 1/12

combining all 3 gives us

1/6 + 1/8 + 1/12

which simplifies to 3/8

Answer:

9.4 cm^3

Step-by-step explanation:

This figure is a cylinder so the formula is V=πr^2h

r is the radius and h is the height

Here we can see the height is 3 and the radius is 1

V=π(1)^2(3)

V=π3

V=9.42 (assuming π is 3.14)

Rounded to the nearest tenth is 9.4

Answer:

9.4 cm^3

Step-by-step explanation:

This figure is a cylinder so the formula is V=πr^2h

r is the radius and h is the height

Here we can see the height is 3 and the radius is 1

V=π(1)^2(3)

V=π3

V=9.42 (assuming π is 3.14)

Rounded to the nearest tenth is 9.4

Answer:

Prime factorization: 797 is prime. The exponent of prime number 797 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 797 has exactly 2 factors

The answer is : [tex]\left(m+n^2\right)\left(m-n^2\right)[/tex]

Here are the steps below to help you! ^^

Answer:

35⁰

Step-by-step explanation:

180-90-55=35⁰

there is a right angle

The angle sum property of a triangle:

The total measure of the three angles of a triangle is 180°

[tex]\rm\large\rightarrow \: \: x \: + \: 55 \degree \: + \: 90 \degree \: = \: 180 \degree[/tex]

[tex]\rm\large\rightarrow \: \: x \: + \: 145 \degree \: = \: 180 \degree[/tex]

[tex]\rm\large\rightarrow \: \: x \: = \: 180 \degree \: - \: \: 145 \degree [/tex]

[tex]\rm\large\rightarrow \: \: x \: = \: 35 \degree[/tex]

Answer:772

Step-by-step explanation:

5404/7 = 772

Answer:

772 buttons

Step-by-step explanation:

as is stated 5404 buttons are produced in a week

a week contains 7 days, so in order to find out how many buttons are produced in a day we have to divide 5404/7

this gives us 772

meaning, 772 buttons are produced in a day

hope this helped :)

Answer:

No

Step-by-step explanation:

It can still be 8x - 2

first of all you collect like terms

5x + 3x - 2

= 8x -2

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

[tex]\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right][/tex]

Now constructing equations

[tex]\\ \sf\longmapsto 3a+b=3\dots(1)[/tex]

[tex]\\ \sf\longmapsto a-b=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 3c-d=6\dots(3)[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1\dots(4)[/tex]

Adding eq(1) and (2)

[tex]\\ \sf\longmapsto 4a=8[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto a=2[/tex]

Put the value in eq(2)

[tex]\\ \sf\longmapsto a-b=5[/tex]

[tex]\\ \sf\longmapsto b=a-5[/tex]

[tex]\\ \sf\longmapsto b=2-5[/tex]

[tex]\\ \bf\longmapsto b=-3[/tex]

put the values in eq(4)

[tex]\\ \sf\longmapsto a+b+d=2d-1[/tex]

[tex]\\ \sf\longmapsto 2+(-3)+d=2d-1[/tex]

[tex]\\ \sf\longmapsto d-1=2d-1[/tex]

[tex]\\ \sf\longmapsto d-2d=-1+1[/tex]

[tex]\\ \sf\longmapsto -d=0[/tex]

[tex]\\ \bf\longmapsto d=0[/tex]

Put the value in eq(3)

[tex]\\ \sf\longmapsto 3c-d=6[/tex]

[tex]\\ \sf\longmapsto 3c-0=6[/tex]

[tex]\\ \sf\longmapsto 3c=6+0[/tex]

[tex]\\ \sf\longmapsto 3c=6[/tex]

[tex]\\ \sf\longmapsto c=\dfrac{6}{3}[/tex]

[tex]\\ \sf\longmapsto c=2[/tex]

Answer:

(4;-1)

Step-by-step explanation:

Answer:

Area: 2 x 10=20

perimeter: 2(2+10)=24

Step-by-step explanation:

Hopefully this helps

Answer:

P = 24

A = 20

Step-by-step explanation:

The perimeter is calculated by multiplying the sum of width + length by 2

P = 2*(10+2)

P = 24 yd

the area is calculated by multiplying width and length

A = 10*2

A = 20

Answer:

Below

Step-by-step explanation:

First we can find the volume of the box

v = lwh

v = (20)(16)(16)

v = 5120 in^3

Find the volume of the cylinder using this formula

   V = πr^2h

   V = π(5)^2(20)

   V = 1570.79633 (plug this into the final equation, not the rounded one in case it screws up the final value)

   V = 1570.8 in^3

Now we can find the volume of the shaded region by subtraction

5120 - 1570.7963= 3549.2037

Rounding to the nearest 10th and you get....

V = 3549.2

Hope this helps!

Answer:

I think it's 43 and 43 degrees. I just subtracted 180-94, got 86, and divided it so yea.

Answer:

-5/3

Step-by-step explanation:

5 ➗ -3

=> 5/-3

=> -5/3 or -1.66667

5 divided by -3=1.666666666666667

Answer:

y= -13x+77

Step-by-step explanation:

Parallel lines do not share any points but have the same slope.

First, put the equation y-5=-13(x+2) into slope-intercept form.

y= -13x-21

Slope= -13x

Y-Intercept= (0,-21)

Now that we know the slope...

y-(-1)=-13(x-6)

becomes

y+1=-13x+78

y-1=-13x+78-1

y=-13x+77

Answer:

See below.

Step-by-step explanation:

The top number is the product (multiplication) of the two side numbers. The bottom number is the sum (addition) of the two side numbers.

I'll do problem a as an example:

Answer:

Step-by-step explanation:

[tex]\displaystyle \Large \boldsymbol{} 5\cdot \sqrt{3:2\sqrt{3-\sqrt{2} } } =\\\\\\ 5\cdot \sqrt{\frac{3}{2\sqrt{3-\sqrt{2} } } \cdot \frac{2\sqrt{3+\sqrt{2} } }{2\sqrt{3+\sqrt{2} } } } = \\\\\\5\cdot \sqrt{\frac{6\sqrt{3+\sqrt{2} } }{4\cdot \sqrt{9-2} } } =5\sqrt{\frac{6\sqrt{3+\sqrt{2} } }{2\sqrt{7} } }[/tex]

But if the condition would be like this

[tex]\displaystyle \Large \boldsymbol{} 5\cdot \sqrt{3:2\sqrt{3-\boldsymbol2\sqrt{2} } } =\\\\\\5\cdot \sqrt{\frac{3}{2\cdot \sqrt{\underbrace{2+1-2\sqrt{2} \cdot \sqrt{1} }_{(\sqrt{2} -1)^2} } }} =\\\\\\5\cdot \sqrt{\frac{3}{2\cdot (\sqrt{2}-1) } } } = \\\\\\ 5\cdot \sqrt{\frac{3}{2(\sqrt{2}-1 )} \cdot \frac{\sqrt{2} +1}{\sqrt{2}+1 }} =5 \sqrt{\frac{3}{2(2-1)} } =\boxed{5\sqrt{1,5} }[/tex]

Step-by-step explanation:

Universal Set(U)={2,3,4...16}

M={2,4,6,8..16}[Even numbers between 2-16]

N={3,5,7...15}[Odd numbers between 2-16]

(PUM)'=U-(PUM)={2,3,4...16}-[{2,4,6,8..16}U{3,5,7...15}]={}

For shading, Shade the area outside the two circles but inside the square.

Answer:

g(x) has the larger slope.

Step-by-step explanation:

f(x) = 4x + 2

- so its slope = 4.      ( from general form y = mx + c where m = slope).

The slope of g(x) = (3 - (-2) / (1 - 0)

= 5.