30 Points! Please answer each question or just answer one!

the 2 equations given are vertical angles which mean they would equal the same.

Set the two equations to equal each other to solve for x:

6(x-2) = 3x+30

Simplify the left side:

6x-12 = 3x+30

Add 12 to eac side:

6x = 3x+42

Subtract 3x from each side"

3x = 42

Divide both sides by 3:

X = 42/3

X = 14

Now you know X, replace x with 14 in the equation for DHG:

DHG = 6(x-2)

6(14-2)

Simplify:

6(12)

Multiply:

72

Angle DHG is 72 degrees.

x ≠ - 4, 3

the denominator of the fraction cannot equal zero as this would make the fraction undefined. Equating the denominator to zero and solving gives the values that x cannot be

solve x² + x - 12 = 0

(x + 4)(x - 3) = 0

equate each factor to zero abd solve for x

x + 4 = 0 ⇒ x = - 4

x - 3 = 0 ⇒ x = 3

restrictions on x are : x ≠ - 4, 3

Answer:

a = 12 units

Step-by-step explanation:

Equation given is [tex]a^2 + 16^2 = 20^2[/tex]

First we have to evaluate the powers.

[tex]16^{2}[/tex] = [tex]16*16[/tex]=[tex]256[/tex]

[tex]20^{2}[/tex] = [tex]20*20[/tex]=[tex]400[/tex]

So we can now write the equation again as:

[tex]a^2 +256  =400[/tex]

Now we have to undo the addition,

[tex]a^2=400-256 [/tex]

[tex]a^2=144 [/tex]

Now we have to find the square root of [tex]a^2[/tex] to get the value of [tex]a[/tex]

[tex]\sqrt{a^{2}} = \sqrt{144}[/tex]

[tex]a=12[/tex]  or [tex]a=-12[/tex]

But the length of a leg cannot be a negative value, so we can take the +12.

a = 12 units

Answer:

a = 12 units

Step-by-step explanation:

54 nickels and 27 dimes

1 dime = 10 cents = $0.1

1 nickel = 5 cents = $0.05

setting up 2 equations

let n = amount of nickels and d = amount of dimes, then

n + d = 81 → (1)

0.05n + 0.1d = 5.4 → (2)

multiply (2 ) by 10

0.5n + d = 54 → (3)

subtract (3) from (1) to eliminate d

0.5n = 27 ( divide both sides by 0.5 )

n = [tex]\frac{27}{0.5}[/tex] = 54

substitute n = 54 in (1)

54 + d = 81 ( subtract 54 from both sides )

d = 27

Mary has 54 nickels and 27 dimes

If you were to think of this diagram as a map of intersecting roads, corresponding angles are the ones on the same corner:

NW corner: ∠1 and ∠3

NE corner: ∠5 and ∠7

SE corner: ∠6 and ∠8

SW corner: ∠2 and ∠4

The choices in bold font above are the only pairs of corresponding angles that are in your answer list:

Answer:

∠1 and ∠3  , ∠6 and ∠8  , ∠5 and ∠7  are corresponding angles

Step-by-step explanation:

Corresponding Angles are angles which occupy same relative position at intersection when a line intersects two lines.

In pair of corresponding angles, one angle is interior angle and other one is exterior angle.

Option 1:

∠1 is exterior angle and ∠3  is interior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 2:

∠6 is interior angle and ∠8  is exterior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 3:

∠2 and ∠8  both are exterior angle.

Thus they are not Corresponding angles.

Option 4:

∠5 is interior angle and ∠7 is exterior angle. Also Both are at relatively same position.

Thus they are Corresponding angles.

Option 5:

∠2 and ∠7 both are exterior angles.

Thus they are not corresponding angles.

Option 6:

∠3 and ∠6 both are interior angles.

Thus they are not corresponding angles.

4.  Supplementary angles together make a straight line (two right angles).  So BOE is supplementary to BOC

Answer: ∠BOE

5. Distance and midpoint between (4,-2), (6,8)

[tex]d = \sqrt{ (6-4)^2 + (8 - -2)^2} = \sqrt{2^2+10^2}=\sqrt{104}=2 \sqrt{26}[/tex]

midpoint

[tex]\left(\dfrac{4 + 6}{2}, \dfrac{-2 + 8}{2} \right) = (5, 3)[/tex]

Answer: distance 2√26, midpoint  (5, 3)

6.That's a rectangle oriented parallel to the axes, width parallel to the x axis of 7 - -3 = 10 and length along y of  1 - - 4 = 5, so an area of 10(5)=50

Answer: 50

b = - 252 and c = - 1126

the equation of a parabola in vertex form is

y a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

y = - 14(x + 9)² + 8 ← equation in vertex form

expand and compare coefficients

y = - 14(x² + 18x + 81 ) + 8 = - 14x² - 252x - 1134 + 8

compare to y = - 14x² + bx + c

b = - 252 and c = - 1126

First to answer this take note of how much he spends and how much it cost,

456 is the total cost and it is 3 a gallon

To figure how many gallons he got divide 456 by 3

456/3=152

This is a cubic form. I am assuming this should be factored.

With cubics like this it's worthwhile trying to find one root by simply guessing. My guess that worked out is x=-2

To verify:

3(-2)^3+7(-2)^2+(-2)-2 = 0   -> so -2 is a root and we get the first factor: (x+2)

Next we divide the cubic by the factor (x+2). I let you do the division. Here is the result

(3x^3 +7x^2 +x -2):(x+2) = (3 x^2 + x - 1)

(3 x^2 + x - 1) is a quadratic form and you can use the quadratic formula to get the two other roots. I got  [tex]\frac{-1\pm \sqrt{13}}{6}[/tex].

So the entire cubic is now factored as follows:

[tex](x+2) \cdot (x+ \frac{-1+ \sqrt{13}}{6}) \cdot (x+ \frac{-1- \sqrt{13}}{6})[/tex]

Answer: Option C) Raj forgot the negative when substituting -15+9x for y.

Solution:

(1) 9x-y=15

(2) 2x+8y=28

Isolating y in the first equation. Subtracting 9x both sides of the equation:

(1) 9x-y-9x=15-9x

Subtracting:

(1) -y=15-9x

Multiplying both sides of the equation by -1:

(1) (-1)(-y)=(-1)(15-9x)

(1) y=-15+9x

Then Raj found the value of y. It's not option D.

Substitutng y by -15+9x in the second equation:

(2) 2x+8(-15+9x)=28

Then option C) is the answer: Raj forgot the negative when substituting -15+9x for y.

Eliminating the parentheses applying the distributive property in the multiplication:

(2) 2x-120+72x=28

Adding similar terms:

(2) 74x-120=28

Solving for x. Adding 120 both sides of the equation:

(2) 74x-120+120=28+120

Adding:

(2) 74x=148

Dividing both sides of the equation by 74:

(2) 74x/74=148/74

Dividing:

(2) x=2

Solving for y: Replacing x by 2 in the first equation:

(1) y=-15+9x

(1) y=-15+9(2)

Multiplying:

(1) y=-15+18

Subtracting:

(1) y=3  

Answer:

Marked-down price: $19.99

Step-by-step explanation:

The markdown amount is ...

$29.99×33 1/3% = $10.00 . . . . . 9.99667 rounded up

The marked-down price is the original price less the markdown:

$29.99 - 10.00 = $19.99

_____

You will recognize that 33 1/3% = 1/3, so that the calculation is ...

[tex]\text{markdown}\,=\dfrac{\$29.99}{3}=\$9.99\overline{6}\approx\$10.00[/tex]

Biconditionals are statements that work both ways.

Some examples:

If it rains, I go out, and if I go out, it must be raining.

This can be stated concisely in mathematical terms as

I go out IF AND ONLY IF it rains.

So looking at the given statements, only the last two work both ways, namely:

If the sun rises in the east, then it is morning, and if it is morning, the sun rises in the east.

Victoria will play outside if and only if the weather is nice.

Answer:

Step-by-step explanation:

f(x+h)-f(x) / h

f(x) = 2x^2-3x-4

Replace X with (x+h):

2(x+h)^2 - 3(x+h) -4

Simplify:

2x^2 + 4hx +2h^2 -3x -3h -4

Now you have:

(2x^2 + 4hx +2h^2 -3x -3h -4 - 2x^2-3x-4) / h

Simplify to get 4x +2h-3

The answer is C.

∠Y = 64°

since the triangles are similar

∠Y = ∠C

∠C = 180° - (73 + 43 )° = 64° = ∠Y

Alright, so let's make 2 3/5 into an improper fraction.

2 x 5 = 10 + 3 = 13

So 13/5 / 11/25.

Keep, change, flip rule: 13/5 x 25/11.

Now you multiple the numerator and denominator from both fractions. (I'm not going to do the math for you. Hope this helped and sorry if my explanation is...yeah.)

The division of 2 3/5 by 1 1/25 is equal to 2.5.

To perform the division, convert the mixed numbers to improper fractions. 2 3/5 becomes 13/5, and 1 1/25 is 26/25. Now divide the fractions: (13/5) ÷ (26/25) = 13/5 * 25/26 = 325/130 = 2.5.

to determine the nature of the solutions use the discriminant

Given a quadratic equation in standard form : ax² + bx + c = 0

then the discriminant is b² - 4ac

• If b² - 4ac > 0 , then there are 2 real and distinct solutions

• If b² - 4ac = 0, there are 2 real and equal roots

• If b² - 4ac < 0 , there are no real solutions

for x² - 3x + 8 = 0 with a = 1, b= - 3 and c = 8

b² - 4ac = (- 3)² - (4 × 1 × 8 ) = 9 - 32 = - 23

Hence there are no real solutions to the equation

            50*2= 100

               So 50 is one half of One hundred and if we use 100 divided by 2 to get 50 then we need to do 80 / 2 which will give us 40.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = 2x + 10 is in this form

To express in functional notation replace y by f(x), thus

f(x) = 2x + 10

Multiply each term in the parentheses by 10x.  (This is the Distributive Law).:-

10x*6x^2 +10x*7x + 10x*9

= 60x^3 + 70x^2 + 90x    

12600 x  to the power of 2 + 37887 x + 40829

Hello!

To find the equation of the line with a y-intercept of (0, -3) and a x-intercept of (-4.5, 0), we need to use the slope formula.

The slope formula is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

With that, we substitute the given ordered pairs into the formula, and solve.

[tex]\frac{0 - (-3)}{-4.5 - 0} = \frac{3}{-4.5} =\frac{3}{-\frac{9}{2} } = -\frac{2}{3}[/tex]

The slope of this line is -2/3 or -0.667 repeated (doesn't specify).

Therefore, the equation of the line is y = -2/3x - 3. (I also included the graph!) :-)

10 1/2 golf balls to get it

In this case we do not know for how long have they worked. But lets assume that they both will fix the car in an hour.

Case 1: Lets talk about Abe first.

Abe will charge $70.00 per hour plus a part which costs $130.00.

Now, the total cost to be paid to Abe to fix the car is [tex]70+130=200[/tex] dollars.

So we will have to pay $200.00 to Abe to fix the car.

Case 2: Lets talk about Gabe now,

Gabe can fix it for $80 an hour and finds the part just for $60.

Now, the total cost to be paid to Gabe to fix the car is [tex]80+40=120[/tex] dollars.

So we will have to pay $120.00 to Gabe.

Considering the two cases above we can ask Gabe to fix our car but there is another case.

Case 3: What if Abe finds a part for $60.00 rather $130.00

In that case, we will have to pay [tex]70+60=130[/tex] dollars in total to Abe.

Now, we need to pay $130.00 to Abe to fix the car.

Still we can see that we need to pay $10.00 less to Gabe so will ask Gabe to fix the car  (since [tex]130-120=10[/tex]).

Answer:

7 ft.

Step-by-step explanation:

1 ft./12 in. = x/84

Cross multiply:

1 × 84 = 84

x · 12 = 12x

12x = 84

12x/12 = 84/12

12x/12 = x

84/12 = 7

Ans. x = 7

Hope this helps! :)

There are 7 feet in 84 inches.

Given that we need to determine that how many feet in 84 inches.

To convert inches to feet, you need to divide the number of inches by the number of inches in a foot.

There are 12 inches in a foot.

Given that you have 84 inches, you can divide this value by 12 to find the equivalent in feet:

84 inches ÷ 12 inches/foot = 7 feet

So, 84 inches is equal to 7 feet.

Hence there are 7 feet in 84 inches.

Learn more about unit conversion click

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Answer:

B. y = 2x + 29

Step-by-step explanation:

The given graph has a slope of 2 (a rise of 10 for a run of 5), so the last two chioices are not viable. Clearly a parallel line through the given point will have a positve y-intercept, so the first choice is not viable.

The appropriate choice is the second one:

... B. y = 2x + 29

Hence the line parallel to this is  y = 2x + 29.

Hence, option B is correct.

A straight group of points that stretch in opposing directions is what is known as a line. It is endless in both directions and lacks any ends. It is not thick. It only has one dimension.

In the given graph,

The line is passing through (0, 15) and (10, 35).

Therefore the slope of this lien is,

m  = (35-15)/(10-0)

    = 2

Now the parallel line to this line will have same slope.

Which passes through (3, 35),

Hence the line be ,

y - 35 = 2(x - 3)

y - 35 = 2x - 6

       y = 2x + 29

Hence the line is  y = 2x + 29.

Learn more about the equation of line visit:

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[tex]f^{-1}[/tex](x) = [tex]\frac{2x}{x-3}[/tex]

let y = f(x), then rearrange making x the subject

y = [tex]\frac{3x}{x-2}[/tex] ( multiply both sides by (x - 2 ))

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

xy - 2y = 3x ( subtract 3x and add 2y to both sides )

xy - 3x = 2y (factor out x on left side )

x(y - 3 ) = 2y ( divide both sides by (y - 3) )

x = [tex]\frac{2y}{y-3}[/tex]

change y to x for inverse function

[tex]f^{-1}[/tex](x) = [tex]\frac{2x}{x-3}[/tex]

Answer:

C. (12, 0)

Step-by-step explanation:

Try the choices:

A. 10 > -3 -7·10 . . . true

B. 10 > 0 -7·7 . . . . true

C. 10 > 12 -7·0 . . . false . . . this is your answer

D. 10 > 2 -7·10 . . . true

The option that is not a solution of the inequality 10 > x - 7y is C. (12, 0), as substituting these values into the inequality gives 10 > 12, which is false.

To find out which option is not a solution of the inequality 10 > x
- 7y, we need to substitute the values of x and y from each given pair into the inequality and check if it holds true.

The only option that does not satisfy the inequality is C. (12, 0), because 10 is not greater than 12.

Answer:

adults = 40

children = 68

Step-by-step explanation:

Let the children=c

Let the adults = a

Equations

a + c = 108                 (1)

3.75a + 1.5c = 252    (2)

Multiply (1) by 1.5

1.5a + 1.5c = 162        (3)

Subtract (3) from (2)

3.75a + 1.5c = 252

1.5   a + 1.5c = 162    Subtract

2.25a             = 90   Divide by 2.25

a = 90/2.25

a = 40

Find the number of children

a + c = 108

40 + c = 108

c = 108 - 40

c = 68

Check

LHS

3.75 * 40 + 1.50 * 68

150 + 102

252 Which checks with the right hand side.

The odds in favor of picking a white marble from a bag with 4 green and 5 white marbles are 5 to 4.

This is calculated by comparing the number of white marbles to the number of green marbles.

To determine the odds in favor of picking a white marble from a bag containing 4 green marbles and 5 white marbles, we need to calculate the ratio of the number of successful outcomes (picking a white marble) to the number of unsuccessful outcomes (not picking a white marble).

In this case, the successful outcomes are the 5 white marbles, and the unsuccessful outcomes are the non-white marbles, i.e., the 4 green marbles.

The odds in favor are therefore 5 to 4, or simply, 5:4.

Here's how to calculate odds using a probability example:

So, the odds in favor of picking a white marble are 5 to 4.

your answer would be 9h