Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Rewrite the following equation in the form y = a(x - h)2 + k. Then, determine the x-coordinate of the minimum.

y = 2x2 - 32x + 56

The rewritten equation is y =
(x -
)2 +
.

The x-coordinate of the minimum is
.

Answer:

Your answer is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

The way it is written is a bit ambiguous. If you mean

(1/6)*x = 2 then your answer is correct. Multiply both left and right by 6

6*(1/6)*x = 6*2

x = 12

If however, the question meant

1/(6x) = 2 then that is a different question.

Multiply both sides by 6x

1/(6x) * 6x = 2 * 6x

1 = 12*x                      

Divide by 12

x = 1/12

Change to a decimal

x = 0.08333333

Everything depends on how it is written. Try both if you can.

Answer:

D. X=1.75

Step-by-step explanation:

To start, let’s divide both sides by 4.

So 3^x =27.48/4

Since we want to solve for x, we take the log_3 of both sides.

So [tex]log_{3}3^x[/tex]=[tex]log_{3}6.87[/tex]

Using the laws of logs, we get

[tex]x*log_{3}3[/tex]=[tex]log_{3}6.87[/tex]

since [tex]log_{3}3[/tex] is 1, we get

X=[tex]log_{3}6.87[/tex]

Using a calculator, we find that x is about 1.75

Answer:

J

Step-by-step explanation:

The amount he is spending PER DAY is always a variable multiplied by its rate. That will be 8d.

Then you have a MAXIMUM amount of 3,000. That means the amount has to be less than or even equal to 3,000 but no more.

So 8d ≤ 3000 would be the answer

I believe the answer would be J. whenever the open part of the sign is towards a number or value, that means it is greater than the other number on the other side. For example 5 is less than 6 so 5 < 6. whenever the sign in between and has a line underneath it, it means it can also be equal to the number. therefore d is the amount per day and you pay that much for 8 days, so you get 8d. Now we know you can spend $3000, but no more. so you would use this sign < with a line drawn underneath it. now you would have 8d <(with a line underneath) 3000. this means that I'd must be equal to $3000 or less than $3000.

its kind of a difficult concept to learn but once you get it, it is very simple.

The game fair is no, the game is not fair for everybody. Adam has the best advantage.

We have given that,

You and two friends (Adam and Alana) will only play a game if it is fair for all three of you.

Fair game definition, a legitimate or likely object of attack, mockery, etc. With his fat, round face, the politician was fair game for the cartoonists.

The game your friend has proposed is to roll two number cubes (numbered 1-6) and find the sum.

If the sum is from 1-4 you get the point, 5-8 Adam gets the point, and 9-12 Alana gets the point.

You can't get a sum of 1. And there are the most amount of sums of 5-8.

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it's 7

you add them all up and get 96, then divide and get 16

add them up again, finding the difference from 16 and divide by 6 and you get 7

Volume for a triangular prism: = 1/4 of height. base side A^4 + 2(base side A  base side B{ab})^2 + 2(base side A  base side c{ac}) - b^4 + 2 (base side B and base side C {bc])^2 - c^4

Basically, for 2(ab) you do a times b (base1 * base2) and then double it.

Please correct me if i'm wrong.

-Phwee

Answer:

120

Step-by-step explanation:

Answer:

108

Step-by-step explanation:

2 4 or 6 must be at the end. That will make sure the number is even. The other 2 digits can be any one of the 6.

6 * 6 * 3

108

28+8=8+10+p

36=18+p

Subtract 18 on the left and right hand side

36-18=18-18+p

p=18

ANSWER

[tex]x =1 +\frac{1}{2} \sqrt{ 10} \: or \: x =1 - \frac{1}{2}\: \sqrt{10}[/tex]

EXPLANATION

The given quadratic equation is

[tex]2 {x}^{2} - 4x - 3 = 0[/tex]

This function is of the form:

[tex] a{x}^{2} + bx + c = 0[/tex]

This implies that:

a=2, b=-4 and c=-3.

We can solve this equation using the quadratic formula:

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

We substitute the values into the quadratic formula to obtain;

[tex]x = \frac{ - - 4 \pm \: \sqrt{ {( - 4)}^{2} - 4(2)( - 3)} }{2(2)} [/tex]

[tex]x = \frac{4 \pm \: \sqrt{ 40} }{4} [/tex]

[tex]x = \frac{4 \pm \: 2\sqrt{ 10} }{4}[/tex]

[tex]x =1\pm \: \frac{1}{2} \sqrt{10}[/tex]

[tex]x =1 +\frac{1}{2} \sqrt{ 10} \: or \: x =1 - \: \frac{1}{2} \sqrt{10}[/tex]

ANSWER

The area of the triangle is 6.64 square feet.

EXPLANATION

The area of the given triangle is calculated using the formula

[tex]Area = \frac{1}{2} ab \sin(C)[/tex]

where C=62° is the included angle.

a=4.7 ft and b=3.2 ft.

We plug in the values into the formula to get:

[tex]Area = \frac{1}{2} \times 4.7 \times 3.2\sin(62 \degree)[/tex]

Area=6.64 ft² to the nearest hundredth.

You would need to subtract 37 from 125 to find the answer.

125-37=88

Answer:

[tex]\$164.62[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

case A) compounded monthly

in this problem we have  

[tex]t=25\ years\\ P=\$5,000\\ r=0.06\\n=12[/tex]  

substitute in the formula above  

[tex]A=\$5,000(1+\frac{0.06}{12})^{12*25}=\$22,324.85[/tex]  

case B) compounded quarterly

in this problem we have  

[tex]t=25\ years\\ P=\$5,000\\ r=0.06\\n=4[/tex]  

substitute in the formula above  

[tex]A=\$5,000(1+\frac{0.06}{4})^{4*25}=\$22,160.23[/tex]  

Find the difference

[tex]\$22,324.85-\$22,160.23=\$164.62[/tex]

Answer:

$164.62

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given sinP = [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

Then the right triangle has a hypotenuse of 13 and a leg 5

Use Pythagoras' identity to find the other leg x ( adjacent)

x² + 5² = 13²

x² + 25 = 169 ( subtract 25 from both sides )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12 , hence

tanP = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{12}[/tex]

The value of the tanP when sin is equal to 5/13  is 5/12.

We have given that,

[tex]sinP = \frac{5}{13}[/tex]

[tex]sin(\theta)=\frac{Opposite}{hypogenous}[/tex]

Then the right triangle has a hypotenuse of 13 and a leg of 5

Use Pythagoras' identity to find the other leg x ( adjacent)

x² + 5² = 13²

x² + 25 = 169 ( subtract 25 from both sides )

x² = 144 ( take the square root of both sides )

taking square root on both sides

[tex]x=\sqrt{144} \\x=12[/tex]

Therefore we get the value of the tanP.

[tex]tanP = \frac{opposite }{adjucent} = \frac{5}{12}[/tex]

Therefore the value of the tanP is 5/12.

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Answer: A) 6/8

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

Explanation:

The tangent of angle A is the ratio of the opposite and adjacent sides. So you just form a fraction of the opposite side (6) and the adjacent side (8)

The opposite side is the leg furthest from the reference angle A. The adjacent side is the leg closest to the angle A. Normally you would reduce the fraction as much as possible, but your teacher has chosen not to do so in this case.

ANSWER

A. 6/8

EXPLANATION

The tangent ratio is the ratio of the opposite side of the right triangle over the adjacent side of the right triangle.

The side opposite to angle A is 6cm

The side adjacent to angle A is 8cm.

[tex] \tan(A) = \frac{6cm}{8cm} [/tex]

[tex]\tan(A) = \frac{6}{8} [/tex]

The first choice is correct.

Angles C and D are supplementary, meaning they add up to 180 degrees. So, if we add 8u-48 to 5u+46, we get 13u-2. We set that equal to 180, so 13u-2=180. Add the two, so 13u=182. Divide the 13, so u=14. To double check, plug in 14 to both expressions. 8(14)-48 and 5(14)+46. 8(14)-48 is 64. 5(14)+46 is 116. If you add 64+116, you get 180, which proves your answer right! So u= 14

add similar elements: 2.5x-x+3.8x+0.7x= 6x

divide both sides by 6

x=0.09

Answer:

x=0.09

Step-by-step explanation:

2.5x−x+3.8x+0.7x=0.54

(2.5 -1 +3.8+0.7)x =0.54

6x=0.54

x=0.54/6

x=0.09

Answer:

Step-by-step explanation:

when the two angles are added they are equal to 180 degree. (corresponding angles property)

x+8+3X+2=180

4X+10=180

4X=170

X=44.25 DEGREES

Question 1:

For this case we have that by definition, if a and b are two parallel lines, then the corresponding angles are congruent, that is, we can write 3x + 2 and x + 8 as supplementary angles:

[tex](3x + 2) + (x + 8) = 180\\3x + 2 + x + 8 = 180\\4x + 10 = 180\\4x = 180-10\\4x = 170\\x = \frac {170} {4}\\x = 42.5[/tex]

We look for the value of the angles:

[tex]3 (42.5) + 2 = 129.5\ degrees\\42.5 + 8 = 50.5 \ degrees[/tex]

ANswer:

[tex]x = 42.5\\3 (42.5) + 2 = 129.5\ degrees\\42.5 + 8 = 50.5 \ degrees[/tex]

Question 2:

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

Now, in the equation [tex]y = 2x + 3[/tex]

[tex]m = 2\\b = 3[/tex]

By definition, if two lines are parallel, their slopes are equal. Also, if two lines are perpendicular, then the product of their slopes is -1.

So:

The slope of a line parallel to the given line is:

[tex]m = 3[/tex]

The slope of a line perpendicular to the given line is:

[tex]3 * m = -1\\m = - \frac {1} {3}[/tex]

ANswer:

[tex]3\\- \frac {1} {3}[/tex]

Answer:

[tex](0.5,-4.5)[/tex]

Step-by-step explanation:

The given rectangle has diagonals have the endpoints P(-3, -2) ,I(4, -7) and A(4, -2) ,D(-3, -7)

The diagonals of the rectangle bisect each other so we use the midpoint formula to find their point of intersection.

The midpoint formula is;

[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

We use any pair of endpoints of the diagonals to find the point of intersection.

Using A(4, -2) ,D(-3, -7)

[tex](\frac{4+-3}{2},\frac{-2+-7}{2})[/tex]

[tex](\frac{1}{2},\frac{-9}{2})[/tex]

or

[tex](0.5,-4.5)[/tex]

Answer:  C) log₄ 84

Step-by-step explanation:

The rule for condensing (combining) log expressions that are added is MULTIPLICATION

log₄12 + log₄7 = log₄(12 × 7) = log₄ 84

Answer:

Step-by-step explanation:

10.99

Answer:

(-1,8)

Step-by-step explanation:

Look at the top point of the parabola type thing. I know that it's not a parabola, but IDRK how else to describe it. If you see the top point at one of the answers, it is most likely correct.

(-1,8) is most likely to be the relative maximum for this graph.

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Answer:

38

Step-by-step explanation:

because he bought a shirt for $30+he paid an additional sales tax that is 8

so 30+8=38

Answer:

$32.40

Step-by-step explanation:

$30.00 * 0.08 = $2.40

$30.00 + $2.40 = $32.40

i hope this helps !!

the answer is 12 since the sum of the two angles has to equal 180.

first you do

5x+5+115=180

combine like terms

5x+120=180

subtract 120

5x=60

then divide by 5

x=12

D. None, since -3a+3a is 0, leaving 6=7, which is not true.

Answer:

Beans Jing bought=17b

Step-by-step explanation:

You multiply 17 by the m=number of beans per bag, this makes the equation 17b.

Answer: 17 ÷ b = x

Step-by-step explanation:

Jing bought 17 bags, and there are b in each bag. So you should divide 17 by b and then 17 ÷ b = x.

The answer is the first one

(with blue and orange triangles)

Dilation makes things bigger

Answer:

2.5

Step-by-step explanation:

First find the length of RS

x2 = 4

x1 = - 1

y2 = 2

y1 = 2

RS^2 = (2 - 2)^2 + (4 - -1 ) ^2

RS^2 = 0 + 5^2

RS = sqrt(5^2)

RS = 5

That is the length of the diameter. The radius is 1/2 that

r = d/2

d = 5

r = 5/2

r = 2.5

The answer would be 2.5

Answer:

25.5°, 25.5°, 129° and 51°, 64.5°, 64.5°

Step-by-step explanation:

if you read the problem carefully you will notice that there are actually 2 ways of solving this problem. the first is by looking at the arc as if it is across from angle A, while the second is so the arc is across from side BC and bisected by point A (because the triangle is isosceles).

first way:

102/2=51°=m∠A

180-51=129°=m∠B+m∠C

129/2=m∠B=m∠C=64.5°

answers: 64.5°, 64.5°, 51°

second way:

102/2=51

51/2=m∠B=m∠C=25.5°

180-51=129°=m∠A

answers: 25.5°, 25.5°, 129°

Hope this helps!:)

The central angle BOC is twice the measure of arc BC, so it is 204°. Since the circle is 360°, the sum of the other two angles is 156°. Being an isosceles triangle, angles ABC and ACB are equal, thus each is 78°.

To find the measure of the angles of an isosceles triangle ABC inscribed in a circle, with the measure of arc BC being 102°, we utilize the properties of a circle and the fact that an isosceles triangle has two equal angles. In a circle, the angle subtended by an arc at the center is twice the angle subtended on the circumference. Thus, if the measure of arc BC is 102°, the central angle BOC would be 204° (since it's twice the angle at the circumference).

This central angle separates the circle into two segments, one of which is the base of the isosceles triangle. The other two angles of the triangle, angles A and ABC or ACB (since it's an isosceles triangle, these angles are equal), will each occupy the remaining portion of the circle that amounts to 360° - 204° = 156°. Since the angles at B and C are equal in an isosceles triangle, we divide the remaining 156° by 2 to find each angle. Therefore, angle A = 204°, and each of the other two angles is 78°.

Answer:

PQ

Step-by-step explanation:

TANGENT ALWAYS TOUCH TO THE CIRCUMFERENCE OF CIRCLE

Answer:

distance = (22/2) - (5/2) = 8.5 mm

Hope this helps chu

Have a great day

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The difference between the circumferences is 53.4 millimeters.

Remember that for a circle of diameter D, the circumference is:

C = pi*D

where pi = 3.14159...

We know that the outer diameter of the coin is 22mm, then the outer circumference is:

C = 3.14*22mm = 69.1mm

The inner diameter is 5mm, then the inner circumference is:

C' = 3.14*5mm = 15.7mm

Then the difference is:

69.1mm -  15.7mm = 53.4mm

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