Raul ordered 1 small photo enlargement and 4 medium photo enlargements for $29. Patricia ordered 5 small photo enlargements and 2 medium photo enlargments for $28

Answer:

Step-by-step explanation:

Roots:  set y = x^2 + 8x + 12 = 0 and solve for x:  x + 6 = 0, so x = -6 is one root.  The other is x = -2.  The corresponding points are (-6, 0) and (-2, 0).

y-intercept:  Let x = 0.  Then y = 12.  The y-intercept is (0, 12).

Axis of symmetry:  x = -b / (2a) => x = -8/(2*1) = -4:  x = -4

Vertex y-value:  evaluate y at x = - 4:  (-4)^2 + 8(-4) + 12 = -4:    (-4, -4)

Arbitrarily chosen x value:  x = 1 => 1^2 + 8(1) + 12 = 21:     (1, 21)

The five points are:  (-6, 0) and (-2, 0), (0, 12), (-4, -4), (1, 21).  The vertex is (-4, -4).  The parabolic graph opens UP.

The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = x² + 8x + 12

Conver the equation into a vertex form. Then we have

y = x² + 8x + 12

y = x² + 8x + 16 - 16 + 12

y = (x + 4)² - 4

The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).

The graph is given below.

More about the equation of the parabola link is given below.

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Answer:

2

Step-by-step explanation:

x + 1/x = 2

x + 1 = 2x

x = 1

x³ + 1/x³

1³ + 1/1³.

1 + 1/1 = 1 + 1 = 2

Answer:

B

Step-by-step explanation:

15² - 12² = 81

√81 = 9

Answer:

m = 18

Step-by-step explanation:

10/15 = m/12

Cross multiply using the butterfly method.

15m = 10*12

15m = 120

Divide both sides by 15.

m = 8

I personally like to use ratios but I am not sure if that's what you want. Anyway here's my answer

Answer: [tex]337.77\%[/tex]

Step-by-step explanation:

Given

For 70 year old, premium is 79.79 per month

For 80 year old it is 349.30 per month

Percentage increase in premium costs from age 70 to 80 is

[tex]\Rightarrow \%\ \text{increase}=\dfrac{349.30-79.79}{9.79}\times 100\\\\\Rightarrow \%\ \text{increase}=\dfrac{269.51}{79.79}\times 100\\\\\Rightarrow \%\ \text{increase}=337.77\%[/tex]

Answer:

1 picnic table : 9 benches

Step-by-step explanation:

You just simplify the equation down to its simplest form, so since they both have the gcf of 6, you divided both sides by 6, which results in the answer above.

Answer: I think it’s the first one

Step-by-step explanation:

It says per hour and 15 bucks plus 5 bucks PERhour so you would have to be multiplying I did a question like this long ago hope you get it right

The equation represents this linear relationship for total cost is y= 5x + 15​  thus option (D) is correct.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

She charges a flat fee of $15 plus $5 per hour.

For x number of hours, the total cost will be as,

y = 15 + 5x

Hence "y= 5x + 15 is the equation that depicts this linear relationship for total cost". ​

For more about the linear function,

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Answer:

y=2x+6

Hope I helped, have a nice day :)

Answer:

y=2x +6

Step-by-step explanation:

(18-12)

(6-3)

6/3 = 2

m=2

Answer:

0.1

Step-by-step explanation:

According to my calculator lol

Answer:

1/10

Step-by-step explanation:

1/5 / 2/1

1*1/5*2

=1/10

Answer:

1) glazed = 48 people

Chocolate = 72 people

Jelly = 24 people

Coconut = 16 people

2)9th grade = 219 students

10th grade = 167 students

11th grade = 147 students

12th grade = 151 students

Step-by-step explanation:

We are solving the examples;

1) We are told that there are 20 students in Kayla's first period class.

No. that preferred glazed donuts = 6

No. that preferred chocolate donuts = 9

No. that preferred jelly donut = 3

Number that preferred coconut donut = 2

Now,there are a total of 160 students in the entire grade. So to find the Number of students in this entire grade that will each prefer the types of donuts listed above, we will solve as;

For glazed donuts; 6/20 × 160 = 48 people

For chocolate donuts; 9/20 × 160 = 72 people

For jelly donut; 3/20 × 160 = 24 people

For coconut donut; 2/20 × 160 = 16 people

2) Total number of students is;

9th grade = 300 students

10th grade = 275 students

11th grade = 250 students

12th grade = 280 students

73% of 9th grade prefer valorant. Thus;

73% × 300 ≈ 219 students

61% of 10th grade prefer valorant. Thus;

61% × 275 ≈ 167 students

59% of 11th grade prefer valorant. Thus;

59% × 250 ≈ 147 students

54% of 12th grade prefer valorant. Thus;

54% × 280 ≈ 151 students

Answer:

D

Step-by-step explanation:

Using the sine ratio in the right triangle

sin51° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{y}[/tex] ( multiply both sides by y )

y × sin51° = 9 ( divide both sides by sin51° )

y = [tex]\frac{9}{sin51}[/tex] ≈ 11.6 ( to 1 dec. place ) → D

Answer: hello your question has some missing data below is the missing data

There have been 2 attempts on the northern route from Maine to Washington. Both of those riders made it 2,000 miles and quit in Montana. There have been 19 attempts on the central route from Virginia to California; 9 of those riders didn't make it out of Virginia and the other 10 made it all the way to the Pacific. There have been 32 attempts on the southern route from Florida to San Diego. One of those riders made it the whole way. Another realized he was out of shape, and quit before he even started. The other 30 riders quit somewhere in Texas. They were evenly distributed between 1 , 300 and 1 , 700 miles. For the northern route, the median distance covered will be the mean. For the central route, the median distance covered will be the mean. For the southern route, the median distance covered will likely be the mean

answer : Doug should choose the Central route

Step-by-step explanation:

Number of Available routes = 3

Northern route ; Total distance covered =  2000 miles

Central route : Total distance between Virginia and California = 2818.5 miles

percentage of success = 10 / 19 * 100 = 52.63 %

Mean distance covered = 2818.5 * 52.63% = 1483.38 miles

southern route  

Distance to be covered = 2,548 miles

number of attempts = 32

percentage of success = 1 = ( 1 / 32) * 100 = 3.12%

median distance covered by 30 riders = 1300 + ( 400 / 30 ) = 1313.33

Conclusion :

Doug should choose central route because it has the highest percentage of success and longest distance covered  ( i.e. closest to 3000 miles ) and it is also coast to coast

Answer:

-1.3+2 that is point A to find ir

Answer:

[tex]-186 \to -32 \to 6 \to 27 \to 28\ to 38 \to 56 \to 90 \to 115[/tex]

Step-by-step explanation:

Given

See attachment for A and B

Required

Arrange AB in ascending order

We have:

[tex]A = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right][/tex]

and

[tex]B = \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right][/tex]

So:

[tex]C = A * B[/tex]

[tex]C = \left[\begin{array}{ccc}1&7&-1\\5&-2&-9\\-3&8&3\end{array}\right] * \left[\begin{array}{ccc}5&1&7\\3&15&-2\\-1&-9&25\end{array}\right][/tex]

[tex]C = \left[\begin{array}{ccc}{27}&{115}&{-32}\\{28}&{56}&{-186}\\{6}&{90}&{38}\end{array}\right][/tex]

Where:

[tex]C_{1,1} =1*5 + 7*3 + (-1) * (-1)[/tex]

[tex]C_{1,2} =1*1 + 7*15 + (-1)*(-9)}[/tex]

[tex]C_{1,3} = 1*7 + 7*(-2) + (-1)*25}[/tex]

[tex]C_{2,1} = 5*5 + (-2)*3 + (-9) * (-1)}[/tex]

[tex]C_{2,2} = 5*1 + (-2)*15 + (-9)*(-9)}[/tex]

[tex]C_{2,3} = 5*7 + (-2)*(-2) + (-9)*25}[/tex]

[tex]C_{3,1} =(-3)*5 + 8*3 + 3 * (-1)[/tex]

[tex]C_{3,2} = (-3)*1 + 8*15 + 3*(-9)[/tex]

[tex]C_{3,3} = (-3)*7 + 8*(-2) + 3*25[/tex]

In increasing order, we have:

[tex]-186 \to -32 \to 6 \to 27 \to 28\ to 38 \to 56 \to 90 \to 115[/tex]

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

Work Shown:

L = theta*r

12 = theta*4

12/4 = theta

3 = theta

theta = 3 radians, choice C is the answer.

--------

Side note: The formula L = theta*r only works if theta is in radians.

If theta is in degrees, then use L = (theta/360)*2pi*r. So you can see that radian mode is much easier in this case.

Answer:

-8

Step-by-step explanation:

Answer:

x = -8

Step-by-step explanation:

[tex]\frac{3}{4}x+10=4[/tex]

[tex]\frac{3}{4} x-10[/tex] [tex]-10[/tex]        Subtract 10 from both sides

[tex]\frac{3}{4}x=[/tex]       [tex]-6[/tex]        

[tex]\frac{3}{4}(-8)[/tex]  [tex]=-6[/tex]        Substitute x for [tex](-8)[/tex] then Multiply [tex](-8)[/tex] by [tex]\frac{3}{4}[/tex]

[tex]-\frac{24}{4}[/tex]     [tex]=-6[/tex]        Simplify [tex]-\frac{24}{4}[/tex]

     [tex]-6=-6[/tex]      

Answer:

8.7

Step-by-step explanation:

Answer:

A and F

Step-by-step explanation:

Given

Intersecting lines

Required

The vertical and congruent angles

The two vertical lines are not parallel. So, we cannot conclude any relationship between angles A, B, E, F and angles C, D, H, G

Comparing angles A, B, E and F; we have:

[tex]\angle A = \angle F[/tex] --- Vertical opposite angles

[tex]\angle B = \angle E[/tex] --- Vertical opposite angles

From the given options,

[tex]\angle A = \angle F[/tex] is true

Answer:

8/pi or approximately 2.55 ft

Step-by-step explanation:

The formula for the circumference is

C = 2 * pi *r

16 = 2 * pi *r

Divide each side by 2 pi

16 / ( 2 pi) = 2 * pi * r/ ( 2 pi)

8 / pi = r

Using 3.14 for pi

8 / 3.14 = r

2.54777 = r

2.55 =r

Answer:

Radius ≈ 2.55 ft.

Step-by-step explanation:

GIVEN :-

TO FIND :-

FORMULAE TO KNOW BEFORE SOLVING :-

For a circle with radius 'r' & circumference 'c' ,

[tex]r = \frac{c}{2\pi }[/tex]

SOLUTION :-

[tex]Radius = \frac{Circumference}{2\pi } = \frac{16}{2\pi } = \frac{8}{\pi } = 2.55 ft. (appx)[/tex]

Answer:

-7

Step-by-step explanation:

f(x)=4x+5

Let x =-3

f(-3)=4*-3+5

Multiply

f(-3)=-12+5

Add

f(-3) = -7

Answer:

english!? sorry

Step-by-step explanation:

Răspuns:

150 m

Explicație pas cu pas:

Reamintim:

Perimetrul unui dreptunghi, P

P = 2 (lungime + lățime)

P = 400

Lățime = x

Lungime = 3x

Astfel, avem:

400 = 2 (3x + x)

400 = 2 (4x)

400 = 8x

Împărțiți ambele părți la 8

50 = x

Lungime = 3x

Lungime = 3 * 50

Lungime = 150 m

Answer:

B

Step-by-step explanation:

The shape is maintained exactly, it is rotated, not reflected and we can see it became smaller, so dilate it by a value less than one, but greater than 0. (2/3)

Answer:

x = 50

Step-by-step explanation:

<c = <e so:

5y - 4 = 76

5y = 80

y = 16

<c = 76

All triangle interior angles add up to 180 so:

x + 8 + 46 + 76 = 180

x + 130 = 180

x = 50

Answer:

50, 5

Step-by-step explanation:

X=number 1

x-45=number 2

x+(x-45)=55

2x=100

x=50 number 1

x-45 is number 2

50-45=5 number 2

Answer:

90.8

Step-by-step explanation:

20/13 = x/59

13x = 1180

x=90.76

x=90.8

9514 1404 393

Answer:

  25°

Step-by-step explanation:

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(?) = 25/60

  ? = arcsin(25/60) ≈ 24.62°

The indicated angle is about 25°.