Use a system of linear equations to find the quadratic function
f(x) = ax2 + bx + c
that satisfies the given conditions. Solve the system using matrices.
f(−2) = −5, f(1) = −8, f(2) = −25

Answer:

13.6 inches

Step-by-step explanation:

We can use Pythagorean theorem: [tex]c=\sqrt{a^{2} +b^{2} }[/tex]

Let c be the diagonal length, a for length, and b for width.

Substitute the values.

[tex]c=\sqrt{11^{2}+8^{2} }[/tex]

c=13.6 inches

Answer:

10.0

Step-by-step explanation:

see attached for reference.

given two points in the x-y axis (x₁, y₁) and (x₂, y₂)

the distance bettween them is given by

Distance, D = √ (    (x₂-x₁)²   + (y₂-y₁)²   )

In our case we are given points (9,10) and (-1,9)

substituting these into the formula , we get:

D = √ (    (9-10)²   + (-1-9)²   )

= √ (    (-1)²   + (-10)²   )

= √ (    1   + 100   )

=√101

= 10.04988

= 10.0 (rounded to nearest tenth)

Answer: 105

Step-by-step explanation: 35 divided by 7 = 5 , so one monkey eats 5 bananas. 21 x 5 = 105

Hope this helps!

Answer:

105 bannanas

Step-by-step explanation:

Because if 21 is 3 times more than 7 then you have to multiply 35 times 3 to get the amount of bannanas 3 times more monkeys can eat.

Have a great day!

Answer:

3.25

Step-by-step explanation:

thats how absolute value works

Answer:

A is correct

Step-by-step explanation:

Answer:

it's A -2/9

Step-by-step explanation:

it's A

it's A

Answer:

10 - x

Step-by-step explanation:

Answer:

x-10 or 10-x

Step-by-step explanation:

Answer:

934.2 in³

Step-by-step explanation:

The following data were obtained from the question:

Width (W) = 8.5 in

Length (L) = 11 in

Thickness (T) = 0.0037 in

Number of paper = 2700 sheets

Volume occupied by the 2700 sheets of paper =?

Next, we shall determine the volume of 1 sheet of paper. This can be obtained as follow:

Width (W) = 8.5 in

Length (L) = 11 in

Thickness (T) = 0.0037 in

Volume (V) =?

Volume = Length × Width × Thickness

Volume = 11 × 8.5 × 0.0037

Volume = 0.346 in³

Thus, the volume of 1 sheet of paper is 0.346 in³

Finally, we shall determine the volume occupied by the 2700 sheets of paper as follow:

Volume of 1 sheet of paper = 0.346 in³

Volume of 2700 sheets of paper =?

1 sheet of paper occupied 0.346 in³.

Therefore, 2700 sheets of paper will occupy = 0.346 × 2700 = 934.2 in³

Thus, the volume occupied by the 2700 sheets of paper is 934.2 in³.

Answer:

y = -2x

Step-by-step explanation:

First you can find the difference between the two points to find the slope.

0, 4

- 1, 2

-1, 2

Now divide: y/x = 2/-1 = -2

Slope = -2

Formula: y=mx+b

Plug in the points for the variables.

2 = -2(1) + b

2 = -2 + b

Subtract 2 from both sides to get 0 = b so this line is proportional.

Hope that helps and have a great day!

Answer: $8

Step-by-step explanation:

96/12=8/1

Answer: first one = 8

              second one = 25

Step-by-step explanation: 96 divided by 12 = 8

                                             125 divided by 25 = 25

Answer:

There is an initial charge of $35.00 for every mile traveled.

Step-by-step explanation:

From the question, the cost function s given as follows:

c = 0.4x + 35 .................... (1)

Where;

Total cost = c

Variable cost per mile = $0.40

Number of miles traveled = x

Total variable cost = 0.4x = 0.40 * x

Fixed cost = Initial cost = $35

From the above, the fixed cost or initial cost implies that no matter the number of miles a passenger takes, he is going to pay $35 in addition to the variable cost to pay.

From the question, for driving a distance of 100 miles we have:

Number of miles traveled = x = 100

Total variable cost = 0.40 * 100 = 40

Substituting the relevant value into equation (1), we have:

c = 40 + 35

c = 75

Since the total cost obtained above is $75.00, it therefore implies that the correct statement that justifies that the total cost for renting this car and driving a distance of 100 miles is $75.00 is "There is an initial charge of $35.00 for every mile traveled".

Answer:

4r^3

Step-by-step explanation:

because the root dived everything into a have

Answer:

20 square units

Step-by-step explanation:

If you were to graph the four points(creating a table on desmos is a good option) you would find that one side is 4 units long and the other is 5 units long. You multiply 4 times 5 to get that the area is 20 units squared. :)

Answer:

20 units²

Step-by-step explanation:

A = 4 × 5 = 20 units²

Answer:

SV= 26

VST=40

Step-by-step explanation:

Answer:

75/100 = 3/4

Step-by-step explanation:

75% in rate form is: 75/100, which can be also given in reduced fraction form by simplifying two factors "5" : 75/100 = 3/4

Answer:

5 is the width.

Step-by-step explanation:

Answer Check:

22 + 22= 44

5 + 5 = 10

44 + 10 = 54

Step-by-step explanation:

We have to find the distance the jogger must travel each minute. The distance covered in one minute is:

d= 3528/1800= 1.96 m

Therefore, the distance covered in one minute, or 60 seconds is:

dt= 1.96 × 60 = 117.6 m

The solution needed is, dt=588/5 = 117 (3/5) m

Answer:I think it c

Step-by-step explanation:

Answer:

Is letter D. X=6.

Step-by-step explanation:

3/4.5= 4/QR

18/3=6

Answer: D. a reflection across the line x = - 1

Step-by-step explanation:

First, you can see that the lengths of the top and the base of the figure are different, so we can discard the rotations of 180°, because those will give a different figure.

Now, for reflections, we need to reflect the image around a line of symmetry.

A line of symmetry means that the image at the right of the figure is an exact reflex of the image at the left of the figure, for this particular case, we can find a line x = c. Such that the distance between c and the x-component of the top vertexes is the same for both of them.

(Again, because the top and the bottom have different lengths, there is no line y = b such that a reflection across that line will leave the figure invariant)

The left top vertex is at x = -3

The right top vertex is at x = 1.

We can find the mid-value between them as:

c = (-3 - 1)/2 = -2/2 = -1

Then:

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

1 - c = 1 - (-1) = 2

While the numbers are different (in sign) as those represent distance between points, we only care for the absolute value, in that case:

I-2I = I2I

Then the distances are exactly the same, and we can take c = -1

This means that a reflection about the line x = -1 carries the figure onto itself.

Then the correct option is:

D. a reflection across the line x = - 1

It means that they do not have the proper proportions that they normally would in real life. The drawing might be larger or smaller than the bugs but even then it might have the proper proportions, it is only when it has incorrect proportion sizes, that is is considered "not to scale"

I hope this helps :)

Answer:

That means if you measure the bugs from the chart/paper/assignment, the real bugs aren't that size.

Hope that helps and have a great day!

(If you have any questions let me know)

Answer:

b = 4

Step-by-step explanation:

Remember y = mx+b (m = slope, b = y intercept.)

We have the slope, so, no need to solve for that.

To find the y intercept, plug in the ordered pairs to y=mx+b

-2=-3(2)+b

-2=-6+b       multiply like terms

4 = b        Add 6 on both sides

b = 4.

Answer:

The probability that at least 1 car arrives during the call is 0.9306

Step-by-step explanation:

Cars arriving according to Poisson process - 80 Cars per hour

If the attendant makes a 2 minute phone call, then effective λ = 80/60 * 2 = 2.66666667 = 2.67   X ≅ Poisson (λ = 2.67)

Now, we find the probability: P(X≥1)

P(X≥1) = 1 - p(x < 1)

P(X≥1) = 1 - p(x=0)

P(X≥1) = 1 - [ (e^-λ) * λ^0] / 0!

P(X≥1) = 1 - e^-2.67

P(X≥1) = 1 - 0.06945

P(X≥1) = 0.93055

P(X≥1) = 0.9306

Thus, the probability that at least 1 car arrives during the call is 0.9306.

Answer:

I believe that it is 45 but I'm not 100% sure.

Step-by-step explanation:

Answer:

40 miles

Step-by-step explanation:

15 + 0.50m = 25 + 0.25m

0.50m = 10 + 0.25m

0.25m = 10

m = 40

Answer: -5 < x < 6. (-5, 6)

Step-by-step explanation: