A hybrid car can go 400 miles on 8 gallons of gas. How far can the car take you with 1 gallon of gas?

The quadratic function that represents the given graph is:

y = ¹/₂(x − 4)² - 1

The general form of a quadratic equation in Vertex Form is expressed as:

y = a(x − h)² + k,

where

(h, k) is the vertex.

From the given graph, we can see that the coordinates of the vertex is (4, -1). Thus, we have:

y = a(x − 4)² - 1

Looking at the four given options from Option A to Option D, we can deduce that only given option that gives us the coordinates of the quadratic curve vertex is option D.

Thus, we can conclude that the quadratic function that truly represents the given parabolic graph curve is:

y = ¹/₂(x − 4)² - 1

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Answer:

20% of 250 is 50

Answer:

All triangles has a total angle of 180. So x+38+2x+18+x=180

Solve for x: 4x+56=180 so 4x=124, x=31

Answer:

multiply 65 by 5 and divide by 1 fourth

Step-by-step explanation:

Using proportionality, it is found that it would take them 12.5 days.

-------------------------------------

\(t = \frac{k}{mh}\)

\(t = \frac{k}{mh}\)

\(10 = \frac{k}{15(5)}\)

\(k = 15 \times 5 \times 10 = 750\)

Thus

\(t = \frac{750}{mh}\)

\(t = \frac{750}{mh} = \frac{750}{10(6)} = \frac{750}{60} = 12.5\)

It would take them 12.5 days.

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Answer:

The slope is

\( - \frac{4}{3} \)

Step-by-step explanation:

To find the slope given two points we use the formula

\(m = \frac{y2 - y1}{x2 - x1} \)

where

m is the slope

(x1 , y1) and (x2 , y2) are the points

From the question

The points are (3,14) and (6,10)

The slope of the line (3,14) and (6,10) is

\(m = \frac{10 - 14}{6 - 3} = \frac{ - 4}{ 3} \)

\(m = - \frac{4}{3} \)

Hope this helps you

Answer:

2.66666666667

Step-by-step explanation:

2.6666666667x3=8

Answer:

Adter ate \(\frac{1}{4}\) of the remaining pie.

Step-by-step explanation:

equation:

⇒ \(\frac{3}{4} - \frac{1}{6}\)

when subtracting fractions, make sure both denominators are the same, to do this, multiply the first fraction by 3 and the second fraction by 2

⇒ \(\frac{3}{4} x 3 - \frac{1}{6} x 2\)

⇒ \(\frac{9}{12} - \frac{6}{12}\)

solve:

⇒ \(\frac{9}{12} - \frac{6}{12}\)

⇒ \(\frac{3}{12}\)

simplify:

⇒ \(\frac{3}{12}\) = \(\frac{1}{4}\)

Answer:

The required number of cups of frozen mango is 1.125.

Step-by-step explanation:  Given that a smoothie recipe calls for cups of frozen mango and the recipe serves two.

We are to find the number of cups of frozen mango that is needed to serve one.

We will be using the UNITARY method to solve the problem.

We have

The number of cups of frozen mango that needs to serve two is

Therefore, the number of frozen mango that needs to serve one is given by

Thus, the required number of cups of frozen mango is 1.125.

Step-by-step explanation:

Answer:

\(T =56.3\)

Step-by-step explanation:

Given

The attached triangle

Required

Measure of T

This is calculated as:

\(\cos T = \frac{Adjacent}{Hypotenuse}\)

\(\cos T = \frac{5}{9}\)

Take arccos

\(T = \cos^{-1}{(5/9)}\)

\(T =56.3\)

Answer:

A,E

Step-by-step explanation:

Operation: Minus

To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.

6.8 km - 2.3 km = 4.5 km

Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.

Answer:

a and e

Step-by-step explanation:

got it right on homework

Answer:

\(y-9=-\dfrac{8}{3}(x-7)\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}\)

Define the given points:

Substitute the defined points into the slope formula:

\(\implies \textsf{slope}\:(m)=\dfrac{1-9}{10-7}=-\dfrac{8}{3}\)

\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)

Substitute the found slope and one of the points into the point-slope formula:

\(\implies y-9=-\dfrac{8}{3}(x-7)\)

Answer:

7250%

Step-by-step explanation:

To express 72 1/2 as a percentage, you need to convert it to a decimal first and then multiply by 100.

72 1/2 is equivalent to 72.5 as a decimal.

To convert it to a percentage:

72.5 * 100 = 7250

Therefore, 72 1/2 is equal to 7250% when expressed as a percentage.

let me know it is helpful for you or not

Answer:

Step-by-step explanation:

The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

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Answer:

I'm not sure I completely understand what is being asked but this is what I'm going with......

2 every test you have lost 2 points per test on 6 tests so that is a total of 12 lost??

Step-by-step explanation:

Hope I helped even a little Have a great day!!!

Answer: The statue, originally intended to be only 10 feet tall, was on further consideration enlarged so that it finally stood 19 feet tall from head to foot, the scale being such that if Lincoln were standing he would be 28 feet tall.

Step-by-step explanation: hope this helps

Answer: 28 ft

Step-by-step explanation:

You have the following expression:

4t - 8

to factorize the previous expression, take into account that the greatest common divisor of coefficients 4 and 8 is 4. Divide each term by 4 and put the result inside parenthesis, preceeded by 4, just as follow:

4t - 8 =

4(4t/4 - 8/4) =

4(t - 2)

Hence, the factorized expression is

A: 4(t -2)

C: (t - 2)4

Answer:

To check your work, 8 + 8 is 16

Step-by-step explanation:

need bwainlist to maybe u can help out chika???

Answer:

A

Step-by-step explanation:

A

Answer:

Q9 -  Option 1---- A -  15.6 Square Units

Q10 --Option --- (B) RECTANGLE

Step-by-step explanation:

Q9 --

we know area of triangle  = 1/2 ab sin theta

Where theta is the angle included between sides A and side B

A  = 5.2

B = 7

theta  = 121 degrees

1/2 * 5.2 * 7 * sin 121 degrees = 15.6 Square Units

Conclusion

The area of the triangle is 15.6 Square Units

Option --- (B) RECTANGLE

Hope this helps!

Answer: 1. The answer is A. 2. The answer is C again

Step-by-step explanation:

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

i think it is 141.4

Step-by-step explanation:

Answer:

x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 3 x + 15 = 0

The left hand side factors into a product with two terms:

(x + 5) (x^2 + 3) = 0

Split into two equations:

x + 5 = 0 or x^2 + 3 = 0

Subtract 5 from both sides:

x = -5 or x^2 + 3 = 0

x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:

x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2

sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):

x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2

sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):

x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2

(2 i sqrt(3))/2 = i sqrt(3):

x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2

(2 (-i sqrt(3)))/2 = -i sqrt(3):

Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Answer:

C. x = −5, 1.7i, −1.7i

Step-by-step explanation:

Quick answer:

C. x = −5, 1.7i, −1.7i

explanation:

C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.

Complete answer:

All odd degree polynomials have at least one real root.

By the real roots theorem, we know that

if there is a real root, it must be of the form \(\pm\)p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).

Values of \(\pm\)p/q are

On trial and error, using the factor theorem, we see that

f(-5) = 0, therefore -5 is a real root.  By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i

The answer is {-5, +/- sqrt(5) i}, or again,

C. x = −5, 1.7i, −1.7i

Answer:

multiple 18 x 8, then minus 6 from your answer

Answer:

1pack=6cans

18packs=x

=108canspacks=1xpack

Dividing both sides by 1 pack

X=108cans

Answer:

A. You can write the number as a Ratio of two entegers

D. You know what the next number is

(a² + 5a + 5) + (a + 3)

a² + 5a + 5 + a + 3

a² + 6a + 8

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2