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adoni [48]
3 years ago
7

Which of the following is true for the graph of the quadratic function f(x)=2x^2-10x+12

Mathematics
1 answer:
lana [24]3 years ago
4 0
To find the x-intercepts let f(x) = 0 and solve the equation. To find the y-intercept(s) let x = 0 and solve the equation. To find the vertex: the x coordinate of the vertex is -b/2a where a is the coefficient of the x^2 and b is the coefficient of x. Then, substitute the value you get for -b/2a for the x and solve for y. That will give you the x,y coordinates. 
4. a. Solve 2x^2 -10x + 12 =0. Either use the quadratic formula or factor. x = 2 and x = 3. But those are the intercepts. The points of the intercepts are (2,0) and (3,0), NOT the point (3,2). a cannot be true. 4b. In the equation, substitute 0 for x and solve. f(x) or y comes out to 12. b is correct. 4c. -b/2a = 10/4 which reduces to 5/2. Substitute 5/2 for x and evaluate to find y. y = -1/2. Your answers for 4 are b and c. 
5. a. Substitute 0 for x and solve. y = -6, so your y-intercept is (0.-6). a is correct b. Substitute 0 for y and solve. x = 2 and -1. b is correct. That means d is not. c. -b/2a = 3/6 = 1/2. Substitute 1/2 for x and solve for y. The vertex is (1/2, - 27/4), e is correct. Your answers for 5 are a,b, and e. 
7. Substitute 0 for x and solve for y. y = -16/5, so the y intercept is (0/-16/5) a is true. b. x-intercepts always have 0 for the y coordinate, so b is NOT true. c. Expand your binomial and put your equation in ax^2, + bx + c form. -b/2a is 6/5 divided by 3/5 which equals 3. Put 3 in for x and find y. Your answer should be -5, so c is true. d. Let f(x) =0. Solve you equation by using the quadratic formula or factoring. x comes out to be 8 and -2, so d is true. Your ansers for 7 are a,c, and d.
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If x and y vary directly and x=25 when y=100 find x when y=24.<br> PLEASE HELP FASTTTTTTT
Veseljchak [2.6K]

Answer:

x = 6

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 25 when y = 100 , then

100 = 25k ( divide both sides by 25 )

4 = k

y = 4x ← equation of variation

When y = 24 , then

24 = 4x ( divide both sides by 4 )

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6 0
2 years ago
Solve for y.<br> py + qy = -4y + 8<br> y =
Elanso [62]

Answer:

y=8/(p+q+4)

Step-by-step explanation:

py+qy=-4y+8

Collect all terms containing y together

Py+qy+4y=8

Factor out y

y(p+q+4)=8

Divide both sides by (p+q+4)

y(p+q+4)/(p+q+4)=8/(p+q+4)

y=8/(p+q+4)

3 0
3 years ago
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What is the diameter of a hemisphere with a volume of 257 m^3
Alex73 [517]

Answer:

9.9

Step-by-step explanation:

\text{Volume of Hemisphere}\text{:}

Volume of Hemisphere:

\,\,257

257

\text{Volume of Sphere}\text{:}

Volume of Sphere:

\,\,514

514

Double volume of hemisphere to get volume of the entire sphere

\text{Volume of a Sphere:}

Volume of a Sphere:

V=\frac{4}{3}\pi r^3

V=

3

4

​

πr

3

514=

514=

\,\,\left(\frac{4}{3}\pi\right) r^3

(

3

4

​

π)r

3

514=

514=

\,\,(4.1887902)r^3

(4.1887902)r

3

Evaluate 4/3pi in calc

\frac{514}{4.1887902}=

4.1887902

514

​

=

\,\,\frac{(4.1887902)r^3}{4.1887902}

4.1887902

(4.1887902)r

3

​

Evaluate \frac{4}{3}\pi

3

4

​

π in calc

122.7084611=

122.7084611=

\,\,r^3

r

3

\sqrt[3]{122.7084611}=

3

 

122.7084611

​

=

\,\,\sqrt[3]{r^3}

3

 

r

3

​

Cube root both sides

4.9692575=

4.9692575=

\,\,r

r

\text{Then the diameter equals }9.938515

Then the diameter equals 9.938515

diameter is radius times 2

\text{Final Answer:}

Final Answer:

d\approx 9.9\text{ m}

d≈9.9 m

Round to nearest tenth

4 0
3 years ago
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