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3 years ago

Hi. I need help with these questions. See image for question. Please answer no 10 and 11

Mathematics

1 answer:

Tanya [424]3 years ago

3 0

9514 1404 393

Answer:

10. (x, y) = (-3/8, 2 9/16)

11. k = -1

Step-by-step explanation:

10. The value of x at the vertex is ...

x = -b/(2a)

x = -(-3)/(2(-4)) = -3/8

The corresponding value of y is ...

y = 2 +(-3/8)(-3 +(-3/8)(-4)) = 2 +(-3/8)(-3/2) = 2 +(9/16)

The vertex is (x, y) = (-3/8, 2 9/16).

11. The discriminant is zero when the roots are equal.

b² -4ac = 0

(k-1)² -4(1)(-k) = 0

k² -2k +1 +4k = 0

k² +2k +1 = 0 . . . . . collect terms

(k +1)² = 0 . . . . . . . . write as a square

k = -1 . . . . . . . . . . . . the value of k that satisfies

Check

x² -2x +1 = (x -1)² = 0 . . . . has equal roots: x=1.

You might be interested in

Solve (x + 3)2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u –

Verdich [7]

Answer:

The solutions of the original equation are x=-5 and x=-2

Step-by-step explanation:

we have

$(x+3)^2+(x+3)-2=0$

Let

$u=(x+3)$

Rewrite the equation

$(u)^2+(u)-2=0$

Complete the square

$u^2+u=2$

$u^2+u+1/4=2+1/4$

$u^2+u+1/4=9/4$

rewrite as perfect squares

$(u+1/2)^2=9/4$

square root both sides

$(u+1/2)=\pm\frac{3}{2}$

$u=(-1/2)\pm\frac{3}{2}$

$u=(-1/2)+\frac{3}{2}=1$

$u=(-1/2)-\frac{3}{2}=-2$

the solutions are

u=-2,u=1

Alternative Method

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$(u)^2+(u)-2=0$

$a=1\\b=1\\c=-2$

substitute in the formula

$u=\frac{-1\pm\sqrt{1^{2}-4(1)(-2)}} {2(1)}$

$u=\frac{-1\pm\sqrt{9}} {2}$

$u=\frac{-1\pm3} {2}$

$u=\frac{-1+3} {2}=1$

$u=\frac{-1-3} {2}=-2$

the solutions are

u=-2,u=1

Find the solutions of the original equation

For u=-2

$-2=(x+3)$ ----> $x=-2-3=-5$

For u=1

$1=(x+3)$ ----> $x=1-3=-2$

therefore

The solutions of the original equation are

x=-5 and x=-2

4 0

3 years ago

Read 2 more answers

Samir bought 3 pounds of cement to repair the cracks in his sidewalk.

r-ruslan [8.4K]

Answer:

16oz=1lbs

First you need to see how many ounces equals three pounds, so you wanna go 16*3=48

You bought 48 ounces

You now take 48/2=24

You can fill 24 cracks with 3 pounds of cement

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

1 minus what equals 1/4 plus 3/8

AnnZ [28]

1/4 =2/8+3/8 =5/8
1-5/8=3/8

7 0

4 years ago

Perry is buying an I phone that is a sale for 40% off the original price.after he uses a $25 gift card.the total cost before tax

marta [7]

Answer:

$599

Step-by-step explanation:

Given: Discount- 40% off on original price.

Gift card= $25

Total cost before taxes is $334.40

Lets assume the original price be "x".

We know there is 40% on original price and Perry uses $25 gift card.

Remember; Total cost= $Original\ price- discount- gift\ card$

Now, finding the original price of Iphone.

⇒ $x-0.40x-25= 334.40$

⇒ $0.60x-25= 334.40$

Adding both side by 25

⇒ $0.60x= 334.40+25$

⇒ $0.60x= 359.4$

Dividing both side by 0.60

⇒ $x= \frac{359.4}{0.60}$

∴ $x= 599$

Hence, the original price of iphone is $599

5 0

3 years ago

In triangleABC, angle B= 90 degrees, cos(C)=15/17 and AB = 16 what is the measure of Angle A, Angle C and angle AC

Sergeeva-Olga [200]

Answer:

m∠C=28°, m∠A=62°, AC=34.1 units

Step-by-step explanation:

Given In ΔABC, m∠B = 90°, , and AB = 16 units. we have to find m∠A, m∠C, and AC.

As, cos(C)={15}/{17}

⇒ angle C=cos^{-1}(\frac{15}{17})=28.07^{\circ}\sim28^{\circ}

By angle sum property of triangle,

m∠A+m∠B+m∠C=180°

⇒ m∠A+90°+28°=180°

⇒ m∠A=62°

Now, we have to find the length of AC

sin 28^{\circ}=\frac{AB}{AC}

⇒ AC=\frac{16}{sin 28^{\circ}}=34.1units

The length of AC is 34.1 units

3 0

4 years ago