Kayla saves $110 to purchase a new outfit. She decides to but a skirt for $29.65, a sweater for $38.32, and a purse for $31.00

Consider the cubic function f(x) = x^3 + ax^2 + bx + 4 where (a) and (b) are constants. When f(x) is divided by x-3, the remaind

Debora [2.8K]

Answer:

see explanation

Step-by-step explanation:

Using the Remainder theorem

If f(x) is divided by (x - h) then f(h) = remainder, thus

f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is

27 + 9a + 3b + 4 = 10

9a + 3b + 31 = 10 ( subtract 31 from both sides )

9a + 3b = - 21 → (1)

f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is

- 1 + a - b + 4 = 6

a - b + 3 = 6 ( subtract 3 from both sides )

a - b = 3 → (2)

Rearrange (2) expressing a in terms of b

a = 3 + b → (3)

Substitute a = 3 + b into (1)

9(3 + b) + 3b = - 21 ← distribute and simplify left side

27 + 9b + 3b = - 21

12b + 27 = - 21 ( subtract 27 from both sides )

12b = - 48 ( divide both sides by 12 )

b = - 4

Substitute b = - 4 into (3)

a = 3 - 4 = - 1

Hence a = - 1 and b = - 4

8 0

3 years ago

if the following line are parallel peroendicular coinciding or intersectining but not perpendicular ????

Lapatulllka [165]

Answer:In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles.

Step-by-step explanation:

6 0

2 years ago

. The Empire State Building is a 102-story skyscraper. Its height is 1,250 ft. from the ground to the roof. The length and width

Aleks [24]

Answer: a) Dimensions of miniature is 0.17 × 0.08 × 0.5, b) 0.006 ft³.

Step-by-step explanation:

Since we have given that

Height of building = 1250 feet

Length of building = 424 ft

Width of building = 187 ft

Now, we know that The miniature version is just 1/ 2500 of the size of the original.

So, Height of miniature would be

$\dfrac{1250}{2500}=0.5\ ft$

Length of miniature would be

$\dfrac{424}{2500}=0.17\ ft$

Width of miniature would be

$\dfrac{187}{2500}=0.08\ ft$

a) What are the dimensions of the miniature Empire State Building?

Dimensions of miniature is 0.17 × 0.08 × 0.5

b. Determine the volume of the miniature building. Explain how you determined the volume.

$Volume=0.5\times 0.08\times 0.17=0.006\ ft^3$

Hence, a) Dimensions of miniature is 0.17 × 0.08 × 0.5, b) 0.006 ft³.

6 0

3 years ago

DA−2qA=B^3<br> Solve for A

a_sh-v [17]

Answer:

$a=\frac{b^{3} }{d-2q}$

Step-by-step explanation:

i think

8 0

3 years ago

A guy wire runs from the top of a cell tower to a metal stake in the ground. Marques places a 11-foot tall pole to support the g

astra-53 [7]

The Pythagorean theorem computed shows that the length of the guy wire, to the nearest foot, is 207 ft.

<h3>How to solve the length?</h3>

Here, we have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 2 ft

BD = 35 ft

First, find AB:

AB/11 = (35 + 2)/2

AB/11 = 37/2

Cross multiply

AB = (37 × 11)/2

AB = 203.5 ft

Then, apply Pythagorean Theorem to find AE:

AE = √(AB² + BE²)

AE = √(203.5² + 37²)

AE = 207 ft

Therefore, the length of the guy wire is 207 ft.

Learn more about Pythagorean theorem on:

brainly.com/question/654982

5 0

2 years ago