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2 years ago

If −1 is a zero of the polynomial p(x)=ax^3−x^2+x+4, find the value of a.

Mathematics

1 answer:

vitfil [10]2 years ago

8 0

Answer:

a = 2

Step-by-step explanation:

given x = - 1 is a zero then f(- 1) = 0 , that is

a(- 1)³ - (- 1)² - 1 + 4 = 0

- a - 1 - 1 + 4 = 0

- a + 2 = 0 ( subtract 2 from both sides )

- a = - 2 ( multiply both sides by - 1 )

a = 2

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ABCD- parallelogram, If the perimeter of Triangle CPQ is 15cm, Find the perimeter of triangle BAQ. Find the perimeter of triangl

melamori03 [73]

Answer:

The answer is below

Step-by-step explanation:

A parallelogram is a quadrilateral (has 4 sides and 4 angle) with two pair of parallel and opposite sides. Opposite sides of a parallelogram are parallel and equal.

Given parallelogram ABCD:

AB = CD = 18 cm; BC = AD = 8 cm

∠P = ∠P, ∠PDA = ∠PCQ (corresponding angles are equal).

Hence ΔPCQ and ΔPDA are similar by angle-angle similarity theorem. For similar triangles, the ratio of their corresponding sides equal. Therefore:

$\frac{CD}{PC}= \frac{AD}{CQ}\\\\\frac{18}{6}=\frac{8}{x} \\\\x=\frac{6*8}{18}=\frac{8}{3}\ cm$

Perimeter of CPQ = CP + CQ + PQ

15 = 6 + 8/3 + PQ

PQ = 15 - (6 + 8/3)

PQ = 6.33

∠CQP = ∠AQB (vertical angles), ∠QCP = ∠QBA (alternate angles are equal).

Hence ΔCPQ and ΔABQ are similar by angle-angle similarity theorem

$\frac{AQ}{QP}=\frac{AB}{CP} \\\\\frac{AQ}{6.33} =\frac{18}{6} \\\\AQ=\frac{18}{6}*6.33\\\\AQ = 19$

$\frac{BQ}{CQ}=\frac{AB}{CP} \\\\\frac{BQ}{8/3} =\frac{18}{6} \\\\BQ=\frac{18}{6}*\frac{8}{3} \\\\BQ =8$

Perimeter of BAQ = AB + BQ + AQ = 18 + 8 + 19 = 45cm

PA = AQ + PQ = 19 + 6.33 = 25.33

PD = CD + DP = 18 + 6 = 24

Perimeter of PDA = PA + PD + AD = 24 + 25.33 + 8 = 57.33 cm

7 0

3 years ago

Multiply.<br> 3/4 x -5 1/6

navik [9.2K]

Answer:

-3.87500

Step-by-step explanation:

brainliest!! plez

5 0

3 years ago

The Scottsdale fire department aims to respond to fire calls in 4 minutes or less, on average. Response times are normally distr

IgorC [24]

<h2><u>Answer with explanation</u>:</h2>

Let $\mu$ be the population mean.

As per given , we have

$H_0:\mu \leq4\\\\ H_a: \mu >4$

Since the alternative hypothesis is right-tailed , so the test is a right-tailed test.

Also, population standard deviation is given $\sigma=1$ , so we perform one-tailed z-test.

Test statistic : $z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

, where $\mu$ = Population mean

$\sigma$ = Population standard deviation

n= sample size

$\overline{x}$ = Sample mean

For n= 18 , $\overline{x}=4.50$ , $\sigma=1$ , $\mu =4$ , we have

$z=\dfrac{4.5-4}{\dfrac{1}{\sqrt{18}}}\approx2.12$

P-value (for right tailed test): P(z>2.12) = 1-P(z≤ 2.12) [∵ P(Z>z)=1-P(Z≤z)]\

=1- 0.0340=0.9660

Decision : Since P-value(0.9660) > Significance level (0.01), it means we are failed to reject the null hypothesis.

[We reject null hypothesis if p-value is larger than the significance level . ]

Conclusion : We do not have sufficient evidence to show that the goal is not being met at α = .01 .

3 0

3 years ago

A painting is 4 feet long.A photo frame is 10 inches long.How many inches longer is the painting then the photo frame?

Galina-37 [17]

Change 4 feet to inches
4 feet is 48 inches
48-10=38

3 0

3 years ago

Can I get some help plz?

Anika [276]

Answer:

X=20 degree

Step-by-step explanation:

∆A+∆D+∆O=180

2x+10+2x+90=180

collect like terms

2x+2x=180-100

4x=80

(4x)/4=(80)/4

x=20 degree

6 0

3 years ago

Read 2 more answers