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3 years ago

What is the factorization of the expression below?

Mathematics

2 answers:

Ksenya-84 [330]3 years ago

5 0

Answer:

Well factorizing 16x^2-49

You can use the difference of squares

Which is when theirs 2 perfect sqaures and it’s a subtraction problem.

So 16x^2 - 49

the formula is

a^2-b^2= (a+b) (a-b)

16x^2 - 7^2 = (a+b) (a-b)

SO plug it in

(4x+7) (4x-7)

Thats simplified to the max

So your answer would be (c)

sesenic [268]3 years ago

4 0

16x² - 49

= (4x)² - 7²

Identity =》 a² - b² = (a + b) (a - b)

(4x)² - 7²

= (4x + 7) (4x - 7) [3rd option]

_______

Hope it helps ⚜

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√₂

snow_lady [41]

Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

Simple Interest Formula

I = Prt

where:

I = interest earned.
P = principal invested.
r = interest rate (in decimal form).
t = time (in years).

Given:

Total P = $7000
P₁ = principal invested at 5%
P₂ = principal invested at 8%
Total interest = $500
r₁ = 5% = 0.05
r₂ = 8% = 0.08
t = 1 year

Create two equations from the given information:

$\textsf{Equation 1}: \quad \sf P_1+P_2=7000$

$\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500$

Rewrite Equation 1 to make P₁ the subject:

$\implies \sf P_1=7000-P_2$

Substitute this into Equation 2 and solve for P₂:

$\implies \sf 0.05(7000-P_2)+0.08P_2=500$

$\implies \sf 350-0.05P_2+0.08P_2=500$

$\implies \sf 0.03P_2=150$

$\implies \sf P_2=\dfrac{150}{0.03}$

$\implies \sf P_2=5000$

Substitute the found value of P₂ into Equation 1 and solve for P₁:

$\implies \sf P_1+5000=7000$

$\implies \sf P_1=7000-5000$

$\implies \sf P_1 = 2000$

$2000 was invested at 5% and $5000 was invested at 8%.

Learn more about simple interest here:

brainly.com/question/27743947

brainly.com/question/28350785

5 0

1 year ago

Find a possible middle term to make this polynomial factorable:

mafiozo [28]

A. the polynomial can then be factored to (x+10)(x+2).

4 0

3 years ago

Help me please!!! 45 points to whoever helps!!

kap26 [50]

I don’t know 775 re2566

7 0

3 years ago

A survey of 200 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take

Lina20 [59]

Answer:

The 95% confidence interval for the true proportion of university students who use laptop in class to take notes is (0.2839, 0.4161).

Step-by-step explanation:

The (1 - α)% confidence interval for population proportion P is:

$CI=p\pm z_{\alpha/2}\sqrt{\frac{p(1- p)}{n}}$

The information provided is:

x = number of students who responded as"yes" = 70

n = sample size = 200

Confidence level = 95%

The formula to compute the sample proportion is:

$p=\frac{x}{n}$

The R codes for the construction of the 95% confidence interval is:

> x=70

> n=200

> p=x/n

> p

[1] 0.35

> s=sqrt((p*(1-p))/n)

> s

[1] 0.03372684

> E=qnorm(0.975)*s

> lower=p-E

> upper=p+E

> lower

[1] 0.2838966

> upper

[1] 0.4161034

Thus, the 95% confidence interval for the true proportion of university students who use laptop in class to take notes is (0.2839, 0.4161).

7 0

3 years ago

Read 2 more answers

A local high school has both male and female students.

Kitty [74]

Answer:

a. P(male) = 0.4

b. P(no sport and male) = 0.1

c. Unclear question (isn't it the same as b.?)

Step-by-step explanation:

The data below is what I've worked according to, which isn't very clear from the question so the answers are only correct if this is the correct table of data;

$\left[\begin{array}{ccc}&No \ Sports&Sports\\Female&10&32\\Male&7&21\end {array}\right]$

$P(male) = \frac{7 + 21}{70} \\\\ = \frac{28}{70} \\\\ = \frac{2}{5}$

Using the tree diagram in the picture;

$P(no \ sport \ and \ male) = \frac{2}{5} * \frac{1}{4} \\\\ = \frac{1}{10}$

8 0

2 years ago