MATHEMATICS HIGH SCHOOL

I don’t know how to answer this

Answers

Answer 1

Answer:

Answer:

m∠1=66

m∠3=66

m∠4=114

Step-by-step explanation:

m∠1+m∠2=180

m∠1+114=180

m∠1=66

m∠1=m∠3

66=m∠3

m∠4=m∠2

m∠4=114

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What basic trigonometric identity would you use to verify that csc x sec x cot x= csc^2x.

Answers

Answer:

See below.

Step-by-step explanation:

I would use cot x = cos x / sin x:

csc x sec x cot x

= csc x * 1/cos x * cos x / sin x

The cos x disappears:

= csc x * 1 / sin x

= csc^2 x.

Answer: B

Step-by-step explanation: test on edge

solving fraction equations: Write the solution in simplest form

6 1/4 = z + 1 5/8

Answers

6 1/4 = z + 1 5/8
6 1/4 - 1 5/8 = z + 1 5/8 - 1 5/8 Isolate variable
6 2/8 - 1 5/8 = z Least common denominator
4 5/8 = z Simplify

Answer:4 5/8 = z Simplify

What is the solution set for x in log4(x+5)+log4x=log4 14

Answers

$log_ {4} (x+5) + log_4(x) = log_4(14)$

For logs with same base :

$log_b(f(x)) + log_b(g(x)) = log_b(f(x)*g(x))$

$Log_4(x+5) + log_4(x) =log_4((x+5)x)$

$log_4((x+5) = log_4(14)$

When the logs have the same base :

$log_b(f(x)) = log_b(g(x))$

$F(x) = g(x)$

For $log_4((x+5)x) = log_4(14)$

Solve $(x+5)x = 14$

expand

$(x+5)x = x^2 + 5x$

$x^2+5x+14$

$(x-2)(x+7) = 0$

$x = 2 , x = - 7$

Therefore, the final solution : $x = 2$

hope this helps!

Johanna purchases a book for $14.95. There is a sales tax of 6.5%. How much is the final price with tax? What is the total? What is the percent? Use the formula amount = total x percent to find the amount of the sales tax. To find the final price, add the cost of the book to the amount of tax.

Answers

Answer:

Tax = $0.97175

Final Price = $15.92175

Step-by-step explanation:

To calculate the amount of tax of an amount you just must multiply this figure by the percentage of the tax expressed in decimal numbers.

-----------------------------------------------------------------------------------------------

Data:

Price = $14.95

Tax rate = 6.5%

-----------------------------------------------------------------------------------------------

Calculation of tax:

amount = total x percent = $14.95 x 6.5% = $14.95 x 0.065 = $0.97175

Calculation of the final price with tax:

Amount = book cost + tax = $14.95 + $0.97175 = $15.92175

-----------------------------------------------------------------------------------------------

Tax = $0.97175

Final Price = $15.92175

-----------------------------------------------------------------------------------------------

Hope this helps!

Okay so 6.5% of $14.95 is 0.97175. That rounds to 0.97. And to get the total we just add 0.97 to 14.95. Our answer is 15.92. However if you don't want to round then you would add 14.95 and 0.97175 . This would give you15.92175. Hope this helps!

Find the radius of a sphere with a volume of 589 cubic centimeters

Answers

Answer: The radius of a sphere is 5.20 cm.

Step-by-step explanation:

Volume of sphere = $(4)/(3)\pi r^3$ , where r = radius of sphere.

Given : Volume of sphere : 589 cubic centimeters

As per formula , we have

$(4)/(3)\pi r^3=589 \n\n\Rightarrow\ r^3=(589*3)/(4\pi)=(441.75)/(\pi)=(441.75)/(3.14)\n\n\Rightarrow\ r^3=140.684713376\approx140.68\n\n\Rigghtarrow\ r=\sqrt[3]{140.68} \approx5.20$

Thus , the radius of a sphere is 5.20 cm.

volume of sphere = $\pi$ r³

if volume of this sphere = 589 cm³

then πr³ = 589 cm³
r³ = $(589cm^(3) )/( \pi )$

∛r³ = ∛187.485 cm³

∴ r = 5.72 cm

In a rhombus, the sides are 14 inches long. two intersecting sides form a 60 degree angle. what are the exact lengths of the two diagonals

Answers

Long Diagonal AD = Square Root (2•Side² + 2•Side² • cos(A) )
Long Diagonal AD = Square Root (2*14^2 + 2*14^2 * cos(60) )
Long Diagonal AD = Square Root ( 392 + 392*.5)
Long Diagonal AD = Square Root (392 + 196)
Long Diagonal AD = Square Root (588)
Long Diagonal AD = 24.248711306

Short Diagonal BC = Square Root (2•Side² - 2•Side² • cos(A) )
Short Diagonal AD = Square Root ( 392 - 392*.5)
Short Diagonal AD = Square Root ( 392 - 196)
Short Diagonal AD = Square Root (196)
Short Diagonal AD = 14

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