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2 years ago

What is the solution of 7k+2=4k-10?

2 answers:

6 0

$7k+2=4k-10\ \ \ |-2\\\\7k=4k-12\ \ \ \ |-4k\\\\3k=-12\ \ \ \ |:3\\\\k=-4\\\\check:\\L=7(-4)+2=-28+2=-26\\R=4(-4)-10=-16-10=-26\\L=R$

slava [35]2 years ago

4 0

3k = -12 => k = -4

I Hope this helps...

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Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. (Enter your answer

vagabundo [1.1K]

Answer:

Follows are the solution to this question:

Step-by-step explanation:

In point a:

$\to \frac{5 \pi }{6}$

calculating a positive coterminal angle:

$\to \frac{5 \pi }{6} + 2 \pi \\\\ \to \frac{5 \pi +12 \pi }{6} \\\\ \to \frac{17 \pi }{6} \\\\$

calculating negative coterminal angle:

$\to \frac{5 \pi }{6} -2\pi \\\\ \to \frac{5 \pi - 12 \pi }{6} \\\\ \to \frac{ - 7 \pi }{6} \\\\$

In point b:

$\to \frac{-9 \pi }{4}$

calculating a positive coterminal angle:

$\to \frac{ -9 \pi }{4} + 2 \pi \ \ = \frac{-9 \pi + 8 \pi }{4} \\\\$

$\to \frac{ - \pi }{4} + 2 \pi \ \ = \frac{- \pi + 8 \pi }{4} \\\\$

$= \frac{ 7 \pi}{4}$

calculating a negative coterminal angle:

$\to \frac{ -9 \pi }{4} - 2 \pi \\\\ \to \frac{-9 \pi - 8 \pi }{4} \\\\ \to \frac{-17 \pi }{4}$

3 0

2 years ago

The second of two numbers is 3 less than twice the first. Their sum is 36. Find the numbers.

swat32

The first number = x
The second number = 2x-3

x + 2x-3 = 36
3x = 36+3
3x = 39
x = 39/3
x = 13

The first number = x = 13
The second number = 2x-3 = 2*13 - 3 = 26 - 3 = 23

7 0

2 years ago

The ratio of the number of cups of blue paint to the number of cups of red paint that Lara mixed to make a shade of purple paint

katrin2010 [14]

Answer:

Part A: Number of cups of blue paint are 3 that are mixed with each cup of red paint.

Part B: $\frac{1}{3}$

Part C: $8

Step-by-step explanation:

Given that:

The ratio of the number of cups of blue paint to the number of cups of red paint that Lara mixed to make a shade of purple paint is 3:1.

Part A:

The number of cups of blue paint = 3

The number of cups of red paint = 1

In sentence form, it can be written that:

Number of cups of blue paint are 3 that are mixed with each cup of red paint.

Part B:

3 cups of blue paint requires 1 cup of red paint.

$\frac{3}{3}=1$ cup of blue paint requires $\frac{1}{3}$ cup of red paint.

Here, unitary method is used.

So, $\frac{1}{3}$ cup of red paint should be added to each cup of blue paint to make shade of purple.

Part C:

6 cups of blue paint are purchased for $48.

1 cup of blue paint is purchased for $\frac{\$48}{6} = \$8$

5 0

2 years ago

Solve 6 1/8 ÷ 3 5/8 ( meaning six and one eighth divided by three and five eighths )

Stells [14]

The answer is 1 20/29.

3 0

2 years ago

Question 6 (1.25 points)

Lisa [10]

Answer:

Test statistic Z= 1.713

The calculated Z- value = 1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the mean annual salary of all lawyers in a city is different from $110,000

Step-by-step explanation:

Step(i):-

A researcher wants to test if the mean annual salary of all lawyers in a city is

different from $110,000

Mean of the Population μ = $110,000

Sample size 'n' = 53

Mean of the sample x⁻ = $114,000.

standard deviation of the Population = $17,000,

Level of significance = 0.01

Null hypothesis :

There is no difference between the mean annual salary of all lawyers in a city is different from $110,000

H₀: x⁻ = μ

Alternative Hypothesis : x⁻ ≠ μ

Step(ii):-

Test statistic

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{114000-110000}{\frac{17000}{\sqrt{53} } }$

Z = 1.7130

Tabulated value Z = 2.576 at 0.01 level of significance

The calculated Z- value = 1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the mean annual salary of all lawyers in a city is different from $110,000

4 0

2 years ago