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2 years ago

Angle DEF and Angle FEG are complementary. mDef=(3x-4)°, and mDEG=(5x+6). Find x.

Mathematics

2 answers:

Lilit [14]2 years ago

8 0

Answer:

x = 11

Step-by-step explanation:

Complementary means they add up to 90°

So add the angles up and set them equal to 90°

3x - 4 + 5x + 6 = 90

ADD the x's

8x - 4 + 6 = 90

COMBINE the -4 and 6

8x +2 = 90

SUBTRACT 2 from both sides.

8x = 88

DIVIDE by 8 on both sides.

8x/8 = 88/8

x = 11

Phantasy [73]2 years ago

4 0

Answer:

x = 11

Step-by-step explanation:

Complementary angles are the angles which are added up to 90°.

As, the given angles are complementary,

(3x - 4) + ( 5x + 6 ) = 90

Now solve for x.

(3x - 4) + ( 5x + 6 ) = 90

3x - 4 + 5x + 6 = 90

8x -4 + 6 = 90

8x + 2 = 90

8x = 90 - 2

8x = 88

Divide both sides by 8.

x = 11

Hope this helps you :-)

Let me know if you have any other questions :-)

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Name the coordinates for the reflection. Reflect point (4, -1) over the x-axis.

inysia [295]

Answer:

i just took the test its (4,1)

Step-by-step explanation:

6 0

3 years ago

Mr. Kohl has a breaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives ea

77julia77 [94]

Answer:

There were 26 students in his class and the teacher had 83 ml of the solution.

Step-by-step explanation:

Mr. Kohl has a "x" amount of solution, if he divides it by the number of students "n" he'll give each student 3 milliliters and have a left over of 5 milliliters. If the amount of solution Mr. Kohl had was "x + 21" then he'd be able to give each student 4 milliliters of the solution. From these informations we have:

x = 3*n + 5

(x + 21)/n = 4

x + 21 = 4*n

x = 4*n - 21

Now that we have two equations and two variables we can solve the system of equations, as seen bellow:

3*n + 5 = 4*n - 21

3*n - 4*n = -21 - 5

-n = -26

n = 26

x = 4*26 - 21 = 83 ml

There were 26 students in his class and the teacher had 83 ml of the solution.

3 0

2 years ago

Graph the system of equations. {x−y=64x+y=4

Fantom [35]

X-y=6 Equation 1
x+y=4 Equation 2

To graph the given system of equation, first find x and y-intercept of each equation.
x-y=6
When y=0
x=6 Point is (6,0)
When x=0
-y=6
y=-6 Point is (0,-6)

Now x-intercept and y-intercept for equation 2.
x+y=4
When x=0
y=4 Point is (0,4)
When y=0
x=4 Point is (4,0)

Now plot these points on the graph, the lines intersect each other at point (5,-1), which is the solution of the given system.

Answer: (5,-1)

5 0

3 years ago

Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of

tia_tia [17]

Answer:

Using a formula, the standard error is: 0.052

Using bootstrap, the standard error is: 0.050

Comparison:

The calculated standard error using the formula is greater than the standard error using bootstrap

Step-by-step explanation:

Given

Sample A Sample B

$x_A = 30$ $x_B = 50$

$n_A = 100$ $n_B =250$

Solving (a): Standard error using formula

First, calculate the proportion of A

$p_A = \frac{x_A}{n_A}$

$p_A = \frac{30}{100}$

$p_A = 0.30$

The proportion of B

$p_B = \frac{x_B}{n_B}$

$p_B = \frac{50}{250}$

$p_B = 0.20$

The standard error is:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}$

$SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}$

$SE_{p_A-p_B} = \sqrt{0.00274}$

$SE_{p_A-p_B} = 0.052$

Solving (a): Standard error using bootstrapping.

Following the below steps.

Open Statkey
Under Randomization Hypothesis Tests, select Test for Difference in Proportions
Click on Edit data, enter the appropriate data
Click on ok to generate samples
Click on Generate 1000 samples ---- <em>see attachment for the generated data</em>

From the randomization sample, we have:

Sample A Sample B

$x_A = 23$ $x_B = 57$