In the congruent figures ABCD and WXYZ, which angles are corresponding?

What is the value of x? There is isosceles triangle. The measure of angle which is between two congruent sides is (6x+10⁰). The

max2010maxim [7]

<h3><u>Answer</u><u>:</u><u>-</u></h3>

x=17

<h3><u>step-by</u><u>-</u><u>step</u><u> </u><u>Explanation</u><u>:</u><u>-</u></h3>

${\boxed{\quad\:\mapsto\rm Firstly\:Let's\:understand\:the\:concept:-}}$

<h3 />

This is a isosceles triangle. As it is a triangle we can apply sum theory. we have to take the sum of given unknown polynomials as 180° .Then by solving it we can find the value of x.

<h3><u>Solution</u><u>:</u><u>-</u></h3>

Given angles

(6x+10°)
(x+17°)
(4x-34)°

According to sum theory

${\boxed{\sf The \:sum\:of\:angles=180°}}$

Substitute the values

$\qquad \quad{:}\longmapsto\tt (6x+10)+(x+17)+(4x-34)=180$

Remove brackets

$\qquad \quad{:}\longmapsto\tt 6x+10+x+17+4x-34=180$

Together like polynomials and constants

$\qquad \quad{:}\longmapsto\tt 6x+x+4x+10+17-34=180$

$\qquad \quad{:}\longmapsto\tt 11x-7=180$

Interchange sides

$\qquad \quad{:}\longmapsto\tt 11x=180+7$

$\qquad \quad{:}\longmapsto\tt 11x=187$

$\qquad \quad{:}\longmapsto\tt x=\cancel{\dfrac{187}{11}}$

Simplify

$\qquad \quad{:}\longmapsto\tt x=17$

$\therefore\sf The \:value\:of\:x\;is\:17.$

8 0

3 years ago

A study of the number of business lunches that executives in the insurance and banking industries claim as deductible expenses p

gizmo_the_mogwai [7]

Answer:

$t=\frac{9.1-8}{\sqrt{\frac{(1.9)^2}{40}+\frac{(2.1)^2}{50}}}}=2.604$

$p_v =2*P(t_{(88)}>2.604)=0.0108$

So the p value is a very low value and using any significance level for given $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that the two means are significantly different at 5%

Step-by-step explanation:

Data given and notation

$\bar X_{1}=9.1$ represent the mean for the sample 1

$\bar X_{2}=8$ represent the mean for the sample 2

$s_{1}=1.9$ represent the sample standard deviation for the sample 1

$s_{2}=2.1$ represent the sample standard deviation for the sample 2

$n_{1}=40$ sample size for the group 1

$n_{2}=50$ sample size for the group 2

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean are different , the system of hypothesis would be:

Null hypothesis: $\mu_{1} = \mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

If we analyze the size for the samples both are higher than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

We can replace in formula (1) the results obtained like this:

$t=\frac{9.1-8}{\sqrt{\frac{(1.9)^2}{40}+\frac{(2.1)^2}{50}}}}=2.604$

Statistical decision

The first step is calculate the degrees of freedom, on this case:

$df=n_{1}+n_{2}-2=40+50-2=88$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{(88)}>2.604)=0.0108$

So the p value is a very low value and using any significance level for given $\alpha=0.05$ always $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that the two means are significantly different at 5%

3 0

2 years ago

Please help me, I've been stuck on this problem forever and I need help! Please don't answer with something random to get points

vodomira [7]

1. given
2. measure angle 1 plus measure angle 2 equals 90 degrees
3. B D bisects angle A D C
4. definition of angle bisector
5. definition of congruence
6. measure angle 1 is equal to measure angle 3
7. angle 1 is congruent to angle 3
7. definition of congruence
hope that helps

8 0

3 years ago

Can anyone help me on my HW i can't seem to find the answer to it and when i do it doesn't make sence

Nadusha1986 [10]

0.75x-18.5=0.65x
0.75x-0.65x=18.5
0.1x=18.5
x=18.5/0.1=185

Answer: x=185

To checkt:
0.75(185)-18.5=138.75-18.5=120.25
0.65(185)=120.25

4 0

2 years ago

Please Help <br> Write a system of linear Inequalities to represent each graph.

docker41 [41]

Answer:

$\left\{\begin{array}{l}5x-y-7\le 0\\2x+3y-9\ge 0\end{array}\right.$

Step-by-step explanation:

1. Blue region. The boundary blue line passes through the points (0,-7) and (3,8), then its equation is

$\dfrac{x-0}{3-0}=\dfrac{y+7}{8+7},\\ \\15x=3(y+7),\\ \\5x=y+7,\\ \\5x-y-7=0.$

This line is solid, so the sign for the inequality should be with the notion "or equal to".

From the diagram you can see that the origin belongs to the blue region, then its coordinates satisfy the inequality. Thus,

$5x-y-7\le 0.$

2. Green region. The boundary green line passes through the points (6,-1) and (0,3), then its equation is

$\dfrac{x-0}{6-0}=\dfrac{y-3}{-1-3},\\ \\-4x=6(y-3),\\ \\-2x=3y-9,\\ \\2x+3y-9=0.$

This line is solid, so the sign for the inequality also should be with the notion "or equal to".

From the diagram you can see that the origin doesn't belong to the blue region, then its coordinates satisfy the inequality. Thus,

$2x+3y-9\ge 0.$

3. The system of linear inequalities that represents these graphs is

$\left\{\begin{array}{l}5x-y-7\le 0\\2x+3y-9\ge 0\end{array}\right.$

6 0

2 years ago