All categories

2 years ago

Solve for X. Each figure is a parallelogram.

Mathematics

1 answer:

vichka [17]2 years ago

7 0

Answer:

1. x = 8

2. x = 3

3. x = 25

4. x = 6

5. x = 11

6. x = 3

7. x = 6

8. x = 10

Step-by-step explanation:

Since the opposite sides of a parallelogram are congruent, the length of segment QR is equal to the length of segment PS.

10 = -6 + 2x

Add 6 to each side

10 + 6 = -6 + 6 + 2x

Simplify each side

16 = 2x

Divide both sides by 2

16/2 = 2x/2

Simplify

x = 8

to check if x is correct:

you already know that segment QR is 10, so your answer needs to be equal to 10

so sement PS is -6x + 2x

-6 + 2x

= -6 + 2(8)

= -6 + 16

= 10

so PS = 10

2. 34x + 5 = 35x + 2

Step 1: Subtract 35x from both sides.

34x + 5 − 35x = 35x + 2 − 35x

−x + 5 = 2

Step 2: Subtract 5 from both sides.

−x + 5 − 5 = 2 − 5

−x = −3

Step 3: Divide both sides by -1.

-x/-1 = -3/-1

Step 4: Simplify

x = 3

115 = 2x + 65

Step 1: Flip the equation.

2x + 65 = 115

Step 2: Subtract 65 from both sides.

2x + 65 − 65 = 115 − 65

2x = 50

Step 3: Divide both sides by 2.

2x/2 = 50/2

x = 25

84 + 16x = 180

84 - 84 + 16x = 180 - 84

16x = 96

16x/16 = 96/16

x = 6

2(3x − 10) = 46

Step 1: Simplify both sides of the equation.

2(3x − 10) = 46

(2)(3x) + (2)(−10 )= 46(Distribute)

6x + −20 = 46

6x − 20 = 46

Step 2: Add 20 to both sides.

6x − 20 + 20 = 46 + 20

6x = 66

Step 3: Divide both sides by 6.

6x/6 = 66/6

x = 11

6. RH = 1/2 FH or RH = 2 × FH

Step 1: Simplify both sides of the equation.

(2)(12)=13x−2

24=13x+−2

24=13x−2

Step 2: Flip the equation.

13x−2=24

Step 3: Add 2 to both sides.

13x−2+2=24+2

13x=26

Step 4: Divide both sides by 13.

13x/13 = 26/13

x = 3

2x+2=3x−4

Step 1: Subtract 3x from both sides.

2x+2−3x=3x−4−3x

−x+2=−4

Step 2: Subtract 2 from both sides.

−x+2−2=−4−2

−x=−6

Step 3: Divide both sides by -1.

-x/-1 = -6/-1

x = 6

2(2x−6)=28

Step 1: Simplify both sides of the equation.

2(2x−6)=28

(2)(2x)+(2)(−6)=28(Distribute)

4x+−12=28

4x−12=28

Step 2: Add 12 to both sides.

4x−12+12=28+12

4x=40

Step 3: Divide both sides by 4.

4x/4 = 40/4

x = 10

You might be interested in

A counselor at a community college claims that the mean GPA for students who have transferred to State University is more than 3

Lena [83]

Answer:

$t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3$

If we compare the p value and the significance level for example $\alpha=1-0.99=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=3.25$ represent the sample mean

$s=0.3$ represent the sample standard deviation

$n=36$ sample size

$\mu_o =3.1$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is more than 3.1, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.1$

Alternative hypothesis: $\mu > 3.1$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3$

P-value

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

$df=n-1=36-1=35$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(35)}>3)=0.00247$

Conclusion

If we compare the p value and the significance level for example $\alpha=1-0.99=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

5 0

3 years ago

What is the equation for a line

USPshnik [31]

Answer:

y = mx + b

Step-by-step explanation:

y represents the dependent variable (value you are getting).

m represents the slope of the line.

x represents the independent variable (what you are changing).

b represents the y-intercept, or the y value when x is zero.

4 0

2 years ago

Read 2 more answers

If x = 10, which lines are parallel? Check all that apply.

OlgaM077 [116]

Answer:

The answer would be A. 1 1/5

Step-by-step explanation:

1 8/40 Simplify to 1 1/5

48/40 = 1 8/40

The answer to this question is above.

Hope this helps.

3 0

3 years ago

How many zeroes do we write when we write all the integers 1 to 243 in base 3?

Monica [59]

Answer:

289 numbers

Step-by-step explanation:

Above you will find the list of integers from 1 to 243 in base 3:

(1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1200, 1201, 1202, 1210, 1211, 1212, 1220, 1221, 1222, 2000, 2001, 2002, 2010, 2011, 2012, 2020, 2021, 2022, 2100, 2101, 2102, 2110, 2111, 2112, 2120, 2121, 2122, 2200, 2201, 2202, 2210, 2211, 2212, 2220, 2221, 2222, 10000, 10001, 10002, 10010, 10011, 10012, 10020, 10021, 10022, 10100, 10101, 10102, 10110, 10111, 10112, 10120, 10121, 10122, 10200, 10201, 10202, 10210, 10211, 10212, 10220, 10221, 10222, 11000, 11001, 11002, 11010, 11011, 11012, 11020, 11021, 11022, 11100, 11101, 11102, 11110, 11111, 11112, 11120, 11121, 11122, 11200, 11201, 11202, 11210, 11211, 11212, 11220, 11221, 11222, 12000, 12001, 12002, 12010, 12011, 12012, 12020, 12021, 12022, 12100, 12101, 12102, 12110, 12111, 12112, 12120, 12121, 12122, 12200, 12201, 12202, 12210, 12211, 12212, 12220, 12221, 12222, 20000, 20001, 20002, 20010, 20011, 20012, 20020, 20021, 20022, 20100, 20101, 20102, 20110, 20111, 20112, 20120, 20121, 20122, 20200, 20201, 20202, 20210, 20211, 20212, 20220, 20221, 20222, 21000, 21001, 21002, 21010, 21011, 21012, 21020, 21021, 21022, 21100, 21101, 21102, 21110, 21111, 21112, 21120, 21121, 21122, 21200, 21201, 21202, 21210, 21211, 21212, 21220, 21221, 21222, 22000, 22001, 22002, 22010, 22011, 22012, 22020, 22021, 22022, 22100, 22101, 22102, 22110, 22111, 22112, 22120, 22121, 22122, 22200, 22201, 22202, 22210, 22211, 22212, 22220, 22221, 22222, 100000)

If you count them, you will find that there are 289 numbers in total!

8 0

3 years ago

Identify the parent function that can be used to graph the function f(x)=-9(x+5)^2

svetoff [14.1K]

Answer:

Option a) f(x)=x^2

Step-by-step explanation:

The parent function that can be used to graph the function f(x)=-9(x+5)^2 is f(x)=x^2

8 0

3 years ago