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kolbaska11 [484]

4 years ago

15

Algebra question, show steps of how to solve 1=k+14

1 answer:

shtirl [24]4 years ago

6 0

Answer:

k=-13

Step-by-step explanation:

1=k+14

1) Subtract 14 from both sides to <u>ISOLATE</u> k:

k=-13

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Given the set of vertices, determine whether parallelogram ABCD is a rhombus, rectangle or square. List all that apply. A(7,-4),

Sloan [31]

Given:

Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).

To find:

Whether the parallelogram ABCD is a rhombus, rectangle or square.

Solution:

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula, we get

$AB=\sqrt{(-4-(-4))^2+(-1-7)^2}$

$AB=\sqrt{(-4+4)^2+(-8)^2}$

$AB=\sqrt{0+64}$

$AB=8$

Similarly,

$BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8$

$CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8$

$AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8$

All sides of parallelogram are equal.

$AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}$

$BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}$

Both diagonals are equal.

Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.

We know that, a square is special case of rectangles and rhombus.

So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.

7 0

3 years ago

Jada purchases a sweater for $36. The store charges her 8% sales tax on the purchase. How much sales tax will the store charge o

dusya [7]

Answer:

Step-by-step explanation:

36/100=0.36 - 1%

8*0.36=2.88$

6 0

3 years ago

Select the correct answer.

masya89 [10]

Answer:

D

Step-by-step explanation:

Either try all the numbers and see which ones work or do the following.

Times both sides by 2x-5.

3=x(2x-5)=2x^2-5x

Rearrange and solve the quadratic. I will factorise.

2x^2-5x-3=0

(2x+1)(x-3)=0

so x = -1/2 or 3

6 0

3 years ago

A resident of Bayport claims to the City Council that the proportion of Westside residents

Kazeer [188]

Answer:

The test statistics is $z = -1.56$

The p-value is $p-value = 0.05938$

Step-by-step explanation:

From the question we are told

The West side sample size is $n_1 = 578$

The number of residents on the West side with income below poverty level is $k = 76$

The East side sample size $n_2=688$

The number of residents on the East side with income below poverty level is $u = 112$

The null hypothesis is $H_o : p_1 = p_2$

The alternative hypothesis is $H_a : p_1 < p_2$

Generally the sample proportion of West side is

$\^{p} _1 = \frac{k}{n_1}$

=> $\^{p} _1 = \frac{76}{578}$

=> $\^{p} _1 = 0.1315$

Generally the sample proportion of West side is

$\^{p} _2 = \frac{u}{n_2}$

=> $\^{p} _2 = \frac{112}{688}$

=> $\^{p} _2 = 0.1628$

Generally the pooled sample proportion is mathematically represented as

$p = \frac{k + u}{ n_1 + n_2 }$

=> $p = \frac{76 + 112}{ 578 + 688 }$

=> $p =0.1485$

Generally the test statistics is mathematically represented as

$z = \frac{\^ {p}_1 - \^{p}_2}{\sqrt{p(1- p) [\frac{1}{n_1 } + \frac{1}{n_2} ]} }$

=> $z = \frac{ 0.1315 - 0.1628 }{\sqrt{0.1485(1-0.1485) [\frac{1}{578} + \frac{1}{688} ]} }$

=> $z = -1.56$

Generally the p-value is mathematically represented as

$p-value = P(z < -1.56 )$

From z-table

$P(z < -1.56 ) = 0.05938$

So

$p-value = 0.05938$

3 0

4 years ago

The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 6 inches and an un

liubo4ka [24]

Answer: 2.460

Step-by-step explanation:

The formula of Margin of Error for (n<30):-

$ME=t_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n= 18

Level of confidence = 0.90

Significance level : $\alpha=1-0.90=0.1$

Using the t-distribution table ,

Critical value : $t_{n-1, \alpha/2}=t_{17,0.05}= 1.7396$

Standard deviation: $\sigma=\text{ 6 inches }$

Then, we have

$ME=( 1.7396)\dfrac{6}{\sqrt{18}}\approx2.460$

Hence, the margin of error (ME) of the confidence interval with a 90% confidence level = 2.460

5 0

3 years ago