What is the scale factor for the similar triangle?

Solve the system of linear equations by graphing.

Katyanochek1 [597]

The answer is a) x=-4.5, y=-4.25

6 0

2 years ago

Two mechanics worked on a car. The first mechanic charged S95 per hour, and the second mechanic charged S115 per hour.

Norma-Jean [14]

The first mechanic worked for 10 hours and the second mechanic worked for 15 hours.

Step-by-step explanation:

Given,

Charges of first mechanic = $95 per hour

Charges of second mechanic = $115 per hour

Total hours = 25

Total amount charged = $2675

Let,

The number of hours worked by first mechanic = x

The number of hours worked by second mechanic = y

According to given statement;

x+y=25 Eqn 1

95x+115y=2675 Eqn 2

Multiplying Eqn 1 by 95

$95(x+y=25)\\95x+95y=2375\ \ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(95x+115y)-(95x+95y)=2675-2375\\95x+115y-95x-95y=300\\20y=300$

Dividing both sides by 20

$\frac{20y}{20}=\frac{300}{20}\\y=15$

Putting y=15 in Eqn 1

$x+15=25\\x=25-15\\x=10$

The first mechanic worked for 10 hours and the second mechanic worked for 15 hours.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

6 0

3 years ago

Hey can you please help me posted picture of question

Maksim231197 [3]

For this case we have the following equation:
y = x2-4x + 3
Deriving we have the following equation:
y '= 2x-4
We equal zero and clear x:
2x-4 = 0
x = 4/2
x = 2
Substituting in the given equation we have:
y = (2) ^ 2-4 (2) +3
y = 4-8 + 3
y = -1
The vertex will be the ordered pair:
(x, y) = (2, -1)
Answer:
(x, y) = (2, -1)
option B

5 0

3 years ago

Read 2 more answers

Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing i

Nina [5.8K]

Answer:

$z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358$

$p_v =2*P(Z>5.358) = 4.2x10^{-8}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.

Step-by-step explanation:

Data given and notation

$X_{1}=253$ represent the number with no defects in sample 1

$X_{2}=196$ represent the number with no defects in sample 1

$n_{1}=300$ sample 1

$n_{2}=300$ sample 2

$p_{1}=\frac{253}{300}=0.843$ represent the proportion of number with no defects in sample 1

$p_{2}=\frac{196}{300}=0.653$ represent the proportion of number with no defects in sample 2

z would represent the statistic (variable of interest)

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

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference in the the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} - p_2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{253+196}{300+300}=0.748$

z-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

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.843-0.653}{\sqrt{0.748(1-0.748)(\frac{1}{300}+\frac{1}{300})}}=5.358$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>5.358) = 4.2x10^{-8}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that we have singificantly differences between the two proportions.

5 0

3 years ago

Which statement is true about the equations 3x + 4y = 12 and ¿-X- = = 1?

jarptica [38.1K]

Answer:

cfhjytgfhe5tgnbg5etjgnbg345jthgbyu6jtngfyu6jyh

Step-by-step explanation:

4 0

3 years ago