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3 years ago

Solve the system of equations using the substitution method (pic) x=y=

Mathematics

2 answers:

Flura [38]3 years ago

8 0

Answer:

(-2,3)

Step-by-step explanation:

kondor19780726 [428]3 years ago

6 0

Answer: x= -2 and y= 3

Step-by-step explanation:

The given system of linear equations :

$4x+5y=7--------------(1)\\\\ y=3x+9-----------------(2)$

By using Substitution method , we substitute the value of y from (2) in (1) , we get

$4x+5(3x+9)=7$

$\Rightarrow\ 4x+15x+45=7$

$\Rightarrow\ 19x=7-45$

$\Rightarrow\ 19x=-38$

$\Rightarrow\ x=-2$ [Divide both sides by 2]

Now , put the value of x in (2) , we get

$y=3(-2)+9=-6+9=3$

∴ x= -2 and y= 3 .

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Write the ratio of the first measurement to the second measurement. Compare in inches 4 feet to 60 inches

Lunna [17]

Answer:

4:5

Step-by-step explanation:

Recall that 12 inches =1 foot

Therefore 4 feet = 12*4=48 inches

$\frac{4ft}{60 \: inch} = \frac{48 \: inches}{60 \: inches} = \frac{4 \times 12}{5 \times 12} = \frac{4}{5}$

The ratio of 4 feet to 60 inches is 4:5

This ratio is in the reduced form, we cannot simplify further.

7 0

4 years ago

Draq is painting a rectangular wall that is 15 ft. Long and 8ft. High. The wall has three Windows, each measuring 3 ft. by 4ft.

Blizzard [7]

Total area of rectangular wall = 8ft * 15ft = 120 ft²

Each window area = 3ft *4ft = 12 ft²

For the three windows = 3 * 12 = 36 ft²

Area that must be painted = 120ft² - 36ft² = 84 ft²

7 0

3 years ago

Find the slope and the y-intercept of the line. 6x+2y= -4

hodyreva [135]

Answer:

slope is -3

y-intercept is -2

Step-by-step explanation:

3 0

3 years ago

The article cited in Exercise 41 in Chapter 7 gave the following data on work of adhesion measurements (in mJ/m2) for samples of

weqwewe [10]

Answer:

Step-by-step explanation:

Hello!

You have the information of two samples taken from two different normal populations,

Sample 1

Steel: 107.1, 109.5, 107.4, 106.8, 108.1

X₁: work adhesion of ultra-high performance concrete to the steel substrate (mj/m²)

n₁= 5

X[bar]₁= 107.78

S₁²= 1.16

S₁= 1.08

Sample 2

Glass: 122.4, 124.6, 121.6, 120.6, 123.3

X₂: work adhesion of ultra-high performance concrete to the glass substrate (mj/m²)

n₂= 5

X[bar]₂= 122.50

S₂²= 2.37

S₂= 1.54

You need to test the claim that the mean work of adhesion for the glass substrate is more than 12 mj/m² higher than that for the steel substrate, i.e. that the difference between the mean work adhesion for the glass substrate and the mean work adhesion for the steel substrate is greater than 12 mj/m², symbolically: μ₂ - μ₁ > 12

Then the statistic hypotheses are:

H₀: μ₂ - μ₁ ≤ 12

H₁: μ₂ - μ₁ > 12

There is no significant level listed, I'll use 5%

Since both populations are normal and the sample sizes are quite small beside the population variances are unknown but can be assumed equal, you have to use a t-test for independent samples and pooled sample variance:

$t= \frac{(X[bar]2-X[bar]_1)(Mu_2-Mu_1)}{Sa*\sqrt{\frac{1}{n_2} +\frac{1}{n_1} } } ~~ t_{n_1+n_2-2}$

$Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{4*1.16+4*2.37}{5+5-2} } = 1.328= 1.33$

$t_{H_0}= \frac{(122.50-107.78)-12}{1.33*\sqrt{\frac{1}{5}+\frac{1}{5} } } = 3.23$

Using the critical value approach, this test is one-tailed to the right, which means that you will reject the null hypothesis at great values of t, the critical value is:

$t_{n_1+n_2-2;1-\alpha }= t_{5+5-2;1-0.05}= t_{8;0.95}= 1.860$

The deicision rule is:

If $t_{H_0}$ ≥ 1.860, you reject the null hypothesis

If $t_{H_0}$ < 1.860, you do not reject the null hypothesis.

The calculated t-value is greater than the critical value, the decision is to reject the null hypothesis.

Using a significance level of 5% there is significant evidence to conclude that the true average work of adhesion for the glass substrate is more than 12 mj/m² higher than that for the steel substrate.

I hope you have a SUPER day!

7 0

3 years ago

Solve for the proportion below. x/24=5/6 A. 20 B. 10 C. 12 D. 23

Andrei [34K]

Answer:20

Step-by-step explanation:

x/24=5/6

multiply both sides by 24

x=(5*24)/6

simplify

x=5*4

x=20

6 0

4 years ago

Solve the system of equations using the substitution method (pic) x=y=​

Solve the system of equations using the substitution method (pic) x=y=