Solve the given system by the substitution method.
3x + y = 8
7x - 4y = 6​

Answers

Answer 1

Answer:

[tex]{ \tt{y = 8 - 3x}} - - - (i) \\ \\ = > 7x - 4(8 - 3x) = 6 \\ 7x - 32 + 12x = 6 \\ 19x - 32 = 6 \\ 19x = 38 \\ x = 2 \\ \\ = > y = 8 - 3(2) \\ y = 2[/tex]

Answer 2
3x+y=8, so
y=8-3x (rearranged)

7x-4y=6
7x-4(8-3x)=6 (substitute the value of y with 8-3x)
7x-32+12x=6
19x=38
x=2

y=8-3(2)
y=2

Related Questions

A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at
an angle of 38° at point B. The distance from A to B is 18 mi, and the distance from B to C is 12 mi (see
the figure). If the bicyclist can ride 22 mph on the paved roads and 6.8 mph off-road, would it be faster for the bicyclist to ride from A to C on the paved roads or to ride a direct line from A to C off-road? Explain.

Answers

Answer:

Step-by-step explanation:

The diagrammatic expression to understand this question very well is attached in the image below.

By applying the law of cosine rule; we have:

a² = b² + c² - 2bc Cos A --- (1)b² = a² + c² - 2ac Cos B --- (2)c² = a² + b² - 2ab Cos C --- (3)

From the diagram attached below, we need to determine the side "b" by using equation (2) from above:

b² = a² + c² - 2ac Cos B

From the information given:

a = 12 miles;  c = 18 miles;   ∠B = 38°

replacing the values into the above equation:

b² = 12² + 18² - 2(12)(18) Cos (38°)

b² = 144 + 324 - 432 × (0.7880)

b² = 468 - 340.416

b² = 127.584

[tex]b = \sqrt{127.584}[/tex]

b = 11.30 miles

However, we are also being told that the speed from A → C = 6.8 mph

Thus, the time required to go from A → C  can be determined by using the relation:

[tex]\mathbf{speed = \dfrac{distance}{time}}[/tex]

making time the subject of the formula, we have:

[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]

[tex]\mathbf{time= \dfrac{11.30}{6.8}}[/tex]

time = 1.66 hours

By using the paved roads, the speed is given as = 22 mph

thus, the total distance covered = |AB| + |BC|

= (18+12) miles

= 30 miles

[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]

[tex]\mathbf{time= \dfrac{30}{22}}[/tex]

time = 1.36 hours

Therefore, the time used off-road = 1.661 hours while the time used on the paved road is 1.36 hours.

Since we are considering the shortest time possible;

We can conclude that it would be faster for the bicyclist to ride from A to C on the paved roads since it takes a shorter time to reach its destination compared to the time used off-road.

Learn more about Law of cosine here:

https://brainly.com/question/24077856?referrer=searchResults

It would be faster for the bicyclist to ride from A to C on the paved roads since the time to go from A to C on the paved roads is 1.4 h and the time to go from A to C off-road is 1.7 h.        

To calculate which way would be faster we need to find the distance from point A to C with the law of cosines:

[tex] \overline{AC}^{2} = \overline{AB}^{2} + \overline{BC}^{2} - 2\overline{AB}\overline{BC}cos(38) [/tex]

Where:

[tex]\overline{AB}[/tex]: is the distance between the point A and B = 18 mi

[tex]\overline{BC}[/tex]: is the distance between the point B and C = 12 mi        

[tex] \overline{AC} = \sqrt{(18 mi)^{2} + (12 mi)^{2} - 2*18 mi*12 mi*cos(38)} = 11.3 mi [/tex]

Now, let's find the time for the two following cases.

1. From point A to C on the paved roads (t₁)

[tex] t_{1} = t_{AB} + t_{BC} [/tex]

The time can be calculated with the following equation:

[tex] t = \frac{d}{v} [/tex]    (1)

Where:

d: is the distance

v: is the velocity

Then, the total time that it takes the bicyclist to go from point A to C on the paved roads is:

[tex] t_{1} = t_{AB} + t_{BC} = \frac{18 mi}{22 mph} + \frac{12 mi}{22 mph} = 1.4 h = 84 min [/tex]

2. From point A to C off-road (t₂)

With equation (1) we can calculate the time to go from point A to C off-road:

[tex] t_{2} = \frac{\overline{AC}}{v_{2}} = \frac{11.3 mi}{6.8 mph} = 1.7 h = 102 min [/tex]

Therefore, it would be faster for the bicyclist to ride from A to C on the paved roads.  

To find more about the law of cosines, go here: https://brainly.com/question/15740431?referrer=searchResults  

I hope it helps you!                                  

9sin(Θ)-7=0. Solve the trigonometric equation

Answers

Step-by-step explanation:

here's the answer to your question

2. Solve the following system of equations. y = 5 + x 2x + 2y = 30

Answers

x = 5

since we know y= 5 + x , plug this into y in the second equation.

2x + 2 (5 + x) = 30

distribute 2 into the 5 and x

2x + 10 + 2x = 30

combine like terms

4x + 10 = 30

subtract 10 from both sides

4x = 20

divide four by both sides to isolate the variable

x = 5
Answer is d 1+2 y=5 add all cards

Sydney has finished all his work on time, but many of his teammates are still struggling to complete their assignments. What should he do? a) Not distract them; they may get farther behind. O b) Listen to them complain about their workloads O c) Help them complete their work d) Share his thoughts on how they could get their work done faster

Answers

Answer:

I think the correct option is c

Answer:

I think the correct answer is (d)

Step-by-step explanation:

if he shares his thoughts on how they could get their work done faster like using an app like this, then it would be of great help to them

Which could be a binomial expansion of (4x + y)?
16x2 + xy + y2
16x2 + 4xy + y2
O 64x3 + 16x2y + 5xy2 + y3
64x3 + 48x2y + 12xy2 + y3
+

Answers

Answer: D

Step-by-step explanation:

[tex](4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D[/tex]

Answer:

D

Step-by-step explanation:

Which statement is sufficient to prove that quadrilateral ABCD is a parallelogram?


A) m∠A ≅ m∠C, m∠B ≅ m∠D

B) AB ≅ CD

C) AC ≅ BD

D) BC // AD

Answers

Answer:

A) m∠A ≅ m∠C, m∠B ≅ m∠D

Step-by-step explanation:

If both pairs of opposite angles are congruent, then the figure is a parallelogram.

Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have following salaries (in $1000s): 70, 80, 90. The average and the standard deviation of the data in the sample are 80 and 10. Using hypothesis testing, determine if this sample provides a sufficient evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $60,000.
a. Null hypothesis.
b. alternative hypothesis.
c. test statistic.
d. acceptance region.

Answers

Answer:

H0 : μ = 60000

H1 : μ ≠ 60000

Test statistic = 3.464

Step-by-step explanation:

Given :

Sample mean salary, xbar = 80000

Sample standard deviation, s = 10000

Population mean salary , μ = 60000

Sample size, n = 3

Hypothesis :

H0 : μ = 60000

H1 : μ ≠ 60000

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (80000 - 60000) ÷ (10000/√(3))

T = 20000 / 5773.5026

T = 3.464

The Decison region :

If Tstatistic >Tcritical

Tcritical at 10%, df = 2 ; two - tailed = 2.9199

Tstatistic > Tcritical ; He

AABC is reflected across the x-axis and then translated 4 units up to create AA'BC. What are the coordinates of the vertices of AABC?

Answers

When Triangle ABC is reflected on the x-axis the new coordinates are A (-3,-1) B(-1,-3) C(-2,-1)

However the Triangle is then translated 4 units up, so the New and Final coordinates for Triangle ABC is A(-3,3) B(-1,0) and C(-2,4)

Hope this helps

PLEASE ANSWER
Triangle ABC is similar to triangle DEF. find the length of median CP
A. 12
B. 16
C. 24
D.48​

Answers

12/16 = (3x-12)/(2x+8)

16(3x-12)=12(2x+8)

48x-192=24x+96

48x-24x=192+96

24x=288

X=288/24

X=12

3x-12

=(12x3)-12

=36-12

=24

C is the answer

Hope this helps!

Answer:

48

Step-by-step explanation:

2x+8=3x-12(ABCP ~FDQE)

2x-3x= -8-12

-x= -20

x=20

now,

CP=3x-12

3*20-12

48

 evaluate P(6,2) or 6p2

Answers

Answer:

30

Step-by-step explanation:

Permutation equation: [tex]\frac{n!}{(n-r)!}[/tex]

n = Total number of objects, r = Number of objects selected

[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]


To prepare for the town's race, Andrew runs around a rectangular field. The dimensions of the field are 450 feet
by 225 feet. How many times must Andrew run around the field in order to run 12 miles? One mile is 5,280
fect.
Round the answer to one decimal place if necessary?

Answers

Answer:

46.9 times

Step-by-step explanation:

First, we can calculate how many feet it takes to run around the field. To find the perimeter of a rectangle, we can use the formula

2* length + 2 * width. With the length being 450 and the width being 225 here, we can say that

2*450 + 2 * 225 = 1350 feet

Therefore, Andrew runs 1350 feet each time he runs around the field. Next, we need to figure out how much 1350 feet goes into 12 miles as we want to find how many times Andrew runs around the field to get to 12 miles. This can be represented by

12 miles/1350 feet

One thing that we can do here is multiply the fraction by 1 to keep it the same. Because 1 mile = 5280 feet, we can say that

1 mile/5280 feet = 1 = 5280 feet/1 mile. Therefore, it would be safe to multiply

12 miles/1350 feet by 1 = 5280 feet/1 mile. Note that feet is on the bottom in the first fraction (12 miles/1350 feet) and on the top in the second (5280 feet/1 mile) so they will cancel out. Similarly, miles are on top in the first and bottom in the second. We then have

12 miles/1350 feet * 5280 feet/1 mile =63360/1350 ≈ 46.9

Let ​f(x)=−5x+18 and ​g(x)=x2+15.

Find ​f(−2​)−​g(−2​).

Answers

Answer:

21

Step-by-step explanation:

-5(-2)-(-2)²+15

10-(4)+15

10-4+15

21

Answer:

9

Step-by-step explanation:

f(x)=−5x+18

f(-2) = -5(-2)+18 = 10+18 = 28

​g(x)=x^2+15

g(-2) = (-2)^2 +15 = 4+15 = 19

f(02) - g(-2) = 28 - 19 = 9

Primo car rental agency charges $21 per day plus $0.20 por milo. Ultimo car rental agency charges $24 per day plus $1.00 per milo. Find the daily mileage for which the Ultimo charge is four times the Primo charge.
The mileage is

Answers

Answer:

300 miles

Step-by-step explanation:

Let us consider the miles they travelled is 'm'

Mileage for Primo= 21 + (m × 0.20) = 21+0.2m

Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m

Question says The mileage is equal when Ultimo's charge is 4× Primo

Thus,

4 × (21+0.2m) = 24+ m

84 + 0.8m = 24 + m

60 = 0.2m

m = 300

In an experiment, the initial temperature of a solution is -5 °C. The solution is heated up at 3 °C per minute for 19 minutes and then it is cooled at 4 °C per minute for 6 minutes. Calculate the final temperature, in °C, of the solution.​

Answers

Answer:

28°C

Step-by-step explanation:

First you do 3*19=57°C

-5+57= 52°C

then you do 4*6=24 °C

as its being cooled you takeaway

52-24=28°C

the area of a rectangular park is 7/8 sqaure mile. the length of the park is 3/4 mile. what is the width of the park?

Answers

Answer:

7/6

Step-by-step explanation:

since the formula of area is length times width,you have to divide the area by the length to find the width

area=length×width

the width will be

width=area÷length

=7/8÷3/4

7/8×4/3

7/2×1/3

7/6

that's the width you can prove it by multiplying the length times the width to see if you will get 7/8..

I hope this helps

look at the image below

Answers

Answer:

201.1 km²

Step-by-step explanation:

Surface area of the figure,

4πr²

= 4×π×4²

= 64π

= 201.1 km² (rounded to the nearest tenth)

For the partially complete factorization, find the other binomial which will complete the factorization n^2-8n-20=(n+2)(_____)

Answers

Answer:

(n-10)

Step-by-step explanation:

Jdjdjdhbejdudjkdff

vector v has a horizontal vector component with magnitude 19 and a vertical vector component with magnitude 35. what is the acute angle theta formed by v and positive x-axis?

Answers

9514 1404 393

Answer:

  61.5°

Step-by-step explanation:

The tangent relation is useful here. The angle is opposite the vertical side and adjacent to the horizontal side of the right triangle.

  Tan = Opposite/Adjacent

  tan(α) = 35/19

  α = arctan(35/19) ≈ 61.5°

The angle made by v and the positive x-axis is 61.5°.

You have $90 in your bank account. Each work you plan to deposit $3 from your allowance and $25 from your paycheck. The equation b: 90+ (25+5)w gives the amount b in your account after w woeks. How rary works from
now will you have $220 in your bank account?
There will be 5220 in the account after works
(Type a whole number

Answers

90+(25+8)W=220
33w=220-90
33w=130 /33
W = 3.94

What are the slope and the y-intercept of the linear function that is represented by the graph?

Answers

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

find the area of the shaded region

Answers

Answer:

22 cm²

Step-by-step explanation:

Shaded area is the difference of the bigger circle and two smaller ones:

A = π(3²) - 2π(1²) = 7π = 7*3.14 ≈ 22 cm²

HELPPPP PLZ
Witch statement is true about the value of |6|?

Answers

Answer:

The third choice is the correct one.

Step-by-step explanation:

The absolute value of six means that it's the distance from 0 to six, and that distance will be positive regardless of the number being negative or not.

Answer: The third answer is correct

Step-by-step explanation:

Since |6| is the absolute value of positive six, the value of an absolute value of any number is always positive.

Mariah owed her grandfather 52.25 but was recently able to pay him back $1.50. How much does Mariah currently
owe her grandfather?

Answers

Subtract 1.50 from 52.25.

The answer is 50.75.

Answer:

52.25 - 1.50 = 50.75

Step-by-step explanation:

I'd recommend using a calculator or pencil and paper

53.25

-  1.50

--------

50.75

Which of the following has the least value?

30% of 50
O 50% of 30
30% of 30
50% of 50

Answers

Answer:

30% of 30 has the least value out of all answer choices.

Step-by-step explanation:

Solve for the values of the given percentages of each number:

30% of 50:

Divide 50 by 100 to get 1%

50/100 = 0.5

Multiply 1% (0.5) by 50:

0.5 x 50 = 15

So 30% of 50 = 15

50 % of 30:

50% of a number means half of it since 50% is half of 100% so:

30/2 = 15

So 50% of 30 = 15

30% of 30:

Divide 30 by 100 to get 1%:

30/100 = 0.3

Multiply 1% (0.3) by 30:

0.3 x 30 = 9

So 30% of 30 = 9

50% of 50

50% of a number means half of it since 50% is half of 100% so:

50/2 = 25

So 50% of 50 = 25

Let’s arrange all of the values from greatest to least (left to right) to determine the most least value:

25, 15, 15, 9

9 is the most least, it is the value equal to the answer choice “30% of 30”

HOPE THIS HELPED!

what is the aswer to 5 is 2 more than?


Answers

Answer:

Cuz 5 is greater than 2

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

the guys is wrong i checked

Answers

Step-by-step explanation:

the guys is wrong i checked

Can some please help please thank you

Answers

Answer:

b the answer

Step-by-step explanation:

The answer to this is D

½ sejam berapa minit?​

Answers

Answer:

1/2 jam 30 menit mungkin?

1/2 jam adalah 30 minit

1/2 × 60 = 30 mins

English translation

1/2 an hour is 30 minutes

1/2 × 60 = 30 mins

Answered by Gauthmath must click thanks and mark brainliest

How do you complete the square of x2+8x+26?

Answers

Answer:

see below

Step-by-step explanation:

x^2+8x+26

Take the coefficient of the x term

8

Divide by 2

8/2 = 4

square it

4^2 =16

we need to add 16 to 26 = 16+10

x^2 + 8x+16  +10

(x+4)^2 +10

The answer you are looking for is (x+4)²+10.

Solution/Explanation:

Selecting the "x" term's coefficient,

It would be 8.

Now, dividing it by 2,

8/2=4.

Squaring 4,

4²=16.

So, now, since (x+4)²=x²+8x+16, you must solve for 26-16, which equals 10, which you would supplement into the equation.

So, therefore, (x+4)²+10.

I hope this has helped you. Enjoy your day.

if a circumference of a circle is 22cm.find it diameter take pie 22/7.

Answers

Answer:

Step-by-step explanation:

i know the answer ok it is easy

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