(High points) Please solve with explanation

Answer:

None, each of the four given system of equations have only one solution

Step-by-step explanation:

A system of equations have infinitely many solutions, when the equations represent the same line and therefore, the two equations are the same;

Each of the options are examined as follows;

a. 4·x + 2·y = 5...(1)

-4·x - 2·y = 1...(2)

Expressing both equations with y as the subject, we have;

The value of y in equation (1) is given as follows;

4·x + 2·y = 5

2·y = 5 - 4·x

∴ y = 5/2 - 2·x

The value of y in equation (2) is given as follows;

-4·x - 2·y = 1

-2·y = 1 + 4·x

∴ y = -1/2 - 2·x

Therefore, equation (1) and equation (2) represent the same equation and are therefore equal and have only one solution

b. -10·x + y = 4...(1)

10·x - y = 4...(2)

Therefore, we have;

Adding equation (1) to equation (2) gives;

-10·x + 10·x + y - y = 4 + 4

0 + 0 = 8

0 = 8

Given that 0 ≠ 8, equation (1) is not equal to equation (2) and the two equations have only one solution

c. -8·x + y = 2...(1)

8·x - y = 0...(2)

By examination, the values on the left hand side, LHS, of both equations are the same magnitude but opposite in sign, while the right hand side, RHS, of both equations, have different magnitude

Therefore, the two equations are different and have only one solution

d. -x + 2·y = 6...(1)

7·x - 2·y = 12...(2)

Making y the subject of both equations gives;

Equation (1)

2·y = 6 + x

y = 3 + x/2

Equation (2)

2·y = 12 - 7·x

y = 6 - 3.5·x

Therefore, the two equations are different and have only one solution

Answer:

B

Step-by-step explanation:

I'm guessing the answer is B. I know why the other person said all of them only have one solution. But, On b You wrote -10x+y=4  10x-y=4

When really it was supposed to be -10x+y=4  10x-y=-4

Answer:

4/5

Step-by-step explanation:

The first point (-4, -7) lies in the third quadrant and the second one in the first quadrant.  This tells us immediately that the slope is positive; y increases as x increases.  The change in x is 4 - (-4), or 8; this is the 'run.'  The change in y  is 3 - (-7), or 10; this is the 'rise.'

Thus the slope of this line is m = rise/run = m = 8/10, or m = 4/5

Answer:

283 people went this year to the stadium.

Step-by-step explanation:

Let's put this data into pieces so it's less overwhelming.

Last year 260 students went to the prom.

Currently the number of students who attended has increased by 9% from last year.

And the question is asking how many students attended this year?

Well, if this is increasing by 9%, wouldn't we just find 9% of 260 then add it to 260?

0.09 * 260 = 23.4

260 + 23.4 = 283.40. Obviously we can't have 40% of a human being, so let's round it to 283.

Answer:

The surface area of cylinder is 244.92 inches²

hope it helps

have a nice day

Answer:

m∠6 = 116°

Step-by-step explanation:

first find x:

7x - 17 = 2x + 78

subtract 2x from both sides: 5x - 17 = 78

add 17 to both sides: 5x = 95

divide by 5: x = 19

plug x into 7x - 17

7(19) - 17 = 116

∠6 and 7x - 17 are vertical angles and therefore congruent, so m∠6 also = 116°

Answer:

9km

Step-by-step explanation:

30-(13+8)=9km

I hope you understand

Answer:

[tex]\text{A. }\frac{4\sqrt{14}}{{7}}[/tex]

Step-by-step explanation:

In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Therefore, we can form a right triangle with non-right angle [tex]\theta[/tex] and its opposite side [tex]\sqrt{7}[/tex] and its adjacent side [tex]5[/tex].

By definition, [tex]\csc \theta=\frac{1}{\sin\theta}[/tex].

In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle. To find the hypotenuse, use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side, of the right triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.

Solving, we get:

[tex]5^2+\sqrt{7}^2=c^2,\\25+7=c^2,\\c^2=32,\\c=\sqrt{32}=4\sqrt{2}[/tex]

Therefore, we have:

[tex]\csc \theta = \frac{1}{\sin \theta}=\frac{1}{\frac{\sqrt{7}}{4\sqrt{2}}},\\\\\csc \theta=1\cdot \frac{4\sqrt{2}}{\sqrt{7}},\\\\\csc \theta =\frac{4\sqrt{2}}{\sqrt{7}}\cdot \frac{\sqrt{7}}{\sqrt{7}}=\boxed{\text{A. }\frac{4\sqrt{14}}{{7}}}[/tex]

Answer: Choice A)   [tex]\frac{4\sqrt{14}}{7}[/tex]

======================================================

Explanation:

Refer to the figure below. We start off drawing a right triangle that has opposite side sqrt(7) and adjacent side 5.

This is because tan = opposite/adjacent.

Use the pythagorean theorem to find the hypotenuse is sqrt(32) which simplifies like so

sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)

The last thing to do is to take the ratio of the hypotenuse over the opposite side. Recall that csc, aka cosecant, is the reciprocal of sine.

sin = opposite/hypotenuse

csc = hypotenuse/opposite

---------

So we get the following

[tex]\csc{\theta} = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc{\theta} = \frac{4\sqrt{2}}{\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2}*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2*7}}{\sqrt{7*7}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{\sqrt{49}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{7}\\\\[/tex]

So that's why the answer is choice A.

Answer:

O C. x = 3

Step-by-step explanation:

If a line is parallel to y-axis, the equation of the line is x = constant because it is at a constant distance from y-axis. so for the given question, x = 3 is the equation of the line passing through (3,2).

Given:

[tex]8x^3+20x^2+36[/tex] divided by [tex](2x+6)[/tex].

To find:

The quotient by using long division method.

Solution:

We have,

Dividend = [tex]8x^3+20x^2+36[/tex]

Divisor = [tex](2x+6)[/tex]

Using long division method we get

[tex]\underline{2x+6}|\overline{8x^3+20x^2+0x+36}|\underline{4x^2-2x+6}[/tex]

          [tex]\underline{8x^3+24x^2}[/tex]

                   [tex]-4x^2+0x[/tex]                                 (After subtraction)

                  [tex]\underline{-4x^2-12x}[/tex]

                             [tex]12x+36[/tex]                          (After subtraction)

                             [tex]\underline{12x+36}[/tex]

                                [tex]\underline{\quad 0\quad }[/tex]                           (After subtraction)

The quotient is [tex]4x^2-2x+6[/tex].

Therefore, the correct option is C.

Answer:

Step-by-step explanation:

6x² + 108x + 707  = 5

Subtract 707 from both sides

6x² + 108x = 5 - 707

6x² + 108x = - 705

Divide the whole equation by 6

[tex]\frac{6x^{2}}{6}+\frac{108x}{6}= \frac{-702}{6}\\\\x^{2}+ 18x = - 117\\[/tex]

Divide 18 by 2 = 9

Add 9² to both sides

x² + 18x + 9² = -117 + 9²

x² + 18x  + 81 = -117 + 81

(x + 9)² = - 36

Answer:

(x + 9)^2 = -36

Step-by-step explanation:

6x^2 + 108x + 707 = 5

6x^2 + 108x = -702

x^2 + 18x = -117

x^2 + 18x + (18/2)^2 = -117 + (18/2)^2

x^2 + 18x + 81 = -117 + 81

(x + 9)^2 = -36

Now,

x + 35° = 180° ( Co - interior angle )

◆ x = 145°

Then,

◆ y = x = 145° ( Vertically Opposite angle )

Again,

v + 43° = 180° ( Co - interior angle )

◆ v = 137°

Then,

v + w = 180° (Co - interior angle )

137° + w = 180°

w = 180° - 137°

◆ w = 43°

I hope it's help you...

Mark me as brainliest...

Answer:

Dude wt,f? The answer is B. Obviously.

Step-by-step explanation:

COMMON SENSE

Answer:

(v - 6)(v + 4)

Step-by-step explanation:

v² - 2v - 24

v² + 4v - 6v - 24

v(v + 4) - 6(v + 4)

(v - 6)(v + 4)

Answer: True

Step-by-step explanation:

We know in every triangle all the angles add up to 180 so for triangle ABC if you add the 52 to the 90 you’ll find the answer to be 142 if you subtract this then from 180 you’ll find 38 to be your answer

Therefore if you add the 38 the 52 and the 90 you’ll get 180

Based only on the information given in the diagram, it is guaranteed that Δ ABC ≅ Δ XYZ. It is true that Δ ABC ≅ Δ XYZ. Option A is correct.

Triangles that are equivalent in terms of size and form are known as congruent triangles.

It is certain that XYZ gave simply the facts in the diagram, traingle ABC, and XYZ is similar. It is true that triangles XYZ and ABC are similar.

The angle of triangles ABC and XYZ is;

∠A= 180° -(90+52) = 38°

∠B= 90°

∠C=38°

∠X=38°

∠Y=90°

∠Z=180° -(90+38°) = 52°

∠B =∠Y=90°

Based only on the information given in the diagram, it is guaranteed that Δ ABC ≅ Δ XYZ. It is true that Δ ABC ≅ Δ XYZ.

Hence, option A is correct.

To learn more about the congruent triangle refer;

https://brainly.com/question/12413243

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Answer:

1.7ft

Step-by-step explanation:

Given data

Volume of tank=  300π 〖ft〗^3

Height of tank= 10ft

The expression for the volume of a cylinder is given as

Volume= πr^2h

Substitute

300π = π *r^2*10

300= r^2*100

3= r^2

r= √3

r= 1.7 ft

Hence the radius of the cylinder is 1.7ft

Answer:

theres 5 pigs and 5 chickens

Step-by-step explanation:

5 pigs 4 legs 5x4=20

5 chickens and 2 legs 5x2=10

20+10=30

Answer:

v = 27,000 mm³

Step-by-step explanation:

v = s³

v = 30³

v = 27,000 mm³

Answer:

.20$

Step-by-step explanation:

4 1/2=4.5

4.5 divided by 22.50=.20

Answer: Jennifer bought 4 1/2 pounds of hamburger for $22.50.

What was the cost per pound?

.20cents

Answer:

2370 cm²

Step-by-step explanation:

2(32·15+15·15+15·32) = 2370

Answer:

The 18 ounce bottle costs less per ounce and is the better buy

Step-by-step explanation:

First find the cost per ounce for the 18 ounce bottle

1.10 / 18 =.0611111 per ounce

Then find the cost per ounce for the 38 ounce bottle

2.75 / 36 =.076388888

The 18 ounce bottle costs less per ounce

Answer: See explanation

Step-by-step explanation:

The Simple Interest will be calculated as:

= P × R × T

= $3000 × 1.8% × 10.

= $3000 × 0.018 × 10

= $540

The interest that the customer earn in 10 years is $540.

Then, the account balance after 10 years will be:

= Principal + Interest

= $3000 + $540

= $3540

Therefore, the account balance will be $3540

Answer:

26

Step-by-step explanation:

Horizontally:

Like reading = 32

Do not like reading = ?

Total = 58

Total = Like reading + Do not like reading

Do not like reading = Total - Like reading

= 58 - 32

= 26

Do not like reading = 26

Vertically:

Like gardening =

Do not like gardening = 23

Total = 49

Total = Like gardening + Do not like gardening

Like gardening = Total - Do not like gardening

= 49 - 23

= 26

Like gardening = 26

Therefore,

The missing number in the table is 26

Answer:

920

Hope that this helps!

Answer:

2 x 2 x 2 x 3 x 5

Step-by-step explanation:

The first and smallest prime number that can be divisible by 120 is 2; 120/2 = 60, 60/2 = 30, 30/2 = 15; and the smallest prime number divisible by 15 is 3; 15/3 = 5; and the smallest prime number divisible by 5 is 5; 5/5 = 1.

hence, we have 2 x 2 x 2 x 3 x 5 = 2³ x 3 x 5

Answer:

x is greater than or equal to 3

Step-by-step explanation:

x ≥ 3

x is greater than or equal to 3

so you got the plot right

Answer:

Step-by-step explanation:

This is only my guess, as I haven’t done this topic in a few months

A. 398/427

0.93

B. 123/1192

0.10

C. 339/403

0.84

Step-by-step explanation:

there Are 120 possibilities for the top three positions

We will see that there are 120 different possibilities for the top 3 positions.

Here we need to count the number of options for each of the positions.

The total number of different combinations is given by the product between the numbers of options, we will get:

C = 6*5*4 = 120

There are 120 different possibilities for the 3 positions.

If you want to learn more about combinations, you can read:

https://brainly.com/question/11732255

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Answer:

Maria buys merchandise worth $ 2,000,000 which has an estimated profit of 25%, she wants to know the value that she will earn by selling all her merchandise. What will be the value that corresponds to Maria's earnings?

Step-by-step explanation:

2,500,000 $ worth of merchandise

Answer:

[tex]5.8609 \times {10}^{8} [/tex]

Step-by-step explanation:

[tex](3.09 \times 10^6)+(5.83 \times 10^8)[/tex]

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

[tex]5.8609 \times {10}^{8} [/tex]