Which shows the correct first step to solving the system of equations in the most efficient manner ? 3x+2y=17 x+4y=19

Answer:

Explanation:

The vertices of the figure 1 are:

The vertices of figure 2 are:

By simple inspection, you can tell that if you rotate the figure 1 90º clockwise and then reflect the image across the x-axys you obtain the figure 2.

You can prove that analitically.

1. Rotation 90º clockwise

A 90º clockwise reotation is the same that a 270º counterclockwise rotation and the mathematical rule for this is:

Applying that rule to the vertices of figure 1, you obtain:

2. Reflection across the x-axis.

A reflection across the x-axis keeps the same x-coordinate and changes the sign of the y-coordinate. The rule is:

Applying that rule to the previous points yields to:

Which are the coordinates of the figure 2. Thus, you have proved that the sequence of transformations 90° clockwise rotation around the origin, then a reflection across the x-axis (first choice) maps the figure 1 to figure 2.

Answer:

First choice: 90° clockwise rotation around the origin, then a reflection across the x-axis.

Step-by-step explanation:

Answer: Answer is 40%

Step-by-step explanation: The total number of players in the game is 30 (that is boys and girls added together becomes 18 + 12= 30) altogether which is a hundred percent. The percentage of girls playing the game is calculated as;

12/30 × 100%

=2/5 × 100%

=200/5

=40%

Answer:A

Step-by-step explanation:

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Explanation:

Using a calculator,

3/8 = 0.375

The decimal stops and does not go on forever. So it is terminating.

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One way to be able to tell that it terminates is to look at the denominator 8, which factors to 2*2*2 or 2^3. The prime factor 2 indicates that the decimal will terminate. The rule is that if the denominator is factored into 2's or 5's only, then the decimal will terminate.

Examples:

1/5 = 0.2,   4/10 = 0.4,   5/8 = 0.625

Some non-examples would be

1/3 = 0.333333...

5/6 = 0.83333....

2/7 = 0.285714...

Each denominator of these non-terminating fractions do not have solely 2's or 5's as part of the factorizations.

Bisecting diagonals

Two pair of opposite parallel sides

Two pair of opposite equal angles

Solution:

Let us first define the properties of parallelogram.

Now, let us define the properties of square.

From these properties, we can conclude that  every square can always be classified as a parallelogram if

Bisecting diagonals

Two pair of opposite parallel sides

Two pair of opposite equal angles

The 3 angles when added together make a straight line which is 180 degrees. To find x subtract the 2 known angles from 180.

The answer would be x = 180 - (67 + 52)

Answer:

-212.5

Step-by-step explanation:

-212.5 x 0.4 = -85

Final answer:

The student's question regarding dividing -85 by 0.4 results in -212.5. You divide the absolute values first and then apply the negative sign because dividing a negative by a positive yields a negative result.

Explanation:

The student is asking how to divide a negative number by a positive decimal number. Specifically, the question is about dividing -85 by 0.4. To perform this division, we'll divide the absolute values and then apply the negative sign to the result. The steps are as follows:

The division of a negative number by a positive number results in a negative outcome. Hence, -85 divided by 0.4 equals -212.5.

Final answer:

To find the length of the altitude of an equilateral triangle with a perimeter of 36 inches, divide the perimeter by 3 to get the side length, then calculate the altitude using the formula for a 30-60-90 right triangle, resulting in an altitude length of 6\(\sqrt{3}\) inches.

Explanation:

To solve for the length of the altitude of an equilateral triangle with a perimeter of 36 inches, we first need to determine the length of one side of the triangle. Since an equilateral triangle has all sides of equal length, we divide the perimeter by 3 to find the length of one side:

Side length = Perimeter ÷ 3 = 36 inches ÷ 3 = 12 inches

Now, let's draw the equilateral triangle and an altitude. An altitude in an equilateral triangle splits the triangle into two 30-60-90 right triangles. In such a right triangle, the length of the altitude (which is the same as the longer leg) is \(\sqrt{3}/2\) times the length of the shorter leg (which is the side of the original equilateral triangle).

Hence, the altitude (h) can be calculated as:

Altitude (h) = Side length × (\(\sqrt{3}/2\)) = 12 inches × (\(\sqrt{3}/2\)) = 6\(\sqrt{3}\) inches

Therefore, the length of the altitude is 6\(\sqrt{3}\) inches.

Answer:

fraction > -18/5

dec> -3.6

Step-by-step explanation:

In this question, you're trying to transform the equation into slope intercept form.

Slope intercept form equation:

y = mx + b

In this case, you would need to get the "y" variable by itself.

To do so, you would subtract -2x from both sides:

2x + y = 2

y = -2x + 2

Answer:

y = -2x + 2

The equation of the line 2x + y = 2 in slope-intercept form is y = -2x + 2.

The equation of a line is expressed as;

y = mx + b

Given the equation of the line in the question:

2x + y = 2

To convert the equation 2x + y = 2 into slope-intercept form (y = mx + b), where "m" represents the slope and "b" is the y-intercept, follow these steps:

First, Isolate "y" on one side of the equation by moving the term with "x" to the other side.

2x + y = 2

Subtract 2x from both sides:

2x - 2x + y = 2 - 2x

y = 2 - 2x

Rearrange:

y = -2x + 2

Therefore, the slope-intercept form is y = -2x + 2.

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Answer:

The Amount paid by dealers is $20464.75    

Step-by-step explanation:

Given as :

The base price of car = $23,800

The option cost of car stereo = x = $365

The option cost of car wheels and paint = y = $900

Total option cost = $365 + $900

The charges of destination = $640

The Amount paid by dealer = 82% of total base price + 75% of total option cost

Let The Amount paid by dealers = $A

Now, According to question

The Amount paid by dealers =  82% of total base price + 75% of total option cost

i.e A = [tex]\dfrac{82}{100}[/tex] × total base price +  [tex]\dfrac{75}{100}[/tex] × total option cost

Or, A = [tex]\dfrac{82}{100}[/tex] × total base price +  [tex]\dfrac{75}{100}[/tex] × (x + y)

Or, A = [tex]\dfrac{82}{100}[/tex] × $23,800 +  [tex]\dfrac{75}{100}[/tex] × ($365 + $900)

Or, A = [tex]\dfrac{82}{100}[/tex] × $23,800 +  [tex]\dfrac{75}{100}[/tex] × $1265

Or, A = 82 × $238 +  75 × 12.65

Or, A = $19,516 + $948.75

Or, A = $20464.75

So, The Amount paid by dealers = A = $20464.75

Hence, The Amount paid by dealers is $20464.75       Answer

Answer:

x<6

Step-by-step explanation:

4x-13<11

4x<11+13

4x<24

x<24/4

x<6

Try to leave a screenshot of the answers if you can please! Here's the graph for that function :D

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Answer:

Step-by-step explanation:

Let our number be “ xy ”

the tens digit is four less than the units digit means y-4=x

Seven times the tens digit plus five times the units digit is equal to 56 means

7x+5y=56

now we have to solve the system:

y-4=x  (1)

7x+5y=56  (2)

(1) ⇒ y=4+x

Then we substitute y by 4+x into the second equation like this:

7x+5(x+4)=56

⇔ 7x+5(x+4)=56

⇔ 12x+20=56

⇔ x = 3

now using equation (1) we get : y=3+4 = 7

:)

Answer:

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

List your factors first to find the answer

36: 1-36, 2-18, 3-12, 4-9, 6-6

90: 1-90, 2-45, 3-30, 5-18, 6-15, 9-10

Now find in the factors which would be the greatest/largest. The largest factor shared between 36 and 90 is 18.

Answer:

Step-by-step explanation:

Tom and Dipak share $114 in the ratio 7:5

Total amount shared = $114

Ratio of Tom to Dipak = 7:5

Total ratio = 7+5 = 12

Dipak got = 5/12 × $114 = $ 47.5

Answer:

4n(7+3-6)

Step-by-step explanation:

 28n              12n .               24n  

14 .   2 .        6 .  2              12 .   2

7 . 2 . 2 n .   3 . 2 . 2  n .     6 . 2

7                     3                     3 . 2 . 2 . 2  n

                                                  3x2=6

2x2xn=4n

GCF=4n

Answer:

16n

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{Domain:}\ x>0\\\\\log_83+\dfrac{1}{2}\log_825=\log_8x\qquad\text{use}\ n\log_ab=\log_ab^n\\\\\log_83+\log_825^\frac{1}{2}=\log_8x\qquad\text{use}\ a^\frac{1}{2}=\sqrt{a}\\\\\log_83+\log_8\sqrt{25}=\log_8x\\\\\log_83+\log_85=\log_8x\qquad\text{use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_8(3\cdot5)=\log_8x\\\\\log_815=\log_8x\iff15=x\to x=15\in D[/tex]

Answer:

Your answer would be x = 15

I hope his helped and have a wonderful day!

~Real

Answer:

x=14

y=10

Step-by-step explanation:

The median divide the data‘s set into two parts with the same frequency = 50%

then we must have 2+5+x+12+17 = 50 ⇔ 36+x=50 then x =50-36=14

also 20+y+9+7+4=50 ⇔ y=10

Answer:

50-6=14

Step-by-step explanation:

just do the math and then you will find the answer

Final answer:

To find the two numbers whose sum is 38 and difference is 16, we set up and solve a system of equations, which reveals the numbers to be 27 and 11.

Explanation:

The question involves finding two numbers when their sum and difference are known. To solve it, we can set up a system of equations based on the information provided. Suppose the two numbers we are trying to find are X and Y. According to the question, the sum of the two numbers is 38, and their difference is 16. Therefore, we can write the following equations:

Equation 1: X + Y = 38

Equation 2: X - Y = 16

To find the values of X and Y, we can add these two equations to eliminate Y. This gives us 2X = 54, which simplifies to X = 27. Substituting the value of X back into Equation 1, we find that Y = 11. Thus, the two numbers are 27 and 11.

Answer:

[tex]y-8=-5(x-7)[/tex]

Step-by-step explanation:

we know that

The equation of the line in point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-5\\(x1,y1)=(7,8)[/tex]

substitute

[tex]y-8=-5(x-7)[/tex]

Answer:

C. 560

Step-by-step explanation:

50% is one half, so there is another half of 280. 280*2=560

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter = 2(l + w)

Perimeter = 464inches

Length l = 100inches

: 464 = 2(100 + w)

Dividing be 2

464/2 = 100 + w

232 = 100 + w

Collecting like terms

232 - 100 = w

132 = w

It is 132 inches long

Answer:

Step-by-step explanation:

multiples of 4

12/3 = 4

16/4 = 4

4/1 = 4

24/6 = 4

36/9 = 4

The integer 4 can be represented as a fraction by placing it over 1. Therefore, the fraction that represents the integer 4 is 4/1 and it is already in its simplest form.

The integer 4 can be represented as a fraction simply by placing it over 1. Hence, the fraction equivalent of the integer 4 is 4/1. However, it's noteworthy to mention that a fraction can be simplified when the numerator and the denominator have a common factor, other than 1. In this case, there are no other common factors between 4 and 1, so it is already in its simplest form.

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Answer:

She is not correct.

Step-by-step explanation:

If she originally purchases the teas for $100 and then she marks the price up 20%, the retail price would then be 100 + 0.20(100) = 100 + 20 = 120. The sales price would then be 120 - 0.2(120) = 120 - 24 = 96. This is less than the purchase price, so she is losing money, rather than gaining.

I hope this helps. If you download an app called Slader, it has the same math book you are using with the answers.

Step-by-step explanation:

9.

Given that, the measure of [tex]\angle A[/tex] is [tex]45^\circ[/tex]. The measure of [tex]\angle B[/tex]is [tex]b^\circ[/tex]. The measure of[tex]\angle C[/tex] is [tex]3b^\circ[/tex] .

We know that the sum of all angles of triangle is [tex]180^\circ[/tex].

Therefore

[tex]45^\circ + b^\circ +3b^\circ =180^\circ[/tex]

⇔[tex]4b^\circ[/tex] = [tex]135^\circ[/tex]

10.

Given that , the measure of [tex]\angle X[/tex] and [tex]\angle Y[/tex]are same [tex]x^\circ[/tex]. The angle of [tex]\angle Z[/tex] is twice the measure of [tex]\angle Y[/tex].

∴[tex]\angle X[/tex]+[tex]\angle Y[/tex]+[tex]\angle Z[/tex]=[tex]180^\circ[/tex]

⇔[tex]x^\circ[/tex]+[tex]x^\circ[/tex]+2[tex]x^\circ[/tex]=[tex]180^\circ[/tex]

⇔4[tex]x^\circ[/tex]= [tex]180^\circ[/tex]

Answer:

Step-by-step explanation:

[tex]n+1=4(n-8)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\n+1=(4)(n)+(4)(-8)\\\\n+1=4n-32\qquad\text{subtract 1 from both sides}\\\\n+1-1=4n-32-1\\\\n=4n-33\qquad\text{subtract}\ 4n\ \text{From both sides}\\\\n-4n=4n-4n-33\\\\-3n=-33\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3n}{-3}=\dfrac{-33}{-3}\\\\n=11[/tex]