HELP MATH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

7x - 2 = 2y

7x = 2y + 2

so

7x = 2y + 2

3x = 2y - 1  

----------------subtract

4x = 3

 x = 3/4

7x - 2 = 2y

7(3/4) - 2 = 2y

21/4 - 2 = 2y

21/4 - 8/4 = 2y

13/4 = 2y

so

y = 13/4 * 1/2

y = 13/8

answer

(3/4, 13/8)

Step-by-step explanation:

Answer:

The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Step-by-step explanation:

The rule we have is (x, y)→(2x, 2y).  This means that each x-coordinate and each y-coordinate are multiplied by 2.  This is a dilation by a factor of 2.

This will stretch the image by a factor of 2; this means the sides will be twice as long.  This means they will not be congruent.

Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .

Step-by-step explanation:

Rigid motions form congruent figures, the common rigid motions are:  

1) translation (moves figure about some distance)

2) reflection (creates mirror image)

3) rotation (rotate figure about some degrees)

Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .

Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

Here the coordinates of the image are increased by using a scale factor 2.

So △D′E′F′ must be an enlargement of △DEF.

⇒△D′E′F′ is a dilation of △DEF

It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

The chance that both the book are of statistics is [tex]\boxed{\dfrac{1}{21}}[/tex].

Further Explanation:

Given:

The total number of statistics book is [tex]2[/tex].

The total number of biology book is [tex]5[/tex].

Concept used:

Probability is defined as the ratio of favorable outcomes to total outcomes.

[tex]\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}[/tex].

Combination is defined as the selection of all or part of object without considering the order of the object.

[tex]\boxed{^{n}C_{r}=\dfrac{n!}{r!\cdot (n-r)!}}[/tex]

Here, [tex]n[/tex] is the total number of object and [tex]r[/tex] is the number of object to be chosen.

Calculation:

The total number of book is [tex]7[/tex].

The chance of getting the statistics books is the favorable outcomes for the problem.

The selection of two statistics book from two statistics book is represented as follows:

[tex]\boxed{^{2}C_{2}}[/tex]

The total outcomes can be obtained by selection of two books from seven books which is represented as follows:

[tex]\boxed{^{7}C_{2}}[/tex]

Write the formula to obtain the chance that both the books are statistics.

[tex]\boxed{P=\dfrac{^{2}C_{2}}{^{7}C_{2}}}[/tex]

Solve the above equation to obtain the chance that both the books are of statistics.

[tex]\begin{aligned}P&=\dfrac{^{2}C_{2}}{^{7}C_{2}}\\&=\dfrac{\frac{2!}{2!\cdot (2-2)!}}{\frac{7!}{2!\cdot (7-5)!}}\\&=\dfrac{1}{\frac{7\times 6}{2}}\\&=\dfrac{1}{21}\end{aligned}[/tex]

Therefore, the probability that the two selected books are of statistics is [tex]\boxed{\dfrac{1}{21}}[/tex].

Learn more:

1. Simplification: https://brainly.com/question/1602237

2. Quadratic equation: https://brainly.com/question/1332667

Answer details:

Grade: High school.

Subject: Mathematics.

Chapter: Probability.

Keywords: Probability, statistics, favorable, outcomes, total outcomes, 0.047, \frac{1}{{21}}, chance, biology books, 2, 7,  chances, randomly chosen.

The number 8 belongs to the sets of natural numbers, integers, rational numbers, and real numbers, while the number 0.25 only belongs to the sets of rational and real numbers.

In mathematics, numbers can belong to various sets such as the natural numbers, integers, rational numbers, real numbers, etc. In this case, the number 8 belongs to all these sets because it is a whole number without fractions or decimals. Therefore, it is a natural number, integer, rational number and real number.

On the contrary, 0.25 is a decimal which belongs to the sets of rational numbers and real numbers. It does not belong to the sets of natural numbers or integers because it is not a whole number.

https://brainly.com/question/32665385

Answer:

The answer is D. Hope it helps!

Plot the inequality on the number line. the graph is attached below.

Use the tool that has solid dots at both ends

Explanation :

Plot the inequality on the number line.

−7≤x≤−2

We start plotting the point at -7. we use closed circle at -7 because we have less than or equal to sign at -7

Now we plot another point at -2. here also we use closed circle that is solid circle .

Now shaded the region between -7 and -2 because x lies between -7 and -2

The graph of number line is attached below

The tool uses here is a line with solid dot at both ends

Learn more: brainly.com/question/13350310

The two numbers that multiply to 12 and add to negative 4 are -6 and 2.

To find the two numbers, we need to solve the system of equations:

1. xy = 12 (Equation 1)

2. x + y = -4  (Equation 2)

From Equation 2, we can express y in terms of x:

y = -4 - x (Equation 3)

Now, we substitute Equation 3 into Equation 1:

[tex]\( x(-4 - x) = 12 \)\\ \( -4x - x^2 = 12 \)\\ \( x^2 + 4x - 12 = 0 \)[/tex]

We can factor this quadratic equation:

[tex]\( (x + 6)(x - 2) = 0 \)[/tex]

Setting each factor equal to zero gives us two possible solutions for x:

[tex]\( x + 6 = 0 \) or \( x - 2 = 0 \)[/tex]

So, [tex]\( x = -6 \) or \( x = 2 \)[/tex].

Using Equation 3 to find the corresponding y values:

If ( x = -6 ), then ( y = -4 - (-6) = 2 ).

If ( x = 2 ), then ( y = -4 - 2 = -6 ).

Therefore, the two pairs of numbers that satisfy both conditions are (-6, 2) and (2, -6). Since the question asks for two numbers, and both pairs contain the same numbers, the answer is -6 and 2.

Counterexample:

[tex] p=2\\
q=3\\\\
pq-2=2\cdot3-2=4 [/tex]

4 is not a prime number. So, it's false.

A) Variable = x ( miles Tim walked )

B)  Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)

 Equation:  x + x+4 = 10

C) x +x+4 = 10

2x+4 = 10

2x =6

x = 3

D)

 Tim walked 3 miles, Molly walked 7 miles

Answer:

square root of 40

Step-by-step explanation:

a^(2)+b^(2)=c^(2)

3^(2)+b^(2)=7^(2)

9+b^(2)=49

9-9+b^(2)=49-9

b^(2)=40

sqr b^(2)=sqr 40

b=6.32455532034

therefore,the square root of 40 is the answer