PQR is an isosceles triangle in which PQ = PR
M and N are points on PQ and PR such that angle MRQ = angle NQR.
D
Prove that triangles QNR and RMQ are congruent.
R

The value of a for system ax + 12y = −6, 2x − 6y = 4 having no solution is a = -4.

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

Given:

ax + 12y = −6

2x − 6y = 4

Calculate the value of a by using the condition of no solution of the system given below,

[tex]a_1 / a_2 = b_1 / b_2 \neq c_1/c_2[/tex]

So, a₁ / a₂ = b₁ / b₂

a / 2 = 12 / (-6)

a / 2 =  - 2

a = -4

And -4 / 2 ≠ -6 / 4

Therefore, the value of a for system ax + 12y = −6, 2x − 6y = 4 having no solution is a = -4.

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The answer to this question would be (B)

Answer: csc^2x+sec^2x=1

Step-by-step explanation:

The inverse of the given relation  {(5, 1), (4, -3), (3, -1)} is  {(1, 5), (-3, 4), (-1, 3).

The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.

The ordered pair (x, y) of f(x) becomes (y, x) of f⁻¹(x).

Given, A relation in form of a set of ordered pairs {(5, 1), (4, -3), (3, -1)} let this be f(x).

∴ The ordered pair of f⁻¹(x) will be {(1, 5), (-3, 4), (-1, 3).

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Answer: B

Step-by-step explanation:

Multiply matrices

AB = [ 4    5 ]       x    [   3   ]

        [ 8    7 ]             [   9   ]

4 x 3 + 5 x 9 = 12 + 45 = 57

8 x 3 + 7 x 9 = 24 + 63 = 87

[ 57 ]

[ 87 ]

The answer will be in the picture provided below!

Answer: √345600

Step-by-step explanation:

1st step: 10*6√96

2nd step: 60√96

3rd step:240√6

4th step (convert to radical form): √345600

there's your answer

The volume of the cube with a mass of 20 grams and a density of 6 g/cm³ is 3.33 cm³

From the question, we are to determine the volume of the given cube

From the given information,

The mass of the cube is 20 grams

and

The density of the cube is 6 g/cm³

From the formula,

Density = Mass / Volume

Then, we can write that

Volume = Mass / Density

Thus,

The volume of the cube is

Volume = 20/6

Volume = 3.33 cm³

Hence, the volume is 3.33 cm³

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By evaluating the function in x = -2, we will get:

f(-2) = -2

To do that, we need to evaluate the given linear equation:

f(x) = -x - 4

We want to find f(-2), so we need to evaluate the linear equation in x = -2, this means that we just need to replace the variable by the corresponding number.

Then we will get:

f(-2) = -(-2) - 4

f(-2) = +2 - 4

f(-2) = -2

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Answer:

  p = 8

Step-by-step explanation:

Given 4 equations in 4 unknown values, you want to find the value of p.

Substituting for c in the second equation, we have ...

  ts = (t +s) +t -s

  ts = 2t . . . . . . simplify

  s = 2 . . . . . . . divide by 2

Substituting for c and s in the third equation, we have ...

  3(t +2) = t +10·2

  2t = 14 . . . . . . . . . subtract t+6

  t = 7

Substituting for c, t, s in the equation for p gives ...

  p = ((t +s) +t)/s = (2·7 +2)/2 = 8

The value of p is 8.

__

Additional comment

The variable values are (c, p, s, t) = (9, 8, 2, 7).

The A ∩ B ∩ C = {0}, if  A = {1,3,5,7,9,11}, B = {2,4,6,8,12} and C = {5,10,15,20}.

Any group of objects (elements) in mathematics and logic, whether they are mathematical (such as numbers and functions), is referred to as a set.

Given:

Set A = {1,3,5,7,9,11},

B = {2,4,6,8,12},

C = {5,10,15,20}

Calculate the A ∩ B ∩ C by the formula given below,

A ∩ B ∩ C = {0}

As there is nothing common between sets A, B, and C.

Therefore, A ∩ B ∩ C = {0}.

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Answer: No

A correlation is a relationship between two variables that tend to move in the same direction. Therefore, a positive correlation will describe two variables that increase together. However, correlation does not always equal causation, and in this case, this conclusion cannot be made. A more probable explanation is that there is some third variable causing an increase in population, so more people are buying more cars, not the other way around.

The confidence interval gets broader as the confidence level rises because the error bound rises as well. The confidence interval gets narrower as the confidence level is reduced since the error bound is also reduced.

This can be the reason why  you might want to increase the confidence level, even though it means that precision is lost and the interval widens.

We must widen the distance in order to obtain greater trust. The multiplier, which rises with confidence level, shows this clearly. The width of confidence intervals will rise when sample size is increased.

An unknown population parameter's likely range of values is known as a confidence interval. A certain proportion of the confidence intervals will include the population mean if you repeatedly take random samples. The confidence level is expressed as this percentage.

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The following complex number (1-i)³ in a+ bi form is -2+4i

In mathematics, a complex number is a part of a number system that includes an element with the symbol I often known as the imaginary unit, and extends the real numbers. Complex numbers satisfy the equation that any complex number can be represented as a + bi, where a and b are real numbers. Rene Descartes referred to me as an imaginary number because no real number can satisfy the aforementioned equation. A and b are referred to as the real and imaginary parts, respectively, of the complex number a+bi. Complex numbers are accepted in the mathematical sciences as being just as "real" as real numbers despite the historical appellation "imaginary."

(1-i)³

=1³-i³-3(1)(i)(1-i)

=1+i-3(1-i)

=1+i-3+3i

=-2+4i

Therefore, the following complex number (1-i)³ in a+ bi form is -2+4i.

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Answer:

6p+3q

Step-by-step explanation:

1.5(4p+2q)

Distribute property

1.5(4p)+1.5(2q)

6p+1.5(2q)

6p+3q

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Answer:

3 x (2p+q)

Step-by-step explanation:

STEP 1:

                3

Simplify   —

                 2

The equation at the end of step 1:

 3

 — • (4p + 2q)

 2

STEP 2:

Pulling out like terms

3.1     Pull out like factors :

  4p + 2q  =   2 • (2p + q)

Final result :

 3 • (2p + q)

Answer:4f+3t=7.95  2f+10t=9.50

Step-by-step explanation:

Let the cost of fudge be f and taffy be t.

Chris bought 4 pieces of fudge and 3 pieces of taffy for a total of $7.95

 4 f + 3 t = 7.95

Samantha bought 2 pieces of fudge and 10 pieces of taffy for a total of $9.50

 2 f + 10 t = 9.5

Hello,

The slope-intercept form of a linear equation is:

y = mx + b

where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

To write the equation of the line with slope m = -1 that passes through the point (4, 5), you can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line. Plugging in the values, we get:

y - 5 = -1(x - 4)

This simplifies to:

y - 5 = -x + 4

Finally, we can rearrange the terms to put the equation in slope-intercept form:

y = -x + 9

This is the equation of the line with slope m = -1 that passes through the point (4, 5).

---

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Answer:

122.5

Step-by-step explanation:

first you divide 70/4 =17.5 then you multiply 17.5 by 7 and get 122.5

Based on the given rate, which is  4-ounce serving of applesauce has 70 Calories the Calorie level of 7 ounces of applesauce is 122.5 calories

The number of calories in 7 ounces of applesauce is solved by comparing the how many 4 ounce is in 7 ounce

The amount of 4 ounce in 7 ounce = 7 ounce / 4 ounce

The amount of 4 ounce in 7 ounce = 1.75 ounce

Then the equivalent amount of calories is solved by multiplication

The number of calories in 7 ounces of applesauce  = 1.75 * 70 calories

= 122.5 calories

The number of calories in 7 ounces of applesauce is 122.5

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Answer:

1) 3/4 x 7/6
2) 21/24
3) 7/8

Step-by-step explanation:

1) KCF, Keep change flip. 3/4 stays the same, division sign changes into multiplication, and 6/7 changes into its reciprocal.
2) Multiply numerator by numerator and denominator by denominator
3) Find their greatest common factor (GCF) and divide the numerator and denominator by it. There's your simplified answer.

Answer:

7/8

Step-by-step explanation:

Divide 3/4 with 6/7

3

4

÷

6

7

is

7

8

.

Steps for dividing fractions

Find the reciprocal of the divisor

Reciprocal of

6

7

:

7

6

Now, multiply it with the dividend

So,

3

4

÷

6

7

=

3

4

×

7

6

=

3 × 7

4 × 6

=

21

24

After reducing the fraction, the answer is

7/8

1.22ft is the length, in feet, of the model.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.

Main Body:

Length of Clark house = 30.5 ft

Dimensions of the model were 1/25 the dimension of Clark's actual home.

so , we can write as -

Write and solve an equation of ratios:

 1          x

---- = ----------

25      30.5 ft

Then 30.5 ft = 25 x, and x = 1.22 ft, or 14.64 inches.

Hence 1.22ft is the length, in feet, of the model.

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Answer:

Length (L) = 50 m

Step-by-step explanation:

Given information,

→ 400 m long fencing wire is required to surround square flower garden 2 times.

Now the fence taken for 1 time,

→ 400 ÷ 2

→ 200 m

Formula we use,

→ P = 4 × L

[Perimeter of square]

Then the length of the garden is,

→ P = 4 × L

→ 200 = 4L

→ 4L = 200

→ L = 200/4

→ [ L = 50 m ]

Hence, length of garden is 50 m.

One hose can fill a small swimming pool in 75 minutes. Two hoses will fill the pool in 30 minutes when working together.

Given, the volume ( the space occupied by an solid object)  per minute

Smaller hose fills  the pool in 75 minutes. (1/75)

A larger one can fill the pool in 50 minutes. (1/50)

So, together they will fill = (1/ 75 ) + (1/50) , the lcm of 75 and 50 is 150

                                            =  (2/150) + (3/150)  

                                            =  5/150

                                            = 1/30 or 30 minutes

So, we can say that the two hoses will fill the pool in 30 minutes when working together.

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A diagram is provided, on which R S T U's perimeter is 72 and R V's is 16, RT= 32  and UV ≈ 8.2.

A diagram is provided, on which R S T U's perimeter is 72 and R V's is 16.

Finding R T and U V is our goal.

First, let's assume that the figure RSTU is a rhombus since its perimeter and one-half of a diagonal's length are both provided. RT is the result of adding the segments RV and VT.

RT=RV + VT

We are informed that the RV is sixteen. If RV and VT are congruent, then V T equals 16. So:

R T = 16 + 16 = 32

In order to determine the UV length, we must first determine the RU length. Since a rhombus's sides are the same length, we can divide its perimeter by four to determine

RU= Perimeter/ 4

If we simplify and replace Perimeter with 72, we get:

RU = 72 / 4

RU =18

Since UB is a member of the right triangle RUV created by the intersection of the diagonals, we can now use the Pythagorean theorem to determine its length. So:

U V²+ R V² =  RU²

If R V = 16 and R U = 18, we obtain:

U V² + 16 ²= 18²

By way of summary, we have:

U V² + 256 = 324

U V² + 256 − 256 = 324 − 256

√ UV = √ 68

UV = 8.2462

UV ≈ 8.2

Our recommendations are as follows:

RT= 32

UV ≈ 8.2.

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We know that Martin earn $81 last week by raking 27 bags using simple mathematical operations.

A mathematical expression known as an "operation" in mathematics is one that transforms zero or even more input data into a precisely specified actual output.

The number of arithmetic determines the difficulty of the operation.

The four basic operations in arithmetic are addition, subtraction, multiplication, and division, according to the majority of people.

So, money was earned by raking 27 bags.

Martin earns $15 for raking 5 bags.

The amount earned by raking 1 bag:

15/5 = $3

Now, the amount earned by raking 27 bags:

27 * 3 = $81

Therefore, we know that Martin earn $81 last week by raking 27 bags using simple mathematical operations.

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According to the BODMAS rule, the first step to solve the given expression is to solve the bracket.

Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems.

B-Brackets, O-Orders (powers/exponents or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as BODMAS.

So, we have the expression: 3(3½ ÷ 3)-4

The next step would be according to the BODMAS rule.

In the BODMAS rule the letter B stand for brackets.

Hence, the first step will be to solve the bracket.

Therefore, according to the BODMAS rule, the first step to solve the given expression is to solve the bracket.

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The system has no solution.

The solution to the system would be the intersection point of the two lines.  Since these lines don't appear to intersect, there's no solution.

Answer:

Step-by-step explanation:

For an equation or function be linear, it should be in the form:

Y= mX +b

then

a) YES Linear

b) NO linear

c) YES Linear

d) NO linear

Answer:

79.2Million?

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

perp. -1/5

y - 6 = -1/5(x + 3)

y - 6 = -1/5x - 3/5

y - 30/5 = -1/5x - 3/5

y = -1/5x + 27/5

parallel: 5

y - 6 = 5(x + 3)

y - 6 = 5x + 15

y = 5x + 21