-11x-y+3z=-21
(5x-y-5z=-5)
(3x+y+z=13)

Both equations' solutions are found at the point (-2, 2). When point (-1,4), the 2x-y=-6 yields the correct point. The second equation is as a result. The point (2, 14) is the answer to the first equation because it provides the answer to the first equation but not the second.

The word equation and its cognates in other languages may have slightly different meanings; for example, in French an equation is defined as containing one or more variables, while in English any well-formed formula consisting of two expressions related with an equals sign is an equation. An equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.

3x-y=-8

2x-y=-6

given points are (-1,4), (2,14), (-2,2)

On solving the equation,

3x-y=-8

-(2x-y=-6)

x=-2

y=2

The point (-2,2) is the solution to both equations.

The point (-1,4) on putting in the 3x-y=-8 will not give solution but when put in the 2x-y=-6, it gives the result. so it the solution to second equation.

The point (2,14) is the solution to the first equation as it gives the answer to first but not to the second equation.

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By dividing $180 in the ratio of 2:3:4, we get 40,60 and 80

Solution

2 + 3 + 4 = 9

180 ÷ 9 = 20

Hence, we get the quotient of 20.

20 × 2 = 40

20 × 3 = 60

20 × 4 = 80

Hence, by dividing $180 in the ratio of 2:3:4, we get 40,60 and 80

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Given

8 times the quantity of X and 8

Find

Translate into an expression

Explanation

Quantity be X

so , according to the question ,

8 (X + 8)

Final Answer

Hence , the required expression is 8 (X + 8)

Answer: -3/4

Step-by-step explanation: Lucky I just learned about this last week! Multiply 7 and -1 by -2 which makes the equation -14x + 2 = 14. Subtract 2 from both sides to make -16x = 12. Then divide each side by -16 and you get -3/4 = x.

Nice helping out!

Answer:

There are no solutions.

Step-by-step explanation:

Hello!

Isolate the absolute value equation first:

Now stop and think.

An absolute value equation always has a positive outcome, because you are finding the positive value of what's inside. The outcome here is negative, so there is no value of x that makes it so that the absolute value is negative.

So the solution is No Solutions.

Given:

There are given that a total of 42 boys and 28 girls in the photography club.

Explanation:

According to the question:

We need to find the ratio.

So,

We can see a total of 28 girls and 6 more girls.

So,

The total number of girls is:

Then,

The numbers of boys to the numbers of girls in the end is:

Final answer:

Hence, the ratio is shown below:

Proportionately, if there are 6 blue beads in the bag, and blue beards are 6 or 2/9 of the total beads, the number of purple beads in the bag is 21.

Proportion refers to the numerical ratio of a value to another.

Proportion shows the quantity of a value contained in another variable.

Since proportions are fractional values, like ratios, they are represented using decimals, fractions, and percentages.

The ratio of blue beards to purple beads = 2:7 or 2/9

The number of blue beads in the bag = 6

The total number of beads in the bag = 27 (6/2 x 9)

The number of purple beads in the bag = 21 (27 x 7/9)

Thus, based on the given proportional ratio of the blue beads to the purple beads, there are 21 purple beads in the bag.

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The solutions are x = -1,  y = 1 and z = 5  

In Mathematics, the equation which has highest degree 1 is known as a Linear equation. Linear equations are used to calculate unknown values. Here to represent unknown values we will use variables like x, y, z  or a, b, c .. etc.  

According to the number of variables in given equations, the given equations will be called a Linear equation in one variable or Linear equation in two variables and so on. To solve linear equations we will use Elimination method

Here, we have three linear equations with 3 and 2 variables

4x - 2y + 3z = 9 ----(1)

x - 2y = -3 -----(2)

2x + 3y = 1​ -----(3)

Here, to find x, y and z we will use Elimination method

First of all solve (2) and (3) as given below

2 × (2) ⇒  2x - 4y = - 6 -----(4)

1 × (3) ⇒  2x + 3y = 1​  

Now subtract (3) from (4)

(4) - (3) ⇒ 2x - 4y -2x - 3y  = - 6 - 1

⇒ - 7y = -7

⇒   y = 1

Substitute y = 1 in (2)

(2) ⇒ x - 2(1) = -3

x - 2 = -3

x = -1    

Now substitute x = -1 and y = 1 in (1)

(1) ⇒ 4(-1) - 2(1) + 3z = 9  

- 6 + 3z = 9

3z = 15

z = 5

From above calculations

The values of x = -1,  y = 1 and  z = 5

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The average change in sales income per month is $ 3 million.

What is average change and how is it assessed?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Given, for 3 months, the average change in the company's sales
= $ 9 million
Also, for x months, the average change in the company's sales
= $ (9x/3) million
Therefore, for one month, the average change in the company's sales
= $ (9*1/3) million = $ 3 million
Thus, the average change in sales income per month is $ 3 million.

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Answer: 1

Step-by-step explanation: Rise over run, Rise/run. The rise is how much the line goes up or down vertically. The run is how far the line goes until it intersects through a square. The slope is 1 because if you look at the line specifically at the first dot, you just have to go down one and right one as it intersects the square to find the slope.

Answer:

a. 6

b. 16

Step-by-step explanation:

a.

The mode is the number that appears the most

3 appears once

13 appears once

6 appears twice

8 appears once

10 appears once

5 appears once

Since 6 appears the most, it is the mode in this set of numbers

b.

Again, The mode is the number that appears the most

12 appears once

0 appears once

15 appears twice

13 appears twice

19 appears once

16 appears three times

Since 16 appears the most, it is the mode in this set of numbers

The correct answers are:  [A]:  "6 " ; and:   [B]: " 16 ."

____________________

Step-by-step explanation:

The question asks to find the modes of the following sets of numbers:
 Set a)   "{3, 13, 6, 8, 10, 5, 6}."

 Set b) "{12, 0, 15, 15, 13, 19, 16, 13, 16, 16}."

Note that the mode is the number that occurs most frequently within a data set.

To begin:  let's find the mode of Set: a:
_____
First, let's list all the values within Set: a: in order of smallest to largest—to simplify matters:
       →  " { 3, 5, 6, 6, 8, 10, 13 }."  
In this data set, there is only one value that occurs more than once—  
which is 6.   As such, the mode of "Data Set: a" is  6 .

Then:  To continue: let's find the mode of Set: b:
_____

Second, Let's list all the values within Set: b:  in order of smallest to largest—again; to simplify matters:
         →  " { 0, 12, 13, 13, 15, 15, 16, 16, 16, 19 } ."
In this data set, we see the following:
 Each of the three values:   0, 12, and 19 appear only once;
                      13 and 15 individually, appear twice; and:  
                      16 appears "three times".
As such:
     The value, 16 appears the most in this data set;  and:
          →  The mode of "Data Set: b"—is 16.
_____
The correct answers are:  [A]:  "6 " ;  and:  [B]: " 16 ."
_____
Hope this is helpful to you!  

  If you have any questions—Please "comment" below!
_____

Answer:

y = -x + 4

Step-by-step explanation:

(-1, 5), (2. 2)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁        2 - 5          -3           -3

m = ----------- = ----------- = --------- = ------- = -1

        x₂ - x₁        2 - (-1)       2 + 1        3

y - y₁ = m(x - x₁)

y - 5 = -1(x - (-1))

y - 5 = -1(x + 1)

y - 5 = -x - 1

  +5        +5

----------------------

y = -x + 4

I hope this helps!

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = 8, - 4) and (x₂, y₂ ) = (- 1, 5) ← 2 ordered pairs from the table

m = [tex]\frac{5-(-4)}{-1-8}[/tex] = [tex]\frac{5+4}{-9}[/tex] = [tex]\frac{9}{-9}[/tex] = - 1 , then

y = - x + c

to find c use any ordered pair from the table

using (2, 2 ) , then

2 = - 2 + c ⇒ c = 2 + 2 = 4

y = - x + 4 ← in slope- intercept form

with y- intercept c = 4

Answer:

+ 9

Step-by-step explanation:

x²+ 6x

to complete the square

add ( half the coefficient of the x- term )² to x² + 6x

x² + 2(3)x + 3²

= x² + 6x + 9

= (x + 3)² ← a perfect square

When Allison arrived, Austin still had 24 miles to go. Allison drive 116 miles per hour.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

As given, Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 46 mph.  Allison arrived, Austin still had 24 miles to go.

Let t be the time they drove.

Then you have this "distance" equation

58t = 46t + 24

saying that both parts of the equation represent the same distance.  Then

58t - 46t = 24

12t = 24

t = 2  hours.

Hence the distance is, 2 x 58 = 116 mph.

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Answer:

Step-by-step explanation:

it 10

Answer:

The formula for finding the percentage of something is given as: (No. of items you want to find÷Total no. of items)×100

Percentage of red pins = (21÷70)×100

= 30%

Answer:

I think the answer is 0.

Step-by-step explanation:

-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4

Associative property of the sum states that the order the operations are done doesn't matter as long as the sequence of operands also doesn't change. This property is given by:

Therefore, the equation that illustrates the associative property is:

Step 1

Write the slope, y-intercept form of the equation of a line.

The correct representation of the inequality is x > 5 or –6x + 15 < 10 – 5x.

The inequality can be best represented as follows;

–3(2x – 5) < 5(2 – x)

An inequality is a mathematical expression that has the signs <, >, ≤ and ≥.

Therefore,

–3(2x – 5) < 5(2 – x)

open the brackets

- 6x + 15 < 10 - 5x

Lets solve further by subtracting 15 from both sides of the inequality.

- 6x + 15 < 10 - 5x

- 6x + 15 - 15 < 10 - 15 - 5x

- 6x < - 5 - 5x

add 5x to both sides of the inequality.

- 6x < - 5 - 5x

- 6x + 5x < - 5 - 5x + 5x

-x < - 5

divide both sides by  -1

Therefore,

x > 5

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The solution of the given inequality is x > 5 which is the correct representation of x > 5 or –6x + 15 < 10 – 5x.

The inequality is given in the question as

–3(2x – 5) < 5(2 – x)

Open the parenthesis and apply the distributive property of multiplication,

⇒ - 6x + 15  <  10 - 5x

Subtract 15 from both sides of the above inequality,

⇒ - 6x + 15 - 15 < 10 - 15 - 5x

⇒ - 6x < - 5 - 5x

Add 5x to both sides of the inequality,

⇒ - 6x + 5x < - 5 - 5x + 5x

⇒ -x < - 5

Multiply both sides by  -1 and flip the sign of inequality

⇒ x > 5

Therefore, the solution of the given inequality is x > 5.

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Answer:

x = 58°

∠P = 58°

∠PQR = 64°

Step-by-step explanation:

If you add the two nonadjacent angles together they will equal the exterior angle. Setup up an equation using that info.

[tex]58 +x=2x[/tex]

Solve for x.

[tex]58 +x-x=2x-x\\58=x[/tex]

Since ∠P is the same as x, ∠P = 58°

To find ∠PQR, add ∠P and ∠R together and then subtract from 180°. You subtract from 180° because the sum of the three angles of a triangle equal 180°.

58 + 58 = 116

180 - 116 = 64°

∠PQR = 64°

The arc length is equal to the measure of the arc in radians only if the radius of the circle is 1 unit, for all the other circles this is false.

For a circle of radius R, if we have an arc defined by an angle of θ radians, then the length of that arc is:

L = R*θ

Particularly, the length is equal to the measure in radians only if the radius of the circle is R = 1:

L = 1*θ

So the statement is only true for the unit circle but is false for every other circle.

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By likelihood, she can utilize the pens in 1024 distinct ways during the week.

Probability is the study of possible outcomes of events, together with the probabilities and distributions of those occurrences.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

To calculate probability, divide the total number of outcomes by the total number of possible possibilities. There are differences between probability and odds.

Odds are computed by dividing the likelihood that an event will occur by the likelihood that it won't.

From the stated circumstance,

Total ways = [tex]4^{5}[/tex]= 1024

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A complex number z is given in the form:

z = (x.y) = (realpart) x + imaginary part (iy)

In this case:

z1 = -7i

z2 = 3+3i

To write in trigonometric form:

Multiplication in trigonometric form:

Multiplication in standard form:

Using the normal distribution, the probabilities are given as follows:

a. Between 8 and 12 cases with side effects: 0.582 = 58.2%.

b. More than 16 cases with side effects: 0.0174 = 1.74%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the equation presented below:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution in this problem are given as follows:

p = 0.05, n = 200.

Hence the mean and the standard deviation of the approximation are given as follows:

For item a, using continuity correction, the probability of between 8 and 12 cases with side effects is the p-value of Z when X = 12.5 subtracted by the p-value of Z when X = 7.5, hence:

X = 12.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (12.5 - 10)/3.08

Z = 0.81

Z = 0.81 has a p-value of 0.7910

X = 7.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (7.5 - 10)/3.08

Z = -0.81

Z = -0.81 has a p-value of 0.2090.

0.7910 - 0.2090 = 0.582 probability.

For item b, the probability of finding more than 16 cases with side effects is one subtracted by the p-value of Z when X = 16.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (16.5 - 10)/3.08

Z = 2.11

Z = 2.11 has a probability of 0.9826.

1 - 0.9826 = 0.0174 = 1.74% probability.

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Answer:

1/2 -> 3/4 -> 4/5 -> 9/10

Step-by-step explanation:

1/2 = 50%

3/4 = 75%

4/5 = 80%

9/10 = 90%

How to figure out:

1/2 - Divide 100/2 = 50. So 1/2 of 100 is 50 so 50%

3/4 - Divide 100/4 = 25. Now multiply 25 x 3 = 75 so 75%

4/5 - Divide 100/5 = 20. Now multiply 20 x 4 = 80 so 80%

9/10 - Divide 100/10 = 10. Now multiply 10 x 9 = 90 so 90%

The length of the side SU will be equal to 4√2.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.

The formula for the Pythagorean theorem will be given as:-

H² = P² + B²

Here,

H = Hypotenuse

P = perpendicular

B= Base

The length of the sides of the triangle is formed by joining the midpoints of the bigger triangle are xw=2, xv=2, and vw = 3.

Here sv = vt = xw = 2 units. Apply the Pythagorean theorem in a triangle xsv.

H² = P² + B²

sx² = xv² + sv²

sx = √ ( 2² + 2² )

sx = √8

sx = √ ( 2 x 2 x 2 )

sx = 2√2

SU = 2 sx

SU = 2 x 2√2

SU = 4√2

Therefore, the length of the side SU will be equal to 4√2.

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a) 50 elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements.

b) 229 are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each.

c) 23 are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6.

The problem we are dealing with is related to union sets.The union of two sets is a set containing all elements that are in set A and set  B or including more sets

For the first problem, the sets  contain:

n(A)=10, n(B)=15, n(C)=25, n(A∩B)=0 ,n(B∩C)=0 ,n(C∩A)=0,n(A∩B∩C)=0

So,  n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

               = 10 +15+25-0-0-0-0-0

              =  50

For the second  problem, since no student can have  more than one major.

So, (A∪B∪C∪D∪E∪F∪G)=n(A)+n(B)+n(C)+n(D)+n(E)+n(F)+n(G)

As  we know : n(A)=31, n(B)=88, n(C)=19, n(D)=11, n(E)=41, n(F)=22, n(G)=17

So ,  (A∪B∪C∪D∪E∪F∪G) =  31+88+19+11+41+22+17= 229

For the third problem,  we have

n(A)=5

n(B)=3

n(C)=2

n(D)=7

n(E)=6

So, the number of elements will be (A∪B∪C∪D∪E) =  5+3+2+7+6 =23

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Triangle ABC and the triangle EFG are congruent by the first and third statement.

What is the congruent diagram?

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

In the given example triangle ABC and triangle EFG having one same side of length 2.

By the ASA (Angle side angle) criteria, we want two angles are same then the triangles are congruent.

When "m ∠ B and m ∠ F"  and "m ∠ A and m ∠ E" are same then the triangles are congruent.

Therefore, the first option is correct.

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The graph of g(x) with the graph of f(x): Option D, which is a shift of 2 units to the left, is correct.

What is Function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

We are aware that the graph of the modified function is:

for every parent function f(x).

g(x) = f(x + a)

is a left- or right-shift of the parent function f(x), depending on the value of a.

The shift is 'a' units to the left if a>0.

The shift is 'a' units to the right if a0.

Here, G(x) has been changed as follows:

G(x) = F(x + 2)

i.e. a=2>0.

2 units up: G(x) = F(x) + 2.

2 units down: G(x) = F(x) - 2.

2 units to the left: G(x) = F(x + 2).

2 units to the right: G(x) = F(x - 2).

Hence, Option D, which is a shift of 2 units to the left, is correct.

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SINCE A OF A RECTANGLE IS =L×B

[tex] = (12x - 6)(14 \frac{1}{6} ) \\ = (12x - 6)( \frac{25}{6} ) \\ = \frac{25}{6} (12x) + \frac{25}{6} ( - 6) \\ = 50x - 25[/tex]

THE SIMPLIFIED AREA IS =50x-25