Let ∠1 , ∠2 , ∠3 , and ∠4 have the following relationships. ∠1 and ∠2 are vertical angles. ∠3 and ∠4 are right vertical angles. ∠3 is adjacent to both ∠1 and ∠2 . What is the sum of the measure of ∠4 and the measure of ∠1 minus the measure of ∠2 ?

Answer:

x=15°

∡Q= 75°

Step-by-step explanation:

supplementary angles means the sum of the angles =180°

so, 5x+105°=180°

5x=75°

x=15°

∡Q= 75°

The given equations having infinitely many solutions.

What is Solutions of system of equation?

A solution to a system of equations is a collection of variable values that satisfy all of the equations at the same time. To solve a system of equations, one must determine all of the sets of variable values that compose the system's solutions.

The solution to the system of equations y = -2x + 1 and 4x + 2y = -1 can be determined graphically by plotting both equations on the same set of axes and finding the points of intersection.

If there is exactly one point of intersection, then that point represents the unique solution to the system. If there are no points of intersection, then the system has no solution. If there are infinitely many points of intersection, then the system has infinitely many solutions.

Based on the information you provided, the system has two points of intersection: (0, -3) and (-3, 0). This means that the system has two solutions, and the solution set is the set of all points on the line that passes through these two points.

Therefore, The given equations having infinitely many solutions.

To know more about Solutions of system of equation visit,

https://brainly.com/question/25976025

#SPJ1

about 45 of every 300 apples picked at the Newbury apple orchard are rotten, if 3560 apples were picked one week, about 534 many apples were rotten. We drew this answer with the help of algebra,

45/300 = x/3560

x = 3560*(45/300) = 534

At the same rate, about 534 rotten apples can be expected in the week's pickings.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.

To know more about algebra, visit: brainly.com/question/24875240

#SPJ4

By using a system of equations of two variables we concluded that the first number was 6

Let the numbers be x and y and their sum gives z

The equation for the sum of 2 numbers:

                                             x + y = z    -(1)

We know, z = 30 and y = 4 times x = 4x

Putting values of y and z in equation (1), we get

                                             x + 4x = 30

Solving for x, we get

                                                  5x = 30

                                         x = 30/5 = 6

To get the value of y, put the value of x in y = 4x and we get

                                          y = 4 x 6 = 24

So the real equation was

                                              6 + 24 = 30

To learn more about equations of two variables here:

brainly.com/question/29209545

#SPJ4

In rectangle WXYZ, the length of each diagonal are 40.97 units and 39.98 units.

To find the lengths of the diagonals of rectangle WXYZ, we can use the Pythagorean theorem.

The diagonal WX is the hypotenuse of right triangle WXY, so we have:

WX^2 = WY^2 + XY^2

Similarly, the diagonal YZ is the hypotenuse of right triangle XYZ, so we have:

YZ^2 = XY^2 + XZ^2

Substituting the given values for WY and XZ, and x = 2, we get:

WY = 24(2) - 8 = 40

XZ = -18(2) + 13 = -23

Plugging these values into the equations above and simplifying, we get:

WX^2 = 40^2 + XY^2

YZ^2 = XY^2 + (-23)^2

Since XY is a common side of both triangles, we can solve for it by setting the two expressions for XY^2 equal to each other:

40^2 + XY^2 = XY^2 + (-23)^2

Simplifying, we get:

40^2 + 23^2 = 2XY^2

XY^2 = (40^2 + 23^2) / 2 = 1039

Substituting this value for XY^2 in the equations for WX^2 and YZ^2, we get:

WX^2 = 40^2 + 1039 = 1679

YZ^2 = 1039 + (-23)^2 = 1598

Taking the square roots, we get:

WX = sqrt(1679) ≈ 40.97

YZ = sqrt(1598) ≈ 39.98

Therefore, the length of each diagonal of Rectangle are approximately 40.97 units and 39.98 units.

To know more about Rectangle:

https://brainly.com/question/20923979

#SPJ4

_____The given question is incomplete, the complete question is given below:

Find the lengths of the diagonals of rectangle WXYZ.

WY = 24x-8

XZ = -18x+13

x= 2

The length of each diagonal is ___ units.

Answer:

he inequality to determine the years in which more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher is:

0.48t + 18 > 40

Subtracting 18 from both sides:

0.48t > 22

Dividing both sides by 0.48:

t > 45.83

So, for years t greater than 45.83, more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher.

Step-by-step explanation:

The type of sampling that Huw is using is called Convenience Sampling.

Explanation:

Convenience sampling is a non-probability sampling technique where the sample is selected based on ease of access and availability. In Huw's case, he is administering the questionnaire to people who happen to be in the town centre, which is convenient for him. The sample is not selected randomly, and therefore does not accurately represent the population as a whole. Convenience sampling is often used in quick, informal surveys where the researcher does not have the resources or time to conduct a more rigorous, randomized sampling method.

Answer:  Choice D

Explanation:

The notation [tex]-\infty < \text{x} < \infty[/tex] says x is anything between negative infinity and positive infinity. Basically x is any real number. This is because the curve stretches forever to the left and right. Any number can be the x input.

Answer:

7

Step-by-step explanation:

If the ratio of cars to trucks on the lot is 11 to 33 and there are currently 51 trucks for sale, then there are 17 cars for sale

The ratio of cars to truck on the lot = 11 : 33

Total number of trucks for sale = 51 truck

Consider the number of cars for sale = x

Then the ratios will be

11/33 = x / 51

Cross multiply the terms in the equation

33x = 51 × 11

33x = 561

Move 33 to the right hand side of the equation

x = 561 / 33

Divide the terms

x = 17

Therefore, the number of cars does the dealer have for sale is 17

Learn more about ratio here

brainly.com/question/29774220

#SPJ4

Answer:

The value of z is 58    

Step-by-step explanation:

The mean is the average of a set of numbers.  Mean = (sum of the numbers)/(the number of numbers).

We are told that the mean of x+y+z is = 55.  

We can wriote this as:

 55 = (x+y+z)/3

We learn that x+y = 107.  So lets enter that number for x + y:

 55 = (x+y+z)/3

55 = ((x+y)+z)/3    

55 = ((107)+z)/3           [Substitution]

55 = (107+z)/3

165 = 107+z               [Multiply both sides by 3]

z = 58                       [Simplify]

CHECK:

Is the mean of x, y, and z 55?

55 = (x+y+z)/3  ?

55 = ((107)+z)/3 ?   [Since we know x+y = 107]

55 = ((107)+58)/3 ?  [Since z=58]

55 = (165)/3)  ?

55 = 55  YES  The value of z is 58    

Answer:

  1.8 m³

Step-by-step explanation:

You want the volume of the rectangular prism with dimensions L=4 m, W = 0.3m, H = 1.5 m.

The volume formula is given in the problem statement:

  V = LWH

Substituting the given values of L, W, H, we find the volume to be ...

  V = (4 m)(0.3 m)(1.5 m)

  V = 1.8 m³

The volume of the rectangular prism is 1.8 cubic meters.

The requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
From the given data,
Name Number of Cards

Chris      7

Mike       8

Sally       10

Susan     25
Total cards = 50

Now equivalent to Mike’s portion of the total number of cards is given as ,
= Mike cards/total card
= 8 / 50 × 100%
= 4/25×400%
= 16%

Thus, the requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ1

Answer: imma say do 8x3x2= the answer you get then 8x10= the answer you get then multiply the two answer you get that should be you answer.  

Step-by-step explanation: hope this helps

The equation shows how to find the length of each piece is L = R / N and the length of each piece is 1.5 feet.

To find the length of each piece, we can use the following equation:

Length of each piece = Total length of the ribbon / Number of pieces

In mathematical terms, we can represent this equation as:

L = R / N

Where,

L is the length of each piece

R is the total length of the ribbon (66 feet in this case)

N is the number of pieces (44 in this case)

In this problem, we are given a 66-foot ribbon and we are asked to cut it into 44 equal pieces. We need to find out the length of each piece.

Using this equation, we can easily find the length of each piece:

L = 66 / 44

L = 1.5 feet

Therefore, each piece of the ribbon is 1.5 feet long.

To know more about equation here.

https://brainly.com/question/10413253

#SPJ4

Answer:

8π

Step-by-step explanation:

The period of a function f(x)  is the x-distance between two repeating points of the function

Looking at the function graph given we see that the function reaches a peak value(called amplitude) at x = -6π and then again reaches this value at x = 2π

So the x-distance is 2π - (-6π) = 2π + 6π = 8π

From 2π, the function reaches its maximum value again at 10π giving the period once again as 10π - 2π = 8π

The number of seconds does the firework hit the ground is 3 seconds

From the information given, we have the quadratic function;

y = -16x² + 32x + 48

To determine the value of x , let's reduce the expression, we get;

-2x² + 4x + 6

Now, let's factorize the terms

Multiply the coefficient by the constant and find the pair factors

-2x² + 6x - 2x + 6

Factorize in pairs, we get;

-2x(x -3) - 2(x -3)

Then, we have the expressions

-2x - 2 = 0

solve for x

x = -1

x - 3 = 0

x = 3

Hence, the value is 3 seconds

Learn out functions at: https://brainly.com/question/25638609

#SPJ1

Answer:

3

Step-by-step explanation:

i took the test

The secret number is 564 as we solve it by given question.

jack's favorite number is 836 so here we have number 836 and

jill subtracts a secret number from 836 and her answer is the smallest possible combination of all the digits from jack's favorite number

so here we have a number 836

let we subtract x from 836 to get a number which is smallest number by using 836

the number which we can make by using these 3 degits are

368, 386, 638, 683, 836, 863 anf from all these numbers the smallest number which can be using 836 is 368

as given in question we have 836 and we will subtract x and get 368 so

836 - x = 368

x = 836 - 368

x = 564

the secrets number is 564.

know more about smallest numbers click here;

https://brainly.com/question/24023290

#SPJ4

The average change in weight calculated by the researcher for the sample of 25 freshmen is an example of a statistic.

A statistic is a numerical summary of a sample that is used to make inferences about a population. In this case, the sample is the 25 freshmen, and the population could be all freshmen entering college.

The average change in weight is a statistic because it summarizes the data collected from the sample, and is used to make conclusions about the population.

It represents the typical or average amount of weight gained or lost by the freshmen in the sample during their first semester in college.

For more such questions on statistics

https://brainly.com/question/16432947

#SPJ4

Answer:

12.2 pints

Step-by-step explanation:

In all means add.  Add the two decimals together.

4.8 + 7.4

12.2 pints

The volume of given triangular prism is 24,000 cubic yards.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the dimensions of base are 30 yards and 20 yards.

Here, area = 1/2×30×20

= 300 yd²

Volume of a triangular prism = Area of base triangle × Length of the prism.

= 300×80

= 24,000 yd³

Therefore, the volume is 24,000 yd³.

To learn more about the volume visit:

https://brainly.com/question/13338592.

#SPJ1

Answer:

Step-by-step explanation:

To build a sequence, you have to create a rule. For example, if the rule is +2, then you add 2 to 10 to get 12, and then you add 2 to 12 to get 14, and so on. Your sequence would then be 10, 12, 14, 16, 18.

The updated positions are (5, -6) + (-2, 10) = (3, 4)

A vector is a mathematical concept that has both magnitude and direction. The vector's size is determined by size. An arrow-depicted line serves as this representation. The vector's magnitude is represented by the line's length, and its direction is shown by the arrow. additionally referred to as geometric, Euclidean, spatial, or just "vectors."

You can add the components of the vector to the corresponding components of the point to translate point (5, -6) based on vector V:(-2,10).

The updated positions are (5, -6) + (-2, 10) = (3, 4)

Thus, the translated message is (3, 4).

To learn more about vector visit:

https://brainly.com/question/29740341

#SPJ1

After unit conversion of 24 in./s into ft/min the value will be 120

To measure and compare various things we use one term which is known as a unit. When all of the measuring units are the same, comparison is simple. Depending on their intended usage, different units can be categorized.

For example, for  length measurement we use units like:- meter, centimeter, inch, miles.

Given that,

A rate = 24 in./s

The value of rate in ft./min. = ?

It is known that,

1 feet = 12 inches

And 1 minute = 60 second

So,

1 inches = 1/12 feet

1 second  = 1/60 minute

⇒ 24 in./s

⇒  24 ((1/12)ft / (1/60)sec)

⇒ 24 × 60/12

⇒ 24 x 5

⇒ 120

To know more about Units check:

https://brainly.com/question/30168372

#SPJ1

The intercepts of the line are x intercept: (4.3,0) y-intercept: (0,-13)​

From the question, we have the following parameters that can be used in our computation:

y+1=3(x − 4)

To calculate the x-intercept, we set y to 0

So, we have the following representation

0+1=3(x − 4)

This gives

x - 4 = 1/3

So, we have

x = 4.33

To calculate the y-intercept, we set x to 0

So, we have the following representation

y + 1 = 3(0 − 4)

This gives

y + 1 = -12

So, we have

y = -13

Read more about linear function at

https://brainly.com/question/15602982

#SPJ1

The probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.

To calculate the probability that all four of the selected bolts are torqued to the proper limit, we need to find the number of combinations of 4 bolts out of 20 that have been torqued to the proper limit.

Let's call the number of proper bolts n = 20 - 5 = 15.

The number of combinations of 4 proper bolts out of 15 is given by the binomial coefficient nCk, where n is the number of bolts and k is the number of bolts selected.

nCk = n! / (k! (n - k)!).

So, the number of combinations of 4 proper bolts out of 15 is:

15C4 = 15! / (4! (15 - 4)!) = 15! / (4! 11!) = 1365.

Therefore, the probability of selecting all 4 proper bolts out of 20 is:

P = number of combinations of 4 proper bolts / number of combinations of 4 bolts = 1365 / 20C4 = 1365 / 4845 = 0.28

So, the probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.

To learn more about probability please click on below link.

https://brainly.com/question/9793303

#SPJ4