Solve the problem 4p-32=p+7

Answer: 6

Step-by-step explanation:

The value of the variables a, b, c, and d will be 2, 7, 5, and -6, respectively.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

If the expression, 10x² +23x - 42 is factored as (ax + b) (cx-d) where a, b, c, and d are integers.

Factorize the expression, then we have

⇒ 10x² +23x - 42

⇒ 10x² + 35x - 12x - 42

⇒ 5x(2x + 7) - 6(2x + 7)

⇒ (2x + 7)(5x - 6)

Compare the factors with (ax + b) (cx-d).

The value of the variables a, b, c, and d will be 2, 7, 5, and -6, respectively.

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Samuel needs a total of 6 containers for his plan

The complete question is added as an attachment

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

1 cup of rubbing alcohol = 1/(1/2) = 2 shares

Also, we have

1 cup of rubbing alcohol contains = 1 + 1/2 + 16 = 17.5

For the 2 shares calculated above, we have

2 shares = 17.5 * 2

Evaluate

2 shares = 35

Given that each can hold a maximum of 6 cups, the number of containers needed is

Container = 35/6

This gives

Container = 5.83

Round up

Container = 6

Hence, he needs 6 containers

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Answer: 124.3%

318.2 is 124.3% of 256.

Hey there!

Answer:

318.2 is 124.296875% of 256.

Hope this helps!

The solution for the given equation is x=95/7 and for the given inequality is x<25/8.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=12x+6. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given an example: m=12 and b=6

For the other hand an expression mathematical that represents a non-equal relationship between a number or another algebraic expression is called an inequality. Therefore, it is common to the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).

The solutions for inequalities can be given by: a graph in a number line or numbers.

The exercise gives two topics:

70x=850+100

70x=950

x=950/70

x=95/7

8x < 40 - 15

8x< 25

x< 25/8

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The solution of the equation 70x - 100 = 850 is x = 13.6.

The solution of the inequality is x < 3.125.

Equations are mathematical expressions containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Let's solve the equation for the variable x.

70x - 100 = 850

70x = 850 + 100

70x = 950

divide both sides by 70

x = 950 / 70

x = 13.6

Let's solve the inequality as follows:

8x + 15 < 40

subtract 15 from both sides of the inequality

8x + 15 -15  < 40 - 15

8x < 25

divide both sides of the inequality by 8

x < 25 / 8

x < 3.125

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The equation to represent Sand supply of contact lens pairs, y, after x months is 5 + 1.5x.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Here, Sandy wears contact lenses. She starts the year with 5 pairs of lenses, and she uses 3 pairs of contacts every 2 months.

The equation to represent Sand supply of contact lens pairs, y, after x months so be:

5 + (3/2 × x)

5 + 1.5x

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Answer:

210m²

Step-by-step explanation:

We have 2 triangular faces with surface 5m*12m/2 = 30m² each

We have the top face with surface 5m*12m = 60m²

We have the bottom face with surgace 5m*13m = 65m²

And we have the "middle" with surface 5m*5m = 25m²

For a total of

30m² + 30m² + 60m² + 65m² + 25m² = 210m²

The expression that represents the profit Justin made is 1.31c + 1.66m + 1.6b ( option C)

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

Justin earned $1.50c selling cookies but he spent $0.19c. Therefore the profit on cookies = $(1.5-0.19)c. = $1.31c

He earned $2.25m by selling muffins and spent $0.59m on the ingredients. Therefore the profit He made on muffins = $(2.25-0.59) = $1.66m

He earned $1.90b selling brownies and he spent $0.30b on ingredients. The profit he made on brownies = $1.90-$0.30 = $1.60b

Therefore the expression for the total profit = $(1.31c+ 1.66m+1.6b)

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She needs 15 minutes to complete 2 miles, thus completing 4 miles at the same rate will take her 4 hours and 15 minutes.

The average number of points received by students in one math class at the conclusion of the term, for instance, is an example of a statistic since it represents the population of all math classes, if we view that class as a sample. Because it integrates arithmetic ideas to create an analysis of a data set that may be used to comprehend an association in the data, statistics has earned a reputation for being an extremely challenging course, especially when studied in college (whoo that was a mouthful).

given

The unit rate for the ratio of 150 minutes to every 20 miles is obtained by dividing 150 by 20.

150÷20=7.5

Thus, the runner is covering one mile in 7.5 minutes. This unit rate can be multiplied by the number of miles:

6 miles in 7.5 minutes equals 45 minutes.

At this speed, she can complete 6 miles in 45 minutes.

If she runs 6 miles in 45 minutes, she will run 2 miles at the same pace in 453=15 minutes.

She needs 15 minutes to complete 2 miles, thus completing 4 miles at the same rate will take her 4 hours and 15 minutes. She is moving at a speed of 8 miles per hour since 60 minutes equal 1 hour.

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Answer:

The slope of a line is given by the formula "rise over run," or (y2 - y1)/(x2 - x1). In this case, the rise is 7 - 6 = 1, and the run is 4 - p.

So the slope is equal to 1/(4 - p). We are told that this slope is equal to j, so we can set up the equation:

1/(4 - p) = j

To solve for p, we can multiply both sides of the equation by (4 - p) to get:

(4 - p) = j(4 - p)

Then we can simplify the left side and rearrange the terms on the right side to get:

4 - p = 4j - jp

Then we can add p to both sides to get:

4 = 4j - jp + p

Then we can combine like terms to get:

4 = (4 - p)j + p

Then we can rearrange the terms to solve for p:

p = 4 - (4 - p)j

p = 4 - 4j + pj

p = (1 - j)p + 4 - 4j

p(1 - j) = 4 - 4j

p = (4 - 4j)/(1 - j)

This is the value of p that will make the slope of the line with points (p, 6) and (4, 7) equal to j.

Answer:

p = -5

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Given values:

Substitute the given points and slope into the slope formula:

[tex]\implies \dfrac{1}{9}=\dfrac{7-6}{4-p}[/tex]

[tex]\implies \dfrac{1}{9}=\dfrac{1}{4-p}[/tex]

Cross multiply:

[tex]\implies 4-p=9[/tex]

Subtract 4 from both sides:

[tex]\implies -p=5[/tex]

Divide both sides by -1:

[tex]\implies p=-5[/tex]

Therefore, the value of p is -5.

Answer: How are you supposed to know the length if you only know the width. There isn't an answer to this question.

The coordinate of fourth vertex is (-3, 2) determined by using the properties of parallelogram.

The quadrilateral whose opposite sides are equal and parallel to each other along with equal opposite angles is called parallelogram. The only difference of parallelogram from rectangle is that rectangle has four right angles, but parallelogram has not.

we are given, three vertices as (-7, -2), (1, -4) and (5, 0)

let, the fourth vertex is (x, y)

the above vertices can be named as A (-7, -2), B (1, -4) and C (5, 0)

and D (x, y)

We know the distance of two points (x₁, y₁) and (x₂, y₂) is given by the following formula.

√[(x₂-x₁) ²+(y₂-y₁) ²]

Now distance from A to B = √[(1+7)² + (-4+2) ²]

length of AB = √ (64 + 4) = √68

distance from B to C = √ [(5-1)² + (0+4) ²]

length of BC = √32 = 4√2

According to the properties of parallelogram, two opposite sides are equal and parallel to each other.

If ABCD is a parallelogram, then AB = CD and BC = AD

length of CD = √[(x-5) ² + (y- 0) ²] = AB

length of AD = √ [ (x+7) ² + (y+2) ²] = BC

√68 = √[(x-5)² + y²]

after squaring both sides, we get 68 = x² - 10x + 25 +y²

                                            x²+ y² -10x -43 = 0 ... equation 1

4√2 = √[(x+7) ² + (y+2) ²]

32 = x² + 14x + 49 + y² + 4y + 4

x² + y² +14x + 4y +21 = 0 .......... equation 2

solving the equation 1 and 2 we determine the value x = -3 and y =2

hence, the fourth vertex D (x, y) = D(-3, 2)

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Using the properties of a triangle, The answer is Yes, The measure of an exterior angle of triangle is sum of the opposite interior angles of the triangle.

An angle is a measure of the amount of rotation between two lines or planes. It is typically measured in degrees or radians. An angle can be defined as the amount of rotation needed to bring one line or plane into coincidence with another. Angles are often represented graphically as a central point, called the vertex, and two rays that extend from the vertex in different directions. The angle is the amount of rotation needed to rotate one ray so that it coincides with the other ray.

A triangle is a three-sided polygon that has three angles and three sides. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on their side lengths and angles, such as right triangles, acute triangles, and obtuse triangles. A right triangle has one angle that measures exactly 90 degrees, while an acute triangle has all angles that measure less than 90 degrees, and an obtuse triangle has one angle that measures greater than 90 degrees. Triangles can also be classified by the length of their sides as equilateral, isosceles and scalene triangle. An equilateral triangle has all sides of equal length, an isosceles triangle has two sides of equal length, and a scalene triangle has no sides of equal length.

z = exterior angle

x, y = opposite interior angles to z.

z= x + y

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The correct option is B. The matrix must have pivot columns. The statements "A has a pivot position in every row and the columns of A are linearly independent" are logically equivalent.

The data given in this question is,

Suppose A is a 7 × 5 matrix.

The objective of this question is to find how many pivot columns must have if its columns are linearly independent.

Explanation for step 1:

Consider the given data that A is a 7 × 5 matrix.

All fine columns of 7 × 5 matrix A must be Pivot Columns.

Otherwise the equation AX=0, would have a free variable, in which care the Columns of would be linearly dependent.

Explanation:

Therefore, the required answer for the given question is option (B) correct.

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Answer:

0.62 cents

Step-by-step explanation:

divide 5 and 3.10

hope this helps:)

The total volume of coins will remain the same, but the two containers will now each have a volume of 1 L.

1. The two containers each have a volume of 500 mL.

2. Both containers are full of coins: one of quarters and the other of pennies.

3. All of the coins are transferred into separate 1 L containers.

4. The total volume of coins will remain the same (500 mL), but the two containers will now each have a volume of 1 L.

The original two containers each had a volume of 500 mL and were full of coins - one container with quarters, the other with pennies. All of the coins were then transferred into separate 1 L containers. After this, the total volume of coins remained the same (500 mL), but the two containers now had a volume of 1 L each. This means that the same amount of coins were contained in a larger space, which did not affect the amount of coins but did affect the volume of the containers. Therefore, when all of the coins were transferred into separate 1 L containers, the total volume of coins stayed the same, but the two containers each had a volume of 1 L.

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The solution to the system of equations from the graph and the algebraic method correlates with one another i.e. x = 4, y = 3

A system of linear equations is a grouping of one or more linear equations with the same variables. There are various ways for solving a system of two linear equations, these includes:

In the Graphical method, to graph an equation system, we simply do so by plotting the equations on the same set of axes and searching for the point(s) where the two lines cross. This intersection point is the system's solution since it reflects the values of the variables that make both equations true at the same time.

The plot for the two systems of the equation can be seen in the image attached below.

y = x - 1

y = 3x - 9

From the graph, we could see that the two equations intersect at (4,3). It implies that in the order (x,y), x = 4, and y = 3.

Using the algebra elimination method.

y = x - 1          ..... (1)

y = 3x - 9       ..... (2)

From equation (1),

y - x =  -1

y - 3x =  -9

By Elimination method,

2x = 8

x = 8/2

x = 4

Replace the value of x into equation (1),

y = 4 - 1

y = 3

Therefore, we can conclude that the solution to the system of equations from the graph and the algebraic method correlates with one another i.e. x = 4, y = 3

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The length of BD in simplest radical form is √77 units

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

Hypotenuse AC = AD + DC = 7 + 11 = 18

Altitude = square root of the multiplication of AD and DC

√(7 x 11) = X

√77 = X

√77 can't be simplified further

Therefore, the length of BD is √77 units

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Using the concept of fraction and percentage, the percentage increase of the baby at 12 months is 177.7 percent

Percentage increase is a mathematical concept that refers to the increase in a particular value over its initial amount. It is usually expressed as a percentage and is calculated by dividing the increase in the value by the original amount, then multiplying by 100.

In this problem, the data given are;

The percentage increase at 12 months old can be calculated as

percentage increase = [(mass at 12 months - Initial mass) / Initial mass] * 100

percentage increase = [(10 - 3.6) / 3.6] * 100

percentage increase = 1.7 * 100

Percentage increase = 177.7%

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Answer:

so shortcut method for finding slope in equation is simply slope = - coefficent of x/ coefficient of y

Answer:

5/6

Step-by-step explanation:

put the equation into slope-intercept form:  y = mx + b

5x - 6y = 30

-6y = -5x + 30

y = (-5/-6)x - (30/6)

y = 5/6x - 5

Therefore, slope = m = 5/6

The percentage that is the mark-up is 152%

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

Initial value = $0.25

Final value = $0.63

The percentage mark up is then calculated as

Percentage mark up = (Final value - Initial value)/Initial value * 100%

Substitute the known values in the above equation, so, we have the following representation

Percentage mark up = (0.63 - 0.25)/0.25 * 100%

Evaluate

Percentage mark up = 152%

Hence, the percentage mark up is 152%

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Answer:

Veda: 10

Kaleb: 20

Step-by-step explanation:

Veda is seen in the equation:

y = 10x + 600

The 600 is telling us what elevation she started at and the 10 tells us her rate.  

Kaleb:

We see that he went down 20 feet every second (570 - 550)

Answer: Hope This help:)

Step-by-step explanation:

One event A is dependent on another event B if the probability of event A has occurred given event B is the same as the probability that A will occur with no knowledge of B.

When Two events are to be Dependent the outcome of the first event influences the outcome of the second event, and also defines if the outcome of one event affects the outcome of the other.

When two events, A and B are dependent, the probability of occurrence of A and B is:

P(A and B) = P(A) · P(B|A)

P(A)  represents the probability of happening an event A.

P(B) represents the probability of happening an event B.

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Scott pays his nephew $10 per hour, and he initially had $900 for extra labor. Then the correct option is C.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The graph below illustrates how much Scott must spend on additional labor to hire someone to assist him as he works on his property. He recruited his nephew to work on weekends and after school.

From the graph, the two points are (0, 900) and (800, 10). Then the slope of the line is given as,

m = (900 - 800) / (0 - 10)

m = - 100 / 10

m = - 10 dollars per hour

Then the equation is given as,

y = - 10x + 900

Scott pays his nephew $10 per hour, and he initially had $900 for extra labor. Then the correct option is C.

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The equation that shows the relationship between the number of seconds since the boy let the balloon go is y = 3x + 3.

A function can be defined as the outputs for a given set of inputs. The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Here,

Given, A little boy accidentally let go of his balloon, and it floated away. It was 3 feet above the ground when he let go this height is our constant value in the function.

It steadily rose 3 feet per second.

Assuming time in seconds to be x and total height is y.

∴  An equation that shows the relationship between the number of seconds since the boy let the balloon go is,

y = 3x + 3

The link between the amount of seconds after the youngster let go of the balloon is shown by the equation y = 3x + 3.

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Answer:

n = input()

a = 0

while pow(a, 2) < n:

   print(pow(a, 2))

   a += 1

Step-by-step explanation:

The value for a = 10 and b = -[tex]\frac{16}{5}[/tex] to create infinitely many solutions to this system of equations.

       (x1, y1) = (negative 3, negative 4) and (x2, y2) = (2, negative 2).

        m = (y2 - y1) ÷ (x2 - x1) = (-2 - (-4)) ÷ (2 - (-3)) = [tex]\frac{2}{5}[/tex]

       b = y1 - mx1

          = -4 - ( [tex]\frac{2}{5}[/tex])(-3)

          = -4 - (- [tex]\frac{2}{5}[/tex])

          = -4 +  [tex]\frac{2}{5}[/tex]

        y = ( [tex]\frac{2}{5}[/tex])x - 4 +  [tex]\frac{2}{5}[/tex] =  [tex]\frac{2}{5}[/tex] x - [tex]\frac{16}{5}[/tex]

        10x - ([tex]\frac{16}{5}[/tex])y = 60

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With the hit and trial method of infinite number of solutions, the equation can be solved through:

A=20

B= -60

A system with infinite number of solutions is formed by equations which are a multiple of the other one. To create infinitely many solutions, we have to make sure that the line equation is equal to the equation of the other equation we have. Then, the following proportion must be observed:

A=10/-10 = -A/20 = 60/B

A= -1

-A/20 = -1

A=20

60/B= -1

B= -60

Hence the values for A and B are 20 and -60 respectively.

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Answer:

[tex]\frac{1}{36}[/tex]

Step-by-step explanation:

The probability of rolling a 4 is 1/6.

Using the multiplication rule, the required probability is [tex](1/6)^2=\frac{1}{36}[/tex].

Answer:

W = 59 degree

Y = 59 degree

Z = 53 degree

x = 121 degree

v = 121 degree

Step-by-step explanation:

W = 59 degrees because a triangle has a total of 180 degrees, and we know 2 of the angles, one is 31 degrees and the other is 90 degrees, so

90 + 31 = 121

180 - 121 = 59 degrees

So, W = 59 degrees

Y = 59 degrees because w and y are vertical angles.

z = 53 degrees because

68 + 59 = 127

180 - 127 = 53 degree

So, z = 53 degree

x = 121 degree, y = 121 degree because w, x, y, v add up to 360 degree

59 + 59 = 118

360 - 118 = 242

242 / 2 = 118 degree

So, x and y equal to 118 degrees.

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