factorise x squared +3x - 40

The equation of the line that passes through the point and slope (-2, -7) m = 4/5

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The line contains the following point and slope. (-2, -7) m = 4/5

y - y1 = m(x - x1)

y + 7 = 4/5(x + 2)

y = 4x/5 + 8/5 - 7

y = 4x/5 - 27/5

Thus, the equation of the line that passes through the point and slope (-2, -7) m = 4/5

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Answer:

Step-by-step explanation:

Since the two vector have opposite directions, their sum will be the difference of magnitudes:

And the direction is the same with the vector with greater magnitude, so it is south.

Answer:

Magnitude = 39 km

Direction = South

Step-by-step explanation:

Formula we use,

→ r + s

Now the required answer will be,

→ r + s

→ 164 + (-125)

→ 164 - 125

→ 39 km

Thus, answer is 39 km due south.

The equation of the line is y=-x-4

How to find whether line is perpendicular or not?

Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

The given line is

y=x-1

the slope of it is 1

As the slopes of perpendicular lines are negative reciprocals

So, the slope of the perpendicular line is -1

As the point is(-6,2)

y=mx+b

y=(-1)x+b

2=-1(-6)+b

2=6+b

b=2-6

b=-4

∴The equation of the line that is perpendicular is  y=-x-4

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We have elaborate below a real-world problem that involves a decimal divided by a decimal.

Since we are given a problem that says that Jake owns a bakery  amd he makes 8.5 boxes of cupcakes in 15.5 hours,  the question is how many cupcakes he makes in 1 hour .So the time taken is 15.5 and the number of cupcakes made in the  15.5 hours is 8.5. So 15 .5hours=8.5 cupcakes, now dividing both sides by 15.5, we get: 1 hour=8.5/15.5 =0.54 = 1 cupcake, therfore, it needs 1 hour  to make 1 cupcake. Here we had two quantities in form of decimals, so there division of expression of decimal dividing a decimal.

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Answer:960000000

Step-by-step explanation:

Answer: 960000000

Step-by-step explanation:

960 times 1.0 times 10^6 look it up !!

Answer:

1

Step-by-step explanation:

1.5/2.5= 0.6

0.6 nearest tenth is 1

0.0-0.5 --0

0.6-0.9 --1

Answer:

1. -3

2. 6

3.less than

Step-by-step explanation:

The two equations that can be formed by adding or subtracting is

4x−4y = 16 and  2x − 6y = -8 .

the two equations are : x + y = 12 and 3x − 5y = 4

Adding we get :

x + y = 12

3x − 5y = 4

4x -4y = 16

Subtracting we get:

x + y = 12

3x − 5y = 4

-2x + 6y = 8 or 2x - 6y = -8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the unknown parameters variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

It will be regarded as a phrase. In the following section of this article, you will discover the distinction between an equation and an expression.

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Y-intercept(b)= 10

equation wasnt written in the correct order so b is 10

1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

1 + 2 = 3

As we know, from the definition:

Arithmetic can be defined as, an operation in which we do the addition of numbers, subtraction, multiplication, and division.

For the addition of two numbers:

The two numbers are 1 and 2:

Draw a vertical line 1:  |

Draw two vertical lines 2:  | |

Count the lines:  | | | = 3

Thus, 1 + 2 is equivalent to 3 if 1 + 2 = 3 after using the arithmetic operation, the answer is 3.

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The probability that the spinner lands on yellow and the coin toss is tails is 9/10.

What is probability?

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No of blue=1

No of yellow=9

No. of total possible outcome=10

Therefore the probability that the spinner lands on yellow and the coin toss is tails P= 9/10.

           P= 9/10                            

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Step-by-step explanation:

n^2 - n -56 = 0

n^2 -8n +7n-56 = 0

n(n-8) +7(n-8) = 0

(n+7)(n-8) = 0

n = (-7,8)

option B

=====================================================

Work Shown:

x = number of nickels

y = number of dimes

5x = value of the nickels only (cents)

10y = value of the dimes only (cents)

5x+10y = total value of all the coins = 75 cents

One equation we can form is 5x+10y = 75.

"he has twice as many dimes as nickels" tells us that y = 2x. We can replace every copy of y with 2x and solve for x as shown in the steps below.

5x+10y = 75

5x+10(y) = 75

5x+10(2x) = 75 ... plug in y = 2x

5x+20x = 75

25x = 75

x = 75/25

x = 3

This value leads to y = 2x = 2*3 = 6

Johnny has 3 nickels and 6 dimes.

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

Check:

1 nickel = 5 cents

3 nickels = 3*5 = 15 cents

1 dime = 10 cents

6 dimes = 6*10 = 60 cents

3 nickels + 6 dimes = 15 cents + 60 cents = 75 cents = $0.75

The answers are confirmed.

Answer:

AP = 18, PL = 9

Step-by-step explanation:

assuming AL, is a median of the triangle

then AP = [tex]\frac{2}{3}[/tex] AL = [tex]\frac{2}{3}[/tex] × 27 = 18

PL = [tex]\frac{1}{3}[/tex] AL = [tex]\frac{1}{3}[/tex] × 27 = 9

I believe that f(2) would be 10 and f(-2) would be -5.

Answer:

2.9 × 1025

(scientific notation)

= 2.9e25

(scientific e notation)

Step-by-step explanation:

hope this helped

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Write the value of x when y is = 7

x = 7

x = -1

x = -4

Answer:

Angles 2, 3, 6, and 7 will be the same with 41 degrees!

Angles 1, 4, 5, and 8 are the same with 139 degrees!

Step-by-step explanation:

Opposite angles are the same so that makes angles 2, 3, 6, and 7 the same at 41 degrees!

The same rule applies to angles 1, 4, 5, and 8 and we have to subtract!

180 - 41 = 139 degrees!

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Using a linear equation to solve this problem, the charge for a 3.5 hour job is 85.45 dollar.

To find how much was the bill, we need to write an equation or linear equation for this.

For every linear equation, it takes the form of y = mx + c.

Where m and c are the slope and intercepts of the straight line.

In this case, our linear equation can be written as

y = 18.70x + 20

where x = number of hours worked.

If the job took three and a half hour which is 3.5 hours, we can substitute this into the equation and solve.

y = 18.70(3.5) + 20

y = 85.45

The charge is 85.45 dollar.

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A Linear equation in point slope form using the first point 3/4h , 9 in that can be used to determine the level of chocolate syrup in dispenser after x hours is y = -4x + 12 .

In the question ,

it is given that

in 3/4 hours the the level of chocolate syrup was 9 inch ,

So , the first point is (3/4,9) .

in 5/4 hours the level of chocolate syrup in the dispenser was 7 inch .

So , the second point is (5/4,7)

to find the linear equation we first need to find the slope .

Slope = (7-9)/(5/4-3/4)

= -2/(2/4)

= -4

So , the equation in slope intercept form having point (3/4 , 9) and slope -4 is    .

(y - 9) = -4(x - 3/4)

y - 9 = -4x + 3

y = -4x + 3 + 9

y = -4x + 12

Therefore , The linear equation is y = -4x + 12 .

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The point that represent the origin in the number line is Point W

A number line is a horizontal representation of numbers in parts with equal intervals

The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values at right

number line on -5 to 5 will have the origin at the center and te center here is zero which is similar to p

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The smaller tap take 25 hours to fill the tank and the larger tap take 10 hours to fill the tank.

How to calculate time taken to fill the tank for each tap?

Given,

Time taken for two tap together to fill the tank = [tex]9\frac{3}{8}[/tex] hours = [tex]\frac{75}{8}[/tex] hours

Time taken for smaller tap to fill the tank = x hours

Time taken for larger tap to fill the tank = x - 10 hours

So,

Tank filled by two tap together in 1 hour = [tex]\frac{8}{75}[/tex]

Tank filled by smaller tap in 1 hour = [tex]\frac{1}{x}[/tex]

Tank filled by larger tap in 1 hour = [tex]\frac{1}{x-10}[/tex]

Then, tank filled by two tap together is equal to tank filled by smaller tap and larger tap. So,

[tex]\frac{8}{75} = \frac{1}{x} + \frac{1}{x-10}[/tex]

[tex]\frac{8}{75} = \frac{x-10+x}{x(x-10)}[/tex]

[tex]\frac{8}{75} = \frac{2x-10}{x^{2}-10x}[/tex]

[tex]8x^{2}-80x = 150x - 750[/tex]

= [tex]8x^{2} - 230x + 750[/tex]

= [tex]2(4x^2 - 115x + 375)[/tex]

= [tex]4x^2 - 100x - 15x + 375[/tex]

= [tex](4x - 15) (x - 25)[/tex]

If, x = [tex]\frac{15}{4}[/tex] then x - 10 for larger tap equal to [tex]\frac{15}{4}[/tex] - 10 = [tex]- \frac{25}{4}[/tex] < 0 hours, so it is impossible.

Then, x must be 25. So, for larger thank is 25 - 10 = 15.

Smaller tap take 25 hours to fill the tank

Larger tap take 15 hours to fill the tank.

Thus, the smaller tap take 25 hours to fill the tank and the larger tap take 10 hours to fill the tank.

Your question is not complete, but most probably your full questions is (image attached)

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The product of the radical expression is  - 49 + 13√7. option B is the correct answer

From the question, we have

(7-√7)(-6+√7)

= (7) × (-6) + (-√7) × (√7) + (-√7) × (-6) + (7)(√7)

= -42 - 7 + 6√7 + 7√7

= - 49 + 13√7

The product of the radical expression is  - 49 + 13√7

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The equation that shows the relationship between the nights and the length knitted is y = 22x.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the nights = x

Let the length knitted = y

The appropriate equation will be:

y = (22 × x)

y = 22x

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As the sample size (n) increases, the number of degrees of freedom increases, and the t-distribution approaches a normal distribution.

What is degrees of freedom ?

The variety of degrees of freedom is the amount of values within the final calculation of a datum that are liberal to vary. Estimates of applied math parameters are often primarily based upon totally different amounts information|of knowledge or data.

Main Body:

Degrees of freedom typically equals the quantity of observations (or items of information) minus the quantity of parameters calculable. once you perform regression, a parameter is calculable for each term within the model, and and every one consumes a degree of freedom. Therefore, as well as excessive terms during a multivariate analysis model reduces the degrees of freedom on the market to estimate the parameters' variability.

Hence the number of degrees of freedom increases,as the sample size (n) increases.

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A coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables. For example, in the term 2x, 2 is the coefficient.