4. The sum of two numbers is 12 and the difference between these two numbers is 6. What are the values
of these numbers.?

a. Write the system of equations. Be sure to define your variables.

b. Solve.

Answer:

Step-by-step explanation:

The unknown is 5 I.e

1+5 = 6

5 + 5 = 10

8 + 5 = 13

Then n + 5

Answer:

Line B - red line

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

BECAUSE x-25 = 3

shows something mines 25 that equals 3

Answer:

15 more bags.

Step-by-step explanation:

360/6= 60.

270/6=45

60-45=15.

Hope this helps. <3

If the equation is cos x = x^3, the interval of length 0.01 that contains a root is [0.86, 0.87]

The given equation is

cos x = x^3

Move the term x^3 to the left hand side of the equation

cos x - x^3 = 0

Therefore the equation will be

f(x) = cos x - x^3

Here to find the interval of length 0.01 that contains a root, we have to use the intermediate value theorem

Plot the function in the graph

From the graph, we can see that the value of

x = 0.865

The interval of length = 0.01

Then the intervals will be 0.86 and 0.87

Therefore, the interval of length 0.01 that contains a root will be [0.86, 0.87]

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The dimensions of the room are approximately 5.87 meters by 7.63 meters.

Let's assume the width of the room is "x" meters.

According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.

Perimeter = 2(length + width)

Substituting the values we know:

27 = 2(1.3x + x)

Simplifying:

27 = 2(2.3x)

27 = 4.6x

Dividing both sides by 4.6:

x = 27 / 4.6

x ≈ 5.87

The width of the room is approximately 5.87 meters.

To find the length, we can multiply the width by 1.3:

Length = 1.3 * 5.87 ≈ 7.63

The length of the room is approximately 7.63 meters.

Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.

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The observation of the pattern is discussed below.

When we calculate the squares of the numbers from 1 to 10 and observe the digits at the one's place of each square, we notice a pattern:

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

If we focus on the digits at the one's place, we can see that they form a repeating pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0. This pattern repeats itself as we calculate the squares of higher numbers.

This observation is known as the "digit at one's place pattern" or the "units digit pattern." It occurs because the square of any number depends only on the digit at the one's place of that number. Hence, when we square numbers that have the same digit at the one's place, we get the same digit at the one's place in the result.

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Answer:

Let the first number be f.

Let the second number be s.

f = s-12

f+s = 100

Substitute the f in the first equation for the second equation.

s-12+s = 100

2s-12 =100

2s = 112

s = 56

Therefore f = 56-12 = 44

The 2 numbers are 56 and 44.

Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

Mary Lou Mason's total taxes on her purchase would be $1.37.

Taxes are mandatory payments to the government that are used to fund public services such as infrastructure, education, and health care. Taxes can be direct, such as income taxes, or indirect, such as sales taxes.

Mary Lou Mason's total purchase was $19.14.

To calculate the total taxes for her purchase, we can use the following formula:

Tax = (State Sales Tax %) x (Total Purchase) + (County Tax %) x (Total Purchase)

Therefore, the total taxes for Mary Lou Mason's purchase would be:

Tax = (6.5%) x ($19.14) + (1.5%) x ($19.14)

Tax = (0.065 x 19.14) + (0.015 x 19.14)

Tax = 1.24 + 0.13

Tax = $1.37

Mary Lou Mason's total taxes on her purchase would be $1.37.

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The angle m1 will be equal to 50°. The correct answer is option A.

The complete question is as below:-

Mr Jefferson is building a seesaw for the playground using the diagram shown. (see picture) In the diagram, the seesaw board is parallel to ground level and the triangle is an isosceles triangle.

What is m1?

A. 50º

B. 65º

C. 115º

D. 130º

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

We can find the angle using the opposite angles theorem.  When two are lines are crossed, there are four angles formed between them, and the opposite angles will be always equal.

Now, since the seesaw board is parallel to the ground, we can deduct (applying the opposite angles theorem) that both angles formed at the base of the triangle are equal to 65°.

Also, we must remember that the sum of the three interior angles of a triangle will be always equal to 180°, so:

m1 = 180 - ( 65 + 65 0

m1 = 50°

Therefore the angle m1 will be equal to 50°. The correct answer is option A.

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Answer:

Step-by-step explanation:

Given a right angle triangle ABC.

If ∠BCA = 90°

the hypotenuse AB = 26

AC = 10 and BC = 24.

Using the SOH, CAH, TOA trigonometry identity, SInce we are to find tanA, we will use TOA. According to TOA;

Tan (A) = opp/adj

Taken BC as opposite side since it is facing angle A directly and AC as the adjacent;

tan(A) = BC/AC

tan(A) = 24/10

tan(A) = 12/5

Answer:

         \(\ tan \ A = \dfrac{24}{10}\)

Step-by-step explanation:

\(\sf Tan \ A = \dfrac{opposite \ side \ of \ angle \ A}{adjacent \ side \ of \ angle A}\\\\Tan \ A = \dfrac{BC}{AC}\\\\Tan \ A = \dfrac{24}{10}\)

Answer: C

Step-by-step explanation: Round to the nearest 100

Answer:

m=-3

Step-by-step explanation:

Answer:

m = -3

Step-by-step explanation:

Simplify  -5m - 2m  to  -7m

-7m = 21

Divide both sides by -7

m = 21/-7

Simplify 21/-7 to -3

m = -3

Hope this helps!

-Jerc

Answer is (d). 1m & 4 m. The magnitude of the result of P + Q is between P + Q and P - Q. The magnitude of the resultant is between 3 and 5 meters when the displacement is between 1 and 4 meters.

A resultant displacement is produced when displacement vectors are added. However, as long as two vectors have the same vector amount, any two vectors can be added. A resultant velocity is produced when two or more velocity vectors are added. A resultant force is created when two or more force vectors are joined together.

S = x^2 + y^2 is the displacement formula that results. For displacement, use the letter "S." The object is moving in two directions at once: X in the first direction and Y in the second. Y = 0 if your object only moves in one direction.

verify option 1:

(1,1) = P+Q = 1+1=2

P-Q = 1-1 =0

Resultant R = 2+0 = 2 (so, we can add this Option)

verify option 2:

(1,2) = P+Q = 1+2=3

P-Q = 1-2 =-1

R= 3-1= 2 (so, we can add this Option)

verify option 3:

(1,3) = P+Q = 1+3=4

P-Q = 3-1 = 2

R= 4-2= 2 (so, we can add this Option)

verify option 4:

(1,4) = P+Q = 1+4=5

P-Q = 1-4 = 2

R= 5-2= 3 (so, we can't add this Option)

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The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

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The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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Answer:

Step-by-step explanation:

To show that x-3 and x+5 are factors of x^4+2x^3-16x^2-2x+15, we can use polynomial division, synthetic division, and the Remainder theorem.

Using long division, we can divide x^4+2x^3-16x^2-2x+15 by x-3:

x^4 + 2x^3 - 16x^2 - 2x + 15

÷ x - 3

_________________________

  x^3 + 5x^2 - 14x - 12

   |__________

      -3x^3 + 17x^2 + 26x + 36

          |_________

                -14x^2 - 23x - 36

                     |_________

                          -15x + 72

                               |___

                                  57

So, the remainder is 57, which means x^4 + 2x^3 - 16x^2 - 2x + 15 = (x - 3)(x^3 + 5x^2 - 14x - 12) + 57.

Using synthetic division, we can divide x^4 + 2x^3 - 16x^2 - 2x + 15 by x+5:

1   2    -16   -2   15

   x + 5 |x^4 + 2x^3 - 16x^2 - 2x + 15|

____________________________

        x^3 - 3x^2 + 21x + 75

So, the remainder is 0, which means x^4 + 2x^3 - 16x^2 - 2x + 15 = (x + 5)(x^3 - 3x^2 + 21x + 75).

Using the Remainder theorem, we know that if a polynomial p(x) is divided by x-a, the remainder is p(a). So, when we plug in x=3, the remainder should be p(3) = 57. When we plug in x=-5, the remainder should be p(-5) = 0. This confirms that x-3 and x+5 are indeed factors of x^4 + 2x^3 - 16x^2 - 2x + 15.

There are 960 bikes in the repair department and  1.98% of the bikes need two repairs.

The number of bikes with flat tires only is 0.25x, where x is the total number of bikes

The number of bikes with bent handlebars only is 0.05x

The number of bikes with ripped seats only is 0.1x

The number of bikes that need two repairs is 0.01Tx, where T is the percentage of bikes that need two repairs (expressed as a decimal)

The number of bikes that need all three repairs is 0.0833...x

So we have the equation:

0.25x + 0.05x + 0.1x + 0.01Tx + 0.0833...x = 101

Simplifying and solving for x, we get:

x = 960

So there are 960 bikes in the repair department.

To find the number of bikes that need two repairs, we can use the equation:

0.25x + 0.05x + 0.1x + 0.01Tx = 101 - 0.0833...x

Substituting x = 960, we get:

0.25(960) + 0.05(960) + 0.1(960) + 0.01T(960) = 101 - 0.0833...(960)

240 + 48 + 96 + 9.6T = 101 - 80

9.6T = 19

T = 1.98

About 1.98% of the bikes need two repairs.

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The slope intercept form of the line will be \(y=\dfrac{-1}{2}x+\dfrac{1}{4}\)

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

The given expression is:-

\(y=\dfrac{-1}{2}x+\dfrac{1}{4}\)

The general form of the equation of the line is given as:-

y  =  mx    +    c

From the equation, the slope will be given as:-

\(m=\dfrac{-1}{2}\)

Therefore the slope intercept form of the line will be \(y=\dfrac{-1}{2}x+\dfrac{1}{4}\)

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Answer:

volume =  2976 units^3

Step-by-step explanation:

volume = 16x15.5x12 = 2976 units^3

Answer:

I believe that it is C.

Step-by-step explanation:

360x0.15 = 24, 15% is from the given chart...

I am not 100% sure, but I do think that this is right.

The solution is : The weight of an individual who consumes 1,370 calories per day is 137 pound.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

Given:

1,050 calories should be consumed daily for a 105-pound person.

Now, to get the weight of an individual who consumes 1,370 calories per day.

If 1,050 calories should be consumed per day for = 105-pound person.

So, 1 calorie should be consumed per day for =105/1050

                                                                            =1/10                                                                                

Then, 1,370 calories consumed per day for weight of =1370/10

                                                                                         = 137 pounds

Therefore, the weight of an individual who consumes 1,370 calories per day is 137 pound.

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complete question:

The number of calories needed in a daily diet varies directly as the weight of an individual. If 1,050 calories should be consumed daily for a 105-pound person, what is the weight of an individual who consumes 1,370 calories per day?

The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

\(Area = \int\limits^b_a {y} \, dy\)

\(Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy\)

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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x = 145°

the sum of interior angles of octagon formula

S = (n - 2)×180°

n = 8

S = (8 - 2)×180°

S = 6×180°

S = 1080°

we have 1 angle = 65° & others are equal to each other

1080° - 65° = 7x

7x = 1015°

x = 1015° : 7

x = 145°

The correct statement regarding the angle measures is given as follows:

m < 1 + m < 4 > m < 3.

The given angle measure is as follows:

m < 3 = 119º.

Angles 3 and 4 form a linear pair, meaning that they are supplementary, that is, the sum of their measures is of 180º.

Hence the measure of angle 4 is given as follows:

m < 4 + m < 3 = 180º.

m < 4 = 180º - 119º

m < 4 = 61º.

Angles 1 and 4 are opposite by the same vertex, hence they are congruent, thus the measure of angle 1 is given as follows:

m < 1 = m < 4

m < 1 = 61º.

Hence:

m < 1 + m < 4 = 2 x 61

m < 1 + m < 4 = 122º

122º > 119º

m < 1 + m < 4 > m < 3.

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