Match the following terms with the correct definitions

Answer:

The "one number" is equal to 4 and "another number" is equal to 6.

Step-by-step explanation:

1. We can write an equation for "one number": X = 2n - 8 (X is one number and another number is N)

2. Since their sums are 10 we can write it was X + N

3. Plug in the value of X to get: 2n - 8 + N = 10

4. Put 8 to the other side to get + 8 --> 2n + N = 10 + 8

5. Now you form the equation 3n = 18

6. N = 18 / 3 which is 6

7. To get X you do 10 - 6 which is equal to 4

8. To make sure the answer is correct plug in the values into the equation: 4 = 2(6) - 8 which simplifies to 4 = 12 - 8

Therefore, one number is equal to 4 and another number is equal to 6

Answer: $0.92

Step-by-step explanation:

Answer:

92 cents = $0.92 = 0.92 dollars

Step-by-step explanation:

1 quarter = 25 cents

1 dime = 10 cents

6 dimes = 6 × 10 cents = 60 cents

1 penny = 1 cent

7 pennies = 7 cents

1 quarter + 6 dimes + 7 pennies =

= 25 cents + 60 cents + 7 cents

= 92 cents = $0.92 = 0.92 dollars

Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Let's call the height of the goalpost "h". We can use similar triangles to solve for h. Morgan walks a total of 13.85 and placed the mirror and walk 4.25 more, let d = 13.85.

The mirror forms a right triangle with the height of the goalpost, the distance from her eyes to the ground, and the distance d.

So, we have:

h / d = 1.15 / 4.25

Solving for h:

h = (1.15 ×13.85 ) / 4.25

h = 6371 / 1700

Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.

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We can write radicals  [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] forms to help us communicate our answers.

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Suppose, We have a radical [tex]16^{\frac{1}{4}[/tex].

Now, We know 2⁴ = 16.

So, We can rewrite [tex]16^{\frac{1}{4}[/tex] as [tex](2^4)^{\frac{1}{4}[/tex] and multiply the exponents which

results to 1.

Again say we have [tex]9^{\frac{3}{2}[/tex] and we know 3² = 9, Se we can rewrite [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] , and the exponent multiplies to 3 so it is now 3³ which is 27.

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The pendulum will swing at the velocity of 3.06 m/s at the bottom of the swing.

Velocity is the rate of change of position of an object, usually measured in meters per second (m/s). It is a vector quantity, which means it has both magnitude and direction. Velocity is an essential notion in physics since it is used to describe motion and is one of the fundamental principles of classical mechanics. It is connected to other notions such as acceleration, momentum, and force. Velocity is a measure of how rapidly an item moves in a specific direction, and it is computed by dividing the distance travelled by the time it takes for the object to traverse that distance.

The speed of the pendulum at the bottom of its swing can be calculated using the formula:

v = √(2gh)

where v = velocity, g = gravitational acceleration (9.8m/s2), h = height (1.22m)

Therefore, the speed of the pendulum at the bottom of its swing is:

v = √(2*9.8*1.22)

v = 3.06 m/s

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Answer:

u=20

Step-by-step explanation:

The equation formed will be a linear equation, and it will be y=5t/2.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Given Samantha runs on the Lakeside Trail. She runs 2½ times around the loop and then walks the remainder of the way.

Let t=length of loop

then,  total running distance(y)=5t/2

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expression : 75+90m

the 75 is the base payment, plus 90 per month, and the variable m symbolizes the amount of months.

Hope this helped =)

-YinAhara

The expression (X+1)(2x-8) in the form of trinomial is 2x²-6x-8

An expression is combination of variables, numbers and operators.

The given expression is (X+1)(2x-8)

Apply distributive property

(X+1)(2x-8)

x(2x-8)+1(2x-8)

2x²-8x+2x-8

Trinomial is an expression which has three terms.

2x²-6x-8

Hence, the expression (X+1)(2x-8) in the form of trinomial is 2x²-6x-8

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Answer:

Option D) 10mi

Step-by-step explanation:

A rectangle has 90 degree angles. When a line cuts it diagonally, it makes a right angle.

When there is a right angle we think about the Pythagorean theorem.

a²± b² = c²

Plug the values:

8²+6²= c²

Simplify:

64+36 = c²

Combine like terms:

100 = c²

Rooting hypotenuse we get

10 = c

The length of the path is 10 miles.

The likelihood of getting the loan cannot be ascertained. Hence the answer is D. There is not enough information given to determine the answer.

To determine whether Jared is likely to be approved for the home loan, it would be necessary to calculate his debt-to-income ratio, which is one of the main factors that lenders consider when evaluating loan applications. This ratio is calculated by dividing a person's total recurring monthly debt payments by their gross monthly income. If the debt-to-income ratio is higher than 28% or 36% (depending on the lender), the loan application may be declined.

Based on the information provided, it is not possible to determine Jared's debt-to-income ratio. In order to determine the ratio, it would be necessary to know Jared's gross monthly income, which is not provided. Therefore, it is not possible to say whether Jared is very likely, somewhat likely, or not likely to be approved for the home loan.

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The two numbers that when multiplied equal 5/9 and when added together equal -2 will be - 1/3 and - 5/3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let the two numbers be 'x' and 'y'. Then the equations are given as,

xy = 5/9                  ...1

x + y = - 2               ...2

From equations 1 and 2, then we have

x + 5 / (9x) = -2

9x² + 5 = - 18x

9x² + 18x + 5 = 0

9x² + 15x + 3x + 5 = 0

3x(3x + 5) + 1(3x + 5) = 0

(3x + 1)(3x + 5) = 0

x = -1/3, -5/3

At x = - 1/3, the value of y is given as,

- 1/3 + y = -2

y = - 5/3

At x = - 5/3, the value of y is given as,

- 5/3 + y = -2

y = - 1/3

The two numbers that when multiplied equal 5/9 and when added together equal -2 will be - 1/3 and - 5/3.

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32/12 is the distance walked by the four friends.

A fraction represents a part of a whole.

3/4, 1/2,2/3,3/4 is the distance travelled by the four students.

We have to find the distance they walked all together.

We have to add the all the fractions.

3/4+1/2+2/3+3/4

The LCM of 4, 2 3, and 4 is 12

9+6+8+9/12

32/12

Hence, 32/12 is the distance walked by the four friends.

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well, the line y = -5 is simply a horizontal line, a perpendicular line to that will simply be a vertical one, Check the picture below.

225 pounds of the Earl Grey tea and 375 pounds of Orange Pekoe tea are​ required to get 600 pounds of a new blend costing $3.50

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the amount of Earl Grey tea and y represent the amount of Orange Pekoe tea.

Earl Grey tea sells for $6 per pound while Orange Pekoe tea sells for $2 per pound. Both teas were mixed to get 600 pounds of a new blend selling at $3.50. Hence:

x + y = 600    (1)

Also:

6x + 2y = 3.5(600)    (2)

From both equations:

x = 225, y = 375

225 pounds of the Earl Grey tea and 375 pounds of Orange Pekoe tea are​ required

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Answer:

A ≈ 5568.2 cm²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

here the diameter = 84.2 , then r = 84.2 ÷ 2 = 42.1 , then

A = π × 42.1² = π × 1772.41 ≈ 5568.2 cm² ( to 1 decimal place )

Answer:

10%

Step-by-step explanation:

540/600 = 90%

so 10% decrease

The equation that represents the given graph is: D. y = 2/5x - 3.

The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

here, we have,

To find the equation of a line that passes through two points (x1, y1) and (x2, y2), we can use the following steps:

Find the slope (m) using the formula

m = (y2 - y1) / (x2 - x1).

Plug in the slope and one of the points into the equation

y = mx + b to find b.

So, for the line that passes through the points (0, -3) and (5, -1),

the slope is (-1 - (-3)) / (5 - 0)

                 = 2/5,

and the y-intercept can be found by plugging in the slope and the point (0, -3) into the equation y = mx + b:

-3 = (2/5) * 0 + b

-3 = b

Therefore, the equation of the line that passes through (0, -3) and (5, -1) is:  y = (2/5)x - 3

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Th equaton of d in terms of W and L is d = W/LK

From the information given, we have that;

Given that the parameters are;

This is represented as;

W ∝ Ld

Find the constant value

W/Ld = K

Substitute the values

K = 140/4×54

find the value

k = 35/54

To determine , d, we have;

d = W/LK

Hence, the expression is d = W/LK

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The solution is, a) Negative linear; b) about 48

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

a) Type of correlation

The graph shows a negative linear correlation.

b) Prediction

It looks like a student who makes 60 in Science would make about 48 in English.

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Answer:

a. In a class of 58 students, 35 students offer Biology, 28 students offer Economics and 15 students offer Physics.

Using the Principle of Inclusion-Exclusion, we can calculate the number of students who offer all three subjects as follows:

The total number of students who offer at least one subject is 35 + 28 + 15 = 78

The number of students who offer Biology and Economics is 12

The number of students who offer Biology and Physics is 7

The number of students who offer Economics and Physics is 5

So the number of students who offer all three subjects is given by:

35 + 28 + 15 - (12 + 7 + 5) = 58 - 24 = 34

Therefore, 34 students offer all three subjects.

b. A regular polygon with (2m + 1) sides has each interior angle equal to 1440.

Each interior angle of a regular polygon with n sides is given by:

angle = (n-2) * 180 / n

So for a regular polygon with (2m + 1) sides, we have:

1440 = (2m + 1 - 2) * 180 / (2m + 1)

Expanding and simplifying:

1440 = 360m / (2m + 1)

Multiplying both sides by (2m + 1):

1440 * (2m + 1) = 360m

Expanding the left side:

2880 + 1440 = 360m

4320 = 360m

Finally, dividing both sides by 360:

m = 12

Therefore, the value of m is 12.

The discount is $278.59 and the proceeds for the following simple discount note,  using 360 days for a year is $9421.41

Discount refers to a reduction in the price of an item or service. It can be expressed as a percentage or an absolute value, and it is usually calculated as a difference between the original price and the reduced price. In finance, discount is often used to refer to the reduction in the face value of a financial instrument, such as a bond or a bill, before it matures. The amount of the discount is usually based on the interest rate and the time to maturity. The term "discount" is also used in various other contexts, such as in retail sales, where items are sold at a lower price than their regular price to encourage customers to buy.

(a) The discount is calculated by multiplying the face value of the note by the discount rate and then dividing by the number of days in a year (360).

Discount = $9700 * 9.5% * 135/360

Discount = $9700 * 0.095 * 3/10

Discount = $9700 * 0.285/10

Discount = $278.59

(b) The proceeds are calculated by subtracting the discount from the face value of the note.

Proceeds = Face Value - Discount

Proceeds = $9700 - $278.59

Proceeds = $9421.41

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Answer: For each hour worked, the number of tickets sold increases by 12.

Step-by-step explanation:

The constant of proportionality for the table can be found by dividing the value of y by the value of x for one of the data points. For example, when x = 2, y = 24, so the constant of proportionality k can be found as follows:

k = y/x = 24/2 = 12

So, the equation relating the number of hours worked, x, to the number of tickets sold, y, can be written as y = kx, where k is the constant of proportionality, which we found to be 12.

Thus, the equation relating the number of hours worked, x, to the number of tickets sold, y, can be written as:

y = 12x

This equation states that for each hour worked, the number of tickets sold increases by 12.

If a survey was carried out to find the favorite beverage of a particular telemarketing company having 2,000 employees. The statement that is true about the data: B. The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.

The estimated number of employees who voted for coffee from Group A is 42 out of 100 (42%).

The estimated number of employees who voted for coffee from Group B is 44 out of 100 (44%).

The higher percentage of employees who voted for coffee in Group B (44%) suggests that a higher number of employees would have voted for coffee if the entire population of 2,000 employees had been surveyed.

Therefore the correct option is B.

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Answer:b

Step-by-step explanation:

The surface area of the prism is 166 square centimetres.

A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.

Given that the sides of the prism are 5 cm, 4 cm, and 7 cm. The surface area of the prism will be calculated as:-

Surface area = 2 [ ( 5x 4 ) + ( 4 x 7 ) + ( 7 x 5 ) ]

Surface area = 2 [ 20 + 28 + 35 ]

Surface area = 2 x [ 83 ]

Surface area = 166 square cm

Therefore, the surface area of the prism is 166 square cm.

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Answer:

C

Step-by-step explanation:

when multiplying 2 matrices:

a11 a12 a13 ... a1n

a21 a22 a23 ... a2n

...

am1 am2 am3 ... amn

X

b11 b12 b13 ... b1m

b21 b22 b23 ... b2m

...

bn1 bn2 bn3 ... bnm

you have to consider that this is only possible, when A has m rows and n columns, and B has n rows and m columns.

because the rows of A are multiplied by the columns of B.

the resulting matrix C is a square matrix and looks like

c11 c12 c13 ... c1m

c21 c22 c23 ... c2m

...

cm1 cm2 cm3 ... cmm

the different terms are created

cxy = ax1×b1y + ax2×b2y + ax3×b3y ... + axn×bny

so, in our case, we have m=n=2.

therefore, we get also C as 2×2 matrix :

2×3 + 8×2 2×0 + 8×-1

0.6×3 + 3×2 0.6×0 + 3×-1

=

6 + 16 -8

1.8 + 6 -3

=

22 -8

7.8 -3

FYI

as rule of thumb always remember :

first line first column

first line second column

...

first line last column

...

second line first column

second line second column

...

second line last column

...

last line first column

last line second column

...

last line last column

Step-by-step explanation:

x = number of children

y = number of adults

x + y = 364

x = 364 - y

1.75x + 2.25y = 707.5

using the first equation in the second :

1.75(364 - y) + 2.25y = 707.5

637 - 1.75y + 2.25y = 707.5

637 + 0.5y = 707.5

0.5y = 70.5

y = 70.5/0.5 = 141

x = 364 - y = 364 - 141 = 223

there were 223 children at the public pool.

there were 141 adults at the public pool.

Answer:in the latest published financial statements,an amount of $42000 appears against accounts payable.During the year,goods worthy $150000 were purchased on credit .assuming 365 days in a year ,what is the approximate accounts payable payment period.

Step-by-step explanation: