four minus 7 times a number is equal to 12 minus 3 times the number

Answer:

-2(-10x^2 + 3x -5)

Step-by-step explanation:

Combine like terms

Then find the common factor

Answer:

[tex]-20x^{2} -6x+10[/tex]

Step-by-step explanation:

[tex]=-23x^{2} +x^{2} +2x^{2} -6x+10[/tex]

[tex]=-23x^{2} +3x^{2} -6x+10[/tex]

[tex]=-20x^{2} -6x+10[/tex]

Hope this helps

Answer:

[tex]90a+10b[/tex]

Step-by-step explanation:

[tex](100a+10b+c)-(10a+c) \\ \\ =100a+10b+c-10a-c \\ \\ =90a+10b[/tex]

Answer:

We would describe 7x - 3 > 24 as an inequality

Step-by-step explanation:

The definition of inequality is a relationship between two expressions using  one of these inequality symbols:

greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).

Answer:

Inequality

Step-by-step explanation:

Inequalities are never equal just like the question you have

Answer:

[tex]\sf -\dfrac{7}{4}[/tex]

Step-by-step explanation:

  (1, -5)    ⇒ x₁ = 1    ; y₁ = -5

  (-3, 2)  ⇒ x₂ = -3  ; y₂ = 2

[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

            [tex]\sf =\dfrac{2-[-5]}{-3-1}\\\\= \dfrac{2+5}{-4}\\\\=\dfrac{7}{-4}\\\\= -\dfrac{7}{4}[/tex]

The flagpole is 35ft tall.

Given,

A 5ft tall person casts a shadow that is 4 ft long.

Flagpole has a 28-foot shadow.

Solution:

Let x be the height of the flagpole.

5/x = 4/28

x = 35ft

The flagpole is 35ft tall.

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The situation best met through long term saving is retirement (Option B).

In many cases, the retirement fund is taken out of the paychecks at your job and is accumulated over years of your service and job till retirement, it is a long-term saving.

The purpose of long-term saving is the type of saving for long term financial goals. The other options are not long-term financial goals rather unexpected expenses. Hence, a situation best fulfilled through long term saving is retirement.

There are several long-term saving accounts use to save for long term financial goals such as retirement, buying a house, children’s education, or similar one-time, long-term expenses.

Hence, the correct answer is retirement – Option B

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Answer:

382.5 in^2

Explanation in attachment. Hope it helps! :)

Based on the dilation, the scale factor of dilation of the point is 1/3

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

From the question, we have the following parameters

Dilation rule: Do,k

Point = (9, 6)

Image = (3, 2)

As a general rule of dilation, the following are the properties of a scaled copy of another figure

Using the above as a guide, the scaled factor is calculated as

Scaled factor = Image/Poins

This gives

Scaled factor, k = (3, 2)/(9, 6)

This gives

Scaled factor, k = 1/3

Hence, the scale factor is 1/3

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Carol can make a maximum of 4 smoothies with the available yoghurt

Cups of yoghurt Carol has for making smoothies = 1 5/8 cups

Yoghurt Carol has in improper fractions = 13/8 cups

Cup of yoghurt used to make smoothie = 1/3 cups

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Number of smoothies Carol can make = Total available yoghurt with Carol/Yoghurt used to make a smoothie

= (13/8)/(1/3)

= 39/8

Converting the fraction into a mixed fraction we get: 4 7/8 smoothies

So, she can make 4 cups of smoothie

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TheThe number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48,135 miles.

Distance from Station 1 to satellite:

tan8.7 = length of longest leg / length of longest leg

tan8.7 =  3963/length of shortest leg

Length of longest leg=3963/tan8.7°

Length of longest leg=3963/0.15302150298

Length of longest leg =25,898 miles

Distance from Station 2 to satellite:

sin 8.7 = length of longest leg / length of hypotenuse

sin  8.7 =  3963/length of hypotenuse

Length of hypotenuse =3963/ sin 8.7

Length of hypotenuse =3963/0.1526082024

Length of hypotenuse=26, 200 miles

Hence,

26, 200 miles  - 3,963 =22,237 miles

Total distance:

Total distance = 25,898 miles  + 22,237 miles

Total distance = 48,135 miles

Therefore the distance is 48,135 miles.

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The complete question is:

A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.

How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?

Answer:

C. Lines l and m appear to be skew--they are not parallel, and they are not intersecting each other.

If the domain of f is ( -1, 1), then the function g defined by g(x) = f((x + 1)/(x - 1)) has a domain of; (-2, 0)

The domain of a function refers to the set of all possible intput values that make the function possible.

Now, we are given the function;

g(x) = f((x + 1)/(x - 1))

The domain would be a set of real numbers excluding 1 because at x = 1, the function is undefined.

Since the domain of  f(x)  is  -1 < x < 1  ,

Then the domain of  f(x + 1)  is  -1 < x + 1 < 1 .

domain of -1 < x + 1 < 1  will simplify to -2 < x < 0

Thus, we can say that the domain of  f(x + 1)  is  (-2, 0).

Thus;

g(x) = f(x + 1) and as such, the domain of  g(x)  is  (-2, 0) .

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Answer: 2x + 1

Step-by-step explanation:

We will simplify this expression down to it's lowest terms.

      Given:

2(x - 4) + 9

      Distribute:

2x - 8 + 9

      Combine like terms:

2x + 1

Answer:

1: -⅔

2: -⅓

Step-by-step explanation:

You plug the number into the Equation.

1:

2 = 3x + 4

-2 = 3x

x = -⅔

2:

3 = 3x + 4

-1 = 3x

x = -⅓

WE WILL USE THE FORMULA OF CALCULATING GRADIENT

[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{j - 1}{9 - 6} \\ \frac{1}{3} = \frac{j - 1}{3} [/tex]

I WILL USE CROSS MULTIPLICATION

[tex]3(j - 1) = 3 \\ \frac{3(j - 1)}{3} = \frac{3}{3} \\ j - 1 = 1 \\ j = 1 + 1 \\ j = 2[/tex]

ATTACHED IS THE SOLUTION

BE ALERT I INSERTED THE KNOWN VALUES IN THE FORMULA OF FINDING THE GRADIENT.

The expression used for finding the circumference of the circular pond is; C = 2π(d/2) feet.

For the given question;

Let 'd' be the diameter of the circular pond.

The diameter of the pond  = 15 feet.

Let 'C' be the circumference of the circle;

The, the formula for finding the circumference of the circle is;

C = 2π(d/2) feet

For, d = 15 feet

C = 2π(15/2) feet

Take π = 3.14

C = 2×3.14×(15/2) feet

C = 47.1 feet

Thus, the circumference of the circular pond is found as 47.1 feet.

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Answer:

[tex]\textsf{Slope-intercept form}: \quad y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]

[tex]\textsf{Standard form}: \quad 4x+3y=5[/tex]

Step-by-step explanation:

Given linear equation:

[tex]y-11=-\dfrac{4}{3}(x+7)[/tex]

The given linear equation is point-slope form.

[tex]\boxed{\begin{minipage}{3.7cm}\underline{Slope-intercept form}\\\\$y=mx+b$\\\\where $m$ is the slope\\ and $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

To write the equation in slope-intercept form, isolate y:

[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]

[tex]\implies y-11=-\dfrac{4}{3}x-\dfrac{28}{3}[/tex]

[tex]\implies y-11+11=-\dfrac{4}{3}x-\dfrac{28}{3}+11[/tex]

[tex]\implies y=-\dfrac{4}{3}x+\dfrac{5}{3}[/tex]

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Standard form}\\\\$Ax+By=C$\\\\where $A, B$ and $C$ are constants and $A$ must be positive.\\\end{minipage}}[/tex]

To write the equation in standard form, eliminate the fraction, bring the terms in x and y to the left of the equation, and the constants to the right:

[tex]\implies y-11=-\dfrac{4}{3}(x+7)[/tex]

[tex]\implies (y-11) \cdot 3=-\dfrac{4}{3}(x+7) \cdot 3[/tex]

[tex]\implies 3y-33=-4(x+7)[/tex]

[tex]\implies 3y-33=-4x-28[/tex]

[tex]\implies 3y-33+4x=-4x-28+4x[/tex]

[tex]\implies 3y-33+4x=-28[/tex]

[tex]\implies 3y-33+4x+33=-28+33[/tex]

[tex]\implies 4x+3y=5[/tex]

Value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.

As given,

Given function:

f(x) = -2x -1

Express value of  in simplest form:

f( x + h ) = -2 (x + h ) - 1

             = -2x -2h -1                   ___(1)

Simplify the function by substituting value of f(x +h and f(x),

[f(x + h) - f(x) ] /h

= [ (-2x -2h -1 )- ( -2x -1 ) ] /h

= ( -2x -2h -1 +2x +1 ) /h

= -2h /h

= -2

Therefore, value of the function [ f(x+ h) - f(x) ] /h in simplest form when f(x) = -2x -1 is equal to -2.

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Answer:

804,264

Step-by-step explanation:

Evaluate 93×92×94

We have 1 of the number 93

We have 1 of the number 92

We have 1 of the number 94

Group numbers by powers:

93×92×94 = 93[1]92[1]94[1]

93[1]92[1]94[1] = 804,264

The integer is 5 and the next consecutive odd integer will be 7.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

let the integer be x

then, next consecutive odd integer will be x + 2

Now, according to the question :

integer is subtracted from 2 times the next consecutive odd integeb the difference is 9 means :

2(x+2) - x = 9

2x+ 4-x = 9

x + 4 = 9

x = 5

Therefore, The integer is 5 and the next consecutive odd integer will be 7.

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Answer:

48

Step-by-step explanation:

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

6 12 18 24 30 36 40 48

16 32 48

Answer:

70°

Step-by-step explanation:

Since m∠JKH and m∠LKM are verticle angles, they are equal to each other.

Answer:

Step-by-step explanation:

they left at 12:34

The temperature when the pressure is 450 is 225°.

Given:

The pressure of a gas varies directly with the temperature.

So, P ∝ T

P = kT , here k is the constant of proportionality

Pressure(P) = 800psi

Temperature(T) = 400°

Putting the values to get the value of k,

P = kT

800 = 400k

k = 2

We need to find the temperature when the pressure is 450.

​P = kT

450 = 2T

T = 450/2

T = 225°

Therefore, the required temperature is 225°.

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Answer:

x=5

you're welcome

Answer:

read below

Step-by-step explanation:

1. $4, five granola bars cost $20. $20/5 = $4

2. 40 miles per hour, travels 100 miles at a constant speed for 40 miles. 100/2.5 = 40 miles

3. 12.5 situps per minute, 50 situps in 4 minutes. 50/4 = 12.5

4. $1.43 per one ounce, 3 ounces cost $4.29. 4.29/3 = $1.43

The point (1, 60). on the graph how's the speed that the car travels.

It should be noted that car traveled at a constant speed. The distance traveled is 210 miles and the time to travel is 3.5 hours.

Therefore, it should be noted that the point (3.5, 120) shows the distance.

The slope of the like which is the speed will be:

= Distance / Time

= 210 / 3.5

= 60 mph

Therefore, it should be noted that the point B(1, 60) lies on the graph.

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Answer:

10

Step-by-step explanation:

To find the value of the smaller integer, start by letting a variable be that integer. This helps us to refer to the integer with greater ease in our working.

Let the smaller integer be x.

Consecutive numbers refers to numbers coming after one another, such as 1, 2 and 3.

The next integer coming after the integer x would thus be (x +1). Three times the next consecutive integer would then be 3(x +1).

Subtract refers to a minus sign, thus the equation would be:

3(x +1) -x= 23

Expand:

3x +3 -x= 23

Simplify:

2x= 23 -3

2x= 20

Divide both sides by 2:

x= 20 ÷2

x= 10

Thus, the smaller integer is 10.

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*Note that when b is subtracted from a, the expression would be a -b.