How to solve systems using elimination

Answer:

The piecewise model of the function is

[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]

[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]

Step-by-step explanation:

we know that

The general form of absolute value equation is

[tex]f\left(x\right)=a\left|x-h\right|+k[/tex]

where

The variable a, tells us how far the graph stretches vertically, and whether the graph opens up or down

(h,k) is the vertex of the absolute value

In this problem we have

[tex]f\left(x\right)=0.7\left|x-4\right|+2[/tex]

we have

[tex]a=0.7[/tex]

The coefficient a is positive ----> the graphs open up

The vertex is the point (4,2)

Find the piecewise model

case 1) positive value

[tex]f(x)=0.7[(x-4)]+2[/tex]

[tex]f(x)=0.7x-2.8+2\\f(x)=0.7x-0.8[/tex]

Is a linear equation with positive slope

[tex](x-4)\geq 0\\x\geq 4[/tex]

The domain is the interval [4,∞)

case 2) negative value

[tex]f(x)=0.7[-(x-4)]+2[/tex]

[tex]f(x)=-0.7x+2.8+2\\f(x)=-0.7x+4.8[/tex]

Is a linear equation with negative slope

[tex](x-4)< 0\\x<4[/tex]

The domain is the interval (-∞,4)

[tex]x<4[/tex]

therefore

The piecewise model of the function is

[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]

[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]

Answer:

  300

Step-by-step explanation:

12 and 25 have no common factors, so their least common multiple is their product:

  12·25 = 300

Matthew will do both again in 300 days.

Final answer:

To create an equation yielding a solution of 8, use a variable x and the fraction 1/4. By multiplying x by 32, the equation will result in 8.

Explanation:

To write a multiplication equation with one variable and one fraction yielding a solution of 8:

Start with the fraction 1/4.

Multiply that fraction by x = 32 to get a product of 8.

Answer:

135m^2

Step-by-step explanation:

length = l

width = w

l + l + w + w = 48

l = w+6

w+6 + w+6 + w + w = 48

4w + 12=48

4w=36

w=9

l=15

15*9=135

Answer:

A = 135m²

Step-by-step explanation:

Write equations to represent the problem.

l = w + (6m)        The length is 6m more than the width

P = (48m)        Perimeter is 48m

***We put brackets around numbers with the "m" to avoid confusing the units with a variable.

The formula for perimeter of a rectangle is P = 2(l + w)

Substitute "l" and "P" into the perimeter formula with the equations above. Simplify, then isolate "w".

P = 2(l + w)        

(48m) = 2(w + (6m) + w)        Collect like terms (w + w = 2w)

(48m) = 2(2w + (6m))        Distribute over brackets

(48m) = 4w + (12m)        Start isolating "w"

(48m) - (12m) = 4w + (12m) - (12m)        Subtract 12m from both sides

(36m) = 4w        

4w/4 = (36m)/4        Divide both sides by 4

w = 9m        Width of rectangle

Find "l" using the formula for length. Substitute the width.

l = w + (6m)        

l = (9m) + (6m)        Add

l = 15m        Length of rectangle

Use the formula for the area of a rectangle A = lw.

Substitute the values we found for length and width.

A = lw        

A = (15m)(9m)        Multiply

A = 135m²        Area of rectangle

Therefore the area of the rectangle is 135m².

Answer:

-6, -7, -8, -9

Step-by-step explanation:

-2x > 10

x < -5

So x can be -6, -7, -8, -9

Any number less than -5 is a solution.

The listed ones are the solutions because they satisfy the the inequality,

-2x > 10

x = -6, -2(-6) > 10 12 > 10

x = -7, -2(-7) > 10 14 > 10

x = -8, -2(-8) > 10 16 > 10

x = -9, -2(-9) > 10 18 > 10

To factor the expression 15x - 25 using the greatest common factor (GCF), divide each term by the GCF. The factored form is 5(3x - 5).

To factor the expression 15x - 25 using the greatest common factor (GCF), we need to find the largest number that divides both terms evenly. In this case, the GCF is 5. We can then divide each term by 5 to factor out the GCF:

15x ÷ 5 = 3x

-25 ÷ 5 = -5

Therefore, the factored form of the expression 15x - 25 is 5(3x - 5).

The expression 15x - 25 is factored by finding the Greatest Common Factor, which is 5, and then dividing each term by 5 to get the factored expression 5(3x - 5).

To factor the expression using the Greatest Common Factor (GCF), we need to identify the highest number that divides both coefficients in the expression 15x - 25. In this case, both 15 and 25 are divisible by 5, so 5 is the GCF of the expression. Applying the distributive property, we factor out the GCF:

Now, the expression 15x - 25 is fully factored as 5(3x - 5).

Answer:

an individual thing or person regarded as single and complete but which can also form an individual component of a larger or more complex whole

Answer:

Step-by-step explanation:

3(x + 1) + 4x + 3 = 34......distribute thru the parenthesis

3x + 3 + 4x + 3 = 34....combine like terms

7x + 6 = 34....subtract 6 from both sides

7x = 34 - 6

7x = 28....divide by 7

x = 28/7

x = 4 <====

Answer:

look at the picture shown

Answer:

[tex]- (\frac{15 - 4\sqrt{3} }{11} )[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{3}-6}{\sqrt{3} +6} = \frac{(\sqrt{3}-6)(\sqrt{3}-6)}{(\sqrt{3} +6)(\sqrt{3} -6)}[/tex]

[tex]= \frac{(\sqrt{3})^2 - (2\times6\times\sqrt{3}) +6^{2} }{(\sqrt{3})^2 - 6^{2}} = \frac{9 - 12\sqrt{3} + 36}{3 - 36}[/tex]

[tex]\frac{45 -12\sqrt{3} }{-33} =- (\frac{15 - 4\sqrt{3} }{11} )[/tex]

Answers are 1. a = 32, b = 2, 3. c = 4, 4. x = -3, 5. y = -7, 6. z = -2, 7. m = -7, 8. n = -4, 9. s = -3, 10. r = 5, 11. t = 3, 12. p = 2, 13. x = 9, 14. w = 6, 15. g = 1.5, 16. v = -16, 17. b = -6, 18. h = -5, 19. k = -2.5, 20. d = -3.5, 21. r = -8, 22. z = -9, 23. x = -7, 24. y = 3.5, 25. y = 9, 26. w = 8.

Step-by-step explanation:

Step 1; To solve the given equations we keep the unknown variable on one side while the known numbers are taken to the other side. If both sides are negative the answer has a positive value while if one side is positive and one side is negative, the answer is negative.

Step 2; Solve

1. a = 9/3=  3,

2. b = 14/7 = 2,

3. c = 36/9 = 4,

4. x = -15/5 = -3,

5. y = 28/-4 = -7,  

6. z = -16/8 = -2,

7. m = 28/-4 = -7,

8. n = 8/-2 = -4,

9. s = -21/7 = -3,

10. r = -25/-5 = 5,

11. t = -18/-6 = 3,

12. p = -18/-9 = 2,

13. x = 18/2 = 9,

14. w = 24/4 = 6,

15. g = 9/6 = 1.5,

16. v = -32/2 = -16,

17. b = -18/3 = -6,

18. h = -35/7 = -5,

19. k = 20/-8 = -2.5,

20. d = 14/-4 = -3.5,

21. r = -72/9 = -8,

22. z = 27/-3 = -9,

23. x = -35/5 = -7,

24. y = 28/8 = 3.5,

25. y = 81/9 = 9,

26. w = 16/2 = 8.

Answer:

Just multiply four times twenty and youll get your answer

See picture for solution to your problem.

I'm guessing you mean (6/7)x+(1/2)=7/8

Subtract 1/2 (also 4/8) from both sides:  (6/7)x=3/8

Divide both sides by 6/7: x=21/48=7/16

So x is 7/16

Hope this helped!

Simple interest formula: A= P(1+Ryan)

A = 12000(1+ 0.07x4) = 15,360.00

Amount of interest = 15360-12000= 3,360.00

A= 12000(1+0.08x5) = 16,800.00

Interest = 16,800-12,000 = 4,800.00

Difference in interest = 4800 - 3360 = $1,440.00

Answer:

1440

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

read explanation

Step-by-step explanation:

This won't give him the correct answer because if he substitutes zero into anything he will get -5.9. 0 multiplied by anything is 0 and if you put that into bot equations you get the same answer so it won't help him. he should instead try 1 or something like that.

Answer: 16x² + 8x + 1

Step-by-step explanation:

(4x + 1)(4x + 1)

This expansion can be done in two ways either by direct expansion or by indirect expansion

(1) Direct expansion

(4x + 1)(4x + 1 )

4x X 4x + 4x X 1 + 1 X 4x + 1 X 1

= 16x² + 4x + 4x + 1

= 16x² + 8x + 1

(2) Method

This can be written thus:

(4x + 1 )(4x + 1 ) = (4x + 1 )²

= (4x)² + 2( 4x X 1 ) + 1²

= 16x² + 2(4x) + 1

= 16x² + 8x + 1.

(4x + 1)(4x + 1)

4x · 4x = 16x²

4x · 1 = 4x

1 · 4x = 4x

1 · 1 = 1

16x² + 4x + 4x + 1

16x² + 8x + 1

Answer:

[tex]200.96sq.ft.[/tex]

Step-by-step explanation:

Given:

            Circumference= 50.24 ft.

We have to find the area of the circle.

Finding the radius with the help of given circumference

            Circumference of a circle= [tex]2\pi r[/tex]

                           [tex]50.24=2*\pi* r\\\\50.24=2*(3.14)*r\\\\50.24=6.28*r\\\\r=\frac{50.24}{6.28} \\\\r= 8ft.[/tex]

Area of a circle=  [tex]\pi r2[/tex]

                     [tex]=\pi *8*8\\\\=64*\pi \\\\=64*3.14\\\\=200.96sq.ft.[/tex]

The two numbers being asked in the question are 4 and -1.

This question can be solved using a system of linear equations. Let's call the first number x and the second number y.

From the first statement, we can create one equation: 2x + 4y = 4

From the second statement, we can create another equation: x - y = 5

To solve this system, we can use substitution or elimination method. If we multiply the second equation by 2, we get 2x - 2y = 10. Now, we can subtract the second equation from the first: (2x + 4y) - (2x - 2y) = 4 - 10, which simplifies to 6y = -6. Dividing both sides by 6, we get y = -1.

Substitute y = -1 into the equation x - y = 5, we get x - (-1) = 5. Therefore, x = 5 - 1 = 4.

So, the first number x is 4 and the second number y is -1.

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Answer:

★THANKS★

ANY DOUBTS? COMMENT PLEASE

Answer:

70

Step-by-step explanation:

16÷(100%-78%) = 16÷22% = 72.73 =70(correct to the nearest tenth)

Answer:

Step-by-step explanation:

y= 16

x=15

Using the substitution method,

The value of x is -1 and y is 3.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

2x + 6y = 16 _____(1)

3x - 5y = -18 ______(2)

From (1) we get,

2x = 16 - 6y

x = (16 - 6y)/2

Substituting in (2).

3x - 5y = -18

3 x (16 - 6y)/2 ) - 5y = -18

3 x (8 - 3y) - 5y = -18

24 - 9y - 5y = -18

24 + 18 = 9y + 5y

42 = 14y

y = 42/14

y = 3

And,

x = (16 - 6y)/2

x = (16 - 6 x 3) / 2

x = (16 - 18) / 2

x = -2/2

x = -1

Thus,

x = -1 and y = 3.

Learn more about equations here:

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Answer:

700  milligrams of protein is contained in one glass.

Step-by-step explanation:

Given:

Protein present in on glass of soy milk =  7 grams

To Find:

How many milligrams of protein does one glass contain =?

Solution:

​We have to convert grams to milligrams

We know that 1 gram  =  100 milligram

then 7 grams  will be  = [tex]7 \times 100[/tex] milligrams

7 grams  =  700 milligrams

Therefore in one glass of soy milk there will be 700 milligrams of proteins

Answer: Yes

Step-by-step explanation: 7x and 9x are called terms and the numbers in front of the variables, +7 and +9 are called coefficients.

Because the variables, x and x are identical, the two terms in this problem are called like terms so yes, 7x and 9x are like terms.

Answer:  15.67

Step-by-step explanation:

Pot Santa

Answer:

15.67

Step-by-step explanation:

focus only on the underlined area

15.666666666667

round the last 6 underlined is what we are going to use to round the one before it

5 or more goes up so the six is now rounded to a seven on that part leaving you with 15.67

Answer:

[tex]V=(a^{4})(b^{6})\ units^3[/tex]

Step-by-step explanation:

we know that

The volume of a rectangular prism is equal to

[tex]V=LWH[/tex]

In this problem we have

[tex]L=ab^2\\W=ab^3\\H=a^2b[/tex]

substitute

[tex]V=(ab^2)(ab^3)(a^2b)[/tex]

Applying property of exponents

[tex]x^{m} x^{n}x^{r} =x^{m+n+r}[/tex]

[tex]V=(a^{4})(b^{6})\ units^3[/tex]

Answer:

D.)<-50.5, 58.1>

Step-by-step explanation:

The vector can be decomposed into its x and y components using trigonometry.

The x and y components of the vector, together with the vector length forms a right triangle, as shown in the figure attached.

The x-component of the vector is given by

[tex]sin (-41^o)=\dfrac{x}{77}[/tex]

[tex]x=77*sin (-41^o)[/tex]

[tex]x=-50.5[/tex]

And the y-component of the vector is given by

[tex]cos(-41^o)=\dfrac{y}{77}[/tex]

[tex]y=77*cos(-41^o)[/tex]

[tex]y=58.1[/tex]

Thus, the vector as an ordered pair is represent by

[tex]\boxed{ (-50.5, 58.1)}[/tex]

which is choice D.

Answer:

0.25

Step-by-step explanation:

number of trial = 12

probability of getting blue marbles = 3/12

0.25

To meet or beat the sales goal, the inequality 72x + 90y ≥ 360 can be used to represent the number of games that must be sold every day. The graph of this inequality would show the region above or on the line 72x + 90y = 360.

To meet or beat the sales goal of at least $360 per day, we can set up an inequality based on the profits from selling games. Let x be the number of portable game systems sold and y be the number of standard game systems sold. The inequality representing the number of games that must be sold every day is 72x + 90y ≥ 360.

To graph this inequality, we can plot the points on a graph where each point represents a combination of x and y. Then we shade the region that satisfies the inequality, which is the region above or on the line 72x + 90y = 360.

See the graph in the attached image for visual representation.

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See picture for answer and explanation.

We can completely define a line equation by only knowing two points on the line, so we will use that to find our line's slope.

The slope is positive. (We will see that the slope is equal to 1/5).

The first general rule is that, if the line, readen from lest to right increases, then the slope is positive. (Here by the description we know that it increases).

But let's find the slope to see this.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then we can write the slope as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we can use two of the given points to find the slope, I will use the first two: (-5, -1) and (0, 0)

We will get:

[tex]a = \frac{0 - (-1)}{0 - (-5)} = \frac{1}{5}[/tex]

So the slope is 1/5, which is positive.

Then the correct option is the first one.

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The monthly payment of the loan is  =$ 437.5

Step-by-step explanation:

Given , the simple interest due on a six month loan of $2500 is $125.

Total amount he paid =$ (2500+125)

                                    =$2625

The monthly payment of the loan is =$(2625÷6)

                                                                =$ 437.5