(this is multiple choice and i raised points make sure to EXPLAIN !)

whats the sum of f and g ?
f(x)=10-2x and g(x)=7x+5

a) (f+g)(x)=5+5x
b) (f+g)(x)=5+9x
c) (f+g)(x)=15+5x
d) (f+g)(x)=15+9x

Final answer:

To rewrite 11/35 and 3/10 with a common denominator, find the LCD, which is 70 and it will result in 22/70 and 21/70.

Explanation:

To rewrite the fractions 11/35 and 3/10 so they have a common denominator, we need to find the Least Common Denominator (LCD) for both fractions. The denominators are 35 and 10. Prime factorizing 35, we get 5 and 7. Prime factorizing 10, we get 2 and 5.

The LCD for both will therefore be the product of these prime factors taken at the highest power that appears in each, which is 2 * 5 * 7 = 70. To rewrite the fractions, we multiply the numerator and the denominator of each fraction by any factors needed to reach the LCD.

For 11/35 to have 70 as its denominator, we observe that 35 already has the factor 7 and 5, hence it only needs to be multiplied by 2. So, 11/35 = 11 * 2 / 35 * 2 = 22/70.

For 3/10 to have 70 as its denominator, we see that 10 has the factor 2 and 5, so it needs to be multiplied by 7. Therefore, 3/10 = 3 * 7 / 10 * 7 = 21/70.

Now both fractions have the same denominator of 70, which is 22/70 and 21/70 respectively.

Answer:

5/8 of a pizza

Step-by-step explanation:

Answer:

The answer is f = 24

Step-by-step explanation:

In order to find this, multiply both sides by 3/2

16 = 2/3f

24 = f

If you put the red 3 where it is, you would be forced to put another 3 on the top-left corner of the central-left square. This would violate the first column.

This implies that the 3 in the central square must be in the top-central place.

Answer:

 x²  -x + 1   Quotient

Step-by-step explanation:

Given in the question,

the numerator = x^4 + x³ + 7x² - 6x + 8

the denominator = x² + 2x + 8

Dividing :

x^4+x^3+7x^2-6x+8  ("Dividend")

By :

 x2+2x+8    ("Divisor")

                                                                 x²  -x + 1                      Quotient

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

dividend          x² + 2x + 8     | x^4 +   x^3 +  7x² -6x + 8

divisor  *x²                                  x^4 + 2x^3 + 8x²

remainder                                                 -x³   - x²   -6x + 8

divisor  * -x1                                              -x³  -2x² . -8x  

remainder                                                           x²   +2x   +8

divisor  *1                                                            x²   +2x   +8

remainder                                                                          0

B)

(x²  -x + 1)   (x² + 2x + 8)    

= x^4 +   x^3 +  7x² -6x + 8

hence proved 

Answer:

[tex]\boxed{\bold{-5x+8}}[/tex]

Step-by-step explanation:

Combine Similar Elements: [tex]\bold{8x-11x=-3x}[/tex]

[tex]\bold{4\cdot \:2x-3x+6-5\cdot \:2x+2}[/tex]

Multiply: [tex]\bold{4\cdot \:2=8}[/tex]

[tex]\bold{8x-3x+6-10x+2}[/tex]

Group Like Terms

[tex]\bold{8x-3x-10x+6+2}[/tex]

Combine Similar Elements: [tex]\bold{8x-3x-10x=-5x}[/tex]

[tex]\bold{-5x+6+2}[/tex]

Add Numbers: [tex]\bold{6+2=8}[/tex]

[tex]\bold{-5x+8}[/tex]

To simplify the expression, combine like terms resulting in -1[tex]x^2[/tex] - 8x + 8.

To simplify the given algebraic expression, we need to combine like terms. The terms in the expression are: 4[tex]x^2[/tex], 8x, -11x, 6, -5[tex]x^2[/tex], and 2. Combining the [tex]x^2[/tex] terms and the x terms separately, we get:

[tex]4x^2 - 5x^2 = -1x^2[/tex]

8x - 11x - 5x = -8x

Finally, we add the constant terms: 6 + 2 = 8.

Putting it all together, the simplified version of the expression is: -1[tex]x^2[/tex] - 8x + 8.

When x=0, that’s the y-intercept. So in this case the y-intercept would be (0,2)

Answer:

Please refer to step-by-step.

Step-by-step explanation:

Let's solve all of these one at a time.

15. -2x - y = -5

To find the x-intercept, we need to equate the value of y to 0.

-2x - 0 = -5

[tex]\dfrac{-2x}{-2}=\dfrac{-5}{-2}[/tex]

[tex]x=2.5[/tex]

To find the y-intercept, we need to equate the value of x to 0.

-2(0) - y = -5

Now since we cannot have a negative value, we need to divide both sides by -1.

[tex]\dfrac{-y}{-1}=\dfrac{-5}{-1}[/tex]

[tex]y=5[/tex]

To find the slope form, we can simply transpose the value of -2x to the other sides of the equal sign.

-y = 2x - 5

Now we cannot have a negative value for the slope, we need to divide both sides by -1, leaving us with.

y = -2x + 5

16. 6x + 3y = -9

Let's start with the x-intercept.

6x + 3y = -9

6x + 3(0) = -9

[tex]\dfrac{6x}{6}=\dfrac{-9}{6}[/tex]

[tex]x=1.5[/tex]

Now we solve for the y-intercept.

6x + 3y = -9

6(0) + 3y = -9

[tex]\dfrac{3y}{3}=\dfrac{-9}{3}[/tex]

[tex]y = -3[/tex]

Now for the slope.

3y = -6x - 9

Now we need to divide all our variables by 3 to get y.

[tex]\dfrac{3y}{3}=\dfrac{-6x}{3}-\dfrac{9}{3}[/tex]

[tex]y=-2x-3[/tex]

17. x - y = 4

Let's start with the x-intercept.

x - y = 4

x - 0 = 4

[tex]x=4[/tex]

Now we solve for the y-intercept.

x - y = 4

0 - y = 4

-y=4

[tex]\dfrac{-y}{-1}=\dfrac{4}{-1}[/tex]

[tex]y = -4[/tex]

Now for the slope.

x - y = 4

-y = -x + 4

We need to divide all our variables by -1 to get y.

[tex]\dfrac{-y}{-1}=\dfrac{-x}{-1}+\dfrac{4}{-1}[/tex]

[tex]y=x-4[/tex]

18. 3x + 4y = 12

Let's start with the x-intercept.

3x + 4y = 12

3x + 4(0) = 12

[tex]\dfrac{3x}{3}=\dfrac{12}{3}[/tex]

[tex]x=4[/tex]

Now we solve for the y-intercept.

3x + 4y = 12

3(0) + 4y = 12

[tex]\dfrac{4y}{4}=\dfrac{12}{4}[/tex]

[tex]y = 3[/tex]

Now for the slope.

3x + 4y = 12

4y = -3x + 12

[tex]\dfrac{4y}{4}=-\dfrac{3x}{4}+\dfrac{12}{4}[/tex]

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

19. -7x + 2y = -16

Let's start with the x-intercept.

-7x + 2y = -16

-7x + 2(0) = -16

[tex]\dfrac{-7x}{-7}=\dfrac{-16}{-7}[/tex]

[tex]x=-2\dfrac{2}{7}[/tex]

Now we solve for the y-intercept.

-7x + 2y = -16

-7(0) + 2y = -16

[tex]\dfrac{2y}{2}=\dfrac{-16}{2}[/tex]

[tex]y=-8[/tex]

Now for the slope.

-7x + 2y = -16

2y = -7x - 16

[tex]\dfrac{2y}{2}=-\dfrac{7x}{2}-\dfrac{16}{2}[/tex]

[tex]y=-\dfrac{7x}{2}-8[/tex]

20. x - 5y = 55

Let's start with the x-intercept.

x - 5y = 55

x - 5(0) = 55

x = 55

Now we solve for the y-intercept.

x - 5y = 55

0 - 5y = 55

[tex]\dfrac{-5y}{-5}=\dfrac{55}{-5}[/tex]

[tex]y=-11[/tex]

Now for the slope.

x - 5y = 55

-5y = x + 55

[tex]\dfrac{-5y}{-5}=-\dfrac{x}{-5}+\dfrac{55}{-5}[/tex]

[tex]y=-\dfrac{x}{5}-11[/tex]

Answer:

There are 2 sets of numbers that work...

x = 3, y = 5

and

x = 6, y = 2

Step-by-step explanation:

Let x be one number, and let y be the other number.  We have 2 equations...

x + y = 8    (two positive numbers have a sum of 8)

xy = y + 10   (their product is equal to the larger number plus 10)

solve the first equation for y, and substitute that into the second equation...

y = 8 - x

  x(8 - x) = 8 - x + 10

now solve for x...

  8x - x² = 18 - x  

This is a quadratic, so get everything to one side so it's equal to zero...

   -x² + 9x - 18 = 0   (add x and subtract 18 from both sides)

Now solve for x...

     x² - 9x + 18 = 0    (divide both sides by -1)

         (x - 6)(x - 3) = 0    (factor)

so

x - 6 =  0  becomes   x = 6    (add 6 to both sides)

and

x - 3 = 0  becomes x = 3      (add 3 to both sides

If x is 3, then y = 5     (3 + 5 is 8, and 3(5) = 5 + 10, both equations hold up)

If x is 6, then y = 2    (6 + 2 is 8, and 6(2) = 2 + 10, both equation hold up)

Answer:

h > 6000

Step-by-step explanation:

Let h be the height of the Cirrus clouds in the inequality.

h > 6000

This states that  h  is greater than  6000

Answer:

[tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

Step-by-step explanation:

Given: [tex]A=\frac{1}{2}(b_{1} +b_{2})h[/tex]

We need to completely isolate [tex]b_{1}[/tex] to solve.

[tex]A=\frac{1}{2}(b_{1} +b_{2})h[/tex]

[tex]A=(\frac{1}{2}b_{1} +\frac{1}{2} b_{2})h[/tex]

[tex]A=\frac{1}{2}b_{1} h+\frac{1}{2}b_{2}h[/tex]

[tex]-\frac{1}{2}b_{1}h+A=\frac{1}{2}b_{2}h[/tex]

[tex]-\frac{1}{2}b_{1}h=-A+\frac{1}{2}b_{2}h[/tex]

[tex]-\frac{1}{2}b_{1}=\frac{-A}{h}+\frac{1}{2}b_{2}[/tex]

Finally, multiply both sides by -2 to completely isolate [tex]b_{1}[/tex].

[tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]

The right option is D

See the image

Answer:closing cost increase and savings are gained after the break-even point

Step-by-step explanation:

The disadvantage to purchasing points is closing costs are an increased option (B) is correct.

Fees paid at the conclusion of a real estate transaction are known as closing costs.

The complete question is:

Which of the following is a disadvantage to purchasing points

As we know, the payments paid directly to the lender during closing in exchange for a lower interest rate are referred to as mortgage points or discount points.

By doing this, the buyer lowers the rate, which lowers his monthly mortgage payments.

Thus, the disadvantage to purchasing points is closing costs are an increased option (B) is correct.

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To find the area of a rectangle, you multiply the length by the width. In this case, the area is calculated as 7.5 (length) multiplied by 5.3 (width) equaling 39.75 square units.

The question you asked refers to calculating the area of a rectangle. The formula to calculate the area of a rectangle is length times width. Given the numbers 7.5 and 5.3, we can assume these are the measurements for length and width, respectively.

To calculate the area, multiply the length (7.5) by the width (5.3). The calculation would be as follows: 7.5 * 5.3 = 39.75.

Therefore, the area of the rectangle is 39.75 square units.

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Step-by-step explanation:

By using the distributive formula, you can solve this:

-a(b - c + d) = -ab + ac - ad

-3(4x - 5y + 6) + 8x - 9

Use distributive property:

-12x + 15y - 18 + 8x - 9

Add/Subtract by the common terms:

-12x + 8x = -4x

-18 - 9 = - 27

Plug it back into an equation:

= -4x + 15y - 27

That is your answer!!

Hope that helped

~A̷l̷i̷s̷h̷e̷a̷♡

Answer:

-4x + 15y - 27

Step-by-step explanation:

-3 (4x -5y + 6) = -3*4x, -3* -5y and -3*6

-3*4x= -12x

-3*-5y= 15y

-3*6= -18

-12x + 15y -18 +8x - 9

Combine like terms (-12x + 8x) and (-18 - 9)

12-8 = 4 and 18+9 = 27 now flip the signs, add the variables back on (the letters) and carry down what was remaining (15y)

-4x + 15y -27

SUM, Addition and Atogether

Step-by-step explanation: When solving word problems, it's helpful to use keywords. Keywords tell us when to use addition, subtraction, or estimation. However, we will be only focusing on the keywords for addition.

For addition, some common keywords are altogether, total, and in all.

For example, if the problem asks for the total cost or how many people altogether, then we will probably use addition.

13 quarts of coffee

Answer:

13 quarts

Step-by-step explanation:

1 quart = 32 ounces

mug = 16 ounces = 1/2 quart

26 * 1/2 = 13

Answer:the answer is c

Step-by-step explanation:

this question was on usatestprep and i got it wrong with the answer b that was given.

The correct diagram that shows ∠1 and ∠2 as vertical angles is Option C.

Vertical angles are formed when two lines intersect. They are opposite angles and have equal measures.

If we consider the diagram given, option C shows two intersecting line, ∠1 and ∠2 are opposite angles formed by the intersecting lines, so they are vertical angles.

∠1 = ∠2 (because they are vertically opposite angles)

Thus, the correct diagram that shows ∠1 and ∠2 as vertical angles is option C.

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The missing diagram is in the image attached

Answer:

66.67%

Step-by-step explanation:

If there is 1 US open tennis championship and 1 Wimbledon per year, there are a total of 9 US open and 9 wimbledon from 1988 to 1998. So in total there are 18 championships.

Steffi Graf won 5 US open and 7 Wimbledons = 12

Essentially we want to know, 12 is what percent of 18? We can solve this by:

[tex]\frac{12}{18}*100=66.67[/tex]

Hence, 66.67% won

[tex]12 {g}^{2} + 4g - 1[/tex]

Answer:

[tex]12g^2 + 4g - 1[/tex]

Step-by-step explanation:

Hello!

We can add the two polynomials vertically.

The simplified form is  [tex]12g^2 + 4g - 1[/tex].

Twelve divided by the sum of x and 2 equals the quotient of 4 and the difference of x and 2 , the value of x is 4

Given

Twelve divided by the sum of x and 2 equals the quotient of 4 and the difference of x and 2

we need to write the given expression in equation

Twelve divided by the sum of x and 2 is written as  [tex]\frac{12}{x+2}[/tex]

quotient of 4 and difference of x  and 2 can be written as

[tex]\frac{4}{x-2}[/tex]

Now make them equal and solve for x

[tex]\frac{12}{x+2} =\frac{4}{x-2} \\12\left(x-2\right)=\left(x+2\right)\cdot \:4\\12x-24=4x+8\\12x=4x+32\\8x=32\\x=4[/tex]

So the value of x is 4

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To solve the given equation 12 / (x + 2) = 4 / (x - 2), we cross multiply, simplify and solve for x, the solution is x=4.

The equation given in this problem translates to the following algebraic equation: 12 / (x + 2) = 4 / (x - 2)

To solve for x, we first cross multiply to remove fractions: 12 * (x - 2) = 4 * (x + 2) which simplifies to 12x - 24 = 4x + 8

Then, subtract 4x from both sides: 8x - 24 = 8 and finally add 24 to both sides: 8x = 32. Therefore, solving for x by dividing both sides with 8, we get x = 4.

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Answer: $175.50

Step-by-step explanation: Since you are given the formula, your next step is to put your information into it.

I = PRT

I = 450 x .13 x 3

Now to solve for it:

I = $175.50

Answer:

34°

Step-by-step explanation:

The angle made when a tangent and a radius intersect=90°

Therefore angle OQP =90°

The triangle made by the two radii is isosceles ( base angles are equal) hence angle POQ=180-2(62)

=56°

The right triangle  OPQ can hence be solved as follows

angle POQ=56°

angle OQP=90°

angle x=180-(56+90)=34° as all the interior angles of any triangle add up to 180°

The equation 4x + y = 7 can be rewritten in slope-intercept form as y = -4x + 7, where -4 is the slope and 7 is the y-intercept. This format makes it easier to graph the line as it directly gives us the slope and y-intercept.

To rewrite the equation 4x + y = 7 in slope-intercept form (y=mx+b), we need to solve for y. This equation can be transformed by subtracting 4x from both sides, resulting in y = -4x + 7. Here, -4 is the slope (m) and 7 is the y-intercept (b).

In comparison, if we look at the given graphic (Figure A1), we see another equation where the slope or 'm' is 3 and the y-intercept 'b' is 9. This slope and y-intercept gives us the equation y = 3x + 9. Thus, it can be seen that y = mx + b format helps to better understand the geometry of a linear equation on a graph, with 'm' indicating the slope and 'b' being the y-intercept.

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Hey there!

52.08 ÷ 3 = 17.36

The correct answer is D

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

Answer:   A. (3,-2)

Step-by-step explanation:

Solve by Substitution :

// Solve equation [2] for the variable  x  

 [2]    4x = 5y + 22

 [2]    x = 5y/4 + 11/2

// Plug this in for variable  x  in equation [1]

  [1]    2•(5y/4+11/2) + 5y = -4

  [1]    15y/2 = -15

  [1]    15y = -30

// Solve equation [1] for the variable  y  

  [1]    15y = - 30  

  [1]   y = - 2  

// By now we know this much :

   x = 5y/4+11/2

   y = -2

// Use the  y  value to solve for  x  

   x = (5/4)(-2)+11/2 = 3  

Solution :

{x,y} = {3,-2}  

For Those of You With 10 Questions and Are on the Same Topic!

____________________________________________________

1. What is the apparent solution to the system of equations graphed above?

_______________________________________________________

2. A jet ski company charges a flat fee of $26.00 plus $3.25 per hour to rent a jet ski. Another company charges a fee of $24.00 plus $3.50 per hour to rent the same jet ski. Using a graphing calculator, find the number of hours for which the costs are the same. Round your answer to the nearest whole hour.

_______________________________________________________

3. Which graph best represents the solution to the following system?

[tex]\left \{ {{-3x+y < 1} \atop {-x+y\leq 2}} \right.[/tex]

_______________________________________________________

4. A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket. A group of 12 people paid $204.00 for tickets. Which system of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased.

_____________________________________________________

5. Which graph best represents the feasibility region for the system shown above?

[tex]\left \{ {{y\geq 2;x\leq 6} \atop {y\leq 3x+2;y\leq -x+10}} \right.[/tex]

____________________________________________________

6. (Graph Shown in Question) [tex]\left \{ {{x\leq 8;y\geq 0} \atop {y\leq 3x+2;y\leq -x+10}} \right.[/tex]

What is the minimum value for P = x - 2y over the feasibility region defined by the constraints shown above?

_______________________________________________________

7. A candy store makes a 13-pound mixture of gummy candy, jelly beans, and hard candy. The cost of gummy candy is $1.00 per pound, jelly beans cost $2.00 per pound, and hard candy costs $2.00 per pound. The mixture calls for three times as many gummy candy pieces as jelly beans. The total cost of the mixture is $20.00. How much of each ingredient did the store use?

______________________________________________________

8. How many solutions does the following system have?

[tex]\left \{ {{2x+3y=1} \atop {-3x-2y=-1}} \right.[/tex]

______________________________________________________

9. Which linear system of equations does the matrix represent?

[-3  5 | 15 ]

[ 2  3 | -10]

______________________________________________________

10. What is the solution to the above system of equations?

[tex]\left \{ {{2x+3y=-4} \atop {4x-5y=22}} \right.[/tex]

______________________________________________________

Should be 10/10. Also, good luck on Part 2 guys!

it is neither, it cannot be raised to a power unless it is 0 or 1 :)

The function is neither an odd function nor an even function

The function is given as:

f(x)=2x^3-x^2

Calculate f(-x)

f(-x)= 2(-x)^3 - (-x)^2

f(-x)= -2x^3 - x^2

Calculate -f(x)

-f(x)= -2x^3 + x^2

From the above computation,

f(x), f(-x) and -f(x) are not equal

Hence, the function is neither an odd function nor an even function

Read more about functions at:

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Answer:

C) J' (-3, 4), N' (1, 4), M' (1, 1), P' (-2,-1)

Step-by-step explanation:

The rule (x, y)→(x - 4, y + 4), means to translate the figure four points to the left and four points up. If we apply this rule to each vertex of the figure, the resulting coordinates are J' (-3, 4), N' (1, 4), M' (1, 1), P' (-2,-1).

Answer:

The length of side [tex]x[/tex] is 4.9 cm

Step-by-step explanation:

The first thing we need to do is find the third angle using the angle sum theorem.

The angle sum theorem states that the sum of the interior angles of a triangle is always 180°. A + B + C = 180°

Let's call our missing angle A, so

A + 41° + 62° = 180°

A + 103° = 180°

A = 180° - 103°

A = 77°

Now we can use the rule of sines to find side [tex]x[/tex]:

[tex]\frac{x}{sin(41)} =\frac{14}{sin(77)}[/tex]

[tex]x=\frac{14sin(41)}{sin(77)}[/tex]

[tex]x=9.4[/tex]

We can conclude that the correct answer is 9.4 cm

In order for the line to be parallel it has to be the same slope. So basically you want to put the equation in slope intercept form Y=Mx+b. Do isolate the Y.

Answer

y-4=2/3(x-3)

y-4=2/3x-2

+4. +4

y=2/3x+2

Answer:

y + 2 = (2/3)(x - 1)

Step-by-step explanation:

Two lines with the same slope are parallel; if two lines are parallel, they have the same slope.

Starting with the standard point-slope formula for the straight line,

y - k = m (x - h), where (h, k) is the given point, we get:

y -[-2] = (2/3)( x - 1), or

y + 2 = (2/3)(x - 1) This is the desired equation of the parallel line.

Answer:

[tex]\frac{13}{1}[/tex]

[tex]\frac{195}{15}[/tex]

[tex]\frac{130}{10}[/tex]

Step-by-step explanation:

we have the ratio

[tex]\frac{65}{5}[/tex]

step 1

Divide both sides (numerator and denominator) by 5

[tex]\frac{65/5}{5/5}=\frac{13}{1}[/tex]

therefore

[tex]\frac{13}{1}[/tex] is proportional to [tex]\frac{65}{5}[/tex]

step 2

Multiply both sides (numerator and denominator) by 3

[tex]\frac{65*3}{5*3}=\frac{195}{15}[/tex]

therefore

[tex]\frac{195}{15}[/tex] is proportional to [tex]\frac{65}{5}[/tex]

step 3

Multiply both sides (numerator and denominator) by 2

[tex]\frac{65*2}{5*2}=\frac{130}{10}[/tex]

therefore

[tex]\frac{130}{10}[/tex] is proportional to [tex]\frac{65}{5}[/tex]