Mathematics High School

Name the property of real numbers illustrated by the equation.
-3(x+4)=-3x-12

A: Distributive property
B: Associative property of addition
C: Associative property of multiplication
D: Commutative property of addition

Answers

Answer 1
Answer: Choice A) Distributive property

We're multiplying the outer -3 with the inner x to get -3x
Also, multiply the outer -3 with the inner +4 to get -12

So that's why -3(x+4) = -3x-12

Related Questions

root of 108 is between______ and ______
Determine what two whole numbers the square root is between without using a calculator or table. Then use a calculator or table to check.

Answers

Without using a calculator I would say the root is between 10 and 11 

How I found the answer:
I know 10 * 10 = 100
I know 11 * 11 = 121
So the root of 100 = 10 and the root of 121 = 11 so that means the root of 108 is somewhere between 10 and 11, which the root of 108 =  10.3923

If you know how to do this, can you show the work, please?
Thanks

Answers

Answer: The original area of the square is 64 square feet

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Let x be the original side length of the square. The original area is therefore going to be x*x = x^2. For now we don't know the area but once we figure out x, we can compute the area.

The original side length x is increased by 7 ft to jump up to (x+7) ft
At the same time, the other dimension is reduced to (x-2) ft, which is a decrease of 2 ft

The old square is x ft by x ft with area x*x = x^2

The new rectangle is (x+7) ft by (x-2) ft

Let's find the area of this rectangle

Have a look at the image attachment to see how to multiply out (x+7)*(x-2) using the box method

The terms in red are x^2, 7x, -2x and -14 which are found by multiplying the headers

x times x = x^2
x times 7 = 7x
-2 times x = -2x
-2 times 7 = -14

The like terms are 7x and -2x which combine to 5x

Overall the result of multiplying out (x+7)*(x-2) is x^2+5x-14

Note: we can get the same result if we use the FOIL or distribution rule. The box method is a handy way to visually keep track of all the terms.

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

The area of the rectangle, in terms of x, is x^2+5x-14

We are told that the area is 90 square feet

So equate the two expressions and solve for x

x^2+5x-14 = 90
x^2+5x-14-90 = 90-90
x^2+5x-104 = 0
(x-8)(x+13) = 0 ... see note below
x-8 = 0 or x+13 = 0
x = 8 or x = -13

note: find two numbers that multiply to -104 and add to 5. Those numbers are -8 and 13 which helps us factor

We ignore x = -13 as a negative side length makes no sense

The only practical root is x = 8

The side length of the original square is 8 feet

The area is
x*x = 8*8 = 64 square feet

We can check the answer by adding 7 to 8 to get 15, and subtracting 2 from 8 to get 6. The 8 by 8 square turns into a 15 by 6 rectangle. Since 15*6 = 90, we have confirmed the right answer. 

Give the first four nonzero terms of the series about x=8 representing the function x^(1/3)

Answers

empire state building

When the function f(x) is divided by x-2 the quotient is 3x^2+8x-4 and the remainder is 9 find the function f(x) and write the result in standard form?

Answers

dividend ÷ divisor = quotient + remainder
∴ dividend = divisor(quotient) + remainder  ... there is a reason why I am not multiplying the remainder by the divisor in this case... your remainder is not represent as a fraction with the divisor as the denominator..

[tex]f(x)=(x-2)(3x^2+8x-4)+9=3x^3+8 x^{2} -4x-6 x^{2} -16x+8+9[/tex]
[tex]f(x)=3x^3+2x^2-20x+17[/tex]

The expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

When the function f(x) is divided by (x - 2) the quotient is 3x² + 8x - 4 and the remainder is 9

By using the division algorithm:

f(x) = (x - 2)(3x² + 8x - 4) + 9

After simplification:

f(x) = 3x³ + 8x² - 4x - 6x² - 16x + 8 + 9

f(x) = 3x³ + 2x² - 20x + 17

Thus, the expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.

Learn more about the function here:

brainly.com/question/5245372

#SPJ5

Given 11 is conguent to 3, which lines, if any, must be parallel based on the given information? Justify your conclusion


A. a || b, Converse of the Alternate Exterior Angles Theorem

B. c || d, Converse of the Same-Side Interior Angles Theorem

C. a || b, Converse of the Corresponding Angles Theorem

D. not enough information to make a conclusion

Answers

To draw a conclusion with parallel lines, you need two lines cut by a transversal. You don't have that situation here, so you cannot draw any conclusion about parallel lines.

Triangles XYZ and PQR are drawn on a square grid. What fraction of the area of triangle XYZ is the area of trianglePQR?

Answers

The area of a triangle is given by [tex] \frac{1}{2} bh[/tex].

From the given figure: The base of the bigger triangle is 6 units and the height is 3 units.
The base of the smaller triangle is 3 units and the height is 2 units.

The area of the big triangle is [tex] \frac{1}{2} \times6\times3=9\, square\, units[/tex]
The area of the small triangle is [tex] \frac{1}{2} \times3\times2=3\, square\, units[/tex]

The required fraction is [tex] \frac{3}{9} = \frac{1}{3} [/tex]

To determine the fraction of area of triangle XYZ that is occupied by triangle PQR on a square grid, we can compare their linear dimensions and use the fact that area is proportional to the square of these dimensions, or we can approximate the area through summation of small rectangular areas on the grid. Alternatively, vector methods such as the cross product can provide precise area calculations for triangles with known vertices.

Finding the Area of Triangles on a Square Grid

To find what fraction of the area of triangle XYZ is the area of triangle PQR, we follow several steps. First, we can draw both triangles on a square grid and establish their respective areas. If we assume that XYZ is the larger triangle and PQR is the smaller one, we can use the fact that area scales in proportion to the square of the linear dimensions. This means, if the linear dimensions of PQR are half that of XYZ, the area of PQR would be one-fourth that of XYZ. In mathematical terms, if the side length of XYZ is scaled by a factor of 's', the area is scaled by s².

Another method to approximate the area of irregular shapes like these triangles, as mentioned in a reference, is by dividing the shape into smaller, manageable rectangular areas whose sum approximates the total area. Counting the smallest square units within the grid and making rough estimates of the fractional squares can yield the area as well.

To demonstrate the calculation of the area of a triangle through vector methods, one can use the cross product of two vectors defined by the triangle's vertices. Given vertices A(1,2,3), B(2,4,5), and C(1,-8,0), their position vectors can be used to compute the cross product, and the magnitude of this cross product gives twice the area of the triangle ABC. This is a more advanced method and offers a precise way to calculate the area without relying on the grid.

Find the next two terms of the sequence. 2, 6, 10, 14, ... (1 point)

Answers

The sequence given is 2, 6, 10, 14
Noticing this sequence, we will find that the sequence increases by 4 each time. This means that:
The next number = the current number + 4

In other words:
2
2+4 = 6
6+4 = 10
10+4 = 14
14+4 = 18

Therefore, the next number in the sequence would be 18

Answer:

C. 18,22

Step-by-step explanation:

tell weather the side lengths can form a trangle

Answers

I really think that it can

$40 is discounted into $32 what is the percent decrease

Answers

about 28.5 percent is the decrease I hope this helps :)

The population of bees has been decreasing at a rate of 10% per year in 2012 there were 6000 bees in particular hive how many bees were there in 2014

Answers

2012 = 6000 bees
10% of  6000 is 60
so 6000 - 60 = 5940
2013 = 5940 bees
 10% of 5940 = 59.4
so 5940 - 59.4 = 5880.6
so in 2014 you 5881 because you cant have a 0.6 of a bee

A card is drawn from a deck of 52 cards. find the probability of drawing a king or a red card

Answers

drawing a king:4/52
drawing a red car:26/52
drawing a red king: 2/52
4/52 +26/52 -2/52=28/52
change to decimal if required: 0.5385

Please Help With This. What is the equation of the line shown in this graph? Answer your answer in the box.

Points are:
(-2,-3) (3,-3)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ 3}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-(-3)}{3-(-2)} \\\\\\ \cfrac{-3+3}{3+2}\implies \cfrac{0}{5}\implies 0[/tex]

[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=0[x-(-2)] \\\\\\ y+3=0\implies y=-3[/tex]

The solution to f - (-4) = 12 is f = 8.

True or False

Answers

Answer is true. two -'s turn into + (8+4=12)
True, because 8 +4=12. It's "+4" because 2 negatives make a positive.

Fatema loves to run marathons. The last one she participated in took her 2 hours to complete. The year before (2016) , she completed the same marathon in 8/11 of the time and the year before that (2015) she completed it in 9/12 of the time. What year did Fatema run the fastest? JUSTIFY YOUR ANSWER PLEASE I NEED HELP ASAP!

Answers

2017 = 2 hrs x 60 mins = 120 mins
2016 = 8/11 x 120 mins = 87.27 mins
2015 = 9/12 x 120 mins = 90 mins

Therefore, Fatema ran the fastest in 2016.

PLAESE HELP ME FAST THIS IS WORTH 20 POINTS

Answers

Where is the question
Wheres the question?

Kevin has $4.85 in nickels and dimes. If he has 34 fewer dimes than nickels, how many coins (nickels and dimes) does he have altogether?
A.) 74 coins
B.) 75 coins
C.) 76 coins
D.) 77 coins

Answers

D.) 77 coins That's what I got

Answer:

The answer would be (D) 77 coins :)

Step-by-step explanation:

A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad picks her up and drives her through the remainder of the way at 30 miles per hour. If they arrived at school at 9:00, how far did she walk?

Answers

The girl walked 5 miles.

Answer:

She walked 5 mi

the average cost for a company to produce x items is x^2-10x+43 dollars. how many items should the company produce to minimize the average cost per item?

Answers

the cost equation is a parabolic graph, whose "lowest value" is at its vertex, it is up and goes down down down, reaches the U-turn and then goes up up up again.

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llll} y = &{{ 1}}x^2&{{ -10}}x&{{ +43}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{(-10)}{2(1)}~~,~~43-\cfrac{(-10)^2}{4(1)} \right)\implies (\stackrel{\textit{items to produce}}{5}~~,~~\stackrel{\textit{production cost}}{18})[/tex]

LANDSCAPING The equation 3x+7y =105 represents the number of bags of sand x and bags of multch y that can be bought with $105. If no bags of sand are bought, how many bags of mulch can be bought with $105 ?

Answers

You could buy 15 bags of mulch with $105.
To find the answer, plug in 0 for x since you aren't buying any bags of sand and then you have 7y=105 and divide by 7 to find y which is 15.
Final answer:

When no bags of sand are bought, you can buy 15 bags of mulch with $105.

Explanation:

To find the number of bags of mulch that can be bought with $105 when no bags of sand are bought, we need to substitute x = 0 into the equation 3x+7y = 105. This will allow us to solve for y.

Since x = 0, the equation becomes:

3(0) + 7y = 105

0 + 7y = 105

7y = 105

Dividing both sides by 7, we get:

y = 15

Therefore, when no bags of sand are bought, you can buy 15 bags of mulch with $105.

What is 120 degrees in radians?

Answers

Answer:

[tex]\frac 23 \pi [/tex]

Step-by-step explanation:

120 degrees is one third of the whole circle, or [tex] \frac 13 2\pi [/tex]

Answer:

the answer is 2pi/3

Brock is a plumber. He charges a flat rate of $40 to visit a house to inspect it's plumbing. He charges an additional $20 for every hour he spends inspecting or making repairs.

Which graph below correctly shows the price of using Brock's plumbing service vs time?

Answers

it would be graph W because the cost will increase, so that gets rid of Y... It has to start at 40 for the original cost, getting rid of Z and X

W is correct. the red line starts at 40 which is the initial fee

 then it crosses 60 and 1.0 and 80 at 2.0 which is 20 dollars for 1 hour

Write an equation of the line through (5,5)and parallel to the line 4x+3y=-2

Please help

Answers

First out the equation 4x + 3y = -2 into slope-intercept form (y = mx + b).

4x + 3y = -2

Subtract 4x from both sides.

3y = -4x - 2

Divide all terms by 3.

y = -4/3x - 2/3

The slope in this equation is -4/3 (4 down, 3 to the right).

Using that slope, input the coordinates (5, 5) into the equation of a line:

y - y1 = m(x - x1)

y - 5 = -4/3(x - 5)

y - 5 = -4/3x + 20/3

y = -4/3x + 35/3

The equation of the line is y = -4/3x + 35/3.

Find the diameter of a cone that has a volume of 56.52 cubic inches and a height of 6 inches. use 3.14 for pi. (1 point) 3 inches 6 inches 9 inches 12 inches

Answers

Diameter= 6 inches
To find the answer, set the volume of the cone (56.52) equal to the formula for the volume of the cone (3.14(r)squared times height) Plug in the height and solve for the radius. When you have the radius (3) multiply it by 2 to get the diameter (6).

Answer:

Diameter= 6 inches

Step-by-step explanation:

What number is diviscible by 2?

Answers

all even numbers are divisible by two, which means some answers would be 4, 6, 8, 10, 12, 14, etc.
Any number that ends with an even number can be divided by 2. 18/2=9 100/2=50,etc

Which is an equation of the line with x-intercept 2 and y-intercept 12?

Answers

Your answer should be y=2x+12

What is the next term in the sequence 1/2 1/6 1/18 1/54

Answers

1/162
2*3=6
6*3=18
18*3=54
54*3=162

QUICKK EXPERTS/ACE OR ANYONE WHO WANTS TO HELP!!

Answers

bottom left,

 since the lines are parallel with each other there is no solution

Maybelle looked at a hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and the same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent. Explain and Show your work.

-20 points. Better yet, 30 points!! Please help!

Diff in price = %
_________ _________ thats the formula i think...
original price 100

Answers

The formula for percent increase is (final-initial)/initial*100
Plug in to get (2075-1195)/1195*100
880/1195*100
.7364*100
73.64% rounding we get
74%

is (3,4) a solution of y=-x+5

Answers

3=x
4=y

4=-3+5

So no it’s not.

Is the square root of 37 rational or irrational

Answers

All rational numbers can be expressed as a fraction or decimal. Since √37 can not, it is irrational.

Hope this helps!
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