ANSWER
[tex] (x + 6)(x - 6)[/tex]
EXPLANATION
The given expression is
[tex] {x}^{2} - 36[/tex]
We write to obtain;
[tex] {x}^{2} - {6}^{2} [/tex]
Recall that;
[tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex]
We apply this difference of squares formula to get;
[tex]{x}^{2} - {6}^{2} = (x - 6)(x + 6)[/tex]
The correct choice is A
Answer:
(x+6)(x-6)
Step-by-step explanation:
Use the number line to find the ratio AC/CF simplify the ratio
A. 8/20
B 2/5
C 8/12
D 2/3
Answer:
The correct option is D.
Step-by-step explanation:
From the given number line it is clear that A=0, B=2, C=8, D=14, F=20 and G=22.
The length of line segment AC is
[tex]AC=C-A=8-0=8[/tex]
The length of line segment CF is
[tex]CF=F-C=20-8=12[/tex]
The ratio of line segment AC to CF is
[tex]\frac{AC}{CF}=\frac{8}{12}[/tex]
Cancel out the common factors.
[tex]\frac{AC}{CF}=\frac{2}{3}[/tex]
The simplified ratio of [tex]\frac{AC}{CF}[/tex] is 2/3.
Therefore the correct option is D.
Which graph shows the equation y = x + 2?
How could the relationship of the data be classified? (1 point)
scatter plot with points loosely scattered going down to the right
Jeremiah scored 28 points in yesterday's basketball game. He made a total of 17 baskets. Some of the baskets were field goals (worth two points) and the rest were free throws (worth one point). How many field goals did Jeremiah make? How many free throws did he make?
Answer:
6 and 11
Step-by-step explanation:
HELP! ASAP!
What is the measure of ∠A?
What is the measure of ∠B?
Answer:
What is the measure of ∠A?
72°
What is the measure of ∠B?
108°
Step-by-step explanation:
I literally copied and pasted from edge
Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? Explain your reasoning.
Sample Response: A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand. Using a calculator might also be more time efficient because it might accept a line in any form. A calculator’s window can be adjusted quickly instead of having to redraw a graph by hand when adjusting the scale.
Number of security staff = a over 100 if a audience, is 10500, how many security staff are needed for the event
Question 11 options: you take a ride on a ferris wheel which has a diameter of 300 feet. if you ride for four revolutions, what linear distance did you travel? use 3.14 for pi when completing your calculations. round your answer to the nearest whole number, if necessary. the distance traveled is
Debra is on the swim team. Each week she swims a total of 7000 meters. How many kilometers does she swim each week?
Find the exact value of sin ( 2
a. if cos a = 3 /5 . assume a is a quadrant i angle in standard position.
Find all real values of $v$ that satisfy the equation $(v+6)^2 = 324$. If you find more than one, then list your values in increasing order, separated by commas.
Answer:
The values of v in increasing order are, -24, 12
Step-by-step explanation:
Given equation is,
[tex](v+6)^2=324[/tex]
[tex]v+6=\pm 18[/tex]
[tex]v=-6\pm 18[/tex]
[tex]\implies v=-6-18\text{ or }v=-6+18[/tex]
[tex]\implies v = -24\text{ or }v=12[/tex]
Since, -24 < 12
Thus, the values of v in increasing order are,
-24, 12
Find the smallest value of k if 264k is a perfect square
Which equivalent expression would you set up to verify the associative property of addition for (3x + 4) + ((5x2 – 1) + (2x + 6))
(3x + 4) + (5x2 – 1)
(5x2 – 1) + ((3x + 4) + (2x + 6))
((3x + 4) + (5x2 – 1)) + (2x + 6)
(3x + 4) + (5x2 – 1) + (2x + 6)
It's C.
Trust me, I had trouble figuring out this answer...
Solve the following system of equations using matrices.
4x – 2y = -6
3x – 6y = -18
(40, 90)
(3, 0)
(0, 3)
(-6, 18)
The volume of a sphere is 3,000π m3. What is the surface area of the sphere to the nearest square meter? 165 m2 2,158 m2 1,079 m2 37,699 m2
2.1 + (–3.7h) + 1.9h – 1.4
Which linear function has the greatest y-intercept?
A) x + 6y = 36
B) y = 15x + 5
C) 3x + 8y = 24
D) y = 4x + 7
Answer:
the answer is y=4x+7
Step-by-step explanation:
The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)? PLEASE ANSWER
X =
a. (-7.2, 3.4)
b. (1.2, 6.6)
c. (3.2, 0.6)
b. (9.2,-0.4)
A 10-foot ladder is leaning against a tree. The bottom of the ladder is 4 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?
A.2.4
B.6.0
C. 9.2
D. 10.8
kelly ran 2 miles and burned 240 calories. the next day she ran 3 miles and burned 360 calories. the next day4 miles and 480 miles. if this pattern continues, how
many calories will she burn if she runs 8 miles?
Answer:
She will burn 960 calories if she runs 8 miles
Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets. {jill, john, jack}, {susan, sharon}
The smallest possible set that contains the given sets as subsets is,
⇒ {jill, john, jack, Susan, sharon}
What is mean by Subsets?
A set 'A' is a subset of another set 'B' , if all the element of the set A are element of set of 'B'.
Given that;
The subsets are;
⇒ {jill, john, jack} , {Susan, sharon}
Now,
Clearly, A subsets of a set is contain all the elements of subsets.
So, We get the set;
Set = {jill, john, jack, Susan, sharon}
Thus, The smallest possible set that contains the given sets as subsets is,
⇒ {jill, john, jack, Susan, sharon}
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What is value of x?
https://static.k12.com/nextgen_media/assets/8093716-NG_GMT_SemB_08_UT_12.png
The calculated measure of the angle x is 76 degrees
How to determine the measure of the angle xFrom the question, we have the following parameters that can be used in our computation:
The figure
Also, we have
Angle with a measure of 76 degrees
By the theorem of corresponding angles, we have
x = 76
Hence, the measure of the angle x is 76 degrees
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Mr Savage used 3 gallons of paint to cover 1,350 square feet of wall space. At this rate, how much paint will be needed to cover 1,800 square feet
What is the denominator of the fraction 1/9?
Please help me it's homework.
A town has a population of 2000 and grows at 4% every year what will be the population after 15 years to the nearest whole number
Answer:
3602
Step-by-step explanation:
The population of the town after 15 years will be approximately 3495.
Explanation:To find the population of the town after 15 years, we need to use the formula for compound interest: A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate expressed as a decimal, and t is the number of time periods. In this case, P = 2000, r = 0.04, and t = 15.
Using this formula, we can calculate the population after 15 years:
A = 2000(1 + 0.04)^15
A = 2000(1.04)^15
A ≈ 2000(1.747422)
A ≈ 3494.84
Rounding to the nearest whole number, the population after 15 years will be approximately 3495.
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Which algebraic expression represent the phrase “ seven more than half of a number”?
Answer:
The given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]
Step-by-step explanation:
Given phrase “ seven more than half of a number”
We have to write the algebraic expression for the given phase.
Algebraic expression is the way of writing an expression in mathematical form using mathematical operations and variables.
Consider the given phrase “ seven more than half of a number”
Let the number be N,
Then half of number is [tex]\frac{1}{2}N[/tex]
and seven more means seven is added to this, the expresion becomes [tex]7+\frac{1}{2}N[/tex]
Thus, the given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]
You are preparing to tile the floor of a rectangular room that is 15.5 feet by 18 feet in size. The tiles you plan to use are squares, measure 12 inches on each side, and are sold in boxes that contain enough tiles to cover 25 square feet. Each box costs $30.
To determine the cost of materials you multiply 15.5 by 18, divide by 25, round up to the next whole number, and multiply by 30. Is this correct?
A) Yes.
B) No, you need to round down and then multiply by 30.
C) No, you need to round down and then multiply by 144.
D) No, you need to divide by 144, round up, and then multiply by 30.
E) No, you need to divide by 144, round down, and then multiply by 30.
To find the cost of tiling the room, you have to calculate the area in square feet, convert tile size to the same units, calculate how many boxes needed and round up, then multiply by the cost per box. The correct answer is D).
Explanation:The correct answer is D). The process to determine the cost of the tiles needed to cover the room starts with calculating the area of the room in square feet. This is done by multiplying the room's length and width, so 15.5 feet * 18 feet which equals 279 square feet.
The tiles are 12 inches in size on each side, but the dimensions of the room are in feet. Therefore, we need to convert the tile size to square feet. Since 1 foot = 12 inches, 1 square foot = 144 square inches. Our tile is 12 inches * 12 inches = 144 square inches, which equals 1 square foot.
However, the tiles are sold in boxes that cover 25 square feet. So, we will divide the total room area by the area covered by one box of tiles. 279 square feet / 25 = 11.16 boxes needed, approximately.
It's important to round up at this stage, as you can't buy a fraction of a box. So, you'd need 12 boxes.
The last step is to calculate the total cost, which is done by multiplying the number of boxes by the cost of each box. So, 12 * $30 equals $360.
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Please help me solve for r
Use the quadratic formula to solve for the roots of the following equation. x 2 – 4x + 13 = 0
By using the quadratic formula, the roots of the equation are,
⇒ x = 2 ± (√3/2) i
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The quadratic equation is,
⇒ x² - 4x + 13 = 0
Now, By using the quadratic formula, the roots of the equation are,
⇒ x² - 4x + 13 = 0
⇒ x = - (- 4) ± √ (- 4)² - 4×1×13 / 2
⇒ x = 4 ± √16 - 52 / 2
⇒ x = 4 ± √- 36 / 2
⇒ x = 4 ± √6 i / 2
⇒ x = 2 ± (√3/2) i
Thus, We get;
⇒ x = 2 ± (√3/2) i
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Final answer:
The roots of the quadratic equation x² - 4x + 13 = 0 are complex numbers, specifically 2 + 3i and 2 - 3i, obtained through applying the quadratic formula.
Explanation:
To solve the quadratic equation x² – 4x + 13 = 0 using the quadratic formula, we first identify a, b, and c from the equation. Here, a=1, b=-4, and c=13. The quadratic formula is ‘x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c', all over two 'a'. Applying these values, we get:
x = – (-4) ± √((-4)² – 4(1)(13)) / (2)(1)
This simplifies to:
x = 4 ± √(16 – 52) / 2
x = 4 ± √(-36) / 2
Since the square root of -36 is 6i (where i is the imaginary unit √(-1)), the solutions are:
x = (4 ± 6i) / 2
x = 2 ± 3i
Therefore, the roots of the equation are 2 + 3i and 2 - 3i, which are complex numbers.