The factors of the expression x² - x - 12 are 4 and -3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x² - x - 12
Using middle-term factorization.
x² - (4 - 3)x - 12
x² - 4x + 3x - 12
x(x - 4) + 3(x - 4)
(x - 4) (x + 3)
x - 4 = 0
x = 4
x + 3 = 0
x = -3
Thus,
The factors are 4 and -3.
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The base diameter and the height of a cone are both
equal to x units.
X
Which expression represents the volume of the cone
in cubic units?
О лх2
О 27x3
0x²
0x³
volume of cone is =1/3 x³.
What is volume of cone ?The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.
here, given that,
The base diameter and the height of a cone are both equal to x units.
Volume = ⅓ r²h
=1/3 x²x
=1/3 x³
Hence, volume of cone is =1/3 x³.
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If x−5=2, then what is the value of 2x
Answer:
x=7
Step-by-step explanation:
hope this helps :)
18. The Great Pyramid of Giza has a square base. The length of each side of the base is approximately 230 meters. The height of the pyramid is approximately 147 meters. Using these dimensions, what is the volume, in cubic meters, of the pyramid?
Enter a number in the box.
________ cubic meters
The volume of the pyramid, in cubic meters, given the length of each side and the height, is 2, 592, 100 meters ³
How to find the volume of a pyramid ?The Volume of a pyramid can be found by the formula :
= ( Base length x Base width x Height ) / 3
Base length = 230 meters
Base width = 230 meters as this is a square base
Height = 147 meters
The volume is therefore:
= ( 230 x 230 x 147 ) / 3
= 2, 592, 100 meters ³
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What number is 10 times greater than 318.625
Answer:
3186.25
Step-by-step explanation:
318,625*10 = 3186.25
Consider the following two circles.
Segment d1 is a diameter of ⨀A, and segment d2 is a diameter of ⨀B.
If d1=1 and d2=2r, and if CB denotes the circumference of ⨀B, which equation is true?
1/2r = CB/2π
1/2r = π/CB
1/2r = CB/π
The equation 1/2r = π/CB is true. Choose the second option
How to determine which equation is true?The circumference of a circle is the distance around the circle, or the length of the perimeter of the circle. It is given by the formula:
circumference = 2πr = πd
where r is the radius and d is the diameter
Note: d = 2r
Given: d2 = 2r and CB denotes the circumference of ⨀B
CB = πd2
CB = 2πr (d2 = 2r)
Divide both sides by CB:
CB/CB = 2πr/CB
1 = 2πr/CB
Divide both sides by 2r:
1/2r = 2πr/2rCB
1/2r = π/CB
Thus, the second equation is true
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How many more 41+ year olds have a preference for
Enterprise Content Management in comparison to 18-25 year
olds (as a %)?
There are 23% more 41+ year olds have a preference for Enterprise Content Management in comparison to 18-25 year olds
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
We are given that the table shows the Technology career types for different ages groups.
The 41+ year olds have a preference for Enterprise Content Management = 3215
The percent become
3215 / (3215 + 4673 + 5822) x 100
3215 / (3215 + 4673 + 5822) x 100
3215 / 13710 x 100
23.45
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The dollar value vt of a certain car model that is t years old is given by the following exponential function.
v(t)= 25,900(0.90)^2
Find the initial value of the car and the value after 11 years.
Round your answers to the nearest dollar as necessary.
Initial Value:
Value after 11 years:
Answer:
$25,900 initially
$8,128 after 11 years
Step-by-step explanation:
One thing to note, is I'm assuming you meant: [tex]v(t)=25,900(0.90)^t[/tex] and not [tex]v(t)=25,900(0.90)^2[/tex], otherwise that would just be a constant function and not an exponential function.
Exponential Function Key Features:There are a couple key features of exponential functions we can derive from simply analyzing the equation.
For now I will be using the form: [tex]y=a(b)^x\text{ where b} > 0, \text{b}\ne 1[/tex]
y-intercept:The y-intercept, is just the "a" value, which is because the y-intercept is simply when x=0, and if we raise a number to the power of zero, we get one (excluding zero as a base), so we get the form: [tex]y=a[/tex], so "a" is our y-intercept.
Rate of Change:there's actually two type of exponential functions: exponential growth and exponential decay.
Exponential Decay:
Exponential decay, as the name implies, is when a function is decaying or decreasing. This occurs when [tex]0 < b < 1[/tex].
The decay rate can be represented as "r" in decimal form, where: [tex]b=1-r[/tex].
The reason for this is because "1" can be thought of as 100% and "r" is r%, so you're taking away r% or decaying the value by r%, also known as a decay rate.
Exponential Growth:
Exponential growth as the name implies, is when a function is growing or increasing. This occurs when b > 1
The growth rate can be represented as "r" in decimal form where: [tex]b=1+r[/tex]
The reason for this is similar to decay rate except instead of taking away r% or decaying, it's "giving r%" or growing.
Solving the Question:The question doesn't actually require finding exponential growth or decay, but it's still an important key feature.
In this case, we really just need to find the y-intercept and plug in t=11.
The y-intercept in many graphs, not just exponential graphs, represents some sort of initial value, which in this case, is the initial value of the car. As stated above, this y-intercept is just the value in front, which is 25,900.
As for the value after 11 years, we simply need to plug in t=11 to get the following: [tex]v(11)=25,900(0.90)^{11}[/tex], from here we can use a calculator to simplify this: [tex]v(11)\approx25,900(0.31381059609)\approx 8,127.694438731[/tex], which rounds to 8,128
7518 [tex]7518 divided by 3[/tex] 3
Answer:
2,506
Step-by-step explanation:
1/5/2023
7:37PM
Which ordered pairs represent points on the graph of this equation? Select all that apply.
Answer: (0,0) (4, -3) (8, -6)
Step-by-step explanation:
It is correct.
Write an equation of the line that passes through the given points.
(-2,8) and (1,0)
The equation is ______. (Type your answer in slope-intercept form.)
Answer:
y = -8/3x + 8/3
Step-by-step explanation:
(-2, 8) and (1, 0)
m = 0-8/1+2
m = -8/3
y = -8/3x + b
0 = -8/3(1) + b
0 = -8/3 + b
b = 8/3
y = -8/3x + 8/3
Which description does NOT guarantee that a quadrilateral is a rectangle?
a quadrilateral with four right angles
a quadrilateral with all congruent angles
a quadrilateral with diagonals that are congruent and bisect each other
a parallelogram with congruent sides
The description does NOT guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other
What is a quadrilateral?A quadrilateral is a four-sided polygon. It is a closed geometric figure with four straight sides and four angles and A rectangle is a four-sided shape with two pairs of parallel, perpendicular sides. Its opposite sides are equal in length and also opposite angles are equal in measurement.
Therefore, the correct answer is as identified. It can be concluded that the one that does not guarantee that a quadrilateral is a rectangle is option C. a quadrilateral with diagonals that are congruent and bisect each other
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Find the measure of
The measure of ∠A is 123 degrees.
How to find the measure of angles?The angle made between the radius and the tangent at the point of contact on a circle is 90°.
Therefore,
∠D = 90 degrees
∠E = 90 degrees
The diagram ACDE forms a quadrilateral. The sum of angles in a quadrilateral is 360 degrees. Therefore, we have to equate the sum of the quadrilateral angles to 360 degrees.
Hence,
90 + 90 + 2x + 7 + 5x - 2 = 360
180 + 7x + 5 = 360
7x = 360 - 180 - 5
7x = 180 - 5
7x = 175
x = 175 / 7
x = 25
Therefore,
∠A = 5(25) - 2 = 125 - 2 = 123 degrees.
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1. What is the range of the quadratic function?
Round 241.0063 to the nearest thousandth
just need help
Answer:
the nearest thousandth is 241.006.
division homework need help
Answer:
8296/17 = 488
4590/34 = 135
4550/26 = 175
8132/38 = 214
5265/15 = 351
8760/24 = 365
5643/33 = 171
4403/37 = 119
2400/48 = 50
AXY Z is translated left 4 units to form the image AX'Y'Z'.
What are the coordinates of the vertices of AX'Y'Z' ?
Enter your answer by filling in the boxes.
X'=(
Y' = (0)
Z' = (00)
On solving the provided question we can say that - Pythagorean Theorem triangle [tex]5^2+x^2=10^2 = > x²=100−25=75[/tex]x=√75=√3×25=5√3
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
On solving the provided question, we can say that the value of x = 5√3
values of x and y
Pythagorean theorem,
The trigonometric ratio: soh-cah-toa, and
According to the given question:
Using the table of trig values, we find that
sin30°=1/2
So, this gives us:
[tex]1/2 = sin 30° = 5/y\\1/2 = 5/y\\(1xy)/2 = 5\\y= 2×5 =10\\[/tex]
Pythagorean Theorem
[tex]5²+x²=10²\\x²=100−25=75\\[/tex]
x=√75=√3×25=5√3
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assume that ryan does save 10% for retirment. if he alloctes the remainder of his take home pay to entertainment, then what percent of his total budget wil entertainment comprise?
For a company picnic, Dale ordered a box of fresh-baked gingerbread cookies and sugar cookies. He got 49 gingerbread cookies and 1 sugar cookie. What percentage of the cookies were gingerbread
The percentage of the cookies were gingerbread is 60%.
Given that, the total number of gingerbread cookies and sugar cookies= 55 and the number of gingerbread =22.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%"
Here, Difference =55-22
=3
Percentage =33/55 ×100
= 0.6 ×10
= 60%
Therefore, the percentage of the cookies were gingerbread is 60%.
Answer:
Step-by-step explanation:
cccccc
A company is expanding its building area from 18,000 square feet to 25,380 square feet. What is the percentage increase of the area of the building space?
Answer:
Below
Step-by-step explanation:
(25380 - 18000) / 18000 * 100% =
7380/18000 * 100 = 41 % increase
Question content area top
Part 1
A car with a full tank that holds 11.6 gallons of gasoline is using 1.45 gallons per hour. Is the tank more than half full of gasoline after 3.5 hours? Explain your answer.
Answer:
Yes, the tank is more than half full of gasoline after 3.5 hours.
Step-by-step explanation:
To calculate the amount of gasoline left in the tank after 3.5 hours, we need to subtract the amount used (1.45 gallons per hour) from the total capacity (11.6 gallons). So 11.6 - (1.45 x 3.5) = 9.3 gallons, which is more than half the tank's capacity of 11.6 gallons. Hope this helps!
divied 3.64× 10^8 by 3.3×10^4
3.64 x [tex]10^8[/tex] divided by 3.3 x [tex]10^4[/tex] is equal to 110.12121212121212.
What is division?The division is an arithmetic operation that is the inverse of multiplication. It involves splitting a quantity into a number of equal parts. The symbol for division is typically a forward slash (/) or a horizontal line. For example, if you have 10 apples and you want to divide them equally among 5 people, each person would receive 2 apples (10 ÷ 5 = 2). The result of division is called the quotient.
Here is one way to divide 3.64 x 10^8 by 3.3 x 10^4 step by step:
Write the numbers as decimal numbers: 3.64 x 10^8 is equal to 364000000 and 3.3 x 10^4 is equal to 33000.
Divide the decimal numbers: 364000000 ÷ 33000 = 11006.06
The result is 11006.06.
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72 boxes is 5% of how many boxes?
Answer:
1440
Step-by-step explanation:
"Percent" means "out of 100"
5 "percent" means 5 out of 100
[tex]\frac{5}{100} =\frac{72}{x}[/tex]
We need to find the number that when multiplied by 5, equals 72.
72 / 5 = 14.4
Now, we need to multiply 100 by 14.4 to "scale" proportionately.
100 * 14.4 = 1440
We can check our work:
1440 * (0.05) = 72
The diet of a jellyfish consists primarily of plankton, which are tiny
organisms living in the ocean. One species of plankton has an average length
of 0.08 inches. Suppose a certain jellyfish has a length of 12 cinches. Write
a percent that compares the length of the plankton to the length of the
jellyfish.
Answer:
To compare the length of the plankton to the length of the jellyfish, we can express the length of the plankton as a percentage of the length of the jellyfish.
First, we need to convert the length of the jellyfish from inches to centimeters so that we can compare the two measurements in the same unit.
12 inches = 12*2.54 = 30.48 cm
Next, we divide the length of the plankton by the length of the jellyfish and multiply by 100 to get the percentage.
0.08 inches / 30.48 cm * 100 = 0.00262 * 100 = 0.262%
So, the length of the plankton is 0.262% of the length of the jellyfish.
What is the slope of the line that contains the points (2, −8) and (−4, 4)? 2 one half negative one half −2
Answer;
-2
Step-by-step explanation;
Well take the last numbers in these points and subtract them
4 - (-8)
4+8
12
You've got the upper part of the slope fraction now subtract the first two numbers.
-4-2
-6
Put this fun together, 12/-6 = -2
hence, slope=-2 .
Answer:
Step-by-step explanation:
-2
Please help me. I have been trying to figure out this assignment forever! Can you please show your work
1. The length of the sides of the two smaller squares are 3 and 4
2. Area of 4 triangles and middles square = 25
3. Area of the big square = 5
How to find the area of the 4 triangles and and the squareThe dimensions of the the triangle and the square are
length of square = 1
base = 3
height = 4
Area of the triangle
= 1/2 base * height
= 0.5 * 3 * 4
= 6
For four triangles
= 4 * 6
= 24
Area of small square
= 1 * 1
= 1
summation of the areas
= 24 + 1
= 25
Solving for side of the big square from the area
= √25
= 5
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Hellllllpppp I Neeeeeeedddddd Heeeeellllllllpppp
Answer: 5
Step-by-step explanation:
A triangle's area is half of a squares, so we can treat this as a square for now. It says the area is 20 units squared, and if we convert this to the area of the square, it is 40 units. 40/8 is 5, and so 5 is the length of x
O LINEAR EQUATIONS AND INEQUALITIES
Graphing a compound inequality o...
Graph the compound inequality on the number line.
x>-8 and x≤-3
The compound inequality on the number line is shown below.
We have been given a compound inequality. We are asked to graph the given inequality on number line.
x>8 and x≤3
The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.
We will have solid dots at x>-8 and x≤-3 .
One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.
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There are 3400 students at Central High School and 3/8 of these students are freshmen. If 3/5 of the freshmen are in favor of the school forming a track team and 1/5 of the remaining students (not freshmen) are also in favor of forming a track team, how many students are opposed to this idea?
First, we need to find the number of students that are freshmen: 3400 students x 3/8 = 1050 students
Next, we need to find the number of students that are in favor of forming a track team: 3/5 of the freshmen are in favor = 3/5 * 1050 = 630 students
To find the number of non-freshmen students: 3400 students - 1050 students = 2350 students
Now we need to find the number of non-freshmen students in favor of forming a track team: 1/5 of the non-freshmen students are in favor = 1/5 * 2350 = 470 students
Finally, to find the number of students opposed to the idea we need to subtract the number of students in favor from the total number of students: 3400 students - (630 students + 470 students) = 3400 - 1100 = 2300 students
So there are 2300 students at Central High School that are opposed to the idea of forming a track team.
Solve negative 4 times y plus five halves times y equals negative 4 minus three halves times y minus 3 for y.
y = −7
y = 0
Infinite solutions
No solution
Answer:
No solution
Step-by-step explanation:
When you solve it, it ends up as 0=-7 which isn't true.
Answer:
No solution!
Step-by-step explanation:
Given g(x) = -x + 4, solve for x when g(x) = 0
The value of the equation g ( x ) = -x + 4 , when g ( x ) = 0 , is x = 4
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
g ( x ) = -x + 4 be equation (1)
On simplifying the equation , we get
when g ( x ) = 0
Substitute the values in the equation , we get
0 = -x + 4
Adding x on both sides of the equation , we get
x = 4
Therefore , the value of x = 4
Hence , the value of the equation is x = 4
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