Answer:
(x-1)(x+1)(x+3)
Step-by-step explanation:
[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]
Use point-slope form to write the equation of a line that passes through the point (18,16) with slope -\frac{11}{8}− 8 11 .
The equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.
What is point-slope form?The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. Several techniques include:
Form of point slope, Form of a slope-intercept, Two-point form for intercepting.
The point slope form is given as:
(y - y1) = m (x - x1)
The point is (18, 16) and the slope is 11/8.
Substituting the values we have:
y - 16 = 11/8 (x - 18)
8(y - 16) = 11(x - 18)
8y - 128 = 11x - 198
8y = 11x - 70
Hence, the equation of the line that passes through (18, 16) and has a slope of 11/8 is 8y = 11x - 70.
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This year, Clean Machine used 4,508.8 gallons of soap. That is 16.5% less than last year, How many gallons of soap did the company use last year? (round your answer to the nearest tenth)
The soap used by the machine last year is 5399.76 gallons.
What are percentages?The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage." This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."
Let the soap used last year = x.
Then, according to the given condition:
4,508.8 = x (1 - 16.5%)
4,508.8 = x (83.5/100)
x = 4,508.8(100) / 83.5
x = 5399.76
Hence, the soap used by the machine last year is 5399.76 gallons.
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Need help with homework
Answer:
lower quartile = 75
Step-by-step explanation:
the lower quartile Q₁ is situated at the left side of the box.
lower quartile Q₁ = 75
In a circle, a 315° sector has area 504π in2. What is the radius of the circle?
Let's call the radius of the circle "r". The formula for the area of a sector of a circle is given by:
(θ/360) * π * r^2,
where θ is the central angle of the sector in degrees.
In this case, we know that the central angle is 315° and the area of the sector is 504π, so we can set up an equation as follows:
(315/360) * π * r^2 = 504π
Solving for r, we can isolate it on one side of the equation:
r^2 = 504 / (π * (315/360))
To simplify the expression on the right-hand side, we can divide both the numerator and denominator by 45 (which is a factor of both 315 and 360):
r^2 = 504 / (π * (7/8))
Finally, taking the square root of both sides gives us:
r = sqrt(504 / (π * (7/8)))
So the radius of the circle is approximately 17.14 inches.
< A and < B are complementary angles.
< A = 3 x - 2 and < B = 2 x + 12
Find the measure of < A :
Answer: The measure of Angle A is 46 degrees.
Step-by-step explanation:
Complementary angles are angles that when both added together are equal to 90 degrees. So the measure of angle A plus the measure of angle B is equal to 90 or 3x - 2 + 2x + 12 = 90. Add like terms so you get 5x + 10 = 90. Subtract 10 on both sides you get 5x = 80. Divide by 5 on both sides and you get x = 16. To find the measure of angle A, plug in your x value. So M<A = 3(16) - 2. Ange A is equal to 46. I double checked my answer too and plugged my x value into M<B and got 44. So indeed 44 + 46 = 90.
An art teacher is making packages
a. The greatest number of packages the teacher can make using all the paintbrushes and paint is 8
b. The number of paintbrushes in each package would be 3 and the number of tubes of paints would be 5
How do we determine the number of packages?In order to determine the greatest number of packages the teacher can make using all the paintbrushes and paint, we have to determine the highest common factor of the number of brushes and the number of tubes of paint
Highest common factor is the highest factor that is common to two or more numbers:
Factors of 24 = 1,2,3,4,6,8,12 and 24
Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40.
Common factors of 24 and 40 = 1, 2, 4, 8
Therefore, the highest common factor is 8.
The number of paintbrushes in each package:
= Number of brushes / number of package
= 24/8
= 3 brushes
The number of tubes of paint:
= number of tubes of paints / number of package
= 40 / 8
= 5 tubes of paints
Full question "An art teacher is making packages of paint brushes and paint for his. He has 24 brushes and 40 tubes of paint. Each package will have the same number An art teacher is making packages of paintbrushes and paint for his students. of brushes and the same number of tubes of paint. Part a. What is the greatest number of packages that the art teacher can make using all the paintbrushes and paint? Show your work Part b. How many paintbrushes and tubes of paint are in each package?".
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ABC and QRS are supplementary angles.
If the measure of ABC = 170°, what is the
measure of QRS?
m/QRS =
If the measure of ABC = 170°, the measure of QRS is equal to 10°.
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of angles ABC and QRS are supplementary angles:
m∠ABC + m∠QRS = 180°
Substituting the given parameters into the formula, we have the following;
170° + m∠QRS = 180°
m∠QRS = 180° - 170°
m∠QRS = 10°
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A concert venue wants to make at least $3,750.00 profit for their Saturday night show.
Adult tickets cost $10.00 and children's tickets cost $5.00. The venue can seat up to
500 people. Find three combinations of adult and children's tickets that will make the
profit goal and not be more than 500 total people. Enter your answer as ordered pairs
(A,C) separated by a comma where A is the number of adult tickets sold and C' is
the number of children's tickets sold.
Answer:
(126, 101), (127, 100), (128, 99).
Step-by-step explanation:
The profit from selling one adult ticket is $10.00 and from selling one children's ticket is $5.00.
The total profit from selling A adult tickets and C children's tickets can be represented as 10A + 5C.
The goal is to find combinations of A and C that meet the following conditions:
10A + 5C >= 3750
A + C <= 500
One way to solve this problem is to use a brute force approach and try different values of A and C until we find three combinations that meet the conditions. Another way is to use a more efficient method and find the values of A and C that maximize the number of adult tickets while still meeting the profit and seating limit conditions.
Let's start by finding the maximum number of adult tickets that can be sold while still meeting the profit goal:
10A + 5C >= 3750
10A >= 3750 - 5C
A >= 375 - 0.5C
Since C must be an integer, we can round down the value of A to the nearest integer.
For example, if C = 100, then A >= 125. If we round down A to 125, then the profit from selling 125 adult tickets and 100 children's tickets would be:
10 * 125 + 5 * 100 = 1250 + 500 = 1750
which is less than the profit goal of 3750.
If we increase C by 1, then A would increase by 0.5, and the profit would increase by 5.
So, to reach the profit goal, we need to increase C until the profit is at least 3750.
Let's try C = 101. Then A >= 125.5, which we can round down to 126.
The profit from selling 126 adult tickets and 101 children's tickets would be:
10 * 126 + 5 * 101 = 1260 + 505 = 1765
which is greater than or equal to the profit goal of 3750.
So, the first combination of adult and children's tickets that meets the profit and seating limit conditions is (126, 101).
We can repeat the same process to find the second and third combinations.
For example, the second combination could be (127, 100), and the third combination could be (128, 99).
The final answer is (126, 101), (127, 100), (128, 99).
Answer:
250 $3 tickets and 100 $2 tickets were sold.
Step-by-step explanation:
3(350 – y) + 2y = 950
1050 – 3y + 2y = 950
3y – 2y = 1050 – 950
y = 100
Substitute y = 100 into equation 1
x + 100 = 350
x = 250
A plant is already 9 centimeters tall, and it will grow one centimeter every month.
Let be the plant's height (in centimeters) after months.
Write an equation relating to . Then graph your equation using the axes below.
Answer:
p + (m × 1) = t
If a plant is already ___cm tall and it will grow one cm every month, an equation to find out how much the plant grew in __ months is this:
(Let t = total number of centimeters, m = number of months, and p = the length of the plant already.)
p + (m × 1) = tTherefore, the equation you can use is p + (m × 1) = t.
Please help :) 10 points (Geometry)
Answer: (2,0)
Step-by-step explanation:
Midpoint formula( [tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
P(-4, 6)
Q(8, -6)
Substitute into formula
-4+8/2
4/2
x = 2
6-6/2
0/2
y = 0
Answer (2,0)
please help with 4(i)-4(iii). with steps please
1) Given that the perimeter of the rectangle is at least 40 cm, the inequality and show that it reduces to x ≥ 3 2/3 is: 12x - 4 >= 40
2) The smallest possible value of x is 4
3) The area of the rectangle is 57 cm²
What is the rationale for the above response?(i) The perimeter of a rectangle is given by the formula P = 2(l + b), where l is the length and b is the breadth. Substituting the given values, we get:
P = 2(4x + 3 + 2x - 5) cm
P = 2(6x - 2) cm
P = 12x - 4 cm
We are given that the perimeter is at least 40 cm, so we can write the inequality:
12x - 4 ≥ 40
Simplifying this inequality, we get:
12x ≥ 44
Dividing both sides by 12, we get:
x ≥ 11/3
x ≥ 3 2/3
So the inequality reduces to x ≥ 3 2/3
II) Note that if x is a perfect square, the smallest possible value of x is 4, because 4 is the smallest perfect square.
III) Substituting x = 4 in the length and breadth of the rectangle, we get:
Length = 4x + 3 = 19 cm
Breadth = 2x - 5 = 3 cm
Therefore, the area of the rectangle is:
Area = Length x Breadth = 19 cm x 3 cm = 57 cm²
Thus, it is correct to state that the area of the rectangle is 57cm².
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slips of paper numbered 1 through 14 are placed in a hat. in how many ways can two numbers be drawn so that the sum of the numbers is 12? assume the random selection is without replacement.
We are assuming that the random selection is without replacement, which means that once a slip is drawn, it is not put back into the hat.
There are 5 possible pairs of numbers that add up to 12 when drawing two slips of paper numbered 1 through 14 without replacement. These pairs are:
1 and 11
2 and 10
3 and 9
4 and 8
5 and 7
Next, we need to find the number of ways to draw each pair. Since the order in which the slips are drawn does not matter, each pair can be drawn in 2 different ways. So, for each of the 5 pairs, there are 2 ways to draw the pair.
Each pair of numbers can be drawn in 2 different order (the order in which the slips are drawn does not matter in this case), so the total number of ways to draw two slips so that the sum of the numbers is 12 is [tex]5 * 2 = 10[/tex].
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What is the measure of ∠w? and What is the measure of ∠y?
Answer:
angle w = 50; angle y = 130
Step-by-step explanation:
because of supp. angles, y + w = 180
12x-2+4x+6=180
16x+4=180
16x=176
x=11
to calculate, sub 11 in
w = 4(11) + 6 = 50
y = 12(11) - 2 = 130
the only items in each of containers a, b, and c are 28 disks. in each container, each of the disks is numbered with a different integer from the integers 1 through 28 inclusive. one disk is to be selected at random from each of the 3 containers. what is the probability that at least one of the disks selected has a number greater than 24?
The probability that at least one of the disks selected has a number greater than 24 is 127/343.
To find the probability that at least one of the disks selected has a number greater than 24, we can find the probability that all three disks have numbers less than or equal to 24 and subtract this from 1.
The probability that a disk selected from a container has a number less than or equal to 24
24/28= 6/7
Since,
there are 24 disks with numbers less than or equal to 24 out of a total of 28 disks in each container.
We can assume that the selection of a disk from one container is independent of the selection of a disk from another container, so the probability that all three disks selected have numbers less than or equal to 24 is (6/7)³
since we are making three independent selections.
Therefore,
The probability that at least one of the selected disks has a number greater than 24 is 1 - (6/7)³ ,
which simplifies to 343/343 - 216/343 = 127/343
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The graph of the linear function f(x) = -5x + 6 shows the number of cases of the flu, y, in thousands, x months after a vaccine was administered. What are the rate of change and the initial
value?
A 6,000 cases of the flu per month; initial value: -5,000 cases
B-5 cases of the flu per month; initial value: 6 cases
C 1 case of the flu per month, initial value: 0 cases
D -5,000 cases of the flu per month; initial value: 6,000 cases
Answer:
D
Step-by-step explanation:
The 6 represents the initial value of 6000. The cases are going down 5,000 a month.
A small town has a cylindrical water tower with a radius of 10 feet and a capacity of 12,560 gallons. Explain how you could use the formula for the volume of a cylinder to determine the height of the water tower.
Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, height of the water tower is 40.16 feet tall.
To calculate the height of the water tower, we can use the formula for the volume of a cylinder. This formula is V = πr^2h, where V is the volume, π is the constant pi (3.14), r is the radius of the cylinder, and h is the height of the cylinder. In this case, the radius of the cylinder is 10 feet and the volume of the cylinder is 12,560 gallons. We can rearrange the formula to solve for h, giving us h = V/πr^2. Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, the water tower is 40.16 feet tall.
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ASAP Select the correct answer.
What is the slope of the line that goes through the points (-4,2) and (8,5)?
A.-4
B.-1/4
C.1/4
D.4
find the missing length 5 11 c
The missing length of the triangle is the hypotenuse which is given by 12.08
What is the hypotenuse?Pythagorean theorem states that the sum of the square of the opposite and adjacent sides of a triangle is equal to the square of the hypotenuse.
a² + b² = c²
c = √a² + b²
a = 11
b = 5
c = √a² + b²
= √11² + 5²
= √121 + 25
= √146
c = 12.08304597359
Approximately,
c = 12.08
Consequently, the hypotenuse of the triangle is approximately 12.08
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If a least-squares regression line fits the data well, what characteristic should the residual plot exhibit?
If a least square regression line fits the data well, the characteristic should the residual plot exhibit is random scatter
The least squares regression line fits the data well.
The least squares regression is defined as the method that used to find the regression line or best suitable line for the given pattern
So if the data shows a linear relationship between the two given variable so such line will be called least squares regression line
The residual plot is the measure that vertical line how much misses from the data point
Here the least square-square regression lines fits the data well so the characteristics will be random scatter
Therefore, the characteristic that the residual plot exhibit is random scatter
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What is an equation of the line that passes through the points (6, 5) and (4, 1)?
Answer:
1/4
Step-by-step explanation:
On a graph that's up 1 over 4 and its rise over run or (rise/run)
Kate intends to give her 12 good friends a treat at the school cafeteria. Her friends can have either a cupcake
or an ice cream cup. A cupcake costs $1.20 and an ice cream cup costs $1.50.
(i) What is the maximum and minimum amount of money Kate may have to spend?
(ii) Kate intends to spend not more than $16 on the treat. If two of her friends insist on having cupcakes,
what is the maximum number of ice cream cups her friends can have?
Answer:
minimum is $14.40
maximum is $18
she can get 9 ice cream cups
Step-by-step explanation:
Which expression is equivalent to (14x)⁰y-⁷z?
The expression which is equivalent to (14x)⁰y-⁷z as required in the task content is; z / y⁷.
Laws of indicesIt follows from the task content that the expression which is equivalent to the given expression (14x)⁰y-⁷z is to be determined.
Recall from the laws of indices that a⁰ = 1 where a represents any mathematical entity.
Therefore, the resulting expression is;
1 • y -⁷ • z
= z • 1 / y⁷
= z / y⁷.
Ultimately, the resulting expression which is equivalent is; z / y⁷.
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10 point cuz its all i got rn
In the scale drawing, what is the area of the lawn (that is, the area of the whole backyard, except for the deck)?
The area of the lawn in the scale drawing is approximately 996 square feet.
1. Measure the length and width of the lawn in inches on the scale drawing.
Length = 16.5 inches
Width = 15.5 inches
2. Convert the measurements to feet by dividing the inches by 12.
Length = 16.5/12 = 1.375 feet
Width = 15.5/12 = 1.291 feet
3. Calculate the area of the lawn by multiplying the length and width.
Area = 1.375 x 1.291 = 1.75 square feet
4. Multiply the area by the scale factor (in this case, 560) to get the actual area.
Area = 1.75 x 560 = 996 square feet
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suppose that you have a fair coin. you start with $0. you win 1$ each time you get a head and loose $1 each time you get tails. calculate the probability of getting $2 without getting below $0 at any time.
The probability of winning $2 without getting below $0 at any time is 1/4 or 0.25.
To calculate the probability of winning $2 without getting below $0 at any time, we can use a branching diagram to track the possible outcomes.
Starting from $0, there are two possible outcomes for the first flip: heads or tails. If the first flip heads, the outcome is $1 and there are two possible outcomes for the second flip: heads or tails. If the second flip heads, the outcome is $2 and we have won the game. If the second flip is tails, the outcome is back to $0 and we have to start over. If the first flip is tails, the outcome is $-1 and we also have two possible outcomes for the second flip: heads or tails. If the second flip heads, the outcome is back to $0 and we have to start over. If the second flip is tails, the outcome is $-2 and we have lost the game.
Putting all of the possible outcomes together, we get the following branching diagram:
H T
/ \ / \
H T H T
/ \ / \
H T T H
$2 $0 -$1 -$2
The only way to win $2 without getting below $0 at any time is to get two heads in a row. This can only happen along the top branch of the diagram, which has a probability of (1/2) * (1/2) = 1/4.
Therefore, the probability of winning $2 without getting below $0 at any time is 1/4 or 0.25.
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10. Find the measure of each missing angle.
Answer:
see explanation
Step-by-step explanation:
A segment joining the midpoints of two sides of a triangle is
parallel to the third side
∠ 1 and 144° are same- side interior angles and sum to 180° , so
∠ 1 + 144° = 180° ( subtract 144° from both sides )
∠ 1 = 36°
----------------------
∠ 2 and 56° are corresponding angles and are congruent , so
∠ 2 = 56°
-------------------------
∠ 3 and 56° are a linear pair and sum to 180°
∠ 3 + 56° = 180° ( subtract 56° from both sides )
∠ 3 = 124°
--------------------------
the sum of the 3 angles in a triangle = 180° , then
∠ 1 + ∠ 2 + ∠ 4 = 180° , that is
36° + 56° + ∠ 4 = 180°
92° + ∠ 4 = 180° ( subtract 92° from both sides )
∠ 4 = 88°
--------------------------------
∠ 5 and ∠ 1 are corresponding angles and are congruent , so
∠ 5 = 36°
----------------------------------
Answer:
m∠1 = 36° , m∠5 = 36° , m∠4 = 88° , m∠3 = 124° , m∠2= 56°
Step-by-step explanation:
m∠1 and 144° are Co-Interior angles, or the angles which are on the same side of the transveral
m∠1 + 144° = 180°
m∠1 = 36°
angle 5 and 144° are in a linear pair-
144 °+ angle 5 = 180°
m∠5 = 36°
angle 5 + 56° + angle 4 = 180° because addition of angles of a triangle is 180°
36° + 56° + angle 4 = 180°
angle 4 = 180° - 92°
angle 4 = 88°
56° and angle 3 are in a linear pair
56° + angle 3 = 180°
angle 3 = 124°
angle 3 and angle 2 are Co-Interior angles
angle 3 + angle 2 = 180°
124° + angle 2 = 180°
angle 2 = 56°
Hope it helped and you understood it :)
10m+ 4 n 2 10, m, plus, start fraction, n, squared, divided by, 4, end fraction when m=5m=5m, equals, 5 and n=4n=4n, equals, 4.
According to the given question, when m=5 and n=4, the value of the expression 10m + 4n²/4 is 66.
What does a mathematical expression mean?A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operations may be add, subtraction, multiply, or divide. An expression's basic components are as follows: (Math Operator, Number/Variable, Expression)
What are some illustrations of expression?Keep in mind that words can be variables, constants, or coefficients. Therefore, 1+1 is a straightforward example of an expression. This equation has two constant terms and one operation (addition). x³ is another illustration.
To evaluate the expression 10m + 4n²/4 when m=5 and n=4, we substitute these values into the expression and simplify:
10m + 4n²/4
= 10(5) + 4(4^2)/4
= 50 + 4(16)/4
= 50 + 16
= 66
Therefore, when m=5 and n=4, the value of the expression 10m + 4n^2/4 is 66.
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Evaluate the expression if x= -2 and y=7.
(xy)^2 - 2x^5
Thank you.
btw this is Algebra I
Answer:
260
Step-by-step explanation:
Substitute: (-2 · 7)² – 2 x (-2)⁵
Remove parenthesis: (2 · 7)² + 2 · 2⁵
Calculate the first two terms: 14ײ + 2 × 2⁵
Calculate the power: 196 + 2 × 32
Calculate the first two terms: 196 + 64
Calculate the first two terms: 260
Answer: 260
What are the zeros of this function?
Question 1 of 10
esc
The equation y
Complete the statements.
When the outside temperature is 30°F, the sales are estimated to be [DROP DOWN 1].
When the outside temperature is [DROP DOWN 2], the sales are estimated to be $1, 993.33.
DROP DOWN 1
Select a Value
DROP DOWN 2
Select a Value
O
Please select an answer.
32.9-572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, x, in degrees Fahrenheit (F).
Help me out
When the outside temperature is 30°F, the sales is $414.13
When the sale is $1,993.33, the outside temperature is 78°F
How to find the sales when the outside temperature is 30°F?
Since the equation y = 32.9x - 572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, x, in degrees Fahrenheit (F).
Thus, when the outside temperature is 30°F, the sales can be estimated by substituting x = 30°F into the equation and solving for y. That is:
y = 32.9x - 572.87
y = 32.9(30) - 572.87
y = 987 - 572.87
y = $414.13
Thus, when the sale is $1,993.33, the outside temperature can be estimated by substituting y = $1,993.33 into the equation and solving for x. That is:
y = 32.9x - 572.87
1,993.33 = 32.9x - 572.87
32.9x = 1,993.33 + 572.87
32.9x = 2566.2
x = 2566.2/32.9
x = 78°F
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Determine whether the sequence is an arithmetic or a geometric sequence. If it is geometric, what is the common ratio? 0.5, 2, 8, 32, 148, ...
The sequence is a geometric sequence with a common ratio of 4.
What is a geometric sequence?
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed non-zero number called the common ratio (r).
To determine whether the sequence is arithmetic or geometric, we can look at the differences between consecutive terms.
The difference between the second and first terms is 2 - 0.5 = 1.5.
The difference between the third and second terms is 8 - 2 = 6.
The difference between the fourth and third terms is 32 - 8 = 24.
The difference between the fifth and fourth terms is 148 - 32 = 116.
Since the differences are not constant, the sequence is not arithmetic.
To determine if it is a geometric sequence, we can look at the ratios of consecutive terms.
The ratio of the second and first terms is 2/0.5 = 4.
The ratio of the third and second terms is 8/2 = 4.
The ratio of the fourth and third terms is 32/8 = 4.
The ratio of the fifth and fourth terms is 148/32 = 4.
Since the ratios are constant, the sequence is geometric with a common ratio of 4.
Therefore, the sequence is a geometric sequence with a common ratio of 4.
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