Answer:
Step-by-step explanation:
Solving by factoring is a strategy used to find the solutions or roots of a quadratic equation in the form of ax^2 + bx + c = 0. The goal of factoring is to rewrite the equation in the form of (x-r)(x-s) = 0, where r and s are the solutions or roots of the equation. Once the equation is in this form, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
Here is an example to illustrate the process:
Example: Solve the equation x^2 + 5x - 14 = 0 using factoring.
Step 1: Rewrite the equation in standard form (ax^2 + bx + c = 0). In this case, a = 1, b = 5, and c = -14.
Step 2: Factor the equation by looking for two numbers that multiply to give c and add to give b. In this case, the two numbers are -7 and 2, since (-7)(2) = -14 and -7 + 2 = -5.
Step 3: Rewrite the equation as (x + 7)(x - 2) = 0.
Step 4: Use the zero product property to set each factor equal to zero and solve for x.
x + 7 = 0 or x - 2 = 0
x = -7 or x = 2
So the solutions or roots of the equation are x = -7 and x = 2.
It's important to note that not all quadratic equations can be factored, and in such cases, other methods like completing the square or using the quadratic formula should be used.
It's also important to understand that when factoring, it's important to make sure that you have correctly factored the equation, if not the solution will be wrong.
If a1=8 and an= an-1
Answer:
Step-by-step explanation:
242424
If P = 4s represents the square’s perimeter in terms of the square’s side length (in inches), write a formula that represents the perimeter’s side length 's' in terms of the square’s perimeter 'P.'
The side of the square in terms of the perimeter is P/4.
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,
P = 4s
Where s is the side of the square and P is the perimeter of the square.
Now,
The side of the square.
P = 4s
Divide 4 into both sides.
s = P/4
Thus,
The side of the square is P/4.
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Set up a ratio. If the ratio cannot be reduced to an equivalent ratio in terms of small integers, then express it as a ratio of decimal equivalents with the smallest term set at 1. Maintain three-figure accuracy.
Don, Bob, and Ron Maloney’s partnership interests in Maloney Bros. Contracting are in the ratio of their capital contributions of $78,000, $52,000, and $65,000, respectively.
What is the ratio of Bob's to Ron's to Don's partnership interest?
The ratio of Bob's to Ron's to Don's partnership interest is 26.6% : 33.3% : 40.0%.
What does partnership interest mean?A partnership interest is the percentage of a partnership that a specific member or individual owns. In this context, partnerships refer to a specific method of organizing business ownership in which each owner is a partner, with equal rights, privileges, and obligations to the company as a whole.
Data
Partnership interests in Maloney Bros:
Don - $78,000
Bob - $52,000
Ron Maloney’s - $65,000
The total capital contribution is:
= $78,000 + $52,000 + $65,000
= $195,000
Bob's partnership interest is:
= $52,000/$195,000
= 0.266 or 26.6%.
Ron's partnership interest is:
= $65,000/$195,000
= 0.333 or 33.3%.
Don's partnership interest is:
= $78,000/$195,000
= 0.400 or 40.0%.
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Match each of the equations with their corresponding graph.
a) y= x^3 +2x^2-1
b) 2x^2-x-3
c) 1/x +1
d) 2-3x^2 -x^3
Answer:
I think so the answer is a)y=x³+2x²-1
Use the parallelogram to find m
m
The angles in the parallelogram are as calculated below
How to find the angles in the parallelogram?
A parallelogram is a quadrilateral with opposite sides parallel. This means that both pairs of opposite sides are parallel and of equal length. The opposite angles of a parallelogram are also equal in measure.
m ∠BEA = 60° (alternate angles)
m ∠BAE = 42° (alternate angles)
m ∠DAE = 40° (alternate angles)
m ∠ABE = 180 - m ∠BEA - m ∠BAE = 78° (angle in a triangle)
m ∠CBE = 78° (vertically opposite angles)
m ∠ABD = 180 - m ∠ABE = 102° (angle on a straight line)
m ∠CBE = 102° (vertically opposite angles)
m ∠BEC = 180 - m ∠CBE - m ∠BEC = 38° (angle in a triangle)
m ∠ADB = 38° (alternate angles)
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PLEASE HELP ME IREADY DUE TODAY HELP NOW
37 hundredths= ____ tenths + ____ hundredths
Answer:
30 TENTHS + 7 HUNDREDTHS
Step-by-step explanation:
PLS HELP ME PLSSS plsssss
Answer:
The circumference of a tire can be found by using the formula C = πd, where C is the circumference, and d is the diameter.
For the old bicycle with 12 inch diameter tires, the circumference is:
C = π * 12 = 12 * π inches
For the new bicycle with 16 inch diameter tires, the circumference is:
C = π * 16 = 16 * π inches
To find the difference in the circumference of the tires, we subtract the circumference of the old tire from the circumference of the new tire:
16π - 12π = 4π inches
So the difference in the circumference of the two tires is 4π inches.
It's around 12.56 inches.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36. Therefore, option A is the correct answer.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²
The standard form for finding the equation of a circle is expressed as;
(x-a)²+ (y-b)² =r²
Where; (a, b) is the center of the circle and r is the radius of the circle
Given that, diameter = 12 units
So, radius = 12/2 = 6 units
If the center lies on the y-axis, the center will be at (0, 3)
Substituting into the formula, we will have (x-0)² + (y-3)² = 6² equivalent to x²+ (y-3)² = 36
Therefore, option A is the correct answer.
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Please help, having trouble getting answer.
Answer:
C. 2 ≤ x
Step-by-step explanation:
EDGE
simplify 7m-2(3m^2 +mn)
Answer: 7m-6m²-2mn
Step-by-step explanation:
Multiply each term in parenthesis by -2
Calculate product (2x3=6)
7m-6m²-2mn
Marco budgets $1,600 a month for expenses.
According to the graph, how much does he pay
for his credit card, groceries, and rent?
$1,008
$908
$1,142
$1,029
Marco pays $1008 for for his credit card, groceries, and rent.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Marco budgets $1,600 a month for expenses.
According to the graph he pays 4% of credit card
Now let us find 4% of 1600
4/100×1600
0.04×1600
$64 Marco pays for credit card.
From graph, he pays 17% for groceries
17% of 1600
17/100×1600
0.17×1600=$272
$272 Marco pays for Groceries.
From graph, he pays 42% for rent
42/100×1600
0.42×1600=672
$672 Marco pays for Rent.
Hence, Marco pays $1008 for for his credit card, groceries, and rent.
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I don't understand this, USE YOUR SKILLS AND HELP MEEEEEEEEEEEEEEEEEEEEEEEEEE
The required cost of the construction of a 4.5-inch tower is the amount of $114.75.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
The cost of construction is $25.50 per inch.
We have to determine the amount it costs to fund 4.5 inches of the construction.
As per the question, we have
The cost of construction is $25.50 per inch.
The cost of 4.5 inches of construction would be:
= 25.50 × 4.5
Apply the multiplication operation, and we get
= $114.75.
Thus, the required cost of the construction is $114.75.
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2 people push a box from different directions, why doesnt the box move?
Answer:
Newton's 3rd law of motion
Step-by-step explanation:
Newton's 3rd law of motion states that for every force in nature there is an equal and opposite reaction.
So, assuming the people are both pushing with the same force, their forces are basically canceling each other out, and a net force of 0 is acting uponm the box, which explains why it is not moving.
Borrowed 600$ from the bank. Interest is $14.25 for 90 days. What is interest rate?
Answer:
0.01 %
Step-by-step explanation:
The interest rate is the percentage of the principal (the amount borrowed) that is charged as interest over a certain period of time.
To find the interest rate, we can use the formula:
Interest Rate = Interest / Principal x Number of days / 365
We know that the principal is 600$, the interest is 14.25$ and the number of days is 90
so we can substitute the values into the formula:
Interest Rate = 14.25 / 600 x 90 / 365
Interest Rate = 0.02375 * 90 / 365
Interest Rate = 0.0104
Rounded to the nearest thousandth, the interest rate is 0.010 or 0.01 %
. Descompuneti in factori:
a) 4x + 4x -35;
c) 4x2+ 20x - 11;
e) 4x2 + 12x - 16;
g) 16x7 + 24x - 40;
i) 25x + 10x - 48;
h ) 25x2 -
j) 16x2 + 40x - 39.
The factors of the expression 16x²+40x-39 are (4x-3)(4x+13).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
A) 4x+4x-35
= 8x-35
C) 4x²+20x-11
= 4x²+22x-2x-11
= 2x(2x+11)-1(2x+11)
= (2x+11)(2x-1)
E) 4x²+12x-16
= 4x²+16x-4x-16
= 4x(x+4)-4(x+4)
= (4x-4)(x+4)
= 4(x-1)(x+4)
G) 16x⁷+24x-40
= 8(2x⁷+3x-5)
I) 25x+10x-48
= 35x-48
J) 16x²+40x-39
= 16x²-12x+52x-39
= 4x(4x-3)+13(4x-3)
= (4x-3)(4x+13)
Therefore, the factors of the expression 16x²+40x-39 are (4x-3)(4x+13).
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One serving of Campbell Soup Company's Campbell's® Pork & Beans contains 5 grams of protein and 21 grams of carbohydrates.† A typical slice of white bread provides 2 grams of protein and 11 grams of carbohydrates per slice. The U.S. RDA (Recommended Daily Allowance) is 60 grams of protein each day.
(a)
I am planning a meal of "beans on toast" and wish to have it supply one-half of the RDA for protein and 139 grams of carbohydrates. How should I prepare my meal? (Fractions of servings are permitted.)
beans
serving(s)
bread
slice(s)
(b)
Is it possible to have my meal supply the same amount of protein as in part (a) but only 61 grams of carbohydrates?
Yes
No
The way we should prepare the meal to supply one half of the RDA for protein and 139 grams pof carbohydrates is 4 beans serving and 5 bread slices (answer A). It not possible to have the same amount of protein as in part A but only 61 grams of carbohydrates.
How to calculate the meal of point A?To calculate the meal of point A we have to consider the amount of grams of protein and carbohydrates in each food. In this case, we try with 4 servings of beans and 5 slices of bread, and it get the protein and carbohydrates required as shown in the following explanation:
Servings of beans
4 * 5 = 20 grams of protein
4 * 21 = 84 grams of carbohydrates
Slices of bread
5 * 2 = 10 grams of protein
5 * 11 = 55 grams of carbohydrates
Totals
20 + 10 = 30 grams of protein
84 + 55 = 139 grams of carbohydrates
According to the previous explanation the meal have to be composed by 4 servings of beans and 5 slices of bread. On the other hand, if we want to make a meal with the same amount of protein but only 61 grams of carbohydrates, it is imposible because the amount of carbohydrates of each food is bigger than we need.
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Mark plays field hockey. He makes a goal 55% of the time he shoots. A = the event Mark is successful on his first goal attempt. P(A) = 0.55. B = the event Mark is successful on his second goal attempt. P(B) = 0.55. Mark tends to make goals in streaks. The probability that he makes a second goal given that he made the first goal is 0.80.
If Mark attempts two goals, what is the probability that he makes both goals?
Answer:
We can use the formula for conditional probability to find the probability that Mark makes both goals:
P(A and B) = P(A) * P(B | A)
We know that:
P(A) = 0.55 (the probability that Mark makes a goal on his first attempt)
P(B | A) = 0.80 (the probability that Mark makes a goal on his second attempt given that he made the first goal)
So:
P(A and B) = 0.55 * 0.80 = 0.44
Therefore, the probability that Mark makes both goals is 0.44.
pls help w geometry (see picture)
The given geometry of the figure does not show any of the options, so option D is correct.
What is a triangle?A polygon with three vertices and three sides is called a triangle. The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180 degrees.
Given a ΔSTU
a line from point T intersects at SU at point V and divides SU, given SV is 60 units and UV is 42 units.
The line TV is not a median, because a median divides the side into two equal halves, and the figure does not have SV equal to UV.
The line TV is not an attitude because the figure has not specified the angle of V in line SU, if given that the ∠TVU = ∠TVS = 90° then TV will be called altitude.
The line is not a perpendicular bisector because The line segment drawn from a vertex to the opposite side of a triangle, bisecting that side at a right angle, is known as the perpendicular bisector of the triangle.
Hence option D is correct.
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Elimination
3x-y=-1 and -3x-y=5
The equation 3x - y = - 1; - 3x - y = 5 when solved using the elimination method is x = -1 and y = -2 respectively.
How to solve simultaneous equation using elimination method?3x - y = - 1
- 3x - y = 5
Subtract the equation to eliminate y
3x - (-3x) = - 1 - 5
3x + 3x = - 6
6x = - 6
divide both sides by 6
x = -6 / 6
x = -1
Substitute x = -1 into
3x - y = - 1
3(-1) - y = -1
-3 - y = - 1
- y = - 1 + 3
-y = 2
y = -2
Therefore, the solution to the simultaneous equation is (x, y) = (-1, -2)
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What are the dimensions of this matrix? I WILL MARK BRAINLIEST.
Answer:
1 * 3 ==> 4th option
Step-by-step explanation:
Matrix dimensions are:
number of rows by number of columns
The number of rows is 1 : ( -4 1/4 -1 is the row)
The number of columns is 3 : (-4, 1/4, and -1 are the columns)
Hence, the dimensions is 1 * 3.
Answer:
1 x 3
Last choice
Step-by-step explanation:
The dimensions of a matrix are represented by number of rows x number of columns
There is only one row here (don't be confused by the 1/4) and there are three columns
So 1 x 3
(last choice)
k=3/2
y=kx
y=3/2x
what is the table of x and y
x -0 y-0
x___ y___
x___ y____
Using the proportionality relationship equation, y = 3/2x, the complete table is:
x | y
0 0
1 3/2
2 3
How to Complete a Table Using the Constant of Proportionality?The equation of a proportional relationship between x and y can be represented as y = kx, which means that the constant of proportionality, k, is y/x.
For example, if the constant of proportionality between two variables x and y is given as 4, therefore, the equation of the proportional relationship will be stated as y = 4x.
Given the following:
Constant of proportionality, k = 3/2.
The equation of the proportional relationship is: y = 3/2x
Use the equation, y = 3/2x to complete the table by substituting the values of x into the equation:
For x = 1:
y = 3/2(1)
y = 3/2
For x = 2:
y = 3/2(2)
y = 3
Therefore, the complete table is:
x | y
0 0
1 3/2
2 3
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In September, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest. Jennifer plans to repay the loan in January. Assume this loan is a simple interest loan calculated monthly. What will be the total amount she will owe to the bank on January 31st? If necessary, round to the nearest cent.
Answer: The total amount Jennifer will owe to the bank on January 31st is $3,458.75
Step-by-step explanation: In September, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest for 4 months. As this loan is a simple interest loan calculated monthly, we need to calculate the total amount she will owe to the bank on January 31st.
We use the formula for simple interest which is:
Interest = Principal x Interest rate x Time
Interest = $2,500 x 11.75/100 x 4/12 = $958.75 (rounding to the nearest cent)
Now we can add the interest to the principal amount to get the total amount that Jennifer will owe to the bank on January 31st.
Total amount = Principal + Interest
Total amount = $2,500 + $958.75 = $3,458.75 (rounding to the nearest cent)
So, the total amount Jennifer will owe to the bank on January 31st is $3,458.75
Question 8
You decide to begin saving toward the purchase of a new car in five years. If you put
RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent
compounded annually, how much will you accumulate after 5 years?
If you save RM1,000 at the end of each of the next 5 years in a savings account paying 6 percent compounded annually, the future value or the amount you will accumulate after 5 years is RM5,637.09.
What is the future value?The future value is the compounded present value of the periodic deposits.
The future value formula or FV table can determine the accumulated future value of periodic investments.
We can also use an online finance calculator to determine the future value.
N (# of periods) = 5 years
I/Y (Interest per year) = 6%
PV (Present Value) = RM0
PMT (Periodic Payment) = RM1,000
Results:
Future Value (FV) = RM5,637.09
Sum of all periodic payments = RM5,000(RM1,000 x 5)
Total Interest = RM637.09
Thus, in 5 years, you will have an accumulated future value of RM5,637.09 in the savings account.
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2. In 2000, Social Security tax was 7.5%, to the maximum income of $53,000. If Mary earned $61,711 in 2000, how
much Social Security did she pay?
Mary paid Social Security tax of $4,378.325 in 2000. This is calculated by multiplying 7.5% by the amount of income over the maximum taxable income of $4,378.325.
How much Social Security did she pay?The theory used in this question is the marginal tax rate, which is the tax rate that applies to the income earned over the maximum taxable income. In this case, the marginal tax rate is 7.5%, which is the Social Security tax rate.
Step 1: Calculate the amount of income over the maximum taxable income.
Maximum taxable income: $53,000
Income earned: $61,711
Amount of income over the maximum taxable income: $8,711 ($61,711 - $53,000 = $8,711)
Step 2: Calculate the Social Security tax.
Social Security tax rate: 7.5%
Amount of income over the maximum taxable income: $8,711
Social Security tax paid: $4,378.325 ($8,711 x 0.075 = $4,378.325)
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There is 25 pounds of dog food in a bag. There are approximately 2.2 kilograms in 1 pound. PLEASE HELP ME !! THANK YOU SMM!!
Which statement is true?
A. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/22.
B. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
C. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25
According to the given information, there is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/55
Conversion between units: Calculating kilograms of dog foodFrom the question, we are to determine the statement that is true
From the given information,
There is 25 pounds of dog food in a bag.
and
There are approximately 2.2 kilograms in 1 pound.
If there are 2.2 kilograms in 1 pound
Then,
There would be x kilograms in 25 pounds
x = 2.2 × 25
x = 55 kilograms
Hence, there are 55 kilograms
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One aircraft has a capacity of 64 more seats than a second aircraft. A third aircraft has 152 seats less than twice the seating capacity of the second aircraft. If their total number of seats is 1900, find the number of seats for each aircraft.
The number of seats in the first, second and third aircraft are 561 seats, 497 seats and 842 seats respectively
How to find the number of seats for each aircraft?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Let F, S and T represent number of seats in the first, second and third aircraft respectively
We can set up three equations to represent the situation:
F = 64 + S --- (1)
T = 2S - 152 --- (2)
F + S + T = 1900 --- (3)
Put (1) and (2) in (3):
F + S + T = 1900
(64 + S) + S + (2S - 152) = 1900
64 + S + S + 2S - 152 = 1900
4S - 88 = 1900
4S = 1900 + 88
4S = 1988
S = 1988/4
S = 497 seats
F = 64 + S
F = 64 + 497 = 561 seats
F + S + T = 1900
561 + 497 + T = 1900
1058 + T = 1900
T = 1900 -1058 = 842 seats
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56,259 divided 57=i ?
Answer:
987
Step-by-step explanation:
57√56259= 987
Answer:
987
Step-by-step explanation:
56259 ÷ 57 = 987
Write and solve an inequality.
Please show work
Chris earns $8 per hour working on the weekends. He needs at least $320.00 for his class trip. How many hours, h, does Chris need to work on the weekends to be able to go on the class trip
We can start solving the problem by using the formula:
Hours worked = Total cost / Hourly wage
In this case, we know that Chris needs at least $320.00 for his class trip, and he earns $8 per hour working on the weekends. So, we can plug in these values into the formula:
Hours worked = $320.00 / $8.00
To solve this equation, we divide 320 by 8:
Hours worked = 40
So Chris needs to work 40 hours on the weekends to be able to go on the class trip.
I hope this helps :)
Answer:
Chris needs to work at least 40 hours.----------------------------------------
Chris earns $8 per hour and he needs at least $320.00 for his class trip.
If he works h hours, he will get 8h dollars.
Set up inequality:
8h ≥ 320Solving we get:
h ≥ 320/8h ≥ 40Chris needs to work at least 40 hours.
Use z scores to compare the given values. In a recent awards ceremony, the age of the winner for best actor was 37 and the age of the winner for best actress was 52. For all best actors, the mean age is 45.2 years and the standard deviation is 8.3 years. For all best actresses, the mean age is 32.3 years and the standard deviation is 11.6 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
1.6982 is the actress age is more extreme when winning the award, the actor or the actress .
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.
Essentially, standard deviation is a measure of the degree of variability within a given data collection.
Z score for actor = ( 37 - 45.2 )/8.3
= - 0.9879
Z score for actress = ( 52 - 32.3 )/11.6
= 1.6982
since I - 0.9879 l < l 1.6982 l , the actress age is more extreeme .
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