2b (3a – c) + 12 ac –b^{2}[/tex]
The value of the equation is A = 6ab - 2bc + 12ac - b²
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
Substituting the values in the equation , we get
A = 2b ( 3a - c ) + 12ac - b² be equation (1)
On simplifying the equation , we get
A = 2b ( 3a ) - 2b ( c ) + 12ac - b²
On further simplification , we get
A = 6ab - 2bc + 12ac - b²
Hence , the equation is A = 6ab - 2bc + 12ac - b²
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Find the vertex of the parabola y = x2 − 8.
Simplify both coordinates and write them as proper fractions, improper fractions, or integers.
(
,
)
The vertex of the parabola is (0, -8).
What is Parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
We have to find the vertex of the parabola y = x² - 8,
x = -b/2a
where a is the coefficient of the x² term,
b is the coefficient of the x term, and
x is the x-coordinate of the vertex.
a = 1 and b = 0, so:
x = -0/(2.1) = 0
Now let us find the y-coordinate of the vertex, we can substitute x = 0 into the equation for the parabola:
y = (0)² - 8 = -8
Hence, the vertex of the parabola is (0, -8).
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Chloe borrows 800 from the bank for 3 years at simple interest. The interest she is charged after 3 years is 168. Calculate the rate of simple interest charged at this bank. Give the answer as a percentage
After 3 years the rate of simple interest charged at this to Chloe bank is 7%
We can start by using the formula for simple interest:
Simple Interest = Principal * Rate * Time
where the principal is the amount borrowed, the rate is the interest rate as a decimal, and the time is the duration of the loan in years.
Plugging in the given values, we get:
168 = 800 * Rate * 3
Solving for the rate, we get:
Rate = 168 / (800 * 3) = 0.07
Hence,
The rate of simple interest charged at this bank is 0.07, or 7% as a percentage.
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Robert plans to make a box-and-whisker plot of the following set of data.
27, 14, 46, 38, 32, 18, 21
Which of the following should Robert's box-and-whisker plot look like?
Robert's box-and-whisker plot should look like the following: C. box-and-whisker plot C.
What is a box-and-whisker plot?In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Next, we would sort the observations (data set) from the least to greatest as follows:
14, 18, 21, 27, 32, 38, 46}.
Based on the information provided above, the five-number summary for the given data set include the following:
Minimum = 14
First quartile = 18.
Median = 27.
Third quartile = 38.
Maximum = 46.
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what is the cubed root of -343
Answer:
-7
Step-by-step explanation:
Answer: -7
Step-by-step explanation: I hope this helped you out!!!! Please mark me as brainiest.
what expressions can be used to calculate the total price of a DVD that cost d dollars if the tax rate is 7.5%
If , which equation describes the graphed function? A. y = f(-x) − 3 B. y = -f(x) + 3 C. y = -f(x) – 3 D. y = f(-x) + 3
The equation that describes the graphed function is -
g(x) = - f(x) - 3.
What is root function?A root function in mathematics is given as -
y = [tex]$\sqrt[n]{x}[/tex]
We can further write the function as -
y = [tex]$x^{\frac{1}{n} }[/tex]
Given is the graph of the function as shown in the image attached.
We can write the function f(x) as -
f(x) = √x
Inverting the f(x) across the {x} axis, we can write -
- f(x) = - √x
After downward translation, we can write g(x) as -
g(x) = - f(x) - 3
Therefore, the equation that describes the graphed function is -
g(x) = - f(x) - 3.
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1. What must the values of a and b be for PQRS to be a parallelogram?
2. The diagonals of parallelogram ABCD intersect at P. Select all the statements that must be true.
The value of a and b are; a = 2, b = 4
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Given that the diagonals of parallelogram ABCD intersect at P.
4a + b = 2a + 8
4a - 2a + b = 8
2a + b = 8 -----------------(I)
b = 8 - 2a
11b - 10a = 6b
11b - 6b -10a = 0
5b - 10a = 0 ---------(II)
Substitute b = 8 - 2a in equation (II)
5(8-2a) - 10a = 0
40 - 10a - 10a = 0
40 - 20a = 0
-20a = - 40
a = -40/-20
a = 2
Plugin a = 2 in equation (I)
b = 8 -4
b = 4
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-3k2g - [8kg2 -(6k2g - 2kg2)]
Answer:
Step-by-step explanation:
ghjhkvfgfgnfdgn
Franny's suitcase weighs 35.7 pounds. Which statement is not true?
A. The 35 represents whole pounds. The 7 represents part of a
pound.
B. The 7 represents more weight than the 5.
OC. The suitcase weighs more than 35 pounds, but less than 36
pounds.
OD. All of these statements are true.
Point G is located at -18 on a number line. Point H is 24 more than Point G. Where is Point h?
Point H is located at 6 on the number line, which is 6 units to the right of the zero point.
We know that Point G is located at-18 on the number line, and that Point H is 24 further than Point G. To find the position of Point H, we need to add 24 to the position of Point G
Point H = Point G + 24
Substituting the position of Point G, we get
Point H = -18 + 24
Simplifying the expression, we get
Point H = 6
thus, Point H is located at 6 on the number line.
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Sidney made root beer floats for her friends when they came over. The table shows the ratio of cups of ice cream to cups of soda used to make the floats. Ice Cream (cups) Soda (cups) 3.5 10.5 8 24 12.5 37.5 17 ? At this rate, how much soda will Sidney use for 17 cups of ice cream? 42 cups 51 cups 54 cups 62 cups
Answer: the correct answer is 51
Step-by-step explanation: i solved this on my quiz
i hope this helps!
Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.
What is the ratio?
A ratio is a relationship between two things when it is expressed in numbers or amounts. For example, if there are ten boys and thirty girls in a room, the ratio of boys to girls is 1:3, or one to three.
We can start by noticing that the ratio of cups of ice cream to cups of soda used to make the floats is always 1:3.
To find out how much soda Sidney will use for 17 cups of ice cream, we can set up a proportion:
3.5/10.5 = 8/24 = 12.5/37.5 = 17/x
Solving for x, we can cross-multiply:
3.5x = 10.5 * 17
x = 54
Therefore, Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.
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what is the standard error? group of answer choices the standard error is the standard deviation of the sampling distribution the standard error is a measure of how representative a sample statistic is likely to be of the population parameter. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.
The correct option is "the standard error is the standard deviation of the sampling distribution." Correct option is A.
The standard error is a measure of the variability of a sampling distribution, which is the distribution of sample statistics (e.g., mean, proportion) that would be obtained from multiple random samples of the same size from the same population.
The standard error represents the standard deviation of the sampling distribution, and it provides a measure of the precision of the sample statistic in estimating the population parameter.
The standard error is not the same as the standard deviation of the sample, which is a measure of the variability of the individual observations in the sample.
The standard deviation of the sample is typically used to estimate the standard deviation of the population, while the standard error is used to estimate the variability of the sample statistic and to construct confidence intervals or perform hypothesis tests.
While the other options are related to the concept of the standard error, they are not equivalent or fully accurate descriptions of what the standard error represents.
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Complete question is:
What is the standard error?
group of answer choices
A. the standard error is the standard deviation of the sampling distribution
B. the standard error is a measure of how representative a sample statistic is likely to be of the population parameter.
C. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.
Each pair of polygons is similar. Find the value of x.
The value of x for the similar triangles is equal to 13.
How to calculate for x for the similar trianglesWe have the triangles to be similar, this implies that the length 8 of the smaller triangle is similar to the length x - 1 of the larger triangle
and the length 10 of the smaller triangle is similar to the length x + 2 of the larger triangle
so;
10/(x + 2) = 8/(x - 1)
10(x - 1) = 8(x + 2) {cross multiplication}
10x - 10 = 8x + 16
10x - 8x = 16 + 10 {collect like terms}
2x = 26
x = 26/6 {divide through by 6}
x = 13.
Therefore, the value of x for the similar triangles is equal to 13.
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Reena bought 53. 882 grams of spinach and 49. 883 grams of chili. Did Reena buy more spinach or chili?
Reena bought more spinach as the total weight of spinach is more than chili.
The weight of an object refers to as the force of gravity that is acting on the object. It is the amount of gravitational force applied by the Earth on that object.
Weight of spinach - 53.882 grams or 0.053882 kg
Weight of chili - 49.883 grams or 0.049883 kg
When comparing the above information, we get the weight of spinach to be more than the weight of chili as the weight of spinach is 53.882 grams which is more than the gross weight of chili i.e., 49.883 grams. So, Reena bought more spinach as compared to chili.
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there are c different types of coupon, and each coupon obtained is equally likely to be any one of the c types. find the probability that the first n coupons which you collect do not form a complete se
The probability that the first n coupons which you collect do not form a complete set is (c^n - (c-1)^n) / c^n.
To find the probability that the first n coupons collected do not form a complete set, we need to count the number of ways in which the first n coupons can be collected so that they do not form a complete set and divide it by the total number of ways in which n coupons can be collected, which is c^n.
Let S be the set of all possible complete sets of coupons. The number of ways in which the first n coupons can form a complete set is the number of ways to choose any one of the complete sets in S, multiplied by the number of ways to order the coupons within that set. There are (c choose n) ways to choose n coupons out of c, and for each complete set of n coupons, there are n! ways to order them. Therefore, the number of ways to choose n coupons that form a complete set is (c choose n) * n!.
The total number of ways to choose n coupons out of c is c^n.
So, the probability that the first n coupons collected do not form a complete set is:
P = 1 - [(c choose n) * n! / c^n]
Alternatively, we can count the number of ways in which the first n coupons can be collected so that they do form a complete set. There are (c-1)^n ways to choose n coupons out of c-1 types of coupons, and for each set of n coupons, there is exactly one way to add the missing coupon to form a complete set. Therefore, the number of ways to choose n coupons that form a complete set is c^n - (c-1)^n.
So, the probability that the first n coupons collected do not form a complete set is:
P = (c^n - (c-1)^n) / c^n
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porter is on the swim team. IN addition to swimming he runs as part of his training porterchecks his heart rate halfway through his training session . (swimming 53 beats in 1/3 minute running 42 beats in 1/4 minute). What is porters heart rate when he swims?
Answer: 159 bpm
Step-by-step explanation:
if his rate is 53 beats in 1/3 of a minute, in 3/3 of a minute, (1 full minute), it will be 53 x 3 = 159 beats
so we can say his heart rate is 159 beats/minute, or 159 bpm
which expression is equivalent to 4(x-4)
Answer:
4x * -16
Step-by-step explanation:
You use the distributive property and multiply 4 by everything in the parentheses. The 16 is negative because you keep the minus sign with the number behind it.
The graph represents the amount of money, in thousands, that you make over a
time period of years. According to the graph, what is the original price you invested?
Answer:
$2,000
Step-by-step explanation:
The initial investment price is given by the y-value where the graph intersects the y-axis
This is at y = 2
Since the scale is in thousands of $, that would mean $2,000 as the original price
Kingsley knows that 1 inch is about 2. 54 centimeters. He wants to write an equation he can use to convert any given length in inche (I) to centimeters (c)
Kingsley knows that 1 inch is about 2. 54 centimeters.6 inches is equivalent to 15.24 centimeters.
To convert any given length in inches (I) to centimeters (c), Kingsley can use the following equation:
c = I * 2.54
This equation works because we know that 1 inch is equal to 2.54 centimeters. So, to convert any given length in inches to centimeters, we simply multiply the number of inches by 2.54. The result gives us the equivalent length in centimeters.
For example, if we want to convert a length of 6 inches to centimeters, we can use the equation:
c = 6 * 2.54 = 15.24
So, Kingsley knows that 1 inch is about 2. 54 centimeters. 6 inches is equivalent to 15.24 centimeters.
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023) You are the owner of a AT&T store that
has two employees working at all times.
The first employee scheduled to work next
Wednesday makes $10.50 per hour and
averages $50 per day for commision. The
other person that is scheduled earns
$10.50 per hour and averages $60 per day
for commision.
i) Write a function that predicts your
expected payroll for the day.
+12
ii) Next Wednesday the store is going to
be open for 5 hours. How much do you
expect to pay your employees?
(i) The function that predicts your expected payroll for the day is,
For first person; y = $50 + $10.50x
For second person; y = $60 + $10.50x
Where, y is total amount and x is number of working hours.
(ii) In Wednesday; The amount expect to pay your employees is,
For first person;
⇒ y = $102.50
For second person;
⇒ y = $112.50
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 first employee scheduled to work next Wednesday makes $10.50 per hour and averages $50 per day for commission.
And, The other person that is scheduled earns $10.50 per hour and averages $60 per day for commission.
Let total amount earn = y
And, Number of working hours = x
Hence, We can formulate;
The function that predicts your expected payroll for the day is,
For first person;
⇒ y = $50 + $10.50x
For second person;
⇒ y = $60 + $10.50x
And, For 5 hours, the amount is,
For first person;
⇒ y = $50 + $10.50x
⇒ y = 50 + 10.50 × 5
⇒ y = 50 + 52.50
⇒ y = $102.50
For second person;
⇒ y = $60 + $10.50x
⇒ y = 60 + 10.50 × 5
⇒ y = 60 + 52.50
⇒ y = $112.50
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A bride-to-be had already finished assembling 15 wedding favors when the maid of honor came into the room to help. The bride assembles at a rate of 2 favors per minute. In contrast, the maid of honor works at a speed of 5 favors per minute. Eventually, they will both have assembled the same number of favors. How many favors will each have made? How long will that take?
The bride-to-be and her maid of honor will each have made __ favors in __ minutes.
Using an equation, the bride-to-be and her maid of honor will each have made 25 favors in 5 minutes.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
Equations are depicted using the equal symbol (=), while mathematical expressions, which combine variables, constants, and values only use mathematical operands.
The total number of wedding favors assembled by the bride-to-be = 15
The bride's assembling rate per minute = 2 favors
The maid of honor's assembling rate per minute = 5 favors
Let x = the number of minutes used
Let the number of favors assembled by the bride = 15 + 2x
Let the total number of favors assembled by the maid of honor = 5x
For the two to assemble the same number of favors, 15 + 2x = 5x
15 = 3x
5 = x
Thus, in 5 minutes the bride-to-be and her maid of honor will have assembled 25 favors each.
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Evaluate3(x-1+2)when x=5
Translate the following sentence into an equation "the sum of 8 times x and 4 is 68"
Answer:
The equation is:
8x + 4 = 68
and the solution is:
x = 8
Step-by-step explanation:
The equation is:
8 time x and 4 is 68
8x+4 = 68
Solve:
8x + 4 - 4 = 68 - 4
8x + 0 = 64
8x = 64
x = 64/8
x = 8
Check:
8*8 + 4 = 68
The distance between two towns is 600km,correct to the nearest 10km
A car takes 8 hours 40minute, correct to the nearest 10 minute, to travel this distance
Calculate the lower bound for the average speed of the car in km/h
Answer:
Below
Step-by-step explanation:
rate X time = distance
rate = distance / time <=====we want minimum of this so make denominator as large as possible and numerator as small as possible
distance = 595 KM ( rounds up to 600 km)
time = 8 hr 44 min rounds down to 8 :40 you could make it 8:44.99)
595 km / (8 + 44.99/60) hr = 68 km/hr
Find the values of x, y, and z
The values of x, y and z are given as follows:
x = 6.25.y = 6.67.z = 5.What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.There are two similar trapezoids for this problem, hence the proportional relationship for the side lengths is given as follows:
x/15 = 10/24 = y/16 = z/12.
Applying cross multiplication, the value of x is given as follows:
24x = 15 x 10
x = 15 x 10/24
x = 6.25.
The value of y is given as follows:
y = 16 x 10/24
y = 6.67.
The value of z is given as follows:
z = 12 x 10/24
z = 5.
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what is the solution to the number sentence k - 1.6 / 6 = 5.4
Answer:
k = 48.4
Step-by-step explanation:
[tex] \frac{k - 16}{6} = 5.4 \\ 6 \times \frac{(k - 16)}{6} = 5.4 \times 6 \\ k - 16 = 32.4 \\ k = 32.4 + 16 \\ k= 48.4 [/tex]
A small town has two local high schools. High School A currently has 1000 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 55 students each year. Let A represent the number of students in High School A in t years, and let B represent the number of students in High School B after t years. Write an equation for each situation, in terms of t, and determine after how many years, t, the number of students in both high schools would be the same.
The linear equation for A and B will be A=1000+35t and B=700+55t where t=no. of years and A will be same as B in 15 years.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
As given that High School A currently has 1000 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 55 students each year.
Let A represent the number of students in High School A in t years, and
Let B represent the number of students in High School B after t years.
Then A=initial students+35*no. of years and B=initial students+55*no. of years i.e. A=1000+35t and B=700+55t
and for A=B
1000+35t=700+55t
55t-35t=1000-700
20t=300
t=15
hence,
The linear equation for A and B will be A=1000+35t and B=700+55t where t=no. of years and A will be same as B in 15 years.
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A game lasts 3/8 hours. Tammy played 12 of these games.
The total time that tammy sent in total playing games is; 4.5 hours
How to solve Fraction Word problems?The parameters given for Tammy in playing the game are;
Number of games played = 12 games
Time spent per game = ³/₈ hours
Thus;
Total time she spent playing game will be gotten by multiplying the time per game by number of games played to get;
Total time spent = ³/₈ * 12
= 9/2
= 4.5 hours
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Complete question is;
A game lasts 3/8 hours. Tammy played 12 of these games. For how long did she play in total? Write your answer in simplest form.
John brings $15 to the candy store. He buys a bag of jelly beans for $4 and plans to buy some chocolate that costs $5 per pound. He wrote the inequality 4+5x≤15 to solve for all the possible values of x , the number of pounds of chocolate John could buy
John can buy any amount of chocolate between 0 and 2.2 pounds (rounded to one decimal place) and still have enough money to buy the jelly beans.
John brings $15 to the candy store and buys a bag of jelly beans for $4. He plans to buy some chocolate that costs $5 per pound. Let x be the number of pounds of chocolate John could buy.
The cost of the chocolate John plans to buy is $5 per pound, so the total cost of x pounds of chocolate is 5x. John's total budget is $15, so he must have enough money to buy the jelly beans and the chocolate. Therefore, the inequality that represents this situation is:
4 + 5x ≤ 15
To solve for x, we can begin by isolating the variable on one side of the inequality. We can do this by subtracting 4 from both sides of the inequality:
5x ≤ 11
Next, we can isolate x by dividing both sides of the inequality by 5:
x ≤ 11/5
Therefore, the possible values of x, the number of pounds of chocolate John could buy, are all real numbers less than or equal to 11/5. However, since John cannot buy a negative amount of chocolate, we must also restrict x to be greater than or equal to 0. Therefore, the solution to the inequality is:
0 ≤ x ≤ 11/5
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