Answers
Related Questions
Solve the compound inequality and graph its solution:8r-3 ≥7r - 7 or 2r + 4≤ r-3
Answers
Answer:
Step-by-step explanation:
o solve the compound inequality, we'll start by solving each inequality separately, and then find the intersection of their solutions.
For the first inequality: 8r - 3 ≥ 7r - 7
Adding 7r to both sides: 8r - 3 + 7r ≥ 7r - 7 + 7r
Combining like terms: 15r - 3 ≥ 14r
Subtracting 14r from both sides: 15r - 14r - 3 ≥ 0
Combining like terms: r - 3 ≥ 0
Adding 3 to both sides: r ≥ 3
For the second inequality: 2r + 4 ≤ r - 3
Subtracting 2r from both sides: 2r + 4 - 2r ≤ r - 3 - 2r
Combining like terms: 4 ≤ -r - 3
Adding r and 3 to both sides: 4 + r + 3 ≤ -r
Combining like terms: 7 ≤ -r
Multiplying both sides by -1: r ≤ -7
The solution to the compound inequality is the intersection of the solutions to each inequality, which is the range of r that satisfies both conditions. So, the solution is 3 ≤ r ≤ -7.
To graph the solution, we can plot the two inequalities on the number line, and shade the region between 3 and -7:
A map of a farm is shown in a coordinate plane in which the coordinates are measured in yards. The map shows the barn at
(-2, 3). A well is dug at (-2, y). What are two values of y such that the barn is 50 yards from the well?
Answers
The two values of y such that the barn is 50 yards from the well are given as follows:
y = -47 and y = 53.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following equation:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For this problem, we have that D = 50, hence the equation is given as follows:
sqrt[(-2 - (-2))² + (y - 3)²] = 50
y - 3 = ±50.
Hence the values of y are given as follows:
y - 3 = -50 -> y = -47.y - 3 = 50 -> y = 53.More can be learned about the distance between two points at https://brainly.com/question/7243416
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5x +6y = 4
10x+12y = 8
What is the system of equation is it no solution, one solution, or infinitely many solutions?
Answers
The equation 5x + 6y = 4, 10x + 12y = 8 has infinitely many solution.
How to solve system of equation?System of equation can be solved using elimination method, substitution method and graphical method.
Therefore, let's solve the system of equation using elimination method.
5x + 6y = 4
10x + 12y = 8
multiply equation(i) by 2
Hence,
10x + 12y = 8
10x + 12y = 8
subtract the equations
0 = 0
Therefore, the equation has infinitely many solution.
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you can choose one of three boxes. box a has four $5 bills and a single $100 bill, box b has 400 $5 bills and 100 $100 bills, and box c has 24 $1 bills. you can have all of box c or blindly pick one bill out of either box a or box b. which offers the greatest expected winning?
Answers
Secured loans are less costly than unsecured loans because _________.
They usually have a lower interest rate.
They require collateral.
They are less risky for the financial institution.
All of these are true.
Answers
Due to the fact that secured loans often have lower interest rates than unsecured loans, they are less expensive. They require collateral. They are less risky for the financial institution. The correct option is D.
What are secured loans?A secured loan is one in which the borrower pledges an asset as security for the loan, turning the pledged asset into a secured debt owing to the lender (the creditor).
Some loans may be backed by assets other than your house; for instance, they may be backed by your automobile, jewelry, or other possessions. Because lenders can collect the asset in the event of a default on a secured loan, secured loans often have lower interest rates than unsecured loans.
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Which statement describes the relationship between −2 and −4? Responses −2 is located to the left of −4 on a horizontal number line because −2>−4. negative 2 is located to the left of negative 4 on a horizontal number line because negative 2 is greater than negative 4. −2 is located to the left of −4 on a horizontal number line because −2<−4. negative 2 is located to the left of negative 4 on a horizontal number line because −2<−4. −2 is located to the right of −4 on a horizontal number line because −2>−4. negative 2 is located to the right of negative 4 on a horizontal number line because negative 2 is greater than negative 4. −2 is located to the right of −4 on a horizontal number line because −2<−4. negative 2 is located to the right of negative 4 on a horizontal number line because −2<−4.
Answers
−2 is located to the right of −4 on a horizontal number line because −2>−4. Therefore, option C is the correct answer.
What is number line?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.
Given that, -2 and -4 is located on number line.
Negative integers on the number line located left to zero.
If the greater integer with negative sign and go farther on left of 0 on number line, the value of integers decreases.
Therefore, option C is the correct answer.
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Skye’s grandparents invest $1500 in a college account. It earns 4. 9% interest that is compounded annually. How much money will be in the account after 10 years?
Round to the nearest cent, if necessary
Answers
The total amount accrued, principal plus interest, with compound interest on a principal of $ 1,500.00 at a rate of 4.9 % per year compounded 1 times per year over 10 years is $2,420.17.
Using the compound interest formula is
Compound interest is calculated by multiplying the initial principal amount (P) by one plus the annual interest rate (R) raised to the number of compound periods (nt) minus one.
[tex]$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{r}}{\mathrm{n}}\right)^{\mathrm{nt}}$[/tex]A= Total amount =?
P= Principal amount = 1500
r=Rate of interest =4.9 %=0.049
t= time =10years
n= compounding = annually =1
Using the above data and formula, we get:
First, convert R as a percent to r as a decimal
[tex]& \mathrm{r}=\frac{\mathrm{R}}{100} \\[/tex]
[tex]& \mathrm{r}=\frac{4.9}{100} \\[/tex]
[tex]& \mathrm{r}=0.049 \text { rate per year, }[/tex]
Then solve the equation for A
[tex]& \mathrm{A}=1,500.00\left(1+\frac{0.049}{1}\right)^{(1)(10)} \\[/tex]
[tex]& \mathrm{A}=1,500.00(1+0.049)^{10} \\[/tex]
[tex]& \mathrm{~A}=\$ 2,420.17[/tex]
The total amount accrued after 10 years is $2,420.17.
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Solve the word problem below. Enter your answer in simplest terms, using the
slash (/) to represent the fraction bar.
A recipe for a soup calls for 2/4 cup of chopped onion and 1/6 cup of chopped
celery. What is the total amount of celery and onion needed for the soup
Answers
Answer:
2/3 cups
Step-by-step explanation:
The recipe calls for 2/4 cup of onion and 1/6 cup of celery. To find the total, we need to add the two fractions together; the amount of onions(2/4 cup or 1/2 a cup if simplified), and the amount of celery(1/6). To do this, we need to find a common denominator. We can do this buy finding a common multiple between 2 and 6.
Multiples of 2: 2, 4, 6, 8, 10, 12...
Multiples of 6: 6, 12, 18, 24, 30...
A common multiple is 6. 1/2x3/3=3/6 <--- an equivalent fraction of 1/2
Now both fractions have the same denominator:
Onions: 3/6
Celery: 1/6
3/6+1/6 = 4/6
4/6 simplifies to 2/3.
The total amount of celery and onion need for the soup is 2/3 cup
Answer:
2/3 cups
Step-by-step explanation:
Mimi Divided a block of chese weighing 10kg into pieces weighing 5/8 kg how many pieces did she get? (Show Working)
Answers
Let's call the number of pieces of cheese Mimi got "n". Then, we can write the following equation:
10 kg = n * (5/8 kg)
To solve for n, we need to convert both sides of the equation to the same units, such as grams. 1 kg = 1000 g, so:
10 kg * 1000 g/kg = 10,000 g
5/8 kg * 1000 g/kg = 625 g
Now, we can write the equation using the same units:
10,000 g = n * 625 g
To solve for n, we need to divide both sides of the equation by 625 g:
n = 10,000 g / 625 g = 16
So, Mimi divided the block of cheese into 16 pieces, each weighing 5/8 kg.
Bronze is a mixture of copper and tin. The copper and tin are mixed in the ratio 9:1 by weight.
a. How much copper is there in a bronze brooch weighing 360 g?
b. Another bronze brooch contains 670.5g of copper.
How much does it weigh altogether?
Answers
a. The amount of copper in a bronze brooch weighing 360g is 216g.
b. The total weight of the bronze brooch is 745g.
What is the ratio of two items?If an item is made of two different items, the ratio of the quantities of those two items contributes to the amount of the compound item. With the help of that ratio, the unknown quantity can be determined.
a.
The ratio of copper to tin in bronze is 9:1.
So, the portion of copper in the bronze is 9 out of 10, that is, 0.9.
The total weight of the bronze brooch is 360g.
Find the amount of copper in that brooch.
360×0.9=324
Therefore, the copper in a 360g bronze brooch is 324g.
b.
The amount of copper in the bronze brooch is 670.5g.
Also, the portion of copper in the bronze is 0.9.
Let, the total weight of the bronze brooch is Xg.
So, the equation becomes 0.9X=670.5.
Find the value of X.
0.9X=670.5
X=745
Therefore, the total weight of the bronze brooch is 745g.
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To simplify 8. 3 − 4 1 5 ( 6. 1 + 1 2 ) , which operation must be performed first? Which operation must be performed second? Which operation must be performed last? Which is the simplified expression in the decimal form?
its a mutilpy choice question the choices are addition, multiplication, and subtraction
Answers
Answer:
Step-by-step explanation:
Use PEMDAS to determine order of operations.
P = Parentheses
E = Exponents
M/D = Multiplication/Division
A/S = Addition/Subtraction
The operation in the parentheses must be performed first, which is the addition of 6.1 + 12.
The next operation to perform is multiplication, which is 415 times (6.1 + 12).
The last operation to perform is the subtraction of 415 times (6.1 + 12) from 8.3.
6.1 + 12 = 18.1
8.3 - 415(18.1)
8.3 - 7511.5 = -7503.2
the flashlight batteries produced by one of the northern manufacturers are known to have an average life of 60 hours with a standard deviation of 4 hours. assuming that the this phenomenon is not normally distributed (ie not symmetric) please answer the following questions: a. at least what percentage of flashlights will have a life of 54 to 66 hours? b. at least what percentage of the batteries will have a life of 52 to 68 hours? c. determine an interval for the batteries' lives that will be true for at least 80% of the batteries.
Answers
a) The percentage of flashlights that have a life of 55 to 65 is about 36%
b) The percentage of the batteries that have a life of 52 to 68 hours is about 75%.
Probability Under Normal Distribution:Standard normal distribution is a type of continuous distribution with a mean of zero and standard deviation of one. The random variables are standardized into z scores using z score formula.
a) The Chebyshev's theorem states that; for sample or population, percentage (p) of values are contained within two, three or more standard deviations within the mean, provided that the values of k is greater than 1:
P(%) = [tex]1-\frac{1}{k^2}[/tex]
Calculate the value of k:
[tex]k =\frac{65-60}{4}=1.25[/tex]
The percentage is calculated as;
p(%) = [tex]1-\frac{1}{1.25^2}[/tex] = 36%
The percentage of flashlights that have a life of 55 to 65 is about 36%
b) k = [tex]\frac{68-60}{4}=2[/tex]
p(%) = [tex]1-\frac{1}{2^2}[/tex] = 75%
The percentage of the batteries that have a life of 52 to 68 hours is about 75%.
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Use the given scale factor and the side lengths of the scale drawing determine the side lengths of the real object.
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Side a is 2.5 inches long, side b is 5 inches long and side c is 6.5 inches long. Therefore, option C is the correct answer.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, scale factor =2:1
Scale drawing to object the scale factor is 2:1.
Now,
a=1/2 *5 =2.5 inches
b= 1/2 *10 = 5 inches
c= 1/2 * 13 = 6.5 inches
Therefore, option C is the correct answer.
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1. A number is divided in the ratio 5:9. If the 1st is 35, find the other.
Answers
Step-by-step explanation:
solution
let first part be 5x and second part be 9x
so ,
5x = 35
x = 35\5
x = 7
Now 9x = 9*7 = 63
this might help you thank you
Louis rolled a fair six-sided die and recorded the number that was facing up on the die. He continued this for a total of 60 rolls. The table shows the frequency of each number rolled.
Outcome 1 2 3 4 5 6
Frequency 8 11 6 14 9 12
Based on the table, what is the experimental probability that the number rolled was odd?
1 over 2
5 over 12
23 over 60
37 over 60
Answers
The experimental probability that the number rolled was odd is
23 over 60.
What is experimental probability?
Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A trial is a repeating of an experiment that is performed a certain number of times.
We are given a table showing he frequency of each number rolled.
We know that the odd number outcomes are 1, 3 and 5.
So,
P (x = 1) = 8/60
P (x = 3) = 6/60
P (x = 5) = 9/60
So, the experimental probability that the number rolled was odd is
⇒P ( x is odd) = P (x = 1) + P (x = 3) + P (x = 5)
⇒P ( x is odd) = 8/60 + 6/60 + 9/60
⇒P ( x is odd) = 23/60
Hence, the experimental probability that the number rolled was odd is 23 over 60.
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Consider the function as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days.†
R(t) = 240 + 30t^3; t = 1
Find the average rate of change of R(t) over the time intervals [t, t + h], where t is as indicated and h = 1, 0.1, and 0.01 days. (Use smaller values of h to check your estimates. Round your answers to one decimal place.)
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The average rate of change of R(t) over the time intervals [t, t + h] , where t is as indicated and h = 1, 0.1, and 0.01 are 210,100 and 100.
What is Differentiation?
Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilising only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
Given function : R(t) = 240 + 30t^3
R'(t) = 90 t²
So, the average rate of change of R(t) is 90 t² .
Now, over the time interval [t, t + h], it will be as follows:
we know that, f'(t) = {f(t+h) - f(t)} / h
So, when h = 1, f'(1) = {f(1+1) - f(1)} / 1
= f(2) - f(1)
= 480 - 270 = 210
when h = 0.1 , f'(1) = {f(1+0.1) - f(1)} / 0.1
= {f(1.1) - f(1)} / 0.1
= (280 - 270) / 0.1 = 100
when h = 0.01 , f'(1) = {f(1+0.01) - f(1)} / 0.01
= {f(1.01) - f(1)} /0.01
= (271 - 270) / 0.01 = 100
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12. Tickets to a school play cost $5.00 for general
admission (g) and $3.50 with a student ID (s). On
opening night, 400 tickets were sold for a total of
$1580. How many of each kind of ticket were sold?
Answers
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Answer:
120 general admission
280 with student with a student ID
Step-by-step explanation:
x is tickets for general admission
y is tickets with a student ID
5x+3.5y=1580
x+y=400
y=400-x
5x+3.5(400-x)=1580
5x+1400-3.5x=1580
1.5x=180
x=120
120+y=400
y=280
1.If AG=12,what is EF
a.12 b.13 c.7 d.not enough info to determine
2.What is m angle ECB (not shown in the picture)
a.40 b.140 c.72 d.not enough info
Answers
1. The value of line EF is 14.3
2. not enough info to get angle ECB
What are congruent triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical.
EF is congruent to AB
GB is congruent to EH
Therefore AG will be congruent FH
therefore FH = 12
tan 40 = 12/EF
EF = 12/tan40
EF = 12/0.839
EF = 14.3
There is not enough info to get angle ECB
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Please help I’ll give brainliest!!!!!!!!
Answers
Answer:
Step-by-step explanation:
PLS HELP ASAP!
in ABC, mC=90, mA=50, and AB=35. find the length of the altitude CH
Answers
Answer:
Step-by-step explanation:
no idea sorry :/
The length of the altitude CH is 17.234.
What is Altitude of a Triangle?Altitude of a triangle is defined as the perpendicular line segment joining the vertex to the opposite side.
The figure for the triangle is given below.
Here the area of a triangle can be found in two ways.
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
Consider the triangle ABC given below.
Area of the triangle when considered base as BC and altitude as AC is,
Area, A = [tex]\frac{1}{2}[/tex] × BC × AC
BC = AB Sin (50) = 35 sin(50)
AC = AB Sin (40) = 35 sin(40)
A = [tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40))
Area of the triangle when considered base as AB and altitude as CH is,
Area, A = [tex]\frac{1}{2}[/tex] × AB × CH
A = [tex]\frac{1}{2}[/tex] × 35 × CH
Area of the same triangle will be equal when find in different ways.
[tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40)) = [tex]\frac{1}{2}[/tex] × 35 × CH
Cancelling the terms which are on both sides,
CH = 35 sin(50) sin(40)
CH = 35 × 0.766 × 0.643
CH = 17.234
Hence the length of the altitude is 17.234.
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Una compañía de teléfonos ofrece dos planes mensuales. El plan a cuesta $15 más $0. 12 adicionales por cada minuto de llamadas. El plan b cuesta $8 más 0. 17 adicionales por cada minuto de llamadas
¿para cuantos minutos de llamadas los dos planes cuestan lo mismo?
¿cual es el costo al que dos planes cuestan lo mismo?
Answers
The two plans cost the same for 60 minutes of calls. And the two plans cost the same for 60 minutes of calls.
We can set the cost of the two plans equal to each other and solve for the number of minutes:
Plan A: $15 + $0.12x (where x is the number of minutes)
Plan B: $8 + $0.17x
$15 + $0.12x = $8 + $0.17x
Subtracting $8 from both sides:
$7 + $0.12x = $0.17x
Subtracting $0.12x from both sides:
$7 = -0.05x + $0.17x
Adding 0.05x to both sides:
$7 + 0.05x = $0.17x
Dividing both sides by 0.12:
x = (7 / 0.12) / (1 - 0.17/0.12) = 60 minutes
So the two plans cost the same for 60 minutes of calls. To find the cost, we can plug x = 60 into either equation:
Plan A: $15 + $0.12 x 60 = $15 + $7.20 = $22.20
Plan B: $8 + $0.17 x 60 = $8 + $10.20 = $18.20
So the two plans cost the same when there are 60 minutes of calls, and they both cost $18.20
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Complete Question
A telephone company offers two monthly plans. The a plan costs $15 plus $0. 12 additional for each minute of calls. Plan b costs $8 plus an additional 0.17 for each minute of calls For how many minutes of calls do the two plans cost the same? What is the cost at which two plans cost the same?
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.
Answers
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
1. Polygon ABCDE is congruent to polygon TVSRK.
Answers
The angle that VSR would correspond to, given that polygon ABCDE is congruent to polygon TVSRK, is 2. Angle C.
How to find the angle ?When polygons are said to be congruent, then it means that their sides are the same lengths, and they have the same angles which means that they are corresponding.
This therefore means that the angle at A in polygon ABCDE would be congruent to the angle at T in TVSRK.
This therefore means that the angle VSR would correspond to the angle C in ABCDE because S is the third letter in TVSRK and C is the third letter in ABCDE.
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The full question is:
Polygon ABCDE is congruent to polygon TVSRK. what do angle VSR correspond to _____?
1. Angle B
2. Angle C
3. Angle D
4. Angle A
Pls show your work thank you will mark the Brainliest
Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's start with eliminating choices first ~
The value decreases as years pass by, so the value multiplied by initial value should be an exponent on the value that is less than 1.
So, only the choices with exponent on 0.9 should be qualified, eliminating the choices A and C
Next, the initial value of motorcycle is 12000 according to table. so at x = 0, v(x) should be equal to 12000.
Now, let's check option B
[tex]\qquad \sf \dashrightarrow \: v(x) = 12000(0.9) {}^{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: v(0) = 12000(0.9) {}^{0} [/tex]
[tex]\qquad \sf \dashrightarrow \: v(0) = 12000(1)[/tex]
[tex]\qquad \sf \dashrightarrow \: v(0) = 12000[/tex]
And since choice B satisfy each and every condition, that's the correct answer ~
three vertices of ABCD are A(2,4) b(5,2) c(3,-1) find the coordinates of vertex D
Answers
The coordinates of vertex D of the parallelogram is; (0, 1)
How to find the coordinates of a Parallelogram?We are given the coordinates of the parallelogram as;
A(2,4), B(5,2) and C(3,-1)
Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.
The formula for the midpoint between two coordinates is;
(x1 + x2)/2, (y1 + y2)/2
Thus;
Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2
Midpoint of BD = (5 + x)/2, (2 + y)/2
Thus;
(5 + x)/2 = 5/2
x = 0
(2 + y)/2 = 3/2
2 + y = 3
y = 1
Coordinate of D = (0, 1)
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THERES A PICTURE
HELP ME PLEASEEEEE AND THANK YOUUUUU
Answers
The equation of the quadratic curve are:
Curve 1: y = -(x + 5)² + 4Curve 2: y = (x + 5)² + 4How to write the equation of parabolaQuadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex for curve 1
v (h, k) = (-5, 4)
h = -5
k = 4
substitution of the values into the equation gives
y = a(x - h)² + k
y = a(x + 5)² + 4
Using (-3, 0) to solve for a
y = a(x + 5)² + 4
0 = a(-3 + 5)² + 4
-4 = a (2)²
a = -1
The equation is y = -(x + 5)² + 4
The vertex for curve 2
v (h, k) = (5, -4)
h = 5
k = -4
substitution of the values into the equation gives
y = a(x - h)² + k
y = a(x - 5)² - 4
Using (3, 0) to solve for a
y = a(x - 5)² - 4
0 = a(3 - 5)² - 4
4 = a (-2)²
a = 1
The equation is y = (x + 5)² + 4
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Mark and jada share 5 yards of ribbion equally how much ribbon will each one get
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If Mark and jada share 5 yards of ribbon equally, then each one will get 2.5 yards of ribbon using division method.
When Mark and Jada share 5 yards of ribbon equally, it means that they will divide the total amount of ribbon equally between the two of them. This is a common type of problem in mathematics that involves dividing a given quantity equally among a certain number of people or objects.
To solve this problem, we used the division operation to divide the total amount of ribbon (5 yards) by the number of people who are sharing it (2). The resulting quotient (2.5 yards) represents the amount of ribbon that each person will receive.
Using the division operation, we can write,
5 yards ÷ 2 = 2.5 yards
This problem illustrates an important concept in mathematics: the division of quantities into equal parts. This concept is used in many real-world applications, such as dividing up a pizza among a group of people or allocating resources in a company among different departments or teams.
Understanding how to divide quantities into equal parts is an important skill that can be applied in many different contexts, making it a valuable mathematical concept to learn and understand.
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sita wants to filled the ice cream cone with chocolate cream making hemisphere tops for this she bring some cones each of having based diameter 4.2 cm and slant height 7.5cm and a cone of cream with capacity of 800 cm .how many cones can be enough
Answers
Each cone has a volume of around 60 [tex]cm^{3}[/tex]. As a result, 800 [tex]cm^{3}[/tex] of cream would be sufficient to fill around 13 cones.
What is a volume?The quantity of space that an item or substance occupies is measured by its volume. Typically, it is expressed in cubic quantities like cubic metres or cubic feet. Volume is frequently used to describe liquids, gases, or other pourable materials like a cup of water or a gallon of fuel. The capacity of a container, such as a tank or box, is also determined by volume.
In this question, the volume of a cone is given by the formula:
V = (1/3)π[tex]r^{2} h[/tex]
Where r is the radius of the base and h is the slant height.
In this case, the radius of the base is equal to half the base diameter (4.2/2 = 2.1 cm) and the slant height is 7.5 cm.
So, the volume of each cone is (1/3)π x (2.1)2 x 7.5 = 28.7 cm3
Therefore, the number of cones needed to fill the ice cream cone with 800 cm3 of cream is 800/28.7 = 27.9 (rounded up to 28).
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F(x)=3x+5
G(x)=4x^2-2
H(x)=x^2-3x+1
Find f(x) + g(x)-h(x)
A.-5x^2+4
B.5x^2+4
C.5x^2+6x+4
D.-5x^2+6x+6
Answers
The value of the function expression evaluation; f (x) + g (x) - h (x) as required is; 3x² + 6x + 2.
What is the expression which represents f (x) + g (x) - h (x)?It follows from the task content that the expression which represents f (x) + g (x) - h (x) be determined.
Since;
F(x) = 3x + 5
G(x) = 4x² - 2
H(x) = x² - 3x + 1
Therefore,
f (x) + g (x) - h (x) = 3x + 5 + 4x² - 2 - (x² -3x + 1)
= 3x² + 6x + 2
Ultimately, the value of f (x) + g (x) - h (x) is; 3x² + 6x + 2.
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Pls answer! Lots of points! Question down below!
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The dimensions of Yura's picture 10×7 square units. The length of Yura's picture 10 units and the width of 7 units.
What is a rectangle?
An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.
The number of lines along the length is 11.
The length of the frame is 10 units.
The number of lines along the width is 8.
The width of the frame is 7 units
The dimension of an object is length × width.
The dimension of the frame is 10 units × 7 units.
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