Answer:
D-16
Step-by-step explanation:
Answer:
D. 16
Step-by-step explanation:
On one shelf, she can put 4 baskets.
So, on 4 shelves, she can put (4 x 4) 16 baskets.
Hope this helps :)
I'll mark brainliest!
Answer:
C is your answerrrr
can i have brainliest?
Step-by-step explanation:
Answer:
The answer is c
this is the answer because Find the least common denominator or LCM of the two denominators:
LCM of 3 and 8 is 24
Next, find the equivalent fraction of both fractional numbers with denominator 24
For the 1st fraction, since 3 × 8 = 24,
1/3 = 1/3 × 3/8 = 8/24
Likewise, for the 2nd fraction, since 8 × 3 = 24,
3/8 = 3/8 × 1/3= 9/24
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
8/24 < 9/24
or 1/3 < 3/8
Which word describes the slope of the line?
O positive
O negative
zero
O undefined
The slope of a horizontal line is always zero.
What is slope?
The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are any two points on the line.
The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.
By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:
slope = change in y / change in x = 0 / (any non-zero value of x) = 0
So, the slope of a horizontal line is always zero.
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a bank teller has 50 $20 and $5 bills in her cash drawer the value is $535 how many $20 bills are there
Answer:
19 $20 bills
Step-by-step explanation:
Let's assume the number of $20 bills in the cash drawer is "x."
The value of the $20 bills can be calculated by multiplying the number of bills by the denomination:
Value of $20 bills = 20 * x
Similarly, the value of the $5 bills can be calculated by multiplying the number of bills by the denomination:
Value of $5 bills = 5 * (50 - x) (since there are a total of 50 bills)
According to the given information, the total value of all the bills is $535:
Value of $20 bills + Value of $5 bills = $535
Substituting the expressions for the values:
20 * x + 5 * (50 - x) = 535
Simplifying the equation:
20x + 250 - 5x = 535
Combining like terms:
15x + 250 = 535
Subtracting 250 from both sides:
15x = 285
Dividing both sides by 15:
x = 19
Therefore, there are 19 $20 bills in the cash drawer.
Zarika earns the same amount each week by walking her neighbor's dogs. When she started this job, she had $300 in her savings account.
The table shows Zarika's savings account balance for her first month of work.
Week 0 1 2 3 4
Balance $300 $550 $800 $1050 $1300
Let x represent the number of weeks Zarika has been working and let y represent Zarika's account balance.
Which equation, expressed in Slope-Intercept Form, represents the amount of money in Zarika's bank account over time?
y=250x+300
y=300x+250
y=300x−250
y=250x−300
Answer:
y=250x+300
Step-by-step explanation:
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The amount of money in Zarika's bank account over time after x weeks is represented by the equation.
y = 250x + 300
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 4 is an equation.
We have,
Amount earned each week = same.
Amount in her account = $300.
Number of weeks = x
Amount in the account = y
The equation represents the account balance after x weeks.
Total amount = $300 + Amount earned per week
This can be written as,
y = 250x + 300
Thus,
The amount of money in Zarika's bank account over time after x weeks is represented by the equation.
y = 250x + 300
Option A is the correct answer.
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The first shelf on Hannah’s bookshelf hoods an equal number of fiction and nonfiction. If Hannah’s selects 5 books randomly, what is the probability that 3 of the books will be fiction and 2 will be nonfiction
Answer:
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
Step-by-step explanation:
What is probability?
Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.
To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.
Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.
Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.
Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.
Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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Please answer ASAP I will brainlist
Answer:
There is one solution. The solution is 2, 18, 19.
Step-by-step explanation:
If you want me to show working tell me in the comments and I'll edit the answer
Answer:
A. (2, 18, -19)
Step-by-step explanation:
To solve:
Z is the most suitable variable to remove first
Add the first equation to the second equation: (this conveniently removes both y and z)
(x+y-z) + (4x-y+z) = 1+9
Simplify
5x = 10
Solve
x = 2
Multiply the second equation by 2 and minus it to the third equation: (Solve for y)
2(4x-y+z) - (x-3y+2z) = 2(9) - (-14)
Simplify
8x-2y+2z-x+3y-2z=18+14
7x+y=32
Substitute using x=2
7(2) + y = 32
y = 32 - 14
y = 18
Now substitute x and y for their respective values into Equation 1
2 + (-18) - z = 1
Simplify
-z = 19
z = -19
So :
x = 2, y = 18 , z = -19
42x^2y^4+18x^4y^9+6x^6y gcf
Answer:
18x^4 y^9 + 6x^6 y + 42x^2 y^4
Step-by-step explanation:
A normally distributed data set has a mean of 0 and a standard deviation of 0.5. Which is closest to the percent of values between –1 and 1?
34%
50%
68%
95%
As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.
Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.
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There are 26 boys and 20 girls in a class.
The boys and the girls have some counters.
The mean number of counters that the boys have is 28.
The mean number of counters that the girls have is 19.
Work out the mean number of counters the 46 children have.
Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.
What is the mean?The mean refers to the average value.
The average is the quotient of the total value divided by the number of items in the data set.
The number of boys in the class = 26
The number of girls in the class = 20
The total number of boys and girls in the class = 46
The mean number of counters that the boys have = 28
The total number of counters that the boys have = 728 (28 x 26)
The mean number of counters that the girls have =19
The total number of counters that the girls have = 380 (19 x 20)
The total number of counters that the class has = 1,108 (728 + 380)
The average or mean number of counters in the class = 24 (1,108 ÷ 46)
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Es el conjunto de deshielo determinante de la matriz x 2
5 7
Es igual a 4 cual es el valor de x
con un conjunto de deshielo determinante igual a 4, es x = 2.
Para determinar el valor de x en la matriz x 2
5 7
dado que el conjunto de deshielo determinante es igual a 4, necesitamos utilizar la propiedad de que el determinante de una matriz 2x2 se puede calcular utilizando la siguiente formula:
determinante = (a × d) - (b × c)
Donde a, b, c, y d son los elementos de la matriz.
En este caso, tenemos la matriz:
x 2
5 7
Aplicando la formula del determinante, podemos establecer la siguiente ecuacion:
( x × 7 ) - ( 2 × 5 ) = 4
Simplificando la ecuacion, obtenemos:
7x - 10 = 4
A continuacion, vamos a resolver la ecuacion para encontrar el valor de x:
7x = 4 + 10
7x = 14
Dividiendo ambos lados de la ecuacion por 7, obtenemos:
x = 2
Por lo tanto, el valor de x en la matriz x 2
5 7
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Correct answer please
Answer:
50.75
Step-by-step explanation:
We have:
\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)
\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)
What is the product of 2.8\times 10^32.8×10
3
and 9.7 \times 10^39.7×10
3
expressed in scientific notation?
The product of two numbers 2.8 × 10³ and 9.7 × 10³ can be represented in scientific notation as, 2.716 x 10⁷
What is the scientific notation of a number?The standard form for a number is a method by which we write number in a format like b×10ˣ. The value of b should be in between 0 to 10.
Given that,
The numbers,
2.8 × 10³
And 9.7 × 10³
the product in scientific notation = ?
the product in scientific notation = 2.8 × 10³ x 9.7 × 10³
It is known that,
if same numbers are in multiplication form,
their powers can be added
the product in scientific notation = 27.16 x 10³⁺³
= 27.16 x 10⁶
It can be further written as,
multiplied and divide by 10
the product in scientific notation = 27.16 x 10⁶x10/10
= 2.716 x 10⁷
Hence, the product is 2.716 x 10⁷
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Please look at the pic and help!!
Answer:
4x² + 22x - 12
Step-by-step explanation:
A = bh/2
A = (4x - 2)(2x + 12)/2
A = (8x² + 48x - 4x - 24)/2
A = (8x² + 44x - 24)/2
A = 4x² + 22x - 12
What is the new function’s equation (green)?
Answer:
\(f(x)=-(x+3)^2\)
Step-by-step explanation:
The parent function is f(x) = x^2.
This can be reasoned by the fact that this is a postive parabola that is on the origin.The green function is moved 3 units to the left. This means that the function changes like this:
\(x^{2}\) --> \((x+3)^2\)The green function is also reflected over the x-axis.
Functions that are reflected over the x-axis take are multiplied by an exterior negative (literally, a negative on the outside)
Ex; f(x) flipped over x-axis= -f(x)So, we put a negative on the outside.
\((x+3)^2\) --> \(-(x+3)^2\)
The function isn't moved up or downwards, so we don't have to add or subtract anything on the outside.
The function is also not stretched or shrunk.
So, the equation of the green function is:
\(f(x)=-(x+3)^2\)
Jeff find some bugs .He finds 10 fewer grasshopers than crickets. He finds 5 fewer crickets than ladybugs . If jeff finds 5 grasshoppers, how many ladybugs does jeff dind ? How many crickets does he find ?write two equations to solve the problem .
Step-by-step explanation:
I think the answer is zero
Una sala de cine de New York vende las entradas para niños a 3 dólares y las de los adultos a 5 dólares. Si para ver una película pueden ingresar tanto niños como adultos y en un día
ingresan 345 espectadores, recaudando por concepto de venta de boletas 1365 dólares. Se
puede afirmar que el número de niños y adultos que ingresaron fue:
A la sala de cine ingresaron 180 niños y 165 adultos.
¿Cuántos niños y adultos ingresaron a una sala de cine?
De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:
3 · x + 5 · (345 - x) = 1365
Donde x es el número de niños que asistieron a la sala de cine.
Ahora despejamos la variable correspondiente mediante propiedades algebraicas:
3 · x + 1725 - 5 · x = 1365
1725 - 2 · x = 1365
2 · x = 1725 - 1365
2 · x = 360
x = 180
Ahora, el número de adultos es:
y = 345 - 180
y = 165
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Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
Hint: Think about the point where they both meet. For example, if you were to place the graphs on top of each other, what would be the point of intersection?
Type the correct number below without the dollar sign.
Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.
Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.
Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.
At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.
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The Monday relates to the Thursday so than, the Friday relation the ….? A: Tuesday B : Saturday C : Sunday D: Monday E:
Wednesday
Answer:
The correct answer is B: Saturday.
The relationship between Monday and Thursday is that they are two days apart in a typical Monday-to-Sunday week. Similarly, Friday is also two days apart from Tuesday in a typical week, so the relationship between Friday and Tuesday would be the same as the relationship between Monday and Thursday. Therefore, the correct answer is B: Saturday.
I’m am really confused on this question
Answer:
2x^7
Step-by-step explanation:
add the exponents because they both are x
2x^4*x^3=2x^7
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Launch realize. 8-2: Find Volume of Cylinders (LMS graded)
8.2.PS-13
The cylinder shown has a volume of 824 cubic inches.
a. What is the radius of the cylinder? Use 3.14 for .
b. If the height of the cylinder is changed, but the volume
stays the same, then how will the radius change? Explain.
a. The radius of the cylinder is about 8.2 in³.
(Type an integer or decimal rounded to the nearest tenth as needed.)
10.7 in.
Question Help
◇
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the volume is 824 cubic inches, we can rearrange the formula to solve for the radius:
824 = πr²h
Since the height is not given, we cannot find the exact radius. However, we can still determine the relationship between the height and radius if the volume remains the same.
b. If the height of the cylinder is changed, but the volume stays the same, the radius will change inversely proportional to the height. This means that as the height increases, the radius will decrease, and vice versa. This relationship ensures that the volume remains constant.
Therefore, we cannot determine the exact radius without knowing the height, but we can conclude that the radius and height have an inverse relationship.
Danny says 4 < 6, so 204 < 216. Is his reasoning correct? Explain.
As given by the question
There are given that 4<6, so 204<216.
Now,
On the number line, 4 is less tha6 and 204 is also less than 216
Hence, the given reasoning is correct.
24
A
Step 1
Algebra 1
1A: 2198 262 2A:
3A:
Topic 6-Quadratic Functions - Assessment 2 Retake A
4A:
Here is a pattern of squares.
2. Draw a diagram to show that 5(x+2) = 5x + 10.
Step 2
Step 3
3A: Write an expression for step n of this pattern:
2A: Is this pattern linear, exponential, or quadratic?
How do you know?
5A:
revenue (dollars)
1000
800
600
400
200
Name Marc burke
2 4 6 8 10 12 14 16 18 20
price (dollars)
Use the graph to answer the following question:
5A: What is the domain of this graph?
loodsholt tohut 69
The function of the sequence is T(n) = n² + n and it is quadratic
The domain of the graph is [0, 18]
The expression for the n-th termFrom the question, we have the following parameters that can be used in our computation:
Step Cells
1 2
2 6
3 12
From the table, we have
T(n) = n * (n + 1)
This gives
T(n) = n² + n
Hence, the function is T(n) = n² + n
The sequence typeThe sequence T(n) = n² + n is a quadratic sequence
The domain of the graphThis is the set of the x values
From the graph, we have
x = 0 to 18
So, we have
Domain = [0, 18]
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A cup of tea is placed on a table. At a time of t minutes after being placed on the table, its temperature in degrees Celsius is given by
T = 20 + Ae⁻ᵏᵗ
Where A and K are positive constants. The initial temperature of the tea was 70℃
a. Find the value of A
b. The tea takes 4 minutes to decrease in temperature from 70℃ to 50℃
show that k = 1/4 In (5/3)
please can someone explain how to get the time (t minutes) as well as a. and b. as i am baffled! i dont know what to do
Thankyouu!!
Step-by-step explanation:
To solve the problem, we'll use the information given to find the values of A and k in the equation T = 20 + Ae^(-kt), where T is the temperature in degrees Celsius at time t.
a. Finding the value of A:
We're given that the initial temperature of the tea was 70℃. Substituting this into the equation, we get:
70 = 20 + Ae^(0) (since e^0 = 1)
70 - 20 = A
A = 50
So the value of A is 50.
b. Finding the value of k:
We're told that it takes 4 minutes for the tea to decrease in temperature from 70℃ to 50℃. We can use this information to set up an equation and solve for k.
Substituting T = 70 and t = 4 into the equation, we have:
70 = 20 + 50e^(-4k)
Subtracting 20 from both sides:
50 = 50e^(-4k)
Dividing both sides by 50:
1 = e^(-4k)
Taking the natural logarithm (ln) of both sides:
ln(1) = ln(e^(-4k))
0 = -4k
Dividing both sides by -4:
0 = k
However, we need to check if this solution satisfies the condition for the tea to decrease in temperature from 70℃ to 50℃ in 4 minutes.
Substituting T = 50 and t = 4 into the equation, we have:
50 = 20 + 50e^(-4(0))
50 = 20 + 50e^0
50 = 20 + 50(1)
50 = 20 + 50
50 = 70
Since 50 is not equal to 70, the value of k = 0 does not satisfy the given condition.
Let's try another approach:
Substituting T = 50 and t = 4 into the equation, we have:
50 = 20 + 50e^(-4k)
Subtracting 20 from both sides:
30 = 50e^(-4k)
Dividing both sides by 50:
0.6 = e^(-4k)
Taking the natural logarithm (ln) of both sides:
ln(0.6) = ln(e^(-4k))
ln(0.6) = -4k ln(e)
ln(0.6) = -4k(1)
ln(0.6) = -4k
Simplifying further:
k = ln(0.6) / -4
Using a calculator or computer to evaluate ln(3/5) / -4, we get approximately:
k = ln(5/3) / 4
To recap:
a. The value of A is 50.
b. The value of k is approximately k = ln(5/3) / 4
.
Note: The calculations provided are based on the given information and assumptions. If there are any additional details or specific conditions provided, please let me know, and I'll be happy to assist you further.
(PLEASE HELP DUE TODAY!!!!!!!!!!!!!!!!!1) Did you know that 1000 can be written as the sum of the 5 consecutive positive integers beginning with 198? That is,1000=198+199+200+201+202 Also, 1000 can be written as the sum of 16 consecutive positive integers beginning with 55. That is,1000=55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70 It is also possible to write 1000 as a sum of 25 consecutive positive integers. This is the maximum number of consecutive positive integers that could be used to create the sum. Determine the smallest of the positive integers in this sum. Explain or show how you got your answer.
Answer:
Alright! So, the formula is
x+x+1+x+2+x+3+x+4....x+24
You can do 25x+300=1000
25x=700
x=28
what is the solution to the equation:
5(n - 1/10) = 1/2
a. n= 13/5
b. n= 3/25
c. n= 0
d. n= 1/5
\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)
\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)
\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)
\( \sf \longrightarrow \: \: 100n =20\\ \)
\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)
\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)
Answer:-
Answer:- D) n = ⅕ ✅To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:
Step 1: Distribute the 5 on the left side:
\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)
Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:
\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)
\(\sf 5n = 1 \\\)
Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):
\(\sf \frac{5n}{5} = \frac{1}{5} \\\)
\(\sf n = \frac{1}{5} \\\)
Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).
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The perimeter of a rectangle is 40 feet. The ratio of the width to the length is 2:3 find the length and the width
Width : Length
2 : 3
Perimeter = 2* width + 2*length
Ratio becomes:
Width : Length
4 : 6
Total units = 4 + 6 = 10
Perimeter = 40
Answer: Width is 8 ft and Length is 12 ft.
NO LINKS!!! URGENT HELP PLEASE!!!
Find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1).
(x, y) = __________
Answer:
(-8.89, -26.69)
Step-by-step explanation:
To find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1), we can use the following steps:
Since the point is in the third quadrant, both the x-coordinate and the y-coordinate must be negative. Therefore, we can write (a, 3a) as (-|a|, -3|a|).We know that the distance between P(2,1) and (-|a|, -3|a|) is 5. We can use the distance formula to set up an equation and solve for |a|:\(\sqrt{(2 - (-|a|))^2 + (1 - (-3|a|))^2} = 5\\\sqrt{(2 + |a|)^2 + (1 + 3|a|)^2} = 5\)
Squaring both sides of the equation and simplifying, we get:\(a^2 + 8a - 8 = 0\)
Solving for a using the quadratic formula, we get:\(a = \frac{-8 ±\sqrt{8^2 - 4(1)(-8)}} {(2(1))}\\a = \frac{-8 ± \sqrt{96}}{ 2}\\a = -4 ± 2\sqrt{6}\)
Since the point is in the third quadrant, we want the negative root, so:\(a = -4 - 2\sqrt(6)\)
Substituting this value of a into (-|a|, -3|a|), we get:(x, y) =\((-|-4 - 2\sqrt(6)|, -3|-4 - 2\sqrt(6)|)\)
(x, y) ≈ (-8.89, -26.69)
Therefore, the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1) is approximately (-8.89, -26.69).
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Answer:
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A recipe called for the ratio of sugar to flour to be 10 : 3 if you used 70 ounce of sugar, how many ounces of flour would you need to use?
Answer:
21
Step-by-step explanation:
10*7 = 70
3*7 = 21
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Answer:cool
Step-by-step explanation: