Answer:
k=8
Step-by-step explanation:
2(1)+3(2)=k
2+6=8
k=
The answer is:
k = 8
Work/explanation:
If x = 1, and y = 2, we can plug these values into the equation 2x+3y = k:
[tex]\bf{2(1) + 3(2) = k}[/tex]
Multiply
[tex]\bf{2 + 6 = k}[/tex]
Add
[tex]\bf{8 = k}[/tex]
Hence, k = 8.F i n d space t h e space n u m e r i c a l space v a l u e space o f space
left parenthesis 3 cross times 4 plus 4 ² plus 15 minus 4 right parenthesis cross times 2 plus open parentheses 4.5 plus 5 over 10 close parentheses
Answer:the space is 7 in the text below
Step-by-step explanation:
Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.9 in. and a standard deviation of 1.1 in. Find P99. That is, find the hip breadth for men that separates the smallest 99% from the largest 1%.
The hip breadth for males that separates the smallest 99% from the largest 1% is determined to be 17.03 inches using the Z-score formula and percentile calculations.
According to the question, the engineers want to design seats in commercial aircraft that can accommodate at least 99% of all males. The mean and standard deviation of male hip breadth are 14.9 in. and 1.1 in., respectively.
To determine P99, we need to find the hip breadth for males that separates the smallest 99% from the largest 1%. The value of P99 can be determined using the Z-score formula, which is given by Z = (X - μ)/σ where X is the raw score, μ is the mean, σ is the standard deviation and Z is the standard score.
Since we are looking for the hip breadth for males that separates the smallest 99% from the largest 1%, we need to find the Z-score for the 99th percentile.
Using a Z-score table, we can find that the Z-score for the 99th percentile is 2.33. Substituting the given values into the Z-score formula, we get 2.33 = (X - 14.9)/1.1. Solving for X, we get:X = 2.33(1.1) + 14.9 = 17.03 inches
Therefore, the hip breadth for men that separates the smallest 99% from the largest 1% is 17.03 inches.
For more questions on the Z-score formula
https://brainly.com/question/25099892
#SPJ8
please helppppp willlll give brainliest
Answer:
Step-by-step explanation:
try (3,-1)
Answer:
Step-by-step explanation:
A rhombus has all equal sides and two parallel sides.
Notice how Point C is 2 units to left and 1 unit below Point D>
Thus, our missing point, A, should be 2 units to left of B and 1 unit below it.
We therefore get (1,3)
So the point is (1,3)
Please help me. i need urgent help
Answer:
Step-by-step explanation:
I think there is a typo in the question
Qn : let p(n) be [tex]\sum\limits^n_{i = 1}{i2^i} = 2 + (n-1)2^{n+1} \;\;\;\;\;\;:n\geq 1[/tex]
When n = 1:
LHS: 1(2¹) = 2
RHS: 2 + (1 - 1)(2¹ ⁺ ¹) = 2
LHS = RHS
⇒ p(n) holds for n = 1
Let us assume that the proof holds for p(n): n = x
ie.
[tex]p(x): \sum\limits^x_{i = 1}{i2^i} = 2 + (x-1)2^{x+1}[/tex]
To prove that the proof holds for n = x+1
ie [tex]p(x+1): \sum\limits^{x+1}_{i = 1}{i2^i} = 2 + (x)2^{x+2}[/tex]
Consider LHS
[tex]\sum\limits^{x+1}_{i = 1}{i2^i}\\\\= \sum\limits^{x}_{i = 1}{i2^i}+\sum\limits^{x+1}_{i = x+1}{i2^i}\\\\= p(x) + (x+1)2^{x+1}\\\\= 2 + (x-1)2^{x+1} + (x+1)2^{x+1}\\\\= 2 + 2^{x+1} (x-1 + x+1)\\\\= 2 + 2^{x+1} (2x)\\\\= 2 + (x)2^{x+2}\\\\= RHS[/tex]
Solve the problem bellow and reduce to lowest terms:
Find 4/7 of 1/8
A: 4/8
B: 4/56
C: 4/7
D: 1/14
Pls I need your help
Answer: D
Step-by-step explanation:
we will multiply
4/7* 1/8
we will get 1/14
Answer:
Step-by-step explanation:
After reducing 4/7 of 1/8 to the lowest terms we get 1/14. Thus, option C is the answer.
For reducing a number to its lowest terms, first, we need to simplify the numbers to a more significant number, i.e. 4/7 of 1/8 means 4/7*1/8=4/56.
Now we know that 56 is a multiple of 4 when multiplied by 14. Hence, when we get it in the lowest term we would get 1/14
Simplify three fifths times the quantity 1 plus the square root of 16 end quantity squared minus the quantity five minus two end quantity cubed.
PLS HURRRYYYY
Answer:
-12
Step-by-step explanation:
3/5 * (1 + sqrt(16))^2 - (5 - 2)^3 =
= 3/5 * (1 + 4)^2 - (3)^3
= 3/5 * (5)^2 - 27
= 3/5 * 25 - 27
= 15 - 27
= -12
a) Find the simplified form of the difference quotient for the function f(x) = 4x² - 2x + 1.
Answer:
Step-by-step explanation: f'(x)=0. Explanation: f'(x)=8x+2=0. critical value =−14. hope that helped.
Solve for x.
11cm
5cm
x°
x=[?]°
Answer:
65.56°
Step-by-step explanation:
Trigonometric ratios:
Opposite side of x° is 11 cm and adjacent side of x° is 5 cm.
To find x°, we have to use Tan ratio.
[tex]\boxed{\bf Tan \ x = \dfrac{opposite \ side \ of \ \angle x }{adjacent \ side \ of \angle x}}[/tex]
[tex]\sf = \dfrac{11}{5}\\\\ = 2.2[/tex]
[tex]\sf x = tan^{-1} \ 2.2\\\\ x = 65.56[/tex]
you are sent to the local tea shop to pick up 9 drinks. You purchase 3 sweet teas and 6 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.
The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21
The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:
Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84
Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14
Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28
Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21
For more question probability
https://brainly.com/question/25839839
#SPJ8
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
a. The probability that this whole shipment will be accepted is ??.
b. The company will accept ??% of the shipments and will reject ??% of the shipments, ??.
Answer:
a. The probability that this whole shipment will be accepted is the probability that none or only one of the 42 randomly selected tablets is defective.
b. The company will accept approximately 36.8% of the shipments and will reject approximately 63.2% of the shipments, so many shipments will be rejected.
Step-by-step explanation:
POLYNOMIAL AND RATIONAL FUNCTIONS
Please look at the photo for the question. Thank you!
Domain: (-∞, ∞)
Range: [0, ∞)
Step-by-step explanation:Domain and range help describe the values that the function covers.
Domain
The domain of a function describes the x-values covered by a function. This means that any x-value that can be input into the function is part of the domain. The domain of this function is all real numbers. This is because any x-value could be input into the function and give an output. Additionally, the graph will continue for infinity and cover all x-values. In interval notation, the domain is (-∞, ∞). The domain for all quadratic functions is all real numbers, also written as (-∞, ∞).
Range
The range of a function describes the y-values covered by a function. Any y-values that are possible outputs are a part of the range. In this function, we can see that the parabola does not cover the positive y-values. So, the only possible outputs for the function are negative values. This means that our range will only be the negative values. In interval notation, the range is [0, ∞). We use brackets to show that the 0 is included in the range. Since infinity cannot be included in a domain or range, we use parentheses.
2
1
-1
-2
Determine the period.
2 4
6 8 10 12 14
Acellus
According to the information we can infer that the period of the graph is 8.
How to determine the period of the graph?To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.
In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.
Learn more about period in: https://brainly.com/question/23532583
#SPJ1
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 60 batteries and determine whether each is within specifications. The entire shipment is accepted if at most batteries do not meet specifications. A shipment contains 5000 batteries, and 1% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
a. The probability that this whole shipment will be accepted is ??.
b. The company will accept ??% of the shipments and will reject ??% of the shipments, ??.
Answer:
To determine the probability that the whole shipment will be accepted, we need to calculate the probability that at most one battery does not meet specifications.
Given that 1% of the batteries do not meet specifications, it means that out of 5000 batteries, 0.01 * 5000 = 50 batteries do not meet specifications.
Now, using the binomial probability formula, we can calculate the probability of at most one battery not meeting specifications:
P(X ≤ 1) = P(X = 0) + P(X = 1)
Where X follows a binomial distribution with parameters n = 60 (sample size) and p = 50/5000 = 0.01 (probability of a battery not meeting specifications).
P(X = 0) = (60 choose 0) * (0.01)^0 * (1 - 0.01)^(60 - 0)
P(X = 1) = (60 choose 1) * (0.01)^1 * (1 - 0.01)^(60 - 1)
Calculating these probabilities:
P(X = 0) ≈ 0.301
P(X = 1) ≈ 0.401
Therefore,
P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.301 + 0.401 ≈ 0.702
a. The probability that this whole shipment will be accepted is approximately 0.702.
b. The company will accept approximately 70.2% (0.702 * 100) of the shipments and will reject approximately 29.8% (100 - 70.2) of the shipments.
What are the domain and range of the inequality y <= sqrt(x - 1) - 4 ?
Answer:To determine the range is the same as to determine which numbers appear as the second number (the y-value) in an ordered pair that is part of the graph. Here are some examples: y ≥ x2 + 3. graph {y >= x^2+3 [-11.6, 13.72, 0.15, 12.81]} Although it is not 100% certain from just the graph, this graph does get wider and wider.
Step-by-step explanation:
f(g(x)) g(f(x)) ANSWER QUESTION BELOW BRIEF RESPONSE
Given statement solution is :- "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)).
"f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)).
The expressions "F(g(x)) g(f(x))" and "f(g(x)) g(f(x))" are compositions of functions. The answer to the question posed would depend on the specific functions F(x) and g(x), as well as f(x) and g(x) in the second expression.
To provide a brief response:
For the expression "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)). The order of composition is F(g(x)) first, followed by g(f(x)).
For the expression "f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)). The order of composition is f(g(x)) first, followed by g(f(x)).
For such more questions on Compose Function Expressions.
https://brainly.com/question/13033002
#SPJ8
Find the value of Y using the given diagram below
Answer:
i dont know
Step-by-step explanation:
give proper diagram please
what is (45 )(4−3 ) =
Answer:
45
Step-by-step explanation:
Do the operation in parentheses first.
(45)(4 - 3) = (45)(1) = 45
Answer:
Step-by-step explanation:
The answer is 45.
Given,
[tex](45)(4-3)\\=(45)(1)\\=45[/tex]Using subtraction and multiplication rule.
To learn more subtraction and multiplication:
https://brainly.com/question/723406
https://brainly.ph/question/4542362
-0.4(5+100)+80(5)+60
Answer:
418
Step-by-step explanation:
-4.0(5+100)+80(5)+60
We will consider the '+' outside the bracket as the dividers.
Therefore,
=-0.4(105)+400+60
=-42+400+60
=358+60
=418
n quadrilateral ABCD, AD ∥ BC. Quadrilateral A B C D is shown. Sides A D and B C are parallel. The length of A D is 3 x + 7 and the length of B C is 5 x minus 9. What must the length of segment AD be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 units
Answer:
(c) 31 units
Step-by-step explanation:
Given quadrilateral ABCD has AD║BC, with AD=3x+7 and BC=5x-9, you want to know the length of AD for the quadrilateral to be a parallelogram.
Congruent sidesOpposite sides of a parallelogram are congruent, so for ABCD to be a parallelogram, we must have ...
BC = AD
5x -9 = 3x +7
2x = 16
x = 8
AD = 3x +7 = 3(8) +7 = 31
The length of AD must be 31 units if ABCD is to be a parallelogram.
<95141404393>
Determine the period.
MAY
4 8 12 16
20 24 28
SAMLAYA
3
2
-1
-2
-3
-4
-5
Enter
The period of oscillation of the wave is 8 seconds
What is period of oscillation ?The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle.
Period is measured in seconds and it is the inverse of frequency of the oscillation. This means that T = 1/f
where f is the frequency and T is the period.
An oscillation can also be called cycle or Revolution or vibration.
From the graph, the oscillating wave made a complete oscillation at 8 seconds.
Therefore the period of oscillation of the wave is 8 seconds.
learn more about period of oscillation from
https://brainly.com/question/22499336
#SPJ1
Find the equation of the hyperbola that has foci at (±3,0) and vertices at (±2,0).
The equation of the hyperbola with foci at (±3,0) and vertices at (±2,0) is[tex](x^2 / 4) - (y^2 / 5) = 1[/tex].
To find the equation of a hyperbola, we need to determine its center, vertices, and foci. In this case, we can observe that the hyperbola is centered at the origin (0, 0) since the foci and vertices lie along the x-axis.
Let's denote the distance between the center and each focus as c, and the distance between the center and each vertex as a. In this scenario, the foci are located at (±3, 0), and the vertices are at (±2, 0).
From the given information, we can deduce that c = 3 and a = 2. Now, we can calculate the value of b using the relationship between a, b, and c in a hyperbola:
[tex]c^2 = a^2 + b^2[/tex]
Plugging in the values, we have:
[tex]3^2 = 2^2 + b^2\\9 = 4 + b^2\\b^2 = 9 - 4\\b^2 = 5[/tex]
Now we have all the necessary values to write the equation of the hyperbola. Since the foci lie on the x-axis and the center is at the origin, the equation of the hyperbola in standard form is:
[tex](x^2 / a^2) - (y^2 / b^2) = 1[/tex]
Plugging in the values for a and b, we get:
[tex](x^2 / 2^2) - (y^2 / 5) = 1\\(x^2 / 4) - (y^2 / 5) = 1[/tex]
Therefore, the equation of the hyperbola with foci at (±3,0) and vertices at (±2,0) is[tex](x^2 / 4) - (y^2 / 5) = 1[/tex].
for such more question on hyperbola
https://brainly.com/question/16454195
#SPJ8
Please Solve, Thank you!
Answer:
1711
Step-by-step explanation:
[tex]4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711[/tex]
Make sure to follow order of operations!
[tex]x - \dfrac{x-1}{2} = 1 - \dfrac{x-2}{3}[/tex]Solve
No spamming
Don't ignore my questions
[tex]\begin{gathered} \; \color{pink}{\frak{\qquad \: x - \dfrac{x - 1}{2} = 1 - \dfrac{x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{(2 \times x) - x - 1}{2} = \dfrac{(3 \times 1) - x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{2x - x - 1}{2} = \dfrac{3 - x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{x - 1}{2} = \dfrac{1 - x}{3}}} \\ \end{gathered}[/tex]
Cross Multiplying,,
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3(x - 1) = 2(1 - x)}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x - 3 = 2 - 2x}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x + 2x = 2 + 3}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{5x = 5}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{x = \dfrac{\cancel{ \: 5}}{\cancel{ \: 5}}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{cyan}{\hookrightarrow \: \underline{\boxed{\frak{x = 1}}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \qquad{\qquad{\pmb{━━━━━ღ◆ღ━━━━━}}} \end{gathered}[/tex]
Suppose you got 95% of the questions on your last test correct. If there were 140 equally weighted questions on the test, what was your ratio of correct to incorrect answers on the test? Write your answer in lowest terms.
Answer:
Step-by-step explanation:
To find the ratio of correct to incorrect answers on the test, we need to determine the number of correct and incorrect answers.
If you got 95% of the questions correct, it means you got 95% of 140 questions correct.
Number of correct answers = 95% of 140 = (95/100) * 140 = 133
To find the number of incorrect answers, subtract the number of correct answers from the total number of questions:
Number of incorrect answers = Total number of questions - Number of correct answers = 140 - 133 = 7
Therefore, the ratio of correct to incorrect answers on the test is 133:7, which is already in its lowest terms and cannot be simplified further.
Final result:
Of the 140 questions, you properly answered 133 of them, while 7 of them were incorrect. You have a 133:7 chance of winning because you provided the right answers.
Explanation:
We need to know how many questions were correctly and wrongly answered before we can fix this issue. You correctly answered 140 out of 140 questions, or 95 percent of them, giving you a total of 133 valid answers.
Thus, 133 correct answers out of 140 total questions equals 7 incorrect answers. As a result, the ratio of correct to incorrect answers is already very low at 133:7.
Learn more about Ratio here:https://brainly.com/question/32531170
#SPJ2
Write each fraction in terms of the LCD.
X-2
x2
X + 3x - 28
X
x + 9x + 14
Answer:
a) [tex]\frac{x^2-4}{(x + 7)(x - 4)(x+2)}[/tex]
b)[tex]\frac{x^2-4x}{(x + 7)(x + 2)(x-4)}[/tex]
Step-by-step explanation:
x² + 3x - 28
= x² + 7x - 4x -28
= x(x + 7) - 4(x + 7)
=
= x² + 7x + 2x + 14
= x(x + 7) + 2(x + 7)
= (x + 7)(x + 2)
LCM of x² + 3x - 28 and x² + 9x + 14 is
(x + 7)(x - 4)(x + 2)
We can write:
[tex]\frac{x-2}{x^2 + 3x - 28}\\ \\= \frac{x-2}{(x + 7)(x - 4)}\\\\= \frac{x-2}{(x + 7)(x - 4)} *\frac{x+2}{x+2} \\\\=\frac{(x-2)(x+2)}{(x + 7)(x - 4)(x+2)} \\\\=\frac{x^2-2^2}{(x + 7)(x - 4)(x+2)} \\\\=\frac{x^2-4}{(x + 7)(x - 4)(x+2)}[/tex]
and
[tex]\frac{x}{x^2 + 9x + 14 }\\ \\= \frac{x}{(x + 7)(x + 2)}\\\\= \frac{x}{(x + 7)(x + 2)} *\frac{x-4}{x-4} \\\\= \frac{x(x-4)}{(x + 7)(x + 2)(x-4)} \\\\= \frac{x^2-4x}{(x + 7)(x + 2)(x-4)}[/tex]
Find the value of x using the image below
The solutions for x are approximately x ≈ 7.888 and x ≈ -4.263.
To solve the equation, let's simplify the equation and then isolate the variable x.One of the properties of triangle Pythagorous theorem
The given equation is: 27^2 + (4x - 4)^2 = 36^2.
First, evaluate the exponents: 27^2 = 729 and 4^2 = 16.
Substituting these values back into the equation, we have: 729 + (4x - 4)^2 = 1296.
Next, simplify the equation further: 729 + (4x - 4)(4x - 4) = 1296.
Expanding the squared term: 729 + (16x^2 - 32x + 16) = 1296.
Combine like terms: 16x^2 - 32x + 729 + 16 = 1296.
Simplify further: 16x^2 - 32x + 745 = 1296.
Rearrange the equation: 16x^2 - 32x + 745 - 1296 = 0.
Combine like terms: 16x^2 - 32x - 551 = 0.
To solve the quadratic equation, we can either factor it or use the quadratic formula. However, this equation does not factor easily, so we'll use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a).
In this case, a = 16, b = -32, and c = -551.
Substituting these values into the quadratic formula:
x = (-(-32) ± √((-32)^2 - 4(16)(-551))) / (2(16)).
Simplifying further:
x = (32 ± √(1024 + 35328)) / 32.
x = (32 ± √(36352)) / 32.
x = (32 ± 190.413) / 32.
Therefore, the two possible solutions for x are:
x1 = (32 + 190.413) / 32 ≈ 7.888.
x2 = (32 - 190.413) / 32 ≈ -4.263.
Therefore, the solutions for x are approximately x ≈ 7.888 and x ≈ -4.263.
Learn more about triangle here:
https://brainly.com/question/1058720
#SPJ8
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of carpet needed for the living room is how many times greater than the amount of carpet needed for the bedroom?
The amount of carpet needed for the living room is three times greater than the amount of carpet needed for the bedroom.
To calculate the amount of carpet needed for each room, we need to consider the dimensions of the rooms. Let's assume the length of the bedroom is x units.
Since the living room is two times as long as the bedroom, its length will be 2x units.
Similarly, the width of the living room is one and a half times as wide as the bedroom. So, the width of the living room will be 1.5x units.
To find the area of each room, we multiply the length by the width.
The area of the bedroom is x units * x units = x^2 square units.
The area of the living room is 2x units * 1.5x units = 3x^2 square units.
The amount of carpet needed is directly proportional to the area of the room. Therefore, the amount of carpet needed for the living room is 3x^2 square units, while the amount needed for the bedroom is x^2 square units.
To find the difference, we divide the area of the living room by the area of the bedroom: 3x^2 / x^2 = 3.
Thus, the amount of carpet needed for the living room is three times greater than the amount needed for the bedroom.
For more similar questions on dimensions
brainly.com/question/31460047
#SPJ8
I need all the roots of the graph
Answer:
It looks to be -4, -2, 1, and 3
Which equation represents the line that is perpendicular to y=4/5x + 23 and passes through (-40,20)?
Answer:
y = [tex]\frac{-5}{4}[/tex]x - 30
Step-by-step explanation:
we will use the x = -40 and the y = 20 from the point given (-40,20). The perpendicular slope would be the opposite reciprocal from the slope given. The slope given is 4/5. The reciprocal is 5/4 and the opposite would be -5/4
y = mx + b Plug in what we know and solve for b
20 = [tex]\frac{-5}{4}[/tex] ( -40) + b
20 = [tex]\frac{-5}{4}[/tex] ·[tex]\frac{-40}{1}[/tex] + b
20 = [tex]\frac{200}{4}[/tex] + b
20 = 50 + b Subtract 50 from both sides
20 - 50 = 50 - 50 + b
-30 = b
To write the equation we need the slope (m) ([tex]\frac{-5}{4}[/tex]) and the y-intercept (b) (-30)
y = mx + b
y = [tex]\frac{-5}{4}[/tex]x - 30
Helping in the name of Jesus.
it costs $80.50 to buy 7 skirts. how much does it cost to by 10 skirts?
Answer:
To get the price of 1 each
$80.50÷7=
$11.50
To get the price of 10
$11.50×10
=$115
