Answer:
The only possible value of x is 12
Step-by-step explanation:
The rectangular shape has an area of 150 square units. The sides of the rectangle measures (x + 3) and (x - 2). The value of x can be computed below
area of a rectangle = length × breadth
area = 150 unit²
The sides are (x + 3) and (x - 2)
Therefore,
(x + 3)(x - 2) = 150
x² -2x + 3x - 6 = 150
x²+ x - 6 = 150
x²+ x - 6 - 150 = 0
x²+ x - 156 = 0
(x - 12)(x + 13) = 0
Therefore,
x = 12 or x = -13
It cannot be - 13 because the sides cannot result to negative . We are left with only 12.
x = 12
The only possible value of x is 12
The value of x is 12
The dimensions of the rectangle are given as:
Length = x + 3Width = x - 2The area is given as:
Area = 150The area of a rectangle is:
[tex]Area = Length \times Width[/tex]
So, we have:
[tex](x + 3)(x -2) = 150[/tex]
Expand
[tex]x^2 + 3x - 2x - 6 = 150[/tex]
[tex]x^2 + x - 6 = 150[/tex]
Subtract 150 from both sides
[tex]x^2 + x - 156 = 0[/tex]
Factorize the above equation
[tex](x + 13)(x - 12) = 0[/tex]
Solve for x
[tex]x = -13[/tex] or [tex]x =12[/tex]
The value of x cannot be negative.
So, the value of x is 12
Read more about areas at:
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Rewrite the equation in Ax+By=C form.
Use integers for A, B, and C.
y+6=-6(x+1)
Answer:
-6x+y=0
Step-by-step explanation:
y+6=-6(x+1)
y+6=-6x-6
-6x+y=0
On converting y + 6 = -6(x + 1) to Ax+By=C form, get 6x + y = -6 with A=6, B=1, and C=-6.
To rewrite the equation y + 6 = -6(x + 1) in the Ax+By=C form, where A, B, and C are integers, we need to distribute the -6 and then move all terms involving variables to one side of the equation and the constant term to the other side.
First, distribute the -6:
y + 6 = -6x - 6
Now, move the variable terms to one side by adding 6x to both sides:
6x + y + 6 = 0
Finally, subtract 6 from both sides to isolate the constant:
6x + y = -6
Now the equation is in the desired format with A=6, B=1, and C=-6.
Ignacio is curious about the average age of cars in the commuter lot at Mis large university. He takes a random
sample of 16 cars and finds that their average age is 2 = 14.5 years and their standard deviation is 8, = 4.6
years. The distribution of ages in the sample was roughly symmetric with no obvious outliers.
Based on this sample, which of the following is a 90% confidence interval for the mean age of cars (in years) in
this commuter lot?
Therefore, the correct answer is (D) [tex]$(12.61,16.39)$[/tex]
To calculate the confidence interval for the mean age of cars in the commuter lot, we'll use the formula:
[tex]\[ \text{Confidence interval} = \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \][/tex]
where:
- [tex]\(\bar{x}\)[/tex] is the sample mean age (14.5 years),
- [tex]\(s\)[/tex] is the sample standard deviation (4.6 years),
- [tex]\(n\)[/tex] is the sample size (16),
- [tex]\(t\)[/tex] is the critical value from the t-distribution corresponding to the desired confidence level (90% in this case).
First, we need to find the critical value \(t\) for a 90% confidence level with [tex]\(n-1 = 15\)[/tex] degrees of freedom. Using a t-distribution table or calculator,[tex]\(t \approx 1.753\).[/tex]
Now, we can plug in the values:
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \left( \frac{4.6}{\sqrt{16}} \right) \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \times \frac{4.6}{4} \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \times 1.15 \][/tex]
[tex]\[ \text{Confidence interval} = 14.5 \pm 2.12595 \][/tex]
[tex]\[ \text{Confidence interval} = (12.37405, 16.62595) \][/tex]
Complete question:
Ignacio is curious about the average age of cars in the commuter lot at his large university. He takes a random sample of 16 cars and finds that their average age is [tex]$\bar{x}=14.5$[/tex] years and their standard deviation is [tex]$s_x=4.6$[/tex]years. The distribution of ages in the sample was roughly symmetric with no obvious outliers.
Based on this sample, which of the following is a [tex]$90 \%$[/tex] confidence interval for the mean age of cars (in years) in this commuter lot?
Choose 1 answer:
(A) [tex]$(6.44,22.56)$[/tex]
(B) [tex]$(12.05,16.95)$[/tex]
(c) [tex]$(12.48,16.52)$[/tex]
(D)[tex]$(12.61,16.39)$[/tex]
(E) [tex]$(13.35,15.65)$[/tex]
The 90% confidence interval for the mean age of cars in the commuter lot is (12.48, 16.52). The correct answer is: c) (12.48, 16.52)
Step 1
To determine the 90% confidence interval for the mean age of cars in the commuter lot, we can use the formula for the confidence interval of the mean for a normally distributed sample:
[tex]\[ \text{CI} = \bar{x} \pm t \left(\frac{s}{\sqrt{n}}\right) \][/tex]
Where:
- [tex]\(\bar{x}\)[/tex] is the sample mean (14.5 years)
- [tex]\(s\)[/tex] is the sample standard deviation (4.6 years)
- n is the sample size (16)
- t is the t-value for the 90% confidence level with [tex]\(n-1\)[/tex] degrees of freedom (df = 16 - 1 = 15)
First, we find the t-value for 90% confidence and 15 degrees of freedom. Using a t-table or a calculator, the t-value (two-tailed) is approximately 1.753.
Step 2
Next, we calculate the margin of error:
[tex]\[ \text{Margin of Error} = t \left(\frac{s}{\sqrt{n}}\right) = 1.753 \left(\frac{4.6}{\sqrt{16}}\right) = 1.753 \left(\frac{4.6}{4}\right) = 1.753 \times 1.15 \approx 2.016 \][/tex]
Now, we calculate the confidence interval:
[tex]\[ \text{CI} = 14.5 \pm 2.016 \][/tex]
So, the lower bound is:
[tex]\[ 14.5 - 2.016 = 12.484 \][/tex]
And the upper bound is:
[tex]\[ 14.5 + 2.016 = 16.516 \][/tex]
Thus, the 90% confidence interval for the mean age of cars is approximately:
[tex]\[ (12.48, 16.52) \][/tex]
This interval suggests that we are 90% confident that the true mean age of cars in the commuter lot lies between 12.48 and 16.52 years.
Complete question : Ignacio is curious about the average age of cars in the commuter lot at Mis large university. He takes a random sample of 16 cars and finds that their average age is 2 = 14.5 years and their standard deviation is 8, = 4.6
years. The distribution of ages in the sample was roughly symmetric with no obvious outliers. Based on this sample, which of the following is a 90% confidence interval for the mean age of cars (in years) in this commuter lot?
a) (6,44,22,56)
b) (12,05,16,95)
c) (12,48,16,52)
d) (12,61,16,39)
e) (13,35,15,65)
The perimeter of the triangle shown is 30 inches. What is the length of the longest side of the triangle
Answer:
The length of the longest side of the triangle is 13 inches
Step-by-step explanation:
step 1
Find the value of x
we know that
The perimeter of triangle is equal to the sum of its three length sides
so
[tex]P=x+(2x+3)+(4x-8)[/tex]
[tex]P=(7x-5) \ in[/tex]
we have
[tex]P=30\ in[/tex]
substitute
[tex]30=(7x-5)[/tex]
solve for x
[tex]7x=30+5\\7x=35\\x=5[/tex]
step 2
Find the length of the longest side of the triangle
Remember that in a right triangle, the longest side is the hypotenuse
so
(2x+3) is the longest side
substitute the value of x
[tex]2(5)+3=13\ in[/tex]
Joe needs to replace the carpet in his living room and hallway with hardwood flooring. A floor plan is shown below. what is the total area of the floor plan? Each box of flooring contains 2.05 square meters of flooring. How many boxes should Joe buy? One box costs $54.80. How much will the flooring cost?If Joe gets a coupon for 20% off, how much would the flooring cost?
Answer:
A. Area total= 30 m2
B. 14 boxes
C. 596.40
D. 477.12
Step-by-step explanation:
A, 3.2 (1.5) A=4.8 A=6(4.2)= 30m2
B= 30/2.5= 13.95= 14 boxes
C. 12(42.6)= 596.40
D= 80/100= x/596.4 = 477.12
The total area Joe needs to cover with hardwood flooring would determine the number of boxes of flooring he should buy. Assuming the area is 100 square meters, Joe would need 49 boxes, which would cost $2,685.20 without a discount, and $2,148.16 after a 20% discount.
To determine the total area that Joe needs to floor and the number of boxes of flooring he should buy, we need to calculate the square meters of the combined living room and hallway. Unfortunately, the floor plan measurements are not provided in the question, so let's assume we have those measurements. For example, if the living room and hallway together are 100 square meters, Joe will divide the total area by the area covered by one box of flooring to find out how many boxes he needs.
The calculation for the number of boxes is as follows: total area divided by area per box. If each box contains 2.05 square meters of flooring, and the total area is 100 square meters, Joe would need 48.78 boxes. Since he can't buy a fraction of a box, he would need to purchase 49 boxes.
To find the total cost, we multiply the number of boxes by the cost per box. At $54.80 per box, the cost for 49 boxes is $2,685.20. With a 20 percent discount, the new cost is 80 percent of the original cost, which would be $2,148.16 (0.80 x 2,685.20).
What’s the largest fraction you can make using the numbers 1,2,3,4,5
Answer:
5/1
Step-by-step explanation:
The diameter of a circle is 8 kilometers. What is the angle measure of an arc kilometers long?
55
Step-by-step explanation:
Find the value of x
A) 6.0
B) 7.7
C) 60
D) 12
Answer:
D 12
Step-by-step explanation:
The product of the lengths of the segments of one chord equal the product of the segments of the other.
x*4 = 6*8
4x = 48
Divide each side by 4
4x/4 = 48/4
x = 12
Can anyone help with question one I keep getting 2:5
Answer:
B= 2:7
Step-by-step explanation:
First add all the marbles.
16+12+4+10
16+12=28
28+4=32+10=42
There are 12 white.
Simplify
12:42= 6:21=2:7
B
Step-by-step explanation:
Because 16+12+4+10= 42
so you have 12 white marble and you have 42 marbles in total so
12 : 42 simplified would be 2 : 7
You were just adding all the other colors and leaving out the white ones but you have to add them all together.
If each unit cube has edges of length 12 foot, what is the volume of the blue-outlined prism?
A) 2.5 ft
b) 5 ft
C) 10 ft
D) 20 ft
Answer:The other guy Lied it’s A
Step-by-step explanation:Just took test
What is the sign of y divided by x?
Answer:
zero
Step-by-step explanation:
the answer is zero brainley please don't delete this... hope this helps with your question! please give me brainiest
The relationship "x divides y" is denoted by the notation x|y. The sign of y divided by x will be positive.
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
The relationship "x divides y" is denoted by the notation x|y. Or, to put it another way, y is divisible by x and x is a factor of y.
For instance, the expression 3|15 denotes a division of 15 by 3 because 15=35 and 3 is a component of 15.
Therefore, The sign of y divided by x will be positive.
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If triangle ABC is similar to triangle DEC, find the values of x and y.
The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal, it is obtained by Pythagoras theorem.
Step-by-step explanation:
The given are,
From ΔABC,
AB= 6
BC= 10
AC = x
From ΔDEC,
CD= 28
DE= 21
CE = y
Step:1
Pythagoras theorem from ΔABC,
[tex]BC^{2}=AB^{2} + AC^{2}[/tex]...............(1)
Substitute the values,
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]AC^{2}[/tex]
100 = 36 + [tex]AC^{2}[/tex]
[tex]AC^{2}[/tex] = 100 - 36
= 64
AC = [tex]\sqrt{64}[/tex]
AC = 8
AC = x = 8
Step:2
Pythagoras theorem for ΔDEC,
[tex]CE^{2} = CD^{2} + DE^{2}[/tex]................(2)
From the values,
[tex]CE^{2}[/tex] = [tex]28^{2}[/tex] + [tex]21^{2}[/tex]
[tex]CE^{2}[/tex] = 784 + 441
= 1225
CE = [tex]\sqrt{1225}[/tex]
CE = 35
CE = y = 35
Result:
The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal.
pauline uses 2/5 of a cup of sugar in each batch of cookies.Yesterday, pauline used 1 cup of sugar .How many batches of cookie did pauline make yesterday?
Answer:
Step-by-step explanation
two and a half batches?
Final answer:
Pauline used 1 cup of sugar and each batch of cookies requires 2/5 cup. By dividing 1 cup by 2/5 cup, we get 2.5 giving us ≈2 batches.
Explanation:
The question asks how many batches of cookies Pauline was able to make if she used 1 cup of sugar, with each batch requiring 2/5 of a cup of sugar. To find this, we can use a simple division process as our conversion factor. You divide the total amount of sugar used by the amount needed per batch.
Steps to calculate the number of batches:
Pauline uses 2/5 of a cup of sugar for each batch of cookies.
She used a total of 1 cup of sugar yesterday.
To find the number of batches made, divide the total amount of sugar by the amount per batch: 1 cup / (2/5 cup per batch) = 5/2 = 2.5 batches.
However, since you cannot make half a batch of cookies, Pauline must have made 2 batches.
3x-23=13
I need an answer
Somebody once told me the world is gonna roll me
I ain't the sharpest tool in the shed
She was looking kind of dumb with her finger and her thumb
In the shape of an "L" on her forehead
Well the years start coming and they don't stop coming
Fed to the rules and I hit the ground running
Didn't make sense not to live for fun
Your brain gets smart but your head gets dumb
So much to do, so much to see
So what's wrong with taking the back streets?
You'll never know if you don't go
You'll never shine if you don't glow
In March in Austin, Texas, the temperatures for 7 consecutive days were 20°C, 22°C, 20°C, 24°C, 21°C, 26°C, and 23°C. What was the median of the temperatures for these days?
A) 20°C
B) 21°C
C) 22°C
D) 23°C
find x and y 5x=2y-5
Answer:
[tex]x = 2/5y - 1, y = 5/2x + 5/2[/tex]
Step-by-step explanation:
Step 1: Solve for x
[tex]5x / 5 = (2y - 5) / 5[/tex]
[tex]x = 2/5y - 1[/tex]
Step 2: Solve for y
[tex]5x + 5 = 2y - 5 + 5[/tex]
[tex](5x + 5) / 2 = 2y / 2[/tex]
[tex]5/2x + 5/2 = y[/tex]
Answer: [tex]x = 2/5y - 1, y = 5/2x + 5/2[/tex]
Please help on number 5, multiple choice
Answer:
Final Answer B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Answer B is correct because all the side lengths are multiply by 3.
5 times 3= 15, 12 times 3=36, and 13 times 3=39.
Have a nice day and stay safe!
Simplify this expression.
-2x + 3 – (5 – 6x).
Answer:
4x-2
Step-by-step explanation:
hope this helps
Kevin has 30% less money than Erin. Kevin has $140. How much money does Erin have
Answer:
Erin has $200
Step-by-step explanation:
Kevin = K
Erin = E
30% of Erin = 0.3E
K = E - 0.3E
K = 140
Substitute
140 = E - 0.3E
140 = 0.7E
Divide both sides of the equation by 0.7
E = 200
Erin has $200
Hope this helps :)
8n+6<46
need answer asap!!!
Answer:
n < 5
Step-by-step explanation:
8n+6 < 46
1. subtract 6 from both sides
8n < 40
2. Divide both sides by 8
40/8 = 5
So n<5
Answer:
(explanation)
Step-by-step explanation:
[tex]8n + 6 < 46\\8n +6 (-6) < 46 - 6\\8n < 40\\\frac{8n}{8} <\frac{40}{8}\\ n < 5[/tex]
Definition: To get the volume of a ______, multiply pi by the radius squared and then multiply by the height.
Answer:
Cylinder
explanation:
The formula for the volume of a cylinder is V=πr²h
To find the volume of a cylinder, the formula V = πr²h is used, where you multiply the square of the radius by π and then by the height, ensuring consistent units throughout.
Explanation:To get the volume of a cylinder, you need to use the formula V = πr²h, where V stands for volume, π is a mathematical constant approximately equal to 3.14159, r represents the radius of the cylinder's base, and h denotes the height of the cylinder. To calculate the volume, first square the radius, then multiply that by π, and finally multiply by the cylinder's height. For example, if a cylinder has a radius of 0.750 cm and a height of 5.25 cm, you would calculate the volume as follows: 3.142 × (0.750 cm)2 × 5.25 cm, which equals approximately 9.278 cm3. Remember to use consistent units throughout the calculation.
negative five divided by 5/7
Answer:
-7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
-5 ÷ 5/7 = -7. the fives cancel each other out and you're left with -7.
HELP NOW PLZ!!! IM IN A QUIZ!!! IM GIVING BRAINLIEST AND 15 POINTS!!!!
Vikram is studying the square pyramid below. A square pyramid. The square base has side lengths of 34.2 inches. The triangular sides have a height of 28.4 inches and length of 33.2 inches. To find the surface area of the pyramid, in square inches, Vikram wrote (33.2) (34.2) + 4 (one-half (34.2) (28.4)). What error did Vikram make?
A) He used the same expression for the area of all four lateral faces.
B) He used the wrong expression to represent the area of the base of the pyramid.
C) He used the wrong value as the height when he found the area of the lateral faces.
D) He used an expression for surface area that only finds the total area of three faces.
Answer:
He used the wrong expression to represent the area of the base of the pyramid.
Step-by-step explanation:
i just took it yesterday
Vikram made an error in the expression to represent the area of the base of the pyramid. So, Option B is correct.
What is the surface area of a square pyramid?The surface area of a square pyramid is given by the formula,
[tex]SA=s^2+4(\frac{1}{2}bh)[/tex]
Where, s-length of the side of the square, b- length of the base,
and h- the height of the pyramid.
Given data:The square base had a side of length s=34.2 inches
The height h=28.4 inches
Calculating the surface area:The surface area is given by the expression:
[tex]SA=s^2+4(\frac{1}{2}bh)[/tex]
On substituting the values
[tex]SA=(34.2)^2+4(\frac{1}{2}(34.2)(28.4))[/tex]
But Vikram wrote,
[tex]SA=(33.2)(34.2)+4(\frac{1}{2}(34.2)(28.4))[/tex]
So, he used the wrong expression for the area of the base of the pyramid.
Therefore, option B is correct.
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If (2, −7) and (8, 15) are the endpoints of a diameter of a circle, what is the equation of the circle?
A) (x + 5)2 + (y − 4)2 = 60
B) (x − 5)2 − (y − 4)2 = 80
C) (x − 5)2 − (y + 4)2 = 110
D) (x − 5)2 + (y − 4)2 = 130
Answer:
D
Step-by-step explanation:
If (2,-7) and (8,15) is the end points of the diameter, they must be on the circle.
Here is a graph: search up https:// www . desmos. com /calculator/ yl9uiyhttps, sorry I couldn't put up a link cause of brainly. Type it in without spaces.
Answer:
D
Step-by-step explanation:
Which linear function has a y-intercept at –3? On a coordinate plane, a line goes through points (negative 1.5, 0) and (0, 3). On a coordinate plane, a line goes through points (0, negative 1) and (2, 0). On a coordinate plane, a line goes through points (negative 2.5, 0) and (negative 2, negative 2). On a coordinate plane, a line goes through points (negative 3, 0) and (0, negative 3).
Answer:
(-3,0) and (0,-3)
Step-by-step explanation:
When you are looking for an intercept one of the coordinates is going to be 0.
The line or linear function which has a y-intercept at -3 will be that line that passes through (-3,0) and (0, -3).
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
F(x) = x is a line through the origin and is the parent linear function.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
A linear function has a single and unique constant slope.
In the given problem the line which intercepts y at -3 will be that line in which one y coordinate should be -3 since, it is coordinated with 0, -3) hence, it will be the correct answer.
For more about the linear function
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Is 6cups of coffee for $8 and 9 cups of coffee for $12 proportional
Answer:
They are proportional
Step-by-step explanation:
Let's simplify the ratio of coffee to cost:
6:8 :: 3:4
9:12 :: 3:4
Both simplify to 3:4, so they are proportional
Answer:
Yes, proportional
Step-by-step explanation:
Price 'P' in dollars
No. of cups 'C'
P = kC
8 = 6k
k= 8/6
k = 4/3
12 = 9k
k = 12/9
k = 4/3
Same constant, so proportional
a mountain bike tire has a diameter of 26 inches to the nearest foot how far does the tire travel when it makes 32 revolutions and does this require circumference and area?
The distance it covers in 32 revolution is 217.9 ft .
Step-by-step explanation:
Given,
The diameter of the tire of the bike = 26 in
The radius (r) = 13 in
To find the distance it travels in 32 revolutions.
To find the revolution we need to find the circumference.
Formula
The circumference of a circle = 2πr
Now,
The circumference of a circle = 2×[tex]\frac{22}{7}[/tex]×13 in
= 81.71 in (approx)
The distance it covers in 32 revolution is = 81.71×32 in
= 2614.85 in
We know that 1 ft = 12 inch
2614.85 in = 2614.85 ÷ 12 ft = 217.9 ft (approx)
math question (picture linked)
Answer:
the graph that represents the inequality is f.
0 is greater than or equal to and it is going to the right
Answer:
F
Step-by-step explanation:
f means x is above or at 0 and 0 counts because it is a closed circle, if it was open it would not have a line underneath.
Item 10
Evaluate the expression. Write your answer in scientific notation.
(4.2×10^8)+(5.9×10^9)=
Answer:
1420000005.9
Step-by-step explanation:
(4.2*10^8)+(5.9+10^9)
(4.2*100000000)+(5.9+100000000)
420000000+1000000005.9
1420000005.9
To the nearest hundredth, what is the surface area of the triangular prism?
A) 74.91 m2
B) 88.65 m2
C) 94.37 m2
D) 104.23 m2
Answer:
c) 94.37 is the correct answer.
Step-by-step explanation:
The right rectangular prism is packed with unit cubes of the appropriate unit fraction edge lengths. Find the volume of the right rectangular prism in centimeters. (Figure not to scale)
Answer:
You find the area first
L x W of the rectangle only.
To find volume : you find the depth of the square and multiply this by the area above.
Whatever the number is you add 'unit sq'
Lets say the rectangular prism measured L12 units x W6units x D4units
A =72unit square
V = D4 x A72 = 4 x 72 = 288unitsq cubes
Step-by-step explanation: