Answers
Area of the carpet needed = 38 ft²
Solution:
The given image is splitted into two shapes.
One is trapezoid and the other is triangle.
Top base of the trapezoid = 8 ft
Bottom base of the trapezoid = 12 ft
Height of the trapezoid = 3 ft
Area of the trapezoid = [tex]\frac{1}{2} (a+b)\times h[/tex]
[tex]$=\frac{1}{2}(8+12)\times3[/tex]
[tex]$=10\times3[/tex]
= 30
Area of the trapezoid = 30 ft²
Base of the triangle = 12 ft – 8 ft = 4 ft
Height of the triangle = 4 ft
Area of the triangle = [tex]\frac{1}{2} b h[/tex]
[tex]$=\frac{1}{2} \times4\times4[/tex]
= 8
Area of the triangle = 8 ft²
Area of the carpet = Area of the trapezoid + Area of the triangle
= 30 ft² + 8 ft²
= 38 ft²
Area of the carpet = 38 ft²
Hence 38 square feet of outdoor carpet will need for this hole.
Related Questions
What is the answer for 25% of 450
Answers
Answer:
112.5
Step-by-step explanation:
112.5 ÷ 450 =
0.25 =
0.25 × 100/100 =
0.25 × 100% =
(0.25 × 100)% =
25%
or
25% × 450 =
(25 ÷ 100) × 450 =
(25 × 450) ÷ 100 =
11,250 ÷ 100 =
112.5
Answer:
112.5
Step-by-step explanation:
First you would divide 450÷100=4.5. Then you would multiply 4.5×25=112.5.
this would give you 25% of 450
400÷100=4.5
4.5×25=112.5
Is this right? If not someone explain to me why it’s not. :)
Answers
Answer:
x= 14√3
y= 28√3
Step-by-step explanation:
Please see attached picture for full solution.
(tan30° and cos30° are special angles so there's an exact value to it in which we can memorise.)
In this case, by Pythagoras's Theorem, you should ensure that:
[tex] {y}^{2} = 42^{2} + {x}^{2} [/tex]
✓ Let's check:
[tex]{y}^{2} = (28 \sqrt{3} )^{2} \\ y^{2} = 2352 \\ {x}^{2} + {42}^{2} = ( 14\sqrt{3})^{2} + 1764 = 2352[/tex]
This satisfies Pythagoras' Theorem :)
For this kind of questions, first label the adjacent side, opposite side and the hypotenuse side of the triangle.
Cosine angle= adjacent/ hypotenuse
Sine angle= opposite/ hypotenuse
tangent angle= opposite/ adjacent
Then substitute the known side and angle to find the unknown side.
Please help! How do I simplify -16(0.47)^2?
I know the answer, I'm just not sure of the steps.
Answers
Step-by-step explanation:
We have,
[tex]-16(0.47)^2[/tex]
To find, the value of [tex]-16(0.47)^2[/tex] = ?
∴ [tex]-16(0.47)^2[/tex]
= [tex]-16(\dfrac{47}{100} )^2[/tex]
= [tex]-16\times \dfrac{47}{100}\times \dfrac{47}{100}[/tex]
= [tex]-4\times \dfrac{47}{25}\times \dfrac{47}{100}[/tex]
= [tex]- \dfrac{47}{25}\times \dfrac{47}{25}[/tex]
=[tex]- \dfrac{2209}{625}[/tex]
= - 3.5344
∴ The value of [tex]-16(0.47)^2[/tex] = - 3.5344
Thus, the value of [tex]-16(0.47)^2[/tex] is equal to - 3.5344.
question and answer choices in the attachment
Answers
The additive inverse is the idea of adding a negative number, which is the same as subtraction. Example: 2 + (-3) = 2-3
Based on the example above, if we start off with 3 and add on its additive inverse -3, then 3 + (-3) = 3-3 = 0. In general, x + (-x) = x-x = 0. So adding any number with its additive inverse gets you 0 every time.
-----------------------------------------------
Extra info:
Choice A is ruled out because the commutative property of multiplication is the idea that we can multiply two numbers in any order we want. Eg: 7*8 = 56 and 8*7 = 56, so 7*8 = 8*7Choice B is ruled out as well. The commutative property of addition is similar to the rule mentioned in choice A. But now we're adding. This rule says we can add two numbers in any order. Eg: 4+5 = 5+4 = 9Choice D is ruled out also. The multiplicative inverse of x is 1/x. Multiplying the two together gets you 1. Keep in mind that x cannot be zero. Example: The multiplicative inverse of 99 is 1/99, since 99*(1/99) = 99/99 = 1.if you know abc=def can you state bc=ef
Answers
Answer:
CPCTC
Step-by-step explanation:
If abc=def is given,
then using the cpctc rule. (corresponding parts of congruent triangles are congruent) should state this answer.
Solve the system of equations. y = 6x - 27 y = 4x - 17 a. ( -5, 3) c. ( 5, 3) b. ( -3, -5) d. No solution Please select the best answer from the choices provided A B C D
Answers
Answer:
c. ( 5, 3)
Step-by-step explanation:
6x-27=4x-17
6x-27-4x=4x-17-4x
2x-27=-17
2x-27+27=-17+27
2x=10
x=10/2
x=5
y=6(5)-27
y=30-27
y=3
100 points for the first five people!!!!!
Answers
Answer:
cj sjx soiebxidhevdi hi
Answer: hi
Step-by-step explanation:
Lol
Which equation uses the distributive property to show 6 × 78 = 468? A) 6 + (70 × 8) = 468 B) 6 × (70 + 8) = 468 C) 6 + (70 + 8) = 468 D) 6 × (70 × 8) = 468
Answers
Answer:
b
Step-by-step explanation:
you can break the 78 into 70 and 8, and multiply them separately by 6 and then add the two answers to get 468
Answer:
B
Step-by-step explanation:
literally the only equivalent equation
6. Find the value of x.
19x - 36
6x + 31
Answers
Final answer:
To find the value of x, set the expressions equal to each other and solve for x.
Explanation:
To find the value of x in the given equation, we need to set the two expressions equal to each other and solve for x. So, we have:
19x - 36 = 6x + 31
Subtracting 6x from both sides, we get:
13x - 36 = 31
Adding 36 to both sides, we get:
13x = 67
Dividing both sides by 13, we get:
x = 67/13
So the value of x is approximately 5.15.
can some one plz help me with this question
Solve the equation.
6(2x - 3) + 4 = 16 - (-18)
Answers
Answer:
x=4.16
Step-by-step explanation:
12x -18 +4 = 16+18
12x-16= 16+18
12x-16=34
+16 +16
12x=50
50/12
4.16
the solution to 5 - 3x> 35 is either x>-10 or -10> x. which solution is correct
Answers
WILL GIVE BRAINIEST!!!
Dominic collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected: Favorite Sport Swimming Running Volleyball Row totals Grade 8 0.24 0.17 0.05 0.46 Grade 9 0.18 0.14 0.22 0.54 Column totals 0.42 0.31 0.27 1 Based on the data, which statement is most likely correct? In Grade 8, 14 students liked swimming. In Grade 8, 17% of students liked running. In Grade 9, 31% of students liked volleyball. In Grade 9, 22 students liked volleyball.
Answers
Answer:
The only correct statement is ii) In Grade 8, 17% of the students liked
running.
Step-by-step explanation:
Favorite Sports
Swimming Running Volleyball Total
Grade 8 0.24 0.17 0.05 0.46
Grade 9 0.18 0.14 0.22 0.54
Total 0.42 0.31 0.27 1
i.) In Grade 8 14 students liked swimming.
This cannot be said with accuracy as the total number of students is not
known.
ii) In Grade 8, 17% of the students liked running.
This statement is TRUE.
iii) In Grade 9, 31% of students liked volleyball.
This statement is NOT TRUE. In Grade 9, 22% of the students liked
volleyball.
iv) In Grade 9, 22 students liked volleyball.
This cannot be said with accuracy as the total number of students is not
known.
The only correct statement is ii) In Grade 8, 17% of the students liked
running.
Answer:
In Grade 8, 17% of the students liked running.
John is 3 years younger than twice Monica's age. If m represents Monica's age, which equation can be used to find j, John's age?
A. j = 2m-3
B. m = 2j-3
C. j = 3-2m
D. m = 3-2
Answers
Answer:
J =2m -3
Step-by-step explanation:
2m is twice Monica's age
-3 represents 3 years younger
How do I find the value of X for the equation (3x+1)+(4x-5)=8x-9
Answers
To solve the equation (3x+1)+(4x-5)=8x-9, we simplify and solve for x, obtaining x=5 as the solution. Verification by substitution confirms that our solution is correct.
Explanation:To find the value of X for the equation (3x+1)+(4x-5)=8x-9, we first simplify both sides of the equation by combining like terms. On the left side, we combine the x terms and the constant terms: 3x + 4x + 1 - 5. This simplifies to 7x - 4. The right side of the equation remains as 8x - 9.
Next, we set the simplified left side of the equation equal to the right side: 7x - 4 = 8x - 9. To solve for x, we can subtract 7x from both sides to get x on one side of the equation, resulting in -4 = x - 9. Adding 9 to both sides gives us x = 5 as the solution.
To verify, we substitute x=5 back into the original equation: (3(5)+1)+(4(5)-5) = 15 + 1 + 20 - 5 = 31, and on the right side, 8(5) - 9 = 40 - 9 = 31, which confirms our solution since both sides equal 31.
Tony believes that x = -9 is a root of the polynomial x^2 + 13x + 36. Erika, however, believes that x = 4 is a root of the same polynomial. Who is correct?
Answers
Tony is correct.
Step-by-step explanation:
Given polynomial is;
[tex]x^2+13x+36=0[/tex]
Tony's answer is x = -9
We will put x = -9 in given polynomial.
[tex](-9)^2+13(-9)+36=0\\81-117+36=0\\0 = 0[/tex]
Tony's solution satisfies the equation.
Erika's answer is x = 4
We will put x = 4 in given polynomial.
[tex](4)^2+13(4)+36=0\\16+52+36=0\\104\neq 0[/tex]
Erika's solution does not satisfy the equation, therefore
Tony is correct.
Keywords: polynomial, roots
Learn more about polynomials at:
brainly.com/question/11258952brainly.com/question/11343416#LearnwithBrainly
Calculate the mean of 12, 15, 6, 4, and 3.
Answers
Answer:
8
Step-by-step explanation:
12+15=27 27+3=30 30+6+4=40 40/5=8
Answer:
the answer is 8
Step-by-step explanation:
12+15+6+4+3 / 5 = 8
Need help understanding how to work these math problems
Answers
Answer:
1. B. x = 11
2. E. [tex]m\angle BEF=140^{\circ}[/tex]
3. D. 4.3 in
4. D. 40.8 ft
Step-by-step explanation:
1. By Angle Addition Postulate,
[tex]m\angle KLM=m\angle KLV+m\angle VLM[/tex]
Since
[tex]m\angle KLV=34^{\circ}\\ \\m\angle KLM=14x+19\\ \\m\angle VLM=12x+7,[/tex]
then
[tex]14x+19=34+12x+7\\ \\14x-12x=34+7-19\\ \\2x=22\\ \\x=11[/tex]
2. By Angle Addition Postulate,
[tex]m\angle FED=m\angle DEB+m\angle BEF[/tex]
Since
[tex]m\angle FED=14x+8\\ \\m\angle DEB=22^{\circ}\\ \\m\angle BEF=13x-3,[/tex]
then
[tex]14x+8=22+13x-3\\ \\14x-13x=22-3-8\\ \\x=11[/tex]
Therefore,
[tex]m\angle BEF=(13\cdot 11-3)^{\circ}=(143-3)^{\circ}=140^{\circ}[/tex]
3. The area of trapezoid is
[tex]A_{trapezoid}=\text{Midsegment}\times \text{Height}[/tex]
From the diagram,
[tex]\text{Smaller base}=1.2\ in\\ \\\text{Bigger base}=4.2\ in,[/tex]
then
[tex]\text{Midsegment}=\dfrac{1.2+4.2}{2}=2.7\ in[/tex]
Since the area of trapezoid is [tex]11.6\ in^2,[/tex] then
[tex]11.6\ in^2 =2.7\ in\times \text{Height}\\ \\\text{Height}=\dfrac{11.6\ in^2}{2.7\ in}\approx 4.3\ in[/tex]
4. Use formula for the area of the circle to find the radius of the circle:
[tex]A_{circle}=\pi r^2[/tex]
So,
[tex]132.7=\pi r^2\\ \\r^2=\dfrac{132.7}{\pi}\\ \\r=\sqrt{\dfrac{132.7}{\pi}}\ ft[/tex]
Now, find the circumference of the circle:
[tex]C=2\pi r\\ \\C=2\pi \cdot \sqrt{\dfrac{132.7}{\pi}}=2\sqrt{132.7\pi}\approx 40.8\ ft[/tex]
The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the
legs of the triangle? Select three options.
3 0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x - 24 = 0
10 ft
(x + 2) ft
* x2 + 2x - 48 = 0
* x2 + (x + 2)2 = 100
xft
Not drawn to scale
Answers
The equations used to find the length of leg of triangle are:
[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]
Solution:
From given,
Area of right triangle = 24 square feet
Also from given figure in question (attached below )
base = x and height = x + 2
The area of triangle is given by formula:
[tex]Area = \frac{1}{2} \times base \times height[/tex]
Substituting the values we get,
[tex]24 = \frac{1}{2} \times x \times (x+2)\\\\24 = 0.5x(x + 2)\\\\48 = x(x+2)\\\\x^2 + 2x - 48 = 0\\\\[/tex]
Also, the above equation can be written as,
[tex]x^2 + (x+2)^2 =100[/tex]
Thus the equations used to find the length of leg of triangle are:
[tex]0.5x(x+2) = 24\\\\x^2+2x-48=0\\\\x^2+(x+2)^2 = 100[/tex]
Answer:
A, D, E
Step-by-step explanation:
From the answer above, but the letters to make it easier :)
find the sum of the product of 10 and 36 and the product of 12 and 51
Answers
Answer:
972
Step-by-step explanation:
10 x 36= 360
12 x 51= 612
360+612= 972
Brainliest please :)
Answer:
972
Step-by-step explanation:
Product = Multiplication
Sum = Addition
10 * 36 + 12 * 51
Multiply first
360 + 612
Add
972
Hope this helps :)
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked
from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the
total distance Courtney walked was 8 kilometers,
Let 6 be the number of hours it took Courtney to walk from her house to the beach, and p the number of hours
it took her to walk from the beach to the park.
Which system of equations represents this situation?
Answers
Question:
Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.
Let b be the number of hours it took Courtney to walk from her house to the beach, and p the number of hours it took her to walk from the beach to the park.
Which system of equations represents this situation?
Answer:
CORRECT (SELECTED)
⎪b+p=2
⎨4b+5p=8
Please help me asap i will mark branlist please explain
Answers
Answer:
195in^2 is the correct answer.
Step-by-step explanation:
points (0,12) and (1,3) in linear function
Answers
Answer:
y = -9x + 12
Step-by-step explanation:
first find the slope
m= 3 - 12
1 - 0
m = -9
y = mx + b
y = -9x + 12
(the 12 is the y intercept and is given in the question so there is no need to solve for it)
The ratio of men to women working for a company is 4 to 7. If there are 105 women working for the company, what is the total number of employees? (Help please)
Answers
Answer:
165 people
Step-by-step explanation:
If there are 105 woman then there are going to be 60 men because 105/7=14, so you multiply 4*15 and get 60. 60 + 105= 165. So the total employees will be 165.
The total number of employees is the sum of men and women, which is 105 (women) + 60 (men) = 165 employees.
To find the total number of employees, calculate the number of men from the given ratio 4:7 and the number of women (105), and then add the number of men to the number of women to get the total.
The question is about finding the total number of employees in a company given the ratio of men to women and the number of women.
Let's use the provided ratio of men to women, which is 4 to 7, to calculate the number of men.
Since there are 105 women, and the ratio dictates that for every 7 women there are 4 men, we divide 105 by 7 to find the number of units that represent women, which is 15.
We then multiply this by 4 (the number of men) to find the number of men, which is 60.
105 + 60 = 165
Own arranges 48 beads into an array. There are 6 rows of beads. How many columns are there.
Answers
Answer:
There will be 8 columns
Step-by-step explanation:
So first you get 48 and divide it by 6 then you get 8 as your answer
Final answer:
To determine the number of columns in a 48-bead array with 6 rows, divide the total beads by the number of rows, which results in 8 columns.
Explanation:
The student has arranged 48 beads into an array with 6 rows. To find out how many columns there are, we divide the total number of beads by the number of rows. Therefore:
Divide 48 by 6.
48 ÷ 6 equals 8.
Thus, there are 8 columns of beads.
Each row has the same number of beads, so with 6 rows and 8 columns, we can visualize the array as a rectangle where every row contains 8 beads.
Simplify 3(1/6+2/9) + (-2)
Answers
Answer:96
Step-by-step explanation:
Answer:
-5/6
Step-by-step explanation:
3(1/6+2/9)+(-2)
1/6+2/9= 7/18
3*7/18 = 21/18 = 1 1/6
1 1/6 - 2 = -5/6
a syrup is made by dissolving 2 cups of sugar to 2/3 cups of boiling water. how many cups of sugar should be used for 2 cups of boiling water
Answers
Answer:
6 cups
Step-by-step explanation:
did the math
For two cups of boiling water, 6 cups of sugar would be needed
The first step is to determine how many cups of sugar that would be needed for one cup of boiling water
The number of cups of sugar needed for a cup of boiling water = cups of sugar / cups of boiling water
2 ÷ [tex]\frac{2}{3}[/tex]
2 x [tex]\frac{3}{2}[/tex] = 3 cups
The second step is to determine the number of cups of sugar that would be needed with two cups of boiling water
Cups of sugar needed for 2 cups of water = cups of sugar needed for one cups of boiling water x 2
3 cups x 2 cups = 6 cups
In order to determine the cups of sugar needed for two cups of boiling water, first determine the number of cups of sugar needed for a cup of boiling water. Use the figure determined to find the cups of sugar needed for 2 cups of water
A similar question was solved here: https://brainly.com/question/16614723?referrer=searchResults
Let f(x)=2x^2+3x-15 and g(x)=x-1. Perform the function operation and then find the domain.
(F+G)(X)=
Answers
Answer:
[tex](F+G)x=2x^2+4x-16[/tex]
[tex]Domain[/tex] [tex]=(-\infty,\infty)[/tex]
Step-by-step explanation:
Given that
[tex]F(x)=2x^2+3x-15[/tex]
and [tex]G(x)=x-1[/tex]
then [tex](F+G)x = F(x)+G(x)[/tex]
[tex]=(2x^2+3x-15)+(x-1)\\=2x^2+3x-15+x-1\\\\(F+G)x=2x^2+4x-16[/tex]
Domain
since it is a polynomial of degree [tex]2[/tex], the domain will be whole real line
[tex]domain[/tex] [tex]=(-\infty,\infty)[/tex]
Final answer:
To perform the function operation (F+G)(X), add the functions f(x) and g(x) together to get (F+G)(X) = 2x² + 4x - 16. The domain of this function is all real numbers.
Explanation:
To perform the function operation (F+G)(X), where f(x) is given as 2x² + 3x - 15 and g(x) is x - 1, we simply add the two functions together:
(F+G)(X) = f(x) + g(x)
(F+G)(X) = (2x² + 3x - 15) + (x - 1)
This simplifies to:
(F+G)(X) = 2x² + (3x + x) - (15 + 1)
(F+G)(X) = 2x² + 4x - 16
The domain for this new function is all real numbers, since there are no restrictions such as division by zero or taking the square root of a negative number that would limit the values that x can take.
The hypotenuse of a right triangle is 14 centimeters long. One of the legs of the
triangle is 6 centimeters. What is the length of the triangle's other leg?
Answers
Find the slope for the following pair of points:
(10,4) and (-2, 17)
Answers
Final answer:
The slope of the line passing through the points (10,4) and (-2, 17) is calculated using the slope formula and is approximately -1.08.
Explanation:
To find the slope for the line passing through the two points (10,4) and (-2, 17), we use the slope formula which is (change in y)/(change in x) or (y2 - y1) / (x2 - x1). Applying this formula to our points:
m = (17 - 4) / (-2 - 10)
m = 13 / -12
m = -1.0833...
So, the slope of the line that passes through the points (10,4) and (-2, 17) is approximately -1.08.
Simplify the expression.
Answers
Answer:
The answer is (t4)-7
Step-by-step explanation:
First you simplify the like terms so t add the 2s together and you get t4 then add the negative numbers and it equals -7.
Answer:(t4)-7
Step-by-step explanation: