A. 272 1/4 ft
B. 68 5/8 ft
Hope this helps!
Shannon and Leslie need to carpet 272.25 square feet in a room with an entertainment system that takes up 12.25 square feet. Therefore, they need to buy 12.25 square feet of carpet.
Shannon and Leslie are planning to carpet a square room that measures 16.5 feet by 16.5 feet. However, they need to account for an entertainment system that juts out into the room, taking up 3.5 feet by 3.5 feet of space.
A. Area of the space with no carpet:
To determine the area of the space with no carpet, we first calculate the area of the entertainment system:
Area of entertainment system = 3.5 feet * 3.5 feet = 12.25 square feet
Next, we subtract the area of the entertainment system from the total area of the room:
Total area of room - area of entertainment system = area of space with no carpet
272.25 square feet - 12.25 square feet = 260 square feet
Therefore, the area of the space with no carpet is 260 square feet.
B. Carpet needed for the room:
To calculate the amount of carpet Shannon and Leslie need to buy, we simply subtract the area of the space with no carpet from the total area of the room:
Total area of room - area of space with no carpet = area of carpet needed
272.25 square feet - 260 square feet = 12.25 square feet
Shannon and Leslie need to buy 12.25 square feet of carpet.
Find the perimeter of parallelogram ABCD with vertices A(–2, 6), B(1, 2), C(–2, –2), and D(1, –6).
Answer:
The perimeter = 26 unites
Step-by-step explanation:
* Lets revise some facts of parallelogram
- Every two opposite sides are parallel and equal
- Every two opposite angles are equal
- Every two adjacent angles are supplementary
- Th two diagonals bisects each other
- The perimeter = 2(S1 + S2)
* Now lets solve the problem
- ABCD is a parallelogram, where
A = (-2 , 6) , B = (1 , 2) , C = (-2 , -2) , D = (1 , -6)
- To find the perimeter we need the length of AB and BD
- The rule of the distance between two point is
d = √[(x2 - x1)² + (y2 - y1)²]
* Lets find AB
∵ AB = √[1 - -2)² + (2 - 6)²] = √[(3²) + (-4)²]
∴ AB = √25 = 5
* Lets find BD
∵ BD = √[(1 - 1)² + (-6 - 2)² = √[(0)² + (-8)²]
∴ BD = √64 = 8
* Lets find the perimeter
∵ The perimeter = 2 (5 + 8) = 26 unites
Answer:
26 units
Step-by-step explanation:
The attached image shows the coordinates drawn as a parallelogram.
The perimeter is sum of all the sides, AB + BD + DC + CA
Both BD and CA are straight lines with 8 units
AB and DC are not straight lines. So we need to find it using the pythagorean theorem, which is , one leg squared of a triangle + another leg squared will give us hypotenuse squared.
Looking at the triangle AYB, we can write and solve for AB:
[tex]AY^2+YB^2=AB^2\\4^2 + 3^2 = AB^2\\16+9=AB^2\\25=AB^2\\AB=5[/tex]
we can use the same argument and lengths for the triangle CXD. We will have DC = 5 units
Perimeter = AB + BD + DC + CA = 5 + 8 + 5 + 8 = 26 units
How to convert 186 into radians?
Answer:
see explanation
Step-by-step explanation:
To convert from degree to radian measure
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex], thus
radian measure = 186 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{31\pi }{30}[/tex]
What’s is the next number?
2,3,5,7,11,13,17
Answer:
19
Step-by-step explanation:
It is all prime numbers. The next prime number after 17 is 19.
Find the area of a circle with a circumference of 31.42 centimeters.
Answer:
A≈78.56cm²
Hope this helps you out!
c = 2(pi)r = 31.42cm
2(3.14)r = 31.42cm
6.28r = 31.42cm
r = 31.42cm / 6.28
r = 5cm
A = (pi)r^2
= (3.14) (5)^2
5x5 = 25cm
25x3.14= 78.5cm
the area equals 78.5cm
PLEASE ANSWERRRR!! (4 x 3) + (4 x 7) = 4 x (? + ?)
Answer:
? = 5
Step-by-step explanation:
Replacing "?" with x and doing parenthesis first, we have:
[tex](4 * 3) + (4 * 7) = 4 * (? + ?)\\=(4 * 3) + (4 * 7) = 4 * (x + x)\\=12+28=4*2x[/tex]
Now simply doing algebra and solving for "x", we will get the value of "?":
[tex]12+28=4*2x\\40=8x\\x=\frac{40}{8}=5[/tex]
9. Which of the following is the value of x in the solution to the
system of equations given below?
8 + 2x = 5y
4x - y = 2
A: 1
B: 2
C: 3
D: 4
Hi there,
9. Which of the following is the value of x in the solution to the
system of equations given below?
8 + 2x = 5y (1)
4x - y = 2 (2)
▪ (1)
y = ( 8 + 2x ) ÷ 5
▪ (2)
4x - [( 8 + 2x ) ÷ 5] = 2
( 20x - 8 - 2x ) ÷ 5 = 2
20x - 8 - 2x = 2 × 5
20x - 2x = ( 2 × 5 ) + 8
18x = 10 + 8
18x = 18
x = 18 ÷ 18
x = 1
The answer is : A. 1
•It was nice to help you, SkullNoggin!
Given: k(O, r), AB = BC
m∠B =120°, r=14cm
Find: AB
Answer:
AB=14 cm
Step-by-step explanation:
step 1
Find the measure of major arc AC
we know that
The inscribed angle is half that of the arc it comprises.
so
m∠B=(1/2)[major arc AC]
we have
m∠B=120°
substitute
120°=(1/2)[major arc AC]
240°=major arc AC
so
major arc AC=240°
step 2
Find the measure of arc ABC
we know that
arc AC+arc ABC=360°
substitute
240°+arc ABC=360°
arc ABC=120°
step 3
Find the measure of angle AOC
m∠AOC=arc ABC=120° ------> by central angle
so
The triangle AOC is an isosceles triangle
OA=OC=14 cm ------> is the radius
The internal angles of triangle AOC are
m∠CAO=m∠OCA=30°
The triangle ABC is an isosceles triangle
AB=BC
The internal angles of triangle ABC are
m∠BAC=m∠ACB=30°
so
Triangles AOC and ABC are congruent by ASA similarity postulate ( two angles and included side)
therefore
AO=AB=14 cm
What is the volume of the square pyramid? Round to the nearest tenth
ANSWER
[tex]Volume = 480.0{cm}^{3} [/tex]
EXPLANATION
The volume of the square pyramid is given by;
[tex]Volume = \frac{1}{3} {l}^{2} \times h[/tex]
Where l=12cm is the length of the square base and h=10cm is the height of the pyramid.
We substitute the values into the formula to get;
[tex]Volume = \frac{1}{3} \times {12}^{2} \times 10 {cm}^{3} [/tex]
This simplifies to,
[tex]Volume = \frac{1}{3} \times {12} \times 12\times 10 {cm}^{3} [/tex]
[tex]Volume = 4 \times 12\times 10 {cm}^{3} [/tex]
[tex]Volume = 480.0{cm}^{3} [/tex]
Third option is correct.
Answer:
The correct option is 3.
Step-by-step explanation:
The volume of a square pyramid is
[tex]V=\frac{1}{3}(\text{Base area})h[/tex]
[tex]V=\frac{1}{3}a^2h[/tex] .... (1)
Where, a is th side of base and h is the height of pyramid.
From the given figure it is clear that the height of the pyramid is 10 cm and the length of base is 12 cm.
Substitute a=12 and h=10 in equation (1), to find the volume of the square pyramid.
[tex]V=\frac{1}{3}\times (12)^2\times (10)[/tex]
[tex]V=\frac{1}{3}\times (144)\times (10)[/tex]
[tex]V=(48)\times (10)[/tex]
[tex]V=480[/tex]
The volume of pyramid is 480 cm³. Therefore the correct option is 3.
what is a nonlinear function
Answer: A set of dots that arent in a line-esc shape.
(Think of a scatter plot)
I'm bad at explaining, sorry.
The best way to define this is *any highest degree term greater than 1⃣*.
5÷7=35÷(y+1)
Added some points :)
Answer:
y=48
Step-by-step explanation:
5/7=35/y+1
Step 1: Cross-multiply.
5 /7=35/y+1
5*(y+1)=(35)*(7)
5y+5=245
Step 2: Subtract 5 from both sides.
5y+5−5=245−5
5y=240
Step 3: Divide both sides by 5.
5y /5=240/5
y=48
HOPE THIS HELPS!!
If the variable x represents the employee’s pay before tax-exempt expenses and taxes are removed, which expression represents the employee’s take-home pay after these deductions?
Answer: The expression that represents the employee’s take-home pay after all deductions is (0.85x-297.5) dollar.
Source:
https://brainly.in/question/5606640
Let f(x)=10x+2,g(x)=2^x, and h(x)=x^2+2x+1. Which function has the greatest output value for x=2.
A. Function f
B. Function g
C. Function h
The right answer is Function F.
Explanation:
f(x)=10(2)+2=22
g(x)= 2^(2)=4
h (x)=(2)^2+2 (2)+1=9
Answer:
A, Function f
Step-by-step explanation:
to see which function has the greatest output when x = 2, we simply plug in 2 into each function
f(2) = 10(2) + 2 ---> 20 + 2 = 22
f(2) = 22
g(2) = [tex]2^(2)[/tex] = 4
g(2) = 4
h(2) = (2)² + 2(2) + 1 ----> 4 + 4 + 1 = 9
h(2) = 9
comparing the functions, we see that the function with the largest output is f(x)
our answer is A, Function F
The height of a cylinder is 4 yards. The volume of the cylinder is 452.16 cubic yards. What is the radius of the cylinder?
Answer:
r = 5.9984789350480924657633167413961 yards
Step-by-step explanation:
h = 4 yards
V = 452.16 yards Cubed (cubic yards)
V = π[tex]r^{2}[/tex]h
452.16 = π[tex]r^{2}[/tex]*4
divide by pi and 4 and you get approx 35.98
35.981 = [tex]r^{2}[/tex]
the square root of 35.98 is approx 5.9984789350480924657633167413961
which is equal to r, or the radius
r = 5.9984789350480924657633167413961 yards
Which logarithmic graph can be used to approximate the value of y in the equation 3^y = 8?
Answer:
The graph of function f of x equals log base 3 of x.
Step-by-step explanation:
We have the following equation:
3^y = 8
Taking logarithm(Logarithm with base equal 3) in both sides, we have:
lg_3 (3^y) = lg_3 (8)
ylg_3 (3) = lg_3 (8)
y = lg_3 (8)
So, you can approximate the value of y using the function f(x) = base 3 log (x). Just look for the value of that function for x = 8.
Please put in order to least to greatest.
Answer:
1/3, 1/2, and 4/5.
Step-by-step explanation:
This is the correct answer to this question.
Hope this helps!!!
Kyle.
What is the answer to 1/4c+2/3=1/3
Simplify 1/4c to c/4
c/4 + 2/3 = 1/3
Subtract 2/3 from both sides
c/4 = 1/3 - 2/3
Simplify 1/3 - 2/3 to -1/3
c/4 = -1/3
Multiply both sides by 4
c = -1/3 × 4
Simplify 1/3 × 4 to 4/3
c = -4/3
WILL GIVE BRAINEST IF CORRECT!!!!!
The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 8 inches?
Answer:
6
Step-by-step explanation:
Help me with this problem
Answer:
XY = 74
Step-by-step explanation:
Using the information given, plug it into the perimeter formula [P=2(l)+2(w)]
90 = 2 (5y - 1) + 2 (4y + 1)
Distribute
90 = 10y - 2 + 8y + 2
Combine like-terms
90 = 18y
Isolate the variable
y = 15
Then, plug it into XY
5 (15) - 1
Multiply
75 - 1
Combine
74
Answer:
XY = 24
Step-by-step explanation:
The perimeter of the rectangle is
2(5y - 1) + 2(4y + 1) = 90 ← distribute parenthesis on left side
10y - 2 + 8y + 2 = 90
18y = 90 ( divide both sides by 18 )
y = 5
XY = 5y - 1 = (5 × 5) - 1 = 25 - 1 = 24
Mike 55 pieces of gum playing hoops at the County Fair. At school he gave 4 to every student in his math class he only has 3 remaining. How many students are in his class?
13 classmates because 55/4 = 13.75 and the .75 is the extra three pieces
I did 55-3=52 and then divided 52 by 4 to get 13 !!
calculate the angle between the longest side and the diagonal of a 577mm by 1000mm rectangle
Final answer:
The angle between the longest side and the diagonal of a 577mm by 1000mm rectangle can be found by first calculating the diagonal using the Pythagorean theorem and then using the arccosine function to find the angle with the longest side.
Explanation:
To calculate the angle between the longest side of a 577mm by 1000mm rectangle and the diagonal, we first need to determine the length of the diagonal using the Pythagorean theorem. The diagonal (d) can be found using the formula d = [tex]\sqrt{(width^2 + height^2)}[/tex]. After calculating the diagonal, we can find the angle using trigonometric ratios, specifically the arccosine function or cos-1.
Step 1: Calculate the diagonal
d = [tex]\sqrt{(577mm^2 + 1000mm^2) }[/tex]= [tex]\sqrt{(333929 + 1000000) }[/tex] = [tex]\sqrt{1333929}[/tex] ≈ 1155mm
Step 2: Calculate the angle
The angle (θ) between the longest side (adjacent side) and the diagonal (hypotenuse) is given by:
θ = cos-1(adjacent side / hypotenuse) = cos-1(1000mm / 1155mm)
To find the angle, use a calculator to compute the arccosine of 1000/1155.
Tiffani works in a baby shop in which she prints personalized bibs. She uses a probability model to predict that the next customer ordering a white bib would be 30%. For one day, Tiffani gathers data by tallying the the number of customers who order each color in this table.
Color Tally
white 21
grey 9
blue 15
pink 26
Based on her experiment, which statement is true?
Tiffani's prediction is valid. The probability of the next customer ordering a white bib is about 30%.
Tiffani's prediction is not valid. The probability of the next customer ordering a white bib should be about 21% because 21 people ordered white in her data.
Tiffani's prediction is not valid. The next customer ordering a white bib would be the same as any color, so the probability should be about 25%.
There is not enough information to determine the validity of her prediction.
Answer:
Tiffani's prediction is valid. The probability of the next customer ordering a white bib is about 30%.
Step-by-step explanation:
First you add all of your amounts together
21 + 9 + 15 + 26 = 71
Then to find the probability of the next customer buying a white bib you divide 21 by 71
21/71 = 0.295
Which is approximately 30%
I hope this helped!
Which is the graph of f(x) = (x + 3)(x – 2)? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
image 1
Step-by-step explanation:
Given data:
f(x) = (x+3)(x-2)
= x^2 + x-6
As the given expression is a quadratic expression so the graph will be parabola.
Also coefficient of x^2 is 1, 1>0 hence we'll the parabola opens upwards
that reduces our options to image 1 and 2 only
now to find the x-axis points of parabola
let (x+3)(x-2)=0
(x+3)=0 and (x-2)=0
x= -3 and x= 2
when at y=0, x= -3 and x=2
hence the image 1 !
Martin bought a flower vase from a florist. The box in which the vase was packed was shaped like a rectangular prism.
What is the surface area of the box?
A. 2,148 sq cm
B. 1,500 sq cm
C. 1,932 sq cm
D. 966 sq cm
Answer:
the answer is C: 1932 sq. cm
Step-by-step explanation:
You want to break down the sections (which is double for each)
there are 6 rectangles but you will only need to calculate for 3
1st rectangle
a = (25) (12)
a = 300 sq. cm
**then multiply by 2 = 600 sq. cm**
2nd rectangle
a = (12) (18)
a = 216 sq. cm
then 216 * 2 = 432 sq. cm
3rd rectangle
a = (25) (18)
a = 450 sq. cm
then 450 * 2 = 900 sq. cm
Total Surface Area
SA = 600 sq. cm + 432 sq. cm + 900 sq. cm
SA = 1932 sq. cm
What is the difference and what is their value?
g+g+g+g = g^4 or 4g
g•g•g•g= g^4 or 4g
Step-by-step explanation:
We know that g^4 is g multiplied by itself 4 times, so it has to be g·g·g·g.
We know that 4g is g 4 times, which means it is g+g+g+g.
It's important to focus on the fact that g^4 is g multiplied by itself 4 times, while 4g is g multiplied by 4.
Answer:
Step-by-step explanation:
We know that g^4 is g multiplied by itself 4 times, so it has to be g·g·g·g.
We know that 4g is g 4 times, which means it is g+g+g+g.
It's important to focus on the fact that g^4 is g multiplied by itself 4 times, while 4g is g multiplied by 4.
Step-by-step explanation:
The large rectangle below represents one whole. What percent is represented by the shaded area?
Answer: 44%
Step-by-step explanation:
From the given picture , it can be seen that the rectangle is divided into 25 equal sections.
The number of shaded sections= 11
Now, the percent is represented by the shaded area is given by :_
[tex]\dfrac{\text{Number of shaded sections}}{\text{Total sections}}\times100\\\=\dfrac{11}{25}\times100=44\%[/tex]
Hence, the percent is represented by the shaded area =44%
Answer:
44%
Step-by-step explanation:
The ratio of shaded pieces to total pieces is 11 : 25.
Percent means per hundred.
So, we need an equivalent ratio that will tell us how many pieces would be shaded out of 100 total pieces.
44:100= 44 per hundred = 44%
44% is represented by the shaded area.
Hope this helped!! :D
Compare the fractions. Use <, =, or >. -2/3 -2/8
Answer:
[tex]-\frac{2}{8} >-\frac{2}{3}[/tex]
Step-by-step explanation:
To compare fractions is useful to express the fractions as decimals and compare the values of the decimals first.
Using a calculator we can find that [tex]-\frac{2}{3} =-0.66666...[/tex] and [tex]-\frac{2}{8} =-0.25[/tex].
Now, remember that wen comparing negative numbers the smallest number is the greater one; this is because the closest a negative number is to zero the greatest is value.
-0.66666... and -0.25 are both negative. Since -0.25 is smaller (closer to zero), -0.25 is bigger than -0.66666... In other words, -0.25 > -0.66666...
We know that [tex]-\frac{2}{3} =-0.66666...[/tex] and [tex]-\frac{2}{8} =-0.25[/tex], so we can get back to our original fractions:
[tex]-\frac{2}{8} >-\frac{2}{3}[/tex]
We can conclude that [tex]-\frac{2}{8}[/tex] is greater than [tex]-\frac{2}{3}[/tex]
Find the inverse of the given function f(x) =2^x+6
Answer:
[tex]f^{-1}(x) = log_2(x-6)[/tex]
Step-by-step explanation:
To find the inverse [tex]f^{-1}(x)[/tex] of a function follow the following steps.
1) Do y = f (x)
[tex]f(x) =y= 2 ^ x + 6[/tex]
[tex]y= 2 ^ x + 6[/tex]
2) Solve the equation for the variable x.
[tex]y= 2 ^ x + 6\\\\y-6 = 2^x\\\\log_2(y-6) = x\\\\x=log_2(y-6)[/tex]
3) exchange the variable y with the variable x
[tex]x=log_2(y-6)\\\\y=log_2(x-6)[/tex]
Finally the inverse is:
[tex]f^{-1}(x) = log_2(x-6)[/tex]
Solve x/12+1/3=5/6 please help me resolve
Subtract 1/3 from both sides
x/12 = 5/6 - 1/3
Simplify 5/6 - 1/3 to 1/2
x/12 = 1/2
Multiply both sides by 12
x = 12 × 12
Simplify 1/2 × 12 to 12/2
x = 12/2
Simplify 12/2 to 6
x = 6
PLEASE HELP!! WILL MARK BRAINLEST!!!! 2/n=2/3
2/n=2/3 ok to start you cross multiply so you would end up with 2*3=2n then you simplify and you get 6=2n now you divide both sides by 2 and end up with 3 so you answer is C. n=3
Answer:
The correct answer option is C. n = 3.
Step-by-step explanation:
We are given the following expression and we are to solve for [tex] n [/tex]:
[tex] \frac { 2 } { n } = \frac { 2 } { 3 } [/tex]
To solve this, we will use the method called cross multiplication where the numerator of left side is multiplied with the denominator of right side and vice versa.
[tex]3 \times 2 = 2 \times n[/tex]
[tex]2n = 6[/tex]
[tex]n=\frac{6}{2}[/tex]
[tex]n=3[/tex]
Therefore, the correct answer option is C. n = 3.
Factor the polynomial. 3x^3 - 12x^2 + 27x
Answer:
3x(x^2-4x+9)
Step-by-step explanation:
The polynomial 3x^3 - 12x^2 + 27x is factored by first taking out the greatest common factor of 3x, resulting in the final form of 3x(x^2 - 4x + 9), which cannot be factored further over the real numbers due to a negative discriminant.
To factor the polynomial 3x^3 - 12x^2 + 27x, we look for common factors in each term.
We can see that each term of the polynomial has a factor of 3x. So, we factor out 3x from the polynomial:
3x(x^2 - 4x + 9)
Now, we try to factor the quadratic expression x^2 - 4x + 9. However, this quadratic does not have real roots since the discriminant (b^2 - 4ac) is negative (-4^2 - 4 ×1 ×9 = -20). Therefore, it cannot be factored over the real numbers. Our final factored form of the polynomial is 3x(x^2 - 4x + 9), as we factored out the greatest common factor (GCF).