To find the area of the outer part of the square rug, calculate the total area using the length of the entire square (x + 8)² and subtract the area of the inner square (x²), yielding (x + 8)² - x² square inches.
Explanation:The subject of this question is geometry - specifically area calculations in mathematics. The student is asking for the area of an outer part of a square rug. The main rug is comprised of a square within another square, with the side length of the smaller square being x inches and the distance in between the small and large square (representing the outer region) being 4 inches.
To calculate the area of the outer region, first, we need to calculate the side length of the outer (entire) square. This would be x + 2*4 = x + 8 inches (4 inches from each side). The total area of the rug would be squared side length of the outer square, which is (x + 8)² square inches.
Subsequently, the area of the inner part of the rug can be calculated as x² square inches (since it's a square). Therefore, the area of the outer part of the rug would be obtained by subtracting the area of the inner square from the total area of the rug, yielding: (x + 8)² - x² square inches.
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To find the area of the outer part of the rug, we first need to find the area of the entire rug and then subtract the area of the inner square.
Let s be the side length of the outer square.
The area of the entire rug is the area of the outer square:
Area of outer square = [tex]s^2[/tex]
Since the width of the outer region is 4 inches, we know that the side length of the outer square is [tex]\( s = x + (2 \times 4) = x + 8 \).[/tex]
So, the area of the outer square is:
Area of outer square = [tex](x + 8)^2[/tex]
Now, let's find the area of the inner square:
Area of inner square = [tex]x^2[/tex]
The area of the outer part of the rug is the difference between the area of the outer square and the area of the inner square:
Area of outer part = Area of outer square - Area of inner square
[tex]\[ = (x + 8)^2 - x^2 \][/tex]
Now, let's expand and simplify:
[tex]\[ = x^2 + 16x + 64 - x^2 \][/tex]
= 16x + 64
So, the area of the outer part of the rug is 16x + 64 square inches.
Please help!
I really can't figure it out.
Answer:
x = 5 (pleaaaaaase give branliest)
Step-by-step explanation:
An equilateral triangle is a triangle that has all congruent sides
This means that 30 = 4x + 10
30 - 10 = 4x
20 = 4x
20/4 = x
x = 5
Hope this helps
Answer:
x=5
Step-by-step explanation:
All sides are equal length because it is an equilateral triangle.
30 = 4x+10
Subtract 10 from each side
30-10= 4x+10-10
20 =4x
Divide each side by 4
20/4 = 4x/4
5 =x
Mrs. McAlister wrote the equation 10 t minus 4 t + 3 t = 8 on the board and asked students to write an equivalent equation. The table below shows the responses from four students.
Student Responses
Michele
3 t = 8
Piotr
6 t = 8
Ronnie
Negative 1 t = 8
Tanisha
9 t = 8
Which student wrote an equation that is equivalent to Mrs. McAlister’s?
Michele
Piotr
Ronnie
Tanisha
Answer:
Tanisha wrote an equation that is the same as Mrs. McAlister's equation.
9t = 8
Step-by-step explanation:
Mrs. McAlister wrote an equation on the board is:
10t-4t+3t=8
Now we simplify this
In order to simplify the left side, we combine like terms.
Here 10t, -4t, & 3t are like terms
So, 10t - 4t + 3t is equivalent to 9t
Thus,
9t = 8
This equation is written by the Tanisha.
That's the final answer.
I hope it helps you.
Answer:
Tanisha
Step-by-step explanation:
10t - 4t + 3t = 8 (given)
= 10t - 4t + 3t = 8
= 9t = 8
This is what Tanisha wrote (9t = 8)
Hope this helps, and please mark me brainliest if it does!
Find the area of a polygon using the given apothem
Plz anwser, will mark brainest!!
What is 9/72 in simplest form
Answer:
[tex]1/8[/tex]
Step-by-step explanation:
Step 1: Divide both top and bottom by 9
[tex](9/9) / (72/9)[/tex]
[tex](1) / (8)[/tex]
[tex]1/8[/tex]
Answer: [tex]1/8[/tex]
Answer: the answer is 1/8
Step-by-step explanation:
Ok use a Calculator to help you.
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Which description can be written as the expression 66+5?
the difference of six times a number and five
O the sum of six times a number and five
0 the quotient of six times a number and five
the product of six times a number and five
Answer:
B
Step-by-step explanation:
An internet company, K-mobile, charges $60 per month for use of up to 100 hours but then charges $100 per month for 100 hours and more. Another company, AK & K, charges $1.50 per hour of use. When is the K-mobile a better deal?
can 45/5 be simplified
45/5 Simplified
What is 45/5 Simplified? - 9/1 is the simplified fraction for 45/5. Simplify 45/5 to the simplest form. Online simplify fractions calculator to reduce 45/5 to the lowest terms quickly and easily.
Simplify 45/5
Fraction:
45
------
5
45/5 Simplified
Answer:
45/5 = 9/1 = 9
Simplify 45/5
Simplify 45/5 reduces the fraction 45/5 to the lowest form. You can change the numerator or denominator to simplify any other fraction.
Write this word sentence as an inequality. A number y is greater than 1 and is less than or equal to 8 .
Answer:
1<y≤8
Step-by-step explanation:
step 1
The number is y and it is greater than one.
The sign for greater than in mathematics is '>'
Therefore, we can write
y>1
And it means 1 is less than y
Less than = <
1<y
Step 2
y is less than or equal to 8. In mathematics, the 'less than or equal to' sign is '≤'
Therefore, we can write
y≤8
Step 3
We then combine these two inequalities
1<y≤8
Final answer:
The inequality 1 < y ≤ 8 represents a number y that is greater than 1 and less than or equal to 8.
Explanation:
An inequality representing the statement 'A number y is greater than 1 and is less than or equal to 8' can be expressed as:
1 < y ≤ 8
This inequality signifies that y is greater than 1 (1 < y) and at the same time, less than or equal to 8 (y ≤ 8), fulfilling both conditions simultaneously.
What are the coordinates of the image ABC after a dilation with center (0,0) and a scale factor of 1/2? HELP ASAP
Answer:
A: 1,1 B: 2,3 C;3,1
Step-by-step explanation:
Divide each number by 1/2 or times by .5
test achievement series.com/asot.aspx
Alice wants her cat to lose some weight. If she wants her cat to lose weight at a rate of 2 lbs per month, which graph represents this rate of loss?
1
Cat Weight Loss
Cat Weight Loss
x
Weight (lbs)
öö
Weight (lbs)
0
5
# of Months
1 2 3 4
#of Months
Cat Weight Loss
Cat Weight Loss
L
ū8
right (lbs
ight (lbs)
The temperature at the top of a mountain is 10.8°C less than the
temperature at the base of the mountain. If the temperature at the
base is -4.4°C. what is the temperature at the top? *
Answer:
-15.2°C
Step-by-step explanation:
-4.4 - 10.8 = -15.2
Hope this helps <3
The temperature at the top of the mountain is -15.2°C.
The solution to the problem:
Given:
The temperature at the base of the mountain is -4.4°C.
The temperature at the top of the mountain is 10.8°C less than the temperature at the base of the mountain.
Objective:
Determine the temperature at the top of the mountain.
Solution:
Let x be the temperature at the top of the mountain. We know that the temperature at the top of the mountain is 10.8°C less than the temperature at the base of the mountain, so we can write the following equation:
x = -4.4 - 10.8
Simplifying the right side of the equation, we get:
x = -15.2°C
A frame maker is hired by an art museum to make a special frame for a large rectangle painting. The painting is 3 times as long as it is tall.The expression 2(x+3x) represents the perimeter of the painting, where x represents the length of the short side of the painting in feet. What is the total feet of framing needed if the short side of the painting measures 2.6 feet?
We have been given that the painting is 3 times as long as it is tall.The expression [tex]2(x+3x)[/tex] represents the perimeter of the painting, where x represents the length of the short side of the painting in feet.
To find the the amount of framing needed when short side of the painting measures 2.6 feet, we will substitute [tex]x=2.6[/tex] in our given expression.
We can simplify our expression as:
[tex]2(x+3x)=2(4x)[/tex]
[tex]2(4x)=2(4\times 2.6)[/tex]
[tex]2(4x)=2(10.4)[/tex]
[tex]2(4x)=20.8[/tex]
Therefore, a total of 20.8 feet of framing is needed.
By using the given expression 2(x+3x) and substituting the short side measurement of 2.6 feet, we find that the total framing needed is 20.8 feet for the large rectangle painting.
Explanation:To calculate the total framing needed for the painting, we start by using the expression 2(x+3x), which represents the perimeter of the painting. Given that the short side (x) of the painting measures 2.6 feet, we substitute x with 2.6 feet in the expression, resulting in 2(2.6 feet + 3(2.6 feet)), which simplifies to 2(2.6 feet + 7.8 feet). This gives us 2(10.4 feet), equaling 20.8 feet of framing that is needed.
The dimensions of the painting are based on the fact that the painting is three times as long as it is tall.
The short side is the height of the painting, and the long side, therefore, is 3 times the short side. Since the painting is a rectangle, we apply the formula for the perimeter of a rectangle, which is P = 2(length + width), to get the overall framing length.
What is the product of 2x-1 and 2x+6? Write your answer in standard form.
Show your work.
Is the product of 2x-1 and 2x+6 equal to the product of 1x-2 and 6+2x? Explain your answer.
Answers and Step-by-step explanations:
We need to use FOIL (first, outer, inner, last) to solve this.
The first terms of each of the two expressions (2x - 1) and (2x + 6) are 2x and 2x. Multiply these together: 2x * 2x = 4x².
The outer terms are 2x and 6, respectively, and their product is 2x * 6 = 12x.
The inner terms are -1 and 2x, respectively, and their product is -1 * 2x = -2x.
The last terms are -1 and 6, respectively, and their product is -1 * 6 = -6.
Add these together:
4x² + 12x + (-2x) + (-6) = 4x² + 10x - 6
Let's see if this is equal to (1x - 2) * (6 + 2x) by expanding this one using FOIL as well:
The first terms are 1x and 6, respectively, and their product is 1x * 6 = 6x.
The outer terms are 1x and 2x, respectively, and their product is 1x * 2x = 2x².
The inner terms are -2 and 6, respectively, and their product is -2 * 6 = -12.
The last terms are -2 and 2x, respectively, and their product is -2 * 2x = -4x.
Add all these up:
6x + 2x² + (-12) + (-4x) = 2x² + 2x - 12
Clearly, 2x² + 2x - 12 is NOT the same as 4x² + 10x - 6, so (2x - 1)(2x + 6) is not equal to (x - 2)(6 + 2x).
Hope this helps!
Answer:
4x² + 10x - 6
Not equal
Step-by-step explanation:
(2x - 1)(2x + 6)
4x² - 2x + 12x - 6
4x² + 10x - 6
(1x - 2)(6 + 2x)
6x - 12 + 2x² - 4x
2x² + 2x - 12
Not equal
Kevin and Jenny are making plaster. Kevin mixes 3 cups of water with 4 pounds of plaster powder. Complete the ratio table. How much water will Kevin need for 20 pounds of plaster?
Use the diagram below to answer the following questions.
Name all segments parallel to XT.
Name all segments parallel to ZY.
Name all segments parallel to ZS.
Name a plane parallel to plane STU.
Name a plane parallel to plane UVZ.
Name all segments skew to SW.
Name all segments skew to UT.
HELPPPPPP PLEASE
Answer:
Segments parallel to XT: YU, ZV, WS
Segments parallel to ZY: VU, WX
Segments parallel to ZS: None
Plane parallel to plane STU: WXY
Plane parallel to plane UVZ: TSW
All segments skew to SW: WX, ST
All segments skew to UT: UY, TX
Step-by-step explanation:
Let's begin by explaining the following:
Two line segments are parallel only if their slopes are identical, allowing them to never intersect.
Hence, according to this definition we have:
Segments parallel to XT: YU, ZV, WS
Segments parallel to ZY: VU, WX
Segments parallel to ZS: None
Now, if we go to the three-dimensional space, two planes are parallel, when they do not share any line, which allows them to never cross in space.
Hence, according to this definition we have:
Plane parallel to plane STU: WXY
Plane parallel to plane UVZ: TSW
Two lines are skew if and only if they are not in the same plane (also known as not coplanar). So, if two lines are not coplanar, they are not parallel and cannot intersect, either.
Hence, according to this definition we have:
All segments skew to SW: WX, ST
WZ and SV do not match the condition, since they are in the same plane where SW is,
All segments skew to UT: UY, TX
UV and ST do not match the condition, since they are in the same plane where UT is.
The following answers can be given as the solution to the given questions:
a) All segments parallel to XT: YU, ZV, WS
b) All segments parallel to ZY: VU, WX
c) All segments parallel to ZS: YT
d) A plane parallel to plane STU: WXY
e) A plane parallel to plane UVZ: TSW
f) All segments skew to SW: ZY, VU, XY, UT
g) All segments skew to UT: SW, WX, VZ, ZY
To give the appropriate answers to the given questions, the following terms must be understood.
i. Parallel lines: Two or more lines are parallel if and only if they do not meet even when extended to infinity.
ii. Skew lines: Two or more skew lines are lines that are neither parallel nor intersecting.
iii. Plane: This is flat surface which can either be in x-axis, y-axis or z-axis.
Therefore, the answers to each of the questions are:
a) All segments parallel to XT: YU, ZV, WS
b) All segments parallel to ZY: VU, WX
c) All segments parallel to ZS: YT
d) A plane parallel to plane STU: WXY
e) A plane parallel to plane UVZ: TSW
f) All segments skew to SW: ZY, VU, XY, UT
g) All segments skew to UT: SW, WX, VZ, ZY
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Convert 5/4 into minutes
Answer:
75 minutes
Step-by-step explanation:
1 /4 = 15 minutes
15 x 5 = 75
hope i helped
how do you write 6.1 x 10^2 in standard form
The expression [tex]6.1 \times 10^2[/tex] in standard form is 610
How to write the expression in standard form
From the question, we have the following parameters that can be used in our computation:
[tex]6.1 \times 10^2[/tex]
To write [tex]6.1 x 10^2[/tex] in standard form, we need to convert it into a regular number.
using the above as a guide, we have the following:
[tex]6.1 * 10^2 = 6.1 * 100[/tex]
Evaluate
[tex]6.1 * 10^2 = 610[/tex]
Hence, the expression in standard form is 610
negative 8/9 divided by 2/3
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Step 1: Divide
[tex]\frac{8}{9} / \frac{2}{3}[/tex]
[tex]\frac{8}{9} * \frac{3}{2}[/tex]
[tex]\frac{8 * 3}{9 * 2}[/tex]
[tex]\frac{24/6}{18/6}[/tex]
[tex]\frac{4}{3}[/tex]
Answer: [tex]\frac{4}{3}[/tex]
Find the area of the triangle that has a base of 16 yd and a height of 9 yd.
72 yd2
144 yd2
25 yd2
50 yd2
Which is more, 2 pound or 22 ounces
Answer:
2 pounds. Two pounds is 32 oz. so if 22 oz. is less than 32 (which it obviously is), 2 pounds is more.
Answer:
2 pounds
Step-by-step explanation:
Pia a circumference of approssimately 75 inches
What is the approximate length of the radius,
for 2. Round to the nearest inch
Use 3.14
12 inches
24 inches
38 inches
46 inches
Answer:
radius: 12 inches or OPTION A
Step-by-step explanation:
C = 2r × 3.14
75 = 2r × 3.14
23.885 = 2r
r = 11.94
what’s the size of the missing angle
Answer:
Option D, 44
Step-by-step explanation:
Step 1: Find the size of the missing angle
All triangles add up to 180 degrees.
[tex]106 + 30 + x = 180[/tex]
Step 2: Combine like terms
[tex](106 + 30) + x = 180[/tex]
[tex]136 + x = 180[/tex]
Step 3: Subtract 136 from both sides
[tex]136 + x - 136 = 180 - 136[/tex]
[tex]x = 44[/tex]
Answer: Option D, 44
Answer:
44
Step-by-step explanation:
106 + 30 = 136
180 - 136 = 44
Right △EFG has its right angle at F, EG=8 , and FG=2 .
What is the value of the trigonometric ratio of an angle of the triangle?
tan E
sin G
sec G
In triangle EFG, the right angle is at F. Using the Pythagorean theorem, we can find the length of the hypotenuse and use it to calculate the trigonometric ratios.
Explanation:In triangle EFG, the right angle is at F. Given that EG = 8 and FG = 2, we can use the Pythagorean theorem to find the length of EF. Using the formula a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse, we can calculate that EF = sqrt((EG^2) + (FG^2)) = sqrt((8^2) + (2^2)) = sqrt(64 + 4) = sqrt(68).
To find tan E, we can use the ratio of the opposite side (FG) to the adjacent side (EG). tan E = FG/EG = 2/8 = 1/4.
To find sin G, we can use the ratio of the opposite side (FG) to the hypotenuse (EF). sin G = FG/EF = 2/sqrt(68).
To find sec G, we can use the ratio of the hypotenuse (EF) to the adjacent side (EG). sec G = EF/EG = sqrt(68)/8.
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1. Points A and B are in the first quadrant in the coordinate plane. What might be their coordinates?
2. Points D and E are in the second quadrant in the coordinate plane. What might be their coordinates?
3. Points G and H are in the third quadrant in the coordinate plane. What might be their coordinates?
4, Points J and K are in the fourth quadrant in the coordinate plane. What might be their coordinates?
5. Points M and N are on the y-axis in the coordinate plane. What might be their coordinates?
6. Points Q and Rare on the x-axis in the coordinate plane. What might be their coordinates?
Quadrant one: positive x and positive y. (5,6)
Quadrant two: negative x and positive y. (-5,6)
Quadrant three: negative x and negative y. (-5,-6)
Quadrant four: positive x and negative y. (5,-6)
the y-axis goes up and down so im guessing the x coordinates will be 0 and the y will be whatever you want it to be. the same goes for the x-axis excepted switched around.
Apologies if I got any of these wrong, and please comment if you are confused so I can explain more.
1.) First quadrant: x > 0, y > 0.
2.) Second quadrant: x < 0, y > 0.
3.) Third quadrant: x < 0, y < 0.
4.) Fourth quadrant: x > 0, y < 0.
5.) On y-axis: x = 0, y ≠ 0.
6.) On x-axis: x ≠ 0, y = 0.
1.) Points in the First Quadrant: In the first quadrant, both x and y coordinates are positive. Therefore, the coordinates of points A and B might be of the form (x, y) where x > 0 and y > 0. For instance, point A might be (3, 4) and point B might be (5, 7).
2.) Points in the Second Quadrant: In the second quadrant, x coordinates are negative and y coordinates are positive. Thus, the coordinates of points D and E might be of the form (-x, y) where x > 0 and y > 0. For example, point D might be (-2, 3) and point E might be (-6, 8).
3.) Points in the Third Quadrant: In the third quadrant, both x and y coordinates are negative. Therefore, the coordinates of points G and H might be of the form (-x, -y) where x > 0 and y > 0. For instance, point G might be (-4, -5) and point H might be (-7, -9).
4.) Points in the Fourth Quadrant: In the fourth quadrant, x coordinates are positive and y coordinates are negative. Thus, the coordinates of points J and K might be of the form (x, -y) where x > 0 and y > 0. For example, point J might be (3, -2) and point K might be (8, -5).
5.) Points on the Y-Axis: Points on the y-axis have x coordinates equal to 0, and their y coordinates can be positive or negative. Thus, the coordinates of points M and N might be of the form (0, y). For instance, point M might be (0, 4) and point N might be (0, -7).
6.) Points on the X-Axis: Points on the x-axis have y coordinates equal to 0, and their x coordinates can be positive or negative. Thus, the coordinates of points Q and R might be of the form (x, 0). For example, point Q might be (5, 0) and point R might be (-3, 0).
Consider the data set:
20, 30, 39, 44, 52
How much does 52 deviate from the mean?
Answer:
15
Step-by-step explanation:
mean = 20 + 30 + 39 + 44 + 52 /5
mean = 185 ÷ 5
mean = 37
52 - 37 = 15
The mean of the data set is 37. The number 52 deviates from the mean by 15. Key concepts include mean, deviation, and data set.
Explanation:The first step in answering the question 'How much does 52 deviate from the mean?' is to calculate the mean (also called the average) of the data set. We do this by adding together each of the numbers in the data set and then dividing by the number of elements. The calculation looks like this: (20 + 30 + 39 + 44 + 52) / 5 = 37. Then, to determine how much 52 deviates from the mean, subtract the mean from 52. This gives us: 52 - 37 = 15. So, 52 deviates from the mean by 15. Mean, deviation, and data set are key mathematical concepts related to this question and answer.
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What is 0.05% of 400? Round to the nearest hundredth (if necessary).
Answer:
.2
Step-by-step explanation:
Whenever we see "of," we know we have to multiply.
.05% = .0005 in decimal form, so
.0005 * 400 = .2
Answer:
.2
Step-by-step explanation:
hope this helps
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Last month Margo bought a tree that grows 2.5cm each day. It was 5 cm talk when she bought it and now it is 65 cm tall
Help me!!!!!!.......
Answer:
D
Step-by-step explanation:
The highest point is the vertex, (-3,5), making all y-values less than or equal to 5.
What is the surface area of a cylinder that is 5 centimeters high and has a diameter of 1.5 centimeters?
A. 7.5π cm^2
B. 8.625π cm^2
C. 10.5 π cm^2
D. 19.55π cm^2
The surface area of cylinder is 8.625[tex]\pi[/tex] [tex]cm^{2}[/tex], if the cylinder has 5 centimeters high and 1.5 cm of diameter.
Step-by-step explanation:
The given is,
Cylinder has a 5 centimeters height
Diameter of the cylinder is 1.5 centimeters
Step:1
Formula for the surface area of cylinder is,
[tex]A=2\pi r h + 2\pi r^{2}[/tex]......................................(1)
Where,
h - Height of cylinder
r - Radius of cylinder
From the values of h and r,
[tex]r=\frac{d}{2}[/tex]
= [tex]\frac{1.5}{2}[/tex]
r = 0.75 cm
From the formula,
= ( 2 × [tex]\pi[/tex] × 0.75 × 5 ) + ( 2 × [tex]\pi[/tex] × [tex]0.75^{2}[/tex] )
= ( 7.5 [tex]\pi[/tex] ) + ( 1.125 [tex]\pi[/tex] )
A = 8.625[tex]\pi[/tex] [tex]cm^{2}[/tex]
Result:
The surface area of cylinder is 8.625[tex]\pi[/tex] [tex]cm^{2}[/tex], if the cylinder has 5 centimeters high and 1.5 cm of diameter.
The surface area of a cylinder is 8.625π cm². Thus, the correct answer is B.
First, calculate the radius of the cylinder, which is half of the diameter:
r = 1.5 cm / 2
= 0.75 cm
Next, find the area of the two circular bases of the cylinder using the formula for the area of a circle, A = πr²:
Area of one base = π(0.75 cm)²
= 0.5625π cm²
Total area of the two bases = 2 × 0.5625π cm²
= 1.125π cm²
Then, calculate the lateral surface area using the formula for the circumference of a circle (C = 2πr) multiplied by the height (h):
Lateral surface area = 2π(0.75 cm)(5 cm)
= 7.5π cm²
Finally, add the areas of the two bases and the lateral surface area to find the total surface area:
Total surface area = 1.125π cm² + 7.5π cm²
= 8.625π cm²
The correct answer is B. 8.625π cm².
NEED HELP ASAP! 10 points
Answer:
C. 6 gallons < 25 quarts.
E. 80 pints = 40 quarts.
Step-by-step explanation:
A. There are 8 fluid oz in 1 cup.
Multiply 8 with 6:
6 cups x 8 = 48 fl oz.
44 fl oz < 48 fl oz ∴ A. is false.
B. There are ~6.67 pints in 1 gallon.
Multiply 6 gallon with 6.67:
6 gallon x 6.67 = ~40.02 pint.
47 pint > 40.02 pint ∴ B. is false.
C. There is 4 quarts in 1 gallon.
Multiply 6 gallons with 4:
6 gallon x 4 = 24 quarts.
24 quarts < 25 quarts ∴ C. is true.
D. There is 4 cups in 1 quarts.
Multiply 7 with 4 and add 4:
7 quarts x 4 = 28 + 4 = 32
32 cups < 34 cups ∴ D. is false.
E. 1 quart = 2 pint
You are given 80 pints:
80/2 = 40 quarts ∴ E. is true.
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