To find the area of the orange band, subtract the area of the yellow square from the area of the larger square.
Explanation:To find the area of the orange band, we need to subtract the area of the yellow square from the area of the larger square. The side length of the larger square is 8 inches because it is twice the side length of the yellow square, which is x inches. So, the area of the larger square is 8 * 8 = 64 square inches. The area of the yellow square is x * x = x^2 square inches. Therefore, the area of the orange band is 64 - x^2 square inches.
Final answer:
To calculate the area of the orange band, find the area of the larger square using the side length of x + 22 inches and subtract the area of the smaller yellow square with side length x. The expression for the area of the orange band is [tex](x + 22)^2 - x^2[/tex], which simplifies to 44x + 484 square inches.
Explanation:
To calculate the area of the orange band, you need to determine the area of the outer (larger) square and subtract the area of the inner (smaller) yellow square. First, find the side length of the larger square, which is the side length of the yellow square plus twice the width of the orange band, so it's x + 2(11) inches. Thus, the side length of the larger square is x + 22 inches.
Now, calculate the area of both squares. The area of the larger square is [tex](x + 22)^2[/tex] square inches, and the area of the yellow square is [tex]x^2[/tex] square inches. The area of the orange band is the difference between these two areas:
Area of the larger square:[tex](x + 22)^2[/tex]
Area of the yellow square: [tex]x^2[/tex]
Area of the orange band: [tex](x + 22)^2 - x^2[/tex]
To find the area of the orange band, you expand the expression [tex](x + 22)^2[/tex], which gives you [tex]x^2 + 44x + 484[/tex], then subtract the area of the yellow square [tex]x^2[/tex], resulting in 44x + 484 square inches, which is the area of the orange band.
Find the area of the following figure.
6.4 in^2
10.24 in^2
12.8 in^2
Yo sup??
area of a square =a*a
=a^2
where a is the lenght of its side
area=3.2*3.2
=10.2 unit2
pls do the conversion into inches
Hope this helps
The answer is: 10.24 in^2
Whoever gives me the right answer gets extra points, please help me
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.
A bag contains red,blue,and green marbles in the ratio of 7:6:8. If the bag contains 147 marbles, how many red marbles are there?
Answer:
49
Step-by-step explanation:
7:6:8 so 7+6+8=21
147 divided by 21 is 7
so 1 ratio equals 7
red = 7 so its gonna be 7x7=49
A miners' cage of mass 420 kg contains 3 miners of total mass 280 kg. The cage
is lowered from rest by a cable. For the first 10 seconds the cage accelerates
uniformly and descends a distance of 75 m. What is the force in the cable during
the first 10 seconds?
Answer:
5817 Newtons.
Step-by-step explanation:
Total mass of the cage + the miners = 700 Kg which is a downward force of 700g N.
The net downward force = 700g - T where T is the tension (force) in the cable. The g = acceleration due to gravity = 9.81 m s-2.
We calculate the acceleration of the cage by using an equation of motion:
Distance = ut + 1/2 a t^2 where u = initial velocity , t = time and a = acceleration:
75 = 0(t) + 1/2 a (10^2)
50a = 75
a = 1.5 m s-2.
So using Newtons second law of motion
Force = mass * acceleration:
700*9.81 - T = 700 * 1.5
T = 700 * 9.81 - 700*1.5
= 5817 N.
The force in the cable during the first 10 seconds is 7930N. This was determined using the formulas s = ut + 1/2at² (to calculate acceleration) and F = ma + mg (to calculate the force).
Explanation:The subject of this question is Physics, specifically dealing with forces and acceleration. The total weight of the miners and the cage equals the sum of the miners' weight and the cage's weight, giving a total of 700kg, using the formula weight = mass x gravity (assumed to be 9.8m/s²). Therefore, the total weight is 700kg x 9.8m/s² = 6860N.
Then, we'd calculate the acceleration. The formula used is s = ut + 1/2at², where s is distance, u is initial velocity, a is acceleration, and t is time. Given that initial velocity is 0, the formula is simplified to s = 1/2at². After rearranging, we get acceleration (a) = 2s/t² = 2*75/10² = 1.5m/s².
Finally, we can determine the force on the cable using the formula F = ma + mg (F = force, m = mass, a = acceleration, g = gravity). Substituting, we get F = 700kg x 1.5m/s² + 700kg x 9.8m/s² = 7930N. Therefore, the force in the cable during the first 10 seconds is 7930N.
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(1 point
4. A regression line has a correlation coefficient of r=-0.91. Which of the following statements
must be true?
The data are so varied that there is almost no discernible trend whatsoever.
O The data are very tightly clustered around the trend line.
The trend line has a very steep negative slope.
The trend line reliably represents only 91 percent of the data.
Answer:
A: The data are so varied that there is almost no discernible trend whatsoever.
Step-by-step explanation:
The other 3 don't make sense and are not true for the question
An eagle is flying from point A to point B in order to catch a sparrow. Its flying trajectory is a parabola shape
that has the equation y = -5(x+6) +10, where x and y are measured in meters. If the eagle is at a height of
20 meters, how far away are the two points from one another?
Answer:
From 10 to 20 meters.
Step-by-step explanation:
1) If the sparrow has a parabolic trajectory then it must be actually:
[tex]y=-5\left ( x+6 \right )^{2}+10[/tex]
2) If the eagle is at 20 meters high, then we write:
[tex]y=20[/tex]
Since the exact x coordinate was not given.
But since it wants to get the sparrow
3) If we expand the equation we have:
[tex]-5x^{2}-60x-170=0\\\\X_{v}=\frac{-b}{2a}=\frac{60}{-10} = -6\\Y_{v}=\frac{-\Delta}{4a} =\frac{-200}{-20} =10[/tex]
Since the maximum point is equal to 10. The distance where the sparrow is flying ranges from 10 to 20 meters to the eagles spot.
[tex]10\leq d \leq20 \:or \:[10,20][/tex]
4) Since the x coordinate was not given then we can neither precisely calculate the distance where A is nor where B is located.
Answer:
3 meters
Step-by-step explanation:
Shira’s Shoes sold 875,000 pairs of sandals in June, which was 70% of the total number of shoes sold. How many shoes did the company sell in June? Analyze Emily’s calculations. What error did she make?
Answer:
Emily solved for a part when she should have solved for the whole. 875,000 should be the numerator of the equivalent ratio. 70 x 12,500 is 875,000. So the answer is 100 x 12,500 which is 1,250,000.
Step-by-step explanation:
Shira Shoes sold 875,000 pairs of sandals in June, which was 70% of the total number of shoes sold. The number of shoes that the company sold in June is 612500.
If we looked carefully at the question, we will understand that it was from the total pairs of sandals sold that they deduce the percentage of the shoes sold.
From the information given:
Number of pairs of Sandals sold in June = 875,000Pairs of shoes sold = 70% of the pairs of sandals sold.To determine the number of pairs of shoes sold, we have:
[tex]\mathbf{= 875000 \times \dfrac{70}{100}}[/tex]
[tex]\mathbf{= 8750 \times70}[/tex]
= 612500
Therefore, we can conclude that the number of shoes sold by the company in June is 612500
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Solve for x
X cubed =27/64
[tex]$x=\frac{3}{4}[/tex]
Solution:
Given expression is [tex]x^3=\frac{27}{64}[/tex].
To solve the expression and find the value of x.
[tex]$\Rightarrow x^3=\frac{27}{64}[/tex]
27 can be written as 3 × 3 × 3 = [tex]3^3[/tex]
64 can be written as 4 × 4 × 4 = [tex]4^3[/tex]
[tex]$\Rightarrow x^3=\frac{3^3}{4^3}[/tex]
Taking cube root on both sides of the function.
[tex]$\Rightarrow\sqrt[3]{x^3}=\sqrt[3]{\frac{3^3}{4^3}}[/tex]
Cube and cube roots are cancelled.
[tex]$\Rightarrow x=\frac{3}{4}[/tex]
Therefore, [tex]x=\frac{3}{4}[/tex].
A the slope of f(x) is greater than the slope of g(x)
B the slope of f(x) is less than the slope of g(x)
C the slope of f(x) is equal than the slope of g(x)
The slope of g(x) is undefined
To find the slope of g(x), use the slope formula(m):
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] And plug in two points, I will use:
(0, 2) = (x₁, y₁)
(5, 4) = (x₂, y₂)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-2}{5-0}[/tex]
[tex]m=\frac{2}{5}[/tex]
You could do the same to find f(x) by finding two points and using the slope formula, or you could use this to tell visibly:
[tex]m=\frac{rise}{run}[/tex]
Rise is the number of units you go up(+) or down(-) from each distinguished point
Run is the number of units you go to the right from each distinguished point
If you look at the graph, you can see the points (0, -1) and (3, 1). From each point, you go up 2 units and to the right 3 units (you can make sure by using another point). So the slope of f(x) is [tex]\frac{2}{3}[/tex]
Whichever line looks more vertical(and is positive) has the greater slope. So the slope of f(x) is greater than the slope of g(x). The answer is option A
Gumballs are 2 for 8 cents. How many gumballs can I get for 32 cents
Answer: 8 gumballs
Step-by-step explanation:
We can solve this problem with the Rule of three, since we are given as data three factors and one is unknown.
If 2 gumballs cost 8 cents, how many gumballs can we buy with 32 cents?:
[tex]2 gumballs[/tex]-----[tex]8 cents[/tex]
[tex]x[/tex]-----[tex]32 cents[/tex]
Then:
[tex]x=\frac{(2 gumballs)(32 cents)}{8 cents}[/tex]
[tex]x=8 gumballs[/tex] We can buy 8 gumballs with 32 cents
An architect is planning to make two triangular prisms out of iron. The architect will use ∆ABC for the bases of one prism and ∆DEF for the bases of the other prism.
-
-
(a) What is the scale factor from ∆ABC to ∆DEF?
(b) Suppose the height of the prism made by ∆ABC is 15 centimeters. What is the volume of the prism made by ∆ABC? Remember to show your work.
(c) Suppose the volume of the prism made by ∆ABC is 4459 cm^3. What is the volume of the prism made by ∆DEF? Remember to show your work.
a) 5/7
b) 4459 cm cube
c) 2275 cm cube
Step-by-step explanation:
Step 1 :
a)
The Side AB (28 cm) has been scaled to side DE (20 cm)
Let x b the scale factor.
Then we have 28 *x = 20
=> x = 20/28 = 5/7
Hence the scale factor is 5/7
Step 2 :
b)
Given the height of the triangular prism is 15 cm
Volume = ( 1/2 ) * base* height of the triangle * height of the prism
= (1/2)* 21*28*15 = 4410 cm cube.
Step 3 :
c)
Given volume of the triangular prism with base ABC is 4459 cm cube
The scale factor is 5/7
Hence the volume of the prism with DEF as base is
4459 * (5/7)*(5/7) = 2275 cm cube.
You are painting the walls and ceiling of a rectangular 20 x 30 ft room. The walls are 10 feet tall. You need two coats of paint. If a gallon of paint covers 400 square feet and cost $53 per gallon, how much will you spend on painting this room?
Answer:
The cost for painting will be $212.
Step-by-step explanation:
I am painting the walls and ceiling of a rectangular 20 x 30 ft room. The walls are 10 feet tall.
So, the total area to be painted = {2 × (20 + 30) × 10} + (20 × 30) = 1600 sq. ft.
Now, a gallon of paint covers 400 square feet and cost $53 per gallon.
So, the number of gallons of paint required will be [tex]\frac{1600}{400} = 4[/tex] gallons.
And the cost for painting will be $(4 × 53) = $212. (Answer)
Tommy purchased a riding lawnmower with an original value of $2,500. If the value of the riding lawnmower decreases by $300 per year, what should be the value of the lawnmower after five years?
A. $1,000
B. $1,300
C. $1,500
D. $2,200
Answer:
A
Step-by-step explanation:
I also took a quiz with this question and I got the right answer.
Mixed numbers 5 3\8 x 2 7\8
Answer:
15 29/64
Step-by-step explanation:
You will turn them both improper and then multiply
prove that sin^4x - cos^4x = 2sin^2x - 1
Step-by-step explanation:
Step 1: From the given equation, taking the Left Hand Side (LHS) of the equation
Step 2: Simplify the LHS to make it equal to the Right Hand Side (RHS)
LHS = sin^4x - cos^4x = (sin²x)² - (cos²x)²
= (sin²x - cos²x)(sin²x + cos²x)
= sin²x - (1 - sin²x) since sin²x + cos²x = 1
= 2 sin²x - 1
= RHS
Hence proved.
Find the equation of the line between (-7,4) and (5,9) in slope intercept form
Step-by-step explanation:
(9-4)/(5+7)= 5/12
y - 4 = 5/12(x + 7)
y - 48/12 = (5/12)x + 35/12
y = (5/12)x + 83/12
12. What steps do you need to take to solve
the equation 2x + 6 - 187
A Add 6. Then multiply by 2.
B Subtract 6. Then divide by 2.
C Add 6. Then divide by 2.
D Subtract 6. Then multiply by 2.
Answer:
B is the right answer.
In the order of operations, what is the first operation that you should take care of?
Answer: Remember PEMDAS. Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. But when trying to solve a problem with a variable, remember to go backwards.
A city law states that the area, x, of a new building on a lot must be less than 3/5 of the total area, y of the lot on which it is built which inequality shows the relationship?
Answer:
It’s A. I go To Uva too
Step-by-step explanation:
What is the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth?
Final answer:
The approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth is about 14.7 meters.
Explanation:
To find the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth, we can use the formula for the period of a pendulum:
T = 2π √(L/g)
Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Given that the period is 2.4 pi seconds, we can substitute this value into the formula:
2.4 pi = 2π √(L/g)
Simplifying the equation, we can divide both sides by 2π:
1.2 = √(L/g)
Squaring both sides of the equation, we get:
1.44 = L/g
Since we don't have the value of g, we cannot solve for L exactly. However, if we assume that g is approximately 9.8 m/s², which is the average acceleration due to gravity on Earth, we can estimate the value of L:
1.44 = L/9.8
Multiplying both sides by 9.8, we find:
L ≈ 14.7 m
How do you graph y=5/3x +5
Answer:
Step-by-step explanation:
y = 5/3x + 5...in y = mx + b form, the slope is in the m position and the y int is in the b position.
so we have a slope of 5/3 and a y int of 5.....(0,5)
the x int can be found by subbing in 0 for y and solving for x
0 = 5/3x + 5
-5/3x = 5
x = 5 * -3/5
x = -15/5
x = -3......so ur x int is (-3,0)
go ahead and plot ur intercepts....(0,5) and (-3,0).....now start at (-3,0)....and since ur slope is 5/3....go up 5 spaces and to the right 3 spaces...plot that point.....then go up 5 and to the right 3...plot that point....keep doing this pattern....u should cross the y axis at (0,5). Then just connect ur dots and u have ur line.
About 50 percent of the math questions are multiple choice and 50 percent are grid-in.
True. False
Answer:
True
Step-by-step explanation:
Dalton has 7 bills, all tens and twenties, that total $100 in value. How many of each bill does he have?
Dalton has 4 ten-dollar bills and 3 twenty-dollar bills.
Explanation:To find out how many of each bill Dalton has, we can set up a system of equations.
Let's assume Dalton has x number of ten-dollar bills and y number of twenty-dollar bills. The total number of bills he has is given as 7, so we have the equation: x + y = 7.
Additionally, the total value of the bills is given as $100. Since each ten-dollar bill is worth 10 dollars and each twenty-dollar bill is worth 20 dollars, we have the equation: 10x+20y = 100.
Now we can solve the system of equations to find the values of x and y.
Multiplying the first equation by 10 to eliminate x, we have: 10x + 10y = 70.
Subtracting this equation from the second equation, we get: 10x + 20y - (10x + 10y) = 100 - 70.
Simplifying, we have: 10y = 30.
Dividing both sides of the equation by 10, we find that y = 3.
Substituting this value back into the first equation, we can solve for x: x + 3 = 7.
Subtracting 3 from both sides, we find that x = 4.
Therefore, Dalton has 4 ten-dollar bills and 3 twenty-dollar bills.
Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11
Answer:
Since this dude got a Bird Brain I got ya'll
Step-by-step explanation:
Whats in Bold is what you put in the drop down menu. :)
So, f(3) = 26. This means that after 3 months, the number of products sold were 26,000.
If f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11 the sale after three months will be 26 thousand.
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Finding profit, populations, and distance traveled are some applications of functions. By entering a number into the formula, locating the independent variable on a table or graph, and then computing the resulting dependent variable, functions are employed.
It is given that,
f(t)=5t+11
So for the given condition after three months,
Substitute the value of t as 3,
f(3)=5(3)+11
f(3)=15+11
f(3)=26
Thus, if f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11 the sale after three months will be 26 thousand.
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can someone please help me with this?
tysm!
Answer:
yes
Step-by-step explanation:
Answer:
Area of shades region [tex]=45[/tex] square inches
Step-by-step explanation:
In the given figure accordingly, we have to find the Area of the shaded region
Area of shaded region= Area of big triangle - Area of the small triangle.
Area of a triangle= [tex]\frac{1}{2} *base*altitude[/tex]
Altitude is the perpendicular height of the triangle from its top to base.
Base of big triangle=12 inches, Altitude of big triangle=6+3= 9 inches
Area of Big triangle
[tex]=\frac{1}{2}* 12*9\\\\=6*9\\\\=54[/tex]
Base of small triangle= 6 inches, Altitude of small triangle= 3 inches
Area of the small triangle=
[tex]=\frac{1}{2} *6*3\\\\=3*3\\\\=9[/tex]
Area of shades region [tex]=54-9\\[/tex]
[tex]=45[/tex] square inches
Min-jun travels 27 miles per hour. How long does it take him to travel 21 miles. Nearest tenth
Answer:
0.8 hours
Step-by-step explanation:
From the question;
Speed of Min-jun is 27 miles per hour Distance covered is 21 milesWe need to determine the time he takes to cover the distance given;
We need to know that;
Speed = Distance ÷ time
Rearranging the formula;
time = Distance ÷ speed
Thus;
Time = 21 miles ÷ 27 miles per hour
= 7/9 hours
= 0.8 hours
Thus, he took 0.8 hours to cover the distance covered
3x + 6y= 6
9x - 12y = 18 elimination with multiplication
Answer: x = 4y/3+2
y = 0
Step-by-step explanation:
The sum of 2 angles is 90 degrees and their difference is 40 degrees
Answer:
65 degrees
25 degrees
Step-by-step explanation:
x=first angle
y=second angle
x+y=90 x-y=40
x=40+y
(40+y)+y=90
40+2y=90
2y=50
y=25
x=40+25
x=65
Final answer:
The sum and difference of two angles can be found by setting up a system of equations and solving it. In this case, the two angles are 65 degrees and 25 degrees.
Explanation:
The question is asking for the sum and difference of two angles. Let's represent the two angles as x and y. We know that the sum of the two angles is 90 degrees, so we can write the equation x + y = 90. We also know that the difference of the two angles is 40 degrees, so we can write the equation x - y = 40.
We can solve this system of equations using substitution or elimination. Let's use the substitution method. From the second equation, we can rewrite it as x = y + 40. Substitute this value of x into the first equation:
(y + 40) + y = 90. Combine like terms: 2y + 40 = 90. Subtract 40 from both sides: 2y = 50. Divide by 2: y = 25.
Now substitute this value of y back into the equation x = y + 40: x = 25 + 40 = 65.
So, the two angles are x = 65 degrees and y = 25 degrees.
In a system of two linear equations what is the relationship between the slope of the lines and the numbers of solutions to the system?
In a system of two linear equations if the slopes are same then no solutions and different slope means exactly one solution.
Step-by-step explanation:
Let us consider two linear equations, each linear equation has slope and y-intercept.
Among those slope plays a major role, if there are no slope means than the line equation will be parallel to the x-axis. The slope will indicate the line's direction.
If two linear equations, having an identical slope then they will become like parallel lines. Thus the parallel lines won't intersect with each other. So there will be no solutions to the system. (refer 1st image of both equations having slope 5)
If two linear equations have different slope they will intersect at any point. That is, it will result in exactly one solution. (refer 2nd image of both equations having different equations 1 and -1).
What does m equal?
3 3/4 m = 33 3/4