Find the area of the square below. Each unit on the grid represents one unit. Make sure you show your work and/or explain how you solved it.
Answers
Answer:
Area of the rectangle A = 17 units²
Step-by-step explanation:
Area of the rectangle A = Area of rectangle ACEG - (Area of the triangle ABH + Area of triangle BCD + Area of triangle DEF + Area of the triangle FGH )
Area of rectangle ACEG = Length × Width
= (5 units) × (5 units)
= 25 square units
Area of the triangle ABH = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(4)(1)[/tex]
= 2 units²
Area of the triangle BCD = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(1)(4)[/tex]
= 2 units²
Similarly, area of the triangle DEF = 2 units²
And area of the triangle FGH = 2 units²
Now area of the rectangle A = 25 - (2 + 2 + 2 + 2)
= 25 - 8
= 17 square units
Therefore, area of the rectangle A = 17 square units
Related Questions
Felipe is working to find the quotient of 6 and 3/4
Answers
Answer:
Felipe's answer is 8.
6 divided by 3/4
= 6 * 4/3
= 24/3
= 8
Answer:
8
Step-by-step explanation:
6÷3/4=6×4/3=8
A boy saves up $79 for a gift for his friend. However, upon reaching the store, he realizes that he saved 257% of the actual amount he needed to buy the present. How much does the present cost? Round to the nearest cent.
Hint: This is a Part = Percent × Whole problem.
You're given the part (79) and the percent (257%, or 2.57).
Substitute these into the equation to find the whole.
Answers
Answer:
$30.74
Step-by-step explanation:
Justin and Alexis were Dave and Busters. What you need to pay an initial fee of $ 5.00 and a price per game. Justin played 5 games and paid $ 12.50 in total. Alexis played 7 games and paid $ 15.25 in total. We can express the relationship between the number of games played and the total cost with the ordered pairs (5, 12.75) and (7, 15.25).
Find the rate of change and explain the importance of the rate of change in terms of the problem.
Answers
Answer:
The equation of the relationship is y = 1.25x + 6.5
Step-by-step explanation:
I graphed the ordered pairs on the graph below and found the slope and y-intercept of the line.
The price per game is $7.75. (If needed)
Easy points for y’all mathy people, fairly easy question. It’s in the photo!!
Answers
Answer:
W
Step-by-step explanation:
The input is the x-axis.
The output is the y-axis.
Make them coordinates. Hope this helped!
Mark created a flower bed that is semicircular in shape, as shown in the image. The diameter of the flower bed is 5m. What is the perimeter of the flower bed? (Approximate to be 3.14.) Round your answer to two decimal places.
Answers
Answer:
12.85
Step-by-step explanation:
P=1/2(3.14xd)+d
P=1/2x15.7+5
P=12.85
Which equation is equivalent to the following?
4x^2 + 4y^2 +16x – 24y = 34
Please answer it:(
Answers
Answer:
The correct answer is the third expression.
Step-by-step explanation:
We have the following equation:
[tex]4*x^2 + 4*y^2 + 16*x - 24*y = 34[/tex]
Let's organize it by variables, putting together the ones that have the same letter or no letter at all. We have:
[tex]4*x^2 + 16*x + 4*y^2 - 24*y = 34[/tex]
We can extract the common factor on the left side by dividing them by 4, we have:
[tex]4*(x^2 + 4*x) + 4*(y^2 - 6*y) = 34[/tex]
We need to complete the squares on the parenthesis without changing the value of the equation, to do that we will sum the proper values inside the parenthesis and those multiplied by four on the other side of the equation, we have:
[tex]4*(x^2 + 4*x + 4) + 4*(y^2 - 6*y + 9) = 34 + 16 + 36\\4*(x + 2)^2 + 4*(y - 3)^2 = 86[/tex]
The correct answer is the third expression.
Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!
Answers
Answer:
25
Step-by-step explanation:
To find the constant
take the coefficient of x
10
divide by 2
10/2 =5
Square it
5^2 =25
Add this
x^2 +10x+25
PLZ HELP! WILL GIVE BRAINIEST!!
Answers
Answer:
i think its c idk if im wrong im sorry
Step-by-step explanation:
The formula for the slant height of a cone is t equals StartFraction S minus pi r squared Over pi EndFraction. , where S is surface area of the cone. Use the formula to find the slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft.
Answers
Answer:
275 ft
Step-by-step explanation:
The formula given to use for the slant height l of the cone is ;
l = (s - πr^2)/π
Now substituting the parameters given in the question, 500 π for area and radius of 15, we have
l = {500π-15^(2)π}/π
l =( 500 π -225 π)/π
l = 275 π/π
l = 275 ft
Answer:
275
Step-by-step explanation:
^ and what they said
Somebody, please help me!! I will mark the brainiest
Answers
Answer:
65 = <JKL
Step-by-step explanation:
There are two expressions that represent the same thing.
The diagram shows that <JKL = 45 + x
The question states that JKL = 3x + 5
The two expressions must be equal since they represent the same thing.
3x + 5 = x + 45
Subtract 5 from both sides
3x + 5 - 5 = x + 45 - 5
3x = x + 40 Subtract x from both sides
3x - x = x - x + 40
2x = 40 Divide by 2
2x/2 = 40/2
x = 20
So x + 45 = 20 + 45 = 65
or
3x + 5 = 3*20 + 5 = 60 + 5 = 65
A concrete driveway is 5 feet longer than twice its width. It has a brick walkway 3 feet wide on the front and side of the driveway. The area of the brick walkway is 213
square feet. Find the dimensions of the driveway.
Answers
Answer:
The dimensions of the driveway are 21 ft x 47 ft, which is option "D" in your list of possible answers
Step-by-step explanation:
Notice that the length "L" of the driveway can be written in terms of its width as:
L = 2 w + 5
based on the given information.
Please see the attached diagram to understand the geometry of the problem, and what the area of the brick walkway involves (depicted in brick color) as the addition of the area of two rectangles:
1) one of length L= 2 w + 5 (w being the width of the driveway - depicted in grey) times 3 feet (the width of the brick walkway
and the other one:
2) w + 3 times 3
Therefore the total area of the brick walkway is given by the formula:
(2 w + 5) * 3 +(w + 3) * 3 = 213 square feet
Now we can solve for "w" in the above equation:
6 w + 15 + 3 w + 9 = 213
9 w + 24 = 213
9 w = 213 - 24
9 w = 189
w = 189/9
w = 21 feet
We can now solve for the L of the driveway, using the first formula we created:
L = 2 w + 5
L = 2 (21) + 5
L = 42 + 5
L = 47 feet
Therefore the driveway's width is w = 21 feet
and its length is L = 47 feet
Please answer correctly !!!!!!!!! Will mark brianliest !!!!!!!!!!!!
Answers
Answer:
g(x) has a greater y intercept than f(x)
Step-by-step explanation:
f(x) = 6x^2 + 18x +3
f(0) = 0+0+3
The y intercept is 3
g(x) crosses the y axis at 6
The y intercept is 6
g(x) has a greater y intercept than f(x)
Answer:
g(x) has a greater y intercept than f(x)
Step-by-step explanation:
f(x) = 6x^2 + 18x +3
f(0) = 0+0+3
The y intercept is 3
g(x) crosses the y axis at 6
The y intercept is 6
g(x) has a greater y intercept than f(x)
hope I could help
All i have to ask is what is this polygon or figure called ???? Picture is supplied
Answers
Answer:
Step-by-step explanation:
rectangle + semicircle
= 8*6 + pi r^2/2
=48 + 22/7 * 3/2 * 3/2
then simplyn..
Answer:
The figure is a rectangle and a semicircle
Step-by-step explanation:
Originally the dimensions of a rectangle were 20cm by 23cm. When both dimensions were decreased by the same amount, the area of the rectangle decreases by 120. Find the dimensions of the rectangle.
Answers
The original area is 460cm (20x23), minus 120cm gives a new area of 340cm.
20cm-3cm=17cm and 23cm-3cm=20cm
17cmx20cm = 340cm
A rectangle or prism with a volume of three cubic units is filled with Cubes with side length of one for a few how many 1/4 unit does it take to fill the prism
Answers
Answer:
192 cubes.
Step-by-step explanation:
The volume of each cube = (side)³ = (1/4)³ = 1/64 units ³
Next is to find how many cubes are needed to fill the prism.
The number of cubes that will fill the prism :
Vol. of prism / Vol. of cube = 3 / [tex]\frac{1}{64}[/tex]
=192 cubes.
Therefore, it takes 192 cubes to fill the prism.
help me help me help me asap
Answers
Answer:
9 cubic feet
Step-by-step explanation:
Assuming that the garden box is a rectangular prism, its volume is:
[tex]4\dfrac{1}{2} \cdot 4 \cdot \dfrac{1}{2}=9 \text{ ft}^3[/tex]
Hope this helps!
Solution,
Length(L)=4 1/2 ft
Breadth(b)= 4 ft
Height(H)=1/2 ft
Now,
Volume=L*B*H
= 4 1/2*4*1/2
=9/2*4*1/2
= 9 cubic feet
Hope it helps
Good luck on your assignment
how many diagonals are there in a polygon of 6o sides
Answers
Answer:
9 diagonals
Bit by bit clarification:
Number of Diagonals = n(n-3)/2
For instance, in a hexagon, the complete sides are 6.
Along these lines, the complete diagonals will be 6(6-3)/2 = 9.
Answer:
9 diagonals hope its helpful
Which is the best description of the equivalency of the two expressions?
Expression 1
Expression 2
5 x squared minus 2 x minus 4 + 6 x + 3
6 x squared minus 6 x + 6 minus x squared + 10 x minus 7
Answers
Answer:
The answer is option D
Took the quiz
Answer: They are equivalent because when x=2, the two expressions have the same value.
Step-by-step explanation:
a store employees 11 women and 12 men.what percentage of employees are men?
Answers
Answer:
easy just find the total of how many people work there then put that no. as a denominator and put 12 on the numerator then times it by 100 and the answer should be 52.2% or 52.17%
Answer:
52.2% or 52.17%
12 men
Total = 23
12 / 23 =
(8 + 2 x 6)2 =
the two at the end before the equals is a squared number is a small 2
Answers
(8+2x6) 2^2
= (8+12)2^2
=(20)2^2
=20x4
=80
The expression [tex](8 + 2 \times 6)^2[/tex], following PEMDAS, simplifies to 400.
Let's break down the steps in solving the expression [tex](8 + 2 \times 6)^2[/tex] in more detail (Follow PEMDAS).
Step 1: MultiplicationWe start by evaluating the multiplication operation, which is 2 x 6. The result of this operation is 12.
Step 2: AdditionNext, we evaluate the addition operation, which is 8 + 12. The sum of 8 and 12 is 20.
Step 3: SquaringFinally, we square the result of the addition, which is 20. Squaring a number means multiplying it by itself. In this case, [tex]20^2[/tex] means 20 multiplied by 20, which equals 400.
Therefore, the expression [tex](8 + 2 \times 6)^2[/tex] simplifies to 400.
Learn more about PEMDAS here:
https://brainly.com/question/36185
#SPJ4
The angle \theta_1θ
1
theta, start subscript, 1, end subscript is located in Quadrant \text{II}IIstart text, I, I, end text, and \cos(\theta_1)=-\dfrac{12}{19}cos(θ
1
)=−
19
12
cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 12, divided by, 19, end fraction .
What is the value of \sin(\theta_1)sin(θ
1
)sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Answers
Answer:
[tex]sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]
Step-by-step explanation:
It is given that:
[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]
And we have to find the value of [tex]sin\theta_1 = ?[/tex]
As per trigonometric identities, the relation between [tex]sin\theta\ and \ cos\theta[/tex] can represented as:
[tex]sin^2\theta + cos^2\theta = 1[/tex]
Putting [tex]\theta_1[/tex] in place of [tex]\theta[/tex] Because we are given
[tex]sin^2\theta_1 + cos^2\theta_1 = 1[/tex]
Putting value of cosine:
[tex]cos\theta_1 = -\dfrac{12}{19}[/tex]
[tex]sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}[/tex]
It is given that [tex]\theta_1[/tex] is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.
[tex]\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}[/tex]
Answer:
− square root 15/4
Step-by-step explanation:
A contractor is building a circular swimming pool. The radius of the circle 12 feet. He needs to know the
circumference in order to buy tile to put around the edge of the pool.
What is the circumference if he uses n=2217 ?
Answers
Answer:
75.41 ftStep-by-step explanation:
This problem is on the mensuration of flat shape, a circle.
we know that the circumference of a circle is expressed as
[tex]C= 2\pi r[/tex]
Given that radius = 12 ft
The circumference can be solved for by substituting the value of r in the formula
C=2*3.142*12
C= 75.408ft
to 2 d.p the circumference is 75.41 ft
please help will mark brainliest
Answers
Answer:
see below
Step-by-step explanation:
2* (4*8) = (2*4) * 8
This is the associative property of multiplication
There are 300 boys in a mixed school. If the ratio of the boys to the girls is 4:5 what is the total number of students in the school?
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
4 : 5
300 : ?
Divide 300 by 4 to find out what '1 part' would count as:
300/4 = 75
Multiply this by 5
75 x 5 = 375
Add the two values together
375 + 300 = 675
There are 675 students
Have A Nice Day ❤
Stay Brainly! ヅ
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｡☆✼★ ━━━━━━━━━━━━━━ ☾
Step-by-step explanation:
Number of boys=300
Ratio of boys to girls=4:5
let the number of girls=y
300/y=4/5
Cross multiply
300×5=4×y
1500=4y
Divide through both sides by 4
1500/4=4y/4
374=y
Number of girls is 375
Total number of students=Number of boys+Number of girls
Total number of students=300+375
Total number of students=375
^^^
Quickly answer please
Answers
Answer:
400
Step-by-step explanation:
A bag contains 9 red marbles, 18 orange marbles, 2 yellow marbles, and 5 purple marbles. A marble is drawn at random from the bag. What is the probability that the marble drawn will not be orange?
Answers
Answer:
8/17
Step-by-step explanation:
total balls= 9 + 18 + 2 + 5 = 34
balls drawn should NOT be Orange.
so, 34 - 18 (as there are 18 orange balls)
16 balls
probability= 16/34 = 8/17
answer = 8/17
Question attached Simultaneous equations
Answers
Answer:
9 spoons knives =12
9 spoons cost= £ 82.80
total no of 1 knife = 12x9 = 108
1 knife = 82.80 x 108 = 8,94, 240
so, 1 knife Cost's =£ 8,94,240
-a+(-b) where a= 6.05 and b= 3.611
Answers
Answer:
-9.661
Step-by-step explanation:
In the given equation, a and b are negative. The values of a and b are given. If you insert the values into the given formula, the values become negative because of "-" in front of the a and b values.
-a + (-b) = -6.05 + (-3.611)
Because the second value is negative, the plus sign references to adding BOTH negative values together so it is just the same as saying:
-6.05 - 3.611
This gives you -9.661
Hope this helps!
The measure of angle 1 is (10 x + 8) degrees and the measure of angle 3 is (12 x minus 10) degrees. what is the measure of angle 2 in degrees?
Answers
Answer:
82 degrees
Step-by-step explanation:
First set 10x+8 equal to 12x-10 to find that the variable is equal to 9. Then solve for 10(9)+8 which equals 98. Since angle 1 is supplementary to angle two and supplementary angles add up to 180 degrees, subtract 98 from 180 to find that your answer is 82 degrees.
A 20-foot ladder leans against a wall so that it is 16 feet high at the top. The ladder is moved so that the base of the ladder travels toward the
wall twice the distance that the top of the ladder moves up. How much higher is the top of the ladder now? (Hint Let 12 – 2x be the distance from
the base of the ladder to the wall.)
х
2x
The top of the ladder is
feet higher now.
Answers
Answer:
3.2 ft
Step-by-step explanation:
The initial distance from the base of the ladder to the wall is:
[tex]20^2=16^2+d^2\\d=12\ ft[/tex]
After moving the ladder, the distance from the base to the wall is 12 - 2x while the height of the ladder is 16 + x. The distance x is given by:
[tex]20^2 = (12-2x)^2+(16+x)^2\\400 = 144-48x+4x^2+256+32x+x^2\\5x^2-16x=0\\5x=16\\x=3.2\ ft[/tex]
Therefore, the top of the ladder is 3.2 ft higher now.
Answer:
3.2ft higher
Step-by-step explanation: