Answer:
[tex]\large\boxed{\large\boxed{47unit^2}}[/tex]
Explanation:
The complete question is:
A hole the size of a photograph is cut from a red piece of paper to use in a picture frame.
On a coordinate plane, 2 squares are shown. The photograph has points (-3, -2), (- 2, 2), (2, 1), and (1, -3). The red paper has points (- 4, 4), (4, 4), (4, -4), and (-4, -4).
What is the area of the piece of red paper after the hole for the photograph has been cut?
Solution
The area of the piece of redpaper after the hole has been cut is equal to the area of the big square less the area of the small rectangle.
1. Area of the big rectangle
Vertices:
(- 4, 4) (4, 4)(4, -4)(-4, -4)The side length is the distance between two consecutive vertices:
The two points (-4,4) and (4,4) has the same y-coordinate, thus the length is just the absolute value of the difference of the x-coordinates:
[tex]4-(-4)=4+4=8[/tex]The area of this square is [tex](8unit)^2=64unit^2[/tex]
2. Area of the small square
Vertices:
(-3, -2)(- 2, 2) (2, 1)(1, -3)To find the side length use the distance formula for two consecutive points, for instance (2,1) and (-2,2):
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\ \\d=\sqrt{(2-(-2))^2+(2-1)^2}=\sqrt{4^2+1^2}=\sqrt{17}[/tex]
The area is:
[tex](\sqrt{17}unit)^2}=17unit^2[/tex]
3. Area of the piece of red paper after the holw for the photograph has been cut:
Find the difference:
[tex]64unit^2-17unit^2=47unit^2[/tex]
Answer:
47
Step-by-step explanation:
To the nearest tenth, find the area of
a circle with d= 8 km. Use 3.14 for pi
Answer:
25.1
Step-by-step explanation:
the formula for the area of a circle is A=3.14(pi)r² or A=3.14(pi)d
r = radius d = diameter
so
a = 3.14d
a= (3.14)(8)
a= (25.12) rounded to the nearest tenth = 25.1
hope this helps
HELP PLEASEEE I really need it I’m stuck and don’t know the answer
Answer:
.3-.6 ; 0-.6 ; .1-.3 ; 0-.3 ; 0-.1
Step-by-step explanation:
The "points" are:
(0,96.44), (.1,97.6), (.3, 98.57), and (.6, 98.3)
The "rate of change" is the slope. This means that the change from...
0-.1 is (97.6-96.44)/.1 = 1.16/.1= 11.6
0-.3 is (98.57-96.44)/.3 = 2.13/.3 = 7.1
0-.6 is (98.3-96.44)/.6 = 1.86/.6 = 3.1
.1-.3 is (98.57-97.6)/.2 = .97/.2 = 4.85
.3-.6 is (98.3-98.57)/.3 = -.27/.3 = -.9
Find the value of each trigonometric ratio
The value of each trigonometric ratio is
[tex]$\sin A=\frac{15}{17}, \ \cos A=\frac{8}{17}, \ \tan A =\frac{15}{8}[/tex]
[tex]$\csc A=\frac{17}{15}, \ \sec A=\frac{17}{8}, \ \cot A =\frac{8}{15}[/tex]
Solution:
The given triangle is right triangle.
AC (hypotenuse) = 34, AB (adjacent) = 16, BC (opposite) = 30
To find the trigonometric ratios:
Using trigonometric formulas for right triangle,
[tex]$\sin \theta=\frac{\text { opposite }}{\text { hypotenuse }}[/tex]
[tex]$\sin A=\frac{BC}{AC}[/tex]
[tex]$\sin A=\frac{30}{34}=\frac{15}{17}[/tex]
[tex]$\cos \theta=\frac{\text { adjacent }}{\text { hypotenuse }}[/tex]
[tex]$\cos A=\frac{AB}{AC}[/tex]
[tex]$\cos A=\frac{16}{34}=\frac{8}{17}[/tex]
[tex]$\tan \theta=\frac{\text { opposite }}{\text { adjacent }}[/tex]
[tex]$\tan A=\frac{BC}{AB}[/tex]
[tex]$\tan A=\frac{30}{16}=\frac{15}{8}[/tex]
[tex]$\csc A =\frac{1}{\sin A}[/tex]
[tex]$\csc A =\frac{17}{15}[/tex]
[tex]$\sec A =\frac{1}{\cos A}[/tex]
[tex]$\sec A =\frac{17}{8}[/tex]
[tex]$\cot A =\frac{1}{\tan A}[/tex]
[tex]$\cot A =\frac{8}{15}[/tex]
Hence the value of each trigonometric ratio is
[tex]$\sin A=\frac{15}{17}, \ \cos A=\frac{8}{17}, \ \tan A =\frac{15}{8}[/tex]
[tex]$\csc A=\frac{17}{15}, \ \sec A=\frac{17}{8}, \ \cot A =\frac{8}{15}[/tex]
Four times What divided by two equals 5.2
My answer was wrong sorry
Answer:
Step-by-step explanation:
2.6 becuase 4a/2= 5.2
4a=10.4
a=2.6
What is the common difference between the elements of the arithmetic sequence below?
–18, –22.5, –27, –31.5, –36
Answer:
-4.5Step-by-step explanation:
-22.5-(-18)=-4.5
-27-(-22.5)=-4.5
-31.5-(-27)=-4.5
then the common difference is -4.5
Answer: -4.5
Step-by-step explanation:
It is the most common difference.
A die is rolled. Find the probability of getting a 2. (answer in fraction form)
Answer:
The theoretical probability of getting a 2 when a fair die is rolled is 1/6 so its a low chance
Step-by-step explanation:
Given that the volume of a cylinder is 720 pi m^3, find the radius of the cylinder if the height is 5 m. What is the radius?
Answer:
12m
Step-by-step explanation:
720 pi = pi × r² × 5
720 = 5r²
r² = 144
r = 12 meters
Solve the equation:-|b+4|-1=10
Step-by-step explanation:
[tex]|b + 4| - 1 = 10 \\ \\ \therefore \:|b + 4| = 10 + 1 \\ \\ \therefore \:|b + 4| = 11 \\ \\ \therefore \:b + 4 = \pm \: 11 \\ \\ \therefore \:b + 4 = 11 \: \: or \: \: b + 4 = - 11 \\ \\ \therefore \:b = 11 - 4 \: \: or \: \: b = - 11 - 4 \\ \\ \therefore \:b = 7 \: \: or \: \: b = - 15 \\ \\ \therefore \:b = \{ - 15, \: \: 7 \}[/tex]
at age 27, jill deposited $4,000 into an ira, where it earns 9.8% interest compounded monthly. what will it be worth when she is thirty-five?
The amount when she is 35 is $8,733.01221.
Given that,
The deposited amount is $4,000.The rate of interest is 9.8%.The time is 8 years.Based on the above information, the calculation is as follows:
[tex]= \$4,000 \times (1 + 9.8\%\div 12)^{8\times 12}\\\\= \$4,000 \times (12.098\div 12)^{96}[/tex]
= $8,733.01221
Therefore we can conclude that The amount when she is 35 is $8,733.01221.
Learn more: brainly.com/question/6201432
Final answer:
At age 35, Jill's IRA investment, which started with a $4,000 deposit at age 27 and earns 9.8% interest compounded monthly, will be worth approximately $8,159.55.
Explanation:
To determine the future value of Jill's IRA investment, we will use the formula for compound interest, which is A = [tex]P(1 + \(\frac{r}{n}\))^n^t[/tex], where:
P is the principal amount (the initial amount of money)
r is the annual interest rate (decimal)
n is the number of times that interest is compounded per year
t is the time the money is invested for in years
A is the amount of money accumulated after n years, including interest.
In Jill's case, she deposited $4,000 into an IRA at age 27, and we want to find out what it will be worth when she is 35. The annual interest rate is 9.8%, but since it is compounded monthly, we will have to convert this to a monthly rate and adjust the time accordingly
The steps to solve for the amount A are as follows:
Convert the annual interest rate to a decimal: 9.8% = 0.098
Find the monthly interest rate by dividing the annual rate by 12: \[tex](\frac{0.098}{12}\)[/tex]
Calculate the number of years money is invested: 35 - 27 = 8 years
Find the number of times interest is compounded: 12 months/year × 8 years
Use the compound interest formula to calculate A.
Now, let's do the math:
P = $4,000
r = 0.098 / 12
n = 12
t = 8
A = 4000(1 + [tex]\(\frac{0.098}{12}\))^(12\(\times\)8)[/tex]
Using a calculator we get:
A = $4000(1 + 0.0081667)⁹⁶
A = $4000(1.0081667)⁹⁶
A = $4000 [tex]\(\times\)[/tex] 2.0398873
A ≈ $8,159.55
Therefore, at age 35, Jill's IRA investment will be worth approximately $8,159.55.
The expected rainfall, in inches, for a city for the month of July is given by the inequality |x − 4.25| ≤ 0.15. Find the city’s expected maximum and minimum rainfall amounts.
The minimum rainfall expected is ______
inches, and the maximum rainfall expected is ______
inches.
Answer:
4.1 ; 4.4
Step-by-step explanation:
For min:
x - 4.25 = -0.15
x = 4.1
For max:
x - 4.25 = 0.15
x = 4.4
Answer:
The minimum rainfall expected is 4.1 inches, and the maximum rainfall expected is 4.4 inches.
Step-by-step explanation:
#platofam
A plastic storage bin is shaped like a rectangle or prism. The height of the band is 9 inches. The bottom of the band has an area of 180 in.². What is the volume of the storage bin
Answer:
v = 1620 ^3
Step-by-step explanation:
If the area of the bottom is 180 sq in and the height is 9 in then this is how you would solve the problem.
To get area of the volume is l * w * h
Because of the associative property we can do this in any order we want
If we know that l * w is 180, then all we have to do is multiply 180 by 9
180 * 9 = 1620
Bonito is selling T-shirts for $8 each for his school fundraiser. So far, he has sold 16 T-
shirts. How many more does he need to sell to reach his goal of $200 in sales?
Three of these equations solve for the number of T-shirts, l, he still needs to sell to
reach $200 in sales. Which equation does NOT?
Answer:
The equations that does fit would be 8x+128=200, 8x=72. I don't know your answer choices but these are the equations that does fit so read what I wrote :)
Step-by-step explanation:
The equation would be 8x = 200 but knowing that he has already sold 16T shirts it should be 8x + 16*8 = 200 -> 8x+128 = 200 or 8x = 72. so x would be 9.
Translate the sentence into an inequality.
The sum of a number times 9 and 30 is at least - 15
Use the variable c for the unknown number.
[tex]9x +30\geq 30[/tex]
Solution:
Given that,
Translate the sentence into an inequality
The sum of a number times 9 and 30 is at least - 15
Let "c" be the unknown variable
"at least" means "greater than or equal to"
From given,
sum of a number times 9 and 30 = 9x + 30
Which means,
[tex]9x +30\geq 30[/tex]
Thus the given sentence is translated into inequality
The sentence 'The sum of a number times 9 and 30 is at least - 15' can be translated into the inequality
[tex]9c + 30 \geq -15[/tex]Explanation:The sentence 'The sum of a number times 9 and 30 is at least - 15' can be translated into an inequality by first recognizing the mathematical operations being described. The phrase 'a number times 9' is multiplication, so let's represent this number with the variable c. Thus, this part is 9c. The word 'sum' represents addition. Finally, 'is at least' indicates that the sum is greater than or equal to a particular value (-15 in this case).
Putting these elements together, we get the inequality
[tex]9c+30\geq -15[/tex]This is the inequality that represents the sentence.
Learn more about Inequality here:https://brainly.com/question/32625151
#SPJ3
Anyone knows how to do this
Answer:
length = x - 2
Step-by-step explanation:
The area (A) of a rectangle is calculated as
A = length × width
Here A = x² - 7x + 10 and width = x - 5
x² - 7x + 10 = length × (x - 5) ← divide both sides by (x - 5)
length = [tex]\frac{x^2-7x+10}{x-5}[/tex] ← factor the numerator
= [tex]\frac{(x-5)(x-2)}{x-5}[/tex] ← cancel common factor (x - 5) on numerator/ denominator
= x - 2
Thus length = x - 2 metres
Find the equation of the axis of symmetry for this function
F(x)= 5x^2 - 3x + 5
Answer:
x = [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
Given a quadratic in standard form, ax² + bx + c : a ≠ 0
Then the axis of symmetry is a vertical line with equation x = h
where h is the x- coordinate of the vertex.
The x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = 5x² - 3x + 5 ← is in standard form
with a = 5 and b = - 3, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-3}{10}[/tex] = [tex]\frac{3}{10}[/tex]
Thus the equation of the axis of symmetry is x = [tex]\frac{3}{10}[/tex]
PLS HELP WILL MARK BRAINLIST IF ANSWER IS CORRECT !! :) FILL IN THE BLANKS
Answer:
Part 1) The volume of the storage body is 576 cubic feet
Part 2) To find out how many boxes can she fit in the storage body, divide the volume of the storage body by the volume of each box
Part 3) Sheila can fit 64 boxes into the truck
Step-by-step explanation:
step 1
Find the volume of the storage body
we know that
The volume of the of the storage body is equal to the volume of two rectangular prism
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
First rectangular prism (top)
[tex]V=(15)(6)(8-6)=180\ ft^3[/tex]
Second rectangular prism (bottom)
[tex]V=(15-4)(6)(6)=396\ ft^3[/tex]
The volume of the storage body is
[tex]V=180+396=576\ ft^3[/tex]
step 2
we know that
To find out how many boxes can she fit in the storage body, divide the volume of the storage body by the volume of each box
step 3
substitute the given values
[tex]\frac{576}{9}= 64\ boxes[/tex]
therefore
Sheila can fit 64 boxes into the truck
Marsha walked 14 miles to school yesterday morning. After school, she w
of a mile to her aunt's house. How many miles did she walk altogether yester
day?
Answer:
Step-by-step explanation:
55
please help me again
Answer:
y = 10
Step-by-step explanation:
Since all sides are equal, that means all angles are 60 degrees. 60 + 60 + 60 = 180
5y + 10 - 10 = 60 - 10
5y / 5 = 50 / 5
y = 10
Answer: y = 10
How do you find the equality of 4/12=A/3
Answer:
A = 1
Step-by-step explanation:
[tex] frac. \: \frac{4}{12} = \frac{a}{3} [/tex]
[tex] \frac{ \: \: \: 4 \: \div \: x \: = \: a}{12 \: \div \: x \: = \: 3} [/tex]
[tex] \frac{ \: \: 4 \: \div \: x \: = \: a}{12 \: \div \: 4 \: = \: 3} [/tex]
[tex] \frac{ \: \: 4 \: \div \: 4 \: = \: a}{12 \: \div \: 4 \: = \: 3} [/tex]
[tex] \frac{ \: \: 4 \: \div \: 4 \: = \: 1}{12 \: \div \: 4 \: = \: 3} [/tex]
[tex] a= 1[/tex]
Find 30% of 70
a. 21
b. 36
c. 40
welppp fastttt!!!!!!!!!!!!!!!!!!
Answer: B
Step-by-step explanation:
Grade must be greater than or equal to 88
Answer:
The answer for this is B
If h hours and 30 minutes is equal to 450 minutes,
what is the value of h?
Answer:
h = 7
Step-by-step explanation:
1 hour = 60 mins
h hours = 60h mins
60h + 30 = 450
60h = 420
h = 7
Answer:7
Step-by-step explanation:
h+30=450
h=450-30
h=420minutes
But 1hour=60minutes
Therefore 420minutes=420/60 hour =7hours
7x - 7 = 126 what is x
Answer:
19
Step-by-step explanation:
7x-7=126
add+7 to 126 and you will get 133
7x/133
x=19
Answer:
x = 19
Step-by-step explanation:
7x - 7 = 126
Add 7 to each side
7x - 7+7 = 126+7
7x = 133
Divide each side by 7 to isolate x
7x/7 = 133/7
x = 19
What is the slope of the line.
Answer:
The slope is 2
Step-by-step explanation:
The slope of the line is change in y over change in x.
The formula is: [tex]\frac{y2-y1}{x2-x1}[/tex]
Step 1: Identify the two points
(x1, y1) -> (0, 0)
(x2, y2) -> (1, 2)
Step 2: Plug into the equation
The formula is: [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{2 - 0}{1-0}[/tex]
Slope = 2/1
Slope = 2
Answer: The slope is 2
can somebody tell me the answer to -5/8 - 3/4
Step-by-step explanation:
= -5/8-3/4
= -5-6/8
= -11/8
Answer:-11/8
Step-by-step explanation:
Solve for x. x^2−9=16
Answer:
x=5 or x=-5
Step-by-step explanation:
either one of those
x2−9=16
Step 1: Add 9 to both sides.
x2−9+9=16+9
x2=25
Step 2: Take square root.
x=±25
x=5 or x=−5
What is this limit? Without using lopital rule
Answer:
60.
Step-by-step explanation:
(x^2 - 25) / (√(x + 4) - 3).
We rationalise the expression by multiplying top and bottom of the fraction by the complement of the denominator.
That is by (√(x + 4) + 3):
(x^2 - 25)(√(x + 4) + 3)
= ------------------------------------
(√(x + 4) - 3)(√(x + 4) + 3)
= (x + 5)(x - 5)(√(x + 4) + 3)
----------------------------------
(x - 5)
= (x + 5)(√(x + 4) + 3).
The limit as this---> 5
is (5 + 5)(√(5 + 4) + 3)
= 10 * 6
= 60.
what is a reflex angle
Answer:
an angle that is larger than 180 degrees but is smaller than 360 degrees
Answer:
A reflex angle is any angle larger than 180 degrees and smaller than 360 degrees.
Step-by-step explanation:
Angle one is the Angle of incidence, Angle two is the Angle of reflection, and Angle one is equal to Angle two.
Find the mean and the MAD of the following data set. Do not round your answers.
PLEASE HELP 85 POINTS ASAP.
10, 15, 20, 25, 30, 35
Mean=
MAD=
Answer:
Mean = 22.5
MAD = 7.5
Step-by-step explanation:
Mean = 135/6
= 22.5
|x-22.5|
= 12.5, 7.5, 2.5, 2.5, 7.5, 12.5
MAD = 45/6 = 7.5
can u help me plz and thank u
Answer:
hey
Step-by-step explanation:
angle 7x-9 +angle 4x=90°
11x=90+9
11x=99
x= 9°
Answer:
∠CBD = 54°
Step-by-step explanation:
∠ABC = 90°
∠ABD + ∠CBD = ∠ABC
4X + 7X -9 = 90
11X = 90+9
11X = 99
X = 99/11
X=9°
∠CBD = (7X -9)° = 7 * 9 - 9 = 63-9 = 54°