Michael is finding the area of parallelogram abcd. to do this, he follows the steps in the table. step 1 draw a rectangle around parallelogram abcd. step 2 find the area of the rectangle. step 3 find the area of the four right triangles created in the corners of the rectangle. step 4 subtract the area of the right triangles from the area of the rectangle. to solve the problem using these steps, what are the dimensions of the rectangle he should draw? on a coordinate plane, parallelogram a b c d has points (1, negative 1), (3, 2), (1, 3), and (negative 1, 0). 2 units by 4 units 3 units by 2 units 4 units by 4 units 5 units by 6 units
Answers
The dimensions of the rectangle Michael should draw is given by: C. 4 units by 4 units.
What is a rectangle?A rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles formed are right angle.
In this scenario, the rectangle would be drawn to touch the parallelogram at its four vertices (A, B, C, and D). Also, this would lie outside the parallelogram with the formation of four (4) right-angle triangles.
Therefore, the dimensions of the rectangle Michael should draw is given by:
Dimension = 4 × 4 units.
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Answer:
option C
Step-by-step explanation:
Related Questions
pls help me find all missing sides and angles. ;-;
Answers
Answer:
see explanation
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180° , then
∠ BAC + 51° + 90° = 180°
∠ BAC + 141° = 180° ( subtract 141° from both sides )
∠ BAC = 39°
using the tangent ratio in the right triangle
tan51° = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{12.8}[/tex] ( multiply both sides by 12.8 )
12.8 × tan51° = AC , then
AC ≈ 15.8 ( to 1 dec. place )
using the cosine ratio in the right triangle
cos51° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{12.8}{AB}[/tex] ( multiply both sides by AB )
AB × cos51° = 12.8 ( divide both sides by cos51° )
AB = [tex]\frac{12.8}{cos51}[/tex] ≈ 20.3 ( to 1 dec. place )
Add.
Your answer should be an expanded polynomial in standard form.
(8r^27r-9) + (−r²+ r) =
Answers
The standard form of the expanded polynomial, is expressed as: 7r² - 6r - 9.
What is the Standard Form of a Polynomial?The standard form of a polynomial is expressed by writing the term with the highest exponent or power first, while the constant is written last.
Given the polynomial:
(8r² - 7r - 9) + (-r² + r)
Distribute to open the bracket
8r² - 7r - 9 - r² + r
Combine like terms
7r² - 6r - 9 (standard form)
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(A-5)² + (B- 3)² = 18 B=A-2 A = ?, B = ?
Answers
Answer:
A = 8 and B = 6
Step-by-step explanation:
Since (B = A - 2), we can substitute (A - 2) in for the "B" variable in the first equation to isolate "A".
(A - 5)² + (B - 3)² = 18 -----> Original equation
(A - 5)² + ((A - 2) - 3)² = 18 -----> Plug in B = A - 2
(A - 5)² + (A - 5)² = 18 -----> Subtract
(A² - 10A + 25) + (A² - 10A + 25) = 18 -----> Expand parentheses
2A² - 20A + 50 = 18 ------> Add like terms
2A² - 20A + 32 = 0 -----> Subtract 18 from both sides
2(A² - 10A + 16) = 0 -----> Remove common factor
2(A - 2)(A - 8) = 0 -----> Factor within parentheses
A = 2 -----> Find A - 2 = 0
A = 8 -----> Find A - 8 = 0
Since "A" gave two possible values, we need to plug them into both equations to see which value gives reasonable "B" values.
When A = 2:
B = A - 2 -----> Original equation
B = 2 - 2 -----> Plug in A = 2
B = 0 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(2 - 5)² + (B - 3)² = 18 ------> Plug in A = 2
(-3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
When A = 8:
B = A - 2 -----> Original equation
B = 8 - 2 -----> Plug in A = 8
B = 6 -----> Subtract
(A - 5)² + (B - 3)² = 18 -----> Original equation
(8 - 5)² + (B - 3)² = 18 ------> Plug in A = 8
(3)² + (B - 3)² = 18 -----> Subtract within first parentheses
9 + (B - 3)² = 18 -----> Square value within first parentheses
(B - 3)² = 9 -----> Subtract 9 from both sides
B - 3 = 3 -----> Take square root of both sides
B = 6 -----> Add 3 to both sides
As you can see, when A = 2, there are two possible values of "B" depending on the equation. However, when A = 8, both equations give a "B" value of B = 6. Therefore, A = 8 and B = 6 are the answers.
Solve -3(x - 4) > -2x + 5
Answers
Answer:
x<7
Step-by-step explanation:
-3(x - 4) > -2x + 5 Distribute
-3x+12>-2x+5 Subtract 12 from both sides
-3x>-2x-7 Add 2 to both sides
-5x>-7 Simplify
x<7
Answer:
x < 7.
Step-by-step explanation:
-3(x - 4) > -2x + 5
-3x + 12 > -2x + 5
-3x + 2x > 5 - 12
-x > -7 Note: we divide by -1 so the sign flips:
x < 7.
Kyle buys a car for $58,000. His car immediately starts depreciating, losing 23% of its value every year. How much will the car be worth in 12 years?
Answers
The depreciated value of the car after 12 years that Kyle buys for $58,000 today, which declines 23% annually, will be $2,520.
What is depreciation?Depreciation is the reduction or decrease in the value of an asset over time.
Depreciation occurs because an asset is put to use, and undergoes wear and tear.
The current price of the car = $58,000
The annual depreciation rate = 23%
The depreciated value after one year = 0.77 (1 - 23%)
Let the number of years of depreciation = x
The worth of the car after 12 years = 58,000 x 0.77^x
= 58,000 x 0.77^12
= 58,000 x 0.04344
= $2,519.52
= $2,520
The car's depreciated value can be modeled by the exponential function (decay) abˣ, which yields $2,520 in this situation.
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A meteorologist predicts that there is a 42% chance of rain on Saturday and a 54% chance of rain on Sunday.
Use the meteorologist's predictions to enter the probability that it will not rain on both Saturday and Sunday. Write your answer as a percent and round it to the nearest whole number.
Answers
The rule is "Star, Circle, Heart."What is the
17th shape?
Answers
Answer:
Circle
Step-by-step explanation:
4. Andrew purchased some drinks and some chips. Each bag of chips cost $2.00 and each drink cost $2.50. The expression 2x + 2.5y gives the total amount of money spent by Andrew on chips and drinks. What is the meaning of the term 2.5y?
A. The number of chips plechased by Andrew
B. The cost of one drink
C. The total amount spent on drinks by Andrew
D. The number of drinks purchased by Andrew
Answers
Answer:
The answer is C, the total amount spent on drinks
A mining company has identified a mineral layer below ground.
The mining company wishes to drill down to reach the mineral layer and mode
situation as follows.
With respect to a fixed origin O,
• the ground is modelled as a horizontal plane with equation z = 0
• the mineral layer is modelled as part of the plane containing the points
A(10, 5, -50), B(15, 30, -45) and C(-5, 20, -60), where the units are in
(a) Determine an equation for the plane containing A, B and C, giving your ans
the form r.n=d
Answers
Answer:
90
bc i don't care about this
The equation of plane containing the points ABC is 13x+y-18z = 1035.
What is equation of plane?A plane in 3D coordinate space is determined by a point and a vector that is perpendicular to the plane. The equation of plane is defined as the position vectors and the Cartesian product of the vector perpendicular to the plane.
For the given situation,
The plane containing the points
A(10, 5, -50), B(15, 30, -45) and C(-5, 20, -60).
The equation of the plane in the form r.n=d can be represented as
[tex](r-a).[(b-a)[/tex] × [tex](c-a)]=0[/tex] ------ (1)
Let r = xi + yj +zk
a = 10i + 5j - 50k
b = 15i + 30j - 45k
c = -5i + 20j - 60k
[tex](r-a)=(x-10)i+(y-5)j+(z+50)k[/tex] ------- (2)
[tex](b-a)=(15-10)i+(30-5)j+(-45-(50))k[/tex]
⇒ [tex](b-a)=5i+25j+5k[/tex]
[tex](c-a)=(-5-10)i+(20-5)j+(-60-(50))k[/tex]
⇒ [tex](c-a)=-15i+15j-10k[/tex]
Now, [tex](b-a)[/tex] × [tex](c-a)[/tex]
⇒ [tex](5i+25j+5k)[/tex] × [tex](-15i+15j-10k)[/tex]
⇒ [tex]\begin{vmatrix}i&j&k\\5&25&5\\-15&15&-10\end{vmatrix}[/tex]
⇒ [tex]i(-250-75)-j(-50+75)+k(75+375)[/tex]
⇒ [tex]-325i-25j+450k[/tex] -------- (3)
Substitute all values in equation 1,
⇒ [tex][(x-10)i+(y-5)j+(z+50)k].[(-325i-25j+450k)]=0[/tex]
⇒ [tex]-325(x-10)-25(y-5)+450(z+50)=0[/tex]
⇒ [tex]-325x+3250-25y+125+450z+22500=0[/tex]
⇒ [tex]-325x-25y+450z=-22500-3250-125[/tex]
⇒ [tex]-325x-25y+450z=-25875[/tex]
On dividing by 25 and multiply with negative sign on both sides,
⇒ [tex]13x+y-18z=1035[/tex]
Hence we can conclude that the equation of plane containing the points ABC is 13x+y-18z = 1035.
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1.4x10 -2 in standard form
Answers
Answer:
12
Step-by-step explanation:
1.4x10 is moving the decimal point one spot to the left, so it would be 14., which is just simply 14. Finally, 14-2=12 which is the answer.
Find the area of the kite
Answers
Answer:
180
Step-by-step explanation:
(10×11)+(10×7)=110+70
The area of the kite is expressed as 1/2 × (Product of its diagonals)
In this case, we have;
Diagonal₁ - 10 + 10 feet = 20 feetDiagonal₂ - 7 + 11 feet = 18 feetTherefore, when we substitute the diagonals in the formula, we get;
⇒ 1/2 × (Product of its diagonals)⇒ 1/2 × (20 × 18)When simplified, we get;
⇒ 1/2 × (20 × 18)⇒ 1/2 × (360)⇒ 360/2 = 180 ft²Therefore, the area of the kite is 180 ft².
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I need help finding the value of x which is the base of a triangle.
Answers
Answer:
sqrt(13)
Step-by-step explanation:
The entire base is 4, so 1/2 of the base is 2
We can use the pythagorean theorem
a^2 = b^2 = c^2
2^2 + 3^2 = x^2
4+9 = x^2
13 = x^2
Taking the square root of each side
sqrt(13) = x
Check the picture below.
List all of the factors of 78. (Type the factors in numeric order from smallest to largest. Separate each factor with a comma and a space after the comma.)
Answers
Answer:
1, 2, 3, 6, 13, 26, 39, 78
Step-by-step explanation:
The factors of a number are the numbers that "go into" 78 "evenly" that is, without a remainder. You can make a factor tree or divide to find the prime factors. Any combination "goes into" 78. That's why we'll include 6 and 26 on this list.
1×78
2×39
3×26
6×13
all make 78!
Please belpppp don’t understand
Answers
Answer:
[tex]\huge 3w^2\sqrt[4]{2\:w^{3}}[/tex]
Step-by-step explanation:
[tex]\huge\sqrt[4]{162\:w^{11}}[/tex][tex]=\huge\sqrt[4]{81*2\:w^{8}*w^{3}}[/tex][tex]=\huge\sqrt[4]{3^4*2\:(w^{2})^4*w^{3}}[/tex][tex]=\huge 3w^2\sqrt[4]{2\:w^{3}}[/tex] (Elements with power 4 within the radical will come out and the rest will be within the radical sign)PLEASE HELP NEED TO PASS
Answers
Answer:
The second answer
Step-by-step explanation:
Answer:
-3 ± √41
Step-by-step explanation:
Numerator of Quadratic Formula
-b ± √b² - 4aca = 2b = 3c = -4⇒ -3 ± √(-3)² + 4(2)(-4)
⇒ -3 ± √9 + 32
⇒ -3 ± √41
Freida has 12 red apples and 15 green apples. She is going to share the apples equally among 8 people and keep any extra apples for herself. How many apples will Freida keep for herself?
Answers
Answer: 3 apples
Step-by-step explanation:
Given:
12 red apples
15 green apples
8 people
Freida
..............................................................................................................................................
12 + 15 = 27
Since she is going to give the apples equally among 8 people,
27 / 8 = 3 remainder 3
Each of the 8 people will get 3 apples each.
Freida will get the remaining 3 apples.
Use formulas to find the lateral area and surface area of the given prism. Round your answer to
the nearest whole number. The figure is not drawn to scale. The bases are right triangles.
8.94 m
4m
8m
41 m
Answers
Answer:
The answer is option B
[tex]859[/tex] [tex]m^2[/tex] [tex],[/tex] [tex]891[/tex] [tex]m^2[/tex]
Step-by-step explanation:
Step 1
Find the lateral area
we know that
The formula to calculate the lateral area is equal to
[tex]LA=Ph[/tex]
where
P is the perimeter of the base of the prism
h is the height of the prism
In this problem we have
[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]
[tex]h=41[/tex] [tex]m[/tex]
substitute in the formula
[tex]LA=20.94*41=858.54[/tex] [tex]m^2[/tex]
[tex]LA=859[/tex] [tex]m^2[/tex]
Step 2
Find the surface area
we know that
The formula to calculate the surface area is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base of the prism
P is the perimeter of the base of the prism
h is the height of the prism
In this problem we have
[tex]B=8*4/4=8[/tex] [tex]m^2[/tex]
[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]
[tex]h=41[/tex] [tex]m[/tex]
substitute in the formula
[tex]SA=4(8)+20.94*41=890.54[/tex] [tex]m^2[/tex]
[tex]SA=891[/tex] [tex]m^2[/tex]
HELP! need help ASAP, 50 points and brainiest will be given to whoever helps.
Solve for x:
Answers
Answer:
12
Step-by-step explanation
Give the following number
in Base 10.
E16 = [?]10
Enter the number that belongs in the green box.
Answers
Answer:
14
Step-by-step explanation:
A hexadecimal (base 16) number can have any of 16 digits. Conventionally, digits 0–9 are used, along with letters A–F. The letters are assigned the values ...
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
Which of these tables does NOT represent a function?
Answers
Find the surface area of the square pyramid.
A) 35 ft^2
B) 30 ft^2
C) 45 ft^2
D) 20 ft^2
Answers
Area of base
side²5²25ft²Area of one triangle side
1/2(2)(5)=5ft²Area of 4 sides
5(4)=20ft²TSA
20+25=45ft²
Answer:
C) 45 ft²
Step-by-step explanation:
Formulae
Area of a square = x² (where x is the side length)
Area of a triangle = 1/2 × base × height
The surface area of a square pyramid comprises:
square base4 congruent triangles⇒ area of square base = 5² = 25 ft²
⇒ area of triangular face = 1/2 × 5 × 2 = 5 ft²
⇒ Total surface area = area of square base + 4 triangular areas
= 25 + 4(5)
= 25 + 20
= 45 ft²
Martin takes a test that has five multiple choice questions. Each question has three possible
answers. If Martin guesses on each question, in how many different ways can he answer the
questions on the test?
Answers
Answer:
The answer is 243
Step-by-step explanation:
Since there are 3 answers for each question and a total of 5 questions, you could do 3*3*3*3*3 or 3^5. Both will equal 243. 243 is the amount of possible different combinations that exist in this problem.
Hope this helps!
If 25% of the people in a small town are voters and there are 2360 voters, what is the population of the town?
Answers
Answer:
x=11800
Step-by-step explanation:
make a proportion:
2360/.2=X/1
2360(1)=.2x
x=11800
help giving branliest
Answers
Answer:
a
34
b
17
c
46
Step-by-step explanation:
a
Lowest age = 21
Highest age = 55
Range = 34
b
Add them all together and you get 17
c
Median is middle
17 total people
Formula for median:
(n + 1)/2 = th
n is the total
17 + 1 is 18
18 halved is the 9th number
The 9th number is 46
Pleaseeee helplpppppp
Answers
Answer:
Step-by-step explanation:
I NEED HELP WITH THISSS PLSSS I HAVE NO IDEA HOW TO DO IT
Answers
I need help too cause i have a quiz for it to take please help me
Step-by-step explanation:
an account transaction log is simply a sequence of basic additions and subtractions.
he made a mistake in line 4 : $180 - $188 = -$8 and not $8.
he missed that this was going below zero and needed a "-" sign.
from there on everything else is wrong too (although the individual calculations are correct) - the balances are off by $16 (2×8 from -8 to +8) :
+$20 gave the real balance of $12 and not $28.
-$5.95 gave the real balance of $6.05 and not $22.05.
Solve the system of equation using ELIMINATION (solve for x)
x + 3y = 14
-x + y = 10
Answers
Answer:
x = -1.5 , y = 5.17
Step-by-step explanation:
Solve the system of equation using ELIMINATION (solve for x)
x + 3y = 14
-x + y = 10
Solution
x + 3y = 14 ------- equation 1 * 1
-x + y = 10 ------- equation 2 * 3
x + 3y = 14 ------- equation 3
-(-3x + 3y = 30)------ equation 4
Using the ELIMINATION METHOD.
x-(-3x) + 3y-3y = 14-30
4x = -6
x = [tex]\frac{-6}{4}[/tex]
x = -1.5
Substuting -1.5 into equation one
x + 3y = 14
-1.5 + 3y = 14
Adding 1.5 to both sides
-1.5 + 1.5 +3y = 14 +1.5
+3y = 15.5
Dividing by the coeffient of y
[tex]\frac{3y}{3} = \frac{15.5}{3}[/tex]
y = 5.166666666666
y =5.17
Therefore x = -1.5 , y = 5.17
An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Select the diagrams that would represent the types of animals adopted.
How many of each type of animals were adopted?
Answers
There are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
An animal shelter had 45 animals adopted over one week. The ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
Combine ratio dogs:ferrets:cats = 5:1:9
Let's suppose the number of ferrets is x then:
5x + x + 9x = 45
15x = 45
x = 3
Ferrets x = 3
Dogs = 5x = 5(3) = 15
Cats = 9x = 9(3) = 27
Thus, there are total 15 dogs, 27 cats, and 3 ferrets were adopted if the ratio of dogs to ferrets was 5:1. The ratio of cats to dogs was 9:5.
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What is an equation of a line that perpendicular to y=8x-3?
Question 4 options:
y=8x + 10
y=10x - 3
y= -1/-8 (-3)
y= -1/-8 +1
Answers
Hi Student!
Reading the question we can pull out specific bits of information that would help us find our answer. One of the bits of information that is useful is that we are trying to find the perpendicular line. However, in order to determine a line that is perpendicular to the other line we first need to determine the slope of the first line. Looking at the equation given, we can see that it follows the y = mx + b form where m is the slope and in this case our slope is 8.
Now that we have completed the information gathering, we can move onto the next part which is determining a slope that is perpendicular to that of the original line. In order to find that we first need to negate our slope which would turn our 8 into a -8. The second step that we need to do is take the reciprocal of the number which means that we basically flip the number and so we convert -8 into -1/8. Looking at the given options, there is none that match our answer so that either means that the question is wrong or the choices that are given are wrong.
You are told that in a sample of size 225 the mean is 48.5 and the standard deviation is 1.8. the study is reported with 90% confidence level. explain how to determine if 48.8 is within the confidence interval.
Answers
Using the t-distribution, it is found that the 90% confidence interval is (48.3, 48.7), hence 48.8 is not within the interval.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 225 - 1 = 224 df, is t = 1.6517.
The other parameters are given as follows:
[tex]\overline{x} = 48.5, s = 1.8, n = 225[/tex].
Hence the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 48.5 - 1.6517\frac{1.8}{\sqrt{225}} = 48.3[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 48.5 + 1.6517\frac{1.8}{\sqrt{225}} = 48.7[/tex]
The 90% confidence interval is (48.3, 48.7), hence 48.8 is not within the interval.
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