Answer:
Sin x = a / b.
Step-by-step explanation:
The opposite side =a and the adjacent side = 4 (because tan x = a/4.
Cos x = 4/b so the hypotenuse = b ( because Cos = adjacent /hypotenuse.
So sin x = opposite /hypotenuse = a / b.
Answer:
sin x° = a divided by b is the answer
Step-by-step explanation:
I got 100% on the test!
HELP WITH ANGLE THEOREMS! Brainliest! Find the values of c and d.
Give reasons for each value you find.
Please EXPLAIN each theorem please!
Thank you!
Answer:
c = 25, d = 65
Step-by-step explanation:
∠d + 90 = 155 ( vertical angles )
Subtract 90 from both sides
d = 65
The angle above 155 = 180 - 155 ( straight angle ) = 25
Hence c = 25 ( corresponding angles )
Answer:
<d = 65 degrees.
<c = 25 degrees.
Step-by-step explanation:
<d + 90 = 155 since vertically opposite <'s are equal. Therefore <d = 155-90
= 65 degrees.
The angle adjacent to <d is 180-155= 25 degrees since <'s on a line = 180 degrees.
Therefore <c= 25 degrees since corresponding <'s on parallel lines are equal.
The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 2. cross sections of the solid perpendicular to the base are squares. what is the volume, in cubic units, of the solid?
The volume of the solid is 8/3 cubic units.
Explanation:Visualization:
Imagine a right triangle with one leg on the x-axis and the other on the y-axis. The hypotenuse of the triangle intersects the line x + y = 2 at a point (x, y). The solid is formed by stacking square cross-sections perpendicular to the base triangle, with each square having a side length equal to the distance between the line x + y = 2 and the triangle's hypotenuse at that point.
Volume Calculation:
Let x be the distance from the origin to the point where the hypotenuse intersects the line x + y = 2. Then, the length of the side of each square cross-section is (2 - x). The area of each cross-section is therefore (2 - x)^2.
As we move from the origin to the vertex of the triangle where the hypotenuse intersects the line, the distance x increases from 0 to 2. Thus, the volume of the solid can be calculated by integrating the area of the cross-sections over the range of x:
Volume = ∫(2 - x)^2 dx from x = 0 to x = 2
Integration:
Solving the integral using the power rule, we get:
Volume = [4/3 * x^3 - 2x^2 + x] from x = 0 to x = 2
Evaluating the expression at the limits of integration:
Volume = (32/3 - 8 + 2) - (0 - 0 + 0) = 32/3 - 6 = 8/3 cubic units
Therefore, the volume of the solid is 8/3 cubic units.
Which of the following is the statement of the triangle inequality theorem?A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle.B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.C. The longest side of a triangle is opposite the largest angle.D. The largest angle of a triangle is between the two longest sides.
Answer:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side ⇒ answer B
Step-by-step explanation:
* Lets explain the triangle inequality theorem
- The triangle Inequality Theorem is the sum of the lengths of any two
sides of a triangle is greater than the length of the third side.
- That means when we add the lengths of the shortest two sides,
the answer will be greater than the length of the longest side.
- Examples:
# Is the set of {4 , 5 , 9} could form a triangle
- Add 4 , and 5 because they are the shortest sides
∵ 4 + 5 = 9
∵ The third side is 9
∵ In any triangle the sum of the lengths of any two sides of a triangle
must be greater than the length of the third side
∴ The set {4 , 5 , 9} couldn't form a triangle
# Is the set of {4 , 5 , 8} could form a triangle
- Add 4 , and 5 because they are the shortest sides
∵ 4 + 5 = 9
∵ The third side is 8
∵ In any triangle the sum of the lengths of any two sides of a triangle
must be greater than the length of the third side
∴ The set {4 , 5 , 8} could form a triangle
# Is the set of {3 , 5 , 9} could form a triangle
- Add 3 , and 5 because they are the shortest sides
∵ 3 + 5 = 8
∵ The third side is 9
∵ In any triangle the sum of the lengths of any two sides of a triangle
must be greater than the length of the third side
∴ The set {3 , 5 , 9} couldn't form a triangle
* Lets solve the problem
∵ The triangle inequality theorem is the sum of the lengths of any two
sides of a triangle is greater than the length of the third side
- It talks about the relation between the lengths of the sides
∴ The right answer is B. The sum of the lengths of any two sides of
a triangle is greater than the length of the third side
Answer:
B
Step-by-step explanation:
A cannot be correct as it is measuring angles, and the theorem is not abt the angles.
B is correct because the theorem is abt triangle sides.
C is incorrect because that is just ridiculous.
D is incorrect because is not always true and the theorem once again, is not abt angles.
20. The perimeter of a square is 72 in. What is its area? 72 in2 324 in2 18 in2 5,184 in2
Determine the image of the point (-5, 2) under a rotation of 90° about the origin.
(-2,-5)
12,5)
(2,-5)
(2,5)
Answer:
(2, 5)
Step-by-step explanation:
Rotation clockwise 90° can be accomplished by the transformation ...
(x, y) ⇒ (y, -x)
so
(-5, 2) ⇒ (2, 5)
((PLEASE ANSWER WITH A B C or D))
What is m NMO?
A. 90°
B. 30°
C. 45°
D. 60°
Answer:
D. 60°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relationship of interest is ...
Sin = Opposite/Hypotenuse
sin(M) = ON/OM = 4(√3)/8 = (√3)/2
M = sin⁻¹((√3)/2) = 60°
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 2 of the recall, the manufacturer fixed 192 cars. In week 4, the manufacturer fixed 184 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week at the mechanic.
A.) f(x) = 4x + 200
B.) f(x) = 2x + 192
C.) f(x) = −4x + 200
D.) f(x) = −2x + 192
Answer:
C.) f(x) = −4x + 200
Step-by-step explanation:
Since the number is decreasing, you know the slope will be negative, eliminating the first two choices. The equation in the last choice does not match the given data, so it can be eliminated.
In other words, the easiest way to solve this problem is to check the answers against the given data.
_____
If you want to write the equation from scratch, you need to find the slope. That is ...
(change in number of cars)/(change in weeks) = (184 -192)/(4 -2) = -8/2 = -4
This matches only one answer, but you can go on to finish the equation by starting with point-slope form:
y -192 = -4(x -2)
y = -4x +8 +192 . . . . add 192, eliminate parentheses
y = -4x + 200 . . . . matches choice C.)
Answer:
c.f(x)= -4x+200
Step-by-step explanation:
i took the test
Can someone please help find X.
Answer:
32°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the trig function relating angles to the opposite and adjacent sides of the triangle is ...
Tan = Opposite/Adjacent
The side opposite the angle x is shown as having measure 5; the side adjacent has measure 8. Putting all this in the above equation gives ...
tan(x) = 5/8
To find the angle from the value of the tangent, you use the inverse of the tangent function. The name of that is the arctangent function. It is often written as tan⁻¹(x) and often accessible on your calculator using a "second function" key. Some calculators, like the one shown in the attachment, recognize the arctan function name.
x = arctan(5/8) ≈ 32°
The value of x rounded to the nearest whole degree is 32°.
Opps, forgot to link the picture, this is the real question.
Answer:
a. 18 units, 18 units, 13 units
Step-by-step explanation:
P = 49 means the sum of side lengths is 49. Only answer choice A has numbers that sum to 49.
___
As here, you often do not need to work a multiple-choice problem. You only need to check to see which answers make sense.
__
If you want to actually compute the side lengths, you know the two sides with a hash mark are the same length, so the perimeter is ...
P = 49 = (2n+2) + (2n+2) + (2n-3) = 6n +1
48 = 6n . . . . . subtract 1
8 = n . . . . . . . divide by 6
Then ...
2n +2 = 2·8 +2 = 18 . . . . . . . matches only the first answer choice.
Find the value of a in the equation 5/a+3 = 3/a-2
Answer:
D 9 1/2
Step-by-step explanation:
5/(a+3) = 3/(a-2)
We can use cross products to solve
5 * (a-2) = 3 * (a+3)
Distribute
5a - 10 = 3a +9
Subtract 3a from each side
5a -3a -10 = 3a -3a +9
2a -10 =9
Add 10 to each side
2a -10+10 = 9+10
2a = 19
Divide each side by 2
2a/2 = 19/2
a = 19/2
a = 9 1/2
Answer:
Option D
Step-by-step explanation:
Please see attached picture for a detailed answer.
Sam is 5 years old. His older brother Tom, is three times as old as Sam. When Sam is 20, how old will Tom be?
Answer:
60
Step-by-step explanation:
Sam is 5, Tom is 3 times as old, 5 times three is 15, so tom is 15, 20 is 4 times 5, so you take 15, and multiply it by 4, and that's your answer
Is trapezoid ABDC the result of a dilation of trapezoid MNPQ by a scale factor of ? Why or why not? Yes, because AB and CD are each the lengths MN and QP. Yes, because sides AB and CD are parallel to sides MN and QP. No, because AB is the length MN but CD is the length QP. No, because sides AB and CD have different slopes from sides MN and QP.
No, because AB is 2/5 the length MN but CD is 1/3 the length QP.
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
Given:
As, Comparing the corresponding sides, the length of AB is 4.
The length of MN is 10. This makes their ratio 4/10 = 2/5.
and, the CD length is 2.
QP has a length of 6. Consequently, their ratio is 2/6 = 1/3.
Therefore, because the side ratios differ, the figure is not proportionate and is not a dilation.
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Trapezoid ABCD is not the result of the dilation of trapezoid MNPQ by a scale factor of 2/5 because AB is 2/5 the length MN but CD is 1/3 the length QP.
What is Scale Factor?Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.
Given a trapezoid ABCD and another trapezoid MNPQ.
From the figure,
length of AB = 2 + 2 = 4
Length of MN = 5 + 5 = 10
Scale factor = 4/10 = 2/5
Now,
Length of CD = 1 + 1 = 2
Length of QP = 3 + 3 = 6
Scale factor = 2/6 = 1/3
That is, the scale factor differs.
Hence the correct option is C.
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PLEASE HELP ASAP I WILL MARK BRAINLIEST!! ABCD is rotated counterclockwise about the origin. By how many degrees was ABCD rotated?
Answer:
270 degrees
Step-by-step explanation:
180 would be diagonal from original, 360 would be where the original is and 90 would be in the second quadrant so therefore its 270
Answer:
B) 270°
Step-by-step explanation:
it was correct for me
Select all that apply.
Describe the transformations.
The yellow rectangle was translated up 3 units and reflected over the y-axis.
The yellow rectangle was translated right 5 units and reflected over the x-axis.
The yellow rectangle was reflected over both axes.
The yellow rectangle was translated right 5 units and up 3 units.
Answer: i'm pretty sure the only answer that applies is the last one.
Good luck!
Answer:
b) The yellow rectangle was translated right 5 units and reflected over the x-axis.
d) The yellow rectangle was translated right 5 units and up 3 units.
Step-by-step explanation:
Translation in geometry describes a function that moves an object a certain distance without altering it. The object is not rotated, reflected or re-sized after translation. Every point of the object is moved in the same direction through the same distance.
Reflection is a rigid transformation in which the given object is flipped across a line to create its image. Each point of the image maintains their distance from the line as in the object. In reflection, every point of the object changes initial location.
The options that describe the transformation are: The yellow rectangle was translated right 5 units and reflected over the x-axis, and the yellow rectangle was translated right 5 units and up 3 units.
Let Events A & B be described as follows: P(A) = watching a movie P(B) = going out to dinner The probability that a person will watch a movie is 62% and the probability of going out to dinner is 46%. The probability of watching a movie and going out to dinner is 28.52% Are watching a movie and going out to dinner independent events? No, because the P(A) + P(B) ≠ P(A and B). Yes, because the P(A) + P(B) is greater than 100%. No, because the P(A)P(B) ≠ P(A and B). Yes, because the P(A)P(B) = P(A and B).
Answer:
Yes, because the P(A) · P(B) = P(A and B) ⇒ last answer
Step-by-step explanation:
* Lets study the meaning independent and dependent probability
- Two events are independent if the result of the second event is not
affected by the result of the first event
- If A and B are independent events, the probability of both events
is the product of the probabilities of the both events
- P (A and B) = P(A) · P(B)
* Lets solve the question
∵ P(A) = watching a movie
∵ P(B) = going out to dinner
∵ The probability that a person will watch a movie is 62%
∴ P(A) = 62% = 62/100 = 0.62
∵ The probability of going out to dinner is 46%
∴ P(B) = 46% = 46/100 = 0.46
∵ The probability of watching a movie and going out to dinner
is 28.52%
∵ P(A and B) = 28.52% = 28.52/100 = 0.2852
- Lets find the product of P(A) and P(B)
∵ P(A) = 0.62
∵ P(B) = 0.46
∵ P(A and B) = 0.2852
∴ P(A) · P(B) = 0.62 × 0.46 = 0.2852
∴ P (A and B) = P(A) · P(B)
∴ Watching a movie and going out to dinner are independent events
because the P(A) · P(B) = P(A and B)
Find the distance between the points (3, 8) and (-1, 9).
Square root 15
Square root 15
Square root 17
Answer:
√17
Step-by-step explanation:
The distance formula is ...
d = √((x2 -x1)² +(y2 -y1)²)
Filling in the point values, we have ...
d = √((-1-3)² +(9-8)²) = √(16 +1)
d = √17
PLEASE HELP ME WITH THIS MATH QUESTION
WHERE IS THE QUESTION ??
Multiple-choice questions have a special grading rule determined by your instructor. Assume that your instructor has decided to grade these questions in the following way: If you submit an incorrect answer to a multiple-choice question with n options, you will lose 1/(n−1) of the credit for that question. Just like the similar multiple-choice penalty on most standardized tests, this rule is necessary to prevent random guessing.If a multiple-choice question has five answer choices and you submit one wrong answer before getting the question correct, how much credit will you lose for that part of the question?
Answer:
1/4 of the credit
Step-by-step explanation:
The problem statement tells you n=5. Putting that into the expression for lost credit, you get ...
1/(5-1) = 1/4
of the credit is lost for a question with 1 wrong answer.
You will lose 1/4 of the credit.
Answer:
The credit will you lose for the part of question is 1/4 or 25%.
Step-by-step explanation:
Consider the provided information.
It is given that, if you submit an incorrect answer to a multiple-choice question with n options, you will lose 1/(n−1) of the credit for that question.
Suppose the given multiple choice question has 5 answer. So for one wrong answer the loss will be:
Substitute the value of n=5 in above formula.
[tex]\frac{1}{n-1} \\\frac{1}{5-1} \\\frac{1}{4}=0.25[/tex]
That means you will lose 1/4 or 0.25credit.
Now convert it into %.
[tex]\frac{1}{4}\times 100=25\%[/tex]
Hence, the credit will you lose for the part of question is 1/4 or 25%.
Please Help! I need to get this right
Answer:
sin(x) = -2(√6)/5csc(x) = -5/(2√6)tan(x) = 2√6cot(x) = 1/(2√6)Step-by-step explanation:
In the third quadrant, sine and its inverse, cosecant, are negative. In that quadrant, tangent and its inverse, cotangent, are positive. The sine function always has a magnitude less than or equal to 1, while the cosecant function always has a magnitude at least 1.
The negative numbers on your list can be assigned to sin(x) and csc(x) based on their magnitudes. 2√6 = √24 < 5, so 2(√6)/5 < 1. The number with this magnitude is the sine; its inverse is the cosecant.
sin(x) = -2(√6)/5csc(x) = -5/(2√6)The tangent is the ratio of sine to cosine, so is ...
tan(x) = ((-2√6)/5)/(-1/5) = 2√6
and the cotangent is the inverse of that:
tan(x) = 2√6cot(x) = 1/(2√6)Of course, the secant is the inverse of the cosine, so would be -5. That is not one of the number choices, so sec(x) can be ignored.
I need help with (half way done
which probability symbols do I use for each one 'P(R)="
7.Drawing a yellow marble, given that a red marble was drawn on the first draw and not replaced?
The probability of drawing a blue marble will be 1/3.
How to calculate probability?Blue marbles = 3
Red marbles = 2
Yellow marbles = 4
Total marbles = 3 + 2 + 4 = 9
The probability of drawing a blue marble will be:
= 3/9
= 1/3
The probability of drawing a marble that isn't red will be:
= 3/9 + 4/9
= 7/9
The probability of drawing a red and yellow marbles will be:
= 2/9 + 4/9
= 2/3
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(20 points) You are writing a research paper on plant cells. You got 48,600,000 results on the online search. How do you write 48,600,000 in scientific notation?
Answer:
4.86 × 10^7
Step-by-step explanation:
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
For example, 650,000,000 can be written in scientific notation as 6.5 × 10^8
So;
48,600,000 = 4.86 × 10^7
count backward to the last number.
Answer:
4.86 × 10^7
Your welcome!
Ryan is trying a low-carbohydrate diet. He would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:
110 < 2x + 10 and 2x + 10 < 310
Solve for x in this inequality, and explain what the answer represents.
x > 50 and x < 150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.
x < 50 and x > 150; Ryan needs to consume less than 50 grams of carbohydrates or more than 150 grams of carbohydrates.
x > 60 and x < 160; Ryan needs to consume more than 60 grams of carbohydrates, but less than 160 grams of carbohydrates.
x < 60 and x > 160; Ryan needs to consume less than 60 grams of carbohydrates or more than 160 grams of carbohydrates.
Answer:
A. X>50 and X<150; Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.
Step-by-step explanation:
1. 110<2x+10
First, switch sides.
2x+10>110
Then, subtract by 10 both sides of equation.
2x+10-10>110-10
Simplify.
110-10=100
2x>100
Divide by 2 both sides of equation.
2x/2>100/2
Simplify, to find the answer.
100/2=50
x>50
x>50 is the correct answer.
__________________________
2. 2x+10<310
First, you subtract by 10 from both sides of equation.
2x+10-10<310-10
Then, simplify.
310-10=300
2x<300
Divide by 2 from both sides of equation.
2x/2<300/2
Simplify, to find the answer.
300/2=150
x<150
x<150 is the correct answer.
A. the first option is the correct answer.
Option A - x > 50 and x < 150 Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates is the correct answer.
We have amount of carbs consumed in grams between the levels shown in the following compound inequality :
110 < 2x + 10
2x + 10 < 310
We have to solve for x in this inequality, and explain what the answer represents.
Consider the following : if is between α and β, such that -α < 0 and β > 0, then express this statement as inequality.We can write the inequality as follows -
α < x < β (Since α is less then 0, it will be less then β)
According to question, we have -
110 < 2x + 10
110 - 10 < 2x + 10 - 10
100 < 2x
x > 50
2x + 10 < 310
2x + 10 - 10 < 310 - 10
2x < 300
x < 150
Hence, x > 50 and x < 150 : Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.
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Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
A. 2x² +12x
Step-by-step explanation:
If the mobile is balanced, the weights at each level are the same. Each of those in the lowest tier will be equivalent to 3x, for a total of ...
4×3x = 12x
Each of those in the top tier shown will be equivalent to x², for a total of ...
2×x² = 2x²
Then the sum of all parts will be ...
top tier + bottom tier = 2x² +12x
Need help with this counterclockwise rotation
Answer: [tex](-2,1)[/tex]
Step-by-step explanation:
It is important to remember that a rotation is a transformation in which the shapes and sizes do not change, but the object can be turned in different directions.
By definition, the rule for 180° counterclockwise rotation is this:
[tex](x,y)[/tex]→ [tex](-x,-y)[/tex]
Therefore, we know that the image of the point [tex]P=(2,-1)[/tex] under a 180° counterclockwise rotation is:
[tex](2,-1)[/tex]→ [tex](-2,1)[/tex]
help with a geometry problem???
Volume = 9in • 9in • 9in
Volume = 729 in^3
Now multiply the volume by 6 grams.
Let H = total weight of the cube in terms of grams.
H = V • 6
H = 729 • 6
H = 4,374 grams
The _______ of a discrete random variable represents the mean value of the outcomes.
Answer:
expected value
Step-by-step explanation:
Answer:
Expected value
Step-by-step explanation:
Expected value- Any discrete variable's expected value is probability-weighted average of all of its possible values.
In simple words, any possible value that can be inferred by the any given variable is compounded by its probability of occurrence and the resulting products are added up to deliver the expected value.
PLEASE HELP
divide. (3x-2)(x-4)-(x-4)(6-5x)
/(4-x)(8x-1)
Answer:
x = 39/74 - sqrt(1817)/74 or x = 39/74 + sqrt(1817)/74
Step-by-step explanation:
Solve for x:
(x - 4) (3 x - 2) - ((6 - 5 x) (x - 4) (8 x - 1))/(4 - x) = 0
Simplify and substitute y = 4 - x.
(x - 4) (3 x - 2) - ((6 - 5 x) (x - 4) (8 x - 1))/(4 - x) = -434 + 257 (4 - x) - 37 (4 - x)^2
= -37 y^2 + 257 y - 434:
-37 y^2 + 257 y - 434 = 0
Divide both sides by -37:
y^2 - (257 y)/37 + 434/37 = 0
Subtract 434/37 from both sides:
y^2 - (257 y)/37 = -434/37
Add 66049/5476 to both sides:
y^2 - (257 y)/37 + 66049/5476 = 1817/5476
Write the left hand side as a square:
(y - 257/74)^2 = 1817/5476
Take the square root of both sides:
y - 257/74 = sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74
Add 257/74 to both sides:
y = 257/74 + sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74
Substitute back for y = 4 - x:
4 - x = 257/74 + sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74
Subtract 4 from both sides:
-x = sqrt(1817)/74 - 39/74 or y - 257/74 = -sqrt(1817)/74
Multiply both sides by -1:
x = 39/74 - sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74
Add 257/74 to both sides:
x = 39/74 - sqrt(1817)/74 or y = 257/74 - sqrt(1817)/74
Substitute back for y = 4 - x:
x = 39/74 - sqrt(1817)/74 or 4 - x = 257/74 - sqrt(1817)/74
Subtract 4 from both sides:
x = 39/74 - sqrt(1817)/74 or -x = -39/74 - sqrt(1817)/74
Multiply both sides by -1:
Answer: x = 39/74 - sqrt(1817)/74 or x = 39/74 + sqrt(1817)/74
PLEASE HELP ASAP!!!!
Answer:
a = -4
b = 3
c = 6
Step-by-step explanation:
x^2 + 8x = 38
We take the coefficient of the x term
Divide by 2 and then square it
8/2 =4
4^2 = 16
Add 16 to both sides
x^2 +8x + 16 = 38 + 16
x^2 +8x +16 = 54
Take b/2 and use it in the the (x+b/2)^2
(x+4)^2 = 54
Take the square root of each side
sqrt((x+4)^2) = ± sqrt(54)
x+4 = ± sqrt(54)
Subtract 4 from each side
x+4-4 = -4 ± sqrt(54)
x = -4 ± sqrt(54)
Simplify the square root
x = -4 ± sqrt(9*6)
x = -4 ± sqrt(9) sqrt(6)
x = -4 ± 3 sqrt(6)
1. Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today?
A.8,000 + 24x
B.8,000 − 24x
C.8,000 + 2x
D.8,000 − 2x
2. Avi and Sergi are saving money to buy a game system. Avi has $2 more than double the amount of money Sergi has. Together, they have $40. Write an equation to determine how much money Sergi and Avi have together.
A.x + 2x + 2 = 40
B.2x + 2 = 40
C.x + 2x − 2 = 40
D.2x − 2 = 40
Isabella solved the following equation:
4x − 2x + 8 = 6(x + 4)
Step Work Justification
1 4x − 2x + 8 = 6x + 24 Distributive Property
2 2x + 8 = 6x + 24 Combine like terms
3 −4x + 8 = 24 Addition Property of Equality
4 −4x = 16 Subtraction Property of Equality
5 x = −4 Division Property of Equality
Which step has an incorrect justification?
A.Step 1
B.Step 2
C.Step 3
D.Step 4
Answer:
1. C. 8000 - 24x; 2 A. x + 2x + 2 = 40; 3. C. Step 3
Step-by-step explanation
1. Desmond
[tex]\begin{array}{rcl}\text{Value of car two years ago} & = & 8000\\\\\text{Less depreciation = 24 mo} \times\dfrac{x}{\text{1 mo}} & = & -24 x\\\\\text{Current value} & = & \mathbf{8000 - 24x}\\\end{array}[/tex]
2. Avi and Sergi
[tex]\begin{array}{rcl}\text{Sergi's money} & = & x\\\text{Double Sergi's money} & = & 2x\\\text{Avi's money} & = & 2x + 2\\\text{Avi's money + Sergi's money} & = & x + 2x + 2\\\text{Avi's money + Sergi's money} & = & 40\\x + 2x + 2 & = & 40\\\end{array}[/tex]
3. Isabella
[tex]\begin{array}{crl} \textbf{Step} & \textbf{Work} & \textbf{Justification} \\ & 4x - 2x + 8 = 6(x + 4) & \\ 1 & 4x - 2x + 8 = 6x + 24 & \text{Distributive Property} \\ 2 & 2x + 8 = 6x + 24 & \text{Combine like terms} \\ 3 & -4x + 8 = 24 & \textbf{Subtraction Property of Equality}\\ 4 & -4x = 16 & \text{Subtraction Property of Equality} \\ 5 & x = -4 & \text{Division Property of Equality} \\ \end{array}[/tex]
Step 3 has the incorrect justification. Isabella subtracted 6x from each side, so she should have used the Subtraction Property of Equality
in circle P, what is the measure of ADB?
Answer:
arc ADB = 270°
Step-by-step explanation:
Arc ADB is the remainder of the circle after subtracting 90° arc AB. Its measure is ...
ADB = 360° -90° = 270°