Solve the equation.
-5x + 2 = 67
A) x = 13
Eliminate
B) x = -13
C) x =
69
5
D) x = -
69
5
Lydia is trying to prove that a quadrilateral in a coordinate plane is a square. First, she uses the slope formula to prove that there are two pairs of parallel sides. Next, she uses the distance formula to prove that all sides are equal. What additional step must Lydia perform before reaching a conclusion that the quadrilateral is a square?
A) Use the distance formula to prove that the diagonals of the quadrilateral are not equal.
Eliminate
B) Use the slope formula to prove that four right angles exist as a result of perpendicular sides.
C) Use the midpoint formula to prove that the diagonals of the quadrilateral do not bisect each other.
D) Use the Pythagorean Theorem to prove that the diagonals of the quadrilateral are twice the length of each side.
Answer:
slope
Step-by-step explanation:
In how many distinct ways can the letters in engineering be arranged?
Geometry! What describes line FI?
Find the Least Common Multiple of these two monomials:
9a^2bc^3 and 30ab^2c^3
9a^2b^2c^3
3ab^3
90ab^3
90a^2b^2c^3
the LCM for 9 and 30 is 90
LCM for a = a^2 and ab^2 = a^2
LCM for b = bc^3 and abb^2 =b^2
LCM for c = bc^3 and c^3 = C63
so answer is 90a^2b^2c^3
The radius of a cylindrical construction pipe is 2ft . if the pipe is 23ft long, what is its volume? use the value 3.14 for π , and round your answer to the nearest whole number. be sure to include the correct unit in your answer.
Which scientist arrived at a fairly accurate calculation of the value of pi?
Rotate 90 clockwise around the origin (-6,-2) (-3,1) (-1,1) (2,-4) please help me!
A magazine has 96 pages. there are advertisements on 75% of those pages. how many pages do not have advertisements?
There are 24 pages in the magazine that do not have advertisements.
To find the number of pages without advertisements in a 96-page magazine, we first calculate the number of pages with advertisements.
Calculate 75% of 96 (since 75% of the pages have advertisements).
[tex]\( 75\% \times 96 = 0.75 \times 96 = 72 \)[/tex] pages with advertisements.
Subtract the pages with advertisements from the total number of pages to find the pages without advertisements.
[tex]\( 96 - 72 = 24 \)[/tex] pages without advertisements.
So, there are 24 pages in the magazine that do not have advertisements.
The sum of the circumference of a circle and the perimeter of a square is 16. find the dimensions of the circle and square that produce a minimum total area. (let x be the length of a side of the square and r be the radius of the circle.)
A total of 15000 is to be divided between jon and wendy with jon to receive 2500 less than wendy how much will she receive
Wendy will get $8750.
We have a total of 15000 that is to be divided between Jon and Wendy with Jon to receive 2500 less than Wendy how much will she receive.
We have to determine how much money will Wendy receive.
A total of 20 chocolates are to be divided between you and your brother such that you will get 6 more chocolates than your brother. How many chocolates will your brother get?Assume your brother gets x number of chocolates.
Then, you will get - x + 5.
Therefore -
x + x + 6 = 20
2x = 14
x = 7
According to the question -
Assume that Wendy receives $x.
Then Jon will receive $(x - 2500).
Then -
x + x - 2500 = 15000
2x = 17500
x = 8750
Hence, Wendy will get $8750.
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IS THIS TRUE OR FALSE
A dilation is a function because every point on the pre-image corresponds to exactly one point on the image.
Polygons QRST and Q’R’S’T’ are shown on the coordinate grid: A coordinate plane with two polygons is shown. Polygon QRST has vertices Q at 3 comma negative 5, R at 2 comma negative 1, S at 5 comma 0, and T at 5 comma negative 4. Polygon Q prime R prime S prime T prime has vertices at Q prime negative 5 comma negative 4, R prime at negative 1 comma negative 3, S prime at 0 comma negative 6, and T prime at negative 4 comma negative 6. What set of transformations is performed on QRST to form Q’R’S’T’? A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the right A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin
The transformation performed on QRST to form Q'R'S'T' is a 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left.
Explanation:The transformation of the polygon QRST to Q’R’S’T’ involves a series of steps. To determine these steps, we look at the movement of each vertex from the original polygon to the new. The coordinates of Q change from (3, -5) in QRST to (-5, -4) in Q'R'S'T'. This signifies a 180-degree clockwise rotation about the origin followed by a translation. Given the options, the answer is ‘A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left.’
Let's walk through how this works: The rotation leaves us with points Q at (-3, 5), R at (-2, 1), S at (-5, 0) and T at (-5, 4). The translation of 1 unit to left then changes these coordinates to Q' at (-4, 5), R' at (-3, 1), S' at (-6, 0), and T' at (-6, 4), hence matching the given coordinates of Q'R'S'T'.
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Which of the following inequalities is equivalent to 8 ≤ x.
Answer:
The answer is D
Step-by-step explanation:
(3a3 − 5b3) + a3 + b3 = (a3 + b3).
Answer:
-2
6
Step-by-step explanation:
Is this function even, odd, or neither?
Answer:
The given function is neither even nor odd.
Step-by-step explanation:
A function is an even function if
[tex]f(-x)=f(x)[/tex]
A function is an odd function if
[tex]f(-x)=-f(x)[/tex]
From the given graph it is clear that graph is passing though the points (-3,2), (-1,2), (0,1/2), (1/2,0), (1,-1), (2,-1) and (3,1).
Here,
[tex]f(3)=1[/tex]
[tex]f(-3)=2[/tex]
[tex]f(-3)\neq f(3)[/tex] and [tex]f(-3)\neq -f(3)[/tex]
Since [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], therefore the given function is neither even nor odd.
Leia is operating a digital spinner game in which a player spins an arrow and is given a prize based on where the spinner lands. Leia can program the probability of each of the outcomes. The stuffed teddy bear is the best prize, so she programs the spinner so that the probability of not getting a bear twice in a row is greater than 3 times the probability of getting the teddy bear in one spin.
Write an inequality that compares the probability of getting the teddy bear to the probability of not getting the teddy bear, using p to represent the probability of getting the teddy bear in one try.
In the problem, we are given that the probability of getting a bear is equal to p. Where probability is the share of successful outcome in this case is the bear) over total outcomes (total amount of prizes).
The likelihood of not receiving a bear two times in a row is containing of 2 tries:
try 1: 1st spin gets a bear, 2nd spin does not receive a bear
total probability of try 1 = p * (1 – p)
try 2: 1st spin does not get a bear, 2nd spin gets a bear
total probability of try 1 = (1 – p) * p
The total probability of the 2 tries is just the sum of the 2:
Overall probability of not getting a bear twice in a row= p * (1 – p) + (1 – p) * p
Simplifying this will give us:
Overall probability of not getting a bear twice in a row = 2p * (1 – p)
Therefore, the likelihood of not receiving a bear twice in a row > 3 times the probability of getting the teddy bear. Rewriting the statement, will give us the inequality of 2p * (1 – p) > 3 p
To compare the probability of getting the teddy bear to the probability of not getting the teddy bear, use the inequality p^2 + 3p - 1 < 0.
Explanation:To write an inequality that compares the probability of getting the teddy bear to the probability of not getting the teddy bear, we can use the inequality sign. Let's represent the probability of getting the teddy bear in one try as 'p'. Since we want the probability of not getting a bear twice in a row to be greater than 3 times the probability of getting the teddy bear in one spin, we can write the inequality as:
1 - p * p > 3p
Simplifying the inequality, we get:
1 - p^2 > 3p
Then, rearranging the terms, we get:
p^2 + 3p - 1 < 0
This is the inequality that compares the probability of getting the teddy bear to the probability of not getting the teddy bear.
Identify the segment bisector of JK
Answer:
A segment whose length is 9 units.
Step-by-step explanation:
A segment whose length is 9 units.
All we have is a bisection that divides equally segment JK in two parts. And M is the Midpoint what reassures us that JM=MK, so plugging in:
3x+15=8x+25
3x-8x=25-15
-5x=10
5x=-10
x=-2
JM=3(-2)+15 =9
MK=8(-2)+25=9
Answer:
Step-by-step explanation:
Select the graph of the solution. Click until the correct graph appears. 3x + 1 < 7 (line graph)
The solution of the inequality [tex]3x + 1 < 7[/tex] is [tex]\boxed{x < 2}.[/tex]
Further explanation:
There are two types of the interval close interval and open interval.
If the values of [tex]\text{x}[/tex] doesn’t includes the number than it is represented by hollow dot on the number line and if the values of [tex]\text{x}[/tex] includes the number than it is represented by the solid dot on the number line.
Given:
The inequality is [tex]3x + 1 < 7.[/tex]
Explanation:
The given inequality is [tex]3x + 1 < 7.[/tex]
Subtract 1 from both side of the inequality.
[tex]\begin{aligned}3x + 1 - 1 &< 7 - 1\\3x &< 6\\\end{aligned}[/tex]
Now divide both sides by 3.
[tex]\begin{aligned}\frac{{3x}}{3} &< \frac{6}{3}\\x&< 2\\\end{aligned}[/tex]
The solution of the inequality [tex]3x + 1 < 7[/tex] is [tex]\boxed{x < 2}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Compound inequalities
Keywords: solution, [tex]3x + 1 < 7[/tex], inequalities, graph, compound inequality, graph representation, number line, close interval, open interval, line graph.
A boat takes 3.6 h to travel downstream from its dock to a fishing hole. If the water were still, it would have taken 4.5 h to make the trip. Let x represent the speed of the boat and let y represent the speed of the water.
(a) Write an expression for the distance traveled in moving water, using 3.6 h for the time. Then write an expression for the distance traveled as if in still water, using 4.5 h for the time.
(b) Set the expressions in Part (a) equal to each other. Then solve the equation for y. Show your work.
(c) What percent of the boat’s speed is the water current?
In a cafeteria, there are the same number of 3-legged stools as there are of 4-legged chairs. If stools have 120 fewer legs than chairs, how many people can sit in this cafeteria?
The cafeteria can seat 120 people.
Let's denote the number of 3-legged stools as S and the number of 4-legged chairs as C. According to the problem, there are the same number of stools and chairs, so we have:
S = C
Next, we are told that the stools have 120 fewer legs than the chairs. Since each stool has 3 legs and each chair has 4 legs, we can set up the following equation:
3S + 120 = 4C
Since S = C, we can substitute C for S in the equation:
3C + 120 = 4C
Now, let's solve for C:
120 = 4C - 3C
120 = C
Now that we know there are 120 chairs, and since the number of stools is the same as the number of chairs, there are also 120 stools. Each chair can seat one person, and each stool can also seat one person, so the total number of people that can be seated is the sum of the number of chairs and stools:
Total seating = C + S
Total seating = 120 + 120
Total seating = 240
However, since there are only 120 chairs and 120 stools, and we cannot have half a piece of furniture, the maximum number of people that can be seated is the number of chairs or stools, which is:
Total seating = 120
Therefore, the cafeteria can seat 120 people.
Solve for x. 9≤17−4x Enter your answer, as an inequality, in the box.
The first thing you need to do is get rid of the 17 to leave -4x isolated..
so subtract -17 from 9 = -8 ≤-4x divide -4 from both sides = x≤2
Both equations in a system of linear equations have y-intercepts at (0,2). is it possible for this system to have only one solution?
Both equations in a system of linear equations have y-intercepts at (0,2) but it is not possible for this system to have only one solution because it depends on another point as well.
Given :
Both equations in a system of linear equations have y-intercepts at (0,2).
The following steps can be used in order to determine the system have only one solution or not:
Step 1 - According to the given data, both equations in a system of linear equations have y-intercepts at (0,2).
Step 2 - The equation of a line is given by:
[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Step 3 - From the above steps, it can be concluded that it does not say that the system to have only one solution because it depends on another point as well.
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Suppose you had d dollars in your bank account. You spent $22 but have at least $28 left. How much money did you have initially? Write and solve an inequality that represents this situation.
A) d + 22 ≤ 28; d ≤ 72
B) d – 22 > 28; d > 50
C) d + 22 ≥ 28; d ≥ 72
D) d – 22 ≥ 28;d ≥ 50
Answer:
D) d – 22 ≥ 28;d ≥ 50
Step-by-step explanation:
Let d represents the initial money ( in dollars ) in the account,
So, after spending $ 22 the remaining amount = initial amount - $ 22 = (d-22) dollars,
According to the question,
The remaining amount ≥ $ 28
⇒ d - 22 ≥ 28
Adding 22 on both sides, ( additive property of inequality ),
⇒ d ≥ 50
Hence, the required inequality and its solution would be,
d - 22 ≥ 28; d ≥ 50
Option 'D' is correct.
What affect does "h" have on the parent function y = 1/x ?
h < 0 moves the graph to the left, h > 0 moves the graph to the right.
Vertical stretch by a factor of |h|
h > 0 moves the graph up, h < 0 moves the graph down.
h > 0 reflects the graph across the y-axis.
Suppose that a number written as a decimal has an infinite number of non–repeating digits after the decimal point. what is this number called?
When a number has an infinite number of non-repeating digits, which is called a non-terminating decimal value, then such number is an irrational number such as 1.3127...
Irrational number are real numbers which cannot be expressed in the form of p/q ; that is they cannot be expressed accurately as a ratio.They are characterized as having repeating decimal values as well as non-terminating decimal digits. When a number has unending or infinite number of non-repeating digits, it is said to be non-terminating, hence, such number is called an irrational number.
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Should your calculator be in radians or degrees for physics
The gas tank in Ms. Brown's car holds a total of 15 gallons. At any given time, how many gallons, g, will Ms. Brown have to pump into her car to fill her tank given the fraction of the tank,f, already filled?
A. g = 15f
B. g = f15/f
C. g = 15−15f
D. g = 15-15/f
Answer:
c cause i took the sat practice
The number of gallons (g) that Ms. Brown have to pump into her car to fill her tank will be g = 15 – 15f. Then the correct option is C.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The gas tank in Ms. Brown's car holds a total of 15 gallons.
At any given time.
The number of gallons (g) that Ms. Brown have to pump into her car to fill her tank given the fraction of the tank, f, already filled will be
The gas in a tank will be
⇒ 15f
Then number of gallons (g) will be
⇒ 15 – 15f
Then the correct option is C.
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20 P[OINTS!!!!!! ppppppllllllllllleeeeeeeeeeeeeeeaaaaaaaassssssseee help asap!!!!!!!
A quadrilateral is shown on the graph:
What effect will a reflection about the x-axis have on the quadrilateral? Be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image.
Answer:
The angles and side length would remain the same, the only thing that would change is the cornents, therefore the original pre image and the image would be congruent.
Step-by-step explanation:
What is 187.023 in word form