Define a function f : R → R by the formula
f(x) = 2x − 8.
Prove that f is one-to-one.
Let a, b is in R, and suppose that
f(a) = f(b).
Then
2a − 8 =
What is the measure of angle 4?
Number 8 please it will help a lot
In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
what is 1 and 6/24 simplified as ?
2n2-24n+72 factor completely
Suppose you buy a movie for $12.98 the sales tax is 6% find the total cost
Choose the system of equations which matches the following graph:
A. 5x - y = 7
2x - y = 0
B. 5x - y = 7
2x + y = 0
C. 5x + y = -7
2x + y = 0
D. 5x + y = -7
2x - y = 0
Answer:
Option B : [tex]5x - y = 7[/tex]
[tex]2x + y = 0[/tex]
Step-by-step explanation:
Intersecting point on the graph = (1,-2)
Substitute this point in the given options .
A. [tex]5x - y = 7[/tex]
[tex]2x - y = 0[/tex]
Substitute (1,-2)
[tex]5(1) - (-2) = 7[/tex] and [tex]2(1) -(-2) = 0[/tex]
[tex]7 = 7[/tex] and [tex]4 \neq 0[/tex]
So, this system of equations does not matches the graph.
B. [tex]5x - y = 7[/tex]
[tex]2x + y = 0[/tex]
Substitute (1,-2)
[tex]5(1) - (-2) = 7[/tex] and [tex]2(1)+(-2) = 0[/tex]
[tex]7 = 7[/tex] and [tex]0= 0[/tex]
So, this system of equations matches the graph.
C.[tex]5x + y = -7[/tex]
[tex]2x + y = 0[/tex]
Substitute (1,-2)
[tex]5(1) - (-2) = -7[/tex] and [tex]2(1)+(-2) = 0[/tex]
[tex]7\neq -7[/tex] and [tex]0= 0[/tex]
So, this system of equations does not matches the graph.
D. [tex]5x + y = -7[/tex]
[tex]2x - y = 0[/tex]
Substitute (1,-2)
[tex]5(1) - (-2) = -7[/tex] and [tex]2(1) -(-2) = 0[/tex]
[tex]7\neq -7[/tex] and [tex]4 \neq 0[/tex]
So, this system of equations does not matches the graph.
Answer:
B. 5x - y = 7
2x + y = 0
Step-by-step explanation:
took test
An architect plans to make a drawing of the room of a house. The segment LM represents the ceiling of the room. He wants to construct a line passing through Q and perpendicular to side LM to represent a wall of the room. He uses a straightedge and compass to complete some steps of the construction, as shown below:
NEED HELP!!! 80 POINTS! (sike)
At the airport, ten people are waiting on standby. Two seats become available, one first class and one coach. How many ways are there to fill the two seats?
A. 10
B. 20
C. 45
D. 90
1st seat there are 10 people so 10 different ways to fill it
2nd set there are 9 people left so 9 different ways to fill it
10 x 9 = 90
there are 90 ways to fill the seats
Answer:
d. 90
Step-by-step explanation:
A regular pentagonal prism has a height of 14 in. and a base edge length of 10 in. Identify its lateral area and surface area.
Can anyone help me solve this?
Answer:
L = 700 in2 ; S = 1044.1 in2
Step-by-step explanation:
Lucky guess :)
I WILL GIVE BRAINLIEST please answer both parts
If 365 work days are split among 12 employees evenly
PART: A How can you rewrite this as a fraction?
PART:B What does the fraction represent?
a pair of jeans cost 75% as much as a pair of corduroy pants what is the cost of each if the total cost for the jeans and courds is $42
j= jeans
c= corduroy
jeans = 0.75C
0.75 +c = 42
1.75c = 42
c = 42/1.75 = 24
jeans cost 24*0.75 = 18
corduroys cost $24
Jeans cost $18
Answer with Step-by-step explanation:
Let j denote the cost of jeans
and c denotes the cost of corduroy
A pair of jeans cost 75% as much as a pair of corduroy pants.
i.e. j = 0.75c
The total cost for the jeans and corduroy is $42
i.e. j+c=42
⇒ 0.75c+c=42
⇒ 1.75c=42
Dividing both sides by 1.75,we get
c=24
Putting value of c in j= 0.75c gives
j=18
Hence, Cost of jeans=$18
and cost of corduroy=$24
Jeff takes 20 mins to jog around the race course one time. And 25 mins to jog arpund second time. What is his average speed in kms per hr fpr the whole jog if the course is 3 kms long?
Jessie received the following scores on her math tests this year. (45, 65, 70, 80, 85, 100) Suppose the teacher removes the lowest and highest scores. (65, 70, 80, 85) What are the interquartile ranges of Jessie’s original scores and her new scores?
Answer:
Interquartile ranges of Jessie’s original scores = 20
Interquartile ranges of Jessie’s new scores = 15
Step-by-step explanation:
Interquartile range IQR = Higher quartile (Q3) - lower quartile (Q1)
Where Q3 is the mid-value of the second half of a dataset and
Q1 is the mid-value of the first half of a dataset.
Original score = 45, 65, 70, 80, 85, 100
Q1 of original score:
First half of original score = 45, 65, 70
Therefore Q1 = 65
Q3 of original score:
Second half of original score = 80, 85, 100
Therefore Q3 = 85
:. Interquartile range IQR of original score = Q3 of original score - Q1 of original score
:. IQR = 85 - 65 = 20
New score = 65, 70, 80, 85
Q1 of new score:
First half of new score = 65, 70
Therefore Q1 = (65+70)/2 = 67.5
Q3 of new score:
Second half of new score = 80, 85
Therefore Q3 = (80 + 85)/2 = 82.5
:. Interquartile range IQR of new score = Q3 of new score - Q1 of new score
:. IQR = 82.5 - 67.5 = 15
Therefore:
Interquartile ranges of Jessie’s original scores = 20
Interquartile ranges of Jessie’s new scores = 15
If T is the point at a distance 3pi/5 from P(1, 0) on the unit circle with its center at (0, 0), in what quadrant does T lie?
Final answer:
The point T lies in the second quadrant of the unit circle when it is at an angular distance of 3π/5 from P(1, 0), because this angle falls between π/2 and π radians.
Explanation:
If T is the point at a distance 3π/5 from point P(1, 0) on the unit circle with its center at (0, 0), to determine in what quadrant T lies, we must consider where this angle places T on the unit circle.
Recall that a point on the unit circle has coordinates (x, y) = (cos θ, sin θ), where θ is the angle measured counterclockwise from the x-axis. An angle of 3π/5 radians is more than π/2 radians but fewer than π radians. Therefore, it falls in the second quadrant of the unit circle, where x-coordinates are negative and y-coordinates are positive.
Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4)?
A pudding recipe makes 4 1/2 cups of pudding. How many 1/3 cup servings does this equal?
4 1/2 cups = 9/2 cups
9/2 / 1/3=
9/2 * 3/1 = 27/2 = 13 1/2 servings at 1/3 cup each
Answer:
13 1/2
Step-by-step explanation:Just trust
Determine the sign of cos pi divided by seven without using a calculator.
Answer:
The [tex]\cos \frac{\pi}{7}[/tex] has positive sign.
Step-by-step explanation:
we need to determine the sign of [tex]\cos \frac{\pi}{7}[/tex] without using calculator
Cartesian system ( shown in figure -1)
The angle [tex]\cos \frac{\pi}{7}[/tex] lies in quadrant-1 , Where angles are zero (0) to [tex]\frac{\pi}{2}[/tex]
and in first quadrant all trigonometric ratios has positive sign
so, [tex]\cos \frac{\pi}{7}[/tex] has positive sign.
How to show numbers are related to each other
Three-fourths of the yard is covered in grass but 4/5 of the grass has died. How much of the yard has dead grass?
multiply the 2 together:
3/4 x 4/5 = 12/20 = 3/5 has dead grass
To find the area of the yard that has dead grass, multiply three-fourths (the grassy area) by 4/5 (the dead portion). Simplifying (3/4) × (4/5) gives us 3/5, which means 3/5 of the yard has dead grass.
To determine how much of the yard has dead grass, we need to calculate the portion of the yard covered in grass and then the fraction of it that has died. Given that three-fourths of the yard is covered in grass, we represent this as 3/4. It is known that 4/5 of this grass has died, hence we multiply the two fractions: (3/4) × (4/5).
Performing the multiplication of these two fractions:
Multiply the numerators: 3 × 4 = 12.Multiply the denominators: 4 × 5 = 20.Combine the products to form the new fraction: 12/20.Now, simplify the fraction 12/20 by dividing both the numerator and denominator by their greatest common divisor, which is 4:
Divide the numerator: 12 ÷ 4 = 3.Divide the denominator: 20 ÷ 4 = 5.The simplified fraction is 3/5.Therefore, the correct answer is that 3/5 of the yard has dead grass.
Use the Distributive Property to simplify each expression:
6(a + 10)
(5 + w)5
14(4f - 8)
2.1(5w -15)
0(3.7x - 4.21)
-(-m + n + 1)
6a + 60
5w + 25
56 f - 122
10.5 w - 31.5
0
m - n -1
Which expression is equal to 7(1+3)
A.) 7+21
B.) 7+3
C.) 1+21
D.) 7+4
I would say D. 7+4 because it is the only one that makes since to me
Which equation can be used to calculate the area of the shaded triangle in the figure below? A rectangle is shown with a width of 8 ft and a length of 14 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey. 2(14 + 8) = 44 square feet 1 over 2.(14 + 8) = 11 square feet 2(14 × 8) = 224 square feet 1 over 2.(14 × 8) = 56 square feet
Answer:
D) 1 over 2. (14 × 8) = 56 square feet
Step-by-step explanation:
You first need to look at the w x h formula (width x height).
W= 14
H= 8
14 x 8= 112
Then, you have to divide 112 by 2. The reason why is because 112 is the area of the whole rectangle, but you only need the area to the triangle, which is half of the rectangle.
112 ÷ 2= 56 sq. ft.
Therefore, the answer is D. Hope this helped!! <3
Six less then two thirds of a number is negative ten what is the number
2/3X-6 = -10
2/3x = -4
x = -4 / 2/3 = -6
X = -6
check:
2/3(-6) - 6 = -4 -6 = -10 TRUE
The table shows the number of students in a school who like dodgeball and/or ping pong:
Like Dodgeball
Do Not Like Dodgeball
Total
Like Ping Pong
26
18
44
Do Not Like Ping Pong
24
32
56
Total
50
50
100
What is the relative frequency, by row, of students who like both dodgeball and ping pong?
0.22
0.40
0.48
0.59
PLEASE HELP !!!
Answer:
0.59
Step-by-step explanation:
Find the area of the parallelogram shown below
What is the sine value of pi over 6?
Answer:
The sine value of pi over 6 is:
[tex]\dfrac{1}{2}[/tex] or 0.5
Step-by-step explanation:
we have to find the value of [tex]sin\dfrac{\pi}{6}[/tex]
we know that value of [tex]sin\dfrac{\pi}{6}[/tex] is [tex]\dfrac{1}{2}[/tex]
Hence, the sine value of pi over 6 is:
[tex]\dfrac{1}{2}[/tex] or 0.5
5b-2=13 what does b equal
5b-2=13
add 2 to both sides
5b=15
divide both sides by 5
b = 15/5 = 3
b=3
The singing club keeps sheet music in files. Each file holds 12 sheets. Of all the club's music, 2/3 fit into 3 files. How many sheets of music does the club have?
The singing club has a total of 36 sheets of music.
Explanation:To find the total number of sheets of music the club has, we can set up a proportion using the given information. Since 2/3 of the club's music fits into 3 files, this means that 1/3 of the music fits into 1 file. So, if 1/3 represents 12 sheets, then 1 represents 12 * 3 = 36 sheets. Therefore, the club has a total of 36 sheets of music.
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