Answer:
x³ + 4x² + 3x + 1
Step-by-step explanation:
fg(x) + f(x)
= x³ + 4x² + 3x + 1
Which expression are equivalent when y=2 and y=5
The equivalent expressions when y = 2 and y = 5 are the expressions that have the same numeric value when y = 2 and when y = 5.
What are equivalent expressions?Equivalent expressions are expressions that have the same numeric value.
Hence, the equivalent expressions when y = 2 and y = 5 have the same value when y = 2 and y = 5.
This numeric value is calculated replacing each instance of y by 2 when y = 2 and each instance of y by 5 when y = 5.
For example:
2y + 3 at y = 2: 2(2) + 3 = 7.2y + 3 at y = 5: 2(5) + 3 = 13.Different numeric values, hence not equivalent, just an example as to how you should proceed.
You will do this for all expressions, and when you find equal values for y = 2 and for y = 5, then they will be equivalent.
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What is the slope of a line that is perpendicular to a line represented by the equation 6y=−7x+4?
Enter your answer, as a fraction in simplest form, in the box.
The slope of the line that is perpendicular 6y=−7x+4 is: 6/7.
What are the Slopes of Perpendicular Lines?If one line has a slope of a/b, the slope of the line that is perpendicular to the line would be the negative reciprocal of a/b, which is -b/a.
If the slopes of perpendicular lines are multiplied together, for example (a/b)(-b/a), we would always have a result of -1.
Rewrite the equation 6y = −7x + 4 in slope-intercept form as y = mx + b, in other to determine the value of m = slope.
6y/6 = −7x/6 + 4/6
y = −7/6x + 2/3
The slope of 6y = −7x + 4 is -7/6. 6/7 is the negative reciprocal of -7/6. Therefore, the slope of the perpendicular line is: 6/7.
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A wise man once said, "300 reduced by 3 times my age is 84." What is his age?
Answer:72
Step-by-step explanation:
Can a triangle have sides with the given lengths?a2 in, 4 in, 6 inYesNo
In general, if the sides of a triangle are a, b, and c, they must satisfy the inequalities below
[tex]\begin{gathered} a,b,c\rightarrow\text{ sides of a triangle''} \\ \Rightarrow a+b>c \\ b+c>a \\ c+a>b \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} 2+4>6\Rightarrow6>6\rightarrow False \\ 4+6>2\Rightarrow10>2\rightarrow True \\ 6+2>4\Rightarrow8>4\rightarrow True \end{gathered}[/tex]The first inequality is false; thus, the triangle cannot exists. The answer is No.Which equation has no solution?
Answer:
1.)|4x-2|=-6
This eguation has not solution.
Answer:
the first one; absolute value cannot be negative
Step-by-step explanation:
|4x-2| = -6
add 2
|4x| = -4
divide 4 on both sides
x = -1
|4x-2| = 6
repeat the same steps
x = 2
PLEASE HELP ME ASAPPP
Sherry needs to sell T-shirts as a fundraiser for a charity. She starts with 40 T-shirts and begins selling at a constant rate of 5 T-shirts each day.
Use the Segment tool to plot a graph representing the number of T-shirts Sherry has left to sell from the time she begins selling until the T-shirts are gone.
Mrs. Harris has 5 blue, 8 red, 3 green, and 7 yellow candies in a bag. If Mrs. Harrisrandomly selects a candy, what is the probability she will select a yellow or blue candy?
Blue = 5
Red = 8
Green= 3
Yellow= 7
Total candles = 5+8+3+7 = 23
Yellow and blue candles = 7+5 = 12
To find the probability divide the number of blue and yellow candles (12) by the total number of candles.
12/23 = 0.52
2. Kieran, Jermaine and Chris play football. Kieran scored 8 more goals than Chris Jermaine scored 5 more goals than Kieran. Altogether they have scored 72 goals. How many goals did they each score?
Answer:
Step-by-step explanation:
k = x+8
c= x+5
j= x+5
3x+18=72
x = 18
Chris = 23
Kieran = 26
Jermaine = 23
Answer:
Chris = 17 goals
Kieran = 25 goals, and
Jermaine = 30 goals
Step-by-step explanation:
Let K, J, and C stand for the goals scored by Kieran, Jermaine, and Chris, respectively.
We learn that:
K = C + 8 [Kieran scored 8 more goals than Chris]
J = K + 5 [Jermaine scored 5 more goals than Kieran]
K + J + C = 72 [Altogether they have scored 72 goals]
-----
We have 3 equations and 3 unknowns. Therefore, we should be able to find a solution by rearranging and substituting.
Let's start with K + J + C = 72 and find ways to eliminate two of the three variables.
We can substitute for K since K = C + 8
K + J + C = 72
(C+8) + J + C = 72
Rearrange:
2C+8 + J = 72
We can also substitute for J since J = K + 5
2C+8 + J = 72
2C+8 + (K + 5) = 72
Again, we can substitute for K since (K = C + 8)
2C+8 + (C+8) + 5 = 72
2C+8 + (C+8) + 5 = 72
3C +21 = 72
3C = 51
C = 17
---
Since C = 17, we can find K with K = C + 8
K = C + 8
K = 17 + 8
K = 25
---
Since K = 25, we can find J with J = K + 5
J = K + 5
J = 25 + 5
J = 30
===
We find:
C (Chris) = 17 goals
K (Kieran) = 25 goals, and
J (Jermaine) = 30 goals
17 + 25 + 30 = 62 total goals.
how do you factor the polynomial expression 16y4-625x4
We have the following:
[tex]16y^4-625x^4[/tex]factoring:
[tex]\begin{gathered} (4y^2)^2-(25x^2)^2=\mleft(4y^2+25x^2\mright)\mleft(4y^2-25x^2\mright)=(4y^2+25x^2)\mleft(2y+5x\mright)\mleft(2y-5x\mright) \\ \end{gathered}[/tex]Therefore, the answer is:
[tex]\mleft(4y^2+25x^2\mright)\mleft(2y+5x\mright)\mleft(2y-5x\mright)[/tex]A 21-foot bean is to be cut into three pieces so that the second and third piece are each 3 times the length of the first piece. If x represents the length of the first piece, find the length of each piece
Answer: 3, 9, and 9
Step-by-step explanation:
X+3x+3x=217x=21x=33, 9, 9=21
Evaluate the function for the following values:
f(1) =
f(2)=
f(3) =
Answer: [tex]f(1)=1, f(2)=0, f(3)=2[/tex]
Step-by-step explanation:
[tex]0 \leq 0 \leq 1 \implies f(1)=1^2 =1\\\\1 < 1 \leq 2 \implies f(2)=-2+2=0\\\\2 < 3 \leq 3 \implies f(3)=3^2 -3(3)+2=2[/tex]
12. The length of one side of
a rectangle is
12cm.
The length of the diagnol of
the rectangle is 13cm
Calculate the area of the
rectangle
Answer :- 60 cm^2
Step-by-Step Solution :-
Let ABCD be the Rectangle.
Given :
AD = 12 cm
BD = 13 cm
To Find : Area of ABCD
Solution :
In ∆ADB,
AD = 12 cm and BD = 13 cm
By Pythagoras Theorem,
(BD)^2 = (AD)^2 + (AB)^2
13^2 = 12^2 + (AB)^2
169 = 144 + (AB)^2
AB^2 = 169 - 144 = 25
AB = √25
Therefore, AB = 5 cm
Now, to find the Area,
Area of Rectangle = length × breadth
Area of ABCD = 12 × 5
Therefore, Area of ABCD = 60 cm^2
find M angle one and M angle to justify your answers
Answer:
Step-by-step explanation:
13.
m1 is 120 because angle 120 and angle 1 are tranversal angle
So now we know that angles m1 and m2 are vertically opposite angle
Then m2 = 120
m1 = 120
m2 = 120
14.
angle 1 and 105 have the sum of 180 because they are Interior angles on the same side of the transversal
So angle 1 equals 180-105=75
angle 2 and angle 1 are on a line so the sum of the 2 angles are 180
So: 180 - 75 = 105
m1 = 105
m2 = 75
2. LeRoy purchased 6 gallons of gasoline for
$19.56. Which describes the constant of
proportionality?
A.
B.
C.
D.
$2.26 per gal
$3.26 per gal
$3.29 per gal
$3.39 per gal
Combine the like terms to create a equivalent expression -4r - 2r + 5
After combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.
As given in the question,
Given expression is equal to :
-4r -2r + 5
Now combine the like terms to get the equivalent expression we have,
Like terms of the given expression -4r -2r + 5 are -4r and -2r
( -4r -2r) +5
= -r (4+2) +5
= -6r +5
Equivalent expression of the given expression -4r -2r + 5 is -6r +5.
Therefore, after combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.
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The circle below is centered at (5,5). Use the graph to answer the following questions. please help!
Answer: I don't know why I'm here
Step-by-step explanation: help
Triangle STU, with vertices S(2,2), T(7,3), and U(5,6), is drawn inside a rectangle, as
shown below.
10
Answer: A =
A =
10
00
7
6
5
S
T
What is the area, in square units, of triangle STU?
10
units²
Submit Answer
The required area of triangle Δ STU would be 4 square units.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.
The given triangle Δ STU, with vertices S(2,2), T(7,3), and U(5,6), is drawn inside a rectangle.
The area of triangle Δ STU = rectangle ABCS - Δ ABS - Δ BTU - Δ STC
The area of triangle Δ STU = 4 × 5 - 1/2 × 3 × 4 - 1/2 × 5 × 1 - 1/2 × 3 × 2
The area of triangle Δ STU = 8/2
The area of triangle Δ STU = 4 square units
Hence, the required area of triangle Δ STU would be 4 square units.
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m(x) = 4x + 15 m(x) needs to be 7 x =
Answer:
x = -2
Step-by-step explanation:
If m(x) = 4x + 15 and m(x) = 7, the we can substitute and get the equation:
4x + 15 = 7
x = -2
does anyone know the answer?
ΔXYZ ≅ ΔUTV
The two angles of the non-included side of the triangle are congruent to the two sides and non-included sides of the second triangle, according to the AAS theorem.
What exactly is the AAS theorem?The AAS theorem is an angel, angle side theorem that states that two angles on any side of a triangle that are congruent to two angles on another triangle are said to be congruent.The triangles are congruent if two pairs of corresponding angles and the side between them are known to be congruent. This is known as the angle-side-angle shortcut. Angle-angle-side (AAS) is another shortcut in which two pairs of angles and the non-included side are known to be congruent.To learn more about congruent triangles refer to :
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Pls Help will give brainliest
Anita earns 60 points every time she shops at a grocery store. She needs a total of 2,580 points to receive a free prize. So far, she has earned 480 points. How many more times will Anita have to shop at the grocery store in order to earn the additional points she needs for a free prize?
Answer:
35Step-by-step explanation:
So she needs 2580 points
she has already earned 480, so let's subtract that
that leaves up with 2100 more points
she earns 60 points every shop
so lets divide 2100 by 60
2100÷60=
35
Anita will have to shop at the grocery store 35 more times to earn the additional points she needs for a free prize.Answer:
43 total ,35 more times need to get 2,580
Step-by-step explanation:
2580:60=43
60x8=480
43-8=35
if a child is 120cm tall, but they grow 4% bigger in a year, how tall will they be?
Answer
The height of the child in a year time = 124.8 cm
Explanation
The child is currently 120 cm tall.
The child grows 4% bigger in 1 year.
We now need to calculate how tall the child is in that 1 year.
New height for the child = (Current height) + (Increase in height)
Current height = 120 cm
Increase in height = 4% of 120 cm = 0.04 × 120 = 4.8 cm
New height for the child = (Current height) + (Increase in height)
= 120 + 4.8
= 124.8 cm
Hope this Helps!!!
£ represents a group of 20 people that visited paris for a weekend break. 8 of the group visited the eiffel tower (ET) 13 of the group visited the no tre-dame cathedral (NDC) 5 of the group did not visit either of these places a person is chosen at random from the group. what is the probability that this person only visited one of the two places?
The probability that this person choosen only visited one of the two places is 9/20
What is Probability?
Probability is a measure of the possibility that an event to occur.
The probability for an event to occur= Possible outcome /Total outcome
to get the possible out come we must Know the number of people that visited ET and NDC only.
using set theory;
if x is the no of people that visited both places then,
8-x =ET only
13-x= NDC only
5= none visited ET and NDC
x+13-x+8-x+5=20
collect like terms
26-x= 20
x =6
therefore ET only= 2
NDC only= 7
probability of ET = 2/20
probability of NDC= 7/20
therefore probability that the person chosen only visited one place = p(ET)+P(NDC)= 7/20+2/20
= 9/20
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Jimmy’s family moved to a tropical climate. For the year that followed, he recorded the number of days that had a temperature above 40 degrees C each month. His data contained -
1-8 is for the data set below
14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13 and 8
1) Find the mean for his data set of days that had a temperature above 40 degrees C.
2) Find the median for his data set of days that had a temperature above 40 degrees C.
3) Find the mode for his data set of days that had a temperature above 40 degrees C.
4) If, instead, there are 5 more days per month that had a temperature above 40 degrees C, what will be the mean for the data?
5) If, instead, there are 2 more days per month that had a temperature above 40 degrees C, what will be the mode for the data?
6) If the number of days per month that had a temperature above 40 degrees C, doubles each month in that year, what will be the median for the data?
7) For what value of x will 9, 16 and x have the same mean (average) as that of 26 and 12?
8) For what value of x will 55 and x have the mean (average) as 67?
9) The mean (average) weight of three boys is 40 pounds. One of the boys weighs 50 pounds. The other two boys have the same weight. Find weight of each of the boys?
10) A cat consumes 2 cups of milk every day. How much milk does that cat drink on an average in a week?
11) What is mode for above question?
The mean, median and mode are as follows:
1. 11.75
2. 11.5
3. 11 and 14
4. 16.75
5. 13 and 16
6. 23
7. 32
8. 79
9. 35
10. 14
11. 2
What are mean, median and mode ?The three measures of central tendency used in statistics are mean, median, and mode. While describing a set of data, we always specify the focal point of any data set. The measure of central tendency is this. Every day, data are presented to us. We discover them in books, articles, bank statements, phone and utility bills, as well as in newspapers. There are so many; they are all around us. The challenge now is if we can identify some key characteristics of the data by focusing on only a few data points. The means, medians, and modes—measures of central tendency or averages—can be used to do this. When describing a set of data, a measure of central tendency locates the set's center.
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Factor completely... Please help me with this
Answer: (5x - 1)(x + 9)
Step-by-step explanation:
Please note the method of factoring may differ per class, but this is how I was taught.
First, we will multiply the coefficient of x² by the constant.
5 * -9 = -45
Next, we will find two numbers that add up to 44 (coefficient of x) and multiply to -45 (the number we got above).
-1 * 45 = 45
-1 + 45 = 44
-1 and 45 ✓
Now, we can start to factor. First, we will rewrite 44x.
5x² + 45x - 1x - 9
Then, we will factor by grouping.
5x(x + 9) -1(x + 9) ➜ (5x - 1)(x + 9)
The completely factored form is:
(5x - 1)(x + 9)
What did I do wrong?
YOU DID NOTHING WRONG ACCORDING TO WHAT YOU WROTE
[tex]2d = f - e \\ \frac{2d}{2} = \frac{f}{2} - \frac{e}{2} \\ d = \frac{f}{2} - \frac{e}{2} [/tex]
RATHER MAYBE IT'S BECAUSE THEY WANT YOU TO WRITE IT IN THIS FORM.
TRY IT THIS WAY
There were 48,500 people at an amusement park on Monday. Forty two percent of the people wanted to ride the new roller coaster. Twenty-three percent of those people decided not to ride the coaster because the line was too long. About how many people waited in line for the new roller coaster that day?
Estimate the percent of a number
( with steps)
The people who waited in line for the new roller coaster that day is 9215?
How to calculate the value?From the information, forty two percent of the people wanted to ride the new roller coaster and twenty-three percent of those people decided not to ride the coaster because the line was too long.
The percentage of those who waited will be:
= 42% - 23%
= 19%
Since there were 48,500 people at an amusement park on Monday, those who waited will be:
= Percentage × Total number
= 19% × 48,500
= 9215
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Expand 3(x - 1)(x + 4) and simplify.
Answer:
3x2-11x-4
Step-by-step explanation:
5. Paetyn is going rock climbing. She starts at 12-yards
above sea level. She ascends 38-yards before lunch. She
descends 15-yards after lunch. What is Paetyn's final height
relative to sea level?
Answer:
35 yards above sea level
Step-by-step explanation:
12 + 38 - 15
50 - 15
35
Find f(0) and find one value of x for which f(x)=-3
given the graph
the point f(0) (x=0) is given at y=-4
then
f(0)= - 4
the point f(x) = -3 (y=-3) is given when x = -1
then
the value of x for which f(x)=-3: -1
If g(x) = 4x + 3 and h(x) = 2x + 5, find g(h(x)) and g(h(0)).
(Show your work here)
Pls helppp I’d rly appreciate it!
Answer:
(4x + 3)(2x + 5)
4x(2x + 5) +3(2x + 5)
8x^2 +20x +6x + 15
8x^2 +26x + 15
so, g(h(x))=8x^2 +26x +15
again
(4x + 3)(2x +5).0
0
so, g(h(0))=0