Answer:
first 10 of 5
5 10 15 20 25 30 35 40 45 50
First 10 of 6
6 12 18 24 30 36 42 48 54 60
Step-by-step explanation:
Just add 5 to 5 and that is your next multiple then keep going 10 time and same thing for 6.
write a polynomial function, p(x) with degree 3 that has p(7)=0
Answer:
[tex]p (x) = x^{3} - 21x^{2}+ 147x - 343[/tex]
is the required polynomial with degree 3 and p ( 7 ) = 0
Step-by-step explanation:
Given:
p ( 7 ) = 0
To Find:
p ( x ) = ?
Solution:
Given p ( 7 ) = 0 that means substituting 7 in the polynomial function will get the value of the polynomial as 0.
Therefore zero's of the polynomial is seven i.e 7
Degree : Highest raise to power in the polynomial is the degree of the polynomial
We have the identity,
[tex](a -b)^{3} = a^{3}-3a^{2}b +3ab^{2} - b^{3}[/tex]
Take a = x
b = 7
Substitute in the identity we get
[tex](x -7)^{3} = x^{3}-3x^{2}(7) +3x(7)^{2} - 7^{3}\\(x -7)^{3} = x^{3}-21x^{2} +147x - 343[/tex]
Which is the required Polynomial function in degree 3 and if we substitute 7 in the polynomial function will get the value of the polynomial function zero.
p ( 7 ) = 7³ - 21×7² + 147×7 - 7³
p ( 7 ) = 0
[tex]p (x) = x^{3} - 21x^{2}+ 147x - 343[/tex]
A polynomial function with degree 3 and P(7)=0 can be written as p(x) = a(x - 7)(x - r2)(x - r3), where r2 and r3 can be any real number and a is any non-zero real number.
Explanation:The student has asked for a polynomial function with a degree of 3 such that P(7) equals 0. By definition, a polynomial function of degree n with given roots can be written as:
p(x) = a(x - r1)(x - r2)... (x - rn)
Since we have been given that P(7)=0 , we can choose 7 as one root, but the other roots can be chosen arbitrarily. So, we can create a polynomial function like below:
p(x) = a(x - 7)(x - r2)(x - r3)
Where r2 and r3 can be any real number and a is any non-zero real number. For example, if we choose r2=1, r3=2 and a=1. The function would be:
p(x) = 1*(x - 7)(x - 1)(x - 2) = ([tex]x^3 - 10x^2[/tex] + 29x - 14)
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Lester needs to add 2/3 of a cup of flour. He only has a 1/3 cup measure. How many scoops of flour does Lester need to add
Answer:
2 scoops
Step-by-step explanation:
Lester needs to add 2 scoops of flour of 1/3 cup measure.
We have Lester who needs to add 2/3 of a cup of flour but he only has a 1/3 cup measure.
We have to find out how many scoops of flour does Lester need to add.
A guy named Bruce wants a total of 100 grams of Protein powder in the bowl. He only has a 10 grams cup to measure and add. How many scoops of powder he need to add?Assume the number of scoops = x
Then -
10x = 100
x = 10
According to question, we have -
Amount of flour needed by Lester = 2/3
Size of Cup measure = 1/3
Assume that the the number of scoops of protein powder be y.
Then -
[tex]\frac{y}{3} = \frac{2}{3} \\\\y = \frac{2}{3} \times 3\\\\[/tex]
y = 2
Hence, Lester needs to add 2 scoops of flour 1/3 cup measure.
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Mr. Thaxton has two daughters. The sum of their ages is twenty-one. The product of their ages is one hundred ten. How old is Mr. Thaxton's youngest daughter?
A.
9
B.
10
C.
11
D.
12
Answer:
B. 10
Step-by-step explanation:
x + y = 21
xy = 110
Rewrite first equation. x + y = 21 becomes y = -x + 21
Now substitute this new equation in the second equation.
x(-x+21) = 110
-x^2 + 21x - 110
Divide by -1
x^2 - 21x + 110
(x - 10)(x - 11)
x = 10, 11
10 is less, so the youngest daughter is 10
Use sigma notation to represent the sum of the first six terms of the following sequence: −10, −13, −16, …
Sigma notation of sequence −10, −13, −16, … is [tex]\sum_{n=1}^{6}-(3 n+7)[/tex]
Solution:Need to determine the sigma notation for the following sequence
−10, −13, −16, …
Let's try to build a generic formula for given sequence
The given sequence is in Arithmetic progression where first term = -10 and common difference = -3
The formula for arithmetic progression is given as:
[tex]a_n = a_1 + (n - 1)d[/tex]
Where,
[tex]a_n[/tex] is the nth term in the sequence
[tex]a_1[/tex] is the first term in the sequence
d is the common difference between the terms
Here in this sequence [tex]a_1[/tex] = -10 and d = -3
[tex]a_n = -10 + (n - 1)(-3)\\\\a_n = -10 - 3n + 3\\\\a_n = -3n - 7[/tex]
So generic formula for a term is – ( 3n + 7 )
[tex]\begin{array}{l}{\text { For } \mathrm{n}=1, \text { term is }-(3 \times 1+7)=-10} \\\\ {\text { For } \mathrm{n}=2, \text { term is }-(3 \times 2+7)=-13} \\\\ {\text { For } \mathrm{n}=3, \text { term is }-(3 \times 3+7)=-16}\end{array}[/tex]
And so on
Using sigma notation for arithmetic sequence:
[tex]\sum_{k=1}^{n} a_{k}[/tex]
So for first six terms value of n will vary from 1 to 6 and in sigma notation it can be represented as
[tex]\sum_{n=1}^{6}-(3 n+7)[/tex]
x^2=3x+3 in standard form
Answer:
x^2-3x-3=0
Step-by-step explanation:
x^2=3x+3
x^2-3x-3=0
the relationship between the distance run and the time for kofi can be represented by the equation y= 15.55x , where he ran y yards in x seconds which two equations could be used to represent this relationship for bella and elsie
Answer:
D
Step-by-step explanation:
The line representing Bella has a steeper slope than Kofi's, so the slope of that line must be greater than 15.55.
Similarly, the line representing Elsie has a shallower slope than Kofi's, so the slope of that line must be less than 15.55.
The only option that fits is D.
Can someone list the amount of numbers that have a GCF of 7 and a product of 490?
Answer:
The amount of numbers that have a G C F of 7 and a product of 490 is 2.
Step-by-step explanation:
On Prime Factorization 490 = 2 x 5 x 7 x 7
G CF = Greatest Common Factor
So, here the possible number who have products as 490 and G C F as 7 is
(a) 2 x 7 = 14 and 5 x 7 = 35
As, 14 and 35 on multiplication,gives 490 as a product.
And, G C F of 14 and 3 5 is also 7.
(b) 7 and 5 x 7 x 2 = 70
As, 7 and 70 on multiplication,gives 490 as a product.
And, G C F of 7 and 70 is also 7.
⇒ (14, 35) and (7,70) are the only such pairs.
Hence, the amount of numbers that have a G C F of 7 and a product of 490 is 2.
Final answer:
The question seeks the number of number pairs with a GCF of 7 and a product of 490. There are only two pairs that meet the criteria: (7, 70) and (10, 49). Each pair multiplies to 490 and has a GCF of 7.
Explanation:
The question asks for the number of pairs of numbers that have a Greatest Common Factor (GCF) of 7 and a product of 490. First, we must note that any pair of numbers with a GCF of 7 must be multiples of 7. So, we divide 490 by 7 to find another factor that is also a multiple of 7, which gives us 70. Now, we have two pairs of numbers that satisfy the condition: (7, 70) and (10, 49) because each pair when multiplied gives 490, and the GCF of each pair is 7. It's important to note that 490 is equal to 7^2 times 10, which means we won't find more than these two pairs without repeating the same factors in a different order.
if 2cm represents 9m on a scale drawing how many meters do 15 cm represent
help me out
Give the correct answer
1+2=21
2+3=36
3+4=43
4+5=?
1 + 2 = 21 (reversing numbers)
2 + 3 = 32 (reversing numbers) + 4 = 36
3 + 4 = 43 (reversing numbers)
4 + 5 = 54 (reversing numbers) + 4 =58
Answer:
58Step-by-step explanation:
This is a sequence using reversed numbers, and alternating a summing fixed amount.
In the first one you can see that it's only numbers being reversed.
The second one is also reversing numbers but adding 4 units, 32+4=36.
The third one has the same pattern in the first one, just numbers being reversed.
The fourth has the same pattern than the second one, reversed numbers and add 4 units. So, it would be 54+4=58.
Therefore, the answer is 58.
Franco read 3/8 of a chapter of his history book in 1/5 of an hour. At this rate, how many chapters of his history book can he read in 1 hour?
Answer:
1 and 7/8 chapter
Step-by-step explanation:
1 ÷ 1/5 = 5
3/8 x 5 = 15/8 or 1 7/8
Answer:
1 7/8 chapters
Step-by-step explanation:
I had a test with this question.a direct variation function contains the points
range values y=3x+1 if the domain is -1,0,1,4
Answer:
Range = {-2, 1, 4, 13}
Step-by-step explanation:
Domain is the set of x-values that are allowed for the function. The values for which the function is defined.
Range is the set of y-values that are allowed for the fucntion. The values for which the function is defined.
Since domain is given as:
Domain = {-1, 0, 1, 4}
We have to plug in each of the 4 values and find the corresponding 4 values for the range. Lets do this below:
y = 3x + 1
y = 3(-1) + 1
y = -2
y = 3x + 1
y = 3(0) + 1
y = 1
y = 3x + 1
y = 3(1) + 1
y = 4
y = 3x + 1
y = 3(4) + 1
y = 13
So, the range would be:
Range = {-2, 1, 4, 13}
What is equivalent to 5/9
Answer:
10/18
Step-by-step explanation:
U only asked for what is equivalent
Answer:
10/18, 15/27, 20/36, 25/45, 30/54, 35/63, 40/72, 45/81, 50/90, 55/99, 60/108.
Step-by-step explanation:
-(2x+2)-1= -x -(x+3)
Answer:
[tex]x \in \mathbb \: R[/tex]
Step-by-step explanation:
The given equation is:
[tex] - (2x + 2) - 1 = - x - (x + 3)[/tex]
We expand to get:
[tex] - 2x - 2 - 1 = - x - x - 3[/tex]
We group like terms to get:
[tex] - 2x + x + x = - 3 + 1 + 2[/tex]
We combine the like terms to obtain:
[tex] - 2x + 2x = - 3 + 3[/tex]
[tex] 0 = 0[/tex]
This is always true therefore the solution is infinite.
Find values of a and b that make the following equality into identity:
x−1/(x+1)(x−4) = a/x+1 + b/x−4
The value of a and b in given expression must be [tex]\frac{2}{5} \text { and } \frac{3}{5}[/tex] respectively so that given equality becomes identity.
Solution:Need to find the value of a and b in following expression so that following equality will become identity.
[tex]\frac{(x-1)}{(x+1)(x-4)}=\frac{a}{(x+1)}+\frac{b}{(x-4)}[/tex] ------- eqn 1
Lets Simplify Right hand Side first,
[tex]\frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{a(x-4)+b(x+1)}{(x+1)(x-4)}[/tex]
[tex]\begin{array}{l}{=\frac{a x-4 a+b x+b}{(x+1)(x-4)}} \\\\ {=\frac{a x+b x-4 a+b}{(x+1)(x-4)}} \\\\ {=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}}\end{array}[/tex]
[tex]=>\frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}[/tex]
[tex]\text {On substituting } \frac{a}{(x+1)}+\frac{b}{(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)} \text { in equation } 1 \text { we get }[/tex]
[tex]\frac{(x-1)}{(x+1)(x-4)}=\frac{(a+b) x-4 a+b}{(x+1)(x-4)}[/tex]
On multiplying both sides by (x+1)(x-4) we get
[tex]\frac{(x-1)}{(x+1)(x-4)} \times(x+1)(x-4)=\frac{(a+b) x-4 a+b}{(x+1)(x-4)} \times(x+1)(x-4)[/tex]
[tex]\Rightarrow x-1=(a+b) x-(4 a-b)[/tex]
On comparing coefficient of x and constant term separately, we get
a + b = 1 and 4a - b = 1
On adding the two equations we get
a + b + 4a - b = 1 + 1
=> 5a = 2
=> [tex]a = \frac{2}{5}[/tex]
[tex]\text {Substituting } \mathrm{a}=\frac{2}{5} \text { in equation } a+b=1, \text { we get }[/tex]
[tex]\begin{array}{l}{\frac{2}{5}+b=1} \\\\ {\Rightarrow b=1-\frac{2}{5}=\frac{3}{5}}\end{array}[/tex]
So the value of a and b in given expression must be [tex]\frac{2}{5} \text { and } \frac{3}{5}[/tex] so that given equality becomes identity.
What is the expression that are equivalent to 5(2x+3)
Answer:
10x+15
Step-by-step explanation:
5(2x+3)=10x+15
Answer:
10x+15.
Step-by-step explanation:
Its just simplified.
5 times 2x is 10x
5 times 3 is 15.
Put it together 10x+15.
30 POINTS!!!! HELP ME ASAP!!!!!
Answer:
18
Step-by-step explanation:
I'm 90% sure I'm right but I could be wrong
4 × 18 = 72
6 × 18 = 108
72 + 108 = 180 degrees
Which means the opposite angle diagonal from 6x would also equal 108 degrees
Same thing for 4x, 72 degrees
72° + 72 ° + 108° + 108° = 360 degrees
is x^2-(x-5)^2=9y linear
Answer:
yes
Step-by-step explanation:
I need a word problem of 5 * 8 equals 40
Word problem - Jose played soccer for 5 hours every afternoon for 8 days. How many hours did Jose play soccer in all?
So this problem is about Jose and the amount of time he spends playing soccer.
Next, let's pick out what we know and what we want to find out.
We know that Jose played soccer for 5 hours every afternoon for 8 days. We want to find out how many hours of soccer he played in all so we need to multiply.
We multiply the amount of time he spent playing soccer each afternoon which is 5 hours by the number of days which is 8 days.
(8) (5) = 40
This means that Jose played 40 hours of soccer in all.
Simplify (x − 4)(3x2 − 6x + 2). 3x3 + 6x2 − 22x + 8 3x3 − 18x2 + 26x − 8 3x3 − 18x2 − 22x − 8 3x3 + 6x2 + 22x + 8
Answer:
3x^3-18x^2+26x-8
Step-by-step explanation:
(x-4)(3x^2-6x+2)
3x^3-6x^2+2x-12x^2+24x-8
3x^3-18x^2+26x-8
Answer:
3x^3-18x^2+26x-8
Step-by-step explanation:
(x-4)(3x^2-6x+2)
3x^3-6x^2+2x-12x^2+24x-8
3x^3-18x^2+26x-8
A woman bought some large frames for $10 each and some small frames for five dollars each add a closeout sale if she bought 17 frames for $100 find how many of each type she bought
Answer:
She bought 3 large frames and 14 small frames
How many solutions does the following have: 14(z+3) = 14z + 21
Answer: this equation has no solutions ,I just got it correct
Step-by-step explanation:
Answer:
No solutions
Step-by-step explanation:
Khan Academy says its right
The graph models function R. The table of values models function S. Which statement is true about these functions?
A) The two functions have the same rate of change.
B) Both functions do not have a constant rate of change.
C) Function R has a greater rate of change than Function S.
D) Function S has a greater rate of change than Function R.
Answer: OPTION D.
Step-by-step explanation:
The rate of change of a linear function is also known as "Slope".
The slope can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose two points on the function "R" graphed:
[tex](1,0)\\(0,-3)[/tex]
You can say that:
[tex]y_2=-3\\y_1=0\\\\x_2=0\\x_1=1[/tex]
Substituting values into the formula, you get:
[tex]m=\frac{-3-0}{0-1}=3[/tex]
Choose two point from the table that models the function "S":
[tex](4,21)\\(6,31)[/tex]
You can say that:
[tex]y_2=31\\y_1=21\\\\x_2=6\\x_1=4[/tex]
Substituting values into the formula, you get:
[tex]m=\frac{31-21}{6-4}=5[/tex]
Therefore, you can conclude that the function "S" has a greater rate of change than Function "R".
Answer:
D: Function S has a greater rate of change than Function R.
Step-by-step explanation:
Function S has a greater rate of change than Function R.
Function R → m =
rise
run
=
6
2
= 3. Function S → m =
change in y
change in x
=
31 − 21
6 − 4
=
10
2
= 5
Since 5 > 3, function S has a greater rate of change.
You need at least $535 to go on a trip to California. You have already saved $200.
You decide to save an additional $25 per week. Which inequality shows the number of
weeks, w, you need to save to be able to go on the trip?
The inequality which shows the number of weeks, w, you need to save to be able to go on a trip is 25w + 200 ≥ 535.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Total amount needed to go for a trip to California = $535
Already saved amount = $200
You decide to save an additional $25 per week.
Let w be the number of weeks needed to save $25 to get the amount needed to go for trip.
These saved amounts must be at least $535 to go for trip.
The amount saved after w weeks is 25w
Total saved amount = 200 + 25w
This saved amount must be ≥ 535.
So the inequality is 200 + 25w ≥ 535.
Hence the inequality which represents the amount need to save to go for trip is 200 + 25w ≥ 535.
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Lobsters Each year, 183 million pounds of lobster are caught in
the United States and Canada. Twenty-five percent of this amount is
sold live. (Source: Lobster Institute at the University of Maine) How
many pounds of lobster are sold live each year in the United States and
Canada?
Firen
Source:
Answer:
The quantity of lobster which are sold live each year in the United States and Canada are 46 million pounds (approximately).
Step-by-step explanation:
Given:
Each year, 183 million pounds of lobster are caught in the United States and Canada. Twenty-five percent of this amount is sold live.
Now, to find how many pounds of lobster are sold live each year in the United States and Canada.
According to question:
25% of 183 million pounds.
[tex]\frac{25}{100}\times 183[/tex]
[tex]=0.25\times 183[/tex]
[tex]=45.75[/tex]
Each year 45.75 million pounds of lobster are sold live in the United States and Canada.
Therefore, the quantity of lobster which are sold live each year in the United States and Canada are 46 million pounds (approximately).
The universal gas law, pV = nRT, describes the relationship among the pressure, volume, and temperature of a gas.
Answer:
R = 8.31
Step-by-step explanation:
From the table choose a corresponding amount for Volume and pressure. Plug it into the equation and solve for R.
Choosing the second row V = 16.62 and p = .5
p = R/V
.5=R/16.62
multiply both sides by 16.62 to isolate R
16.62(.5) = R
R = 8.31
Answer:8.31
Step-by-step explanation:
Write the equation of the line in slope intercept form that contains the point (-2,-1) and is perpendicular to the graph of y=-2x-3
The required equation of line is:
[tex]y = \frac{1}{2}x[/tex]
Step-by-step explanation:
Given equation of line is:
y=-2x-3
The coefficient of x is the slope of line as the equation is in slope intercept form
Let m1 be the slope of given graph of line
So,
[tex]m_1=-2[/tex]
The product of slopes of perpendicular lines is -1
Let m2 be the slope of required line
Then
[tex]m_1.m_2 = -1\\-2 . m_2 = -1\\m_2 = \frac{-1}{-2}\\m_2 = \frac{1}{2}[/tex]
the slope-intercept form of line is:
[tex]y=m_2x+b[/tex]
Putting the value of slope
[tex]y=\frac{1}{2}x+b[/tex]
To find the value of b, putting the given point (-2,-1) in equation
[tex]-1=\frac{1}{2}(-2)+b\\-1 = -1 +b\\-1+1 = b\\b = 0[/tex]
Hence,
The required equation of line is:
[tex]y = \frac{1}{2}x[/tex]
Keywords: Equation of line, slope-intercept form
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Two lines a and b are intersected by a transversal c prove that a//b, if
NEED IN 15 min am giving ABOUT 50 POINTS
ANY CHEATIN ANSWERS R BANNED!!
Pls help
Answer:
Because Alternate Interior angles are equal.
Step-by-step explanation:
STEP - I:
[tex]$ m \angle {5} = 3 . m \angle {\{3}\} $[/tex]
Reason:
This is the given data.
STEP - II:
It has multiplied and the reason is mentioned as well.
STEP - III:
[tex]$ m \angle{3} + m \angle{5} $[/tex] = 45° + 135° = 180°
Reason:
It has substituted the value of [tex]$ m\angle{5} $[/tex] from the previous step. The sum of [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle{5} $[/tex] is 180°.
STEP - IV:
[tex]$ a \parallel b $[/tex]
Reason:
We calculated [tex]$ m\angle{5}[/tex] to be 135°.
Note that [tex]$ \angle {5} $[/tex] and [tex]$ \angle{6} $[/tex] are on the same line. That means their sum should be 180°.
i.e., [tex]$ m\angle{5} + m\angle{6} $[/tex] = 180°.
[tex]$ \implies $[/tex] 135° + [tex]$ m\angle{6} $[/tex] = 180°.
[tex]$ \implies m\angle{6} = $[/tex] 45°.
One of the ways to prove [tex]$ a \parallel b $[/tex] is to check if alternate interior angles are equal.
Here, [tex]$ m\angle{3} $[/tex] and [tex]$ m \angle {6} $[/tex] are alternate interior angles and they are equal.
[tex]$ \implies a \parallel b $[/tex].
2 Points
Which of the items below is not an example of a fixed cost?
O
A. Packaging costs
O
B. Internet access fee
O
C. Monthly rent
O
D. Weekly fixed electricity costs
STI
Answer:
A. packaging costs
Step-by-step explanation:
Packaging costs woupd change based on how many products are being shipped. The other payments are fixed because they are the same amount paid regularly. Packaging would be considered a variable cost.
Internet access fee is not an example of a fixed cost.
What is Fixed Cost?The fixed cost definition states that businesses incur a cost that does not change positively or negatively with the number of goods sold or services given.
A fixed cost is a cost that remains constant regardless of production or sales volume.
Examples of fixed costs include monthly rent, packaging costs, and weekly fixed electricity costs.
Internet access fee is not an example of a fixed cost since it fluctuates based on usage.
The cost of internet access fee will increase or decrease depending on the amount of data used or the duration of usage.
Hence, Internet access fee is not an example of a fixed cost.
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A store sells rope by the meter. The equation p=0.8L represents the price p(in dollars) of a piece of nylon rope that is L meters long.
A. How much does the nylon cost per meter?
B. How long is a piece of nylon rope that costs $1.00?
The cost of the nylon rope is $0.8 per meter. For $1, you can purchase 1.25 meters of nylon rope.
Explanation:The given equation is p=0.8L. Here, 'p' stands for the price in dollars and 'L' is the length of the nylon rope in meters.
A. To determine the cost per meter, we look at the coefficient in front of 'L' in our equation. Here, it is 0.8, signifying that the nylon rope costs $0.8 per meter.
B. To find out the length of rope that could be bought for $1, we use the equation by setting 'p' equal to 1 and solving for 'L'. Doing this gives us 'L' = 1 / 0.8 which equals to 1.25 meters.
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