If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
A) 10, 14, 26
10 + 14 = 24 < 26 INCORRECT :(
B) 10, 14, 16
10 + 14 = 24 > 16 CORRECT :)
C) 10, 10, 14
10 + 10 = 20 > 14 CORRECT :)
D) 8, 10, 14
8 + 10 = 18 > 14 CORRECT :)
E) 5, 10, 14
5 + 10 = 15 > 14 CORRECT :)
F) 2, 10, 14
2 + 10 = 12 < 14 INCORRECT :(
Answer: B) 16, C) 10, D) 8, E) 5Options B, C, D and E are correct answers.
Given that, a triangle has two sides of lengths 10 and 14.
We need to find what value could the length of the third side be and check all that apply.
What is the triangle inequality theorem?Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
Now, from the given options:
A) 10, 14, 26
10 + 14 = 24 < 26 the triangle can not be formed
B) 10, 14, 16
10 + 14 = 24 > 16 the triangle can be formed
C) 10, 10, 14
10 + 10 = 20 > 14 the triangle can be formed
D) 8, 10, 14
8 + 10 = 18 > 14 the triangle can be formed
E) 5, 10, 14
5 + 10 = 15 > 14 the triangle can be formed
F) 2, 10, 14
2 + 10 = 12 < 14 the triangle can not be formed
Therefore, options B, C, D and E are correct answers.
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Tammi deposited $520.00 into a bank account that earned simple interest each year. After 5 years she had earned $156 in interest what was the annual interest rate
Answer:
R=6%
Step-by-step explanation:
Given:
Total money deposited = $ 520
Total years = 5
Total earned = $156
Simple interest
To Find:
interest rate=R=?
Solution:
We know the formula for calculating total amount earned by a simple interest rate and formula for it is
I = P(rT) ..................(i)
where I is total amount earned
P is total money invested
r is rate
and t is time
putting the values gives us
156 = 520 (r)(5)
156 = 2600 r
dividing both sides by 2600
r = [tex]\frac{156}{2600}[/tex]
r= 0.06
We have to find R
Now from simple rules of
we know that
R = r* 100 %
so putting the value of r
R = 0.06 * 100 %
R = 6%
which is the rate at which money was invested
A square picture on the front page of a newspaper occupies an area of 24 square inches. Find the length of each side of the square. Leave your answer in simplest radical form
Answer:
Well if you are trying to find the length of each side you Divide 24 by 4 so your answer would be 6
Step-by-step explanation:
Answer:
2√6 inches
Step-by-step explanation:
Since the picture is a square the lengths of each side are equal and their measure is √24
= √4*√6
= 2√6 in simplest form
The gas gauge in a car shows it has 40% of a tank of gas. If the car has about 5 gallons, approximately how many gallons can the tank hold when it is full?
Answer:
the tank can hold 12.5 gallons when it is full
Step-by-step explanation:
Let's assume
tank can hold 'x' gallons when it is full
we are given
The gas gauge in a car shows it has 40% of a tank of gas
So, gas in car is
[tex]=\frac{40}{100}\times x[/tex]
and we have
the car has about 5 gallons
so, we can set it equal
and then we can solve for x
[tex]5=\frac{40}{100}\times x[/tex]
[tex]5=\frac{4}{10}\times x[/tex]
[tex]5=\frac{2}{5}\times x[/tex]
Multiply both sides 5
[tex]5\times 5=5\times \frac{2}{5}\times x[/tex]
[tex]5\times 5=2x[/tex]
[tex]25=2x[/tex]
we get
[tex]x=12.5[/tex]
So, the tank can hold 12.5 gallons when it is full
Answer:
B
Step-by-step explanation:
Gloria can run 3/4 miles in 8 1/2 minutes. What is her speed in miles per minute ?
Answer:
11.33333...(keeps repeating)
Step-by-step explanation:
8.5 ÷ 3/4 = 11.33333...(keeps repeating)
ou are having a meeting with the CEO of a technology company. You have interpreted the number of laptops produced versus profit as the function P(x) = x4 − 3x3 − 8x2 + 12x + 16. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).
Answer: We can plot the graph with help of below explanation.
Step-by-step explanation:
Since, given equation of polynomial,
[tex]P(x) = x^4 - 3x^3 - 8x^2 + 12x + 16[/tex]
End behavior : Since, the leading coefficient of the polynomial is positive and even.
Therefore, the end behavior of the polynomial is,
[tex]f(x)\rightarrow -\infty[/tex] as [tex]x\rightarrow -\infty[/tex]
And, [tex]f(x)\rightarrow +\infty[/tex] as [tex]x\rightarrow +\infty[/tex]
Points of the curve : since, P(4) = 0
Therefore, (x-4) is the multiple of P(x),
And we can write, [tex]x^4 - 3x^3 - 8x^2 + 12x + 16= (x-4)(x^3+x^2-4x-4)[/tex]
[tex]x^4 - 3x^3 - 8x^2 + 12x + 16=(x-4)(x+1)(x^2-4)[/tex]
[tex]x^4 - 3x^3 - 8x^2 + 12x + 16= (x-4)(x+1)(x+2)(x-2)[/tex]
Thus, the roots of equation are 4, 2, -1 and -2.
Therefore, x-intercepts of the polynomial are (4,0) (2,0) (-1,0) and (-2,0)
Also, the y-intercept of the polynomial is ( 0,16)
Thus, we can plot the graph with help of the above information.
PLease help! 20 points!!
Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 4 as x approaches 4 from the left.
Answer: Negative infinity
note: if your teacher won't allow negative infinity, then try DNE for "does not exist"
=======================================================
Explanation:
As x gets closer to x = 4 from the left side of this value, then x starts at something like x = 3 and moves to x = 3.5, then to x = 3.9, then to x = 3.99, then to x = 3.999, etc
We get closer to x = 4 but never actually get there. If you look at the table attached, then f(x) = 1/(x-4) will keep getting more negative with larger and larger negative values. This growth goes on forever without any bound. So the limit is equal to negative infinity.
As you can see on the graph below, the curve heads downward as you approach x = 4 from the left hand side. Imagine you are a point on the curve, or this point is on a rollercoaster (the curve being the track itself). As you get closer to 4 from the left side, you go downhill. There is on limit to how far downhill you can go.
note: the graph and table in the attachment below were made by the free graphing calculator program GeoGebra
Answer with explanation:
The given rational function is
[tex]y= \lim_{x \to 4^{-}} \frac{1}{x-4}[/tex]
To find the vertical Asymptotes , put
→ Denominator =0
→ x-4=0
→x=4, is the Vertical Asymptote.
Solve for X
Thank you
Answer:
answer is 8
8+14x+6x+12=180
Step-by-step explanation:
he points (-3,4) and (5,-2) are on the graph of function f. If function g is the inverse of function f, what pair of points are on function g? Type the point with the lower x-value first. ( , ) and ( , )
Answer:
(4,-3) and (-2,5)
Step-by-step explanation:
The inverse of a function, is the function or rule formed by reflecting the line over y=x. This means essentially that all (x,y) values from the original function switch to (y,x).
(x,y)--->(y,x) in the new function.
If the function has points (-3,4) and (5,-2) then the inverse has points (4,-3) and (-2, 5).
Answer:
PLATO users, use this order:
(-2,5) and (4,-3)
Step-by-step explanation:
Mira has breakfast at a restaurant. She leaves 20% tip of 1.80 . What is the price of mira breakfast before tip
Answer:
9.00
Step-by-step explanation:
Use proportion:-
20% is equivalent to 1.80
1% is equivalent to 1.80 / 20
100% is equivalent to (1.80 / 20 ) * 100
= 180 / 20
= 9
= 9.00
help me with this math please
Answer:
There would be no solution im pretty sure but not 100%
Step-by-step explanation:
check my answer?
What is the recursive rule for this geometric sequence?
−64,−16,−4,−1,...
Enter your answers in the boxes.
a n =
a 1 =
i think it is
an = a n + 1 * an-1
and
a1=-64
am i right?
A recursive rule for a geometric sequence
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------------------
[tex]a_1=-64;\ a_2=-16;\ a_3=-4;\ a_4=-1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\\\\r=\dfrac{-16}{-64}=\dfrac{1}{4}\\\\\boxed{a_1=-64;\qquad a_n=\dfrac{1}{4}\cdot a_{n-1}}[/tex]
Need Help ASAP! Please!
Answer:
ok first get each corner make a line to the dot with each point
Step-by-step explanation:
In the diagram shown, ∠7 measures 92 degrees. What is the measure of ∠8?
8 degrees
88 degrees
92 degrees
180 degrees
∠8=180°-92°=88°
===================
Answer:
Step-by-step explanation:
The answer is 88 degrees i got that question right.
If it takes 5 bakers 5 minutes to make 5 christmas cookies, how long would it take 100 bakers to make 100 christmas cookies?
Poppy's Pizza is buying square boxes to put their pizzas in. The large box has an area of 196 square inches. What is the area of the largest possible pizza that could be placed into the box?
Answer:
154 square inches
Step-by-step explanation:
Watch the attached figure of the square pizza box and the largest pizza that can fit into it.
Let the each side of the square pizza box be a inches.
Radius of the largest pizza that can fit into it = Half of the side of the pizza box = [tex]\frac{a}{2}[/tex]
So, area of the square box = Side * Side
= a * a
= a² square inches
It has also been given that the large box has an area of 196 square inches.
So,
Area of the box = a²
=> 196 = a²
Flipping the sides of the equation, we get
=> a² = 196
Taking square root on both the sides,
√a² = √196
a = 14 inches
So,
Side of square box = 14 inches
Radius of the largest pizza that can fit into it = [tex]\frac{a}{2}[/tex]
= [tex]\frac{14}{2}[/tex]
= 7 inches
Area of the largest possible pizza that could be placed into the box
= π *radius² [since pizza is circular in shape]
= [tex]\frac{22}{7}[/tex] * 7²
= [tex]\frac{22}{7}[/tex] * 7 * 7
Cancelling out a pair of 7's from the top and bottom, we have
= 22 * 7
= 154 square inches
Eighty-five mall customers were randomly surveyed across the state to determine if the live entertainment provided had increased the amount of money they spent. Can the probability be found by using the binomial probability formula?
Answer:
Yes (under certain conditions)
Step-by-step explanation:
Binomial probability formula can be used if there are success and failure been discussed in the question.
The formula is given by
P(X=x) = \binom{n}{x}p^{x}q^{n-x}
where n= no. trials
p = success
q= failure
x= point at which we need to find the probability
Here, 85 customers are surveyed, then n= 85
we will take, p= live entertainment had increased the amount of money they spent (success)
q = live entertainment had not increased the amount of money they spent (failure)
x should be defined, then only we can use binomial probability formula
Example, x= 10 customers said that the money they spent increased if the live entertainment provided.
Answer:
Yes
Step-by-step explanation:
Binomial distribution is valid for trials which consist of only two outcomes, and each trial is independent of the other.
Here 85 mall customers were randomly surveyed. We have that each customers is independent of the other for the state o determine if the live entertainment provided had increased the amount of money they spent
Hence probability for each person to say yes can be taken as p and q =1-p for no reply.
There are only two outcomes.
Also n =85 is sufficiently large to have np or nq >5
Hence the probability can be found using binomial probability formula provided p = probability for success of a single trial is given.
Identify y = sec(x)
Answer:
D)
Step-by-step explanation:
sec(x) = 1/cos(x)
You know cos(x) = 1 for x=0, so sec(0) = 1.
You also know that sec(x) has vertical asymptotes where cos(x) = 0, at odd multiples of π/2. Only selection D matchest these characteristics.
the density of an object has the equation d= m/v. if an object has a mass of 20 g and a volume of 3.5 cm3, what is it's density?
A.0.175 G/CM3
B.70 G/CM3
C.5.71 G/CM3
D.23.5 G/CM3
[tex]\mathsf{We\;know\;that : Density = \frac{Mass\;of\;the\;Object}{Volume\;of\;the\;Object}}[/tex]
[tex]\mathsf{Given : Mass\;of\;the\;Object = 20\;Grams}[/tex]
[tex]\mathsf{Given : Volume\;of\;the\;Object = 3.5\;cm^3}[/tex]
[tex]\mathsf{\implies Density = \frac{20}{3.5}(\frac{g}{cm^3})}[/tex]
[tex]\mathsf{\implies Density = 5.71\;(\frac{g}{cm^3})}[/tex]
To find the density of an object, we will use the formula for density which is \( d = \frac{m}{v} \), where:
- \(d\) represents the density of the object,
- \(m\) is the mass of the object, and
- \(v\) is the volume of the object.
Substituting the given values into the formula:
\(m = 20 \, \text{g}\) (mass of the object),
\(v = 3.5 \, \text{cm}^3\) (volume of the object),
we get:
\(d = \frac{20 \, \text{g}}{3.5 \, \text{cm}^3}\).
Dividing 20 grams by 3.5 cubic centimeters, we obtain:
\(d ≈ 5.71 \, \text{g/cm}^3\).
Therefore, the correct answer is:
C.5.71 G/CM3
Which graph represents the function f(x)=-(1/3)^-x
[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}=-\Bigg[\left(\dfrac{1}{3}\right)^{-1}\Bigg]^x=-(3)^x\\\\f(x)<0\ \text{for any real values of x}\ (III\ and\ IV\ quadrant)\\\\a^x\ \text{is increased for}\ a>1.\ \text{Therefore}\ 3^x\ \text{is increased}.\\\\\text{We have}\ -3^x,\ \text{therefore the graph is decreased}.[/tex]
Only bottom left graph satisfy the conditions of the end behaviour and y-intercept. The bottom left option is correct.
Given:
The given function is:
[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}[/tex]
To find:
The graph of the given function.
Explanation:
The given function can be rewritten as:
[tex]f(x)=-\dfrac{1}{3^{-x}}[/tex]
[tex]f(x)=-3^{x}[/tex]
For [tex]x=0[/tex], we get
[tex]f(0)=-3^{0}[/tex]
[tex]f(0)=-1[/tex]
So, the y-intercept of the graph is [tex]-1[/tex].
End behaviour of the graph:
[tex]f(x)\to 0[/tex] as [tex]x\to -\infty[/tex]
[tex]f(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]
Only bottom left graph satisfy the above conditions.
Therefore, the bottom left option is correct.
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A car company offers financing to its customers. For the newest model, customers can pay $2000 down and then $250 a month. Write an equation for this situation. What does the independent variable represent? What does the dependent variable represent?
Answer: C: y = 250x + 2000; the independent variable, x, represents the number of months after buying the car and the dependent variable, y, represents the amount of money paid on the car.
Step-by-step explanation:
The equation representing the total cost of the car over time is C(t) = 2000 + 250t, where 't' (the number of months) is the independent variable and 'C(t)' (the total cost) is the dependent variable.
To write an equation for the financing offer of a car company where customers pay a $2000 down payment and then $250 a month, we use a linear equation to represent the total cost of the car (C) over time (t):
C(t) = 2000 + 250t
Here, the independent variable 't' represents the number of months, and the dependent variable 'C(t)' represents the total cost of the car at a particular time. The independent variable is the one we have control over or choose values for, and the dependent variable is the one that changes in response to the independent variable.
In the diagram below m angleXYZ=138° and m angleWXY=60°.What is m angleXWY?
Can you please provide the diagram.
Which of the following shows 18/12 as a mixed number and 1 7/8 as an improper fraction
18/12= [tex]1\frac{1}{2}[/tex] and [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option, [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of [tex]1\frac{7}{8}[/tex].
What is Fraction?
A fraction represents a part of a whole.
If a fraction has a numerator that is less than the denominator then the fraction is proper.
An improper fraction has a numerator that is greater than the denominator.
A mixed number is an integer written with a fraction.
18/12 is a improper fraction, let us simplify it by dividing numerator and denominator by 6
18/12 is 3/2.
The mixed fraction of 3/2 is [tex]1\frac{1}{2}[/tex]
Now the given mixed fraction is [tex]1\frac{7}{8}[/tex]
When we convert to improper we get (8×1)+7/8 , which is 15/8
Hence, 18/12= [tex]1\frac{1}{2}[/tex] and [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option, [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of [tex]1\frac{7}{8}[/tex].
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∠A=8x−8
∘
∠B=5x+25∘\qquad \greenD{\angle B=5x + 25^\circ}
∠B=5x+25
∘
Answer:
80 degrees.
Step-by-step explanation:
The real question was:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The angle measurements in the diagram are represented by the following expressions.
(angle)∠A= 8x −8 and (angle)∠B= 5x +25
Solve for x and then find the measure of (angle)∠B.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x= 11 and then since both angles equal the same......we know that angle B equals 80 degrees!
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Parallelogram ABCD is dilated to form parallelogram WXYZ. What corresponding side is proportional to segment AD? Type the answer in the box below.
Answer: WZ
The sequence ABCD has AD as the first and last letters of that sequence, so this pattern applies to WXYZ as well to pull out WZ. Angle A pairs up with angle W because they are both the first letters of the sequences. These angles are congruent from the fact that the parallelograms are similar. The same can be said for angle D and angle Z.
note: WZ is the same as ZW. The order doesn't matter when it comes to labeling segments based on endpoints.
Jorge bought a crate of floor tiles for $95.94. The crate had 6 boxes of floor tiles. Each box contained 20 floor tiles . Write and slove an equation to dertermine the cost per box,b. Then write and slove a second equation to dertermine the cost per tile,t, to the nearest cent.
Answer:
⇒[tex]6b=95.94[/tex] (equation to determine cost of one box)
cost of one box 'b' = $`15.99
⇒[tex]120t = 95.94[/tex] (equation to determine cost of per tile)
cost of one tile t = $0.7995.
Step-by-step explanation:
Given :
Jorge bought a crate of floor tiles for $95.94.
The crate had 6 boxes of floor tiles.
Each box contained 20 floor tiles .
To Find :
Write and solve equation to determine the cost per box'b'.
Write and solve a second equation to determine the cost per tile't'
Solution :
Cost of one box = b
There are 6 boxes
So, cost of 6 boxes = $ 6b
Since Jorge bought 1 crate( = 6 boxes) of cost $95.94
⇒[tex]6b=95.94[/tex] (equation to determine cost of one box)
⇒[tex]b=\frac{95.94}{6}[/tex]
⇒[tex]b=15.99[/tex]
Thus cost of one box = $`15.99
Since 1 box 20 floor tiles
So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles
We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94
Cost of one tile = t
Cost of 120 tiles = $120t
⇒[tex]120t = 95.94[/tex] (equation to determine cost of per tile)
⇒[tex]t=\frac{95.94}{120}[/tex]
⇒[tex]t=0.7995[/tex]
Thus cost of one tile t = $0.7995.
A standardized test was given to a set of high school juniors and the distribution of the data is bell shaped. The mean score is 800 and the standard deviation is 120.
To qualify for a special summer camp for accelerated students, a student must score within the top 16% of all scores on the test. What score must a student make to qualify for summer camp?
To qualify for the special summer camp for accelerated students, a student must score at least approximately 978 on the standardized test, considering a score within the top 16% of all scores, given a mean score of 800 and a standard deviation of 120.
Explanation:In a bell-shaped or normal distribution, the mean [tex]\(\mu\)[/tex] represents the central tendency of the data, and the standard deviation [tex]\(\sigma\)[/tex] measures the dispersion or spread of the scores. To find the score required to qualify for the top 16%, we use the z-score formula: [tex]\(z = \frac{X - \mu}{\sigma}\)[/tex], where X is the score, [tex]\(\mu\)[/tex] is the mean, and [tex]\(\sigma\)[/tex] is the standard deviation.
Given the mean score [tex]\(\mu = 800\)[/tex] and standard deviation [tex]\(\sigma = 120\)[/tex], the z-score corresponding to the top 16% is found using a standard normal distribution table or statistical software. The z-score associated with the top 16% is approximately z = 1.04.
Next, use the z-score formula to solve for the score X required to be in the top 16%: [tex]\(z = \frac{X - \mu}{\sigma}\)\\[/tex]. Rearranging the formula to solve for X gives us [tex]\(X = z \cdot \sigma + \mu\)[/tex]. Substituting the z-score value and the given mean and standard deviation into the equation yields [tex]\(X = 1.04 \cdot 120 + 800 = 978\)[/tex]. Hence, a student needs to score at least approximately 978 to qualify for the special summer camp for accelerated students, given the distribution of scores on the standardized test.
A function h is defined by h(x)=−4x−72. If x decreases by 11, by how much does h(x) increase?
A function f is defined by f(x)= 3/17 x+2. If x increases by 51, by how much does f(x) increase?
QUESTION 1
The given function is
[tex]h(x)=-4x-72[/tex]
If [tex]x[/tex] decreases by [tex]11[/tex], then the new value is [tex]x-11[/tex].
We need to find the value the function at [tex]x-11[/tex] which is
[tex]h(x-11)=-4(x-11)-72[/tex]
This simplifies to
[tex]h(x-11)=-4x+44-72[/tex]
The increment in [tex]h(x)[/tex] is given by;
[tex]h(x-11)-h(x)=-4x+44-72-(-4x-72)[/tex]
This simplifies to,
[tex]h(x-11)-h(x)=-4x+44-72+4x+72[/tex]
This further simplifies to
[tex]h(x-11)-h(x)=44[/tex]
Therefore the corresponding increment in [tex]h(x)[/tex] is [tex]44[/tex].
QUESTION 2
The given function is
[tex]f(x)=\frac{3}{17}x+2[/tex].
If [tex]x[/tex] increases by [tex]51[/tex], then the new value of [tex]x[/tex] is [tex]x+51[/tex].
The increment in [tex]f(x)[/tex] is given by
[tex]h(x+51)-h(x)=\frac{3}{17}(x+51)+2-(\frac{3}{17}x+2)[/tex]
We expand the brackets to get,
[tex]h(x+51)-h(x)=\frac{3}{17}x+9+2-\frac{3}{17}x-2[/tex]
We simplify further to obtain,
[tex]h(x+51)-h(x)=9[/tex]
Therefore the corresponding increment in [tex]f(x)[/tex] is [tex]9[/tex].
When x decreases by 11, function h(x) increases by -100. When x increases by 51, f(x) increases by 9.
To find how much Function h(x) increases when x decreases by 11, we can calculate h(x) for the original value of x and the new value of x and then find the difference.
Original h(x) for h(x) = -4x - 72:
h(x) = -4x - 72
For x decreased by 11, the new x is x - 11:
New h(x) for h(x) = -4x - 72:
h(x - 11) = -4(x - 11) - 72
Now, we calculate the difference in h(x) values:
Δh = h(x - 11) - h(x)
Δh = [-4(x - 11) - 72] - (-4x - 72)
Now, simplify:
Δh = -4x + 44 - 72 + 4x - 72
The -4x and +4x cancel out:
Δh = 44 - 72 - 72
Now, calculate the difference:
Δh = -100
So, when x decreases by 11, h(x) increases by -100.
For the second part, to find how much f(x) increases when x increases by 51, we can use a similar approach.
Original f(x) for f(x) = (3/17)x + 2:
f(x) = (3/17)x + 2
For x increased by 51, the new x is x + 51:
New f(x) for f(x) = (3/17)x + 2:
f(x + 51) = (3/17)(x + 51) + 2
Now, calculate the difference in f(x) values:
Δf = f(x + 51) - f(x)
Δf = [(3/17)(x + 51) + 2] - [(3/17)x + 2]
Now, simplify:
Δf = (3/17)x + (3/17)(51) + 2 - (3/17)x - 2
The (3/17)x and - (3/17)x cancel out, and 2 - 2 also cancels:
Δf = (3/17)(51)
Now, calculate the difference:
Δf = 3 * 3
Δf = 9
So, when x increases by 51, f(x) increases by 9.
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Emery borrowed money from her brother to buy a new phone, and is paying off a fixed amount each week. After 2 weeks, she will owe $456, and after 5 weeks , she will owe .
Emery initially borrowed $608. Each week, she paid off $76. After 2 weeks she had $456 left to pay and after 5 weeks she owed $228.
Explanation:To find out the original amount borrowed, we need to determine how much Emery is paying off each week. If we look at the information given, after 2 weeks Emery still owes $456, and after 5 weeks, she owes $228. That's a difference of $228 over the span of 3 weeks, which means she is paying off $76 each week ($228 / 3 weeks = $76 per week).
Knowing this, we can figure out that she owed $608 before she started making payments (that is, $456 + $76*2 weeks = $608). Therefore, the original amount Emery borrowed from her brother was $608.
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the complete Question is given below
Emery borrowed money from her brother to buy a new phone and is paying off a fixed amount each week. After 2 weeks, she will owe $456, and after 5 weeks, she will owe $228. a. What was the original amount Emery borrowediginal amount borrowed?
Julian used these steps to solve the equation 9x=?6+3(3x+2) 9 x = - 6 + 3 ( 3 x + 2 ) . Which choice describes the meaning of his result, 0=0 ?
Answer:
see explanation
Step-by-step explanation:
the result 0 = 0
means the equation has an infinite number of solutions
Answer:
All values of x make the equation true... THIS IS THE CORRECT ANSWER!
Step-by-step explanation:
15 Points Please Help
What is the radical form of the expression 4 3/2?
Please don't answer if you don't know the answer.
Answer:
Radical form of the expression [tex]4^{\frac{3}{2} }[/tex] is, 8
Step-by-step explanation:
Given the expression: [tex]4^{\frac{3}{2} }[/tex]
Since, [tex]\sqrt{4^3}[/tex] is same as [tex]4^{\frac{3}{2} }[/tex]
Now, to write an exponent in radical form,
then the denominator or the index goes in front of the radical and
the numerator goes inside of the radical.
we raise the base to the power of the numerator then:
[tex]4^{\frac{3}{2} }[/tex] = [tex]\sqrt{64}[/tex] = [tex]\sqrt{8 \times 8}[/tex] = [tex]\sqrt{8^2} = 8[/tex]
therefore, the radical form of the given expression is, 8