Refer to the table of long distance rates. Write an expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes.
Answers
Answer:
a(n) = 0.55 + (n -5)0.07
Step-by-step explanation:
The cost goes up $0.07 for each additional minute, so that is the slope of the linear function. In point-slope form the equation can be written ...
... a(n) - 0.55 = 0.07(n -5)
adding 0.55, and rearranging slightly, this becomes ...
... a(n) = 0.55 +(n -5)0.07
Related Questions
Uncle Drew scored 2828 points in 5 5/6 ? minutes during a game of basketball. How many points did he average per minute during that 5\dfrac565 6 5 ? minutes?
Answers
Answer:
4.8 points per minute
Step-by-step explanation:
Uncle Drew scored 28 points in [tex]5 \frac{5}{6}[/tex] minutes. We have to convert the mixed fraction first:
[tex]t = 5 \frac{5}{6}=\frac{5\cdot 6+5}{6}=\frac{35}{6}[/tex]
So, the time is 35/6 minutes.
In order to find the number of points he scored in a minute, we have to divide the total number of points by the number of minutes, so:
[tex]mean = \frac{28}{35/6}=28 \cdot \frac{6}{35}=4.8[/tex]
So, he scored 4.8 points per minute.
Answer:
4.8
Step-by-step explanation:
Determine the first four terms of the sequence in which the nth term is
Answers
Answer:
The correct answer option is: [tex]\frac{1}{3} ,\frac{1}{4} ,\frac{1}{5} ,\frac{1}{6}[/tex].
Step-by-step explanation:
We know that the [tex]nth[/tex] term [tex]a_n[/tex] for an arithmetic sequence is given by:
[tex]a_n=\frac{(n+1)!}{(n+2)!}[/tex]
where [tex]n[/tex] is the number of the position of the term.
We are supposed to find the first four terms of the sequence so we will substitute the values of [tex]n[/tex] from 1 to 4 in the given formula to get:
1st term:
[tex]a_1=\frac{(1+1)!}{(1+2)!}=\frac{1}{3}[/tex]
2nd term:
[tex]a_2=\frac{(2+1)!}{(2+2)!}=\frac{1}{4}[/tex]
3rd term:
[tex]a_3=\frac{(3+1)!}{(3+2)!}=\frac{1}{5}[/tex]
4th term:
[tex]a_4=\frac{(4+1)!}{(4+2)!}=\frac{1}{6}[/tex]
Simplify -3d^8(-4d^-14) . Assume d=/0 .
Answers
[tex]\( -3 d^8(-4 d^{-14}) \)[/tex] simplifies to [tex]\(12 d^{-6}\)[/tex].
To simplify the expression [tex]\( -3 d^8(-4 d^{-14}) \)[/tex], you can follow these steps:
1. Distribute the factor [tex]\(-3\)[/tex] to both terms inside the parentheses.
2. Combine the exponents with the same base [tex](\(d\))[/tex].
Let's work through it step by step:
[tex]\[ -3 d^8(-4 d^{-14}) \][/tex]
1. Distribute [tex]\(-3\)[/tex] to both terms inside the parentheses:
[tex]\[ (-3) \cdot d^8 \cdot (-4) \cdot d^{-14} \][/tex]
[tex]\[ = 12 d^8 d^{-14} \][/tex]
2. Combine the exponents with the same base [tex](\(d\))[/tex] by applying the rule [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]:
[tex]\[ = 12 d^{8 + (-14)} \][/tex]
[tex]\[ = 12 d^{-6} \][/tex]
Therefore, [tex]\( -3 d^8(-4 d^{-14}) \)[/tex] simplifies to [tex]\(12 d^{-6}\)[/tex].
The complete question is given below:
Simplify [tex]\( -3 d^8(-4 d^{-14}) \)[/tex]. Assume that [tex]d \neq 0[/tex].
the answer is 12/d^6 , D
given RST = NPQ R=-7x+9, N=-10x find R and N
Answers
Answer:
[tex]m\angle N=m\angle R=30^{\circ}[/tex]
Step-by-step explanation:
We are given that
[tex]\triangle RST=\triangle NPQ[/tex]
[tex]m\angle R=-7x+9,m\angle N=-10x[/tex]
We have to find the measure of angle R and measure of angle N.
When two triangles are equal then their angles are equal
Therefore, [tex]m\angle R=m\angle N[/tex]
[tex]-7x+9=-10x[/tex]
[tex]-7x+10x=-9[/tex]
By subtraction property of equality
[tex]3x=-9[/tex]
By combine like terms
[tex]x=\frac{-9}{3}=-3[/tex]
By division property of equality
Substitute x=-3 then we get
[tex]m\angle R=-7(-3)+9=21+9=30^{\circ}[/tex]
[tex]m\angle N=m\angle R=30^{\circ}[/tex]
Answer:
30
Step-by-step explanation:
Adam drove his car 132 km and used 11 liters of fuel. How many kilometers will he cover with 14 liters of fuel?
Answers
Answer:
168 Km
Step-by-step explanation:
divide 132 Km by 11 to find distance travelled with 1 litre and then multiply this by 14 for distance travelled with 14 litres
= [tex]\frac{132}{11}[/tex] × 14 = 168 Km
What are the zeros of the function? Y=(x-2)(x-3)(x+3)
Answers
Answer:
B 2,3,-3
Step-by-step explanation:
If we use the zero product property, we can set each term =0 to find the roots.
0=(x-2)(x-3)(x+3)
x-2 =0 x-3 =0 x+3=0
x=2 x=3 x=-3
The roots are -3,2,3
Soft drinks cost $1.89 and refills cost $0.25 each. With $3.80 to spend on the soft drink and refills, what is the maximum number of refills that you can get? Refills (Hint: Do not answer with a fraction because you can not get a partial refill. Your answer should be an integer). 2 Game Bonus Solve equations with inequalities word problems
Answers
[tex]1.89+0.25x=3.8[/tex]
This is because the initial price was 1.89$ for the drink, then for every refill, it was a quarter extra. To solve for x we start by subtracting 1.89 from both sides.
[tex]0.25x=1.91[/tex]
So now we divide by 0.25 or multiply by 4 and we get
[tex]x=7.64[/tex]
But x cannot be a fraction. So we round this to the least integer, or 7
The number of times of the soft drink that refills will be 7.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
Soft drinks cost $1.89 and refills cost $0.25 each.
With $3.80 to spend on the soft drink and refills.
Then the maximum number of refills will be given as
Let x be the number of refills.
1.89 + 0.25x ≤ 3.80
0.25x ≤ 1.91
x ≤ 7.64
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Two poles of equal heights are standing opposite to each other on either side of a road, which is 100 meters wide .From a point between them on the road, the angles of elevation of their tops are 30? and 60? .Find the position of the point and also, the height of the poles. ( use = 1.73)
Answers
[tex] \tan( {30}^{0} ) \: = \: \frac{h}{x} [/tex]
[tex]h \: = \: x \tan( {30}^{0} ) [/tex]
[tex]x \: = \: h \cot( {30}^{0} ) [/tex]
[tex]x \: = \: h \sqrt{3} [/tex]
[tex] \tan( {60}^{0} ) \: = \: \frac{h}{100 - x} [/tex]
[tex]100 - x \: = \: h \cot( {60}^{0} ) [/tex]
[tex]100 - x \: = \: \frac{1}{ \sqrt{3} } h[/tex]
[tex]100 \sqrt{3 } \: - \: \sqrt{3} x \: = \: h[/tex]
Substituting the value of x, we get,
[tex]100 \sqrt{3} \: - \: \sqrt{3} ( \sqrt{3} h) \: = \: h[/tex]
[tex]100 \sqrt{3} \: - \: 3h \: = \: h[/tex]
[tex]4h \: = \: 100 \sqrt{3} [/tex]
[tex]h \: = \: 25 \sqrt{ 3} [/tex]
or,
h ≈ 25(1.73)
h ≈ 43.25 m
[tex]x \: = \: \sqrt{3} h[/tex]
[tex]x \: = \: \sqrt{3} ( 25 \sqrt{3} )[/tex]
[tex]x \: = \: 25(3)[/tex]
x = 75 m.
Therefore,
h = 43.25 m, x = 75 m, and (100 - x) = 25 m.
Answer:
Distance to the pole from the vertex of the 60o angle = 25 mDistance to the second pole from the vertex of the 30o angle = 75 mHeight of the pole = 43.3Step-by-step explanation:
The point is somewhere on the road. From that point, two poles can be seen at different angles of elevation. One is 30 degrees, and another is 60 degrees.
Call the height of the poles y and the point on the road as x meters away from the base of 60 degree angle to the base pole
Tan(60) = y/xTan(30) = y/(100 - x) Isolate y for both equationsx*tan(60) = y(100 -x) * tan(30) = y Since both boles are equal in height, equate the two equations.
(100 - x) * tan(30) = x*tan(60)
Using exact values (from the unit circle) tan(30) = sqrt(3)/3tan(60) = sqrt(3)(100 - x) * sqrt(3)/3 = x*sqrt(3) Divide both sides by sqrt(3)(100 - x)/3 = x Multiply both sides by 3 100 - x = 3x Add x to both sides100 = 4x Divide by 4x = 25The distance to the other pole = 100 - 25 = 75
y = x * sqrt(3)y = 25 * 1.73y = 43.3Dakota earned ?$4.50 in interest in Account A and ?$18.00 in interest in Account B after 18 months. If the simple interest rate is 2?% for Account A and 4?% for Account? B, which account has the greater? principal
Answers
The account with the greater principal is Account B with a simple interest of $ 18
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the first account be = A
Let the second account be = B
Now ,
The simple interest of A = $ 4.50
The simple interest of B = $ 18
The time period t = 18 months = 1.5 years
The rate of interest r for A = 2 %
The rate of interest r for B = 4 %
Now , the equation will be
Simple Interest of A = ( Principal of A x Rate of interest of A x Time ) / 100
Substituting the values in the equation , we get
4.50 = ( P x 2 x 1.5 ) / 100
Multiply by 100 on both sides of the equation , we get
450 = 3P
Divide by 3 on both sides of the equation , we get
Principal of A = $ 150
And ,
Simple Interest of B = ( Principal of B x Rate of interest of B x Time ) / 100
Substituting the values in the equation , we get
18.00 = ( P x 4 x 1.5 ) / 100
Multiply by 100 on both sides of the equation , we get
1800 = 6P
Divide by 6 on both sides of the equation , we get
Principal of B = $ 300
Therefore , the principal of B > principal of A
Hence , the simple interest of B with $ 18 has larger principal
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Describe how to find all the points on a baseball field that are equidistant from second base and third base. In the figure, m∠DBE=50.
Answers
The value of y and x is 11 and 6.
The m<BED = 40 degrees
The m<BEA = 40 degrees.
From the given diagram, the following statements are true:
AB = BC
3y = 5y - 22
3y - 5y = -22
-2y = -22
y = 11
Similarly, m<DBE = 50 degrees
m<BED = 90 - m<DBE
m<BED = 90 - 50
m<BED = 40 degrees
Since BE = BC = 3y
BE = BC = 3(11) = 33
Also, 7x - 2 = 40
7x = 40 + 2
7x = 42
x = 6
Get the measure of m<BEA
m<BEA = 7x - 2
m<BEA = 7(6) - 2
m<BEA = 40 degrees
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Question
Describe how to find all the points on a baseball field that are equidistant from second base and third base.
In the figure, m∠DBE=50. Find each of the following.
m∠BEDm angle b e d
m∠BEAm angle b e eh
x
y
BE
BC
Help!! im stupid and just need these 2 questions HELP!!!!!
WILL GIVE BRAINLIEST
The ordered pairs model an exponential function, where j is the function name and e is the input variable.
{(1, 10), (2, 50), (3, 250), (4, 1250)}
What is the function equation in sequence notation?
Enter your answer in the box.
je=
What is the explicit rule for the sequence?
13, 10.5, 8, 5.5, 3, 0.5, ...
an=15+2.5n
an=15.5+2.5n
an=15−2.5n
an=15.5−2.5n
Answers
Answer:
f(n) = 10 * 5^(n-1)
an = 15-2.5n
Step-by-step explanation:
{(1, 10), (2, 50), (3, 250), (4, 1250)}
The formula for a geometric sequence is
an = a1 * r ^(n-1)
where a1 is the first term and r is the rate in which it increase
a1 =10
r = 5, each term goes up by a factor of 5
50/10 = 5
250/50 = 5
etc
f(n) = 10 * 5^(n-1)
What is the explicit rule for the sequence?
13, 10.5, 8, 5.5, 3, 0.5, ...
For an arithmetic sequence the formula is
an = a1 + d(n-1)
where a1 is the first term and d is the common difference
a1= 13 and d = -2.5
10.5 -13 = -2.5
8. - 10 = -2.5
etc
an = 13 - 2.5 ( n-1)
Simplifying
an = 13 -2.5n + 2.5
an = 15-2.5n
Michelle is hiking on a weekend camping trip. She has walked 6 miles so far. This is 30% of the total distance What is the total number of miles she will walk
Answers
This problem is solved by using the concept of percentage as a part of a whole. We find out that 30% of the total distance equals 6 miles. So by setting up the proportion 30/100 = 6/x, we calculate the total distance is 20 miles.
Explanation:This question is an application of percentage problems in real-life situations, specifically hiking distance. When you use a percentage to describe a part of a whole thing, the thing is always considered to be '100%'. In this case, Michelle's hiking trip is the 'whole thing' or '100%'.
We are told that 6 miles is 30% of the total distance. To find the total distance, we can set up a proportion to solve for it. The proportion would be 30/100 = 6/x.
Let x represent the total distance. So we can write the proportion as:
6 / x = 30 / 100
To solve for x, we can cross multiply and then divide:
100 * 6 = 30 * x
600 = 30x
x = 20
Therefore, the total number of miles Michelle will walk is 20 miles.. So, the total distance that Michelle will walk is 20 miles.
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Write the equation of the line that passes through the point (2, 6) and is perpendicular to the line x = 4
Answers
Answer:
The perpendicular line would be y = 6
Step-by-step explanation:
In order to get this, we must first recognize that the equation given is a vertical line. If our new line is to be perpendicular to it, it must be a horizontal line. All horizontal lines are written as y = (a number). Since we have a point it goes through, we can get that value in the ordered pair. The ordered pair has a y value of 6, which means the equation would be y = 6
Sarah and Gavyn win some money and share it in the ratio 5:3.Sarah gets ?26 more than Gavyn.How much did Gavyn get?
Answers
Answer:
$39 did Gavyn get
Step-by-step explanation:
Given the statement: Sarah and Gavyn win some money and share it in the ratio 5:3.
Let the number be x
Then, Sarah win money be 5x and Gavyn win money be 3x.
Also, it is given that Sarah gets $26 more than Gavyn.
⇒ 5x = 26 + 3x
Subtract 3x from both sides we get;
5x -3x = 26 + 3x -3x
Simplify:
2x = 26
Divide both sides by 2 we get;
[tex]\frac{2x}{2} = \frac{26}{2}[/tex]
Simplify:
x =13
∵Gavyn win money 3x = 3(13) = $39
Therefore, Gavyn get, $39.
The area of a rectangle is 180 squared in2. The ratio of the length to the width is 5 : 4Find the length and the width. The length of the rectangle is nothing in.
Answers
Answer:
length = 100 squared Width = 80 squared
Step-by-step explanation:
You add the to ratio number ( 4+5 ). You take that number (9) and divide with 180. You receive the answer 20. Then you multiply 20 by 5 to get the length and multiply 20 by 4 to width. Then you just add back the square operation.
Final answer:
The length and width of the rectangle are found by setting up equations using the given ratio and area. By solving the equations, the length is determined to be 15 inches and the width 12 inches.
Explanation:
To find the length and width of the rectangle with an area of 180 square inches and a ratio of length to width of 5:4, we can set up equations using the ratio and area information. Since the area of a rectangle is equal to the length times the width, we can express the length (L) and width (W) in terms of the ratio:
L = 5x
W = 4x
We know that the area (A) is 180 square inches, so:
A = L × W
180 = (5x) × (4x)
180 = 20x₂
Therefore:
x₂ = 180 / 20
x₂ = 9
x = 3
Now we can find L and W by substituting x back into L = 5x and W = 4x:
L = 5 × 3 = 15 inches
W = 4 × 3 = 12 inches
Hence, the length of the rectangle is 15 inches, and the width is 12 inches.
Which calculation should be used to calculate s9 for the arithmetic sequence an=3n-1
Answers
Answer: Choice A
S9 = (9/2)*(2+26)
===============================================
The formula is
Sn = (n/2)*(a1+an)
where
Sn = sum of the first n terms (nth partial sum)
n = number of terms
a1 = first term
an = nth term
In this case,
n = 9
a1 = 2 (plug in n = 1 into the formula an = 3n-1 and simplify)
an = a9 = 26 (plug n = 9 into the formula an = 3n-1 and simplify)
So,
Sn = (n/2)*(a1+an)
S9 = (9/2)*(2+26)
will help us find the sum of the first 9 terms of this arithmetic sequence
Answer:
A. S9 = (9/2)*(2+26)
What is the range of the function graphed below?
Answers
Option: B is the correct answer.
The range of the function is:
B. 5 < y < ∞
Step-by-step explanation:Range of a function--
The range of a function is the set of all the values that is attained by the function.
By looking at the graph of the function we see that the function tends to 5 when x→ -∞ and the function tends to infinity when x →∞
Also, the function is a strictly increasing function.
This means that the function takes every real value between 5 and ∞ .
i.e. The range of the function is: (5,∞)
Hence, the answer is:
Option: B
PLEASE HELP PLEASE PLEASE
Answers
Answer: 25.13 (choice B)
================================
The formula we'll use is
s = r*theta
with
s = unknown arc length
r = radius = diameter/2 = 12/2 = 6 feet
theta = 4pi/3 radians <--- this angle must be in radian mode for the formula to work
Plug those values into the formula and simplify
s = r*theta
s = 6*(4pi/3)
s = 24pi/3
s = 8*pi
s = 8*3.1416
s = 25.1328
s = 25.13
which is approximate and rounded to the nearest hundredth.
If a standard vodka martini recipe at La-ti-da Lounge calls for 2.5 oz of premium vodka that sells for $35/liter, .5 oz of dry vermouth that sells for $7.99 a liter, and one jumbo gourmet olive for 15 cents, and the martini sells for $15, what is the drink cost percentage?
a. 19.3 percent
b. 14.7 percent
c. 12.5 percent
d. 16.5 percent
Answers
Answer: (A) 19.3%
Step-by-step explanation:
[tex]\text{Vodka: }2.5\text{ oz }\times\dfrac{\$35}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$2.59\\\\\text{Vermouth: }0.5\text{ oz }\times\dfrac{\$7.99}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$0.12\\\\\text{Olive: }\$0.15[/tex]
Vodka + Vermouth + Olive = Total Cost
$2.59 + $0.12 + $0.15 = $2.86
[tex]\dfrac{\text{cost to make}}{\text{selling price}} = \dfrac{\$2.86}{\$15} = 0.19 = 19\%[/tex]
Write the equation of the parabola in vertex form
Answers
Answer:
[tex]y^2=-12(x+2)[/tex]
Step-by-step explanation:
The general vertex form of parabola is,
[tex](y-k)^2=a(x-h)[/tex]
where,
[tex](h.k)[/tex] is the vertex,
[tex]y=h[/tex] is the axis of symmetry.
Given the coordinates of the vertex as [tex](-2,0)[/tex] and focus as [tex](-5,0)[/tex]
a is the 4 times the distance between the vertex and the focus.
The distance between the vertex and focus is -3. Negative is because we are calculating the distance to the left (-ve x direction) of the vertex.
Hence, [tex]a=4\times(-3)=-12[/tex]
Putting the values in the general equation,
[tex](y-0)^2=-12(x-(-2))[/tex]
i.e [tex]y^2=-12(x+2)[/tex]
Shawn drew a rectangle that had a width of 4.2 inches and a length of 8.1 inches. Find the perimeter of Shawn's rectangle
Answers
Answer: 24.6 inches
Step-by-step explanation: Since it's a rectangle, and not a rectangular prism, that means it's 2D. Length is the long sides on the top and bottom, and width is the shorter sides on it's left and right. So since there's two of each, just do 8.1 + 8.1 + 4.2 + 4.2 and you have your answer!
A cell phone company sold 4,000 cell phones in the month of November. In December, the company held its annual sale and sold 22% more cell phones than it did in November. In January, the company experienced its slowest month, managing to sell only 50% of the number of cell phones sold during the month of December. What is the total number of cell phones sold by the company during the three months combined? Select one: A. 10,450 B. 10,900 C. 11,320 D. 11,710
help please, 30 pts
Answers
What is the solution of the equation?
Answers
[tex] \sqrt{2x - 5} = x - 4[/tex]
[tex]2x - 5 = (x - 4) {}^{2} [/tex]
[tex]2x - 5 = x {}^{2} - 8x + 16[/tex]
[tex]x {}^{2} - 10x + 21 = 0[/tex]
[tex](x - 3)(x - 7) = 0[/tex]
[tex]x = 3 \\ x = 7[/tex]
Answer: 7
Step-by-step explanation:
[tex]\sqrt{2x-5}+4 = x[/tex]
[tex]\sqrt{2x-5} = x-4[/tex] subtracted 4 from both sides
[tex](\sqrt{2x-5})^2 = (x-4)^2[/tex] squared both sides to eliminate square root
2x - 5 = x² - 8x + 16 expanded right side
0 = x² - 10x + 21 subtracted 2x and added 5 on both sides
0 = (x - 3) (x - 7) factored right side
0 = x - 3 0 = x - 7 applied zero product property
x = 3 x = 7 solved for x
Check:
x = 3
[tex]\sqrt{2(3)-5}+4 = (3)[/tex]
[tex]\sqrt{1}+4 = 3[/tex]
1 + 4 = 3
FALSE! x = 3 is NOT a valid solution
x = 7
[tex]\sqrt{2(7)-5}+4 = (7)[/tex]
[tex]\sqrt{9}+4 = 7[/tex]
3 + 4 = 7
TRUE! x = 7 IS a valid solution
Given that line segments are taken to line segments of the same length during rigid transformations, which transformation maps the line segment AB onto itself?
A) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → x-axis reflection
B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection
C) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
D) rotation counterclockwise of 180° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
Answers
Answer:
Correct choice is C
Step-by-step explanation:
Points A and B have coordinates (1,-2) and (4,3), respectively.
1. Rotation counterclockwise of 90° about the origin has a rule:
(x,y)→(-y,x).
Then the image of point A is point A'(2,1) and the image of point B is point B'(-3,4).
2. Refection about the x-axis has a rule:
(x,y)→(x,-y).
Then the image of point A' is point A''(2,-1) and the image of point B' is point B''(-3,-4).
3. Rotation counterclockwise of 270° about the origin has a rule:
(x,y)→(y,-x).
Then the image of point A'' is point A'''(-1,-2) and the image of point B'' is point B'''(-4,3).
4. Refection about the y-axis has a rule:
(x,y)→(-x,y).
Then the image of point A''' is point A(1,-2) and the image of point B''' is point B(4,3).
brenda deposits $500 in a saving account that pays a simple interest rate of 2.5% per year. How much interest will Brenda earn after 18 months?
Answers
Brenda will earn $18.75 in interest after 18 months.
Explanation:To calculate the interest Brenda will earn after 18 months, we can use the simple interest formula:
Principal x Rate x Time = Interest
According to the question, Brenda deposited $500 in a savings account with a simple interest rate of 2.5% per year. Since the time period given is 18 months, we need to convert it to years. 18 months is equivalent to 1.5 years.
Therefore, the interest Brenda will earn after 18 months can be calculated as:
$500 x 0.025 x 1.5 = $18.75
Brenda will earn $18.75 in interest.
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If you shift the linear parent function, f(x) = x, down 7 units, what is the equation of the new function? A. G(x) = 7x B. G(x) = x + 7 C. G(x) = x – 7 D. G(x) = x
Answers
Answer:
The correct answer is C. f(x) = x - 7
Step-by-step explanation:
In order to find this, you simply need to know that vertical shifts can be added on to the end of parent equations as constants. Since this is a downward shift, we use a negative number.
Please help me out!!!!!!! :D
Answers
Answer:
decrease
Step-by-step explanation:
75 is a higher than 25% come man its ez
Yolanda and her 3 brothers shared a box of 156 toy dinosaurs . About how many dilnosaurs did each kid get
Answers
The required number of dinosaurs that each of them gets is 39 dinosaurs.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the number of dinosaurs be x that is distributed among Yolanda and her 3 brothers,
Total persons = 1 + 3 = 4
Total dinosaurs = 156
Each of them gets,
x = 156/4
x = 39 dinosaurs.
Thus, the required number of dinosaurs that each of them gets is 39 dinosaurs.
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The equation 4x2 – 24x + 4y2 + 72y = 76 is equivalent to
(1) 4(x – 3)2 + 4(y + 9)2 = 76
(2) 4(x – 3)2 + 4(y + 9)2 = 121
(3) 4(x – 3)2 + 4(y + 9)2 = 166
(4) 4(x – 3)2 + 4(y + 9)2 = 436
I know the answer is choice 1 but how do you get to that answer?
Answers
Answer:
Option 4 is correct.
The equation [tex]4x^2 -24x + 4y^2 + 72y = 76[/tex] is equivalent to [tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]
Step-by-step explanation:'
Given equation: [tex]4x^2 -24x + 4y^2 + 72y = 76[/tex]
First group the terms with x and those with y;
[tex](4x^2-24x)+(4y^2+72y) = 76[/tex]
Next, we complete the squares.
We can do this by adding a third term such that the x terms and the y terms are perfect squares.
For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.
⇒[tex]4(x^2-6x) +4(y+18y) = 76[/tex]
or
[tex]4(x^2 -6x +3^2 -3^2) + 4(y^2 +18y +9^2 -9^2) = 76[/tex]
[tex]4(x^2-6x + 3^2) - 36 + 4(y^2+18y +9^2) - 324 = 76[/tex]
[tex]4(x-3)^2 + 4(y+9)^2 - 360 =76[/tex]
Add 360 on both sides we get;
[tex]4(x-3)^2 + 4(y+9)^2 =360 +76[/tex]
Simplify:
[tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]
Therefore, the given equation is equivalent to [tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]
Guillermo bought some reams of paper for $5 each and a $200 printer.He spent a total of $450.Write and solve an equation to find the number reams of paper Guillermo purchased
Answers
that is the equation.
5x + 200 = 450
-200. -200
5x = 250
divide both sides by 5
and your answer is
=50.