The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)
What transformation rule is used to transform a given function?
In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.
Horizontal translation
g(x) = f(x - k), where k > 0 for a translation in + x direction.
Vertical translation
g(x) = f(x) + k, where k > 0 for a translation in + y direction.
After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down. Then, we find the following transformation formula:
g(z) = f(z) - 2
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5.
A car service charges $2.40 for driving 1 mile. How much does the company charge for
driving 12.45 miles?
) (
$14.85
$24.85
$27.48
$29.88
Show Your Work
Answer:
Step-by-step explanation:
$2.40 12.45 mi
___ * ___ = ? ;
1 mi. 1
The units of miles— "mi" —cancel out to "1" ;
since: " mi/ mi = 1 "
and we have:
$2.40 * 12.45 = ? ;
= $29. 88 ; {using a calculator};
⇒ which corresponds to: Answer choice: [D]: $29.88 .
_____
Hope this is helpful!
Best wishes!
_____
solve for x. "-8+x/4=-4" simplify your answer as much as possible
Answer:
48
Step-by-step explanation:
multiply by 4 to make x whole number
-32+x=16
+32 to isolate x
x=16+32
add for answer
x=48
m∠M = 6x – 6 and m∠P = 4x + 10, what is m∠M?
Choose which property of equality is demonstrated.
a. AB = AB
7. Wanda's Widgets used market surveys and linear regression to develop a demand function based on the wholesale price. The demand function is q = -140p + 9,000. The expense function is E = 2.00q + 16,000.
a. Express the expense function in terms of p.
b. At a price of $10.00, how many widgets are demanded?
c. How much does it cost to produce the number of widgets from part b?
I am so confused on how to answer these 3 sections, so if anyone could help I would really appreciate it!!
a. The expense function in terms of p is - 280p + 34, 000
b. At a price of $10.00, 7, 600 widgets are demanded
c. It costs $31, 200 to produce the number of widgets from part b
How to determine the valuesWe have that;
The demand function is q = -140p + 9,000The expense function is E = 2.00q + 16,000To express the expense function in terms of p, we have to take the following steps;
Substitute the value of q in the demand function into the function for the expense, we get;
Expense function = 2( -140p + 9,000) + 16, 000
Now, expand the bracket, we get;
Expense function = - 280p + 18, 000 + 16, 000
collect and add like terms
Expense function = - 280p + 34, 000
If p = $10. 00
Then,
Demand function is q = -140(10) + 9,000
expand the bracket
q = - 1400 + 9, 000
q = 7, 600
Substitute q in expense function
E = 2.00q + 16,000
E = 2. 00(7600) + 16, 000
E = $31, 200
Hence, the expense function is - 280p + 34, 000
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find the missing angle measures
a=b
b=(b+16)
c=(2b)
Answer:
a = 41°
b = 57°
c = 82°
Step-by-step explanation:
all angles in a triangle must add up to equal 180°
so 4b + 16 = 180180 - 16 = 4b164 = 4b164 / 4 = 41b = 41°therefore a = 41°, b = (41 + 16) --> 57°, and c = 2(41) = 82°Fin the measurement of the angle
A=
B=
C=
D=
E=
F=
G=
45°
Answer:
Step-by-step explanation:
A=60
B=75
C=45
D=60
E=75
F=45
G=90
what is the inequality of the length of a rectangle is 1 unit more than its width.the width of the rectangle is 2 units and the length of the wire that is used to make this rectangle is a maximum of 57 units. what represent this situation using an inequality
Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives
Perimeter = 2(L + W) ≤ 57 units How to determine the inequality that shows the length and width of a rectangleThe perimeter of a rectangle, P is given by the formula
P = 2(L + W) ≤ 57 units of wire
width, W = 2 units
length, L = 1 + W
= 1 + 2
= 3
The perimeter of the rectangle is given by
P = 2(L + W)
plugging the values of L and W
P = 2 (3 + 1)
P = 2 (4 )
P = 8 units
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6x-5=6x-5 pls help fast
Answer:
0=0
Step-by-step explanation:
Answer: Infinite Solutions
Step-by-step explanation:
Hello! Let's solve this equation.
[tex]\textbf{First, add 5 to both sides.}[/tex][tex]\sf{6x-5=6x-5}[/tex]
↓
[tex]\sf{6x=6x-5+5}[/tex]
↓
[tex]\sf{6x=6x}[/tex]
[tex]\textbf{Next, subtract 6x from both sides.}[/tex][tex]\sf{6x-6x}[/tex]
↓
[tex]\sf{0}[/tex]
[tex]\textbf{So as you see, all the terms \textit{cancel out.}}\\\textbf{The \textsf{given equation} has \textit{\underline{infinite solutions.}}}\\\textbf{The equation is true for any x-value.}[/tex]
[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]
Graph a line with a slope of 1/5 and passes through the point (-2, 2).
The equation of line in slope intercept form
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Slope = [tex]\frac{1}{5}[/tex]
Point = (-2, 2)
Required equation of line =
[tex]y - 2 = \frac{1}{5}(x - (-2))\\5y - 10 = x + 2\\5y = x + 2 + 10\\5y = x + 12\\y = \frac{1}{5}x + \frac{12}{5}\\[/tex]
The graph has been attached here.
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Hayley's fuel bills for her house increased from £76 a month in 2021
to £89 a month in 2022. Calculate the percentage increase in Hayley's
fuel bills from 2021 to 2022.
Give your answer correct to three significant figures.
The percentage increase in Hayley's fuel bills from 2021 to 2022 is equal to 17.105%.
What is a Percentage Increase?
The phrase "percentage increase" (or "percentage change" in general) refers to the difference between the final and starting values of a quantity, expressed as a percentage of that number's original value.
Steps to Calculate Percentage Increase?
The formula to calculate Increase (I) is given by, [tex]I=Y-X[/tex], where [tex]X[/tex] is the original value and [tex]Y[/tex] is the new value.The percentage increase formula is given by, [tex]\%I=\frac{I}{X} \times 100[/tex]Here, in the question, it is given that,
The original amount (X) or the fuel bill in 2021 is £76.
The new amount (Y) or the fuel bill in 2022 is £89.
So, the Increase (I) in the fuel bills from 2021 and 2022 is calculated as,
[tex]I=Y-X\\\implies I=89-76\\\implies I=13[/tex]
Now, we can calculate the percentage increase in fuel bills from 2021 to 2022 as,
[tex]\%I=\frac{I}{X} \times 100\\\implies \%I=\frac{13}{76} \times 100\\\implies \%I=17.105\%[/tex]
Therefore, the percentage increase in Hayley's fuel bills from 2021 to 2022 is 17.105%.
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If a circle has an Area of 84.9056, find the radius and the circumference of the circle.
(Use π=3.14 and do not round.)
Radius =
Circumference =
Answer: Radius is estimated to = 5.2
Circumference is estimated to = 32.66
Levine Labs used 50,000 ounces of specimen adhesive during the year. The direct materials standard allows 1.50 ounces of adhesive at a price of $0.40 per ounce for each pathology test. The direct materials quantity variance was $880 Favorable.
How many pathology tests did Levine Labs complete during the year?
(Round per unit value to 2 decimal places, e.g. 15.25 and final answer to O decimal places, e.g. 125.)
Pathology tests ____?
The number of pathology tests that were completed during the year by Levine Labs are 34,800 tests.
What is the calculation showing the above answer?Note that Material quantity variation - Material quantity variation describes the cost difference caused by variations in the actual material used and the standard material to be utilized.
Material quantity Variance =
(Actual material used- Standard material used) x Standard cost
(50000-no of test x 1.5) x 0.4 = -880
-2200 = 50000-(No of test*1.5)
No of test x 1.5 = 52,200
No of test = 52,200/1.5
No of test = 34,800
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1. Write and solve an equation for the following statement: Eight less than one-third of a number,
Answer: (1/3)x - 8
Step-by-step explanation:
one - third means 1/3
one - third of a number means (1/3)x
( x being the number )
Eight less means -8
Eight less than 1/3 of an number is (1/3)x - 8
There are 90 new houses being built in a neighborhood.last month, 1/5 of them were sold. this month,1/3 of the remaining houses were sold. How many houses were left to be sold?
Step-by-step explanation:
1:
1/5 of 90 = 18 hours which are sold.Means are 72 houses left.
2.
1/3 of 72 =24 houses sold again. Sooo means there are 48 houses left to be sold
(2/7 , −3) ; r = 6 standard form of circle
The cost to attend a public university in a recent year is $16,241. The circle graph to
the right shows the percentage of that cost for tuition/fees, room, board, and
computer costs. Determine the cost, in dollars, for each category.
The cost of tuition and fees is $.
(Round to the nearest cent as needed.)
The cost of room is $.
(Round to the nearest cent as needed.)
The cost of board is $.
(Round to the nearest cent as needed.)
The computer costs are $
(Round to the nearest cent as needed.)
Cost to Attend a Public University
Tuition/Fees 36.9%
Room 31.5%
Board 24.9%
Computer costs 6.7%
Using the circle graph, the costs to attend the public university are as follows:
cost of tuition and fees = $ 5992.93cost of room = $5115.92cost of board = $ 4044.01computer cost = $1088.15How to find cost using circle graph or pie chart?A circle graph, or a pie chart, is used to visualize information and data.
Therefore, the circle graph is shows the percentage cost for tuition/fees, room, board, and computer costs.
The cost to attend a public university in a recent year is $16,241.
Using the pie chart, let's find the cost of the various fees.
Therefore,
cost of tuition and fees = 36.9% of 16,241
cost of tuition and fees = 36.9 / 100 × 16241
cost of tuition and fees = 599292.9 / 100
Therefore,
cost of tuition and fees = $ 5992.929
cost of room = 31.5% × 16241
cost of room = 31.5 / 100 × 16241
cost of room = $5115.915
Hence,
cost of board = 24.9% of 16241
cost of board = 24.9 / 100 × 16241
cost of board = $ 4044.009
Hence,
computer cost = 6.7% of 16241
computer cost = 6.7 / 100 × 16241
computer cost = $1088.147
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1. What is the missing number 56/7=?-5
Answer:
13
Step-by-step explanation:
56/7 = 8
13 - 5 = 8
15/7 = 13 - 5
The missing number in the expression is 13.
We have,
To find the missing number in the equation 56 / 7 =? - 5, solve for the unknown value.
Unknown value = x
Starting with the equation 56 / 7 = x - 5, simplify the left side:
56 / 7 = x - 5
8 = x - 5
x = 8 + 5
x = 13
Thus,
The missing number in the expression is 13.
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Only 9 people can be in a roller coaster cart. How many people can fit in nine train carts
Answer:
81 people
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Use the number line to plot –3, 1, and 3.
Which statements are true
Select all that apply.
–3 > 1
–3 = 3
1 < 3
–3 < 1
The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.
The correct statements regarding the number line are given as follows:
1 < 3.–3 < 1.How to plot an integer number on the number line?Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.
These numbers are plotted marking a symbol such as a X or a circle on the number line.
The number line is increasing, so the negative numbers appear before the positive numbers.
This means that if a number a is to the left another number b, the number a is less than b, hence:
1 < 3–3 < 1.As the order in which the numbers appear is given as follows:
-3, 1 and 3.
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Suppose that 14 inches of wire costs 70 cents. At the same rate, how many inches of wire can be bought for 50 cents?
Answer:
10 inches
Step-by-step explanation:
What this question is asking you to do is set up a ratio. So all you do is 14/70 = x/50 and solve for x.
Answer:
14inches = 70cents
X inches = 50cents
70x = 50×14
70x = 700
X = 10inches
At one time the thickness of different gauges of stainless
steel were given in fractions of an inch. Today, these
thicknesses are listed as decimal numbers. Convert each of
the following fractional thicknesses to decimal form.
A fraction can be converted into decimal form by dividing it. The answer to these parts are in main body.
What is a decimal?
When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number.
Main Body:
a) 15/32 = 0.4688
b) 13/64 = 0.2031
c) 9/16 = 0.5625
d) 5/8 = 0.625
e) 7/80 = 0.0875
f) 29/1280 = 0.0227
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35. Rosa plants rows of flowers with exactly the same number
in each row. Each row has more than one flower. She has
28 flowers. What is the largest number of rows she can make?
A 4
B
7
12
D 14
Answer: 10 rows of rose plants
Step-by-step explanation:
The number of rose plants in first, second third,..., and last row are respectively.
23,21,19,....,5.
number of rose plants: n
The sequence 23,21,19,....,5 is an A.P. with first term a(=23), common difference d(=−2) and n
=a+(n−1)d
⟹5=23+(n−1)×−2
⟹5=23−2n+2⟹20=2n⟹n=10
Use the compound interest formula to compute the total amount accumulated and the interest earned.
$3000 for 3 years at %4 compounded semiannually.
The amount in the account is ____.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The amount in the account is $3499. 2
How to determine the compound interestThe formula for determining compound interest is given as;
A = P ( 1 + r/ n) ^nt
Given that;
A is the final amountP is the principal amountr is the ratet is the time taken n is the number of times interest applied per periodSubstitute the values into the formula, we have;
A = $3000 ( 1 + 0. 04 / 0. 5) ^(0.5× 4)
Find the exponential value
A = $3000 ( 1 + 0. 04 / 0. 5) ^2
A = $3000( 1+ 0. 08)^2
Expand the bracket, we get;
A = $3000 (1. 08)^2
A = $3000(1. 17)
multiply through
A = $3499. 2
Hence, the value is $3499. 2
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a) 50 students in a hostel had provisions for 60 days. (i) How long would the provisions last for 1 student? (ii) How long would the provisions last for 40 students?
Answer:0.8
Step-by-step explanation:
0.8 can be used for 1 student and 40. :)
The values are;
i, For 1 student, it would take = 1 1/5 days
ii. For 40 students, 48 days
How to determine the daysFirst, we need to know that proportion is an equation made equal to another.
From the information given, we have that;
50 students in a hostel had provisions for 60 days.
This is represented as;
50 students = 60 days
Then, we get that;
i, If 50 students = 60 days
1 students = x days
cross multiply the values
x = 60/50
x = 1 1/5 days
ii. If 50 students = 60 days
40 students = x days
x = 60(40)/50
divide the values
x = 48 days
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Which graph represents the solution of -3m < 15?
The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c).
Temperature: Days:
50-59 5
60-69 309
70-79 1496
80-89 1521
90-99 533
100-109 6
(a) Approximate the mean and standard deviation for temperature.
B) Use the frequency histogram of the data to verify that distribution is bell shaped. Yes or No
C) According to the Empirical rule, 95% of the days in the month will be between what two temperatures?
Regarding the data-set of the temperatures, it is found that:
a) The mean and the standard deviation are given as follows:
Mean: 80.41Standard deviation: 8.33.b) The histogram is bell shaped.
c) 95% of the days will be between 63.75 ºF and 97.07 ºF.
How to obtain the mean and the standard deviation?The first step towards obtaining the mean and the standard deviation is obtaining the relative frequencies, which are the absolute frequencies divided by the number of observations.
The number of observations is:
5 + 309 + 1496 + 1521 + 533 + 6 = 3870.
Considering the midpoint of each interval, the following distribution is built:
P(X = 54.5) = 5/3870 = 0.0013.P(X = 64.5) = 309/3870 = 0.0798.P(X = 74.5) = 1496/3870 = 0.3866.P(X = 84.5) = 1521/3870 = 0.3930.P(X = 94.5) = 533/3870 = 0.1377.P(X = 104.5) = 6/3870 = 0.0016.The mean is given by the sum of each value multiplied by it's relative frequency, hence:
E(X) = 54.5 x 0.0013 + 64.5 x 0.0798 + 74.5 x 0.3866 + 84.5 x 0.3930 + 94.5 x 0.1377 + 104.5 x 0.0016 = 80.41.
The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their relative frequencies, as follows:
S(X) = sqrt((54.5-80.41)² x 0.0013 + (64.5-80.41)² x 0.0798 + (74.5-80.41)² x 0.3866 + (84.5-80.41)² x 0.3930 + (94.5-80.41)² x 0.1377 + (104.5-80.41)² x 0.0016) = 8.33.
From the histogram, most values are around the mean, with a small percentage of around 0.3% around the bounds, accordingly with the Empirical Rule, hence the distribution is normal.
By the Empirical Rule, a percentage of 95% of the observations is within two standard deviations of the mean, hence:
80.41 - 2 x 8.33 = 63.75.80.41 + 2 x 8.33 = 97.07.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
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A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1487 and the standard deviation was 314. The test scores of four students selected at randon
1870, 1250, 2170, and 1390. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
If a standardized exam's scores are normally distributed. The z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.
How to find the z-score?mu = population mean = 1487
sigma = population standard deviation = 314
x =1870
z = (x - mu)/σ
z = (1870-1487)/314
z = 1.22 (approximately)
x =1250
z = (x - mu)/σ
z = (1250-1487)/314
z = -0.75
x =2170
z = (x - mu)/σ
z = (2170-1487)/314
z = 2.18 (approximately)
x =1390
z = (x - mu)/σ
z = (1390-1487)/314
z = -0.31 (approximately)
Therefore the z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.
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What does “more than” mean in math?
Means if a number is bigger than other number.
(PLEASE OPEN) Need help with triangle proofs.
The missing terms in the two column proof are;
Reason 1; Perpendicular bisector
Reason 2; Definition of perpendicular bisector
Statement 3; CO ≅ BO
Reason 3; Segment division
Reason 4; Reflexive Property of Congruence
Reason 5; Definition of Isosceles Triangle
Reason 6; AAS Congruency Postulate
How to carry out two column proof of triangles?From the given image, we want to use the two column proof to prove that ΔAOB ≅ ΔAOC
Now, we have the two column proof as follows;
Statement 1; AO ⊥ BC
Reason 1; Perpendicular bisector
Statement 2; ∠AOB and ∠AOC are right angles
Reason 2; Definition of perpendicular bisector
Statement 3; CO ≅ BO
Reason 3; Segment division
Statement 4; AO ≅ AO
Reason 4; Reflexive Property of Congruence
Statement 5; AB ≅ AC
Reason 5; Definition of Isosceles Triangle
Statement 6; ΔAOB ≅ ΔAOC
Reason 6; AAS Congruency Postulate
The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.
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