The transformation processes and equation of the transformed function are:
a) f(x) is translated in the negative y direction and the equation of the transformed function is f(x) = 2x - 4
b) g(x) is translated in the positive y direction and the equation is g(x) = 1/3x + 6
c) g(x) is dilated 3 times hat it as and the equation is x + 6
d) f(x) is dilated and the equation is x + 1/2
What is Dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
f(x) is translated by 5 units to the negative y-direction, so f(x) - 5 becomes 2x + 1 -5 = 2x - 4
g(x) + 4 means translation 4 units to the positive y-axis and the function g(x) + 4 becomes x/3 + 2 + 4 = x/3 + 6
3g(x) is dilation which means g(x) would be 3 times what it was initially.
3 x ( x/3 + 2) = x + 6
1/2f(x) is dilation which is a reduction by half. so the function becomes
1/2 x ( 2x + 1) = x + 1/2
In conclusion, the transformation processes are:
a) f(x) is translated in the negative y direction and the equation of the transformed function is f(x) = 2x - 4
b) g(x) is translated in the positive y direction and the equation is g(x) = 1/3x + 6
c) g(x) is dilated 3 times hat it as and the equation is x + 6
d) f(x) is dilated and the equation is x + 1/2
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The x-coordinates of the points of intersection of the given function graphs are;
1) x = 0 and x = 2
2) x = -1
3) x = 0
What is the point of intersection of the graph?
The point of intersection of a graph is defined as the point or coordinates where two lines or curves meet each other.
1) In the first graph, we are given the functions as;
f(x) = -³/₄x² + 3x + 1
g(x) = 2ˣ
Thus;
From the graph, f(x) = g(x) is at (2,4 and (0, 1)
2) In the first graph, we are given the functions as;
f(x) = x² + 4x + 2
g(x) = (¹/₂)ˣ + 1
Thus;
From the graph, f(x) = g(x) is at (-1. 3)
C) In the third graph, we are given the functions as;
f(x) = -⁷/₃x - 3
g(x) = 2ˣ - 4
Thus;
From the graph, f(x) = g(x) is at (0, -3)
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Lindsey bought a picnic basket originally priced at $40 but on sale for 50% off. After 10% sales tax, what was the total cost?
$
Answer:
Step-by-step explanation:
I got 22 my friend hope i helped.
Answer:
$18
Step-by-step explanation:
50% of 40 is 20, so 40-20=20
10% of 20 is 2, so 20-2=18
total price=$18
Joseph runs 2/3 of a mile in 8 minutes. If Joseph runs at that speed, how long will it take him to run four miles? pls include explanation
Joseph runs 4 miles in 48 minutes.
From the question, we have
Joseph runs 2/3 of a mile in 8 minutes.
Joseph runs 1 mile in (3*8)/2 = 12 minutes.
Joseph runs 4 miles in (12*4)= 48 minutes.
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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qrst is a square find Qu if qs =16t-14 and qu=6t+11
You have the square QRST, furthermore, you have that sides QS and QU are given by the following algebraic expressions:
QS = 16t - 14
QU = 6t + 11
Due to QRST is a square, the length of all sides are equal.
You can notice by the symmetry of the figure that QS = 2QU
Equal the expressions for QS and 2QU and solvde for t:
16t - 14 = 2(6t + 11) apply distribution property
16t - 14 = 12t + 22 add 14 both sides
16t = 12t + 22 + 14 subtract 12t both sides
16t - 12t = 22 + 14 simplfy like terms
4t = 36 divide by 4 both sides
t = 36/4 simplify the fraction
t = 9
Hence, the value of t is t = 9
I need help! fast! please help will give 50 points
Answer:
9/2
Step-by-step explanation:
Answer
the commisoin is 270
Bonjour est-ce que vous pouvez m’aider s’il vous plaît voici l’exercice
C’est l’exercice 19
Answer:
a = ⁵⁄₃ = 1⅔
b = ¼
c = ⁵⁄₇
d = ¹³⁄₁₂ = 1¹⁄₁₂
e = -⁷⁄₃₀
f = ³⁷⁄₁₄ = 2⁹⁄₁₄
The circumference of a circle is 22π ft. What is the area, in square feet? Express your answer in terms of \piπ.
Answer:
121 pi
Step-by-step explanation:
pi d =22 pi
divide both side by pi to find diameter
d=22
divide by 2 too find radius
11 is the radius
plugg 11 to pi r ²
121 pi
is the morning temperature was 1 degrees Celsius then there was a rise of 3 degrees Celsius what is the afternoon temperature
the temperature in the morning was 1 degree celsius
then rise of 3 degree
so now the total temperature is 1 + 3 = 4 degree
so the temperature of the afternoon is 4 degrees.
Which of the expressions equal −5
Answer:
-5+0=-5
(-6)+1=-5
-7+2=-5
Step-by-step explanation:
In ΔKLM, l = 710 cm, k = 130 cm and ∠K=161°. Find all possible values of ∠L, to the nearest 10th of a degree.
PLEASE HELP
The value of ∠L is 2.909° as the definition of angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint".
What is angle?An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. Based on measurement, there are different kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees.
Here,
Side k = 130
Side l = 710
Side m = 833.99204
Angle ∠L = 2.909°
Angle ∠M = 16.091°
Angle ∠K = 161°
Angle L=cos⁻¹((m²+ k² - l²)/2mk)
=cos⁻¹((834²+130²-710²)/2*834*130)
= 2.909°
Since the definition of an angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint," the value of ∠L is 2.909°.
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if 1+3 =345+2=275+1=163+5=58then2+4=?what isnthe ?
Answer:
46
Explanation:
In each number to the right of the equality sign, the tenths place is always the rightmost number in addition and the one place is the result of the addition.
For example, in 1 +3 = 34
Therefore, for 2 + 4 we have
Hence,
[tex]2+4=46[/tex]which is our answer!
You used a student deck of 52 cards and selected a card at random find (c) 2 of heart
Definition
Theoretical Probability is the ratio of the number of favorable outcomes to the total possible outcomes of an event.
Expressing probability as a formula:
[tex]\text{probability = }\frac{Number\text{ of favorable outcomes}}{Total\text{ possible outcomes of an event}}[/tex]Information about a standard deck of cards:
A standard deck of cards has four suits: hearts, clubs, spades, diamonds. Each suit has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Thus the entire deck has 52 cards total.
(a) Picture card (J, Q, and K)
In a standard deck, there are 4 Jacks, Queens, and Kings. Hence, the probability of J, Q, and K are:
[tex]\begin{gathered} \text{Number of picture cards = 4 }\times\text{ 3} \\ =\text{ 12} \end{gathered}[/tex]Probability as a fraction:
[tex]=\text{ }\frac{12}{52}[/tex]In decimal:
[tex]=\text{ }0.23[/tex]Percent:
[tex]\begin{gathered} =\text{ 0.23 }\times\text{ 100} \\ =\text{ 23\%} \end{gathered}[/tex](b) 9 or 10
There are 4 cards labeled 9 and 10 each.
Probability as a fraction:
[tex]\begin{gathered} P(9or10)=\text{ P(9) + P(10)} \\ =\text{ }\frac{4}{52}\text{ + }\frac{4}{52} \\ =\text{ }\frac{8}{52} \end{gathered}[/tex]In decimal:
[tex]=\text{ 0.15}[/tex]In percent:
[tex]\begin{gathered} =\text{ 0.15 }\times\text{ 100} \\ =\text{ 15\%} \end{gathered}[/tex](c) 2 of heart
In a standard deck of cards, there are only one 2 of hearts.
Probability as a fraction:
[tex]=\text{ }\frac{1}{52}[/tex]In decimal:
[tex]=\text{ 0.02}[/tex]In percent:
[tex]\begin{gathered} =\text{ 0.02 }\times\text{ 100} \\ =\text{ 2\%} \end{gathered}[/tex]Use the law of sines to solve the triangle if possible
The Sine rule formula is,
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]Given:
[tex]\begin{gathered} a=13.9in \\ A=83^0 \\ b=18.3in \\ B=? \end{gathered}[/tex]Let us solve for solve for the measure of angle B
[tex]\frac{13.9}{sin83^0}=\frac{18.3}{sinB}[/tex]Therefore,
[tex]\begin{gathered} sinB=\frac{18.3\times sin83^0}{13.9}=1.30673342266 \\ \therefore B=sin^{-1}(1.30673342266)=No\text{ solution} \end{gathered}[/tex]Hence, there are no possible solutions for this triangle (OPTION C).
Which linear equality will not have a shared solutionset with the graphed linear inequality?Oy> ²x + 2Oy<-5x-72Oy>-x-5Oy < 5 x + 2
The linear inequality y</5/2 x - 7 does not have any common solution set with the given inequality.
The solution sets of the linear inequality are drawn in the graph attached below,
From the graph it is seen that the yellow part represents the inequality y≥-5/2 x - 3
And the green section of the graph represents the other inequality
y<-5/2 x - 7
As we can see in the graph that the two areas are separate. So there are no common points.
Again if we consider the two inequalities as two lines y= -5/2 x - 3
and y = -5/2 x - 7 . we can see that they both have the same slopes of -5/2 so they are parallel lines. so they will never intersect.
Therefore we can conclude that the inequality y</5/2 x - 7 does not have any common solution set with the given inequality.
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How many subsets does the set T = {salsa, sour cream, queso, guacamole, pico de gallo} have?Question 49 options:a) 5b) 0c) 25d) 32
SOLUTION:
Step 1:
In this question, we are given the following:
How many subsets does the set T = {salsa, sour cream, queso, guacamole, pico de gallo} have?
Step 2:
The details of the solution are as follows:
Recall that:
The empty set and the set itelf are also part of the subsets that must be included as part of the number of subsets.
If a set has “n” elements,
then the number of subset of the given set is
[tex]2^n[/tex]Hence, the total number of subsets will be:
[tex]2^5=\text{ 32 \lparen OPTION D \rparen}[/tex]CONCLUSION:
The final answer is:
[tex]32\text{ \lparen OPTION D \rparen}[/tex]18 pizzas were ordered for a holiday party at Reedy Creek Elementary
ANSWER
C. 12
EXPLANATION
1/3 of the pizzas is:
[tex]18\times\frac{1}{3}=\frac{18}{3}=6[/tex]Therefore, 6 pizzas were cheese and the rest were pepperoni:
[tex]18-6=12[/tex]There were 12 pepperoni pizzas.
x=9 and y=4 what does xy/2
Answer:
18
Step-by-step explanation:
Equation 9 x 4 / 2 = 18
First do 9 x 4 which is 36
Next do 36 / 2 which is 18
Also the "/" is another way to say to divide
WILL GIVE BRAINIEST!!!
Answer:
x=1
Step-by-step explanation:
Both graphs intersect at 1
Answer:
x=1
Step-by-step explanation:
They sectioned at 1
a person must score in the upper 7% of the population on an admissions test to qualify for membership in society catering to highly intelligent individuals. if test scores are normally distributed with a mean of 110 and a standard deviation of 15, what is the minimum score a person must have to qualify for the society? (round your answer to the nearest integer.)
Answer:
Below
Step-by-step explanation:
Look for .9300 on the z-score table
= z-score = + 1.48
1.48 standard deciations = 1.48 * 15 = 22.2
110 + 22.2 = 132.2
132.2 is 1.48 standard deviations above the mean and is .9308 (93.08%)
If the speed of a train is increased by 4 miles per hour from its original speed, then it takes 1 hour less to cover a distance of 288 miles. Find its original speed.
The original speed of the train was 32 miles per hour.
We have a train. The train travels a distance equal to 288 miles. It is given that if the speed of a train is increased by 4 miles per hour from its original speed, then it takes 1 hour less to cover the distance. We need to find out the original speed of the train.
Let the original speed of the train be denoted by the variable "s". We can write the following equations using the given data:
s = 288/t
(s + 4) = 288/(t - 1)
We will substitute the value of "s" from the first equation into the second equation.
(288/t) + 4 = 288/(t - 1)
(288)×(t - 1) + 4×t×(t - 1) = 288×t
288t - 288 + 4t² - 4t = 288t
4t² - 4t - 288 = 0
t² - t - 72 = 0
t² - 9t + 8t - 72 = 0
t(t - 9) + 8(t - 9) = 0
(t - 9)(t + 8) = 0
The value of time cannot be negative, so the value of "t" is 9. Now, we will substitute this value into the first equation.
s = 288/t
s = 288/9
s = 32
Hence, the original speed of the train is 32 miles per hour.
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Valerie earns $28,000.00 per year as an assistant hotel manager. Find her
average pay to the nearest cent if she works 38 hours per week, for 52 weeks
out of the year.
Answer:
$14.17 per hour
Step-by-step explanation:
You want Valerie's average pay to the nearest cent if she works 38 hours per week, for 52 weeks out of the year, receiving annual pay of $28,000.
Pay per HourIn a year, Valerie works ...
(38 hours/week) × (52 weeks/year) = 1976 hours/year
She is paid $28,000 for that number of hours, so her hourly pay is ...
$28,000/(1976 hours) ≈ $14.17/hour
Valerie's average pay is about $14.17 per hour.
The number of cups of strawberries in a shortcake recipe is proportional to the number of cups of sugar in the recipe. The recipe uses 5 cups of strawberries per 1/4 cup of sugar.
PART A - What is the constant of proportionality for the relationship between cups of strawberries and cups of sugar
The constant of proportionality is 20.
What is constant of proportionality?
The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.
Given,
the recipe uses 5 cups of strawberries per 1/4 cup of sugar.
And let constant of proportionality is k.
that is
5 α 1/4
5 = k1/4
k = 5(4)
k = 20
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Given the regular nonagon (9-sided polygon) pictured below, which statements are true? Chose 2 answers. PLEASE EXPLAIN HOW YOU GOT THE ANSWER
A:The polygon has point symmetry.
B:The polygon has 40° rotational symmetry.
C:The polygon has 120° rotational symmetry.
D:The polygon has 90° rotational symmetry.
Answer:
B and C
Step-by-step explanation:
find the hcf of 91 , 112 , 49
Answer: The highest common factor of 91, 112 and 49 is 7
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What is the slope of the line that passes through the points (0, -8) and (0,−10)? Write your answer in simplest form.
Answer:
Undefined
Step-by-step explanation:
The x-coordinates of two points on the line are the same, so the line is vertical. Thus, the slope is undefined.
what are the solutions of the equation 6x^2+x-2= 0
Answer: The answer would be
B. 1/2
C. 1/3
Step-by-step explanation:
The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.
Write the inequality that matches the description. The boundary line is dashed and has a slope of -7 and a y-intercept of 2. The area below the line is shaded.
Answer:
y<-7x+2
Explanation:
The slope-intercept form of a line is: y=mx+b
• When slope, m = -7
,• y-intercept, b = 2
We have:
[tex]y=-7x+2[/tex]Since the boundary line is dashed, the inequality sign has to be < or >.
However, since the area below the line is shaded, we can now conclude that the inequality sign is: <
The inequality that matches this description is:
[tex]y<-7x+2[/tex]The ratio of adults to children is 400 to 150
SOLUTION
In mathematics, a ratio indicates how many times one number contains another.
And when we write quantities in ratio form, we represent ratio with the symbol :
For example: The ratio of A to B is written mathematically as A:B
Another important thing we must note when writing ratios is to always express both quantities in their simplest form.
With the above explanation, we can proceed in answering the question.
The ratio of adults to children which is 400 to 150, can be written mathematically in ratio form as:
[tex]\begin{gathered} =\frac{400}{150} \\ \text{Divide both the numerator and denominator by 10} \\ =\frac{40}{15} \\ \text{Divide both the numerator and denominator by 5} \\ =\frac{8}{3} \end{gathered}[/tex]Final answer: The ratio of adults to children is:
[tex]8\colon3[/tex]1. Find the mean, median, mode and midrange for each gender. Women Men 2. Find the range and standard deviation for each gender. Women Men GENDER WEIGHT Male 191 Male 222 Female 136 Male 168 Female 160 Female 101 Male 154 Female 126 Female 119 Male 178 Male 155 Male 190 Female 165 Male 170 Male 178 Female 102 Male 202 Female 135 Male 169 Female 137 Female 140 Male 184 Female 115 Male 149 Female 126 Male 160 Male 181 Female 140 Female 121 Female 124 Male 158
Answer:
1)To find the mean, median, mode and midrange for each gender.
From the given data,
Male: 191,222,168,154,178,155,190,170,178,202,169,184,149,160,181,158
For Men:
Mean is,
[tex]=\frac{191+222+168+154+178+155+190+170+178+202+169+184+149+160+181+158}{16}[/tex][tex]=\frac{2809}{16}=175.5625[/tex]Mean is 175.5625
Arrange the given data in ascending order,
149,154,155,158,160,168,169,170,178,178,181,184,190,191,202,222
Median is,
[tex]=\frac{170+178}{2}=174[/tex]Median is 174
The mode is one of the values of the measures of central tendency. This value gives us a rough idea about which of the items in a data set tend to occur most frequently.
Mode is 178.
Female: 136,160,101,126,119,165,102,135,137,140,115,126,140,121,124
For Women:
Mean is,
[tex]=\frac{136+160+101+126+119+165+102+135+137+140+115+126+140+121+124}{15}[/tex][tex]=129.8[/tex]Mean is 129.8
Arrange the given data in ascending order,
101,102,115,119,121,124,126,126,135,136,137,140,140,160,165
Median is 126
Mode is 126,140
You are playing miniature golf on the hole shown.
a. Write a polynomial that represents the area of the golf hole. Show your steps and explain how you found the polynomial.
b. Write a polynomial that represents the perimeter of the golf hole. Show your steps and explain how you found the polynomial.
Bonus:
c. Find the perimeter of the golf hole when the area is 216 square feet.
The dimensions of the golf hole found using the indicated variable expressions are as follows;
a. The area of the golf hole is 4·x² + 12·x
b. The perimeter of the golf hole is 8·x + 8
c. The perimeter of the golf hole if the area of the hole is 216 square feet is 56 feet
What is the perimeter of a geometric figure?The perimeter of a geometric figure is found by the length of the boundary of the figure.
a. The area of the gulf hole is found as follows;
The area is a composite figure, which consists of a rectangle of length 3·x and width (x + 4) and a square of length x
Which indicates that the area is A = 3·x × (x + 4) + x×x = 3·x² + 12·x + x²
The area of the hole, A = 3·x² + 12·x + x² = 4·x² + 12·x
The area of the hole is A = 4·x² + 12·x
b. The perimeter of the hole is found as follows;
P = (x + 4) + 3·x + (x + 4) + x + x + x = 8·x + 8
The perimeter of the hole = 8·x + 8
c. The area of the golf hole = 216 square feet, which indicates;
4·x² + 12·x = 216
4·x² + 12·x - 216 = 0
x² + 3·x - 54 = 0
(x + 9)·(x - 6) = 0
x = 6 or x = -9
The perimeter of the golf hole is therefore;
P = 8 × 6 + 8 = 56
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