The parent function is y = x ; shift 2 units downwards.
Given,
In the question:
The function is :
g(x) = x - 2
Now, According to the question ;
Let's know
What is the Parent function and transformation?
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
According to the above statement is;
g(x) = x -2
Hence, The parent function is y = x ; shift 2 units downwards.
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The difference between five-halves of a number
and 17 is 48.
The required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
What are algebraic expressions ?An algebraic expression (or) a variable expression is a aggregate of phrases through the operations together with addition, subtraction, multiplication, division, etc. For instance, allow us to have a study the expression 5x + 7. Thus, we will say that 5x + 7 is an instance of an algebraic expression.
CalculationWords can be expressed algebraically.
The algebraic expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
Let the number be x.
Five-halves of x is: 5/2x
So the difference between and 17 is:
5/2x - 17 = 48 or 17 - 5/2x = 48
Combine both expressions
[tex]| 17 - \frac{5}{2}x|[/tex] = 48
Hence, the required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
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h(x)=x²+3x-2; 12-h(7)
How would I input 12-h(7) in place of x to solve this function?
Solve for 12 - h(7)
First find h(7)
h(7) = 7^2+3(7)-2
h(7) = 49 + 21 - 2
h(7) = 68
12 - 68 = - 56
12 - h(7) = -56.
I'm not sure if the question wants h(-56) as well, but just plug that in.
H(-56)=2966
hope this helps :)
a manufacturer wants to increase the absorption capacity of a sponge. based on past data, the average sponge could absorb 3.5 ounces. after the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. what is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
Reject a null hypothesis because computed t is higher than 2.821 is the decision rule.
Define the term hypothesis?The hypothesis is a succinct statement of the researcher's estimate of the findings of the study, that may or may not be confirmed by the results, in such a scientific experiment or survey. The scientific method's fundamental step is hypothesis testing.A statistical hypothesis known as a null hypothesis asserts because no statistical significance can be found in a collection of provided observations.For the given question;
Test hypothesis:
H₀; μ = 3.5
Upper tailed test:
Hₐ; μ > 3.5
Significance value; α = 10.
Then, degree of freedom.
Df = α - 1
Df = 10 - 1
Df = 9
The critical value;
t(₀.₀₁, ₉) = 2.821
Rejection region;
Rejected H₀ for t > 2.821
Thus, reject a null hypothesis because computed t is higher than 2.821 is the decision rule for the absorption amount of the sponge.
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What is the value of 5/x + 1.25x when x=10
Which of these strategies would eliminate a variable in the system of equations?
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 3 ,multiply the bottom equation by -2 then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
2x + 8y = -3
3x + 6y = -4
We can multiply the top by 3 and the bottom by -2 which will result in:
6x + 24y = -9
-6x - 12y = 8
They are then added to each other to give:
6x - 6x + 24y - 12y = -9+8
12y = -1
y = -1/12
From this we can notice that the variable x was eliminated which is why option B is the correct choice.
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P(A and B)
P(B)
Find P (Junior | Girl) Hint:
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5
7 12
Junior 2
3 5
Senior 1 4 5
12 18
[?]
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
Probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.
As given in the question,
From the given table we have,
Total number of girls and boys in the class = 30
Total number of boys in class = 12
Total number of girls in class = 18
As per given Hint: P(A/B) = P(A and B) / P(B)
A is the Junior
B is the girl
Probability as per given condition is:
P(Junior / Girl) = P(Junior and girl) / P(girl)
= (3/30) / (18/30)
= 3/18
= 1/6 ( lowest term of fraction)
Therefore, probability for the given condition P (Junior / Girl ) from the given table of classroom of students is equal to 1/6.
The complete question is:
Find P(Junior / Girl) Hint: P(A/B) = P(A and B) / P(B) .
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5 7 12
Junior 2 3 5
Senior 1 4 5
12 18
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
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In the diagram below, GH is parallel to DE. If FH is 5 more than GF, DF:
and FE = 48, find the length of GF. Figures are not necessarily drawn to scal
State your answer in simplest radical form, if necessary.
Answer: GF =
The length of side GF from the similar triangles shown is GF = √10 units
What is an equation?A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.
If a pair of triangles share the same shape, all of their angles are equal, and their ratio of comparable sides is proportionate, then they are said to be similar.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." Standard form, slope-intercept form, and point-slope form are the three primary types of linear equations.
In a similar triangle, DE = GF, Hence:
GF/DF = GH/DE
GF / 5 = 2 / GF
GF² = 10
GF = √10
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Rewrite in simplest terms: 6(8v-7)-10v
Step-by-step explanation:
[tex]6(8v - 7) - 10 \\ 48v - 42 - 10 \\ 48v - 52[/tex]
Which equation represents the sentence, "The sum of twenty-four and p minus fifteen is q"?
A. 24 + p + 15 = q
B. 24 + p – 15 = q
C. p + q – 15 = 24
D. 15 + p = q – 24
Answer:
B is correct: also if u add C and D together there both different and if u added B and A correctly u would have got B as your answer.
Step-by-step explanation:
Sorrel has 54 beads, and 16 of them are red. Of the remaining beads, half are yellow and half are green. How many yellow beads does she have?
Sorrel has 19 yellow beads.
What is fraction?Fraction is a ratio of two integers.
Fraction is divided into two section by a dividing line and these sections are numerator and denominator.
Fractions are of different types: proper fraction, improper fraction and mixed numbers.
Total number of beads =54
if 16 are red, the remaining beads would be ( 54 - 16) = 38
Half of the remaining are yellow = 1/2 x 38
Then number of yellow beads = 19
And number of green beads = 38 - 19
= 19
In conclusion, the total number of yellow beads is 19
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Compare the governments of Germany and Russia. Make three lists pointing out similarities and differences. In the first list, point out the unique traits of the German government. In the second list, point out the unique traits of the Russian government. In the third list, point out the traits both governments have in common.
DON'T write an entire essay i just need a paragraph
Answer: During the Russian war, The Russians and Germans were at war with each other, Beating them brutally.
Step-by-step explanation:
Write an expression to represent:
8 less than the product of 2 and x.
Answer:
(2x)-8 is the correct answer
Step-by-step explanation:
Hope this helps
Graph y+3=5/2(x-5) on graph paper
The graph of the function [tex]y+3=\frac{5}{2}(x - 5)[/tex] is attached below.
What is graph of the function?
In mathematics, the set of ordered pairings where f(x)=y exists is the graph of a function. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
Consider the given function, [tex]y+3=\frac{5}{2}(x - 5)[/tex]
It is in the form [tex]y-y_1=m(x-x_1)[/tex]
Where, [tex](x_1, y_1)[/tex]is the point and m is the slope.
Graph passes through the point [tex](x_1, y_1)[/tex] and having slope m.
Here, [tex](x_1, y_1) = (5, -3), m = \frac{5}{2}[/tex]
Therefore, graph passes through the point (5, -3) and having slope 5/2.
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Josie makes fruit punch by mixing fruit juice and lemonade in the ratio
She needs to make 35 litres of punch for a party.
How much of each ingredient does she need?
Fruit juice
7 litres
Lemonade =
28 litres
During the party Josie decides to make some more.
She has 3 litres of fruit juice left and plenty of lemonade.
How much xtra punch can she make?
litres
To make the second batch of punch go further Josie
adds 2 more litres of lemonade.
What is the ratio of fruit juice to
lemonade in the second batch?
Let the lemonade and fruit be Mixed in x ratio.
[tex]\therefore[/tex] Total mixture of fruit punch [tex]= 1\times x \ + \ 3\times x = 4x[/tex]
She needs to make 35 liters of punch.
Requirement of ingredients :
Fruit juice to be added [tex]= \frac{x}{4x} \times 35 = 8.75[/tex] liters of fruit juice
If 8.75 liters of fruit juice is to be added,
then,
lemonade required[tex]=35\ litres - 8.75\ litres = 26.25\ litres .[/tex]
Now ,
According to question she wants to make more fruit punch,
so , given that she had 2 liters of fruit juice.
Here ,
⇒x become 2.
⇒Lemonade required =[tex]2\times x[/tex]
⇒Lemonade required = [tex]2\times3 = 6\ liters[/tex]
There total fruit punch = [tex]6 + 3=9\ liters[/tex]
[tex]\therefore\\[/tex] ratio of fruit juice to lemonade in the second batch = 6:9 = 2:3.
What is ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
What is Proportion?
A proportion is an equation in which two ratios are set equal to each other.
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while eating out, mike and joe each tipped their server 22 dollars. mike tipped 10\% of his bill and joe tipped 20\ % of his bill. what was the difference, in dollars between their bills?
Joe, for the most part, tipped 20% of his bill, compared to 10% for Mike, which is particularly noteworthy. The actually difference between their invoices in dollars was approximately 10.
Let be Mike's bill and be Joe's bill.
(10/100) *m = 2
M = 20
(20/200 )*j = 2
J = 10
So the desired difference is
m-j = 20 – 10
= 10
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the function when x = 3: b(x) = -2x-4
Answer: b(3)=-10
Step-by-step explanation:
Is this what you meant?
helen buys two pineapples she pays with a £5 note and gets £3.60 change work out the cost of one pineapple
Answer:
Each pineapple costs £0.70.
Step-by-step explanation:
Let P be the number of pineapples Helen purchased and C the cost per pineapple, in £.
Helen's total cost would be: P*C = total cost.
The total cost is the difference between £5 and £3.60, which is £1.40.
We are given P (the number of pineapples, 2) and the total cost (£1.40) , so enter those numbers in the equation:
P*C = total cost
2*C = £1.40
C = £0.70
five whole numbers are written in order
4 6 x y 10
median and mean of the five numbers are the same.
Workout the values of x and y
The values of x and y if the mean and median are equal are:
x = 7
y = 8.
What is the Mean and Median of a Data Set?The mean is the total sum of the values in a data set divided by the number of values of the data set.
The median of a data set is the center value when the data distribution is ordered.
Given the ordered data set as, 4, 6, x, y, and 10.
The center value is x. Therefore, the median of the data set is x.
The mean of the data = (4 + 6 + x + y + 10)/5
The mean of the data = (20 + x + y)/5
The mean and the median are equal, therefore:
(20 + x + y)/5 = x
20 + x + y = 5x
20 + y = 5x - x
20 + y = 4x
The value of x cannot be less than 6, if x = 7, we woud have:
20 + y = 4(7)
20 + y = 28
y = 28 - 20
y = 8
The values of x = 7, y = 8.
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There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, what is the probability that everyone in the group is a girl
There are 10 students in a class: 6 boys and 4 girls. If the teachers chooses 3 at random, then the probability that everyone in the group is a girl is 1/30
It is given that,
Total number of students = 10
Number of boys = 6
Number of girls = 4
Total number of ways to select 3 students from 10 students.
10C3= 10!/ 3!7!= 120
Total number of ways to select 3 students from 4 girls
4C3 = 4!/ 3!=4
The probability that everyone in the group is a girls is
P = 4/120
= 1/30
Hence , the probability that everyone in the group is a girl is 1/30
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a department store chain is expanding into a new market, and is considering 24 different sites on which to locate 6 stores. assuming that each site is equally likely to be chosen, in how many ways can the sites for the new stores be selected? a) 144 b) 96,909,120 c) 168 d) 134,596 e) 30 f) none of the above.
Option b. 96,909,120 is the correct answer. The number of ways in which the new site can be chosen to locate 6 stores in 96,909,120 ways
We can find the number of ways by multiplying the number of possibilities each store can have.
Store 1, can be placed on 24 sites. Store 2 can be placed on 23 sites (since store 1 is already on site 1). Store 3 can be placed on 22 sites. Store 4 can be placed on 21 sites. Store 5 can be placed on 20 sites. Store 6 can be placed on 19 sites
Therefore the number of ways is:
C = 24 * 23 * 22 * 21 * 20 * 19
C = 9,69,09,120 possibilities
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pls solve all the question as er the questions given below
1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD
1b) The additional information required using ASA Congruency postulate is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence Postulate that is used is SAS Congruency postulate.
How to use congruency postulates?1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate denotes Side - Angle - Side. That is 2 congruent sides and the included angle. This means we have our additional information as;
∠AOB ≅ ∠BOD
1b) We want to prove that the given triangle ABC is congruent to the other triangle PQR by the ASA Congruency. ASA Congruency means 2 congruent angles and the included side. We are given;
∠Q = ∠B
∠R = ∠C.
Therefore, the additional information is BC ≅ QR
2a) The symbolic form of the given congruent triangles is expressed as;
ΔABC ≅ ΔADC
2b) The congruence postulate that was used here is SAS Congruency postulate.
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Solve for c. You must show ALL of your work.
6c + 14 = -5c + 4 + 9c
Answer:
c = -5
Step-by-step explanation:
6c + 14 = -5c + 4 + 9c
1) We want to first combine the c values on the right side. This would give us 6c + 14 = 4c + 4.
2) Next, we want to move the c value to one side of the equation. This means we would subtract 4c from the right side. This gives us 2c + 14 = 4.
3) We can then subtract 14 from the left side to isolate the c value. This gives us 2c = -10.
3) We can then divide both sides by 2 and get the answer for c.
This gives us c = -5.
Solve the equation: 4 - 2y + 3 = - 9. What is y equal to?
Answer:
b
Step-by-step explanation:
In the given equation 4 - 2y + 3 = - 9, y is equal to 8.
The equation is a statement in which the values of two mathematical expressions are equal (indicated by the sign =).
To find the value of y from the given equation
∴ 4 - 2y + 3 = - 9
=> 4+3 -2y = -9
=> 7 - 2y = -9
=> 7 + 9 = 2y
=> 16 = 2y
=> 16/2 = y
=> 8 = y
=> y = 8
So, the value of y in the above equation 4 - 2y + 3 = -9 is 8.
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Hola, me ayudan a despejar X - 8 = -2
Answer:
x=6
Step-by-step explanation:
x-8=-2
x=-2+8
x=6
Answer:
x = 6
Step-by-step explanation:
x - 8 = -2
x - 8 + 8 = -2 + 8
x + 0 = 6
x = 6
Check:
6 - 8 = -2
A community hall is in the shape of a cuboid.
The hall is 40 m long, 15m wide and
3 m high.
The community hall needs re-decorating
with new paint for the walls and ceiling,
and new tiles on the floor.
A 10 litre tin of paint covers 25 m² and costs £10.
Work out the total cost of paint needed
to re-decorate the community hall.
The total cost of painting is $564.
What is surface area of cuboid ?
A cuboid is a three-dimensional figure enclosed by six rectangular planes, each of which has a different size in terms of length, breadth, and height. Anything in the shape of a rectangle, such as a box, brick, or other object, may be a cuboid if you look about. When viewed from any of the ends, a cuboid (3-dimensional) can be seen to be made up of different-sized rectangles (2-dimensional). A cuboid's area is its surface because it is a solid with three dimensions. Since a cuboid's faces are rectangular, its area may be determined using the formula for the area of a rectangle.
Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units
We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m high and 3m wide.
The paint will be required for 4 walls and ceiling.
Let us find area of walls and ceiling.
Area of walls and ceiling = 2( 40*15) + 2(3*15) + (40*3)
=> Area of walls and ceiling = 2(600)+2(45)+120
=> Area of walls and ceiling = 1200+90+120
=> Area of walls and ceiling = 1410 [tex]m^2[/tex]
Therefore, the area of walls and ceiling is 1410 square meters.
Here Cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter.
Then total cost of paint = 10*[tex]\frac{1410}{25}[/tex] = 10*56.4 = $564.
Hence cost of paint is $564.
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PLEASE EXPLAIN……………………..
The range of the function is y ≥ -2 so , correct option is option c
What is range of a function ?Mathematical functions can be compared to vending machines. They provide some cans or biscuits in exchange for the money provided as input. Similar to this, functions take a set of input numbers and produce a set of results. One may argue that everything in actual life can be formulated and resolved with the aid of functions. It is impossible to avoid the fact that functions are of enormous importance in our daily lives. The mathematical model of almost everything in real life, from building design and architecture to mega skyscrapers, requires functions. One feature that can be used to describe a function is its domain and range.
CalculationThe graph of the range of the given function is attached below .
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If the ratio of men to women in a movie theater is 3:2 and there are 45 men in the theater, how many total people are in the theater?
Answer:
113 people (112.5 if you don't round but you can't have half a person)
Step-by-step explanation:
45 men plus the number of women (x) is how many people there are
so you would do 3/x=2/45 since x is the number of women
do some basic algebra, and you get 67.5 women so round if you want to to 68 (i will round because you can't have half a person)
68+45=113 people
Corinne and Deanna decide to race from one corner of an open field to the other. The field is rectangular in shape, 60 meters long and 80 meters wide. Since Corinne is older and faster, she's going to run along the outside of the field, and Deanna will take the diagonal route. If Deanna can run at a rate of 5 meters per second, how fast will Corinne have to run to get there at the same time as Deanna?
Answer:
Corinna will have to run at 7 meters per second to get there at the same time as Deanna.
Step-by-step explanation:
So to find the distance of Deanna's route, you can use the Pythagorean theorem.
a^2 + b^2 = c^2
60^2 + 80^2 = 10000
c^2 = 10000
Take the square root of both sides.
c = 100
So Deanna runs 100 meters at 5 meters per second.
100/5 = 20
She runs for 20 seconds.
To find Corinne's distance, we add 60 and 80, which is 140.
To find how fast she need to run to get there in 20 seconds, you divide 140 by 20, which gets 7 (meters per second). You can also think of it like this: to run 140 meters in 20 seconds, she has to run at 140 meters per 20 seconds, which you can simplify (like a fraction) to 7/1, or just 7
factorise completely: 9+35x-4x^2
Answer:
- (4x+1) (x-9)
Step-by-step explanation:
-4x^2+35x+9
Factor out the 1:
-(4x^2-35x-9)
Factor:
-(4x+1)(x-9)
If a $900 plasma screen TV
is reduced by 25%, what is
the discount?
Answer: $225
Step-by-step explanation: 900 * .25 = 225
Answer:
$225
Step-by-step explanation:
25 : 100 = x : 900
x = 25 * 900 / 100
x = 25 * 9
x = 225
