Answer:
f(x) = (x + 3) - 7
Step-by-step explanation:
the original function f(x) = x - 9 is the parent function f(x) = x shifted down 9 units
from f(x) = x - 9, we are told that the function is shifted 2 units up, this is a vertical shift. so we add 2 to -9
-9 + 2 = -7
we now have f(x) = x - 7
next we are told that the function is shifted 3 units to the left. this is a horizontal shift. a horizontal shift looks similar to this:
f(x) = (x ± b)
if a function is shifted to the left, we would use an addition sign. if it was going to the right, we would use a subtraction sign
the function looks like the following when we apply the above knowledge
f(x) = (x + 3) - 7 this would be our new function
The new function will be f(x) = (x + 3) - 9 + 2.
Explanation:The function given is f(x) = x - 9. When this function is shifted 2 units up and 3 units to the left, the new function is obtained by transforming the original function accordingly.
Shifting up by 2 units means adding 2 to the function, and shifting 3 units to the left means substituting x+3 for x.
Thus, the new function, after applying the transformations, is:
f(x) = (x + 3) - 9 + 2
Simplifying the above transformation, we get:
f(x) = x - 4
Simplify : 2n - 7 + 3(4n - 3)
Answer:
14n-16
Step-by-step explanation:
Given
[tex]2n - 7 + 3(4n - 3)\\[/tex]
Simplification requires the expression to be in its shortest and concise form. The brackets are opened and addition or subtractions are performed
So,
Multiplying 3 inside bracket
[tex]2n - 7 + 12n - 9[/tex]
Combining alike terms:
[tex]2n+12n-7-9[/tex]
Performing addition and subtractions:
[tex]14n-16[/tex]
Hence the simplified form is:
14n-16 ..
Help pleaseeeeeeeeeeee
Answer:
C
Step-by-step explanation:
Charlene has 8 more dollars so you would have to add it all together to get 86.
marcel said he can find 52 times 10 by adding a 0 to the end of 52 to get 520 is he correct?
Answer:
Yes he is Correct
Step-by-step explanation:
When multiply with numbers like 10,100,1000 ect or even like 20,200,2000 then you have to break it down. Since multiply by zero equals 0 anyways you will only have to focus on the number that is in front of it. And just and the zeros to the back of the number.
Answer:
Yes he is correct
Step-by-step explanation:
Whenever we are multiplying any number with 10 or multiples of ten we simply add the zeros to the end of that number.
For example:
134 x 10 = 1340
As you can see, to get the answer, you simply need to add 0 to the end of 134
Also 10 x 10 = 100
To get the answer we simply added zero to the end of ten which then give us 100
12 x 10= ? all you need to do is to add zero to the end of 12 which will give us 120
13 x 100 =? In this case, since the zeros are two, you will simply add two zeros to the end of 13 which will give you the answer 1300
So Marcel can find 52 times 10 by simply adding a 0 to the end of 52 to get 520 as the correct answer.
What is the difference between a relation
and a function? Is every relation a function? Is every
function a relation? Explain.
Answer:
Not all relationships are functions, but all functions are also relationships
Step-by-step explanation:
A relationship is a correspondence between two sets of values.
A relationship assigns values from an output set called range to a set and input called a domain.
On the other hand, a relation is a function if and only if there is only one value of the output set (Range) assigning to each value of the input set (Domain).
In other words, if an input value [tex]x_1[/tex] is assigned two or more output values [tex]y_1[/tex], [tex]y_2[/tex], [tex]y_3[/tex] .. then the relationship is not a function. This means that not all relationships are functions.
[tex]y=\±\sqrt{x} +3[/tex] is a relation but it is not a function.
because when x = 4 then y = 1 and y = 5.
Not all relationships are functions, but all functions are also relationships
Final answer:
A relation is a set of ordered pairs, while a function is a relation where each input value is associated with only one output value. Not every relation is a function, but every function is a relation.
Explanation:
A relation is a set of ordered pairs where each input value is associated with one or more output values. On the other hand, a function is a relation where each input value is associated with only one output value.
Not every relation is a function. For example, the relation {(1,2), (1,3), (2,4)} is not a function because the input value 1 is associated with two different output values (2 and 3). However, every function is a relation because it establishes a relationship between the input and output values.
please I need help with all my spring packet
Answer:
Point S coordinates= (-4,5)
Step-by-step explanation:
If you would just move the point 5 PLACES TO THE RIGHT, you would get -4, 5, which is the correct answer.
The weight of a basketball is normally distributed with a mean if 17 oz. And a standard version deviation of 2 oz. Suppose 50j0 different basketballs are in a warehouse. How many basketballs weigh more than 19 oz?
There would be 3 basketballs?
3 basketball because subtract
Solve the equation by graphing x2+5x+4=0 . If exact roots cannot be found, state the consecutive integers between which the roots are located.
Answer:
x = -4
x = -1
Step-by-step explanation:
We have been given the following quadratic equation;
x^2 + 5x + 4 = 0
We are required to determine the roots of the above quadratic equation via graphing.
To do this we formulate the following equations;
y = x^2 + 5x + 4
y = 0 (x -axis)
We then proceed to graph these functions on the same graph. The roots of the original quadratic equation will be the points where the graphs of the above functions will intersect.
The attachment below is the graphical solution obtained from desmos graphing tool;
The graph of the functions intersect at;
x = -4 and x = -1
These are the roots of the given quadratic equation
Perform the operation and write the answer in simplest form 5 1/7 * 3 1/9
Answer:
16
Step-by-step explanation:
Input it in the calculator
Answer: 16
Step-by-step explanation:
5 1/7 is 36/7=5.142857
3 1/9 is 28/9=3.1
Do 5.142857 times 3.1
And it equals 15.94 but rounds up to 16.
Rewrite sin^4x so that it involves on the first power of cosine
Use the half-angle identities.
[tex]\sin^2x=\dfrac{1-\cos2x}2[/tex]
[tex]\implies\sin^4x=\left(\dfrac{1-\cos2x}2\right)^2=\dfrac{1-2\cos2x+\cos^22x}4[/tex]
[tex]\cos^2x=\dfrac{1+\cos2x}2[/tex]
[tex]\implies\sin^4x=\dfrac{1-2\cos2x+\frac{1+\cos4x}2}4=\dfrac{3-4\cos2x+\cos4x}8[/tex]
sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.
Rewrite sin^4(x) in terms of cosine by using the Pythagorean identity for trigonometric functions, which relates sin^2(x) and cos^2(x):
sin^2(x) + cos^2(x) = 1
Now, solve for sin^2(x):
sin^2(x) = 1 - cos^2(x)
Now, square sin^2(x) to get sin^4(x):
(sin^2(x))^2 = (1 - cos^2(x))^2
sin^4(x) = (1 - cos^2(x))^2
So, sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.
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The box and whisker plot displays a set of data obtained from a marketing survey. Drag each item to the appropriate position on the number line. Drag the extra item to the box not associated with the number line.
Choices...
mean
median
outlier
minimum number in summary of data
picture is where these are suppose to go
Answer:
the one for the arrow point to #26 is min # in summary of data
the one where the arrow points between#30 and 32: median
arrow pointing to #44 is: outlier
and the bottom choice is: mean
Step-by-step explanation:
Which situation could the expression 1/4÷3 represent A 1/4 of a package of pencils shared equally among three friends. B the number of 1/4 cup servings in three cups of popcorn C 1/3 of a stadium split into four equal sections or D a four-foot-long rope cut into 1/3 -foot pieces
"1/4 of a package of pencils shared equally among three friends" this expression represents expression [tex]\frac{1}{4} /3[/tex].
What is Division?
The action of separating something into parts or the process of being separated is known as Division. Ex: "The division of the land into small fields"
The meaning of the given expression is to divide one fourth part into three persons.
This is clearly represents in option A....1/4 of a package of pencils shared equally among three friends.
Thus, option A express perfectly for the given expression [tex]\frac{1}{4} /3[/tex] as "1/4 of a package of pencils shared equally among three friends".
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Final answer:
The expression 1/4÷3 matches Scenario A, which represents 1/4 of a package of pencils being shared equally among three friends.
Explanation:
The expression 1/4÷3 represents taking one fourth of something and then dividing it into 3 equal parts. Out of the scenarios provided:
Scenario A is about sharing 1/4 of a package of pencils among three friends, which can be represented by this expression.Scenario B involves calculating the number of 1/4 cup servings in three cups, which would imply multiplying, not dividing, so it doesn't fit.Scenario C speaks of splitting 1/3 of a stadium into four sections, which also does not align with the expression.Scenario D is about cutting a four-foot-long rope into pieces that are each 1/3-foot in length. This implies a different division than the one in the expression.Therefore, the expression 1/4÷3 best matches with Scenario A, where 1/4 of a package of pencils is shared equally among three friends.
Write an equation with the point (3,7) and has a slope of 7
Answer:
slope = 7 and point = (3, 7)
b = y - slope*x
b = 7 -7 * 3
b = -14
Then we enter "b" and the slope into this equation:
y = 7x -14
Step-by-step explanation:
subtract (-9x^2+8x-14) from the sum of (-9x^2-10x) and (3x^2+3x+7)
Answer:
[tex]3x^2 - 15x + 21\\or\,\,3(x^2 -5x +7)[/tex]
Step-by-step explanation:
First we will find sum of [tex](-9x^2-10x)\,\, and\,\, (3x^2+3x+7)[/tex]
Adding the like terms:
[tex]= -9x^2-10x + 3x^2 +3x+7\\= -9x^2+ 3x^2 -10x+3x+7\\= -6x^2 - 7x +7[/tex]
Now subtract (-9x^2+8x-14) from (-6x^2 - 7x +7)
[tex]=(-6x^2 - 7x +7) - (-9x^2+8x-14)\\= -6x^2 - 7x +7 +9x^2-8x+14\\= -6x^2 +9x^2 - 7x -8x+7 +14\\= 3x^2 - 15x + 21\\=3(x^2 -5x +7)[/tex]
What is the value of x?
Enter your answer in the box.
Answer:
x = 5
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of squares on the other 2 sides, that is
x² + 12² = 13²
x² + 144 = 169 ( subtract 144 from both sides )
x² = 25 ( take the square root of both sides )
x = [tex]\sqrt{25}[/tex] = 5
Answer:
x = 25
Step-by-step explanation:
We are given a right angled triangle and we are to find the value of x.
For that, we will use the Pythagoras Theorem.
[tex] 1 3 ^ 2 = x ^ 2 + 1 2 ^ 2 [/tex]
[tex] 1 6 9 = x ^ 2 + 1 4 4 [/tex]
[tex] x ^ 2 = 1 6 9 - 1 4 4 [/tex]
[tex] x ^ 2 = 2 5 [/tex]
Taking square root on both sides to get:
x = 25
Geometry pls help
will give 30 points
The 1st and 4th ones
Answer: the correct answers are
1. <EGO ≈ <EOG
4. TW = 1/4GO
Step-by-step explanation:
1. all the angles are corresponding therefore it’s correct
4. TW is 1/2 of PQ therefore it would be 1/4 of GO
how to solve dividing radicals
ANSWER: Multiply out front and multiply under the radicals. "The radical of a product is equal to the product of the radicals of each factor." "The radical of a quotient is equal to the quotient of the radicals of the numerator and denominator."
Which pattern folds into the triangular prism above?
Answer:
the pattern would be W
Step-by-step explanation:
W should be the answer. Hope I helped you lots please count me brainy
A drawer contains 3 red marbles 7 green marbles and 10 white marbles if a Marble is drawn from the jar at random what is the probability that the marble is white
Answer:
1/2
Step-by-step explanation:
3+7+10=20
20/2=10=1/2
A bag contains 10 counters. 6 of them are white. a counter is taken at random and not replaced. A second counter is taken out of the bag at random. Calculate the probability that only one of the two counters are white
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
The ways we can get "1 counter to be white out of 2 draws" is:
1. If 1st one taken out is white and next one different color, and
2. If 2nd one taken out is white and 1st one different color
In probability, AND means MULTIPLY and OR means ADD
Here, we are actually looking for ways of 1st one white, next one different OR first one different and next one white. Let's find them separately.
1. If 1st one taken out is white and next one different color
there are 6 white and 10 total, so 1st one white is 6/10
not replaced, so now there are 9 total and 4 of them are different,so different probabililty is 4/9
We multiply these two to get: 6/10 * 4/9 = 4/15
2. If 2nd one taken out is white and 1st one different color
probabilty 1st one different color is 4/10 since 4 are different and we have total of 10
since not replaced, now we have 9 total and still 6 white.
probability of white in 2nd draw is 6/9
We multiply these two to get: 4/10 * 6/9 = 4/15
Now we add these 2 as stated earlier, so 4/15 + 4/ 15 = 8/15
Answer:
Step-by-step explanation:
X^2+16x+48=0 it says to solve each quadratic equation by factoring.
Answer:
x = -4 and x = -12
Step-by-step explanation:
x^2 + 16x + 48 = 0 is to be factored.
Note that 48 is the product of 4 and 12 and that the sum of 4 and 12 is 16.
Therefore,
x^2 + 16x + 48 = 0 in factored form is:
(x + 4)(x + 12) = 0, so that x + 4 = 0 → x = -4, and
x + 12 = 0 → x = -12
Answer:
(x + 4) (x + 12)
Step-by-step explanation:
to factor x² + 16x + 48 = 0, you need to find 2 numbers that when multiplied together give you 48 and when added together give you 16
you can list the factors of 48 and see what adds up together to give you 16, but here is a hint:
the numbers probably end in a 2, 4, 0, 6, 5, or 1, as a pair of these numbers added together give us 6. i looked at a factor chart and saw that 12 and 4 that when added together, give us 16 and when multiplied, give us 48
in factored form it looks like the following:
(x + 4) (x + 12)
this would be the answer in factored form
What type of relationship does this pair of angles have? 161 and 19 degrees
Answer:
There are supplementary
Step-by-step explanation:
The sum of the given angles is 180 degrees. So, the given angles are supplementary angles.
Important information:
The measures of two angles are 161 and 19 degrees.We need to find the type of relationship between the given angles.
Supplementary angles:Two angles are called supplementary angles if their sum is 180 degrees.
The sum of given angles is:
[tex]161^\circ+19^\circ=180^\circ[/tex]
The sum of the given angles is 180 degrees. So, the given angles are supplementary angles.
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Write a subtraction problem involving pounds and ounces. Solve the problem and show your work.
Answer: Edgur eats 12 ounces of popcorn. Before he ate any, he had 2 pounds of popcorn. How much popcorn, in ounces, of popcorn does Edgur have now? Edgur has 20 ounces of popcorn.
Step-by-step explanation:
Pounds to ounces: 1 pound = 16 ounces.
2 * 16 = 32.
He ate 12 of those ounces. 32 - 12 = 20.
Final answer:
To solve a problem involving subtraction of pounds and ounces, convert everything to ounces, subtract, and convert back if necessary. In this example, after removing 3 pounds 5 ounces from 9 pounds 8 ounces, the remaining weight is 6 pounds 3 ounces.
Explanation:
Let's create a subtraction problem involving pounds and ounces. Imagine you have a sack of potatoes weighing 9 pounds 8 ounces, and you remove a bag of potatoes weighing 3 pounds 5 ounces. How much does the sack of potatoes now weigh?
First, we need to ensure that both weights are in the same units. We have:
Initial weight: 9 pounds 8 ounces
Weight removed: 3 pounds 5 ounces
To subtract these weights, we will convert pounds to ounces for each weight, then subtract, and finally convert back to pounds and ounces if necessary.
Convert 9 pounds to ounces: 9 × 16 = 144 ounces
Therefore, the initial weight in ounces is 144 ounces + 8 ounces = 152 ounces.
Convert 3 pounds to ounces: 3 × 16 = 48 ounces
The weight removed in ounces is 48 ounces + 5 ounces = 53 ounces.
Subtract the smaller weight from the initial weight: 152 ounces - 53 ounces = 99 ounces
Now we convert 99 ounces back to pounds and ounces. Since 1 pound is 16 ounces:
99 ÷ 16 = 6 pounds with a remainder of 3 ounces.
So, the sack of potatoes now weighs 6 pounds 3 ounces.
An artist made purple paint by mixing 1/2 quart of red paint and 3/4 quart of blue paint. What is the ration of red paint to blue paint in simplest form
Answer:
(1/2)/(3/4) = (1/2)(4/3) = 2/3
Step-by-step explanation:
Plz help me with this
Answer: b) -5 ≤ y ≤ 1
Step-by-step explanation:
y = 3 cos (4x) - 2
↓ ↓
amplitude vertical shift
The amplitude is 3 which gives a range of -3 to 3 but there is also a shift down of 2 units so the new range is: -3 - 2 = -5 to 3 - 2 = 1
-5 ≤ y ≤ 1
For a group experiment, your science class measured the fine-particulate concentrations in the air at random places around campus, and estimated a sample average of 22 μg/m3 (micrograms per cubic meter). If 144 readings were taken, and the standard deviation of the sample measurements was 4 μg/m3, you are 99.7% confident that actual concentration of fine particulates at the school is
Answer:
The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).
Step-by-step explanation:
Given : Sample size(n)= 144
Sample mean [tex]\mu= 22 ug/m^3[/tex]
Standard deviation [tex]\sigma=3.5 ug/m^3[/tex]
To find : 99.7% confident that actual concentration of fine particulates at the school is?
Solution :
The formula for confidence interval is
[tex]CI=\mu \pm z\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Substituting the values in the formula,
[tex]CI=22 \pm 3\times\dfrac{3.5}{\sqrt{144}}[/tex]
[tex]CI=22 \pm 3\times\dfrac{3.5}{12}[/tex]
[tex]CI=22 \pm 3\times 0.2916[/tex]
[tex]CI=22 \pm 0.8748[/tex]
[tex]CI=22+0.8748, 22-0.8748[/tex]
[tex]CI=22.8748, 21.1252[/tex]
Therefore, The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).
Answer:
21 ug/m^3 - 23 ug/m^3
Step-by-step explanation:
Just got it right
Solve the equation for y
2x+5y=5
***Plz Help me out***
Here is the answer:...
Answer:
- Solve for y
- Subtract 2 x from both sides of the equation then divide by 5 .
-y = 1 − 2 x 5
Step-by-step explanation:
Use the graph to write the factorization of x^2+2x-8
Answer:
(x-2)(x+4)
Step-by-step explanation:
So it would be A.
Explanation: The middle number is 2 and the last number is -8.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 2
Multiply together to get -8
Can you think of the two numbers?
Try -2 and 4:
-2+4 = 2
-2*4 = -8
Fill in the blanks in
(x+_)(x+_)
with -2 and 4 to get...
(x-2)(x+4)
Answer:
(x−2)(x+4)
A. (x+4)(x-2). The factorization of the quadratic equation x²+2x-8 given by the graph is (x+4)(x-2).
From the graph shown in the image we can see the parabola's cut points, in the y-axis is -4 and the x-axis is 2, then we write the product changing the signs (x+4)(x-2) = x²+2x-8
Can someone help me please
Answer:
L.A. = 60π m² ≈ 188.4 m²S.A. = 85π m² ≈ 266.9 m²Step-by-step explanation:
Lateral Area:
The formula of a Lateral Area of a cone:
[tex]L.A.=\pi rs[/tex]
r - radius
s - slant height
We have r = 5m and s = 12m. Substitute:
[tex]L.A.=\pi(5)(12)=60\pi\ m^2\\\\\pi\approx3.14\to L.A.\approx(6)(3.14)=188.4\ m^2[/tex]Surface Area:
The formula of a Surfaace Area of a cone:
[tex]S.A.=B+L.A.[/tex]
In the base we have the circle with the radius r = 5m.
The formula of an area of a circle"
[tex]A_O=\pi r^2[/tex]
Substiute:
[tex]B=\pi(5^2)=25\pi\ m^2\approx(25)(3.14)=78.5\ m^2[/tex]
[tex]S.A.=60\pi+25\pi=85\pi\ m^2\approx188.4+78.5=266.9\ m^2[/tex]
The dot plot below shows the number of wings contestants in a wing-eating contest ate.
What is the mean absolute deviation of the data set shown?
A. 18
B. 18.1
C. 3
D. 1.52
Answer:
the answer is D. 1.52
Step-by-step explanation:
you want to add all the numbers then divide by 10
15 + 15 + 17 + 18 + 18 + 18 + 19 + 20 + 20 + 21
10
then you find the difference between the mean and data point
Data point = 15 15 17 18 18 18 19 20 20 21
Mean Diff = 3.1 3.1 1.1 0.1 0.1 0.1 .9 1.9 1.9 2.9
then add the differences
3.1 + 3.1 + 1.1 + 0.1 + 0.1 + 0.1 + .9 + 1.9 + 1.9 + 2.9 and divide by 10
10
absolute deviation is 1.52 wings.
The solution is : the answer is D. 1.52 is the mean absolute deviation of the data set shown.
What is mean?The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values. The calculation can be done from raw data or for data aggregated in a frequency table.
here, we have,
we want to add all the numbers then divide by 10
15 + 15 + 17 + 18 + 18 + 18 + 19 + 20 + 20 + 21
__________________________________
10
then you find the difference between the mean and data point
Data point = 15 15 17 18 18 18 19 20 20 21
Mean Diff = 3.1 3.1 1.1 0.1 0.1 0.1 .9 1.9 1.9 2.9
then add the differences
3.1 + 3.1 + 1.1 + 0.1 + 0.1 + 0.1 + .9 + 1.9 + 1.9 + 2.9 [and divide by 10]
_______________________________________
10
=1.52
absolute deviation is 1.52 wings.
Hence, The solution is : the answer is D. 1.52 is the mean absolute deviation of the data set shown.
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in 2000 the world's population was 6.08 billion and was increasing at a rate 1.21 each year. use the function to predict the population in the year 2020
Answer:
the population would be 30.28 billion by 2020
Step-by-step explanation:
y=6.08 + 1.21x
y = 6.08 + 1.21(20)
y = 6.08 + 24.2
y = 30.28