Using translation concepts, it is found that the rule for g is:
[tex]g(x) = \frac{x^2}{5} - 8[/tex]
--------------------------------
The parent function is: [tex]f(x) = x^2[/tex].Shrinking a function f(x) vertically by a factor of [tex]0 < a < 1[/tex] is equivalent to: [tex]a \times f(x)[/tex]f(x) by a factor of 1/5:[tex]\frac{1}{5} \times f(x) = \frac{1}{5} \times x^2 = \frac{x^2}{5}[/tex]
Shifting a function down a units is the same as finding [tex]f(x) - a[/tex].Down 8 units, then, the rule for g is:[tex]g(x) = \frac{x^2}{5} - 8[/tex]
A similar problem is given at https://brainly.com/question/11000713
Find the equation of the parabola with a focus at the point (2,5), and a directrix of y = 3.
Answer:
1,3
Step-by-step explanation:
What equation is graphed in this figure?
You and a friend are playing a game using a spinner divided into 4 equal sections, numbered 1 through Which of the following would not be a fair game? You win the pointer points at 1 or 2; otherwise, your friend wins. You win the pointer points at an even numberotherwise, your friend wins. You win if the pointer points at any number except 3; otherwise, your friend All of the above games are fair.
Answer:
You win if you spin any number except 3, otherwise your friend wins
Step-by-step explanation:
Because the spinner is divided into equal sections, there is an equal probability of spinning any number. In this case, you win by spinning a 1, 2, or 4, and your friend only wins by spinning a 3. The probability of you winning is 34, while the probability of your friend winning is only 14.
8.
Andrew has $76.50. Elijah has $94.30. How much more money does Elijah have than
Andrew
Answer:
$17.80Step-by-step explanation:
This is a fairly simple question. All we need to do is find the difference between the two amounts.
$94.30 - $76.50 = $17.80
Your statement balance is $687.45. You have outstanding checks totaling $332.10 and an outstanding deposit for $124.21. What is your adjusted balance?
Answer:
261.48
Step-by-step explanation:
1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
8x − 4/x(x2 + 1)2
2. Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration).
2x3 - 16x2 - 39x + 20/x2 - 8x - 20 x dx
3. Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration).
x2/x4 - 42x2 - 343 x dx
Answer:
Step-by-step explanation:
1.
To write the form of the partial fraction decomposition of the rational expression:
We have:
[tex]\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}[/tex]
2.
Using partial fraction decomposition to find the definite integral of:
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx[/tex]
By using the long division method; we have:
[tex]x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }[/tex]
[tex]- 2x^3 -16x^2-40x[/tex]
[tex]x+ 20[/tex]
So;
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}[/tex]
By using partial fraction decomposition:
[tex]\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}[/tex]
[tex]= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}[/tex]
x + 20 = A(x + 2) + B(x - 10)
x + 20 = (A + B)x + (2A - 10B)
Now; we have to relate like terms on both sides; we have:
A + B = 1 ; 2A - 10 B = 20
By solvong the expressions above; we have:
[tex]A = \dfrac{5}{2}[/tex] [tex]B = \dfrac{3}{2}[/tex]
Now;
[tex]\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}[/tex]
Thus;
[tex]\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}[/tex]
Now; the integral is:
[tex]\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx[/tex]
[tex]\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}[/tex]
3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.
Please check to the attached image below for the solution to question number 3.
Two of the angles in a triangle measure 55° and 28°. What must be the measure of the third angle?
The measure of the third angle is
Work Shown:
Let x be the third angle
For any triangle, the three angles always add to 180 degrees
x+55+28 = 180
x+83 = 180
x = 180-83
x = 97
David has 4 bales of hay for his 13 cows. What is an equivalent ratio of cows to bales of hay
Answer:
13 : 4
Step-by-step explanation:
13 : 4
he has 13 cows and he has 4 bales of hay so 13:4
you can't simplfy it so its still 13 : 4
Which expression is equivalent to y^3-2y^2+y
Answer:
the first one i did it yesterday
R=14 pie=3.14 round to the nearest hundreths
Answer:
Many situations will call for you to round decimals to the nearest tenth to make the number easier to work with. Once you understand how to find the tenths and hundredths place, the process is very similar to rounding whole numbers.
Step-by-step explanation:
Many situations will call for you to round decimals to the nearest tenth to make the number easier to work with. Once you understand how to find the tenths and hundredths place, the process is very similar to rounding whole numbers.
Answer:
6
Step-by-step explanation:
The way you wrote it, it is already rounded.....
The value I remember for pi is 3.14159. This is rounded to the nearest 10-thousandth. Another way of saying the same thing is that it is "rounded to 5 decimal places".
pi--rounded off in decreasing precision:
3.14159
3.1416
3.142
3.14
3.1
3
Watch out for a trap in rounding:
Suppose I start with 5.49. To the nearest 10th, it would be 5.5. To the nearest whole digit, it is 5, not 6. If the original number were 5.51, then rounded to the nearest whole digit would be 6.
Work out 4/7 + 2 1/3
It's 61/21. That's the answer.
f(x) = -4x-1
g(x) = -3.x2 – 2
Find f (4) and g(6).
Please answer this question! as fast as possible please anyone help
the answer would be in the y=m(m=slope of the line)x + b( the y intercept) so it works be
y=3x+-3
In a proof of the Pythagorean theorem using similarity, what allows you to state that the triangles are similar in order to write the true proportions StartFraction c Over a EndFraction = StartFraction a Over f EndFraction and StartFraction c Over b EndFraction = StartFraction b Over e EndFraction?
the geometric mean (altitude) theorem
the geometric mean (leg) theorem
the right triangle altitude theorem
the SSS theorem
Answer:
C: the right triangle altitude theorem
Step-by-step explanation:
In proof of the Pythagorean theorem using similarity, the right triangle altitude theorem allows us to state that the triangles are similar.
What is geometric mean(altitude) theorem?We know that the geometric mean (altitude) theorem states that the altitude is equal to the geometric mean of the two segments.
We know that the geometric mean (leg) theorem states that a leg is the geometric mean between the hypotenuse and the leg's projection on it in every right triangle.
We know that the right triangle altitude theorem states that If we draw an altitude in a right triangle from the vertex which contains the right angle to the opposite side, the triangles on both sides of the altitude are congruent, and the entire triangle is congruent as a result.
We know that the SSS theorem If the three sides of one triangle are equal to the three sides of the other, then the two triangles are congruent.
How to tackle the problem?Here, we have to find the specific theorem which demonstrates the equality of proportionate values in the Pythagorean theorem. From the above theorems, we can conclude that our required theorem is the right triangle altitude theorem.
Therefore In proof of the Pythagorean theorem using similarity, the right triangle altitude theorem allows us to state that the triangles are similar. So, option C is correct.
Learn more about the right triangle altitude theorem here -
https://brainly.com/question/4470400
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One of the largest cookies made on record had a diameter of 78.75 feet. What was the circumference of the cookie?
Answer:
247.4
Step-by-step explanation:
- you can either use pi*diameter or 2pi*radius
- [tex]\pi (78.75) = 247.4[/tex]
is 0.75 repeating irrational or rational
Answer:
This is a rational decimal and is not a repeating decimal.
Step-by-step explanation:
1. Find the distance from point P to QS
SHOW ALL OF YOUR WORK
S(0,8)
R(-3,5)
Q(-5,3)
P(1, 1)
Answer:
5.7 units
Step-by-step explanation:
The distance from point P to QS is the distance from point P (1, 1) to the point of interception R(-3, 5).
Use distance formula to calculate distance between P and R:
[tex] PR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] P (1, 1) = (x_1, y_1) [/tex]
[tex] R(-3, 5) = (x_2, y_2) [/tex]
Plug in the values into the formula.
[tex] PR = \sqrt{(-3 - 1)^2 + (5 - 1)^2} [/tex]
[tex] PR = \sqrt{(-4)^2 + (4)^2} [/tex]
[tex] PR = \sqrt{16 + 16} [/tex]
[tex] PR = \sqrt{32} [/tex]
[tex] PR = 5.7 units [/tex] (to nearest tenth)
A rectangular garden is divided into four sections. Some dimensions are shown in the diagram, and the distance from
point A to point Cis 16 ft.
12 it
8
15 ft
What is the distance from point A to point B in feet?
A. 8ft B.7ft c.9ft D.6ft
Answer:9 ft
Step-by-step explanation:
The requried measure of the AB is given as 7ft. Option B is correct.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
From the diagram, applying Pythagoras' theorem to the right rectangle,
BC² = 15² - 12²
BC² = 81
BC = 9
Now,
AC = 16
AB + BC = 16
AB + 9 = 16
AB = 7 ft
Thus, the requried measure of the AB is given as 7ft. Option B is correct.
Learn more about Pythagorean triplets here:
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What is 0.12 times 105
Pls help
Answer:
12.6
Step-by-step explanation:
Use long multiplication to evaluate.
Answer:
12.6
Step-by-step explanation:
0.12*105=12.6
E
Learning Task 2. Give the reciprocal of the given fractions below.
Write your answer in your notebook.
6
1.
6.
2
8.
7
2. 7
7.
1
2
8
3.
8.
4
4
33-
5
als -|- ||-|-
5
4. 41
9.
5
6
5.
1
10. 1
54
5
5
A
Reciprocals represent two numbers whose product is one. Multi-6/8
The correct format of the options are
(1) 6/8 (6) 2/7
(2) 7/2 (7) 1/8
(3) 33[tex]\frac{4}{5}[/tex] (8) 4/5
(4) 41 (9) 5/6
(5) 54[tex]\frac{1}{5}[/tex] (10) 1/5
Answer:
Reciprocal are those number which when multiplied by the original number gives 1 as the result. eg [tex]\frac{6}{8}[/tex] reciprocal is [tex]\frac{8}{6}[/tex], on multiplication [tex]\frac{6}{8}[/tex]*[tex]\frac{8}{6}[/tex] =1
Reciprocal of the following are as follows
(1) [tex]\frac{8}{6}[/tex]
(2) [tex]\frac{2}{7}[/tex]
(3) 33[tex]\frac{4}{5}[/tex] =[tex]\frac{ 33*5 + 4}{5}[/tex] = 169/5 => reciprocal = 5/169
(4) 1/41
(5) 54[tex]\frac{1}{5}[/tex] => [tex]\frac{54*5 +1}{5}[/tex] = 271/5 => 5/271
(6) 7/2
(7) 8
(8) 5/4
(9) 6/5
(10) 5
solve for x. 0.9(x+1.4)−2.3+0.1x=1.6
Answer:
=2.64
Step-by-step explanation:
Is line / parallel to line m? Explain.
Note: Not drawn to scale
Parallel lines are defined to be two lines that will never intersect even when they go on infinitely. Think of it like railroad tracks. The rails must always be parallel, or the train will gets stuck. By observing lines L and M, you'll notice both lines make perfect railroad tracks, and they will never intersect. These lines are parallel.
n/4 + 1 =5 how do I solve this and show my work
Answer:
n/4 + 1 =5
n/4 = 5-1
n/4 = 4
n = 4*4
n = 16
Answer:
So do this,
Step-by-step explanation:
stand up and go ask your mom!
Please help. Brainliest to correct answer.
Amir can run 15 kilometers in one hour. How many kilometers can Amir run per minute?
There are 60 minutes in 1 hour.
Label your answer in km.
Answer:
0.25km
Step-by-step explanation:
what is 3.7 plus 2.774
Answer:
4.474 it is simple you just add them
Answer:
6.474
Step-by-step explanation:
i calculated it
What is the volume of a spree with a radius of 6 inches
1/2+1/12 en mínima fracion
Answer:3/4
Step-by-step explanation:
First get the common denominator that is 12 then divide 12 by the first denominator which is 2 then add the numerator which is 1 then you will get 7 then repeat to second denominator just divide 12 by 12 then add 1 then add the numerator and copy the denominator. To simplify your answer just divide both by 3 and you will get the final answer of 3/4.
200z + 50 = 8000 solve this problem
Answer:
39.75
Step-by-step explanation:
First, subtract 50 from both sides
200z + 50 - 50 = 8000 - 50
200z = 7950
Then isolate the variable by dividing both sides by 200
200z/200 = 7950/200
z=39.75
Fifty less than five times a number is one hundred. What is this number?
Answer:
-10 :)
Hey champ! Here's the 'splination!
equation: 50-5x=100
50=-5x. (subtract 50 from both sides)
-10=x (divide both sides by -5)
