Answer:
The rule to transform [tex]f(x)[/tex] into [tex]g(x)[/tex] is:
[tex]g(x) = 0.8\cdot [f(x-7) - 4][/tex]
For [tex]f(x) = x^{2} + 6\cdot x[/tex]: [tex]g(x) = 0.8\cdot x^{2} -6.4\cdot x +2.4[/tex]
Step-by-step explanation:
A vertical translation of a function is described by the following operation:
[tex]y' = y + k[/tex] (1)
Where:
[tex]y[/tex] - Original function.
[tex]y'[/tex] - Translated function.
[tex]k[/tex] - Vertical translation factor ([tex]k > 0[/tex] - Upwards)
And a horizontal translation of a function is described by the following operation:
[tex]y' = f(x-k)[/tex] (2)
Where:
[tex]x[/tex] - Independent variable.
[tex]k[/tex] - Horizontal translation factor ([tex]k > 0[/tex] - Rightwards)
And the dilation of a function is defined by this operation:
[tex]y' = k\cdot y[/tex] (3)
Where [tex]k[/tex] is the dilation factor ([tex]0 < k < 1[/tex] - Contraction)
The rule to transform [tex]f(x)[/tex] into [tex]g(x)[/tex] is:
[tex]g(x) = 0.8\cdot [f(x-7) - 4][/tex]
If we know that [tex]f(x) = x^{2} + 6\cdot x[/tex], then [tex]g(x)[/tex] is:
[tex]g(x) = 0.8\cdot [(x-7)^{2}+6\cdot (x-7) - 4][/tex]
[tex]g(x) = 0.8\cdot [(x^{2}-14\cdot x + 49)+(6\cdot x -42) - 4][/tex]
[tex]g(x) = 0.8\cdot (x^{2}-8\cdot x + 3)[/tex]
[tex]g(x) = 0.8\cdot x^{2} -6.4\cdot x +2.4[/tex]
Plz help I need to understand and I don’t
Answer:
B. [tex] 108 \: {in}^{2} [/tex]
Step-by-step explanation:
Total surface area of the square pyramid
= 4 times the area of one triangle + Area of square
[tex] = 4 \times \frac{1}{2} \times 6 \times 6 + {6}^{2} \\ \\ = 72 + 36 \\ \\ = 108 \: {in}^{2} [/tex]
4x - 7y = 2
X = -y - 5
Systems of equations using substitution
Which expression is equivalent to
4 7/8 / 4 1/4
Answer:
39/34 or 1 5/34
Step-by-step explanation:
4 7/8 is equal to 39/8
4 1/4 is equal to 17/4
39/8 ÷ 17/4 is equal to 39/8 × 4/17
39/8 × 4/17 = 39/34
Explain how a piece of food when eaten is digested and absorbed by the human body
PLS HURRY I NEED IT!!<3
Answer:
The muscles of the small intestine mix food with digestive juices from the pancreas, liver, and intestine, and push the mixture forward for further digestion. The walls of the small intestine absorb water and the digested nutrients into your bloodstream.
Answer & Explanation:
When humans chew food, it is chemically and physically broken down into smaller molecules. Your teeth physically crush the food and enzymes in your saliva break down the food into smaller pieces. Then your food goes through your esophagus and begins the digestion process. When the food reaches the stomach, the stomach walls pound the food to make it into smaller chunks of food. Hormones secreted in the stomach walls release acids and enzyme juices that chemically dissolve the food into even smaller pieces. The liver, pancreas, and gallbladder are major parts of the digestive process as well. They produce digestive juices and transfer bile to prepare for the next stage. After the food has been in the stomach for three hours, the food is now a liquid called chyme and is ready to move into the small intestine! The liver sends the bile to the gallbladder that secretes it into the duodenum. Then it dissolves the fats in the chyme so they can be digested by the juices from the pancreas and intestines. The enzyme juices break down the fat molecules in the chyme into fatty acids. The enzymes carry out the final deconstruction of proteins into amino acids. This happens in the small intestine lower region that is coated with villi. The villi maximizes molecule absorption and transfers it into the bloodstream. The blood then feeds it to the body’s organs and tissues.
That is whole process of digestion. Hope this helps! :3
What is the value of t? Points D and E are midpoints of the sides of triangle ABC. The perimeter of the triangle is 48 units. 2 3 B 6 8 D 37 А 4t 7t + 6 С
Answer:
2
Step-by-step explanation:
A midpoint divides a segment in two equal segments
DB = 3t
AB = 6t
BE = 4t
BC = 8t
8t + 6t + 7t + 6 = 48
21t = 42
t = 2
The value of t in the given triangle is 2.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
ABC is a given triangle.
The points D and E are the midpoints of the triangle ABC.
The perimeter of the triangle is 48 units.
We know that a midpoint divides a segment in two equal segments.
The midpoint is the middle point of a line segment.
DB = 3t
AB = 6t
BE = 4t
BC = 8t
From perimeter definition the sum of the sides is the perimeter.
8t + 6t + 7t + 6 = 48
Add the like terms
21t = 42
Divide both sides by 21
t = 2
Hence, the value of t in the given triangle is 2.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ7
Solve the following quadratic by
completing the square.
y = x2 + 2x – 6
x =
[?]+)
Answer:
x = - 1 ± [tex]\sqrt{7}[/tex]
Step-by-step explanation:
let y = 0
x² + 2x - 6 = 0 ( add 6 to both sides )
x² + 2x = 6
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(1)x + 1 = 6 + 1
(x + 1)² = 7 ( take the square root of both sides )
x + 1 = ± [tex]\sqrt{7}[/tex] ( subtract 1 from both sides )
x = - 1 ± [tex]\sqrt{7}[/tex] , that is
x = - 1 + [tex]\sqrt{7}[/tex] , x = - 1 - [tex]\sqrt{7}[/tex]
Enter the decimal equivalent of 3/5
help in number 3 please
Answer:
The two restrictions that we have for x are:
x < -2
x > -0.5
Step-by-step explanation:
In part 3 we want to solve:
-5 < f(x) < 1
But we don't know the actual equation of f(x), we have only the graph, so let's work with that.
So with the graph, let's find the allowed values of x.
First, let's see the possible values of x such that:
-5 < f(x)
in the graph, we can see that:
f(-2) = -5
And as x decreases we will have:
f(x) > -5
So here we found one restriction for x, if we want:
f(x) > -5, then we must have x < - 2
Now let's find the other case, where:
f(x) > 1
Again, in the graph we can see that:
f(-0.5) = 1
And as x increases, the value of f(x) decreases.
so if x > -0.5
f(x) < 1.
Then we found another restriction for x:
x > -0.5
The two restrictions that we have for x are:
x < -2
x > -0.5
So if x is a value such that one of these two inequalities is true, then the inequality:
-5 < f(x) < 1
is true.
Which value is closest to the perimeter of the window
Answer:
9.82 feet
Step-by-step explanation:
the perimeter of the window is the circumference of a semi-circle with a diameter of 5
P = (πd)/2 (divided in half because it's only half a circle)
P ≈ 3.14(3.5) which is approx 11
11 is closest to 9.82
Answer:
9.82 Is the Closest
Step-by-step explanation:
First of all, you can see its a half circle, meaning if we make it a full circle, the length of the center is 5, so the full circle's area is about 19.5-20. Now to find the area of the half circle/windows we get 9.75 - 10. The only number between that is 9.82, which should be you answer.
Have a nice day!
If this answer helped you, please give Brainliest.
Select the correct answer.
The local library lends an average of 68.24 books to readers each day. What is the average number of books lent to readers in a week?
A.
417.76
B.
427.98
C.
432.79
D.
445.28
E.
477.68
The average number of books that is lent to readers in a week is 477.68.
What is average?
This is the mean data that is contained in a frequency of grouped data. The mean represents the average number in a data set.
The average in the question = 68.24 books
The total number of days in a week = 7
Therefore the number of books lent to readers would be 68.24 books x 7
= 477.68
Read more on average here: https://brainly.com/question/20118982
Help me plz and show work
Answer:
substitute the value of y into the equation 7x+3y = 35
7x + 3(x+5) = 35 (distribute 3 through the parenthesis)
7x + 3x + 15 = 35
collect the like terms
7x + 3x = 35 - 15
10x = 20 (divide both sides by 10)
x = 2
substitute x = 2 into the equation y = x + 5
y = 2 + 5
y = 7
4400 is placed in an account with an annual interest of rate 11%. how much will be in the account after 5 years, to the nearest cent?
Answer: I don't know
Step-by-step explanation:
what's the area of this triangle?
somebody help me pls it would make my day good!!!
36% I think.... Because there's 100 ppl and 36 of them like cats
help me please thanks
The sum angle of triangle is 180°
The angle of line is 180°
The right angle is 90°
x=180-115
x=65°
y=180-65-90
y=90-65
y=25
Suppose you have a deck of 52 cards. Let:
A: draw a 7
B: draw a diamond
Find the probability of A U B and write as a fraction
Answer:
16/52
Step-by-step explanation:
A U B= A + B - A ∩ B
A= 4/52
B= 13/52
A∩B= 1/52 (it's 1/52 because there is only one 7 of diamonds in the deck)
4/52+13/52-1/52= 16/52
the cypertoy company has determined that out of a productuion run of 50 toys 17 are defectives if 5 toys are chosen at random what is the probabilty that at least 1 defective
Answer:2.9
50 divided by 17 is 2.9
Solve this system of equations
3x+3y=36
x=y+2
Answer:
no solution
Step-by-step explanation:
.......................
Answer:
.......................
Step-by-step explanation:
De cuántas maneras se pueden dar primer y segundo premio entre 10 personas?
SOMEONE ANSWER QUICK!!
Steven bought 4 pizzas to share with his family. Together, they ate 2 7/12 pizzas on Friday and another 2/3 of a pizza on Saturday. How much pizza is left??
Answer:
3/4 of a pizza is left.
Step-by-step explanation:
4 pizzas minus (2 and 7/12 plus 2/3). Change 2/3 to 8/12 by multiplying the numerator and denominator by 4 to get both denominators the same. 4 pizzas minus (2 and 7/12 plus 8/12 or 2 and 15/12 or 3 and 3/12 or 3 and 1/4). Restated 4 pizzas minus 3and 1/4 pizzas 3/4 pizzas. 3/4 of a pizza is left.
what is the median of 17, 2,15,10,16,6
Answer:
10
Step-by-step explanation:
10 is the median number
Write an equation in slope-intercept form of the line that passes through (-1, 4) and (0, 2).
y =
Answer:
[tex]y=-2x+2[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-1, 4) and (0, 2)
[tex]=\frac{2-4}{0-(-1)}\\=\frac{-2}{0+1}\\=\frac{-2}{1}\\= -2[/tex]
Therefore, the slope of the line is -2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-2x+b[/tex]
2) Determine the y-intercept
[tex]y=-2x+b[/tex]
Recall that the y-intercept is the value of y when the line crosses the y-axis, meaning that the y-intercept occurs when x is equal to 0.
One of the given points is (0,2). Notice how y=2 when x=0. Therefore, the y-intercept of the line is 2.
Plug this back into the equation:
[tex]y=-2x+2[/tex]
I hope this helps!
Identify the surface area of the composite figure. HELP ME PLEASE!!!
Answer:
512 m²Step-by-step explanation:
The surface area is a sum of areas of four triangles with base of 8 m and hight of 12 m and areas of five squares with sides of 8 m.
Sa = 4×¹/₂×8×12 + 5×8² = 192 + 320 = 512 m²
when a number is doubled andthen eight added it became 60 what is the number
Answer:
26
Step-by-step explanation:
All I did was 60-8
(52)
Then 52/2
26
Answer:
26
Step-by-step explanation:
1) A number is doubled. This number will be represented by X.
8 + (X • 2) = 60
2) Subtract 8 from both sides of the equation
(X • 2) = 60 - 8
3) Simplify the equation
X • 2 = 52
4) Divide each side of the equation by 2
X = 52 ÷ 2
52 ÷ 2 = 26
5) Simplify the equation
X = 26
A gold, a silver, and a bronze medal are awarded in an Olympic event. In how many possible ways can the medals be awarded for a 200-meter sprint in which there are 12 runners
Answer:
The medals can be awarded in 1,320 possible ways.
Step-by-step explanation:
Given that a gold, a silver, and a bronze medal are awarded in an Olympic event, to determine in how many possible ways can the medals be awarded for a 200-meter sprint in which there are 12 runners, the following calculation must be performed:
12 x 11 x 10 = X
12 x 110 = X
1,320 = X
Therefore, the medals can be awarded in 1,320 possible ways.
Overnight, a pipe cracked and started to leak into a basement. The graph shows the depth of the water in relation to time.
How many inches does the water rise each hour?
___ inches.
How deep is the water after four hours? The water is
__ inches deep.
How long will it take for the water to reach a depth of 80 inches? It will take
__ hours.
Answer:
the water will rise 10 in each hour after 4 hours the water will be 40 in deep and it will take 8 hours for the water to reach a depth of 80 in
The water rises 10 inches each hour. The water is 4 inches deep is the water after four hours. It will take 8 hours for the water to reach a depth of 80 inches.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
A pipe cracked overnight and started to leak into a basement.
The graph represents the depth (d) of the water over time (t).
As per the given graph, the required solution would be as:
Take two points (1, 10) and (5, 50) in the given graph
The linear function will be :
d - 10 = (50-10)/(5-1)(t - 1)
d - 10 = (40/4)(t - 1)
d = 10(t - 1) + 10
d = 10t - 10 + 10
d = 10t
Here slope of the given function is 10, which means 10 inches the water rise each hour.
The value of time (t) = 4 hr corresponds to the depth of water (d) is
d = 10(4) = 40
So, the water is 40 inches deep is the water after four hours
The value of depth of water (d) = 80 in corresponds to the time (t) is
80 = 10t
t = 80/10 = 8
So, It will take 8 hours for the water to reach a depth of 80 inches
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ2
(SOMEONE HELP ME PLEASE, AND NO LINKS)
What number is represented by point P on the number line?
Only 0, 1, 2, 3, , 4, 5, 6, 7, 8, 9, ., -, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or decimal.
Answer:
7 I think
Hope's ti helps
Answer the questions below please.
Answer:
(a) 56 m
(b) 91 cm
Step-by-step explanation:
Find the Volume. Plz Help
Answer:
B
Step-by-step explanation:
[tex]V = \frac{l*w*h}{2} = \frac{18*12*9}{2} = \frac{1944}{2} = 972[/tex]
Answer:
1944 cm cubed
Step-by-step explanation:
Volume = L*W*H
18 * 9 = 162
12 * 162 = 1944
1944