Answer:
Shift 1 units towards left and then stretch vertically 3 times.
Step-by-step explanation:
We are given that a parent function
[tex]y=x^2[/tex]
After transformation, we get a graph [tex]y=3(x+1)^2[/tex]
We have to find that how the parent function transformed to produce the graph of [tex]y=3(x+1)^2[/tex]
The parent graph is shifted 1 unit towards left by the rule of transformation
[tex]f(x)\rightarrow f(x+1)[/tex]
By applying this rule then, we get
[tex]y(x)=(x+1)^2[/tex]
Now, the parent function stretched vertically 3 times the previous graph by the rule
[tex]f(x)\rightarrow 3f(x)[/tex]
Apply this rule then, we get
[tex]y(x)=3(x+1)^2[/tex]
simplify the given expression
expression:1
9(2+ 7f)
expression:2
6•7-3^2•9+4^3
show your work
Answer:
Expression: 1 ⇒ 18 + 63 f
Expression: 2 ⇒ 25
Step-by-step explanation:
* Lets revise at first the order of operations
- The order of these operations is:
# Parenthesis
# Exponents
# Multiplication and Division which comes first from left to right
# Addition and Subtraction which comes first from left to right
- There is a word made from the first letter of each operation
PEMDAS to remember the order of operations
* Lets solve the problem
# Expression: 1
∵ 9(2 + 7 f)
- To simplify this expression multiply the bracket by 9
∵ 9(2 + 7 f) = 9 × 2 + 7 f × 9
∵ 9 × 2 = 18
∵ 7 f × 9 = 63 f
∴ 9(2 + 7 f) = 18 + 63 f
* Expression: 1 ⇒ 18 + 63 f
# Expression: 2
∵ 6 × 7 - 3² × 9 + 4³
- At first simplify exponent
∵ 3² = 9 and 4³ = 64
∴ 6 × 7 - 3² × 9 + 4³ = 6 × 7 - 9 × 9 + 64
- Solve the multiplication first
∵ 6 × 7 = 42
∵ 9 × 9 = 81
∴ 6 × 7 - 3² × 9 + 4³ = 42 - 81 + 64
- Solve 42 - 81 first because it comes first from left to right
∵ 42 - 81 = - 39
∴ 6 × 7 - 3² × 9 + 4³ = - 39 + 64
- Add them
∵ - 39 + 64 = 25
∴ 6 × 7 - 3² × 9 + 4³ = 25
* Expression: 2 ⇒ 25
Yara multiplies and divides a certain number by the same
power of 10. The product she gets is 40,000 and the
quotient she gets is 0.000004. Find Yara's number and
the power of 10 she used. Explain your reasoning.
For this case we have to:
x: Represents the unknown number
y: Represents the exponent of base 10
So, considering a system of equations we have:
[tex]x * 10 ^ y = 40,000\\\frac {x} {10 ^ y} = 0.000004[/tex]
From the first equation we have:
[tex]10 ^ y = \frac {40,000} {x}[/tex]
Substituting in the second equation:
[tex]\frac {x} {\frac {40,000} {x}} = 0.000004\\\frac {x ^ 2} {40,000} = 0.000004\\x ^ 2 = 40,000 * 0.000004\\x ^ 2 = 0.16\\x = \pm \sqrt {0.16}[/tex]
We choose the positive value:
[tex]x = 0.4[/tex]
So, the number is 0.4.
So:
[tex]10 ^ y = \frac {40,000} {0.4}\\10 ^ y = 100,000\\y = 5[/tex]
Thus, the exponent is 5.
Answer:
Yara use 0.4 and[tex]10 ^ 5[/tex]
Answer:
0.4 and 10.5
Step-by-step explanation:
HURRY PLZZZZ!!!!!!!!!!
The width of a rectangle is 4 more than half the length. If the perimeter of the rectangle is 74, what is the width? Perimeter of rectangle: P = 2l + 2w
i'll give brainliest
Answer:Width = 15 units .
Step-by-step explanation:
Given : The width of a rectangle is 4 more than half the length. If the perimeter of the rectangle is 74,
To find : what is the width.
Solution : We have given perimeter of the rectangle is 74,
Let the Length = x .
According to question :
The width of a rectangle is 4 more than half the length.
Width = 4 + [tex]\frac{x}{2}[/tex].
Perimeter = 2 length + 2 width .
Plugging the values,
74 = 2 ( x ) + 2 (4+[tex]\frac{x}{2}[/tex]).
74 = 2x + 8 + x .
Combine like terms
74 = 2x +x + 8.
74 = 3x +8.
On subtracting both sides by 8.
74 -8= 3x .
66 = 3x
On dividing both sides by 3
x = 22.
Width = Width = 4 + [tex]\frac{22}{2}[/tex].
Width = 4 +11.
Width = 15 units .
Therefore, Width = 15 units .
The diameter of a circle is 5 kilometers. What is the area?
Answer:
[tex]\large\boxed{A=6.25\pi\ km^2\approx19.625\ km^2}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have the length of a diameter d = 5 km
We know: d = 2r. Therefor r = 5km : 2 = 2.5 km.
Substitute:
[tex]A=\pi(2.5)^2=6.25\pi\ km^2[/tex]
If you want an approximation, then
[tex]\pi\approx3.14\to A\approx(6.25)(3.14)=19.625\ km^2[/tex]
Hey!
-----------------------------
Formula: A = πr²
Diameter: d / 2 = r
-----------------------------
Solution:
A = (3.14)(2.5)²
A = (3.14)(6.25)
A = 19.625km.
-----------------------------
Answer:
The area of the circle is 19.625km. or 6.25π km.
-----------------------------
Hope This Helped! Good Luck!
Between 10 pm and 7:45 am the water level in a swimming pool decreased by 13/16 inch. Assuming the constant rate how much did it drop each hour
Answer:
[tex]\frac{1}{12} [/tex] inches per hour .
Step-by-step explanation:
Between 10 pm and 7:45 am there are 9 hours and 45 minutes i.e. [tex]9+\frac{45}{60} =\frac{39}{4}[/tex] hours
The water level in a swimming pool decreased by amount in [tex]\frac{39}{4}[/tex] hours = [tex]\frac{13}{16}[/tex] inches
The water level in a swimming pool decreased by amount in 1 hour:
= [tex]\frac{\frac{13}{16}}{\frac{39}{4}}[/tex] inches
= [tex]\frac{13}{16} \times \frac{4}{39}[/tex] inches
= [tex]\frac{1}{4} \times \frac{1}{3}[/tex] inches
= [tex]\frac{1}{12} [/tex] inches
Hence it drop by [tex]\frac{1}{12} [/tex] inches each hour .
How much did it drop each hour is 0.08333 inches/hour
First step is to calculate the Decrease
Decrease = 13/16 inches
Decrease=0.8125 inches
Second step is to calculate the time interval
From 10 pm to 7:45 hours will be 9.45 hours
Time interval= (9 + 45/60) hours
Time interval=9.75 hours
Now let determine How much did it drop each hour
0.8125/9.75 inches/hour
=0.08333 inches/hour
Inconclusion How much did it drop each hour is 0.08333 inches/hour
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If two planes are perpendicular to the same line, then
•
.
•
•
A. they form a straight line
B. they are perpendicular to each other
C. they are parallel
D. not enough information
Answer:
option c) they are parallel !!
Step-by-step explanation:
If two lines are perpendicular to the same line that is they both make 90° with the same line have difference in their angle 0° with respect to the same line , and line having difference in their angle as 0° are parallel to each other !
Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value of $13.10. The number of quarters was 15 more than 3 times the number of dimes. How many quarters and how many dimes did Peter have?
it wont give me the answer.. i have to pay for it, and my homework is due in 3 hours...HELP?
Answer: Dimes: 11
Quarters: 48
Step-by-step explanation:
48/4= 12.00
11•0.10= 1.10
12+1.10= 13.10
What is the degree of the polynomial 5a^6bc^2+8d^5+7e^6f^2-10g^4h^7
Final answer:
The degree of the polynomial 5a⁶bc²+8d⁵+7e⁶f²-10g⁴h⁷ is 11, determined by the highest sum of exponents in any term of the polynomial, which is found in the term -10g⁴h⁷.
Explanation:
The degree of a polynomial is the highest exponent of its variables when it is expressed in standard form. To find the degree of the given polynomial 5a⁶bc²+8d⁵+7e⁶f²-10g⁴h⁷, we look at each term individually and sum the exponents of the variables within that term. The terms of the polynomial are:
5a⁶bc² with a degree of 6 + 1 + 2 = 9
8d⁵ with a degree of 5
7e⁶f² with a degree of 6 + 2 = 8
-10g⁴h⁷ with a degree of 4 + 7 = 11
Comparing the sums of the exponents, we see that the term -10g⁴h⁷ has the highest sum which is 11. Therefore, the degree of the given polynomial is 11.
Which two numbers are 4 units away from -1
The two numbers are 3 and -5. Let's start with 3. To get three, add 4 to -1. That means, going 4 to the right on a number line. When you do so, you will end up with 3. Since adding always go up.
Let's move onto -5 now. For this, go 4 to the left. Subtracting from negative numbers will be negative numbers. Since subtracting is going down, you go down on the number line.
Therefore, 3 and -5 is the answer!
Explaining channel:
Type HWsolver-Brainly. It should pop up at the bottom with a person thumbs up.
The two numbers that are 4 units away from -1 are -5 and 3.
What is a number line?In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
Now the given integer is, -1.
To find the numbers that are 4 units away we need to subtract and add 4 to get the required number.
So, 4 units forward from -1 is,
-1 + 4 = 3
And 4 units backward from -1 is,
-1 - 4 = -5
So the two numbers we get are 3 and -5.
Thus, the two numbers that are 4 units away from -1 are -5 and 3.
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For the function f(x) = 6x - 8, identify the values of f(o), f(1/2), and f(-2).
O 8; -5; 4
O -8; -11; -20
O 8; -11; 4
© -8; 15; -20
Answer:
-8, -5, -20.
Step-by-step explanation:
f(0) = 6(0) - 8 = -8
f(1/2) = 6(1/2) - 8 = -5
f(-2) = 6(-2) - 8 = -20.
[tex]\text{Hello there!}\\\\\text{You're plugging in the values 0, 0.5, and -2 to x}\\\\\text{Plug them into the equation:}\,\,f(x) = 6x - 8\\\\\text{Solve:}\\\\f(x) = 6(0) - 8\\\\\boxed{f(x)=-8}\\\\f(x) = 6(0.5) - 8\\\\f(x) = 3 - 8\\\\\boxed{f(x)=-5}\\\\f(x) = 6(-2) - 8\\\\f(x)=-12-8\\\\\boxed{f(x)=-20}\\\\\text{Those three solutions will be your answer}\\\\\large\boxed{\text{Answer:}\,\,-8;-5;-20}[/tex]
Find the sum or difference in simplest form 1 3/7 + 10 6/7
Answer:
[tex]12\frac{2}{7}[/tex]
Step-by-step explanation:
we have
[tex]1\frac{3}{7} +10\frac{6}{7}[/tex]
step 1
Convert mixed number to an improper fraction
[tex]1\frac{3}{7}=\frac{1*7+3}{7}=\frac{10}{7}[/tex]
[tex]10\frac{6}{7}=\frac{10*7+6}{7}=\frac{76}{7}[/tex]
step 2
Substitute in the expression above and find the sum
[tex]\frac{10}{7}+\frac{76}{7}=\frac{86}{7}[/tex]
Convert to mixed number
[tex]\frac{86}{7}=\frac{84}{7}+\frac{2}{7}=12\frac{2}{7}[/tex]
inverse of y= x-6/x+5
as you would already know, we start off to gettting any inverse of any expression by doing a quick switcheroo on the variables and then we solve for "y".
[tex]\bf y = \cfrac{x-6}{x+5}\implies \stackrel{\textit{quick switcheroo}}{x = \cfrac{y-6}{y+5}}\implies x(y+5)=y-6\implies xy+5x=y-6 \\\\\\ xy+5x+6=y\implies 5x+6=y-xy\implies 5x+6=\stackrel{\textit{common factor}}{y(1-x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{5x+6}{1-x}=\stackrel{f^{-1}(x)}{y}~\hfill[/tex]
6 hundreds divided by 10=
2 thousands divided by 10=
Answer:
1. 60 2. 200
Step-by-step explanation:
600÷10= 60
2000÷10=200
Answer:
60 and 200
Step-by-step explanation:
When divideing by 10 you can cancel the zeros from both the numertor and denominator
Starting from the same place, Karina walks due west and Lucas walks due east. On the number line, 0 represents their starting point, negative values represent the distance traveled west and positive values represent the distance traveled east. All values are given in feet. How many feet apart are Karina and Lucas on the number line? Enter your answer in the box.
Answer:
The answer is 480
Step-by-step explanation:
Write an equation that can be used to find the area of any 10 square floor tiles
3. Noah is helping to collect the entry fees at his school's sports game. Student entry
costs $2.75 each and adult entry costs $5.25 each. At the end of the game, Diego
collected $281.25.
Select all equations that could represent the relationship between the number of
students, s, the number of adults, a, and the dollar amount received at the game.
A. 281.25 – 5.25a = 2.75s
B. a = 53.57 - 13:25
C. 281.25 -5.25s = a
D. 281.25 +2.75a = s
E. 281.25 +5.25s = a
281.25-5.25a=2.75
step by step:
so you divide the total amount by two and you get 140.62
then you divide that by 5.25 and you get 26.78
plug that into a and you get 140.62
then you take the remainder which is 140.62 and you divide that by 2.75
which is 51.13 and that will be your number for s
and at the end you should get the remainder of 140.62
then you multiply 140.62 by 2 and you get were you started and thats how you check your answer
Select all equations that could represent the relationship between the number of
number ofstudents, s, the number of adults, a, and the dollar amount received at the game.
The equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s
let
student fee = $2.75
Adult fee = $5.25
Total income = $281.25
Number of students = s
Number of adults = a
The equation:
Total income = (student fee × Number of students) + (Adult fee × Number of adults)
281.25 = (2.75 × s) + (5.25 × a)281.25 = 2.75s + 5.25a281.25 - 5.25a = 2.75sA. 281.25 – 5.25a = 2.75s
True
B. a = 53.57 - 13:25
Not true
C. 281.25 -5.25s = a
Not true
D. 281.25 +2.75a = s
Not true
E. 281.25 +5.25s = a
Not true
Therefore, the equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s
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Which is bigger 0.305 or 0.350
Answer:
0.350 is bigger
Step-by-step explanation:
Answer:
0.305
Step-by-step explanation:
When working with decimals, it would be the smaller number that is bigger. .305 is bigger because .305 is 305 points away from 0 and .350 is 350 points away from 0!!
Hope this helps!!!
-Unicorns110504
given: f(x)=3 - x; g(x) = -2x find f[g(2)]
Answer:
7
Step-by-step explanation:
To calculate f(g(2)) evaluate g(2) then evaluate f(x) for this value
g(2) = - 2(2) = - 4, then
f(- 4) = 3 - (- 4) = 3 + 4 = 7
PLEASE HELP ME(picture is shown) Set up the equation and find the length of BC
Step-by-step explanation:
From the diagram,
AC = AB + BC
BC = AC - AB
BC = 54 - 25 = 29
f(x) = 10x – 4
What is the inverse for this?
Answer:
Step-by-step explanation:
f(x) = 10x – 4
10x = f(x)+4
x = f(x)/10 + 2/5
the inverse is y = x/10 + 2/5
what is the gcf of 25 and 14
A 5-pound bag of apples costs $3.50. Use this rate to complete the table to identify equivalent ratios, then answer the questions. Pounds 5 15 Cost ($) 0.70 3.50 7 Apples cost $ per pound.
Are my answers correct?
Answer:
1lb to $0.70, 5lb to $3.50, 10lb to $7, 15lb to $10.50
Step-by-step explanation:
Turn your ratios into fractions and place them near each other. you multiply across then divide with the remaining number.
4y + 9 = - 4y - 7. Please explain to me how to do it.
You want to keep the variable on the left and number on right.
So, we need to get rid of 9 and -4y. Let's start with 9.
4y+9=-4y-7
Subtract nine from both sides.
4y=-4y-16
Now add 4y on both sides.
8y=-16
Finally, divide both sides by 8 to get y=-?.
8y/8=-16/8
Therefore, the answer is y=-2.
y = (x + 3)^2 -4 and identify the axis of symmetry
Answer:
Step-by-step explanation:
the line for equation : x = - 3
What’s the value of the 3 in 783.97
10 POINTS BOIII
What is the slope of the line on the graph? P.S it's supposed to be a number.
Answer:
1/2
Step-by-step explanation:
the sum of two numbers is 84. The first is 9 more than 4 times the second. Find the numbers.
Answer:
69 and 15
Step-by-step explanation:
Second number=x
First number 4x+9
4x+9 +x = 84
5x+9=84
5x=75
x=15
15*4=60
60+9=69
69+15=84
If you're driving at 25 miles per hour through a school zone and a child runs out in front of you, how much distance will
your car cover before stopping?
Answer:
depending on the car type
probs about 5-10 feet
Step-by-step explanation:
what is the point slope form of a line with slope 3 that contains the point (2, 1)
Answer:
y - 1 = 3(x - 2)
y - 1 = 3x - 6
y = 3x - 5
Answer:
The point slope form of the line is y-1=3(x-2).
Step-by-step explanation:
If a line passes through a points [tex](x_1,y_1)[/tex] with slope m, then the point slope form of the line is
[tex]y-y_1=m(x-x_1)[/tex] .... (1)
where, m is slope.
It is given that the slope of a line is 3 and it passes through the point (2,1).
Substitute m=3, [tex]x_1=2\text{ and } y_1=1[/tex] in equation (1), to find the point slope form of the line.
[tex]y-(1)=(3)(x-(2))[/tex]
[tex]y-1=3(x-2)[/tex]
Therefore the point slope form of the line is y-1=3(x-2).
solve the equation. -x/3=27
Answer:
x=-81
Step-by-step explanation:
Multiply both sides of the equation by 3 to eliminate the fraction on the left side.
[tex]-x/3(3)=27(3)[/tex]
[tex]-x=81[/tex]
Divide both sides by -1 to isolate x on the left side of the equation
[tex]-x/-1=81/-1\\x=-81\\[/tex]
Answer:
x = - 81.
Step-by-step explanation:
Given : [tex]\frac{-x}{3} = 27[/tex].
To find : solve the equation.
Solution: We have given
[tex]\frac{-x}{3} = 27[/tex].
On multiplying both sides by 3
-x = 27*3.
On dividing both sides by -1.
x = - 81.
Therefore, x = - 81.