Answer:
First question: The common ratio r is 3
Second question: The average rate of change is 297.92
Third question: The function's graph of h(x) = 0.5(2^x) + 0.5 has a
y-intercept of 1
Fourth question: The ordered pairs lie on the graph of f(x) are (2 , 18)
and (0 , 2)
Step-by-step explanation:
First question:
* Lets revise the rule of the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric sequence:
- U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
- Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms and n is the position
of the term in the sequence
* Now lets solve the question
∵ The sequence is 16 , 48 , 144 , 432 , ................
∵ a = 16
∵ ar = 48
∴ r = 48/16 = 3
∴ The sequence is geometric withe common ratio 3
* The common ratio r is 3
Second question:
* Lets revise the average rate of change of a function
- When you calculate the average rate of change of a function,
you are finding the slope of the secant line between the two points
on the function
- Average Rate of Change for the function y = f (x) between
x = a and x = b is:
change of y/change of x = [f(b) - f(a)]/(b - a)
* Now lets solve the problem
∵ g(x) = 50(12^x), where x ∈ [-1 , 1]
∵ a = -1 and b = 1
∵ f(-1) = 50(12^-1) = 50/12
∵ f(1) = 50(12^1) = 600
∴ Average Rate of Change = [600 - 50/12]/[1 - (-1)]
∴ Average Rate of Change = [595.8333]/[2] = 297.92
* The average rate of change is 297.92
Third question:
* Lets talk about the y- intercept
- When any graph intersect the y-axis at point (0 , c), we called
c the y-intercept
- To find the y- intercept, substitute the value of x in the
function by zero
* Now lets check which answer will give y- intercept = 1
∵ h(x) = 0.5(2^x) + 0.5 ⇒ put x = 0
∴ h(0) = 0.5(2^0) + 0.5 = 0.5(1) + 0.5 = 1
∵ h(x) = (0.5)^x + 1 ⇒ put x = 0
∴ h(0) = (0.5)^0 + 1 = 1 + 1 = 2
∵ h(x) = 5(2^x) ⇒ put x = 0
∴ h(0) = 5(2^0) = 5(1) = 5
∵ h(x) = 5(0.5)^x + 0.5
∴ h(0) = 5(0.5)^0 + 0.5 = 5(1) + 0.5 = 5.5
* The function's graph of h(x) = 0.5(2^x) + 0.5 has a y-intercept of 1
Fourth question:
* Lets study how to find a point lies on a graph
- When we substitute the value of x of the point in the function
and give us the same value of y of the point, then the point
lies on the graph
* Now lets solve the problem
∵ f(x) = 2(3)^x
∵ The point is (2 , 18) ⇒ put x = 2
∴ f(2) = 2(3)² = 2(9) = 18 ⇒ the same y of the point
∴ The point (2 , 18) lies on f(x)
∵ The point is (0 , 2) ⇒ put x = 0
∴ f(0) = 2(3)^0 = 2(1) = 2 ⇒ the same y of the point
∴ The point (0 , 2) lies on f(x)
∵ The point is (-1 , 1) ⇒ put x = -1
∴ f(-1) = 2(3)^-1 = 2(1/3) = 2/3 ⇒ not the same y of the point
∴ The point (-1 , 1) does not lie on f(x)
∵ The point is (3 , 56) ⇒ put x = 3
∴ f(3) = 2(3)³ = 2(27) = 54 ⇒ not the same y of the point
∴ The point (3 , 56) does not lie on f(x)
* The ordered pairs lie on the graph of f(x) are (2 , 18) and (0 , 2)
Answer:
3eeddw
Step-by-step explanation:
Express this decimal as a fraction.
Answer:
[tex]\large\boxed{1.\overline{21}=\dfrac{40}{33}}[/tex]
Step-by-step explanation:
[tex]x=1.\overline{21}\\\\x=1.212121...\qquad\text{multiply both sides by 100}\\\\100x=121.212121...\\\\\text{subtract x from 100x}\\\\100x-x=121.212121...-1.212121...\\\\99x=120\qquad\text{divide both sides by 99}\\\\x=\dfrac{120}{99}\\\\x=\dfrac{120:3}{99:3}\\\\x=\dfrac{40}{33}[/tex]
PLEASE help me! I will mark brainlist!
Answer:
yes ik
Step-by-step explanation:
Answer:it should be C
Step-by-step explanation:
Algebraic Manipulation: Simplify 15x³ (y-z)² ÷ 10x⁻²(y²-z²)
Thank you!
Answer:
[tex]=\frac{3x^{5}(y-z)}{2(y+z)}[/tex]
Step-by-step explanation:
[tex]\frac{15x^3 (y-z)^2}{10x^{-2}(y^2-z^2)}[/tex] We need to solve this equation.
We know (x^2-y^2) = (x-y) (x+y)
Using the above formula, and taking 5 common:
[tex]=\frac{3x^3 (y-z)^2}{2x^{-2}(y^2-z^2)}\\=\frac{3x^{3+2} (y-z)^2}{2(y^2-z^2)}\\=\frac{3x^{5} (y-z)(y-z)}{2(y-z)(y+z)}\\=\frac{3x^{5}(y-z)}{2(y+z)}[/tex]
A line segment has endpoints at 3,2 and 2,-3 which reflection will produce and image with endpoints at 3,-2 and 2,3
Answer:
A reflection across the x-axis.
Step-by-step explanation:
A reflection across the x-axis changes the signs of the y-coordinates like it does in the problem. (3, 2) becomes (3, -2) and (2, -3) becomes (2, 3).
I hope this helps!
ANSWER
Reflection in the x-axis
EXPLANATION
The given line segment has endpoints at (3,2) and (2,-3).
After this point are reflected the image points are:
(3,-2) and (2,3)
We can observe that the y-coordinates were negated to obtain the image points hence the mapping for the reflection is;
[tex](x,y)\to(x,-y)[/tex]
This is a reflection in the x-axis.
The price of a pair of shoes is $63.20. The sales tax rate is 4.5 percent. How much sales tax would you pay if you bought these shoes?
Answer;
63.20 / .045 = $2.84
Answer:
63.20 / .045 = $2.84
Step-by-step explanation:
Write an algebraic expression in standard form for the shaded area of the following shape
Answer:
x² + 7x + 12
Step-by-step explanation:
The area of a rectangle = length × width
here length = x + 4 and width = x + 3, hence
A = (x + 4)(x + 3)
Each term in the second parenthesis is multiplied by each term in the first parenthesis.
A = x(x + 3) + 4(x + 3) ← distribute each parenthesis
A = x² + 3x + 4x + 12 ← collect like terms
A = x² + 7x + 12 ← in standard form
Plz anwser!!!!!!!!!!!!!
Answer:
23.5
Step-by-step explanation:
x = 4 ; y = 5
x² + y³ = 4² + 5³ = 16 + 125 = 141
2 + x = 2 + 4 = 6
141 ÷ 6 = 23.5
PLEASE DO RATE ME AS BRAINLIEST UWU
Answer:
x² + y³ = 4² + 5³
= 16+ 125
= 141
2 + x =
2 + 4 = 6
your answer is
141 / 6 = 23.5
Step-by-step explanation:
Adrian’s recipe for raisins muffins calls for 1 3/4 cups of raisins for one batch of muffins. Adrian wants to make 2 1/2 batches of muffins for a bake sale. How many cups of raisins will Adrian use?
(HAPPY EID TO ALL!!!)
Adrian will need 4 3/8 cups of raisins to bake 2 1/2 batches.
Convert the mixed fractions into improper fractions:
1 3/4 = 7/4
2 1/2 = 5/2
Multiplying fractions:
1) Multiply numerators
2) Multiply denominators
3) Simplify answer
7/4 * 5/2 = 7*5 / 4*2 = 35/8
35/8 can be simplified into a mixed fraction 4 3/8
Adrian needs to use 4 3/8 cups of raisins.
Answer:
4 3/8
Step-by-step explanation:
Step 1: Convert the numbers into improper fractions. To do this, multiply the denominator value by the whole number and then add the numerator to that product. 1 3/4 becomes 7/4 and 2 1/2 becomes 5/2.
Step 2: Multiply the fractions straight across. Multiply the numerators together and the denominators together. 7 * 5 is 35. 4 * 2 is 8. The improper fraction is 35/8.
Step 3: Convert the improper fraction to a mixed number. Do this by dividing the numerator by the denominator. 35/8 is 4 with a remainder of 3/8. 4 3/8 is the number of cups he will use to make his batches of muffins.
4. How many different bikes
5.how many different meals?
Answer:
4. 30
5. 108
Step-by-step explanation:
4. There are 2 styles, 3 sizes and 5 colors
2 * 3 * 5 = 20
There are 30 different bikes
5. There are 4 appetizers, 9 entrees, and 3 desserts
4*9*3 = 108
We can order 108 different combinations
A rectangle container that has a length of 25cm,a width of 37cm, and a height of 21cm a is filled with water to a depth of 18 cm. When an additional 7 liters of water are poured into the container, some water overflows.How many liters water overflows the container?use words,pictures,and numbers to explain your answer.(Remember:_1cm3=1 mL.)
Answer:
4.225 L
Step-by-step explanation:
The box has a height of 21 cm. After the box is filled to 18 cm, there's 3 cm left of space. The volume of this space is:
V = lwh
V = (25 cm) (37 cm) (3 cm)
V = 2775 cm³
1 cm³ is the same as 1 mL, so the volume of the space is 2775 mL.
1 L is 1000 mL, so this volume is 2.775 L.
7 L of water is then poured in. The box can hold 2.775 L. The rest overflows. The overflow volume is:
7 L - 2.775 L = 4.225 L
Final answer:
The volume of water that overflows from the container after pouring an additional 7 liters is 4,225 mL or 4.225 liters.
Explanation:
The question involves calculating the volume of water that overflows from a rectangular container when additional water is poured in. The existing water depth, dimensions of the container, and the volume of the additional water are given. We know that 1 cm³ of water is equivalent to 1 mL, and there are 1000 mL in 1L.
The initial water volume in the container is the product of the length, width, and depth filled with water. Thus, the initial volume is:
25 cm (length) × 37 cm (width) × 18 cm (depth) = 16,650 cm³ (or mL)
When an additional 7 liters (which is 7,000 mL) of water is added to the container, the total volume of water becomes:
16,650 mL + 7,000 mL = 23,650 mL.The full capacity of the container is calculated by multiplying its length, width, and height:
25 cm × 37 cm × 21 cm = 19,425 cm³ (or mL).By subtracting the full capacity from the total volume after pouring:
23,650 mL - 19,425 mL = 4,225 mL (or 4.225 liters)We find that 4,225 mL (or 4.225 liters) of water overflows.
I WILL MARK BRAINIEST IF CORRECT!
Answer:
I believe I would be the last one D
Answer:
Last choice
Step-by-step explanation:
He spins the spinner and can get Red, White, or Blue.
For each of those three outcomes, the coin can land on Heads or Tails.
The sample space has the following 6 possible outcomes.
Red, Heads
Red, Tails
White, Heads
White, Tails
Blue, Heads
Blue, Tails
The answer is the last choice.
A company did a quality check on all the packs of roasted almonds it manufactured. Each pack of roasted almonds is targeted to weigh 21.25 oz. A pack must weigh within 0.24 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured roasted almonds?
x < 21.01 or x > 21.49 because |x − 0.24| + 21.25 > 0
x < 21.25 or x > 21.49 because |x − 21.25| > 0.24
x < 21.01 or x > 21.49 because |x − 21.25| > 0.24
x < 21.25 or x > 21.49 because |x − 0.24| + 21.25 > 0
Answer:
x < 21.01 or x > 21.49 because |x - 21.25| > 0.24
Step-by-step explanation:
We know that each pack of almonds is targeted to weigh 21.25 oz.and a pack must weigh within 0.24 oz of the target weight to be accepted.
Assuming x to be the weight of a given pack of almonds, we can write it as:
[tex]|x-21.25| > 0.24[/tex]
Now finding the range of rejected masses (x) of the almonds.
[tex]|x-a| >b[/tex]
[tex]-b<(x-a)< b[/tex]
[tex]|x-21.25| >0.24[/tex]
[tex]-0.24>(x-21.25)>0.24[/tex]
[tex]-0.24>x-21.25[/tex] or [tex]x-21.25>0.24[/tex]
[tex]x<21.01[/tex] or [tex]x>21.49[/tex]
Therefore, the correct answer option is x < 21.01 or x > 21.49 because |x - 21.25| > 0.24.
The cover of the book is 28 centimeters long and 18 centimeters wide.what is the perimeter of the book cover
Answer:
the perimeter of the book cover is 504
:)
Step-by-step explanation:
Any and all answers get 5 stars.
Correct answers get a thanks,
Best answer gets brainliest.
Kim wants to know if the number of words on a page in her math book is generally more than the number of words on a page in her poetry book. She takes a random sample of 25 pages in each book, then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.
Book Mean Median Mean absolute deviation
Math 49.9 43 10.2
Poetry 41.5 42 1.1
Kim claims that because the mean number of words on each page in the math book is greater than the mean number of words on each page in the poetry book, the math book has more words per page. Based on the data, is this a valid inference?
A: No, because there is a lot of variability in the math book data
B: No, because the mean is larger in the math book
C: Yes, because the mean is larger in the math book
D: Yes, because there is a lot of variability in the math book data
Answer:
the answer is A I'm 80% sure
If you horizontally stretch the quadratic parent function, f(x)= x^2, by a factor of 4, what is the equation of the new function
Answer:
[tex]f(x) = \frac{1}{16}x^2[/tex]
Step-by-step explanation:
If the graph of the function [tex]y=f(hx)[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]
If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]
In this problem we have the parent function [tex]y=x^2[/tex] And we know that it stretches horizontally by a factor of 4
Therefore
[tex]0 <h <1[/tex] and [tex]h=\frac{1}{4}[/tex]
The transformation is:
[tex]y=f(\frac{1}{4}x)[/tex]
And the function is:
[tex]f(x) = (\frac{1}{4}x)^2[/tex]
Help me please please
It is in the hundredths place
Hundredths
Two places after the decimal is always the hundredths place.
How many terms are in the algebraic expression -7+12x^4-5y^8+x? 1 2 3 4
Answer:
4
Step-by-step explanation:
-7+12x^4-5y^8+x
Terms:
1: -7
2: 12x^4
3: 5y^8
4: x
These are all different terms so there are 4
The diameter of a circle is 8. What is the area of the circle in terms of pi?
Answer:
16pi
Step-by-step explanation:
A=(pi)r^2
A=(pi) 4^2
A=16pi
Line m has a slope of 0. Line n is parallel to line m. What is the slope of line n?
A. O
B. -1
C. Line n has an undefined slope.
D. 1
Answer:
( A )
Step-by-step explanation:
If two lines are parallel, then the slope of both lines SHOULD be the same.
A ladder is 4 meters in length. Jonas places the ladder against a wall and it forms a 70 degree angle with the ground. What is the value of m, the approximate height in meters that the ladder reaches on the wall?
Answer:3.758
Step-by-step explanation:
Sin70= m/4
m= 4*sin70
m = 3.758
Simplify.
9.4c−1.01∙(22b−5.2c)+b
Please help me with this question! I will give title of Brainliest if correct.
Final answer:
To simplify the expression, distribute the -1.01 across the parentheses, combine like terms, and the simplified result is 14.652c - 21.22b. Given values for a, b, and c are not needed.
Explanation:
To simplify the algebraic expression 9.4c - 1.01∙(22b - 5.2c) + b, we first distribute the -1.01 across the parentheses, and then combine like terms.
Step-by-Step Explanation:
Distribute -1.01 to each term inside the parentheses: -1.01 * 22b = -22.22b, and -1.01 * (-5.2c) = 5.252c.
Combine the distributed terms with the original expression: 9.4c - 22.22b + 5.252c + b.
Combine like terms: (9.4c + 5.252c) + (b - 22.22b).
Adding c terms together gives 14.652c, and combining b terms gives -21.22b(because 1b - 22.22b equals -21.22b)
The simplified expression is now 14.652c - 21.22b.
Note: The given values a = 1, b = 0.0211, and c = -0.0211 are not relevant to the simplification process.
Janelle invested $13000 into two mutual funds. Fund A earned 6% profit during the first year, well fund B suffered a 3.5% loss. If she received a total of 324$ profit, how much had she invested in each mutual fund?
Answer:
amount invested in mutual fund B; $4,800
amount invested in mutual fund A; $8,200
Step-by-step explanation:
Let the amount invested in mutual fund B be x. Then the amount invested in fund A would be;
(13000-x)
The loss emanating from fund B would be;
3.5% of x
=(3.5/100)*x
=0.035x
The profit resulting from investment in fund A would be;
6% of (13000-x)
= (6/100)*(13000-x)
=0.06(13000-x)
=780-0.06x
The total profit earned from funds A and B in terms of x will be;
780 - 0.06x + (-0.035x)
=780 - 0.095x
The total profit earned was 324, thus;
780 - 0.095x = 324
solving for x;
780 - 324 = 0.095x
456 = 0.095x
x = 4800
Then the amount invested in fund A would be;
13000 - 4800 = 8200
how many centimeters is a piece of paper that measures 12 in
The answer is:
The piece of paper measures 30.48cm (centimeters)
Why?We need to convert from inches to centimeters, we can do it using the following convertion factor:
[tex]1in=2.54cm[/tex]
Now, calculating we have:
[tex]12in*\frac{2.54}{1in}=30.48cm[/tex]
Hence, we have that the piece of papers measures 30.48cm (centimeters)
Have a nice day!
Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.
10x2 + 80x + 220 = 0
Select the best answer from the choices provided
Answer:
f(x) = 10 [ (x + 4)^2 = -6 ]
Step-by-step explanation:
Please use " ^ " to indicate exponentation. Thanks.
Also, please share the possible answer choices. "Select the best answer from the choices provided."
Start with f(x) = 10x^2 + 80x + 220 = 0
Factor out the 10 to simplify this "completing the square."
f(x) = 10(x^2 + 8x + 22) = 0
Complete the square of x^2 + 8x + 22 only, for now.
Identify the coefficient of the x term. It is 8. Take half of that (it is 4) and square your result: 16
Now add 16 to x^2 + 8x and then subtract 16 from that sum:
x^2 + 8x + 16 - 16 + 22 = 0, or
x^2 + 8x + 16 + 6 = 0
Rewrite x^2 + 8x + 16 as (x + 4)^2
and then the whole expression x^2 + 8x + 16 - 16 + 22 as (x + 4)^2 = -6
Finally, rewrite this as
f(x) = 10 [ (x + 4)^2 = -6 ] which is the desired form of the original equation.
Answer:
The answer is
[tex](x+4)^2=-6[/tex]
Step-by-step explanation:
Follow the steps below.
1) Take common factor 10
[tex]10(x^2 + 8x + 22) = 0[/tex]
2) For an equation of the form [tex]ax ^ 2 + bx + c[/tex]
Calculate [tex](\frac{b}{2})^2[/tex]
In this case the equation is [tex]x^2 + 8x + 22= 0[/tex]
[tex]a=1\\b=8\\c =22\\\\(\frac{b}{2})^2 = (\frac{8}{2})^2 = 16[/tex]
3) Add 16 on both sides of equality
[tex]10(x^2 + 8x + 16) +220= 16*10[/tex]
4) Factor the expression into parentheses and simplify
[tex]10(x+4)^2 +220= 16*10[/tex]
[tex]10(x+4)^2= 16*10-220[/tex]
[tex]10(x+4)^2 =-60[/tex]
[tex](x+4)^2 =-6[/tex]
i need help please ill give 20 points
If this helps you please mark brainliest. As it helps me out.
Output = Input - 2
Input = Output + 2
So
-3 - 2 = -5
And
-1 - 2 = -3
And
0 - 2 = -2
Hope this helps!
I need to find the perimeter.
Answer: 8x - 11
Step-by-step explanation:
(5x-28)+(2x+11)+(x+5)
combine like terms 5x, 2x, x = 8x
combine all regular numbers -28, 11, 5 = -11
So the answer is : 8x-11
Solve for b in the equation –b + 21 = –13.
A. b = 9
B. b = –9
C. b = 34
D. b = –34
Answer:
C. b = 34
Step-by-step explanation:
Given
-b+21= -13
To solve this type of equations that only involve one variable, we have to isolate the variable at on side of the equation. So, for the given equation
We will subtract 21 from both sides
-b+21-21=-13-21
-b= -34
As the minus sign is on both sides of the equation, it will be cancelled and
b=34
So, option C is the correct answer ..
Claudine traded U.S. dollars for Mexican pesos at an exchange rate of 1 U.S. dollar = 12.6577 Mexican pesos. She gave the exchanger a total of 2300 U.S. dollars and was charged a flat fee of 55 U.S. dollars. Approximately how many Mexican pesos does Claudine have?
Answer:
Step-by-step explanation:
You have to start by taking away $55 from the 2300. The 55 does not get exchanged.
2300 - 55 = 2245
1 US dollar = 12.6577 pesos
2245 US dollars = x Cross multiply
x = 12.6577 * 2245
x = 28416.54 pesos. (rounded to 2 places)
Answer:
$28,416.54 Mexican pesos
Step-by-step explanation:
That $2,300 will be divided into two parts: 1) $55 fee and 2) equivalent amount in Mexican pesos:
The amount exchanged into pesos is $2,300 - $55, or $2,245.
Converting this into pesos:
$2,245 12.6577 Mex pesos
------------ * ------------------------------- = $28,416.54 Mexican pesos
1 $1
Write and solve the equation.
The sum of a number and twelve is thirty-five.
Which equation and solution is correct?
Write the equation as x – 12 = 35 and add 12 to both sides. The answer is 47.
Write the equation as x + 12 = 35 and subtract 12 from both sides. The answer is 23.
Write the equation as x + 12 = 35 and subtract 12 from 12. The answer is 35.
Write the equation as x – 12 = 35 and add 12 to 12. The answer is 24.
Answer:
B: x + 12 = 35 and subtract 12 from both sides. The answer is 23.
Step-by-step explanation
Equation of 'The sum of a number and twelve is thirty-five' is x + 12 = 35 and the solution is 23
How to write and solve the equation?Let the number be x
the sum of the numbers x and 12 means x + 12
The sum of a number x and 12 is 35 means x + 12 = 35
solution of x +12 = 35x + 12 = 35
subtract 12 from both sides
x + 12 - 12 = 35 - 12
x = 23
Therefore, the correct option is 'Write the equation as x + 12 = 35 and subtract 12 from both sides. The answer is 23.'
To learn more about solving equations, refer:
https://brainly.com/question/8806877
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For a class picnic two teachers went to the same store to the purchase drinks. one teacher purchased 18 juice boxes and 32 bottles of water and spent $19.92. the other teacher purchased 14 juice boxes and 26 bottles of water and spent $15.76 write a system of equations to represent the costs of a juice box j and a bottle of water w.
18j + 32w = $19.92
14j + 26w = $15.76
HAVE A GREAT DAY MA DUDE!
The system of equations that represent the costs of a juice box j and a bottle of water w are :
18j + 32w = 19.92 ....(1)
14j + 26w = 15.76 ....(2)
As per the given information, Consider that the cost of a juice box be represented by j and the cost of a bottle of water be represented by w.
The teacher who purchased 18 juice boxes and 32 bottles of water spent $19.92, we can write the equation as follows:
18j + 32w = 19.92
Similarly, the other teacher who purchased 14 juice boxes and 26 bottles of water spent $15.76, we can write the equation as :
14j + 26w = 15.76
Hence, the system of equations is:
18j + 32w = 19.92 ....(1)
14j + 26w = 15.76 ....(2)
Learn more about equations here;
https://brainly.com/question/25180086
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