Answer:
−2k=k−7−8
−2k=k+−7+−8
−2k=(k)+(−7+−8)(Combine Like Terms)
−2k=k+−15
−2k=k−15
Step 2: Subtract k from both sides.
−2k−k=k−15−k
−3k=−15
Step 3: Divide both sides by -3.
−3k
−3
=
−15
−3
k=5
Step-by-step explanation:
Which function is a shrink of the exponential growth function shown on the graph?
a. f(x) = 2(3)x
b. f(x) = One-half(3)x
c. f(x) = 2(one-third) Superscript x
d. f(x) = One-half (one-third) Superscript x
Answer:
Option B
Step-by-step explanation:
The function in the graph is an exponential growth function.
Therefore its equation is [tex]g(x)=3^x[/tex]
A transformation that shrinks this graph is of the form: [tex]f(x)=k*3^x[/tex] where [tex]0\:<\:k\:<\:1[/tex]
From the given options, we must have [tex]k=\frac{1}{2}[/tex]
This implies that:
[tex]f(x)=\frac{1}{2} (3)^x[/tex]
Answer:
B
Step-by-step explanation:
Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of blank
The blank is -8
Step-by-step explanation:
Let us revise some rules of indices:
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex] [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] [tex]a^{m}[/tex] = [tex]a^{n}[/tex] , them m = n∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{5}[/tex] × [tex]4^{x}[/tex]
∵ All bases are equal
∴ Use the first and third rule above to find x
∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{3+-6}[/tex]
∴ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{-3}[/tex] ⇒ L.H.S
∵ [tex]4^{5}[/tex] × [tex]4^{x}[/tex] = [tex]4^{5+x}[/tex] ⇒ R.H.S
Equate L.H.S and R.H.S
∴ [tex]4^{-3}[/tex] = [tex]4^{5+x}[/tex]
Equate the indices of the two sides
∴ -3 = 5 + x
- Subtract 5 from both sides
∴ -8 = x
∵ x represents the blank
∴ The blank = -8
The blank is -8
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Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of negative eight.
To solve for the missing exponent, we can use the following properties of exponents:
Multiplying exponents with the same base: When multiplying powers with the same base, we add their exponents.
Negative exponents: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
Applying these properties:
4^3 * 4^-6 = 4^(3 - 6) = 4^-3 (since 4^-6 = 1/4^6)
4^5 * 4^x = 4^(5 + x)
Setting these equal to find x:
4^-3 = 4^(5 + x)
Therefore, x = -3 - 5 = -8.
X Y
3 −2
6 −4
9 −6
12 −8
Determine whether the table represents a proportional relationship. If a proportional relationship exists, what is the constant ratio of y/x
A) yes; − [tex]\frac{2}{3}[/tex]
B) yes; − [tex]\frac{5}{3}[/tex]
C) yes; − [tex]\frac{2}{5}[/tex]
D) The table does not represent a proportional relationship.
Step-by-step explanation:
The given table:
X Y
3 − 2
6 − 4
9 − 6
12 − 8
To find, the constant ratio, [tex]\dfrac{y}{x}[/tex] = ?
The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-2}{3}[/tex],
The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-4}{6}[/tex] = [tex]\dfrac{-2}{3}[/tex],
The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-6}{9}[/tex] = [tex]\dfrac{-2}{3}[/tex] and
The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-6}{9}[/tex] = [tex]\dfrac{-2}{3}[/tex]
Thus, the required option A) yes; [tex]\dfrac{-2}{3}[/tex] is correct.
BRIA is a rectangle. AN=5. NR=x-3. please solve for x, NR, and BI
Answer:
x=8
NR=5 units
BI=10 units
Step-by-step explanation:
In a rectangle BRIA
AN=5 units
NR=x-3
We have to solve for x , NR and BI.
We know that
Diagonals of rectangle bisect to each other.
BI and AR are the diagonals of rectangle BRIA and intersect at point N.
AN=NR
[tex]5=x-3[/tex]
[tex]x=5+3=8[/tex]
[tex]x=8[/tex]
Substitute the value of x
NR=8-3=5
By property of rectangle
BI=AR=AN+NR=5+5=10 unit
BI=10 units
Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood. What is the total number of fliers they gave out
The volunteers gave 1368 fliers in total.
Step-by-step explanation:
Given,
Fliers given by volunteers in first neighborhood = [tex]\frac{21}{38}[/tex]
Remaining fliers = 612
Fraction of remaining fliers = [tex]1-\frac{21}{38}=\frac{38-21}{38}[/tex]
Fraction of remaining fliers = [tex]\frac{17}{38}[/tex]
Let,
x be the total fliers given by volunteers.
[tex]\frac{17}{38}\ of\ x=612[/tex]
[tex]\frac{17}{38}x=612[/tex]
Multiplying both sides by [tex]\frac{38}{17}[/tex]
[tex]\frac{38}{17}*\frac{17}{38}x=612*\frac{38}{17}\\\\x=\frac{23256}{17}\\\\x=1368[/tex]
The volunteers gave 1368 fliers in total.
Keywords: fraction, division
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Will make brainliest if answer correctly
Answer:
D
Step-by-step explanation:
When Y is a function of X, the graph is a v shape.
There are 52 weeks in a year. Ben has lived in london for two fifths of year. How many weeks has ben lived in london?
Answer:
[tex]\frac{104}{5}[/tex] weeks or [tex]20\frac{4}{5}[/tex] weeks
Step-by-step explanation:
To do this we can set up a proportion
[tex]\frac{52}{1} *\frac{2}{5}[/tex]
This will tell us how many weeks are in 2/5 of a year
Let's evaluate this
[tex]\frac{104}{5}[/tex]
We cannot simplifiy this anymore, so we will leave it as an improper fraction, or a mixed number as shown below
[tex]20\frac{4}{5}[/tex] weeks
[tex]\text{We're trying to find how many weeks Ben has lived in London}\\\\\text{We know that there are 52 weeks in a year}\\\\\text{We also know that he's been in London for 2/5 of a year, or 40\%}\\\\\text{To find your answer, you could multiply 52 by 0.40}\\\\52*0.40= 20.8\\\\\boxed{\text{Ben has been in London for 20.8 weeks}}[/tex]
256 to the nearest 100
Answer:
300.
Step-by-step explanation:
256 is closer to 300 than it is to 200 so it rounds to 300.
Answer:300
Step-by-step explanation:
Simplify this please
let's firstly convert the mixed fractions to improper fractions and then multiply.
[tex]\bf \stackrel{mixed}{5\frac{3}{7}}\implies \cfrac{5\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{38}{7}}~\hfill \stackrel{mixed}{2\frac{2}{7}}\implies \cfrac{2\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{16}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{38}{7}\cdot \cfrac{16}{7}\implies \cfrac{(38)(16)}{(7)(7)}\implies \cfrac{604}{49}\implies 12\frac{20}{49}[/tex]
A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?
Answer:
$8.60
Step-by-step explanation:
Answer:
$8.60
Step-by-step explanation:
The area of a circle is 28.26 square kilometers. What is the circles diameter
Answer:
6km
Step-by-step explanation:
Area of circle = πr²
Where r = radius, π= 3.14, A = 28.26km²
A = 3.14 x r²
3.14 r2 = 28.26
Divide both sides by 3.14
r²= 28.26/3.14
r² = 9
Square root both sides
r= √9
r= 3
Radius = 3km
Note : Diameter = 2 x radius
Diameter = 3 x 2
Diameter = 6km
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Find the number of shaded triangles for each
figure.
First triangle:
Second triangle
Third triangle
Fourth triangle:
Answer:
1st triangle = 1
2nd triange= 3
3rd triangle = 9
4th triangle = 27
A triangle exists a three-sided polygon with three vertices and three edges. The number of triangles in the given figure exists 1, 3, 9, and 27.
What is a triangle?A triangle exists a three-sided polygon with three vertices and three edges. It exists one of the major fundamental geometric forms.
The number of shaded triangles in each of the triangles exists shown below, thus, the number of triangles in each triangle can are:
1st triangle = 1
2nd triangle = 3
3rd triangle = 9
4th triangle = 27
Therefore, the number of triangles in the given figure exists 1, 3, 9, and 27.
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I do not deed the answers for 11, or 12 just 13
13.
A
B
C
D
E
F
G
a) ASA congruency
b)SAS congruency
c)SSS congruency
d) Not congruent
Step-by-step explanation:
Step 1:
a)
Angle PRQ = Angle RQS
Angle PRQ = Angle QRS (since PQ is parallel to RS , these form corresponding angles and hence are equal.
QR is the common Side
Hence 2 angles are same and the side which is included are same.Hence the 2 given triangles are congruent.
Step 2 :
b)
Angle IGH = Angle EDF
Side IG = DF and Side GH = DE
Here 2 of the sides of the triangle are same and the Angle which is included are same.
Hence the given triangles are equal
Step 3:
c)
In the given triangles the three sides re equal. Hence as per the side Side Side postulate the triangles are equal.
Step 4:
d) 2 angles are equal but the equal Side is not included and hence the two triangles are not congruent
Is 3/9 a function of y Equals 6X
Answer:
yes
Step-by-step explanation:
well plug it in: y=6x -> y=6(3/9) and solve, yes if theres a slope of 1
wich function represents exponential growth with a growth with a 5% rate of change?
a- f(x) = 4(5)n
b- f(x) = 4(1.05)n
c- f(x)= 4(0.95)n
d- f(x)= 4(0.05)n
Answer:the answer is B
Step-by-step explanation:
The function that represents the exponential growth is
f(x) = 4 x [tex]1.05^n[/tex].
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
An exponential growth function.
Rate of change = 5%
This means,
There is a growth per year of 5%.
The function can be represented as,
f(x) = a [tex](1 +0.05)^n[/tex]
f(x) = a x [tex]1.05^n[/tex]
Where 100% = 1 and 5% = 0.05
Let a = 4
f(x) = 4 x [tex]1.05^n[/tex]
Thus,
The exponential growth function is
f(x) = 4 x [tex]1.05^n[/tex]
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HELP ME I ONLY HAVE 38 MINUTES LEFT I NEED TO GET THIS QUESTION DONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A NUMBER OF Y Increased Increased BY 4 AND ITS AT LEAST IS 25
Answer:
y + 4 ≥ 25
if y is increased by 4 and is at least 25
In September there were 16 members in the music club. In October the member of members was 24. What was the percent increase?
Answer:
9%
Step-by-step explanation:
It is simple because you just count to get to 24 and that is the percentage.
I need help please and thank you
Answer:
∠A = 45°
Step-by-step explanation:
The sum of angles in a triangle = 180°.
That means in the triangle ABC, ∠A + ∠B + ∠C = 180°.
Given ∠B = 90° and ∠C = 45°.
⇒ ∠A + 90° + 45° = 180°
⇒ ∠A = 180 - 90 - 45
⇒ ∠A = 45° is the required answer.
melinda used 8 cups of sugar when baking cookies for valentines day. Each bath of cookies used 2/9 cup of sugar. Approximately how many batches of cookies did melinda make for valentines day?
Answer:
36 batches
Step-by-step explanation:
we know that
Each bath of cookies used 2/9 cup of sugar
so
using proportion
Find out how many batches of cookies Melinda makes for 8 cups of sugar
[tex]\frac{1}{(2/9)}\ \frac{bath}{cups}=\frac{x}{8}\ \frac{bath}{cups}\\\\x=8/(2/9)\\\\x=36\ batches[/tex]
The population of a town with an initial population
of 75,000 grows at a rate of 3.7% per year. What
will the population be in 5 years? In 10 years?
Answer:
5 years = 89,940
10 years = 107, 856
Step-by-step explanation:
75000 * 1.037 ^ 5 for the 5 years one
Then do the answer (89940) and times by 1.037 ^ 5. For 10 years
You do it to the power of 5 because you are adding on another 5 years
9. Four increased by half of a
number is equal to six.
How do u write it??
Answer:
4+ x/2 =6
Step-by-step explanation:
Let the number be X
half of the number is 1/2 multiply X= X/2
Four increased by half the number is 4+X/2
Therefore, Four increased by half of anumber is equal to six is written as
4+ x/2 =6
If the equipment is 30% off and the sale price is $315 what percent of the original price are you paying?
Answer:
Step-by-step explanation:
94 dollars
Answer:
The discount would be $94.50 but the final price would be $220.25.
Hope this helps!
What would be the area?
Total area is 102.3 yd²
Step-by-step explanation:
Step 1:Total area = area of the parallelogram + area of the right triangle
Step 2:Calculate the area of the parallelogram.
Base = 11 yd, Height = 6.2 yd
⇒ Area of the parallelogram = Base × Height = 11 × 6.2 = 68.2 yd²
Step 3:Calculate the area of the right triangle.
Height = 6.2 yd, Base = 11 yd (Since opposite sides of a parallelogram are equal)
⇒ Area of the triangle = 1/2 × base × height = 1/2 × 11 × 6.2 = 34.1 yd²
Step 4:Calculate the total area.
⇒ Total area = 68.2 + 34.1 = 102.3 yd²
Wayne's savings to Stef's savings were in the ratio 5:6
After spending $28 each the ratio became 1:4
I need to find wayne's savings BEFORE he spent 28 and Stef's savings AFTER she spent 28
HELP PLEASE TY
Answer:
a) $30
b) $8
Step-by-step explanation:
Wayne's savings to Stef's savings were in the ratio 5:6.
Let, Wayne's saving is 5x and Stef's saving is 6x.
Now, given that after spending $28 each the ratio became 1:4.
So, we can write the equation as
[tex]\frac{5x - 28}{6x - 28} = \frac{1}{4}[/tex]
⇒ 20x - 112 = 6x - 28
⇒ 14x = 84
⇒ x = 6
a) Therefore, Wayne's savings before he spends $28 is $(5 × 6) = $30
b) And, Stef's savings after she spends $28 will be $(6x - 28) = $(6 × 6 - 28) = $8 (Answer)
Will earns $98 a week bagging groceries. He saves 80% of what he makes per week and spends the rest on lunches. How much does Will spend each week on lunches
Answer:
$19.60
Step-by-step explanation:
$98 is made each week.
80% is saved, and the rest is spend on lunch, so 20% is spent on lunch.
20%=.20
98•.20=19.6
$19.60 is spend on lunches each week.
Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood. What is the total number of fliers they gave out
Answer:
The total number of fliers they gave out is 1368.
Step-by-step explanation:
Given:
Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood.
Now, to find the total number of fliers they gave out.
Let the total number of fliers be [tex]x.[/tex]
Number of fliers they gave out for a political campaign:
[tex]\frac{21}{38}\ of\ x[/tex]
[tex]=\frac{21}{38} \times x[/tex]
[tex]=\frac{21x}{38}[/tex]
Number of fliers remaining they gave out in another neighborhood = 612.
Now, to get the total number of fliers by putting an equation:
[tex]x-\frac{21x}{38} =612[/tex]
[tex]\frac{38x-21x}{38} =612[/tex]
[tex]\frac{17x}{38} =612[/tex]
Multiplying both sides by 38 we get:
[tex]17x=23256[/tex]
Dividing both sides by 17 we get:
[tex]x=1368.[/tex]
Therefore, the total number of fliers they gave out is 1368.
State the quadratic formula
Answer:
Step-by-step explanation:
Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the chair free including the bottom
Answer:
Akira needs 45 square inches of gold foil to cover the chair free including the bottom
Step-by-step explanation:
Total surface = surface area of the base square + area of 4 triangles
Step 1: The surface area of the base square
surface area of the base = surface area of the square = [tex]s^2[/tex]
where s is the side length
The the surface area of the base = [tex]3^2[/tex] = 9 square inches
Step 2: The surface area of the side triangles
The area of the triangle = [tex]\frac{1}{2}\times \text{side length} \times \text{slant height}[/tex]
On substituting the values,
The area of the triangle =[tex]\frac{1}{2} \times 3 \times 6[/tex]
The area of the triangle = [tex]\frac{18}{2}[/tex]
The area of the triangle = 9 square inches
Now the area of 4 triangles = 4 x 9 = 36 square inches
Thus the total surface area = 9 + 36 = 45 square inches
The amount of gold foil needed to cover a trophy in the shape of a square pyramid can be calculated using the surface area formula for square pyramids, which considers the base area and the slant height.
Explanation:To calculate the amount of gold foil needed to cover the trophy, we need to find the surface area of the square pyramid trophy. The surface area of a square pyramid is calculated by the formula: Surface Area = base area + 1/2 * Perimeter of base * slant height. If we know the length of the base (which is a square here), the slant height, we can substitute them into this formula to get the surface area. This is the amount of gold foil Akira used to cover her trophy, assuming the gold foil perfectly fits the trophy shape with no overlap.
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Help me plz on this attachment. Ill give Brainly Award comments thanks and high ratings! 2 questions.
Answer:
C. and A.
Step-by-step explanation:
4. 5(x + 3) - 2x
5x + 15 - 2x
3x + 15
5. -6x + 2.5(x - 1) - 5x
-6x + 2.5x - 2.5 - 5x
-8.5x - 2.5
y = 5x + 15
y = -5x - 15
Answer:
5x + 15 = -5x - 15
10x = -30
x = -3
y = 5(-3) + 15 = -15 + 15 = 0
(-3,0)
Step-by-step explanation: