Answer:
a. a side length is (a+8)
b. a=9. (9+8)= 17
17×4= 68 is the perimeter
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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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:
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
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]
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.
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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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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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.
Janet can read 3.6 pages of a book in a minute. If she read for 2.71 minutes. How much would have she had read
Final answer:
It would have taken Janet about 9.7536 pages to read..
Explanation:
To determine Janet's reading progress, her reading speed is multiplied by the duration she read. With a reading speed of 3.6 pages per minute, if Janet read for 2.71 minutes, the calculation is 3.6 multiplied by 2.71, resulting in 9.7536. Hence, Janet would have read approximately 9.7536 pages. This calculation showcases how the product of reading speed and time provides a quantitative measure of reading accomplishment. It's a straightforward way to estimate the amount of material covered within a specific timeframe, offering insights into reading efficiency and progress.
2, -10, 50, -250,...
Answer:
Multiply by 5
-250, 1250
Step-by-step explanation:
2 x -5 = -10
-10 x -5 = 50
50 x -5 = -250
-250 x -5 = 1250
what is the quotient when (x+3) is divided into the polnomial 2x^2+x-15
Answer:
2x-5
remainder of 0
Step-by-step explanation:
Check the image
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.
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) = $8 (Answer)
9. Four increased by half of a
number is equal to six.
How do u write it??
Answer:
4+ x/2 =6
Step-by-step explanation:
Let the number be X
half of the number is 1/2 multiply X= X/2
Four increased by half the number is 4+X/2
Therefore, Four increased by half of anumber is equal to six is written as
4+ x/2 =6
BRIA is a rectangle. AN=5. NR=x-3. please solve for x, NR, and BI
Answer:
x=8
NR=5 units
BI=10 units
Step-by-step explanation:
In a rectangle BRIA
AN=5 units
NR=x-3
We have to solve for x , NR and BI.
We know that
Diagonals of rectangle bisect to each other.
BI and AR are the diagonals of rectangle BRIA and intersect at point N.
AN=NR
[tex]5=x-3[/tex]
[tex]x=5+3=8[/tex]
[tex]x=8[/tex]
Substitute the value of x
NR=8-3=5
By property of rectangle
BI=AR=AN+NR=5+5=10 unit
BI=10 units
In September there were 16 members in the music club. In October the member of members was 24. What was the percent increase?
Answer:
9%
Step-by-step explanation:
It is simple because you just count to get to 24 and that is the percentage.
The area of a circle is 28.26 square kilometers. What is the circles diameter
Answer:
6km
Step-by-step explanation:
Area of circle = πr²
Where r = radius, π= 3.14, A = 28.26km²
A = 3.14 x r²
3.14 r2 = 28.26
Divide both sides by 3.14
r²= 28.26/3.14
r² = 9
Square root both sides
r= √9
r= 3
Radius = 3km
Note : Diameter = 2 x radius
Diameter = 3 x 2
Diameter = 6km
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Kristin spent 40$ on pampers. If they cost 8$ / package , how many packages did she buy
Answer:
5 Packages
Step-by-step explanation:
40 / 8 = 5
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]
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:
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
If 80 inches is equivalent to 44 inches, then 28 inches would be equivalent to what?
Answer:
Well no cheating not from me
Step-by-step explanation:
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.
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:
State the quadratic formula
Answer:
Step-by-step explanation:
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.
The distance between Quebec City and New York City is 520 miles if Kate leaves Quebec and will leaves New York at 9:09 a.m. And they tried toward each other at 55 miles per hour and 75 miles per hour respectively at what time will they meet?
Kate and Will meet at 1 : 09 pm
Solution:
The distance between Quebec City and New York City is 520 miles.
At the point where Kate and Will meet, they would have traveled 520 miles.
Let "t" represent the time it takes Kate to travel a certain distance before they met.
[tex]Distance = speed \times time[/tex]
If Kate drives at 55 mph, the distance covered would be
[tex]Distance = 55 \times t = 55t[/tex]
If Will drives at 75 miles per hour, then the distance covered will be
[tex]Distance = 75 \times t = 75t[/tex]
Since the total distance covered is 520 miles
Which means,
[tex]55t + 75t = 520\\\\130t = 520\\\\t = \frac{520}{130}\\\\t = 4[/tex]
Given that in question,
If Kate leaves Quebec and will leaves New York at 9:09 a.m
4 hours after 9: 09 am, Kate and Will will meet
9: 09 am + 4 hours = 1: 09 pm
Thus they would meet at 1 : 09 pm
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
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.
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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