The value of the exponential equation is y = 5ˣ + 4
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
The y intercept is ( 0 , 5 )
So , when x = 0 , the value of y = 5
Substituting the values in the equation , we get
y = 5ˣ + 4 be equation (1)
when x = 0
y = 5⁰ + 4
y = 1 + 4
y = 5
when x = 2
y = 5² + 4
y = 25 + 4 = 29
Therefore , the range is all y values greater than 0
Hence , the equation is y = 5ˣ + 4
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5. A rectangle with length 8 cm and width 5 cm is dilated by a scale factor of 3. What are the perimeter and area of the image?
Answer:
The area is 120
The perimeter is 78
Step-by-step explanation:
To find area you have to multiply length x width.
(8x5)
To find perimeter you have to find the length of all the sides and add them
together. To find perimeter of a shape you do length x2 + width x2
(8x2 + 5x2)
Then you need to find the scale factor.
A scale factor of 3 is 3x the size of the original shape
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There were 220 people who voted at the 6th grade meeting. Sixty percent of the voters are in favor of changing the school mascot. How many people are against changing the mascot? Use numbers and words to explain your answer.
Step-by-step explanation:
First I had to find 60% of 220.
220 × .60 = 132.
132 people are in favor so I have to subtract that number from 220 to find how many people were against.
220-132 = 88
88 people were against changing the mascot.
Given Angle 1 = Angle 2, find X.
X =
Answer:x=6
Step-by-step explanation:
Identify the correct explanation for why the triangles are similar. Then find OP and MN.
Options:
A. ∠M≅∠N. Since OP¯¯¯¯¯∥MN¯¯¯¯¯¯¯, ∠LOP≅∠LMN by the Alt. Int. ∠s Thm. Therefore, △LOP∼△LMNby AA∼. OP=8 and MN=4.
B. ∠L≅∠L by the Reflex Prop. of ≅. Since OP¯¯¯¯¯∥MN¯¯¯¯¯¯¯, ∠LOP≅∠LMN by the Corr. ∠s Post. Therefore, △LOP∼△LMNby AA∼. OP=2 and MN=6.
C. ∠L≅∠L by the Reflex Prop. of ≅. Since OP¯¯¯¯¯∥MN¯¯¯¯¯¯¯, ∠LOP≅∠LMN by the Corr. ∠s Post. Therefore, △LOP∼△LMNby AA∼. OP=4 and MN=8.
D. ∠M≅∠N. Since OP¯¯¯¯¯∥MN¯¯¯¯¯¯¯, ∠LOP≅∠LMN by the Alt. Int. ∠s Thm. Therefore, △LOP∼△LMNby AA∼. OP=2 and MN=6.
Answer:
The correct explanation is option B;
B. ∠L ≅ ∠L By Reflexive Prop. ≅.
Since [tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex], ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6
Step-by-step explanation:
The given parameters are;
[tex]\overline {LP}[/tex] = 5
[tex]\overline {NP}[/tex] = 10
[tex]\overline {LN}[/tex] = [tex]\overline {LP}[/tex] + [tex]\overline {NP}[/tex] = 15
[tex]\overline {OP}[/tex] = x - 3
[tex]\overline {MN}[/tex] = x + 1
A two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
∠L ≅ ∠L [tex]{}[/tex] By Reflexive property of congruency
[tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex] [tex]{}[/tex] Given
∠LOP ≅ ∠LMN [tex]{}[/tex] By the Corresponding angles Postulate
Therefore
ΔLOP ~ ΔLMN [tex]{}[/tex] By AA similarity Postulate
Where we have that ΔLOP and ΔLMN, we get;
[tex]\overline {OP}[/tex]/[tex]\overline {MN}[/tex] = [tex]\overline {LP}[/tex]/[tex]\overline {LN}[/tex] = 5/15 = 1/3
∴ (x - 3)/(x + 1) = 1/3
3·(x - 3) = 1·(x + 1)
3·x - 9 = x + 1
3·x - x = 1 + 9 = 10
2·x = 10
x = 10/2 = 5
x = 5
[tex]\overline {OP}[/tex] = (x - 3) = 5 - 3 = 2
[tex]\overline {OP}[/tex] = 2
[tex]\overline {MN}[/tex] = x + 1 = 5 + 1 = 6
[tex]\overline {MN}[/tex] = 6
Therefore, the correct option is ∠L ≅ ∠L By Reflexive Prop. ≅.
Since [tex]\overline {OP}[/tex] ║ [tex]\overline {MN}[/tex], ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6.
what is the answer please help me
7n +2 –(2n +7) pls help I will give you 15 points
Answer:
5n -5
Step-by-step explanation:
7n +2 –(2n +7)
7n +2 -2n -7
5n -5
write 3^n/9^(n-1) as a power of 3
Answer:
[tex]\frac{3^{n} }{3^{2(n-1)} }[/tex]
Step-by-step explanation:
3²⁻ⁿ is the simplification of 3ⁿ/9ⁿ⁻¹ in powers of 3.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 3ⁿ/9ⁿ⁻¹
three power n divided by nine power n minus one.
To express to the power of 2, we have few properties of exponentials.
aˣ/aⁿ=aˣ⁻ⁿ
aˣ.aⁿ=aˣ⁺ⁿ
The given expression is
3ⁿ/9ⁿ⁻¹
3ⁿ/(3²)ⁿ⁻¹
3ⁿ/3²ⁿ⁻²
3ⁿ.3⁻²ⁿ⁺²
When bases are same then we will add the powers
3ⁿ⁻²ⁿ⁺²
3²⁻ⁿ
Hence 3²⁻ⁿ is the simplification of 3ⁿ/9ⁿ⁻¹ in powers of 3.
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4n+1=25
Please help with an explanation
Answer:
n = 6
Step-by-step explanation:
To isolate n, subtract 1 from both sides:
4n + 1 = 25
4n = 24
Then divide by 4 on both sides:
4n = 24
n = 6
Hope this helped :)
Answer:
6
Step-by-step explanation:
4n+1= 25
or,4n= 25- 1
or,4n=24
or,n=24/4
so n= 6
Can somebody help me please
Answer:
I believe it’s 65
Step-by-step explanation:
Not fully sure
Find h is f(h) = 215
please help thank you!!
Answer:
h = 215/f
Step-by-step explanation:
use elimination to solve and please show ur work.
4x + 3y = 6
2x - y = -2
Answer:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Point Form:
(0,2)
Equation Form:x=0, y=2
Answer:
(0,2)
Step-by-step explanation:
Multiply each equation by the value that makes the coefficients of y opposite.
3*2x-y=3*-2
Simplify
6x-3y=-6
Add the two equations
10x = 0
Divide both by 10 and simplify
x=0
Substitute x into the equations.
4*0+3y=6
3y=6
2
y=2
For his long distance phone service, Miguel pays a $3 monthly fee plus 11 cents per minute. Last month, Miguel's long distance bill was $14.22 . For how many minutes was Miguel billed?
Answer: B=3+.11m
18.73=3+.11m
-3 -3
15.73=.11m
143=m
Step-by-step explanation:
Please guys help me. I will give you the brainliest. Answer what you know
Answer:
number 3 is B and number 4 is C
Step-by-step explanation:
7n-1
the 5th term of the sequence 4n+1
look yall i got 10 math questions if you get all ten right brainlliest so if yall could help a man out here it would be great
here they are
1.)Which of the following best describes the squaring property of equality?
A.
if a=b,then [tex]a^{2} =b^{2}[/tex]
B
if [tex]a\leq b then a^{2} \leq b^{2}[/tex]
C
[tex]if a\geq b then a^{2} \geq b^{2}[/tex]
D
[tex]if a \neq b then a^{2} \neq b^{2}[/tex]
2.)Solve for x.
[tex]\sqrt{x-2} =9[/tex]
A.
11
B.
20
C.
83
D
no solution
3.)The length of a side of a square is [tex]\sqrt{x^{2}-4 }[/tex] If the area of the square is 12, find x.
A.
16
B.
4
C.
12
D.
[tex]\sqrt{148}[/tex]
4).Solve for x.
[tex]5x^{2} +3=-122[/tex]
A.
no solution
B.
–5
C.
±5
D.
±25
5.)solve for x[tex]x^{2} +5=30[/tex]
A.
±25
B.
[tex]\sqrt{35}[/tex]
C.
±5
D.
no real solutions
6.)The acceleration of an object can be described by the equation[tex]a=\frac{2d}{t²} where a is acceleration, d is the distance, and t is time. Suppose an object accelerates for a distance of 15 meters. Which of the following equations relates the time to the acceleration?
A.
[tex]t=\sqrt{\frac{a}{30} }[/tex]
B.
[tex]t=\sqrt{\frac{a}{15} }[/tex]
C.
[tex]t=\sqrt{\frac{30}{a} }[/tex]
D.
[tex]t=2\sqrt{\frac{30}{a} }[/tex]
7.)The acceleration of an object can be described by the equation [tex]a=\sqrt{\frac{2d}{t²} }[/tex] , where a is acceleration, d is the distance, and t is time. Suppose an object accelerates at a rate of 5 meters per second squared. Which of the following equations relates the time of the acceleration to the distance?
A.
[tex]t=\sqrt{10d}[/tex]
B.
[tex]t=\sqrt{2d}[/tex]
C.
[tex]t=\sqrt{\frac{5d}{2} }[/tex]
D.
[tex]t=\sqrt{\frac{2d}{5} }[/tex]
8.)Solve for x [tex]\sqrt{2x+8}=2[/tex]
A.
2
B.
–3
C.
–2
D.
no solution
9.)Solve for x:[tex]\sqrt{3x-2}=2[/tex]
A.
2
B.
[tex]-\frac{2}{3}[/tex]
C.
–2
D.
no solution
10.)What is the first step to solve the equation [tex]x^{2} -3=15[/tex]
A.
Take the square root of [tex]x^{2}[/tex], 3, and 15.
B.
Square 15.
C.
Add 3 to both sides of the equation.
D.
Add 1 to both sides of the equation.
can yall help a brother out im in deep sh|t if i dont pass so if your gunna do it do it right thank yall for helpen me out oh and i already tried to look em up so that dont work
Answer:
number 2. is A I think number 8. is -2 or 2 it might be between those two
Step-by-step explanation:
2.explanation: 11-2=9
sorry but that's all i know i'm only in middle school
Answer:
number 2. is A I think number 8. is -2 or 2 it might be between those two
2.explanation: 11-2=9
Step-by-step explanation:
1. Emily bicycle wheel had a diameter of 18 inches.
If the wheel makes 10 revolutions, approximately how far will the
bicycle have to travel? Round your answer correct to the nearest
whole number.
On her first three geometry test, Sarah scored 89, 93, and 84. If there are four tests total and Sarah needs at least a 90 average for the first four test, what is the lowest score she can receive on the final test?
86
94
92
90
95
Answer:
94
Step-by-step explanation:
If you add them all together, you get 266. You subtract that from 90*4= 360
you get 94
. The total area of a rectangular mural has been extended by x feet. The expression to represent the area is 5.5(7.5 + x). Rewrite the expression using the Distributive Property.
Answer and Step-by-step explanation: Distributive Property describes how to solve expressions like a(b +c). According to the property, multiplying the sum of two or more numbers by a number will result in the same as multiplying each number and then add the products. For example:
11(2 + 4)
11(6) = 66 22 + 44 = 66
So, for the expression that represents the area:
5.5(7.5 + x) = 41.25 + 5.5x
As the expression has non-numerical terms, the distributive property will be multiply each term and then add the products.
The expressio for area of a rectangular mural is 41.25 + 5.5x.
HELP PLEASE FOR BOTH QUESTIONS
Answer:
6) x^2+6x+8
7) x^2+3x-10
Step-by-step explanation:
Find the value of each variable.
Answer:
the third option
Step-by-step explanation:
x= 13
[tex] {y}^{2} = {13}^{2} + {13}^{2} \\ {y}^{2} = 338 \\ y = \sqrt{338} = 18.38 = 13 \sqrt{2} [/tex]
to make pink paint, sylvia mixes 7 cups of white paint to every 3 cups of red paint. which table shows possible values of w, the number of cups of white paint sylvia uses, and r, the number of cups of red paint?
Answer: A
Step-by-step explanation:
For every 3 cups she need 7 cups of white paint.
answer a displays that with 3*2=6 and 7*2=14
Answer:
A
Step-by-step explanation:
I did the math
Please help me!! I will give you brainleist!! Thank you!! ❤✨
Answer:
The second option is correct.
Step-by-step explanation:
First you need to find a common denominator in which is 6
You can find it like this:
1 x 3 = 3
2 x 3 = 6
3/6 is the amount of cake that was left
Now do the same thing for the amount of cake that Elisa ate.
1 x 2 = 3
3 x 2 = 6
So in conclusion the second option represents the amount of cake Elisa eats the best.
I hope this is as helpful as possible.
Answer:
Model:
2/3 (original amount of cake) - 1/3 (what was left) = 1/3 (what Elisa ate)
Math:
2/3 - 1/3 = 1/3
Calculation:
2/3 - 1/3 = (2 - 1) / 3
= 1 / 3
Explanation:
To calculate the fraction of the cake Elisa ate, we need to subtract 1/3 from 2/3. First, we need to find a common denominator for both fractions. In this case, the common denominator is 3. Then, we need to subtract the numerator of the second fraction, which is 1, from the numerator of the first fraction, which is 2. The difference is 1, which is the numerator of the fraction that represents the amount of cake Elisa ate. The denominator is 3, so the fraction that represents the amount of cake Elisa ate is 1/3.
Nicholas uses a coordinate system with units of feet to keep track of any items he finds with his metal detector. One day he found a ring at (-2, -6) and a coin at (7, 6). How far apart were the ring and the coin?
Answer: The distance between the ring and the coin = 15 units.
Step-by-step explanation:
Distance between two points (a,b) and (c,d) is given by :-
[tex]D=\sqrt{(c-a)^2+(d-b)^2}[/tex]
Location of rine = (-2,-6)
Location of the coin = (7,6)
Then, the distance between the ring and the coin [tex]=\sqrt{(6-(-6))^2+(7-(-2))^2}[/tex]
[tex]=\sqrt{(12)^2+(9)^2}\\\\=\sqrt{144+81}\\\\=\sqrt{225}=15[/tex]
Hence, the distance between the ring and the coin = 15 units.
In New York, state sales tax rates vary by county. In Allegany County, the sales tax rate is 8 1 2 %. A pair of shoes costs $29.99 and a shirt costs $15.99. Rounded to the nearest cent, how much more is the tax on the shoes than the shirt?
Answer:
$1.19Step-by-step explanation:
The tax is 8 1/2% = 8.5%A pair of shoes = $29.99 A shirt = $15.99The difference in the cost:
$29.99 - $15.99 = $14Tax on the difference:
$14*0.085 = $1.19Which expression represents a factorization of 32m + 56mp?
A 8(4m + 7p)
B 8(4 + 7)mp
C 8p(4 + 7m)
D 8m(4 + 7p)
Answer:
D 8m(4 + 7p)
Step-by-step explanation:
The GCF of 32 and 56 is 8.
m and mp have m in common, so you can factor out 8m.
32m + 56mp = 8m(4 + 7p)
Answer: D 8m(4 + 7p)
Answer: D, 8m(4+7p)
Step-by-step explanation:
8m times 4=32m
8m times 7p=56mp
a = pt + q
p = −1, t = 4 and q = 6
Work out the value of a.
Answer:
2
Step-by-step explanation:
a = (-1 x 4) + 6
a = -4 + 6
a = 2
Lynn is making a snack. The recipes call for 3/8 cup of water for oats and 1/4 cup of water for dried fruit. She only has 1 cup of water. Does she have enough to make her snack? Explain
Answer: She has enough.
Step-by-step explanation:
You need to add up the quantities of water needed first. That will then tell if she has enough water.
Convert the fractions to decimals then add them up:
3/8 = 0.375
1/4 = 0.25
= 0.25 + 0.375
= 0.625 cups of water is required.
This is less than the 1 cup she has so she has enough water to make the snack.
Claire received 3/8 of her allowance on Monday. What decimal shows the part of her allowance that she received?
0.375
0.75
0.83
2.6
Answer:
0.375
Step-by-step explanation:
3/8 = 0.375
Help! Pls I cant solve it help me with explanation also pls.
Given:
The expression is
[tex]\dfrac{2}{a-2}-\dfrac{8}{a^2-4}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\dfrac{2}{a-2}-\dfrac{8}{a^2-4}[/tex]
It can be written as
[tex]=\dfrac{2}{a-2}-\dfrac{8}{a^2-2^2}[/tex]
[tex]=\dfrac{2}{a-2}-\dfrac{8}{(a-2)(a+2)}[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
Taking LCM, we get
[tex]=\dfrac{2(a+2)-8}{(a-2)(a+2)}[/tex]
[tex]=\dfrac{2a+4-8}{(a-2)(a+2)}[/tex]
[tex]=\dfrac{2a-4}{(a-2)(a+2)}[/tex]
[tex]=\dfrac{2(a-2)}{(a-2)(a+2)}[/tex]
Cancel out the common factors.
[tex]=\dfrac{2}{a+2}[/tex]
Therefore, the simplified form of the given expression is [tex]\dfrac{2}{a+2}[/tex].
Creating a password with two letters followed by two one-digit numbers. (Find the total number of outcomes that are possible)
Answer:
67,600 possible outcomes
Step-by-step explanation:
In total, it's a four digit password.
For the first digit, which is a letter, there are 26 possibilities. The same goes for the second digit, so first multiply 26 x 26 (because that's the number of possibilities for the first two digits alone).
! if the letters have to be different then it would be 26 x 25 because there's one less letter for the second digit.
Next, 2 one digit numbers. There are 10 individual digits: 0,1,2,3,4,5,6,7,8,9, so after 26 x 26 x 10 x 10 for the total number of possibilities. If the numbers have to be different (and the letters too) then it'd be 26 x 25 x 10 x 9
so 26 x 26 x 10 x 10 = 67,600
hope this helps!
F(x) = x + 4
A. F(7)=3
B. F(3)=12
C. F(3)=7
Which one is correct and how do you solve it step by step?
Answer:
C. F(3) = 7
Step-by-step explanation:
You have to to substitute the value of the function into each equation.
So...
A. 7+4 does not equal 7
B. 3+4 does not equal 3
C. 3+4 DOES equal 7
Answer:
C
Step-by-step explanation: