The exponential equation [tex]14=5^x[/tex] is equivalent to the given logarithmic equation.
Which is the Exponential function?The exponential function that is represented as y=[tex]m^x[/tex], where:
m=base, m>0
x= exponent
Logarithm PropertiesKnowing some of the main logarithm rules.
Product Rule with the same base: you should repeat the base add the logarithms of the factors.example: [tex]log(a*b)= log a + log b[/tex]
Quotient Rule: you should subtract the logarithm of the numerator with the logarithm of the denominator.example: [tex]log\frac{a}{b} = log a - log b[/tex]
Power Rule: you should multiply the exponent by the logarithm of the base
example: [tex]log\frac{a^b} = b*log a[/tex]
For solving this question, you should apply the logarithm rules and rewrite the function as an exponential equation.
[tex]log_5(x)}-{log_5(25)=7[/tex]
[tex]\frac{log_5(x)}{log_5(25)} =7[/tex]
[tex]{log_5(x)}=7{log_5(25)}[/tex]
[tex]{log_5(x)}=7{log_5(5^2)}[/tex]
[tex]{log_5(x)}=7*2[/tex]
[tex]{log_5(x)}=14[/tex]
[tex]x=5^{14^}[/tex]
Therefore, the exponential function is [tex]14=5^x[/tex]
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(
5
h
3
−
8
h
)
+
(
−
2
h
3
−
h
2
−
2
h
)
Answer: -3h
Step-by-step explanation:
( 5h + 3 - 8h ) + ( -2h x 3 - h x 3 - 2h )
( 15h - 8h ) + ( -6h - 2h - 2h )
15h - 8h - 6h - 2h - 2h
-3h
The student council at Baker High School is planning a dance. The table shows their budget. What is the student council’s expected profit?
Item. Funds raised. Expenses
Dance tickets. $400
DJ fuze. -250
Decorations. -125
The student council’s expected profit as per given budget is equal to $25.
As given in the question,
Budget decided by the student council at Baker High School while planning a dance.
Total expenses on the items used for the dance
DJ fuze. : $250
Decorations. : $125
Total expenses done by student council for dance
= $( 250 +125)
=$375
Total funds raised by dance performance is equal to
Dance tickets. $400
Total revenue =$400
Revenue >Expenses
Student council’s expected profit= $(400 -375)
= $25
Therefore, the student council’s expected profit as per given budget is equal to $25.
The complete question is:
The student council at Baker High School is planning a dance. The table shows their budget. What is the student council’s expected profit?
Funds raised:
Dance tickets : $400
Expenses:
DJ fuze. : $250
Decoration : $125
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ind the intersection of the three sets: A = {–4, 3, 10}, B = {3, 6, 10, 15}, C = {–4, 10, 20}.
{–4, 10}
{–4, 3, 6, 10, 15, 20}
{10}
{–4, 3, 10}
The intersection of the A, B and C sets is { 10}
find the sum of the measure of the angle of a three sided polygon
The sum of the interior angles of a polygon is given by the formula:
Sum = (n - 2)180
where n is the number of sides of the polygon
Since the polygon is a three-sided polygon, n = 3
Sum = (3 - 2)180
Sum = 1 x 180
Sum = 180
How much simple interest does $2,560 earn in 17 months at a rate of 1*1/8 Round to the nearest cent.
The simple interest of the $2,560 earned in 17 months at a rate of 1*1/8 will be; $185.90
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of the principal amount, rate, and period.
The formula for simple interest is:
Simple Interest = (Principal × Rate × Time) / 100
Where I am interested
P ⇒ amount deposited.
R ⇒ interest rate
T ⇒ period for investing
Given that the time is 17 months = 17/12 years
1 and 1/8 = 1.125
I = 2,560 ×17/12 × 1.125/100
= 2560 × 17/12 × 0.01125
= $185.86667
The simple interest of the $2,560 earned in 17 months at a rate of 1*1/8 will be; $185.90
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give an example of a rational function that has a horizontal asymptote at y=3
An example of a rational function is y = (3x²+7x+4)/(x²+3x+2) which has a horizontal asymptote at y = 3.
To give it a horizontal asymptote of y = 3, we require the degrees in the numerator and denominator to be and the lead coefficient ratio to be 1.
Yet, in producing the hole, we need to have the rest of the function, disregarding the (x + 1)'s, = 1 when x = -1 to ensure the y-value of the hole is at + 1. When we add all of this together, we get.
y = (3(x+1)(x+k))/((x+1)(x+2)) and the last condition requires k = + 4/3, so
By distributing the 3 in the numerator to the 2nd linear component, we get.
y = (3(x+1)(x+4/3))/((x+1)(x+2))
y = ((x+1)(3x+4))/((x+1)(x+2))
y = (3x²+7x+4)/(x²+3x+2)
Thus, the example of a rational function is y = (3x²+7x+4)/(x²+3x+2) which has a horizontal asymptote at y = 3.
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- Nathaniel Barnes obtained a single-
payment loan of $1,200 to purchase a
computer. He agreed to repay the loan in
120 days at an ordinary interest rate of 7%.
What is the maturity value of his loan?
Answer: 1.25
Step-by-step explanation: Divide 1,200 in 7 days and the aswer is 1.25
flagpole of height 5 meters is tied to the ground by a 7 meter cable. How far from the base of the flagpole is the cable tied
We know that
• The height is 5 meters.
,• The cable is 7 meters long.
Using the given information, we can represent the situation with a diagram.
In the diagram above you can observe that the x is a leg of the right triangle. So, we have to use Pythagorean's Theorem to find x.
[tex]7^2=5^2+x^2[/tex]Then, we solve for x.
[tex]\begin{gathered} 49=25+x^2 \\ x^2=49-25 \\ x^2=24 \\ x=\sqrt[]{24} \\ x\approx4.9 \end{gathered}[/tex]Hence, the base of the flagpole is 4.9 meters from the cable, approximately.1. Few months ago, Frank purchase stock for
$6, 150. Last week he sold the stock for. $8,250.
what was his gross capital gain?
Frank's gross capital gain was $2,100.
What is gross capital gain?
the discrepancy between the overall cost base of your asset and your capital gains. Your share of the capital gain - If more than one person owns this asset, your share of the gain is equal to the percentage of the asset that you personally hold.
You want the gross capital gain resulting from selling a stock purchased for $6,150 and sold for $8,250.
Capital Gain
The capital gain resulting from the sale is the difference between the selling price and the purchase price:
gain = selling price - purchase price
gain = $8,250 -6,150
gain = $2,100
Frank's gross capital gain was $2,100.
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Determine the range of the following graph: Please help!!!!! I need an answer asap
The range of the function shown on the graph above is: -10 ≤ y ≤ 3.
What is a range?A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values (real numbers), which are shown on the y-axis of a graph.
How to identify the range of this graph?The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown, the range of this graph in interval notation can be rewritten as follows:
Range = [-10, 3]
Range = -10 ≤ y ≤ 3.
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Complete the equation
-67-?=0
Is it 67
yes or no and why?
no it is not 67 becuase if you subtract -67-67 it will equal -134
it is -67 bc -67- -67=0
Ollie borrowed $5000 for 3 years at a compound interest rate of 10%.
How much did Ollie pay back?
Answer: Assuming interest rate is yearly, Ollie would have to pay back 6, 655 dollars :)
Step-by-step explanation:
The formula for compound interest is
Y = P(1 + r/m)^mt, with P being the initial deposit (5000), r being the interest rate (0.10), m being the amount of times it is compounded per year (1), and t being the number of years (3).
(30 points) need answer asap
Answer:
x=38
Step-by-step explanation:
The are supplementary. This is because the 2 lines are parallel and the corresponding angle to 2x-15 is supplementary. And because corresponding angles are congruent 2x-15 and 3x+5 are supplementary.
2x-15+3x+5=180
5x-10=180
5x=190
x=38
Graphing proportional relationships
Answer:
hello fríend nose inglus
Solve the system of linear equations using the substitution method.
5x - 2y = 3 and y = 2x
A. (3, 6)
B. (1, 4)
C. (1, 6)
D. (1, 9)
Answer:
the answer is A. (3,6)
Step-by-step explanation:
5x - 2y = 3
5x - 2(2x) = 3
5x - 4x = 3
x = 3
y = 2x
y = 2(3)
y = 6
Two ways to write k/3+16
The two ways to write the expression k/3+16 are 1/3k + 16 and (k + 48)/3
How to rewrite the expression?From the question, the expression is given as
k/3+16
Start by factoring 1/3 out of the first term
So, we have the following expression
1/3k + 16
The above is one of the ways of rewriting the expression
Another way is by taking the LCM
So,we have
k/3+16 = (k + 48)/3
Hence, the equivalent expressions are 1/3k + 16 and (k + 48)/3
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Which is a formula that can be used to find the area of one triangular section of the door? How do you know the formula work?
A formula that can be used to find the area of one triangular section of the door is; (1/2) * Area 0f rectangle
How to find the Area of the triangle?
From the attachment, we can say let us;
Denote the Length as L
The width as w.
Area of a triangle is given by the formula;
A = 1/2 * base * height
The area of the rectangle is:
A = Length * Width
From the attachment, we can see that the rectangle is divided into two equal triangular sections.
This implies that, the area of one of the triangular sections is half the area of the rectangle. Thus;
Area of Triangle = (1/2) * Area 0f rectangle
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Daisy has two measuring jugs, A and B, which can hold a combined volume of
900 ml.
Daisy fills jug A with water. She then fills jug B by pouring in water from jug A.
After this, there is 500 ml of water remaining in jug A.
Work out the volume of each measuring jug.
Help please
Daisy has two measuring jugs, A and B. The volume of each measuring jug will be A and B will be 500 ml and 400 ml.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Daisy has two measuring jugs, A and B, that together have a capacity of 900 ml, A jug of water is filled by Daisy. Afterward, she transfers water from jug A into jug B. Following this, jug A has 500 ml of water left.
Total volume = volume in jug A + volume in Jug B
If there are 500 ml of water remaining in jug A.
900 ml = 500 ml + volume in Jug B
volume in Jug B = 900 - 500
volume in Jug B = 400 ml
Thus, Daisy has two measuring jugs, A and B. The volume of each measuring jug will be A and B will be 500 ml and 400 ml.
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Please help ASAP, will mark brainliest!
Type SSS, SAS, ASA, AAS, or HL to justify why triangle ABC is congruent to triangle FBD.
Answer:
ASA
Step-by-step explanation:
Answer:
ASA
Step-by-step explanation:
The average temperatures across Washington, Texas, Oklahoma, New York, Missouri, Hawaii and Michigan are48°F, 65°F, 60°F, 45°F, 54°F, 64°F, 70°F, and 45°F respectively.Find the median
SOLUTION
Let's list the values first. These are
48, 65, 60, 45, 54, 64, 70 and 45
Now, we have to arrange these values from the smallest to the largest. Doing this we have
45, 45, 48, 54, 60, 64, 65, 70.
The median will be between the middle items which are 54 and 60. So we will find the median by the following way
[tex]\begin{gathered} \text{Median = }\frac{54+60_{}}{2} \\ \text{Median }\frac{114}{2} \\ \text{Median = 57} \end{gathered}[/tex]Therefore, the Median is 57°F
Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10.
Rectangle C has length 30 and width 15,
B? If so, what is the scale factor?
a, Is Rectangle A a scaled copy a of Rectangle
b. Is Rectangle B a scaled copy of Rectangle
A? If so, what is the scale factor?
C. Explain how you know that Rectangle C is not a scaled copy a of Rectangle B.
d. Is Rectangle
A.a scaled copy of Rectangle
C? If so, what is the scale factor?
Answer:
A. Yes, Rectangle A is a scaled copy of rectangle B.
B. Yes, Rectangle B is a scaled copy of rectangle A.
C. No, Rectangle A is not a scaled copy of rectangle C.
Step-by-step explanation:
Rectangle A has dimensions 12x8 and Rectangle B has length 15x10.
We see that sides of A and B are proportional because
[tex]\frac{12}{15} = \frac{8}{10}[/tex]
So we say that since sides are proportional A and B are similar or scaled copy of each other.
Since A is smaller and B is bigger, a is 0.8 scaled copy of B. Similarly B has an enlargement scale factor = 1.25 Rectangle C has 30x15, not proportion with sides of A and B. Hence we find that C is neither a scaled copy of A nor B
Hope this helps! :))
Write and Solve Equations in Context
A group of friends wants to go to the amusement park. They have $246.75 to spend
on parking and admission. Parking is $14, and tickets cost $33-25 per person,
including tax. Write and solve an equation which can be used to determine 2, the
number of people who can go to the amusement park.
Equation:
?
Answer: 2 =
Answer:
8 people
Step-by-step explanation:
117.50 - 5.50 = 112
112 ÷ 14.8 = 7.56756756757, but you round it up to 8, so the answer is 8 people.
11. Tom borrowed some money from his father seven months ago. Every month,
he pays back $400 to his father. Currently, he owes $2,500.
a) How much will he owe his father three months from now?
b) How much money did he borrow from his father?
In three months, he will owe his father $2500 less $1200, or $1300.
One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
Tom's payment for 7 months is 400 * 7 = $2800.
He borrowed $5300 ($2500 plus $2800).
His monthly payment for three months is 400*3.
In three months, he will owe his father $2500 less $1200, or $1300.
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What is 2 5/8 as a equivalent percent
2 5/8 as an equivalent percent is 262.50%.
What is the percent?Percentage is the rate of a number expressed as fraction out of 100. Percentage is a measure of frequency. The sign that represents percentage is %. In order to change a number to a percentage, multiply the number by 100.
A mixed number is a non-integer that is made up of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is less than the denominator. An example of a mixed number is 2 5/8
In order to convert the mixed number to percentage, multiply it by 100:
2 5/8 x 100
21/8 x 100 = 262.50%
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1 point
Which graph represents the solution x > 3?
Graph 1 represents the solution x > 3.
In Graph 1, the line is highlighted from point 3 with a white dot which is used to assert that all the values from 3 to positive infinity but 3 would not be considered. The highlighted side is toward the positive side.
In Graph 2, the line is highlighted from point 3 with a white dot which is used to assert that all the values from 3 to negative infinity but 3 would not be considered. The highlighted side is toward the negative side.
In Graph 3, the line is highlighted from point 3 with a black dot which is used to assert that all the values from 3 to positive infinity and 3 would be considered as well. The highlighted side is toward the positive side.
In Graph 4, the line is highlighted from point 3 with a black dot which is used to assert that all the values from 3 to negative infinity and 3 would be considered as well. The highlighted side is toward the negative side.
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Use the following image to complete the sentences describing the ratio of spots to eyes.
A ladybug with 2 eyes and 6 spots.
A ladybug with 2 eyes and 6 spots.
There are 6 spots for every
eyes.
There are
spots for every 1 eye.
Using ratios, the sentences are completes as follows:
There are 6 spots for every 2 eyes.There are 3 spots for every 1 eye.What is the ratio between two amounts?The ratio between two amounts a and b is given by the division of a by b, as follows:
r = a/b.
Between two amounts b and a, the ratio is given by the division of b by a, as follows:
r = b/a.
This means that the ratio between two amounts is not commutative, meaning that the order of the amounts matters.
A ladybug with 2 eyes and 6 spots, hence the first sentence is given as follows:
There are 6 spots for every 2 eyes. (ratio is the number of eyes for 6 spots).
The number of spots per eye is the ratio of the number of spots and the number of eyes, as follows:
Spots per eye = 6 spots/2 eyes = 3 spots per 1 eye.
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One person paints 1/4, one 1/3 and one 1/5. When they’re done 15m is unpainted, what is the total length?
Show your calculation
The total length of the wall that the individuals have to paint is 69 3/13 m.
What is the total length?The first step is to add the fractions of the wall painted by the three people together. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
Sum of the fractions:
[tex]\frac{1}{4} + \frac{1}{3} + \frac{1}{5}[/tex]
[tex]\frac{15 + 20 + 12}{60}[/tex] = [tex]\frac{47}{60}[/tex]
The fraction of the wall that has not been painted = 1 - [tex]\frac{47}{60}[/tex] = [tex]\frac{13}{60}[/tex]
13/60 of the wall = 15m
13/60 x w = 15
w = 15 ÷ 13/60
w = 15 x 60 /13 = 69 3/13 m
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Please Help Please ASAP
The graph of the inequality y < 1 - 3x is in the attachment below.
How to Graph an Inequality?Given the inequality, y < 1 - 3x, we need to determine if the line of the inequality graph will be dashed or solid, the slope (m) of the line, and the y-intercept (b).
The slope (m) of the inequality y < 1 - 3x is -3. This means the line would be a declining line where the rise/run = -3.
The y-intercept (b) of the inequality y < 1 - 3x is 1. This means the line would intercept the y-axis at y = 1.
The boundary line of the inequality graph for y < 1 - 3x would be a dashed line because of the inequality sign "<". It also means the shaded part would be below the boundary line, because, the inequality sign, "<" means the the values are not included.
The graph that will represent the inequality given is the image attached below.
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nouOR
36, 27,
81
4'
Find the 10th term.
Submit Answer
Answer:
177
Step-by-step explanation:
Answer: a_10 = 177147/65536. Write the general term through the pattern:: a_n = 36 3/4 n - 1 Substitute and calculate:: a_10 = 177.
a pyramid has an isosceles , triangle base with sides 25,25 and 48 units . the height of the pyramid is 30 units . calculate The volume of the pyramid
A pyramid has an isosceles triangle base with sides of 25,25 and 48 units.
The height of the pyramid is 30 units. The volume of the pyramid is 13What is the volume?We have a pyramid with four sides and a square base. Two-thirds of the pyramid's sides make up its height. The volume of a pyramid is 1, and we need to determine which of them matches our volume. Third, multiplying the length by the width gives us our base's area, which is s times s, or s square.This tells us that our base's height is equal to two-thirds of its side because it is a square base.
That makes it 2 to times s, or 2 s over 3. So we incorporate that into our equations next. We have a volume that is equal to 1/s squared / 2 / s spanning 3 points.Therefore, a pyramid has an isosceles triangle base with sides of 25,25, and 48 units.
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