A population of lizards in a large region doubles every year. The number of lizards can be
modeled by the equation y = 500 * 2 ^ x where
× is the number of vears after a researcher
measures the population size . When x = - 3
-3what does the value of y represent ?
The value of y when x = -3 represents that the population of the lizard three years before the researcher measures the population size is 63
How to interpret the function at x = -3?From the question, we have the following parameters that can be used in our computation:
y = 500 * 2 ^ x
The above equation is an exponential function
Such that
x is the number of years after a researcher measures the population size
When x = -3, we have the equation to be
y = 500 * 2^-3
Evaluate the product
y = 62.5
Approximate
y = 63
This means that the value of y at x = -3 is 63
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A company orders 25 boxed lunches from a deli for $208.75. If each boxed lunch costs the same amount, what is the unit cost of each boxed lunch?
Answer:
8.35
A company orders 25 boxed lunches from a deli for $208.75
What do we need to do to find the unit cost?
Given:
[tex]25\\208.75[/tex]
We need to find the cost.
Therefore, we need to work on the numbers we are given:
If each boxed lunch costs the same amount, then we need to divideWe have to divide the numbers given.$208.75 / 25 = 8.35Therefore, the unit cost is 8.35
The function f(x) is defined as f(x) = One-third(6)x. Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis?
The table of values that could be used to graph g(x), a reflection of f(x) across the x-axis is table (c)
How to determine the table of values?From the question, we have the following equation that can be used in our computation:
f(x) = One-third(6)x
When this statement is represented as an equation, we have the following representation
f(x)= 1/3(6)ˣ
The transformation is given as
A reflection of f(x) across the x-axis
This means that
g(x) = -f(x)
So, we have
g(x) = -1/3(6)ˣ
What this means is that the values of f(x) are negated to get g(x)
The table that represents this is table (c)
Hence, the table of values is table (c)
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Answer: C
Step-by-step explanation:
What is one over 2 X -5 equal 10 -3 over 4X
The value of x is 15 if the expression is 1/2x−5=10−3/4x after applying the arithmetic operation.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The expression is:
1/2x−5=10−3/4x
After solving:
5x/4 = 15
5x = 60
x = 60/5
x = 12
Thus, the value of x is 15 if the expression is 1/2x−5=10−3/4x after applying the arithmetic operation.
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In Exercises 1 and 2, classify the triangle by its sides and by measuring its angles.
Figure 1 is representing a right-angle triangle and figure 2 is representing the isosceles triangle.
What is a triangle?
The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the given diagram in the question,
For figure 1.
It is a right-angle triangle because it contains an angle of 90°.
For figure 2.
It is an isosceles triangle because according to the figure its two sides are the same which indicates that it is an isosceles triangle.
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A new employee charged $7220 on his credit card to relocate for his first job. After noticing that the interest rate for his balance was 27% compounded monthly, he stopped charging on that account. He wishes to pay off his balance in years using automatic payments sent at the end of each month.
a. What monthly payment must he make to pay off the account at the end of 4 years?
b. How much total interest will he have paid?
a. The monthly payment must be $193.53 in order to pay off the account at the end of 4 years.
b. The total interest paid will be $4372.02.
the number of devices a particular manufacturing company can produce is a function of the number of hours spent making the devices. On average, 4 devices are produced each hour. Assume that devices are produced at a constant rate. Write an equation in two variable that describes the number y, as a function of time the company sends making the devices x
Answer: y = 4x
Step-by-step explanation: The number of devices a company can produce is a function of the number of hours spent making the devices. On average, 4 devices are produced each hour. If we let x represent the number of hours spent making the devices and y represent the number of devices produced, we can write an equation to describe this relationship as follows:
y = 4x
This equation states that the number of devices produced is equal to 4 times the number of hours spent making the devices. For example, if the company spends 10 hours making the devices, the number of devices produced will be 4 * 10 = 40.
Therefore, the equation y = 4x describes the number of devices produced by the company as a function of the number of hours spent making the devices.
Question
Evaluate the expression when b=9 .
24/b+8 =
The evaluated expression of 24 / b + 8 when b = 9 is [tex]10\frac{2}{3}[/tex]
How to evaluate an expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) .
In other words, an expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
Therefore, let's evaluate 24 / b + 8 when b = 9
Hence,
[tex]\frac{24}{9}+8 = \frac{24+ 72}{9}=\frac{96}{9} = 10\frac{6}{9}=10\frac{2}{3}[/tex]
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Michael went shopping for a new video game because of a sale. The price on the tag was $46, but Michael paid $34.50 before tax. Find the percent discount.
The discount percentage offered on the new video game as of a sale is 75%.
Explain the term discount percentage?When a product is offered at a discount, the seller is reducing the product's price from what it was originally listed for. The percentage discount just on product is determined by the discount amount stated as a percentage of the initial price.For the stated question-
The listed price on the video game = $46.
price paid exclusive of tax = $34.50.
Let 'x' be the percentage discount of the listed price.
Then,
x% of 46 = 34.50
x = 34.50 x 100 / 46
x = 75%
Thus, the discount percentage offered on the new video game as of a sale is 75%.
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SOLVE Y
4y + 10 = -10 + 6y
Y =
Answer: The answer is y=10.
Step-by-step explanation:
4y + 10 = -10 + 6y First subtract 4y from both sides.
10 = -10 + 2y Then, add 10 to both sides.
20 = 2y Finally, divide both sides by 2.
y = 10.
the sign at the garbage sale said 12 paper back books could be purchased for 8$ how much 3 paper backbooks cost
[tex]\begin{array}{ccll} books&\$\\ \cline{1-2} 12 & 8\\ 3& x \end{array} \implies \cfrac{12}{3}~~=~~\cfrac{8}{x} \\\\\\ 4 ~~=~~ \cfrac{ 8 }{ x }\implies 4x=8\implies x=\cfrac{8}{4}\implies x=2[/tex]
Answer:
2$
Step-by-step explanation:
If 12 paperback books could be purchased for 8$,
We need to divide by 4 on each side to find the answer.
Therefore, 3 paperback books costs 2$.
I would appreciate it if you mark my answer as brainliest.
5 / 7/10 answer in fraction form
When we divide fractions, we multiply the first fraction by the second fraction's reciprocal.
Solving the Question[tex]5\div \dfrac{7}{10}[/tex]
⇒ Multiply by the reciprocal of 7/10:
[tex]= 5\times \dfrac{10}{7}[/tex]
[tex]= \dfrac{50}{7}[/tex]
⇒ If you would like, you can change this into a mixed number fraction. The whole number value from 50/7 is 7. 7 times 7 is 49, which is 1 less than 50. 1 is the numerator and 7 is the whole number:
[tex]= 7\dfrac{1}{7}[/tex]
Answer[tex]\dfrac{50}{7}[/tex] or [tex]7\dfrac{1}{7}[/tex]
I need help, can someone help me
Its graph is a parabola tangent to the x-axis at (4,0) with y-intercept 6. find the equation showing the steps
The equation of the line with y - intercept (0, 6) is [tex]y = -\frac{3}{2}x + 6[/tex].
What is tangent?
The straight line that "just touches" the curve at a given point is referred to as the tangent line to a plane curve in geometry. It was defined by Leibniz as the path connecting two points on a curve that are infinitely close together.
Given:
Graph is a parabola tangent to the x-axis at (4,0) with y-intercept 6.
That is there are two points (4, 0) and (0, 6).
From these two points we have to find the slope of the line.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{0-6}{4-0} = -\frac{6}{4} = -\frac{3}{2}[/tex]
Now to use point slope form of the line.
[tex]y-y_1 = m(x-x_1)\\ y - 6 = -\frac{3}{2}(x-0)\\ y - 6 = -\frac{3}{2}x\\ y = -\frac{3}{2}x + 6[/tex]
Hence, the equation of line is, [tex]y = -\frac{3}{2}x + 6[/tex].
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Help finding answer to problem
Supplementary angles are angles that have a sum of 180 degrees. They are formed on a straight line.
Solving the QuestionLooking at the given diagram, we can notice how angle SUV and SUT are supplementary angles. We know this because they form the straight line, VT.
We are given angle SUT, which is 58 degrees.
Because angles SUV and SUT have a sum of 180 degrees, we can solve for angle SUV by subtracting 58 from 180:
180 - 58 = 122
Therefore, angle SUV is 122 degrees.
Answer122 degrees
Answer:
Angle SUV = 180 - 58
= 122° (adjacent angles on a straight line)
Identify the slope and y-intercept of the line below.
Answer:
Negative slope of 3 so -3x and -9y
Step-by-step explanation:
-3x=-9y
Answer:
slope = -3 ; y- intercept = (0,-9)
Step-by-step explanation:
A (-3,0)
B(0,-9)
slope = (-9-0)/(0-(-3)
-9/3
-3
i’ve been struggling with this and it’s due soon! pictures are below of the question.
a) If the sum of the square of the larger side is smaller than the squares of the shorter sides, then the triangle is an acute triangle.
b) To determine if a triangle is a right triangle.
c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.
What is converse of the Pythagorean Theorem?If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Given,Pictures
According to the converse of the Pythagorean Theorem.
a) If the sum of the square of the larger side is smaller than the squares of the shorter sides, then the triangle is an acute triangle.
b) To determine if a triangle is a right triangle.
c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.
Therefore,
a) If the sum of the square of the larger side is smaller than the squares of the shorter sides, then the triangle is an acute triangle.
b) To determine if a triangle is a right triangle.
c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.
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A town has a population of 17000 and grows at 3% every year. What will be the
population after 10 years, to the nearest whole number?
If the population grows 3% every year, then each year's population is 103% of the previous year's population. This gives us the exponential function:
[tex]f(x) = 17000 (1.03)^x[/tex]
17000 for the current population, 1.03 growth factor for the 103%, raised to the x power because we'll need 103% of 103% of 103% and so on until we multiply by 103% for the correct number of years.
[tex]f(10) = 17000(1.03)^{10} \approx 22846.578448850072648[/tex]
Following standard math rounding this would round to 22,847 people.
If you argue that last 0.57844 of a person really round up, you could argue that this is really 22,846 people.
5(2x - 1) - 11x
evaluate the above for x = 6
Hence, the solution is [tex]-11[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
[tex]5(2x - 1) - 11x[/tex]
When [tex]x=6[/tex]
[tex]5(2x-1)-11x=5(2(6)-1)-11(6)\\=5(12-1)-66\\=5(11)-66\\=55-66\\=-11[/tex]
Hence, the solution is [tex]-11[/tex].
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"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The rocket reaches its maximum height at 2.25 second(s) after launch
The maximum height reached by the object is 88 feet.
What is the maximum height the rocket reached?Given function:
h(t) = -16t² + 72t + 7
By differentiating the function, we have
h'(t) = -32t + 72
Set the function to 0
-32t + 72 = 0
32t = 72
Divide both sides by 32
t = 2.25
Hence, the time is 2.25 seconds
To find the maximum height reached by the rocket,
Substitute t = 2.25 into
h(t) = -16t² + 72t + 7
h(2.25) = -16(2.25)² + 72(2.25) + 7
= -16(5.0625) + 162 + 7
= -81 + 162 + 7
h(2.25) = 88
In conclusion, the maximum height the rocket reached is 88 feet
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need help assap look at attachment
Answer: See the attachment
Step-by-step explanation: You would use the formula y=mx+b and since b is the y-intercept you would plug that into the equation and then plug in 3/4 as m resulting in
y=3/4x -1 then you just graph it!
Place a point on -1 in the y axis, (0,-1) then go up three units up and four units right, (4,2)
-8-x=x-4x for solving linear equations: variable on both sides. Please hurry I need the answer quickly.
Answer: -4
Step-by-step explanation:
1. Add x on both sides
-8-x=x-4x → -8=2x-4x
2. Combine like terms
-8=2x-4x → -8=-2x
3. Divide negative 2 from both sides
-8=2x → -4=x
A jewelry designer plans to make a triangular pendant out of gold wire. The wire costs $31.65 per centimeter. What is the possible range of costs for the wire?
The wire can cost more than $____ and less than $____
The wire used for the triangular pendant can have a cost more than 664.65 USD and less than 791.25 USD.
How to determine the possible lengths of the missing side
In this problem we find the case of a triangle, in which the length of two sides are known and we need to determine the range of costs associated to the set of all possible triangles. This can be derived by the geometric system described in the image attached below. The minimum and the maximum costs of the pendant:
θ = 0°
l = 10.5 cm - 2.5 cm
l = 8 cm
s = 10.5 cm + 8 cm + 2.5 cm
s = 21 cm
C = (31.65 USD / cm) · (21 cm)
C = 664.65 USD
θ = 180°
l = 10.5 cm + 2.5 cm
l = 13 cm
s = 10.5 cm + 2.5 cm + 12.5 cm
s = 25 cm
C = (31.65 USD / cm) · (25 cm)
C = 791.25 USD
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30 PTS, SHOW YOUR WORK How much carbon dioxide will you prevent from entering the atmosphere in one year, if you replace a 100-watt light bulb with a CFL bulb that uses 30 watts in a fixture that you have on 8 hours per day? (round to the hundredths place)
(1.37 pounds of CO2 per kWh)
The amount of carbon dioxide will you prevent from entering the atmosphere in one year is 280028 lb
How much carbon dioxide will you prevent from entering the atmosphere in one year?We are given 1.37 pounds of carbon dioxide per kWh
Using a 100-watt light bulb daily for 8 hours, for a year, the amount of carbon dioxide produced will be:
100 × 1.37 × 8 ×365 = 400040 lb
Using a 30-watt CFL bulb for 8hrs/ day for a year, the amount of carbon dioxide produced will be:
30× 1.37 × 8 × 365 = 120012 lb
Therefore, carbon dioxide prevented:
= 400040-120012
= 280028 lb
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Letters are converted into base two numbers for computer processing The capital letters A through Z are assigned 65 through 90, with each number expressed in base two. Thus, the binary code for A (55) is
1000001. Similarly, the lowercase letters a through z are assigned 97 through 122 in base two. Write the binary representation for the following letter
H
Answer: 1001000
Step-by-step explanation:
IF A= 65
H=72
BINARY OF H= 72 = 1001000
pls help me on this question
Answer:
[tex]B. \;\dfrac{24}{40}[/tex]
[tex]C. \;\dfrac{3}{5}[/tex]
Step-by-step explanation:
What is the solution of this inequality?
r−6>−11
Drag and drop the choices to correctly complete the inequality.
Plss help me
The solution to the inequality r - 6 > −11 will be r > -5.
How to solve inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Based on the information, the solution to the inequality r - 6 > −11 will be solved thus:
r - 6 > −11
Collect the like terms
r > - 11 + 6
r > -5
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PLEASE HELP ME!!! I WILL GIVE YOU BRAINLIST!!!
Which triangle makes this statement true?
ΔABC ≅ _____
Answer:
A.
Step-by-step explanation:
the symbol means "congruent".
that means that both shapes have the same angles and the custodian same side lengths (even if the shape is turned in sine way, to you can reorient in a way, so that it will cover the other shape 1:1).
the only triangle with the same measurements everywhere is A. triangle EFG.
B and C (RST and XYZ) are similar triangles with ABC. the angles are the same, and all side lengths have the same scaling factor to the other shape.
D (KLM) is nothing at all to ABC.
List the percent decrease for each of the following A year old $30,000 Subaru selling for $24,500
well, the decrease is really 30000 - 24500 = 5500.
now, if we take the 30000 to be the 100%, what is 5500 off of it in percentage?
[tex]\begin{array}{ccll} a&b\\ \cline{1-2} 30000 & 100\\ 5500& x \end{array} \implies \cfrac{30000}{5500}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 60 }{ 11 } ~~=~~ \cfrac{ 100 }{ x }\implies 60x=1100\implies x=\cfrac{1100}{60}\implies x=\cfrac{55}{3}\implies x=18\frac{1}{3}[/tex]
100 Points
What is the value of the logarithmic or exponential expression?
Select True or False for each statement
Answer:
True, False, False-------------------------------------------
Let's simplify left sides of each statement and compare with right sides:
[tex]3^{5log_32}=3^{log_32^5}=3^{log_332}=32 \implies True[/tex][tex]2 ln\ e^{1/4}=2*1/4*ln\ e^{}=2*1/4*1=1/2\implies False[/tex][tex]e^{2ln e-1}=e^{2*1-1}=e^{2-1}=e^1=e \implies False[/tex]