Answer:
10
Step-by-step explanation:
7 2/9 + 2 7/9 common denominators already the same so add
7+2=9 first start with the whole number
2/9 + 7/9= 9/9 = 1 then add the fractions
9+1=10 then add the whole number and fraction
Answer:
10
Step-by-step explanation:
Which of the following is a root of the polynomial function F(x)=x^4+2x^3-3x^2-6x?
Answer: x = 0, √3, -√3, -2
Step-by-step explanation:
x⁴ + 2x³ - 3x² - 6x
= x (x³ + 2x² - 3x - 6)
= ↓ x²(x + 2) -3(x + 2)
= x (x² - 3)(x + 2)
= x(x - √3)(x + √3)(x + 2)
Set each factor equal to zero to find the roots:
x = 0 x - √3 = 0 x + √3 = 0 x + 2 = 0
x = √3 x = -√3 x = -2
Real estate values in a town are increasing at a rate of 7% per year. Ms. Keene purchased a building for $245,000 in 2015. How much can she expect to sell the building for in 2020, assuming this trend continues? Enter your answer in the box. Round to the nearest whole dollar.
This is an exponential growth problem.
The formula for this is:
y = a(1+rate)^time
a = the starting value = 245,000
Rate is the percent of increase written as a decimal = 7% = 0.07
Time would be the number of years from the starting year to the year you are trying to find: 2020 - 2015 = 5 years
Now you have y = 245000(1 + 0.07)^5
Simplify:
245000(1.07)^5
Calculate:
New value = $343,625
heyyy help pls with pciutreeeee
Answer:
12 Fetches
Step-by-step explanation:
this one is easy but you probably overthought it,
since 2 is half of 4 then you would just multiply everything by 2
let's just say that didn't work right, for these types of problems you have to make a proportion so in this case it would be 2 minutes/6 fetches= 4 minutes/ x fetches. then you solve by cross multiplication.
The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length. When you put 40 liters of water into the aquarium, it was full to 2/3 its volume. What part of the length makes up the height of the aquarium? (1 liter is equal by volume to 1 decimeter3)
Answer:
[tex]\dfrac{3}{5}[/tex] of the height makes up the height.
Step-by-step explanation:
The length of an aquarium, which has the form of a rectangular solid, is [tex]5\ dm[/tex]
The width is [tex]\dfrac{4}{5}[/tex] of the length, so teh width is,
[tex]=5\times \dfrac{4}{5}=4\ dm[/tex]
Let us assume the height is 'h' dm.
So the volume will be,
[tex]=\text{Length }\cdot \text{ Width }\cdot\text{ Height}[/tex]
[tex]=5\times 4\times h[/tex]
[tex]=20h\ dm^3[/tex]
As 1 liter of water occupies volume of 1 dm³, so volume of 40 liters of water will be,
[tex]=40\times 1=40\ dm^3[/tex]
This [tex]40\ dm^3[/tex] is the [tex]\dfrac{2}{3}[/tex]th of total volume.
Hence total volume will be,
[tex]=\dfrac{40}{\frac{2}{3}}=40\times \dfrac{3}{2}=60\ dm^3[/tex]
Therefore,
[tex]\Rightarrow 20h=60[/tex]
[tex]\Rightarrow h=3\ dm[/tex]
So the part of length makes up to the height will be,
[tex]=\dfrac{3}{5}[/tex]
I cell phone company charges $40 per month plus a $35 activation fee Write anExpression for the total cost for M months
Answer:
$35 + $40M
Step-by-step explanation:
A cell phone company charges per month fees = $40
and an activation fee = $35
Total cost = Activation fees + ($40 × total number of months)
So the expression for the total cost for M months will be
$35 + $40M
Caitlan went to the store to buyschool clothes . She has store credit from a previous return in the amount 39.58. If she bought 4 of the same style shirt in different colors and spent total of 52.22 after the store credit was taken off he total, what was the price of each shirt ahe bought? Write and solve and equation with integrr coefficients
Answer:
Each shirt costs $22.95
Step-by-step explanation:
39.58 + 52.22 = 91.80
91.80/4= 22.95
Final answer:
Caitlan bought 4 shirts for a total cost of $91.80. Therefore, the price of each shirt was $22.95.
Explanation:
To find the price of each shirt Caitlan bought, we can use the equation:
x - 39.58 = 52.22
where x represents the total cost of the shirts before the store credit is applied. To solve for x, we can add 39.58 to both sides of the equation:
x = 52.22 + 39.58 = 91.80
Since Caitlan bought 4 shirts, we can divide the total cost by 4 to find the price of each shirt:
91.80 / 4 = 22.95
Therefore, the price of each shirt Caitlan bought was $22.95.
Bernie's car used 100 cups of gasoline during a drive he paid 3.12 per gallon for gas how much does it gas cost
Answer:
19.50
Step-by-step explanation:
There are 16 cups in a gallon. Divide 100 into 16 to get 6.25. You now just multiply 3.12 by 6.25 to get 19.5. Your answer is $19.50.
The pressure at sea level is 11 atmosphere and increases at a constant rate as depth increases. When Sydney dives to a depth of 23 meters, the pressure around her is 3.3 atmospheres. The pressure p in atmospheres is a function of x, the depth in meters.
Answer:
The function [tex]p(x) = 0.1x+1[/tex] , where x is the depth in meters.
Step-by-step explanation:
As per the statement: The pressure at sea level is 1 atmosphere and increases at a constant rate as depth increases.
Then, we have the two points i,e (0, 1) and (23, 3.3).
An equation of the line is in the form of y=mx+b where m is the slope or rate of the line and b is the y-intercept.
Let x represents the depth in meters and p(x)= y represents the pressure in atmosphere.
Calculate slope of the line:
Slope of line(m) is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given point we have;
[tex]m = \frac{3.3-1}{23-0} = \frac{2.3}{23} = 0.1[/tex]
Then, our equation of line become:
y = 0.1x + b .....[1]
To solve for b;
Substitute the point (0, 1) in [1];
[tex]1 = 0.1(0)+b[/tex]
[tex]1 = b[/tex]
Our equation for this line become: y = 0.1x +1
Now, we write this for x as a function of p,
i.e, p(x) = 0.1x + 1
Then, the function formula become;
[tex]p(x) = 0.1x+1[/tex] where x is the depth in meters.
A square lawn is surrounded by a path 2.5 m wide . If the area of the path is 165 m sq, find the area of the lawn
The music club is having a bake sale as a fundraiser. They sell xx brownies at $5 each and yy cookies at $8 each. They will sell at least 26 brownies and 15 cookies. They need to make at least $250. Which system describes this situation?
Step-by-step explanation:
We are told that the music club is having a bake sale as a fundraiser. They sell x brownies at $5 each and y cookies at $8 each. They will sell at least 26 brownies and 15 cookies.
We can represent this information as:
[tex]x\geq 26[/tex]
[tex]y\geq 15[/tex]
They need to make at least $250. We can represent this information as:
[tex]5x+8y\geq 250[/tex]
Therefore, our system of inequalities will be:
[tex]x\geq 26[/tex]
[tex]y\geq 15[/tex]
[tex]5x+8y\geq 250[/tex].
I rent a gym for $150.00 for 30 students. Another time I rent the gym for $270.00 for 70 students. I need to find a fixed rate.
(y= mx+b)
Answer: y = 3x + 60
Step-by-step explanation:
Set up two equations and solve the system:
270 = 70x + b
- (150 = 30x + b)
120 = 40x
3 = x
Input "x" into one of the equations and solve for "b":
150 = 30x + b
150 = 30(3) + b
150 = 90 + b
60 = b
Equation: y = 3x + 60
This means that there is a flat fee of $60 plus a rate of $3 per student
The fixed rate of gym fee of $60 plus a rate of $3 per student.
The fixed-rate is;
[tex]\rm y=3x+60[/tex]
Given
I rent a gym for $150.00 for 30 students.
Another time I rent the gym for $270.00 for 70 students.
Linear function;A linear function is a function that forms a straight line in a graph.
Let x be the number of students and y be the total cost of renting the gym.
To find the fixed-rate let us write the equation of line representing the total cost of renting a gym for x students.
The equation representing a fixed rate is;
[tex]\rm y = mx+b[/tex]
I rent a gym for $150.00 for 30 students.
[tex]\rm 150 = 30x + b[/tex]
Another time I rent the gym for $270.00 for 70 students.
[tex]\rm 270 = 70x + b[/tex]
Subtracting both the equations;
[tex]\rm 150-270=30x+b-70x-b\\\\-120=-40x\\\\120=4x\\\\x=\dfrac{120}{4}\\\\x=3[/tex]
Substitute the value of x in equation 1
[tex]\rm 150 = 30x + b\\\\150=30(3)+b\\\\150=90+b\\\\b=150-90\\\\b=60[/tex]
Therefore,
The fixed-rate is;
[tex]\rm y=mx+b\\\\y=3x+60[/tex]
Hence, the fixed rate of gym fee of $60 plus a rate of $3 per student.'
To know more about linear function click the link given below.
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The matrix shows the number of different basketball shots three players made in two minutes. These players want to double these results. Which matrix shows what the players want to do?
Answer:
B
Step-by-step explanation:
Javi [5 1]
Victor [3 2]
Chris [4 2]
A.
[10 1]
[6 2]
[8 2]
B.
[10 2]
[6 4]
[8 4]
C.
[7 3]
[5 4]
[6 4]
D.
[10 1]
[3 2]
[4 2]
Answer:B. [10 2]
[6 4]
[8 4]
Step-by-step explanation:
Javi [5 1]
Victor [3 2]
Chris [4 2]
A.
[10 1]
[6 2]
[8 2]
B.
[10 2]
[6 4]
[8 4]
C.
[7 3]
[5 4]
[6 4]
D.
[10 1]
[3 2]
[4 2]
Explanation:
As a general rule, to double, triple or as the case may be, the result of a matrix, we apply what is known in Maths as scalar multiplication.
Scalar multiplication seeks to multiply the entries in a matrix by a scalar. The resulting matrix is called the scalar product of the original matrix.
For instance:
Let matrix A = [a b] [c d] and k be a scalar.
The matrix kA is called a scalar product of the matrix, A and the constant, k is defined as:
kA = k [a b] [c d]
= [ka kb] [kc kd]
So, for the given question, the best option would be the matrix that depicts a scalar multiple of 2 of the original matrix entry. Option B.
I.e:
Javi = 2[5 1] = [2*5 2*1] = [10 2]
Victor= 2[3 2] = [2*3 2*2] = [6 4]
Chris = 2[4 2] = [2*4 2*2] = [8 4]
Please answer this question!! 41 points and brainliest!
Answer:
x > -3
Step-by-step explanation:
5x+ 7 > 2(x-1)
Distribute the 2 on each side
5x+7 > 2x -2*1
5x+7 > 2x-2
Subtract 2x from each side
5x-2x +7 > 2x-2x-2
3x + 7>-2
Subtract 7 from each side
3x+7-7>-2-7
3x>-9
Divide by 3 on each side
3x/3 >-9/3
x > -3
Answer:
[tex]x>-3[/tex]
Step-by-step explanation:
To solve equations, we use inverse operations. Normally, we use PEMDAS to simplify an equation. To solve it, we use the inverse of each in this order SADMEP. Solving an inequality is the same except for step. When dividing by a negative, the sign of the inequality changes.
We have [tex]5x+7>2(x-1)\\5x+7>2x-2[/tex] in simplified form. We begin by subtracting or adding constants across the equal sign. Then doing the same with the variable terms. We finish by dividing by the coefficient of the variable term.
[tex]5x+7>2x-2\\5x+7-7>2x-2-7\\5x>2x-9\\5x-2x>2x-2x-9\\3x>-9\\x>-3[/tex]
To graph, we draw a number line, draw an open circle at -3.
Since it is not equal to, we do not fill it in. We leave it open. We also draw an arrow to the right of -3
Which is the graph of the line with equation:
y + 4 = 2(x−1)
Answer:
The graph in the first picture which intercepts the y-axis at (0,-6) and has a positive slope of 2.
Step-by-step explanation:
We can write the linear equation into slope-intercept form. We do this by simplifying and isolating y.
y+4=2(x-1)
y+4=2(x)-2(1)
y+4=2x-2
y+4-4=2x-2-4
y=2x-6
In y=mx +b form, we can connect the equation to the graph. This equation has b=-6 or (0,-6) for the y-intercept. It also has m=2 for the slope. This is the first graph.
PLEASE HELP! I GIVE 20 POINTS
Answer: (C) 108
Step-by-step explanation:
The corresponding angle to x and (x - 36) form a linear pair, which means they are supplementary angles, hence their sum is 180°
(x) + (x - 36) = 180
2x - 36 = 180
2x = 216
x = 108
Answer:
The Answer is 108
Step-by-step explanation:
Few things to Note:
180 angles are linear (so two angles in straight line ADDS UP to makes 180 degree)
Corresponding angles equal each other (aka the two angles shown is corresponding..meaning BOTH are "x"; also, this problem tells you that)
Knowing this, x-36 and its adjacent(angle next to it) is x and they are on a 180 straight line, set equation (x-36)+x= 180 and solve
(x-36)+x= 180--->2x-36=180--->216/2=x
The length of a rectangle is one inch less than three times its width. If the perimeter of the rectangle is 54 inches, find the length
w - width
3w - 1 - length
54 in - perimeter
w + w + (3w - 1) + (3w - 1) = 8w - 2 - perimeter
The equation:
8w - 2 = 54 add 2 to both sides
8w = 56 divide both sides by 8
w = 7
3w - 1 = 3(7) - 1 = 21 - 1 = 20
Answer: The length = 20 in.The perimeter of the rectangle is twice the sum of the length and the width.The length of the rectangle is 20 inches long.
Given information-
The length of a rectangle is one inch less than three times its width.
The perimeter of the rectangle is 54 inches.
What is the perimeter of rectangle?The perimeter of the rectangle is the boundary by which the rectangle is covered. The perimeter of the rectangle is twice the sum of the length and the width.
It can be given as,
[tex]P=2(a+b)[/tex]
Here,[tex]a[/tex] is the length of the rectangle and [tex]b[/tex] is the width of the rectangle.
Now it is given that the length of a rectangle is one inch less than three times its width. Suppose the length of the rectangle is [tex]x[/tex] inches long. Thus the width [tex]y[/tex] of the rectangle is,
[tex]=\dfrac{x+1}{3} =\dfrac{x}{3} +\dfrac{1}{3}[/tex]
Thus the perimeter of the rectangle is,
[tex]\begin{aligned}\\P&=2(x+\dfrac{x}{3}+\dfrac{1}{3} )\\54-\dfrac{2}{3} &=2\times\dfrac{3x+x}{3} \\\dfrac{160}{3} &=\dfrac{8x}{3}\\160&=8x\\x&=20\\\end[/tex]
Hence the length of the rectangle is 20 inches long.
Learn more about the perimeter of rectangle here;
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Scenario: If the distance from person to the base of tree is 70 ft and the tree is 115 ft tall, how much does the person look up to see the top of the tree (i.e. Find the angle of elevation)? Note: you need to draw the triangle to figure out the layout on your own for this problem.
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
This is a right angle triangle.
Suppose the angle from person to top of the tree is x
Using SOH CAH TOA
Tan x = [tex]\frac{opposite}{adjacent}[/tex]
Tan x = [tex]\frac{115}{70}[/tex]
Tan x = 1.6428
taking tan inverse
x = 58.67 degrees
Means the person need to look up 58.67 degrees. : Answer
Hope it will help :)
Sinea wants to spend money using the same ratios as on her last trip to the car nivel. If she spends $26 on games,how much will she spend on souvenirs? CHART Snacks Games Souvenirs Sinea $5 $8 $12 Ren. $10 $8 $20
Answer:
A. Sinea spends $26 on games, she wants to keep the same ratio, how much does she spend on souvenirs?
A- (snacks- 16.25) (games- 26) (souvenirs- 39)
B. Ren spends $5 on souvenirs, he wants to keep the same ratio, how much does he spend on snacks
B- (snacks- 2.5) (games- 2) (souvenirs- 5)
C. Both spend $40 on snacks, they want to keep their original ratio, who spends more on souvenirs?
C. Ratios
Sinea- (snacks- 40) (game- 64) (souvenirs- 96)
Ren- (snacks- 40) (game- 32) (souvenirs- 80)
Under a dilation, the point (2, 6) is moved to (6, 18).
What is the scale factor of the dilation?
Divide the new X value by the original x value:
6 / 2 = 3
Then check that with the Y value:
Original Y value = 6, 6 x 3 = 18, which is the new Y value.
This means the scale factor is 3.
Please help Mrs.Johnson spend $611 buying lunch for 78 students. If all lunches cost the same, about how much did she spend on each lunch
Answer:
$35.96 to 2.d.p. or 36 to 2.s.f.
Step-by-step explanation:
We can show this by:
611 = 78x
x being the 78 students
To find 1x which is the price of one student, or one lunch, we can simply divide both sides by 78:
[tex]\frac{611}{78} = \frac{78x}{78}[/tex]
Or:
35.95 = 1x
So each lunch cost 35.96 to 2.d.p. or 36 to 2.s.f.
Please help! Urgent!
Answer options:
-180°
-270°
-300°
-360°
Answer:
Step-by-step explanation: answer should be 360
Nadia has 20 more postcards then Pete. After Nadia gives Pete some cards Pete has 2 more postcards than Nadia. How many postcards does Nadia give to Pete?
Nadia gave Pete 11 postcards to balance the numbers as described. This means Pete ended up with 2 more postcards than Nadia after the exchange.
To find out how many postcards Nadia gave to Pete, let's set up some equations based on the information given.
First, let's define the number of postcards Pete has as P.
Since Nadia has 20 more postcards than Pete, we know:
N = P + 20
Now, let's define the number of postcards Nadia gives to Pete as x.
After Nadia gives x postcards to Pete, Nadia will have N - x postcards and Pete will have P + x postcards.
According to the problem, after the exchange, Pete has 2 more postcards than Nadia: P + x = (N - x) + 2
Substitute the first equation (N = P + 20) into the second equation: P + x = ((P + 20) - x) + 2
Simplify the equation:
P + x = P + 20 - x + 2
P + x = P + 22 - x
Now, isolate x on one side of the equation by subtracting P from both sides:
x + x = 22
2x = 22
Divide both sides by 2: x = 11
What type of exponential equation is shown?
y = C(1 - r)t
Exponential growth
Compound interest
Exponential decay
Quadratic
Answer:
Exponential Decay or Growth
Step-by-step explanation:
[tex]y=C(1-r)^t[/tex] represents an exponential.
When r is greater than 0 but less than 1, the function decays by decreasing the values through the rate.
When r is less than 0 or negative, the function grows by increasing the values through the rate.
please help me ill give brainliest
Answer:
The answer would be remove two negative tiles.
Step-by-step explanation:
-5-(-2) becomes -5+2, and since the latter aren't of the same sign, you'd subtract two negative tiles so that it gives you the answer, which would be -3.
How to:
-5-(-2)
-5+2
= -3
Answer:
B) Remove 2 negative tiles
Step-by-step explanation:
-5 - (-2)
-5 + 2 [-(-2) = +2]
= -3
Remove two negative tiles
Answer: Remove 2 negative tiles
A parallelogram has an area of 285 square centimeters and a base length of 19 centimeters. What is the height of the parallelogram? 16 centimeters 28 centimeters 15 centimeters 14 centimeters
Final answer:
To find the height of the parallelogram with an area of 285 square centimeters and a base of 19 centimeters, divide the area by the base, resulting in a height of 15 centimeters.
Explanation:
The question pertains to finding the height of a parallelogram given the area and the base length. The formula for the area of a parallelogram is Area = base × height. Given an area of 285 square centimeters and a base length of 19 centimeters, we can solve for the height by rearranging the formula:
Height = Area / base
By substituting the given values:
Height = 285 cm² / 19 cm = 15 cm
So, the height of the parallelogram is 15 centimeters.
Jina received a $70 gift card for a coffee store. She used it in buying some coffee that cost $7.51 per pound. After buying the coffee, she had $47.47 left on her card. How many pounds of coffee did she buy
Answer: 3 pounds
Step-by-step explanation:
The equation can be set up according to slope form: y=mx+b where x represents cost per round.
$70 = $7.51x + $47.47
Subtract 47.47 to both sides: $22.53 = $7.51x
Divide both sides by 7.51: 3 = x
Answer: 70 - 47.47 = 22.53. She spent $22.53. If one pound is $7.51. And she spent $22.53 = 3.
She bought 3 pounds of coffee. Brainliest is always appreciated. :)
PLEASE HELP. WILL GIVE BRAINIEST AND 60 POINTS if you show work so I can understand these.
1. Find the slope of the line that passes through the
points (-1, 2), (0, 5).
2. Suppose y varies directly with x, and y = 15 and x = 5.
Write a direct variation equation that relates x and y.
What is the value of y when x = 9?
3. Write an equation in slope-intercept form of the line
that passed through (-3, 4) and (1. 4).
4. Use point-slope form to write the equation of a line
that has a slope of 2/3
and passes through (-3, -1).
Write your final equation in slope-intercept form.
5. Write the equation in standard form using integers
(no fractions or decimals): = −2/3 − 1
6. Write an equation of the line that passes through
(2, -1) and is parallel to the graph of y = 5x – 2. Write
your final equation in slope-intercept form.
7. Write an equation of
1) use change in y/change in x to find the slope from two points:
change in y: 5-2=3
change in x: 0-(-1)=1
3/1=3 is your slope
2) if it is a direct variation, you know as x increases, y increases, both at constant rates
since y is 10 more than x in the example, it will always be 10 more than x
y=x+10 is your equation.
when x=9, y=19
now they could not be reffering to their difference in addition, but their difference in multiplication. In that case, y is 3 times x in the example, so it will always be 3 times x
y=3x is your equation
when x=9, y=27
3) the slope of this line is determined by change in y over change in x:
change in y: 4-4=0
you don't need to calculate the change in x because 0 divided by anything is 0, so that is your slope.
y=0x+b
4=0(1)+b
4=0+b
4=b
y=4 is your equation because 0 times x is zero. this means that it is a horizontal line with a constant y value of 4
4)
y - value of y in a point =slope (x - value of x in a point)
y-(-1)=2/3 * (x-(-3))
y+1=2/3x+2/3(3)
y+1= 2/3x+2
y=2/3x+1
from solving point slope form, you can get to slope intercept form
5) not sure what this question is asking for
- a line?
- an expression equivalent to -1 and 2/3?
both of those aren't possible with the information given
6) parallel means same slope different y intercept
y=5x+b
-1=5(2)+b
-1=10+b
-11=b
y=5x-11
Please help ASAP!
What is the value of cosθ given that (−5, −4) is a point on the terminal side of θ ?
A). 5√41/41
B). −4√41/41
C). 4√41/41
D). −5√41/41
Answer:
D
Step-by-step explanation:
The value of the trigonometric expression cos θ, when (-5, -4) is a point on the terminal side of θ is -5√41/41. Hence, option D is the right choice.
What are trigonometric expressions?
Trigonometric expressions are the ratios of the sides of a right triangle, which are always constant despite the increase or decrease in the size of its sides.
These are the trigonometric ratios:
sin θ = perpendicular/hypotenusecos θ = base/hypotenusetan θ = sin θ/cos θ = perpendicular/basecot θ = 1/tan θ = cos θ/sin θ = base/perpendicularsec θ = 1/cos θ = hypotenuse/basecosec θ = 1/sin θ = hypotenuse/perpendicular.How to solve the question?In the question, we are asked to find the value of cos θ, given that (-5, -4) is a point on the terminal side of θ.
This means that we; are in quadrant III. As we know, cos θ is negative in the 3rd quadrant.
The base is the distance of the x-coordinate from the origin, that is, 5 units.
The perpendicular is the distance of the y-coordinate from the origin, that is, 4 units.
By Pythagoras' Theorem,
Hypotenuse² = Base² + Perpendicular²,
or, Hypotenuse² = 5² + 4²,
or, Hypotenuse² = 25 + 16,
or, Hypotenuse = √41.
As we know, cos θ = Base/Hypotenuse = 5/√41 = 5√41/41.
Because of the 3rd quadrant, we will take, cos θ = - 5√41/41.
Thus, the value of the trigonometric expression cos θ, when (-5, -4) is a point on the terminal side of θ is -5√41/41. Hence, option D is the right choice.
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Kristy asks Lonnie to think of a number, and 3 to it, multiply the sum by 2, and then subtract 6. Let n stand for Lonnie's starting numbers. Which expression represents Lonnie's final number?
Answer:
2(n + 3) - 6 is the expression that represents the final number.
Step-by-step explanation:
-Given the number Lonnie thinks of at the beginning is 'n'-
1) adding 3 to n
sum = n + 3
2) multiply the sum by 2
sum = 2(n + 3)
3) subtract 6
sum = 2(n + 3) - 6.
Answer: 2(n + 3) - 6
Step-by-step explanation:
A wildfire is spreading at an alarming rate. The wildfire begins at a size of 8 square feet. It then doubles its width every x hours, and doubles its length every y hours. After a period of time, the wildfire covers 14,000 square feet.
Which equation correctly represents the area of the wildfire in terms of x and y?
A. 14,000 = 16^xy
B. 14,000 = 16xy
C. 14,000 = 8 ⋅ 2^x+y
D. 14,000 = 8 ∗ 2^xy
The equation [tex]\(14,000 = 8 \cdot 2^{x+y}\)[/tex] correctly represents the area of the wildfire in terms of x and y (option C).
How to find the correct equation for the area in terms of x and y?
The initial size of the wildfire is 8 square feet.
It doubles its width every x hours, so the width grows by a factor of [tex]\(2^{\frac{1}{x}}\)[/tex] each hour.
It doubles its length every y hours, so the length grows by a factor of [tex]\(2^{\frac{1}{y}}\)[/tex] each hour.
The area (A) of a rectangle is given by the formula [tex](A = \text{length} \times \text{width}\))[/tex].
So, after a period of time, the area of the wildfire is given by:
[tex]A = 8 \times 2^{\frac{1}{x}} \times 2^{\frac{1}{y}}[/tex]
Combine the exponents:
[tex]A = 8 \times 2^{\frac{1}{x} + \frac{1}{y}}[/tex]
Now, if the area is 14,000 square feet, we can set up the equation:
[tex]14,000 = 8 \times 2^{\frac{1}{x} + \frac{1}{y}}[/tex]
To make it match one of the given options, we can express 8 as 2³:
[tex]\[ 14,000 = 2^3 \times 2^{\frac{1}{x} + \frac{1}{y}} \][/tex]
Combine the exponents again:
[tex]\[ 14,000 = 2^{3 + \frac{1}{x} + \frac{1}{y}} \][/tex]
So, the correct equation that represents the area of the wildfire in terms of x and y is:
[tex]\[ 14,000 = 8 \times 2^{x+y} \][/tex]
Therefore, option C. [tex]\(14,000 = 8 \cdot 2^{x+y}\)[/tex] is the correct representation.