A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard would be able to eat the entire population. The equation is 7x = 3x + 4.
Explain to the biologist how she can solve this on a graph using a system of equations.
Answer:
(-1.307, 0.079), (1, 7)Step-by-step explanation:
Given equation:
7ˣ = 3x + 4To solve this, express each side of the equation as different function and find the intersection of graphs of those functions:
y = 7ˣy = 3x + 4As per graph, the solution is:
(-1.307, 0.079), (1, 7)Break into two parts
y=3x+4y=7^xNow graph and find the solution
Which of the following sets of side lengths could produce a triangle? SELECT ALL THAT APPLY. (7TH GRADE MATH)
A) 3,6,9
B) 13, 5, 6
C) 5, 5, 10
D) 5, 7, 11
E) 4, 4, 4
Answer: C)5,5,10
Step-by-step explanation:
Construct the following shapes:
A concave hexagon with one angle of 45⁰ and one side length of 4 cm.
A trapezoid ABCD where AB = 8cm, and CD = 4 cm. What is the measure of each internal angle (use your protractor to measure)?
[To be solved on grid paper]
A sphere and a cone have the same volume. The sphere has a radius x and height y. The cone has a radius of 1/2x. Find the height of the cone in terms of y.
Answer:
h = 16x
Step-by-step explanation:
The volume of a sphere and a cone is same such that,
[tex]V_s=V_c\\\\\dfrac{4}{3}\pi r^3=\dfrac{1}{3}\pi R^2h[/tex]
We have, r = x, R = (1/2)x, h= ? (height of the cone)
So,
[tex]\dfrac{4}{3}\pi x^3=\dfrac{1}{3}\pi (\dfrac{x}{2})^2h\\\\4x^3=\dfrac{x^2}{4}h\\\\h=\dfrac{16x^3}{x^2}\\\\h=16x[/tex]
So, the height of the cone is equal to 16x.
Which phrase from the text most clearly explains the main idea of the third paragraph? (5 points)
Memory uses general knowledge
Other memories and other stories
When telling a friend about the event
Rather than the actual participant
Answer:
is there an image of the story?
Answer:
A. Memory uses general knowledge
I deeply apologize if it's wrong but that's just what I think.
Also, I just took the test with this question and I'm pretty sure I got it correct.
PLEASE HELP. no links.
Answer:
45 i think
Step-by-step explanation:
4.
Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
A. inverse variation; xy = 20
B. direct variation; y = 20x
C. direct variation; [tex]y=\frac{20}{x}[/tex]
D. inverse variation; [tex]\frac{y}{x} =20[/tex]
Answer: A. inverse variation; xy = 20
ANSWER
Step-by-step explanation: Brainly
B) xy=20
Inverse because it is of the form y=k/x, intuitively you can see that as x increases y decreases, hence "inverse variation".
...............................................................................................................................................
Answer:
Option B is correct
Inverse variation , xy = 20
Step-by-step explanation:
Inverse variation states:
If
then the equation is in the form of:
or
xy = k ....[1]
As per the statement:
Given the data:
x : 2 4 8 12
y : 10 5 5/2 5/3
Let any value of x and y to find k:
x = 4 and y = 5
Substitute in [1] we have;
⇒20 = k
or
k = 20
then we get;
xy = 20
Check:
Substitute x = 12 and y = 5/3
⇒ true.
Therefore, the the data in the table represent a inverse variation and an equation to model the data in the table is, xy = 20
How Roses Got Their Thorns.
Many years ago ,in the land of Lucia, there was a beautiful queen named —————. Queen —————lived in a century old castle surrounded by a forest on the north side,a maze on the east side, a fountain on the west side and a rose garden on the south side. Her private living quarters had a large window facing the south. Each morning she would start her day by opening her window to the sweet aroma coming from her rose garden. She had a special servant whose only job was to care for her roses. Queen ———- rose garden was her favorite place and every day she would spend time there relaxing and caring for her lovely blooms. Her garden was world famous and people came from miles around to visit and enjoy their beauty and lovely fragrance.
One day she notice there were fewer blooms than usual and she became concerned. She thought her servant was not doing his job,so she obtained a new gardener. The blooms continued to disappear and then she noticed that plants were starting to disappear. Finally, she had some of her servants start guarding the roses. They discovered that the visitors were picking and digging up her roses. She loved sharing the beauty of her garden with her subjects but she had to find a way to protect her roses . Several attempts were tried to protect the. She had a fence built,but the people knocked it down. She had a wall built but they climbed over it. She put guards around but the guards could not be everywhere and the people continued to take her roses . Finally, she sought the advice the local wizard . His solution was to put a curse on the roses. Queen———-agreed to a curse as long as it did not affect the aroma or the beauty of them Beginning that day the loveliest of flowers started growing thorns and still do. P
Answer:
Queen Marie Antoinette
Perimeter is used to find the
A: distance from a ceiling to the floor
B: amount of blacktop on a playground
C: amount of floor space covered by a carpet
D: distance around the edge of a swimming pool
Answer:
D: distance around the edge of the swimming pool
Step-by-step explanation:
perimeter is the distance around something.
Step-by-step explanation:
Perimeter is used to find out the boundary of any thing or figure...So,
Option D Distance around the edge of a swimming pool. is correct answer.
Find the area of the semicircle
Answer:
3.92yd
Step-by-step explanation:
pi r²÷2
pi 2.5²÷2=3.92
A boat covers 25 km upstream and 44 km downstream in t hours. Also, it covers 15 km upstream and 22 km downstream in 5 hours. Find the speed of the boat in still water and that of the stream.
9514 1404 393
Answer:
boat speed: (7t -95)/(6t² -110t +500)
stream speed: (37t -345)/(6t² -110t +500)
Step-by-step explanation:
The relation between time, speed, and distance is ...
time = distance/speed
The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...
25/(b-s) +44/(b+s) = t
15/(b-s) +22/(b+s) = 5
This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.
Subtracting the first equation from 2 times the second gives ...
2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)
5/(b-s) = 10 -t
5/(10 -t) = b -s
Substituting for b-s in the second equation gives ...
15/(5/(10-t)) +22/(b+s) = 5
30 -3t +22/(b+s) = 5
22/(b+s) = 3t -25
22/(3t -25) = b+s
Adding the equations for the sum and difference of speeds, we get ...
(b-s) +(b+s) = 5/(10-t) +22/(3t -25)
2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))
b = (7t -95)/(6t² -110t +500)
Subtracting the equations for sum and difference of speeds, we get ...
(b+s) -(b-s) = 22/(3t -25) -5/(10 -t)
2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))
s = (37t -345)/(6t² -110t +500)
__
The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.
The speed of the stream is (37t -345)/(6t² -110t +500) km/h.
__
Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.
An engineer is designing a fuel tank in the shape of a cylinder. The tank must have a volume of 3,500 cubic inches. The height of the cylinder must be twice the radius. What is the approximate radius of the cylinder? PLEASE HELP ME!!!! ITS THE TEST FROM PERFORMANCE MATTERS
Answer: 24 inches
Step-by-step explanation:
Let the radius be represented by x
Therefore, the height will be = 2×x = 2x
Volume of a cylinder = πr²h
where, Volume = 3500
π = 3.14
r = x
h = 2x
We then slot in the values into the formula
Volume = πr²h
3500 = 3.14 × x² × 2x
3500 = 3.14 × 2x²
2x² = 3500 / 3.14
2x² = 1114.65
Divide through by 2
x² = 1114.65 / 2
x² = 557
x = ✓557
x = 23.6 = 24 approximately
The radius is 24 inches
What is 2x^3 if x=3?
Answer:
2^3 when x=3
2*3^3
6^3
6*6*6
36*6
=192Step-by-step explanation:
HURRY PLEASE I DONT WANT TO FAIL
Answer: 62
Step-by-step explanation: In the red empty spot, the #5 would go there and in the blue spot the #6 would go there. 8x2=16 and 16+16= 32: t=This is for the to rectangle shapes on both sides. Now for the square in the middle, since the red spot is 5 and the blue is 6, 5x6= 30. So, 30+32=62.
If the student is a domain/inout and the hair color is the range/output how is these two set of relation not a function?
Answer:
A function is a relation that maps inputs from a set called the domain, into outputs from a set called the range.
Such that each input can be mapped into only one output.
So for example, if we have a relation that maps the input 2 into two different values:
f(2) = 4
f(2) = 8
Then this is not a function.
In the case of the problem, we have a student as the input, and the hair color as the output.
So we will have something like:
f(student) = blond
And if this student decides to change his/her hair color to red?
Then the function becomes:
f(student) = red
So for the same input, we had two different outputs, which means that this is not a function.
We also could have the case where a given student has two colors (Californian for example)
Where again, we would see two different outputs for one single input.
The drama department was considering two options for the winter production. They used the following equations to represent the profit, y, they
would make from the sale of tickets, x, minus the costs.
Option A: y= 5x - 1500
Option B: y = 3x - 500
Which graph correctly shows the point after which Option A becomes more profitable than Option B?
Answer:
Graph D is correct
Step-by-step explanation:
This is complicated because the scales on the x-axis and y-axis are not the same. Graph D has the correct y-intercepts and the correct slopes. The solution is x = 500, where the two lines intersect.
Help me please!!! I’ll mark brainliest!!
Answer:
all the answers are c on that test my teacher did that same exact test
Step-by-step explanation:
mark brainliest!
Rectangle PQRS is rotated 90° counterclockwise about the origin.
Answer:
Can you please provide more information about the rectangle? Do you have a graph or some points?
Answer:c
Step-by-step explanation:
Tanya has a $50 gift card to spend on Amazon. She wants an airpod case cover for $12.
She also wants to buy some bracelets for $9.50 each. How many bracelets can she buy
without going over?
Answer:
4
Step-by-step explanation:
She can buy 4 bracelets because 4 x 9.50 = 38 + 12 = 50. So 4 would fit her budget perfectly without going over. LEt me know if you find any fault in my answer! Thanks! Have a good day! Hope this helps!
What is the slope of the line?
Answer:
2
Step-by-step explanation:
To find slope just compare two points on a graph then put them into a fraction like so y₁ - y₂/x₁ - x₂
Which is an equation in point-slope form for the given point and slope? Point: (1.9); Slope: 5
A: y-1=5(x+9)
B: y-9=5(x+1)
C: y-9=5(x-1)
D: y+9=5(x-1)
answer is D
from y-y'=m(x-x') ,where m is slope and x' and y' are our points then ;
given are;
m=5, x' =1 and y' =9
By substituting our given
y-9=5(x-1)
given g(x)=2(x-4)+7 find 2g(-6)
Answer:
g(x)=2(x-4)+7
2g(-6)=2[2(-6-4)+7]
=2[2(-10)+7]
=2(-20+7)
=2(-13)
=-26
NO FILES I WILL MARK YOU IF RIGHT I ASKED THIS FIVE TIMES ALL I GET IS SCAM FILES!!!!!!!!!!!!! PLZZZZZZ HELP
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $6500 to rent trucks plus an additional fee of 175.25 for each ton of sugar. The second company charges $5696 to rent trucks plus an additional fee of 225.50 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same?
Answer:
14 tons
$3,860.50
Step-by-step explanation:
Let x = the amount of sugar transported.
First company:
The cost is $3157 truck rental plus $50.25 per ton of sugar.
Total cost = 3157 + 50.25x dollars
Second company:
There is no charge for truck rental, but it costs $275.75 per ton of sugar.
The total cost is
275.75x
When the two costs are the same, then
275.75x = 3157 +50.25x
225.5x = 3157
x = 14 tons
The total cost is 275.75*14 = $3,860.50
pls dont put links or I'll report ty
x < 9
_
Step-by-step explanation:
I am not sure if this is correct. but i think the answer is x with closed circle so that will mean underlined.
[tex](x + y) ^{2} [/tex]
Answer:
Step-by-step explanation:
(x + y) 2
x2 + 2xy + y2
Answer:
Step-by-step explanation:
This is an example of "the square of a binomial." There is a formula for such cases;
(a + b)^2 = a^2 + 2ab + b^2 (worth memorizing)
Thus, our (x + y)^2 = x^2 + 2xy + y^2
What is the area of the base ? / / / / /
Answer:
area of base = 20 in²
Step-by-step explanation:
area of base = 2 x 10 = 20 in²
HELP DUE IN 10 MINS! Solve for x in the parallelogram below:
x=??
Answer:
x = 10
Step-by-step explanation:
The opposite angles in a parallelogram are congruent, then
5x - 9 = 3x + 11 ( subtract 3x from both sides )
2x - 9 = 11 ( add 9 to both sides )
2x = 20 ( divide both sides by 2 )
x = 10
Slope-intercept equation from graph
Find the equation of the line.
⚠️WILL GIVE BRAINLIEST⚠️
What is the length of AD??
Answer:
d
Step-by-step explanation:
hiiiiiiii
75250 tickets were available for an international cricket match. 62% of the tickets were sold
within a day. How many tickets are left?
Answer:
46655
Step-by-step explanation:
[tex]75250 \cdot \frac{62}{100} = 46655[/tex]