Answer: x = 7
Step-by-step explanation:
Which of the three situations given below is best modeled by an exponential function?
I'm not good at math :/
The correct answer is (b) a bacteria culture triples in size every day describes a exponential function.
What is a function?A relation is a function if it has only One y-value for each x-value.
The growth of a population, bacteria culture, or puppy can be modeled by an exponential function if the growth rate is proportional to the current size.
In other words, if the growth rate is constant, then the growth can be modeled by an exponential function.
Out of the three situations given, option (ii) is the only one that has a constant growth rate, since the bacteria culture triples in size every day. This means that the growth rate is constant at 200% per day.
Option (i) has a growth rate that is not constant but increases every year, so it is not best modeled by an exponential function.
Option (iii) also has a growth rate that is not constant, since the puppy grows by a fixed amount of 2 pounds every month regardless of its current weight.
Therefore, the correct answer is (b) a bacteria culture triples in size every day describes a exponential function.
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In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm
Answer:
The length of the legs is 8.64cm and 14.64cm respectively
Step-by-step explanation:
I've added an attachment to aid my explanation.
At different intervals, I'll be making reference to it.
Given
[tex]AB = 17[/tex]
[tex]PAMC = 32[/tex]
[tex]PBMC = 25[/tex]
From the attachment, we have:
[tex]y + z = AB[/tex]
Since, M is the Midpoint
[tex]y = z = \½AB[/tex]
Substitute 17 for AB
[tex]y = z = \½ * 17[/tex]
[tex]y = z = 8.5[/tex]
Also, from the attachment
[tex]v + x + z = PAMC[/tex]
[tex]v + x + y = 32[/tex]
Substitute 8.5 for y
[tex]v + x + 8.5 = 32[/tex]
[tex]v + x = 32 - 8.5[/tex]
[tex]v + x = 23.5[/tex] --------- (1)
Also, from the attachment
[tex]v + w + z = 25[/tex]
Substitute 8.5 for z
[tex]v + w + 8.5 = 25[/tex]
[tex]v + w = 25 - 8.5[/tex]
[tex]v + w = 17.5[/tex] ----------- (2)
Subtract (2) from (1)
[tex]v - v + x - w = 23.5 - 17.5[/tex]
[tex]x - w = 6[/tex]
Make x the subject
[tex]x = 6 + w[/tex]
Apply Pythagoras Theorem:
We have that:
[tex]AB^2 = AC^2 + BC^2[/tex]
The above can be replaced with
[tex]17^2 = x^2 + w^2[/tex] (see attachment)
[tex]289 = x^2 + w^2[/tex]
Substitute 6 + w for x
[tex]289 = (6 + w)^2 + w^2[/tex]
[tex]289 = 36 + 12w + w^2 + w^2[/tex]
[tex]289 - 36 = 12w + 2w^2[/tex]
[tex]253 = 12w + 2w^2[/tex]
Reorder
[tex]2w^2 + 12w - 253 = 0[/tex]
Solve using quadratic equation:
[tex]w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 2[/tex]
[tex]b = 12[/tex]
[tex]c = -253[/tex]
[tex]w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}[/tex]
[tex]w = \frac{-12 \± \sqrt{144 + 2024}}{4}[/tex]
[tex]w = \frac{-12 \± \sqrt{2168}}{4}[/tex]
[tex]w = \frac{-12 \± 46.56}{4}[/tex]
Split:
[tex]w = \frac{-12 + 46.56}{4}[/tex] or [tex]w = \frac{-12 - 46.56}{4}[/tex]
[tex]w = \frac{34.56}{4}[/tex] or [tex]w = \frac{-58.56}{4}[/tex]
[tex]w = 8.64[/tex] or [tex]w = -14.64[/tex]
But length can't be negative
So:
[tex]w = 8.64[/tex]
Recall that: [tex]x = 6 + w[/tex]
[tex]x = 6 + 8.64[/tex]
[tex]x = 14.64[/tex]
Hence, the length of the legs is 8.64cm and 14.64cm respectively
Find the slope of the line passing through the points (3, 8) and (-2,5).
A.3/5
B.13
C.3
Answer:
A
Step-by-step explanation:
(8-5)/(3--2)
3/(3+2)
3/5
Answer:
A. 3/5
Step-by-step explanation:
(3,8) (-2,5)
Use the slope formula
(5-8)/(-2-3) = -3/-5 = 3/5
I am really confused help please????
Answer:
the answer is B
Step-by-step explanation:
Answer:
Its C because think about it
Step-by-step explanation:
When planting her garden, Frida is told the ratio of mulch to fertilizer is 1:6 bags. If she uses 4.5 bags of mulch, how much fertilizer should she use?
Answer:
X = 27 bags
Step-by-step explanation:
Given the following data;
Ratio of mulch to fertilizer = 1:6
Quantity of mulch = 4.5 bags
Let the quantity of fertilizer = x
Therefore,
1 mulch = 6 fertilizer
4.5 mulch = x fertilizer
Cross multiplying, we have
x = 6 * 4.5
x = 27
Therefore, if she uses 4.5 bags of mulch, then she should use 27 bags of fertilizer.
Find the nth term of this number sequence.
1,7,13,19...
Answer:
This sequence is arithmetic, and the next term is 25
Step-by-step explanation:
The common difference of the sequence is 6, so the next term is 19+6=25.
The difference between the consecutive terms is constant => sequence is arithmetic.
7-1=6
13-7=6
19-13=6
Answer:
Step-by-step explanation:
a=1
c.d. d=13-7=6
[tex]a_{n} =a_{1}+(n-1)d\\a_{n}=1+(n-1)6\\a_{n}=1+6n-6\\a_{n}=6n-5[/tex]
Francis has a large vegetable garden that covers 47 of her backyard. Her patio covers 13 of the yard, and the rest is grass. What portion of Francis’s yard is grass.
Answer:
611
Step-by-step explanation:
Length times width
47 times 13 = 611
At the end of a snowstorm, Ethan had 11 inches of snow on his lawn. The temperature then increased and the snow began to melt at a constant rate of 1 inch per hour. Assuming no more snow was falling. How much snow would Ethan have on his lawn after t hours of snow melting?
Answer: your formula is y=-1x+11
Step-by-step explanation: this is because the line decreases which means the slope is negative. 11 is the y-intercept.
Answer:
10 inches
Step-by-step explanation:
11 inches - 1 hour =10
what is the gcf (greatest common factor) of 36 and 45
thx
Answer:
9
Step-by-step explanation:
what is the sum of 9² and 6²
Answer:
117
Step-by-step explanation:
9^2 + 6^2 = 81 + 36
= 117
Answer: 117
Step-by-step explanation: To find the sum of 9² and 6², first you’ll have to find the whole number value of both integers (9² and 6²). Next, in order to do this, multiply 9 x 9 and 6 x 6. (9 x 9 = 81; 6 x 6 = 36). Lastly, add your two sums, being 81 and 36 to give you a final answer or sum of 117.
solve
x4 − 8x2 + 16 = 0
Answer:
x=−2
Step-by-step explanation:
need help plz i will give u a brainliest
Answer:
x = -6
Step-by-step explanation:
let's call the number x.
"five less than"
[expression] - 5
"the quotient of a number and 3"
x/3
x/3 - 5
"is -7"
x/3 - 5 = -7
add 5 to both sides of the equation
x/3 - 5 + 5 = -7 + 5
x/3 = -2
multiply both sides of the equation by 3
x/3 * 3 = -2 * 3
x = -6
Answer:
X = number,
so the expression becomes X/5 - 14
Step-by-step explanation:
x
5
<
4
Explanation:
"Quotient" is the answer to a division.
Let's call the number
x
.
The quotient of a number (
x
) and
5
means
x
5
The quotient we have must be less than 4 , which is written
<
4
So,
x
5
<
4
Plz help me with this question!
Answer:
the answer is y=-1/6x-1
Answer:
You put a 1 in the Green Box
Step-by-step explanation:
The full equation is y=1/6x-1
2(-6+-3)over2 - (-6+-4)
Answer:
28
Step-by-step explanation:
BRAINLIEST PLS I NEEED SO MBAD
15 points!!! HELP. 4 Graph x - 2y > 8
5 Write an inequality for the graph shown.
Inequality
6 All values are greater than or equal to two. Write this statement as an inequality and
represent it on the graph
Inequality
Answer:
4). [tex]y<\frac{1}{2}x-4[/tex] (look at my explanation for how to graph)
5.) [tex]y<\frac{?}{?}x+?[/tex] (look at my explanation for how to get the correct numbers)
6.) [tex]x\geq 2[/tex] (look at my explanation for how to graph)
Step-by-step explanation:
Question 4:
Solving for y:
First it's better if you solve for y then graph, it's easier that way.
[tex]x-2y>8\\-2y>-x+8\\y<\frac{1}{2}x-4[/tex]
As you might notice the greater than sign flipped, that doesn't always happen. It only happens when you are dividing by a negative number.
Graphing the inequality:
When you start graphing you should always start by plotting the y-intercept. Which in this case it's [tex](0,-4)[/tex]. Then starting from that point you would go up 1 unit then right 2 units then plot the new point because the slope is [tex]\frac{1}{2}[/tex]. The 1 would be the up and down as for the 2 it will be the right and left. This goes up 1 and right 2 because it's positive. So you keep going creating new points as you go then when you reached the end of the graph you would go back to [tex](0,-4)[/tex] and do the opposite so you will do down 1 then left 2. When you run out of room you will have to draw a line, but be careful the line has to be dotted because the solid lines are used for the greater/less than or equal to signs. Then make sure to add arrows at each side of the dotted line to indicate that this line is infinite.
Question 5:
I'm very sorry but I can't see the picture since it's a bit blurry. So I'll try to explain how to write the inequality the best I can. So first we need to know the y-intercept it should be the point directly on the y-axis. Then find the slope by seeing how it gets to the next perfect point. I can tell you that the slope will be positive. Also for the sign it's dotted that means the sign is [tex]<[/tex]. So the inequality should look something like this [tex]y<\frac{?}{?}x+?[/tex]. Make sure you have the signs correct too don't change the ones I already put in.
Question 6:
For this one the inequality will look like this [tex]x\geq 2[/tex]. Then for the graph you will plot [tex](2,0)[/tex]. Then make a solid line that goes vertically since the only x-value is 3 the y-value will be changing without the x. Then for the shading you will shade the right side of the line.
The ratio of boys to girls in math classes is 3.5. If there are 130 girls in these classes, how many boys must there be?
Answer:
Required Answer:-The ratio of boys and girls =3:5
Let
Number of boys=3x
Number of girls =5x
According to the question Numbers of girls=130[tex]{:}\longrightarrow[/tex][tex]\sf 5x=130 [/tex]
Now interchange both sides and get x[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {130}{5}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=26 [/tex]
NowThe number of boys=3x
=3×26=78
[tex]\therefore[/tex]Number of boys is 78.
What is the slope of the line that passes through the points (-4,-2) and
(-4,-22)? Write your answer in simplest form.
Answer:-20
Step-by-step explanation:
slope= (y2-y1)/(x2-x1)
= -22-(-2)/(-4-(-4)
= -20/0
what is 90% written as a decimal
Answer:
.9
Step-by-step explanation:
Answer:
.9
Step-by-step explanation:
Coach Gannon Bought 8 Bags Of Sunflower Seeds For The Baseball Game. Each Bag Has 2 1/4 Cups Of Seeds. If Coach Gannon Has 12 Baseplayers On The Team, How Many Cups Of Seeds Can Each Player Have?
PLEASE HELP. 35 points and brainliest. I am SO BAD with proofs and I would be grateful if someone helped me here and explained why the reasoning is what it is. Thank you :)
Geometry Writing Prompt 2
Directions: Determine what reason is missing from the proof. Write one paragraph explaining how you know that’s the correct reason. See the grading rubric for all requirements for writing a paragraph.
Option 1:
Answer:A rubric is a grading tool that describes the criteria, or "what counts," for the assignment. It also describes each of the criteria according to gradations of quality, with descriptions of strong, middling, and problematic student work. The criteria are listed in the column on the left. The numbers in the top row indicate quality, with 3 being the best. The number 0 is something everyone wants to avoid. Students may use the rubric as a check list to determine if the writing meets the criteria of the assignment.
Point Value
2 points
1 points
.5 points
0 points
Topic Sentence
Interesting, original topic sentence, reflecting thought and insight; focused on one interesting main idea.
Clearly stated topic sentence presents one main idea.
Acceptable topic sentence presents one idea.
Missing, invalid, or inappropriate topic sentence; main idea is missing.
Supporting Details
Interesting, concrete and descriptive examples and details with explanations that relate to the topic.
Examples and details relate to the topic and some explanation is included.
Sufficient number of examples and details that relate to the topic.
Insufficient, vague, or undeveloped examples.
Organization and Transitions
Thoughtful, logical progression of supporting examples; Mature transitions between ideas.
Details are arranged in a logical progression; appropriate transitions.
Acceptable arrangement of examples; transitions may be weak.
No discernible pattern of organization; Unrelated details; no transitions.
Style
Appropriate tone, distinctive voice; pleasing variety in sentence structure; Vivid diction, precise word choices.
Appropriate tone; Clear sentences with varied structures; Effective diction.
Acceptable tone; some variety in sentence structures; Adequate diction and word choices.
Inconsistent or Inappropriate tone; Awkward, unclear, or incomplete sentences; Bland diction, poor word choice.
Mechanics
Consistent standard English usage, spelling, and punctuation. No errors.
Some errors, but none major, in usage, spelling, or punctuation. (1-2)
A few errors in usage, spelling, or punctuation (3-4)
Distracting errors in usage, spelling, or punctuation
Topic Sentences ______
Supporting Details and Organization ______
Organization/Transitions ______
Style ______
Mechanics ______
Total Points ______ = grade of ______
*Your instructor will average the scores of both paragraphs to generate your final grade for Assignment #1.
Grade Equivalent:
A = 8 - 10 points
B = 6 -7 points
C = 4 - 5 points
D = 2 - 3 points
F = 0 - 1
Step-by-step explanation:
If the common difference in an arithmetic sequence is 4, and the 20th term is 36, what is the first term?A.-40 B. 76 C. 40 D. 2
Answer:
A. - 40Step-by-step explanation:
[tex]a_n=a_1+d(n-1)\\\\a_{20}=a_1+d(20-1)\\\\36=a_1+4\cdot19\\\\36=a_1+76\\\\a_1=36-76\\\\a_1=-40[/tex]
Tomas is planning out a rail trail using a map with a marked grid. The head of the trail, which has an information kiosk, is located at (3, 0). He moves 1 unit east and 3 units north and places a pin at (4, 3) to represent the location of another information kiosk. He continues to move 1 unit east and 3 units north twelve more times, placing a pin each time. Where will the last pin be placed?
Answer:
Step-by-step explanation:
it is 7.12
Answer:
16,39
Step-by-step explanation:
What is the slope for (2,-1) and (6, -1)
Answer:
[tex]m=0[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (2, -1)
Point (6, -1)
Step 2: Find slope m
Substitute: [tex]m=\frac{-1+1}{6-2}[/tex]Add/Subtract: [tex]m=\frac{0}{4}[/tex]Divide: [tex]m=0[/tex]I think of a number, square it, then subtract the original number. The result is 30. What could the number be
Answer:
[tex] \sqrt{x - x = 30 \\ 6 \times 6 - 6 = 30 \\ } 36 - 6 = 30 \\ 30 = 30 \\ 6[/tex]
6 is the answer
The next two terms of the sequence 4, 7, 10, 13 are ..
16 and 19
15 and 19
15 and 18
16 and 18
In a library where the ratio of men to women is 1 to 1, _____ of the total members are men.
Answer:
half
Step-by-step explanation:
if one out of every two people is a man then half
what is 6.2 divieded by 52.08
Answer:
5/42=0.11904762
Step-by-step explanation:
convert to fraction
31/5 divided by 1302/25
do the reciprocal
31/5 x 25/1302
reduce the numbers with the greatest common facter 5
31 x 5/1302
reduce the numbers with the greatest common factor 31
5/42
turn into decimal
5/42=0.11904762
Bakersville and Greenville are 4 inches apart on a
map. If the scale is 1 in: 105 mi, what is their actual
distance?
Answer:
420 miles
Step-by-step explanation:
1 inch is equal to 105 miles. The amount of inches between the two towns is 4, and 4 inches is 4 times the amount of inches in the scale. If the amount of inches is multiplied by 4, then the amount of miles should be multiplied by 4 too:
105 * 4 = 420
The actual distance is 420 miles.
Hope this helps :)
which ordered pair is a solution of the equation?
Answer:
D
Step-by-step explanation:
try all of them
Solve the following inequality.
8(x+5)≥0
x≤5
x≤−5
x≥−5
x≥5
Answer:
the third one
Step-by-step explanation:
8x + 40 ≥ 0
8x ≥ -40
x ≥ -5