Question 2 An exponential model y = a.6 passes through the points (0,9) and (3,243). What are the values of a and b?
Answer:
a = 9, b = 3
Step-by-step explanation:
The exponential function is
y = a [tex]b^{x}[/tex]
Find a and b by using the points it passes through
Using (0, 9 ) then
9 = a [tex]b^{0}[/tex] ( [tex]b^{0}[/tex] = 1 )
a = 9
y = 9 [tex]b^{x}[/tex]
Using (3, 243 ) then
243 = 9b³ ( divide both sides by 9 )
27 = b³ ( take the cube root of both sides )
b = [tex]\sqrt[3]{27}[/tex] = 3
y = 9[tex](3)^{x}[/tex] ← exponential equation
1.Let x, y be any two numbers that satisfies the conditions x ≠0, y ≠0, and x 1
xy 0
2. A pickup truck that can hold up to 3000 pounds is carrying a big machine that is 300 pounds and a few smaller ones that each weigh 60 pounds.
At least how many small machines can you fit so that it will not exceed the weight limit of the truck?
(1 point)
no more than 50
no more than 45
no less than 50
no less than 45
3. It usually takes Claude 40 minutes driving at 48 miles per hour to go from home to work. But due to road maintenance today, Claude has to take a detour, which makes the trip 8 miles longer than usual. What is the minimum speed Claude should travel so that he can reach the destination in less than 48 minutes?
56 miles per hour
30 miles per hour
64 miles per hour
50 miles per hour
4. Raphael is timing how fast he can do a series of 5 math questions, aiming to complete them in less than 20 minutes. He has done 3 questions so far, with each of them taking 3 minutes to complete.
On average, how much time does Raphael have on each remaining question so he can reach his goal?
Raphael has no more than 5 minutes and 50 seconds to complete each remaining question.
Raphael has less than 5 minutes and 50 seconds to complete each remaining question.
Raphael has less than 5 minutes and 30 seconds to complete each remaining question.
Raphael has no more than 5 minutes and 30 seconds to complete each remaining question.
5. A retail store is buying a 500 count for a device and another 200 count for another version of the same device that costs $100 less than the original. What is the maximum cost of the original device, given that the store did not go over the budget of $155,000?
no more than $150
less than $250
less than $150
no more than $250
Answer:
1, no more than 50
2. 50 miles per hour
3.Raphael has no more than 5 minutes and 30 seconds to complete each remaining question.
4. less than 4250
Step-by-step explanation:
what is the surface area of the triangular prism represented by the net below?
9514 1404 393
Answer:
608 cm²
Step-by-step explanation:
The central rectangle is 10+12+10 = 32 cm high and 16 cm wide. Its area is ...
A = LW = (32 cm)(16 cm) = 512 cm²
Each of the two triangles on the side have an area of ...
A = 1/2bh = (1/2)(12 cm)(8 cm) = 48 cm²
There are two triangles and one rectangle, so the total surface area is ...
total area = rectangle area + 2 · triangle area
total area = 512 cm² +2(48 cm²) = 608 cm²
What is one important thing you have to do before solving a word problem?
Answer:
read the answer through and collect all the information you can
what is the possibility that a randomly selected person is on the swim team
Express the probability as a percent rounded to the nearest tenth of a percent
Answer:
What is the probability that a randomly selected person is on the swim team?
28 out of 67 people are on the swim team
so that's 28/67
41.7910448% round to the nearest tenth
41.8% is the answer.
Step-by-step explanation:
A set of 4 consecutive odd integers has a sum of 216. What are the integers?
Answer:
Hope this helps!!
Step-by-step explanation:
So the four consecutive odd integers are: 51 , 53 , 55 and 57 .
If the first integer is n, then the other three are n+2,n+4 and n+6
and we have:
216=n+(n+2)+(n+4)+(n+6)=4n+12
Subtract 12 from both ends and transpose to get:
4n=204
Divide both sides by 4
to get:
n=51
So the four consecutive odd integers are:
51,53, 55 and 57.
help me answer 2/9 divided by 1/6
1.33333
Step-by-step explanation:
Don't worry it checks out.
Answer:
1.33333333333
Step-by-step explanation:
4(m - 3) = 36 PLEASE STEP BY STEP EXPLANATION IN WORDS!
Answer: 12
Step-by-step explanation:
simple math
Maria wants to measure the length of her thumb using a nonstandard unit. Which object would be the best for Maria to use?
A stapler
B chalkboard eraser
C book
D paper clip
Find the slope of the following given points (-3, 1) and (5, 17)
Answer:
slope is 2
Step-by-step explanation:
find the change in y and x to then divide them
17-1/5- -3 = 16/8 = 2
Evaluate f(x) =-3x + 7 for x = 2
Answer:
F(x)=1
Step-by-step explanation:
Just add in 2 were x is. f(x)=-3(2)+7 then multiply -3(2) which is -6 then add 7
In which quadrant is the point (–3, 5) located? quadrant I quadrant II quadrant III quadrant IV
Answer:
B
Step-by-step explanation:
just ended the test
Answer: (-3, 5) : Quadrant 2
StartFraction negative 8 (17 minus 12) over Negative 2 (8 minus (negative 2)) EndFraction
Answer:
2
Step-by-step explanation:
i took the test
GJ bisects ∠FGH and is a perpendicular bisector of FH. Triangle F G H is cut by perpendicular bisector G J. Line segments F J and J H are congruent. Angle F G J and J G H are both 30 degrees. What is true of triangle FGH? It is a right triangle. It is an obtuse triangle. It has exactly 2 congruent sides. It has exactly 3 congruent sides.
Answer:
D: It has exactly 3 congruent sides
Step-by-step explanation:
finished quiz on edg2020
Answer:
the answer is D just took the test
Step-by-step explanation:
just took the test
PLEASE HELP, WILL MARK BRAINLIEST !!!
Answer:
- 2
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ - 4, 3 ] , then
f(b) = f(3) = 3² - 3 - 8 = 9 - 3 - 8 = - 2
f(a) = f(- 4) = (- 4)² - (- 4) - 8 = 16 + 4 - 8 = 12 , tus
average rate of change = [tex]\frac{-2-12}{3-(-4)}[/tex] = [tex]\frac{-14}{7}[/tex] = - 2
A bakery mixes cookie dough in large batches. For chocolate chip cookies,10 cups of sugar and 20 cups of flour are needed. Write the ratio of sugar to flour for chocolate chip cookies. Express your answer as a simplified ratio.
Answer:
1 cup of sugar for every 2 cups of flour 1:2
Step-by-step explanation:
The ratio of sugar to flour for chocolate chip cookies, to maintain the same taste, will be 1/2.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
A bakery mixes cookie dough in large batches.
For chocolate chip cookies, 10 cups (2,365.88 ml) of sugar and 20 cups (4,731.76 ml) of flour are needed.
Then the ratio of sugar to flour for chocolate chip cookies to maintain the same taste, will be
Let S be the amount of sugar and F be the amount of the flour.
Then the ratio of sugar to flour will be
S / F = 10 / 20
S / F = 1 / 2
Thus, the ratio of sugar to flour for chocolate chip cookies, to maintain the same taste, will be 1/2.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ5
Leo bought 4 T-shirts and 2 pairs of pants for Php 3 000.00. If the T-
shirts cost Php 300.00 each, find the cost of each pair of pants.
1) What is asked?
2) What are the given?
3) What operation will be used?
4) What is the hidden question?
5. What is the number sentence?
6. Write the solution:
Answer:
hey
Step-by-step explanation:
An office spends $350 per month on office supplies. The manager
wants the company to decrease office supply costs by 16%. How
much money would that save each month?
А
$334
his
B $54
C $294
D $56
farmers are better than doctors
Answer:
they are both the same
Step-by-step explanation:
farmers give us food and doctors make us healthier
Solve for x.
I need help
Answer:
x = 35
Step-by-step explanation:
The segment from the vertex of the triangle is an angle bisector and divides the opposite side into 2 segments that are proportional to the other 2 sides, that is
[tex]\frac{20}{x}[/tex] = [tex]\frac{8}{14}[/tex] ( cross- multiply )
8x = 280 ( divide both sides by 8 )
x = 35
The sum of the digits of a two digit number is eight the digits are reversed the number increases by 18 find the original number
Answer:
The two digit number is 35.
Step-by-step explanation:
Let xy be the two digit number
According to given statement
[tex]x+y = 8\ \ \ \ Eqn\ 1[/tex]
The place value of xy is 10x+y
Reversing the number will be: 10y+x
It is also mentioned that the new number is previous number increase by 18
So,
[tex]10y+x = 10x+y+18\\10y-y+x-10x = 18\\9y-9x = 18\\9(y-x) = 18\\\frac{9(y-x)}{9} = \frac{18}{9}\\y-x = 2\ \ \ Eqn\ 2[/tex]
From equation 2
[tex]y = 2+x[/tex]
Putting in equation 1
[tex]x+y = 8\\x+2+x = 8\\2x+2 = 8\\2x = 8-2\\2x = 6\\\frac{2x}{2} = \frac{6}{2}\\x = 3[/tex]
Putting x = 3 in equation 1
[tex]3+y = 8\\y = 8-3 = 5[/tex]
xy = 35
Hence,
The two digit number is 35.
Question in picture solve
which inequality matches the graph?
Answer:
The inequality -3x + 2y ≥ 7 matches the graph ⇒ D
Step-by-step explanation:
The slope of the line whose equation is ax + by = c is m = [tex]\frac{-a}{b}[/tex]
From the given graph
∵ The direction of the line is increased from left to right
∴ The slope of the line is positive
∵ The line is solid and the shaded area is over the line
∴ The sign of inequality should be ≥
→ We have only one answer that has a sign of inequality ≥, let us check
its slope
∵ -3x + 2y ≥ 7
∴ a = -3 and b = 2
∵ m = [tex]\frac{-a}{b}[/tex]
∴ m = [tex]\frac{-(-3)}{2}[/tex] = [tex]\frac{3}{2}[/tex]
∴ The slope of the line is positive
∴ The inequality -3x + 2y ≥ 7 matches the graph
If 84 J of work are exerted to pull a wagon, how much force does it take to pull the wagon 7.0 m? Round your answer to the nearest whole number.
It takes N of force to pull the wagon.
Answer:
12N
Step-by-step explanation:
force=workdone/distance
=84/7
=12N
hope it helps
Answer:
12n
Step-by-step explanation:
. A book collector has 425 books,
56% of which were published
prior to 1900. How many books
were published prior to 1900?
Answer:
238
Step-by-step explanation:
all you do is part and whole divide
Please help me with this question asap
Answer:
156 for the first, 14 for the second
Step-by-step explanation:
x = -5 y=4
Plug in (first equation)
(4(4))^2 - (2(-5))^2
(16)^2 - (-10)^2
256-100
156
Second Equation
4y^2-2x^2
Plug in
4(4)^2 - 2(-5)^2
4(16) - 2(25)
64-50
14
Parenthesis make a huge difference
Hope this helps =D
Find f(-3) if f(x) = x 2.
Answer:
...
Step-by-step explanation:
1) Every day, the Clark Pet Store uses 2/3 of a bag of dog food to feed the dogs. How
many days will 4 2/3 bags of dog food last?
BRIANLYEST TO WHOEVER ANSWERS FIRST
Answer:
7 days
Step-by-step explanation:
I'm on crack but I never did it bruh
who mISSES SCHOOL? because i dont rlly...
Not at all, I was doing online school before quarantine started, so this is all normal for me lol
help me pls UoU Uwu
\djjn
Answer:
y = 4x + 14
Step-by-step explanation:
slope-intercept form: y = mx + b
Slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
To write the equation in y = mx + b form, we need to find the slope(m) and the y-intercept(b) of the equation.
To find the slope, take two points from the table(in this example I'll use points (0, 14) and (1, 18)) and input them into the slope formula:
[tex]\frac{18-14}{1-0}[/tex]
Simplify:
18 - 14 = 4
1 - 0 = 1
[tex]\frac{4}{1}=4[/tex]
The slope is 4.
To find the y-intercept, input the values of the slope and one point(in this example I'll use point (1, 18)) into the equation format and solve for b:
y = mx + b
18 = 4(1) + b
18 = 4 + b
14 = b
The y-intercept is 14.
Now that we know the slope and the y-intercept, we can write the equation:
y = 4x + 14