Let's see
y=ab^xCheck coordinates
13.5=ab³-(1)Find a
a=13.5/b³---(2)And
30.375=ab⁵Put value from second one
30.375=13.5b⁵/b³30.375=13.5b²b²=2.25b=1.5Put in second one
a=13.5/b³a=13.5/1.5³a=13.5÷3.375a=4So the equation is
y=4(1.5)^xAnswer:
[tex]y=4(1.5)^x[/tex]
Step-by-step explanation:
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the y-intercept (or initial value)b is the base (or growth factor)x is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Given ordered pairs:
(3, 13.5) and (5, 30.375)
As the y-values are increasing, the function is increasing, so b > 1
Input the given ordered pairs into the general form of the equation:
[tex]\implies ab^3=13.5[/tex]
[tex]\implies ab^5=30.375[/tex]
To find b, divide the second equation by the first:
[tex]\implies \dfrac{ab^5}{ab^3}=\dfrac{30.375}{13.5}[/tex]
[tex]\implies b^2=2.25[/tex]
[tex]\implies b=\pm \sqrt{2.25}[/tex]
[tex]\implies b= \pm 1.5[/tex]
As the function is increasing, b > 1:
⇒ b = 1.5 only
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies a(1.5)^3=13.5[/tex]
[tex]\implies 3.375a=13.5[/tex]
[tex]\implies a=\dfrac{13.5}{3.375}[/tex]
[tex]\implies a=4[/tex]
Therefore, the final exponential equation is:
[tex]y=4(1.5)^x[/tex]
A person has a bag containing quarters and dimes. There are a total of 61 coins in the bag, and the total value of the coins is $10.45.
Answer:
Q+D = 65, multiply both sides by 2525Q + 25D = 162525Q + 10D = 950 subtract to get 15D = 675 D = 675/15 = 135/3 = 45 dimes Q = 65-45 = 20 quarters25(20) + 10(45) = 500+450 = 950
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
e
is congruent with x f is congruent with x and g is congruent with y Step-by-step explanation:
angle E = angle X
angle F = angle Y
angle G = angle Z
hope it helps...!!!
Efficiently solve
A. 30x70+37x70
B. 335x11-135x11
C. 223x87-123x87
D. 3.2x120+16.8x120
E. 555x0.08-545x0.08
F. 3.45x17-1.45x17
G. 0.7x0.7x85
Thanks so Much if you Help me!
Answer:
Step-by-step explanation:
A. 2100+2590= 4,690
B. 3685-1485=2,200
C. 19,401-10,701= 8,700
D. 384+2,016=2,400
E. 44.4-43.6=0.8
F. 58.65-24.65=34
G. 41.65
Line /has a what slope.
1.negative
2.0
3.positive
4.undefined
23) A movie theatre has 900 seats of which 15% are in the balcony. How many seats are NOT in the balcony?
A.
765
B.
90
C.
785
D.
875
Answer:
A.765 seats are not in the balcony
Step-by-step explanation:
if 15% are in the balcony then 85% are not in the balcony so..
900 * 0.85 = 765
Answer:
765
Step-by-step explanation:
900*.15=135
900-135 = 765
. If you have a cube measuring 1 unit on
each side, how many of those cubes
would fit into a space 5 units by 5 units
by 5 units?
Answer:
cubes = (5)(5)(5)
number of cubes =125
to fit
lisa rides her bike 15.25 miles to and from her job each week. How many miles does she bike in all to and from work in 19.5 weeks?
Answer:
297.375 miles
Step-by-step explanation:
Since lisa rides 15.25 miles in 1 week and we are looking for how many miles she rides in 19.5 weeks, we must multiple 15.25 miles by 19.5 because she rides 15.25 miles, 19.5 times.
15.25*19.5=297.375
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
227
Step-by-step explanation:
Since they give you the hypotenuse length of 290in and they ask you to find the length os the adjacent angle, use the cosine to find side b.
So you do tan38=b/290 then calculate.
The true answer is 226.5728 but they ask you to round.
rewrite each equation in exponential form. log 100=2
Answer:
10x^{2} = 100Step-by-step explanation:
Use the definition of a logarithm, logb(x)=y ⟹ by=x, to convert from the logarithmic form to the exponential form.
Hopefully this helps you
- Matthew
Sophia invest money in an account paying simple interest. She invest 100$ and no money is added or removed from the investment. After one year, she has 108. What is the simple percent interest per year ?
Answer:
8%
Step-by-step explanation:
She earned 8 dollars on a 100 dollar investment
8/100 = 8%
The answer is 8%
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: Principal as $100 and return as $108 and t=1
Thus 8=100×1×r /100
r=8%
Hence, The rate of interest is 8%
Learn more about simple interest here:
https://brainly.com/question/25845758
#SPJ2
Rewrite as a single logarithm: 3 log b x+4 log b y
Answer:
log_b x^3y^4
Step-by-step explanation:
see image
will pay the first one that answers this question
Answer:
a. I
b. II
c. IV
3) Solve the equation for x.
10(4x + 4) = 400
A) 2
B) 4
C) 9
D) 18
Answer:
C) 9
Step-by-step explanation:
10(4x + 4) = 400
40x + 40 = 400
40x = 360
x = 9
Answer:
First factor out the expression
(10•4x)+(10•4)=400
40x+40=400
Then solve
40x+40=400
-40 = -40
40x=360
------ ------
40 40
x=9
C) 9
☆anvipatel77☆
•Expert•
Brainly Community Contributor
what is the product of mixed number 2 x 2 7/8?
Answer:
[tex]5\frac{3}{4}[/tex]
----------------------------------------------------------------------------------------------------------
Since we have to convert mixed numbers to fractions, [tex]2\frac{7}{8}[/tex] becomes [tex]\frac{23}{8}[/tex]
And for whole number, add a 1 as the denominator.
[tex]\frac{2}{1}[/tex]
Now, the equation becomes...
[tex]\frac{2~*~23}{1~*~8}[/tex]
[tex]2 * 23 = 46[/tex]
[tex]1 * 8 = 8[/tex]
Convert these two numbers to a fraction.
[tex]46~and~8~-- > ~\frac{46}{8}[/tex]
Simplify 46 over 8 and make it a mixed number.
[tex]\frac{46}{8} -- > 5\frac{3}{4}[/tex]
why is the denominator 4? we had to simplify 8 using its GCF along with 46
the GCF is 2, so simplify using 2. to simplify, divide the number by its GCF.
[tex]\frac{46}{2} = 23\\\\\frac{8}{2} = 4[/tex]
now you have [tex]\frac{23}{4}[/tex]
and that, in mixed number, translates to [tex]5\frac{3}{4}[/tex]
________________________________________________________
Questions?Ask in comments.
Which is the correct option, I’m very confused by this question?
sin2x=
Answer:
The answer is definitely Option A
Ezekiel manages a clothing store. In May, sales were $129,800. In June, sales were $131,975. What was the rate of change?
The rate of change of the sles of the clothing store that Ezekiel manages from May to June is $2,175
What is the rate of change?
Subtraction is the mathematical operation that involves determining the difference between two or more numbers.
Rate of change = sales in June - sales in May
$131,975 - $129,800 = $2,175
To learn more about subtraction, please check: https://brainly.com/question/854115
#SPJ1
Factor the binomial.
4z2 − 25
4z2 − 25 =
[tex]4z^2-25\\\\=(2z)^2-5^2\\\\=(2z+5)(2z-5)[/tex]
An architect drew the blueprint for a new office building. He used a scale in which 1 inch represents 7.5 feet. The floor of an office in the building will have actual dimensions of 14 feet by 24 feet. What will the dimensions on the blueprint be?
A.
105 inches by 180 inches
B.
21.5 inches by 31.5 inches
C.
6.5 inches by 16.5 inches
D.
1.87 inches by 3.2 inches
Since we know the scale factor of 1 inch represents 7.5 feet, we can plug in the dimensions for the scale on which the architect drew.
For 14 feet, we can multiply 14 by 1 inch/7.5 feet to get a product of 1.87 inches. Then, we can do the exact same thing with the other width of the floor, which is 24. 24 × 1/7.5 = 3.2
The final dimensions of the blueprint will be D, 1.87 inches by 3.2 inches.
In the equation 4x4=16, 4 is a:
Answer:
4 is a factor
Step-by-step explanation:
thats what a number being multiplied is called
Help me with this math problem please
Answer:
First Option (-4,-3)
Step-by-step explanation:
x+2y=-10
-y=3x+15
-4+2(-3)=-10
-10=-10
-3=3(-4)+15
-3=-3
A standard number cube is tossed. Find P( greater than 3 or odd).
Answer:
Step-by-step explanation:
P= probablity
P (>3 or odd)
assuming this std. number cube is 1 to 6, then,
greater than 3 is 50%
so we've accounted for 1, 3, 4, 5, 6 on the dice what's left 2 :D
so P( >3 or odd) = 5/6 or 83.3333333333333%
Answergrater than 3
Step-by-step explanation:
What is the probability of landing on an odd number and then landing on a number greater than 7?
Answer:
72%
Step-by-step explanation:
a
It takes 15 minutes to drain a pool containing
45 gallons of water. If a similar pool takes 35
minutes to drain at the same rate, how many
gallons of water are in the similar pool?
Answer:
there is 92.25
Step-by-step explanation:
15x2=30
then you have to find out 5% out of 45 because you need to get 35 not 30.
one day a store sells 14 pairs of jeans . The 14 jeans represents 20% of total number of items sold that day. How many items did the store sell in one day
Answer:
items sold in 1 day = 140
Step-by-step explanation:
14 pairs of jeans = 28 jeans total
the 14 "pair of jeans" repesents 20% of the total = x
28 = 20x/100
2800/20 = x
x = 140
PLS HELP ME I NEED AN A I GIVE 50 POINTS
Answer:
The one on the left shows a proportional relationship between x and y.
Step-by-step explanation:
equation your going to use = y ÷ x or y/x (both mean divide)
2÷4 = 0.5
5÷10 = 0.5
6÷12= 0.5
All have the same answers so that makes it a proportional relationship.
Please see attached photo for problem from my homework set.
Answer: (x - 1)(x - 23)
Step-by-step explanation:
First, we can factor the x² part:
(x)(x)
Next, we will look at the -24x and +23
-> We need two numbers that multiply to 23 and add to -24
-> 23 is a prime number, so we will use 1 and 23
For -24, 1 and 23 must be added together. Since a negative times a negative is a positive, and a negative plus a negative is a positive, we will turn them into -1 and -23.
This gives us a final answer of:
(x - 1)(x - 23)
Answer: (x - 1)(x - 23)
Step-by-step explanation:
attached the picture below of the working...
hope that helps...
Find the surface area of the cylinder. Round your answer to the nearest tenth.
What is the value of x
Answer:
your answer is 20.
Step-by-step explanation:
x^2+4^2=(2+x)^2
If a marble is randomly chosen from a bag thay contains exactly 8 red marbles, 6 blue marbles, and 6 white marbles, what is the probability that the marble will not be white?
Answer: 7/10
Step-by-step explanation:
The probability of an event can be calculated as:
[tex]P(E)=\frac{n(F)}{n(T)}[/tex]
Where n(F) is favorable outcomes and n(T) is total possible outcomes.
The total number of marbles can be obtained as,
8 + 6 + 6 = 20
The probability of marble being white can be calculated as,
[tex]P(W)=\underline{\frac{6}{20}}[/tex]
Now, the probability of the marble not being white can be evaluated as,
[tex]\begin{aligned}P^{\prime}(W) &=1-\frac{6}{20} \\&=\frac{20-6}{20} \\&=\frac{14}{20} \\&=\frac{7}{10}\end{aligned}[/tex]
Therefore, the probability of the marble not being white is 7/10
urgent help please! ^^ <3
Answer:
Lower quartile = 6
Median = 8
Upper quartile = 9
Step-by-step explanation:
If you take away a number from each end of the number set one by one, you will end up with 7 and 9 in the middle. To find the median between two numbers, add them together then divide them by 2.
7 + 9 = 16
16 ÷ 2 = 8
_________________
To find the lower and upper quartiles, split the number set into two where the median is, then, find the median of those two sections.
Lower quartile: 4, 5, 6, 6, 7
Median = 6
-
Upper quartile: 9, 9, 9, 9, 9
Median = 9
So, the median of the whole set is 8, the lower quartile is 6, and the upper quartile is 9.
hope this helps!