[tex]\dfrac 27 >b +\dfrac 57\\\\\implies 2 > 7b +5~~~;[ \text{Multiplying both sides by 7}]\\\\\implies 2-5>7b\\\\\implies -3>7b\\\\\implies -\dfrac 37 >b\\\\\implies b<-\dfrac 37\\\\\\\text{Interval,}~ \left(-\infty, -\dfrac 37 \right)[/tex]
Full explanation and answers on these 2 questions please. Also only answer if u know what ur doing.
Step-by-step explanation:
Q3
25 - (x-8)²/4 = [100 - (x-8)²]/4
[100 - (x²- 16x + 64)]/4
(100 - x² + 16x - 64)/4 = (-x² + 16x + 36)/4
(36 + 16x - x²)/4 = (36 - 2x + 18x - x²)/4
[2(18 - x) + x(18 - x)]/4 = [(2 + x)(18 - x)]/4
....proved
Q4
3(ax + 7) - 2(x + b) = 4x + 29
expanding,
3ax + 21 - 2x - 2b = 4x + 29
3ax - 2x + 21 - 2b = 4x + 29
Comparing terms; x terms,
3ax - 2x = 4x
3a - 2 = 4
3a = 6
a = 6/3
a = 2
constant terms,
21 - 2b = 29
21 - 29 = 2b
2b = -8
b = -8/2
b = -4
.... proved
Write and evaluate algebraic expressions
Answer:
9b+10s
Step-by-step explanation:
you are trying to find an expression for total cost after an unknown amount of hours. you need to multiply the number of hours (defined as b and s in this example) by the cost per hour given ($9/hr for the bike and $10/hr for the scooter).
this would result in the following expression: total cost=9b+10s
Alec invested $1500 in an account with annually compounded interest. The account earns 4% annual interest. How much will Alec have in his account after 4 years?
Answer:
He will have $1,754.79 in his account after 4 yearsStep-by-step explanation:
We can use the compound interest formula to find how much money he will have after 4 years:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex] ;
where
A= final amount
P= initial amount
r= interest rate
n= number of times interest applied per time period
t= number of time periods elapsed,
so from the given information, we know that 1500 is our initial amount, so P= 1500.
Annual interest means once a year, so n= 1, and the interest rate is 4%, so r= 4% or 0.04
and we are asked to find the amount in his account after 4 years, so t= 4
Now, all we need to do is plug in these values for each of the variables and solve.
[tex]A= 1500(1+\frac{0.04}{1} )^{(1)(4)}[/tex]
and we get
A= $1,754.79
IF CAR A TRAVELS AT 45 MI/HR CAR B LEAVES 15 MINUTES LATER TRAVELING AT 60 MI/HR WHEN WILL B CATCH UP TO A
PLEASE HELP
solve for x?
In a cookie jar,
1
5
of the cookies are chocolate chip and
1
2
of the rest are peanut butter. What fraction of all the cookies is peanut butter?
Which tape diagram shows the cookies that are chocolate chip?
All cookies
Chocolate
chip
All cookies
Chocolate
chip
All cookies
Chocolate
chip
Excellent!
Which tape diagram shows the cookies that are peanut butter?
All cookies
Chocolate
chip
Peanut
butter
All cookies
Chocolate
chip
Peanut
butter
All cookies
Chocolate
chip
Peanut
butter
Good work!
Use the tape diagram to solve.
well, a WHOLE is 1, which we can split in many fractions, say 5/5, 10/10 or 999/999 and so on.
we know 1/5 of the jar is chocolate chip, and there's the rest, well, the Whole jar in 5ths have to be 5/5, if we take away 1/5 from 5/5, the "rest" is 5/5 - 1/5 = 4/5.
now, we also know that 1/2 of the "rest" is peanut butter, or namely that 1/2 of 4/5 is peanut butter, how much will that be? let's divide 4/5 by 2
[tex]\cfrac{4}{5}\div 2\implies \cfrac{4}{5}\div \cfrac{2}{1}\implies \cfrac{4}{5}\cdot \cfrac{1}{2}\implies \cfrac{4}{10}\implies \cfrac{2}{5}[/tex]
What is 14ab+10a written in factored form?
Answer:
2a(7b+5)
Step-by-step explanation:
yeah-ya....... right?
[(-4 2/7) x (-18)] x (-3 8/9) x (-1)
Answer:
300
Step-by-step explanation:
[(-4 2/7) x (-18)] x (-3 8/9) x (-1)
= [-30/7 x -18] x -35/9 x -1
= 540/7 x -35/9 x -1
= -300 x -1
= 300
Answer:
check if the question I used is right or not
What Is the answer
Plz it's urgent
for the answer I think it is 2 cm
the answer : 10 cm :>
Use the long division method to find the result when 12x3 + 4x2 - 23x + 10 is
divided by 3x – 2.
-
Refer to attatchment.
Answer:
4x2+4x-5
Step-by-step explanation:
Hopes this helps
Plz markas brainliest
3/5 * 5/7 / 3/14 - 2/5
Answer:
3/5*5/7*14/3-2/5
8/5...
In order to solve the following system of equations by elimination, which process creates opposite coefficients to eliminate the y variable?
2x + y = 5
x + 4y = -7
A. Multiply the first equation by 4
B. Multiply the second equation by 2
C. Multiply the first equation by -4
D. Multiply the second equation by -2
Answer:
C. Multiply the first equation by -4
Step-by-step explanation:
Hi there!
In order to eliminate the y values, we would have to find a number in which the sum of the top y value and the bottom y value would equal 0. In this case, the bottom y value is equal to +4 (the +4y), so we would have to find the number that would add to make that 0, which is -4. Since the y value for the top equation is 1, all we have to do is multiply the equation by -4 so that our y value is equal to -4y and the y can be eliminated.
I hope this helps!!
Carter goes out to lunch. The bill, before tax and tip, was $19.55. A sales tax of 3% was added on. Carter tipped 15% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answer:
$3.02
Step-by-step explanation:
Convert the Percentage to decimals:
3% / 100% = 0.03
15% / 100% = 0.15
3% / 0.03 part:
19.55 * 0.03 = 0.5865
19.55 + 0.5865 = 20.1365
OR, since it was "adde on" you can just use 1.03:
19.55 * 1.03 = 20.1365
15% / 0.15 part:
20.1365 * 0.15 = 3.020475
Round to nearest cent: $3.02
---
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If 3 people share 5 pizzas , how much pizza does each person get
Answer:
1 2/3
Step-by-step explanation:
5 pizzas divided by 3 people = 1 2/3
A box contains 2 red marbles, 3 white marbles, 4 green marbles, and 1 blue marble. Two marbles are drawn at random without replacement. Find the probability of selecting a white marble, then a red marble.
7. Which of the lists of three lengths cannot form a triangle?
7,7,20
13,13, 20
13,13,13
7,7,7
7,13,13
Answer:
7,7,20 I think
Step-by-step explanation:
7+7 is less then 20
Ashley completes 3 homework assignments in 50 minutes. At this rate, how many minutes will it take her to complete 9 homework assignments?
Answer:
144
Step-by-step explanation:
divide 50 by 3 and then multiply by 9
HELP ASAP I don't understand
Answer:
No
Step-by-step explanation:
These are the artists of each subject, not the general function of each genre.
Brainliest for
Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.
7h – 5(3h – 8) = –72
Which statement is true about Pieter’s solution?
1. It cannot be a fraction or decimal because the depth of the well is a whole number.
2. It must be a positive number since it represents a number of hours.
3. It must be a negative number because the depth is below sea level.
4.It cannot be greater than –72 because that is the depth of the well.
Answer:
Step-by-step explanation:
Is this the entire question? Some of it makes no sense without a diagram or something.
To get rid of A you actually have to solve the equation.
7h – 5(3h – 8) = –72 Remove the brackets
7h - 15h + 40 = - 72 Combine the like terms
- 8h + 40 = - 72 Subtract 40 from both sides
- 8h = -112 Divide by -8
h = 14
Well the depth is a whole number so A is true.
We don't know anything about time. But the answer is positive.
C is false because B is true.
We don't know exactly what the depth of the well is.
I would pick A, but you need the entire question.
HELP ASAP PLEASE!!!!
Answers:
c = 7d = 5=========================================================
Explanation:
For equation A, I'll transform the right hand side into a similar form as the left side. Throughout the steps below, the left hand side stays the same.
[tex]\sqrt{448x^c} = 8x^3\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{(8x^3)^2}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{3*2}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}*7x}\\\\\sqrt{448x^c} = \sqrt{64*7x^{6+1}}\\\\\sqrt{448x^c} = \sqrt{448x^{7}}\\\\[/tex]
Therefore, c = 7
Notice that 7/2 = 3 remainder 1. The quotient 3 is the exponent for the term outside the root for [tex]8x^3\sqrt{7x}[/tex] while the remainder 1 is the exponent for the x term inside the root.
---------------------------------------
We do the same idea for equation B.
[tex]\sqrt[3]{576x^{d}} = 4x\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{(4x)^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3*9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64*9x^{3+2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{576x^{5}}\\\\[/tex]
This must mean d = 5
Note: 5/3 = 1 remainder 2, which means [tex]\sqrt[3]{x^5} = x^1\sqrt[3]{x^2} = x\sqrt[3]{x^2}[/tex]
What is an equation of the line that passes through the points (5, 2) and (−5,−6)?
An auto insurance company classifies each motorist as "high risk" if the motorist has had at least one moving violation during the past calendar year and "low risk" if the motorist has had no violations during the past calendar year. According to the company's data, a high-risk motorist has a 50% chance of remaining in the high-risk category the next year and a 50% chance of moving to the low-risk category. A low-risk motorist has a 90% chance of moving to the high-risk category the next year and a 10% chance of remaining in the low-risk category. In the long term, what percentage of motorists fall in each category? (Round your answers to two decimal places.)
high-risk category %
low-risk category %
The percentage of motorists falling in each category, in the long term, are as follows:
High-risk category = 70%
Low-risk category = 30%
Data and Calculations:
Risk Profile Categories of Motorists
High Risk Low Risk
Probability of remaining
in the same category 50% 10%
Probability of moving to another
category 50% 90%
Probability a motorist falling in the high-risk category = (50% x 50%) + (50% x 90%)
= 25% + 45%
= 70%
Probability a motorist falling in the low-risk category = (50% x 50%) + (50% x 10%)
= 25% + 5%
= 30%
Thus, the probability of a motorist falling in the high-risk category is 70%, while the probability of a motorist falling in the low-risk category is 30%.
Learn more about probability here: https://brainly.com/question/24756209
48a^21 b^5
——————-
16a^21 b^4
Answer:
3b
Step-by-step explanation:
How many ounces of juice would you need for 5 ounces of berries
Answer: 4oz
Step-by-step explanation:
If f(x) is an exponential function where f(4.5) = 16 and f(9.5) = 60, then find
the value of f(15), to the nearest hundredth.
The value of f(15), to the nearest hundredth is 253.88
The standard exponential equation is given as:
y = ab^xf(x) = ab^xIf f(4.5) = 16, then;
16 = ab^4.5 ..............1
Similarly, if f(9.5) = 60, then:
60 = ab^9.5 ........................... 2
Dividing both equations will give:
60/16 = ab^9.5/ab^4.5
60/16 = b^9.5-4.5
60/16 = b^5
3.75 = b^5
b = 1.3
Get the value of a. Recall that;
60 = ab^9.5
60 = a(1.3)^9.5
60 = 12.09a
a = 60/12.09
a = 4.96
Get the value of f(15)
f()15 = 4.96(1.3)^15
f(15) = 4.96(51.18)
f(15) = 253.88
Hence the value of f(15), to the nearest hundredth is 253.88
Learn more on exponential functions here: https://brainly.com/question/12940982
Let f(x)=x* + 14x and g(x) = 6 - X. Find the domain off f + g. Determine the domain of f + g.
[tex]\begin{cases} f(x) = x^4+14x\\ g(x) = 6-x \end{cases}\qquad \qquad h(x) = f(x) + g(x) \\\\\\ h(x) = (x^4+14x)+(6-x)\implies h(x) = x^4+14x-x+6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill h(x) = x^4+13x+6~\hfill[/tex]
now, if we graph h(x), Check the picture below, we can see that horizontally the line keeps on moving towards the left, going going and going towards -infinity, and it also keeps on moving towards the right, going going and going towards +infinity, and since the horizontal area used by the function is the domain of it, the domain for h(x) will be (-∞ , +∞).
-16-|-2-4|+7 please solve this for me and explain. i would really appreciate it.
Answer:
-15
Step-by-step explanation:
-16 -|-6| +7
-16 - 6 + 7
= - 15
Absolute value is just taking the positive value of a number.
Step-by-step explanation:
-16-(-2-4)+7=
-16-(-6)+7=
-16+6+7=
-16+13=
-3
Simplify 4.510. (25 points)
a
4.51
b
1
c
0
d
−1
Answer:
A-4.51
Step-by-step explanation:
I was going to ask to what place but then I saw all the others wouldn't make sense.
pls help anyone know dis
Answer:
1st one:5≥x>-infinity
2nd one :5<x<+infinity
3rd one :5>x>- infinity
In solving the following system of equations, how many equations do you need to multiply in order to use the method of elimination?
Equation 1: −5x−20y=−15 Equation 2: 2x + 8y = 6
A. Two
B. None
C. One
Give the solution to the system above
A. No solution
B. (3, 7)
C. IMS
D. ( -2, 5)
Answer:
i think its a and d
Step-by-step explanation: