Answer:
He drove there at 60 mph, and he drove back at 36 mph.
Step-by-step explanation:
one way distance = d = 270 miles
average speed on way back = s
average speed on the way there = s + 24
time driving there = t
time driving back = 12 - t
average speed = distance/time
distance = speed * time
going there:
270 = (s + 24)t
270 = st + 24t
going back
270 = s(12 - t)
270 = 12s - st
We have a system of equations:
270 = st + 24t
270 = 12s - st
Solve the first equation for t.
t(s + 24) = 270
t = 270/(s + 24)
Substitute in the second equation.
270 = 12s - s[270/(s + 24)]
270 = 12s - 270s/(s + 24)
Multiply both sides by s + 24.
270s + 6480 = 12s^2 + 288s - 270s
12s^2 - 252s - 6480 = 0
Divide both sides by 12.
s^2 - 21s - 540 = 0
(s - 36)(s + 15) = 0
s = 36 or s = -15
The average speed cannot be negative, so we discard the solution s = -15.
s = 36
s + 24 = 60
Answer: He drove there at 60 mph, and he drove back at 36 mph.
Which of the following is most likely the next step in the series?
A.
B.
C.
D.
Answer:
B
Step-by-step explanation:
In each one, they add two arrows that are to the right as much as they possibly can be
evaluate without multiplying directly 998³ x 103³
Answer correctly I will mark them as brainlist
Answer:
1,086,183,741,982,184
Step-by-step explanation:
998^3
= (1,000)^3 - (2)^3 - 3 · 1,000 · 2 (1000 - 2)
= 1,000,000,000 - 8 - 6,000 (998)
= 999,999,992 - 5,988,000
= 994,011,992
103^3
= (100 + 3)^3
= (100)^3 + (3)^3 + 3(100) (3) + (100+3)
= 1,000,000 + 27 + 900(103)
= 1,000,027 + 92,700
= 1,092,727
994,011,992 · 1,092,727
= 994,011,992 · (1,000,000 + 90,000 + 2,000 + 700 + 20 + 7)
= (994,011,992 · 1,000,000) + (994,011,992 · 90,000) + (994,011,992 · 2,000) + (994,011,992 · 700) + (994,011,992 · 20) + (994,011,992 · 7)
= 994,011,992,000,000 + 89,461,079,280,000 + 1,988,023,984,000 + 695,808,394,400 + 19,880,239,840 + 6,958,083,944
= 1,086,183,741,982,184
Can you give me same question like this..please
Q. Amina thinks of a number and subtracts 5/2
from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?
Answer:
Three more than twice a number is equal to four less than the number. find the number.
Suppose TM ≈ GL and angle M ≈ G What additional information is needed to prove triangle MTD≈ GLS by SAS?
Answer:
the second option
Step-by-step explanation:
SAS is side angle side. so, we need 2 sides and the enclosed angle.
since G is the transformed M, and GL is the transformed side TM, that also means L correlates to T and S to D.
for SAS we need both sides of the angles M and G.
TD and SL are not satisfying this condition.
only MD and SG do.
Graph the line for y+1 = - 3(2x - 4) on the coordinate plane.
Help me please i have no idea how to do this
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!! Determine the Value of K in the diagram ( secant lines to circles).
Answer:
6
Step-by-step explanation:
5
Answer:
k = 10
Step-by-step explanation:
Given 2 secants from an external point to the circle, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
2x(2x + kx) = 3x(3x + 5x)
4x² + 2kx² = 3x × 8x = 24x² ( subtract 4x² from both sides )
2kx² = 20x² ( divide both sides by 2x² )
k = 10
PLEASEEEE HELLLLP MEEEE
Answer:
c. 20/21
Step-by-step explanation:
You just multiply straight
3×7 = 21
4×5 =20
21/20 <---- and it can't be reduced farther than this.
Answer:
C. ²¹⁄₂₀
Step-by-step explanation:
OKOKOK DON'T WORRY I'M HERE :)))
--
When multiplying fractions, you multiply the numerators together and then multiply the denominators together.
The numerators here are 3 and 7. Multiply those and you get 21 (7 x 3 = 21).
The denominators here are 4 and 5. Multiply those and you get 20 (4 x 5 = 20).
Then you put the newly-multiplied numerator over the newly-multiplied denominator and you get ²¹⁄₂₀.
Hope this helped!!
need help with this!!
Expand and simplify the following. Show all the steps.
a. -4(a-4)
b. 3a(a+2)
c. 4x - 2(5 - x)
d (x-3)(x+2)
e (x+4)2
a. The expanded and simplified form is: -4a + 16
b. The expanded and simplified form is: 3a^2 + 6a
c. The expanded and simplified form is: 6x - 10
d. The expanded and simplified form is: x^2 - x - 6
e. The expanded and simplified form is: x^2 + 8x + 16
Sure, let's expand and simplify each expression step by step:
a. -4(a - 4)
Step 1: Apply the distributive property (multiply -4 by each term inside the parentheses).
-4(a) + -4(-4)
Step 2: Simplify the terms.
-4a + 16
So, the expanded and simplified form is: -4a + 16
b. 3a(a + 2)
Step 1: Apply the distributive property (multiply 3a by each term inside the parentheses).
3a * a + 3a * 2
Step 2: Simplify the terms.
3a^2 + 6a
So, the expanded and simplified form is: 3a^2 + 6a
c. 4x - 2(5 - x)
Step 1: Apply the distributive property (multiply -2 by each term inside the parentheses).
4x - 2 * 5 + 2 * x
Step 2: Simplify the terms.
4x - 10 + 2x
Step 3: Combine like terms.
6x - 10
So, the expanded and simplified form is: 6x - 10
d. (x - 3)(x + 2)
Step 1: Apply the distributive property (multiply x by each term inside the second parentheses and then multiply -3 by each term inside the second parentheses).
x * x + x * 2 - 3 * x - 3 * 2
Step 2: Simplify the terms.
x^2 + 2x - 3x - 6
Step 3: Combine like terms.
x^2 - x - 6
So, the expanded and simplified form is: x^2 - x - 6
e. (x + 4)^2
Step 1: Apply the square of a binomial formula: (a + b)^2 = a^2 + 2ab + b^2
(x)^2 + 2(x)(4) + (4)^2
Step 2: Simplify the terms.
x^2 + 8x + 16
So, the expanded and simplified form is: x^2 + 8x + 16
To know more about simplify:
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Two consecutive even whole numbers have a product of 360. What is the smaller of the
two number?
Answer:
18
Step-by-step explanation:
To find this answer you would need to use the formula x(x+2) = 360 where x is an even number. This is the formula because any number plus 2 equals the next consecutive, even whole number. If we look at the factors of 360 we see the factors-
360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
If we look through all of the factors 18 and 20 are the only ones with a 2 number difference.
Next, if we plug 18 into the equation:
x(x+2) =360
18(18+2) = 360
324+36 = 360
360 = 360
Since the equation works, x = 18.
What is the value of m in the diagram?
Answer:
81
Step-by-step explanation:
The angles shown are formed on a straight line
Angles formed on a straight line add up to 180
So m + m + 18 = 180
We've just created an equation that we can use to solve for m
So we can now solve for m
m + m + 18 = 180
Combine like terms
2m + 18 = 180
Subtract 18 from both sides
2m + 18 - 18 = 180 - 18
2m = 162
Divide both sides by 2
2m/2 = 162/2
m = 81
Which expression is equivalent to 4 + 36x?
Answer:
A
Step-by-step explanation:
4(1)+4(9x)=4+36x
Question 4 (Essay Worth 10 points)
(05.06 MC)
The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph:
A graph titled Motion of Ant is shown. The graph shows time in seconds on the x-axis and the Distance from Hole in centimeters on the y-axis. The scale on the x-axis is shown from 0 to 7 at increments of 1, and the scale on the y-axis is shown from 0 to 24 at increments of 4. The graph has 3 straight lines. The first line is labeled A and joins ordered pairs 0, 0 and 2, 16. The second line is labeled B and joins ordered pairs 2, 16 and 4, 16. The third line is labeled C and joins ordered pairs 4, 16 and 6, 0.
Part A: Is the graph linear or nonlinear? Explain your answer. (2 points)
Part B: In which segments is the graph increasing, decreasing, and constant? (3 points)
Part C: In your own words, describe the motion of the ant, as shown on the graph. (5 points)
Source
StylesFormat
The motion of the ant is a nonlinear graph;
It has its increasing segment at segment A, the constant segment at B and the decreasing segment at C.
THE TYPE OF GRAPH
The graph has 3 different straight lines, all of which point to different directions.
For a graph to be linear, such graph must have just 1 straight line. This means that the graph is nonlinear.
THE SEGMENTS OF THE GRAPH
The increasing segment of the graph is the segment that points in the upward direction.
In the attached graph, line segment A [i.e. from (0,0) to (2,16)] represents an upward movement of the ant because it points upward.
The decreasing segment of the graph is the segment that points in the downward direction.
In the attached graph, line segment C [i.e. from (4,16) to (6,0)] represents a downward movement of the ant because it points downward.
The constant segment of the graph is the segment that is represented by a horizontal line
In the attached graph, line segment B [i.e from (2,16) to (4,16)] represents the constant segment.
THE MOTION OF THE GRAPH
The ant travels at a constant speed through segment A. It then rests for 2 seconds in segment B and finally travels at a constant speed through segment C.
Learn more about graphs at:
https://brainly.com/question/9348683
Answer: got 100% on test
Step-by-step explanation:
Part A: This graph is not a linear function, because a linear function is a function whose graph is represented by a straight line and this graph does not represent a straight line. Which means it is a nonlinear function, because a non-linear function is any function that is not a linear function.
Part B: In line segment A the graph is increasing. In line segment B the graph is remaining constant. In line segment C the graph is decreasing.
Part C: The ant ran 16 cm up the hill in 2 seconds. It took 2 seconds to find his hole after that, then he ran all the way down his hole in 2 seconds.
during a special seasonal sale,a wholesaler allows retailers trade discount of 15% and 10% for prompt cash payment.Calculate the cash price of an article which is marked 115 cedis
The cash price of the article is 88 cedis.
In this question, the article has a price, but paid in cash, there are two discounts.
Price of 115 cedis.Discount of 15%, thus, 1 - 0.15 = 0.85 is paid, that is, the price is multiplied by 0.85.Discount of 10%, thus 1 - 0.1 = 0.9 is paid, that is, the price is also multiplied by 0.9.Thus, the cash price is:
[tex]P = 115\times0.85\times0.9 = 88[/tex]
The cash price of the article is 88 cedis.
A similar question is given at: https://brainly.com/question/14738783
Please enter the missing number: 4, 5, 8, 17, 44, ?
Answer:
81
Step-by-step explanation:
from 4 to 5,the difference is 1 ,and when you multiply by 3, then add 3 to 5 ,it gives you 8 ,to get 17,I multiple 3by 3 and add the answer to 8 ,and the same continues upto when you get the final answer which is 81.
difference is just multiplying the previous difference with 3 and add it with the previous number .
Which is the angle of depression from b to c
1.)<2
2.) <3
3.) <1
4.)<4
<2
Step-by-step explanation:
that the answer. because it below par
PLZZ HELP !!!
If two functions, f(x) and g(x), are inverse of each other, then the:
(select all that apply)
- range of f(x) is the same as the domain of g(x)
-domain of f(x) is the same as the domain of g(x)
-domain of f(x) is the same as the range of g(x)
- range of f(x) is the same as the range of g(x)
Due to employee safety negligence at a nuclear waste facility, 2000 tons of a radioactive element is spilled into the nearby pond. The half-life of the radioactive element is 36 days. In order to be declared safe for swimming, based on its size and the amount of water, there must be less than 100 tons of the material found in the pond. How long, to the nearest day, until it is safe to swim again?
How long, to the nearest day, until it is safe to swim again will be 156 days
Let x represent number of day until it is safe to swim again
First step
=2000 *1/2^x
100=2000 *0.5^x
0.05=0.5^x
Second step
Log 0.05=xLog 0.5
Log 0.05/L0g 0.5=x
x=36 days* Log 0.05/L0g 0.5
x=36 days*43.22
x=156 days
Inconclusion How long, to the nearest day, until it is safe to swim again will be 156 days
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Luis dispone de una cantidad de dinero de 25,000 RD$ para ponerlos en el banco a plazo fijo con un interés de un 1.7% al cabo de 8 meses, ¿Cuánto dinero posee Luis si no ha gastado nada? *
Answer:
Luis's balance = $25,283.33
Step-by-step explanation:
Given the following data;
Principal = $25,000Interest rate, R = 1.7 %Time = 8 monthsTo find how much money Luis will have;
First of all, we would have to convert the value of time in months to a year.
Conversion:
12 months = 1 year
8 months = X year
Cross-multiplying, we have;
12 * X = 8
X = 8/12
X = 2/3 years
To find the simple interest, we would use the formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is the simple interest.P is the principal.R is the interest rate.T is the time measured in years.Substituting the values into the formula, we have;
[tex] S.I = \frac {25,000 * 1.7 * \frac {2}{3}}{100} [/tex]
[tex] S.I = \frac {28333.33}{100} [/tex]
S.I = $283.33
Luis's balance = S.I + Principal
Luis's balance = 283.33 + 25000
Luis's balance = $25,283.33
can y’all help me out
Answer:
B: y = {-13, -5, 3, 15}
Step-by-step explanation:
Let's plug each x-value into this equation: f(x) = 4x + 3
Domain: {-4, -2, 0, 3}
First, let's start with -4:
f(x) = 4x + 3
y = 4x + 3
y = 4(-4) + 3
y = -16 + 3
y = -13
Next, let's do -2:
f(x) = 4x + 3
y = 4x + 3
y = 4(-2) + 3
y = -8 + 3
y = -5
After that, let's do 0:
f(x) = 4x + 3
y = 4x + 3
y = 4(0) + 3
y = 0 + 3
y = 3
Finally, let's do 3:
f(x) = 4x + 3
y = 4x + 3
y = 4(3) + 3
y = 12 + 3
y = 15
Now that we have all our y-values, let's set up the range:
Range (y-values): {-13, -5, 3, 15}
As you can see, the only answer choice that includes this range is B;
{-13, -5, 3, 15}.
Function expressed by the formula y=-0.5x. Is there a value of x for which
y=-150? If there is such a value, compute it.
Answer:
x=300
Step-by-step explanation:
STEPS FOR SOLVING LINEAR EQUATION
−150=−0.5x
Divide both sides by −0.5.
−0.5
−150
=x
Expand
−0.5
−150
by multiplying both numerator and the denominator by 10.
−5
−1500
=x
Divide −1500 by −5 to get 300.
300=x
Swap sides so that all variable terms are on the left hand side.
x=300
Hope this helped!
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Which of the following statements is correct about the data set 2,4,6,8,10,12,14,16?
A. The data set has a mode that is not in the data set
B. The data set has a median that is not in the data set
C. The data set has the same median and mode
D. The data set has an interquartile range of 9
Answer:
A. The data set has a median that is not in the data set
Step-by-step explanation:
The median of the data set is the middle most number because there is an even amount of number its 8+10/2 or 9 and that is not in the data set. There is no mode because no number is repeated. The IQR is 12+14/2-4+6/2 or 8 so that means the correct answer is a.
PLEASE HELP ME OUT I NEED IT RIGHT NOW!! :(((
Help plz and thanks
Lena is asked to write an explicit formula for the graphed geometric sequence.
On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).
What value, written as a decimal, should Lena use as the common ratio
Answer:
Common Ratio = 2.5
Step-by-step explanation:
Given
Points: (1, 1), (2, 2.5), (3, 6.25)
Required
Determine the common ratio
The points can be rewritten as:
x --- f(x)
1 ---- 1
2 --- 2.5
3 ---- 6.25
The data under the x column are the domain of the function and in this case, they are not needed;
To calculate common ration, Lena should use data in function f(x) column
Common ratio is calculated by dividing a term by the previous term;
Hence;
Common Ratio = 2.5/1 or 6.25/2.5
Common Ratio = 2.5 or 2.5
Notice that, the results are the same;
Hence, the usable common ratio is 2.5
Answer: 2.5 or "C"
Step-by-step explanation: this is right on the edge i just did the test.....Hope this helps :D
Planes X and Y and points C, D, E, and F are shown.
Which statement is true about the points and planes?
• С
The line that can be drawn through points C and D is
contained in plane Y.
O The line that can be drawn through points D and E is
contained in plane Y.
O The only point that can lie in plane X is point F.
O The only points that can lie in plane Y are points D
and E.
D
E
.
Mark this and retum
Save and Exit
Next
Submit
Answer:
6
Step-by-step explanation:
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!
Answer:
B, pi
Step-by-step explanation:
The sine wave shown above has two waves until it reaches 2 pi, making the period of the sine graph 2pi divided by the two waves, making the answer pi.
Given 4,7,10,13. Calculate the 20th term.
Answer:
61
Step-by-step explanation:
to calculate the 20th term you use the formula
Tn=a+(n-1)d where a stands for the first term,n the number of terms and d the common difference.in this case the first term is 4 the common difference is 3 cause they were adding 3 to go to the next term.. therefore the solution will be:
Tn=4+(20-1)3
=4+19×3
=4+57
=61
the 20th term is 61
I hope this helps
BONUS: Solve this problem by using the Guess And Check strategy.
I'm thinking of a number. If you multiply it by 4, then subtract 10, and finally add 15,
you get 53. What number am I thinking of?
Answer:
12
Step-by-step explanation:
Let number you are thinking be x
According to problem;
4x-10+15=53
4x+5=53
4x=48
×=12
