Answer:
x =6.0
The base is 6x = 35.8
The side is 3x = 17.9
Step-by-step explanation:
We can use the pythagorean theorem
a^2 + b^2 = c^2
(6x)^2 +(3x)^2 = 40^2
36x^2 + 9x^2 = 1600
Combine like terms
45x^2 = 1600
Divide each side by 45
45x^2 /45 =1600/45
x^2 =35.555555555
Take the square root of each side
sqrt(x^2) = sqrt(35.555555555)
x =5.96284794 = 6.0
The base is 6x = 6*5.9628479 =35.77708 = 35.8
The side is 3x = 3*5.9628479 =17.88854382= 17.9
Answer:
x = 6.0
3x = 17.9
6x = 35.8
Step-by-step explanation:
Using pythagoras theorem
40² = (3x)² + (6x)²
1600 = 9x² + 36x²
1600 = 45x²
x² = 320/9
x = 5.96284794
3x = 17.88854382
6x = 35.77708764
Find the difference
(2/7x-3) - (5/2+1/5y)
Step-by-step explanation:
Distribute the negative sign:
\(\frac{2}{7} x-3 -5/2-\frac{1}{5}y\)
From the given, we can only find the difference with the integers.
Subtract the integers:
\(\frac{2}{7} x-\frac{1}{5}y-0.5\)
hich linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)
The function with the steepest slope is \(y = 7x - 3\).
The correct answer is C.
The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.
Let's compare the coefficients of x in each of the given functions:
\(y = -8x + 5\)
Slope: -8
\(y - 9 = -2(x + 1)\)
Simplifying, we get \(y - 9 = -2x - 2\)
Rearranging, we have \(y = -2x + 7\)
Slope: -2
\(y = 7x - 3\)
Slope: 7
\(y + 2 = 6(x + 10)\)
Simplifying, we get \(y + 2 = 6x + 60\)
Rearranging, we have \(y = 6x + 58\)
Slope: 6
Therefore, the steepest slope is the \(y = 7x - 3\).
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2. Party Land charges a $125 flat fee for a birthday party with an additional charge of $5.00
for each person attending. Lucy has at most $450 to spend on her party. What is the
greatest number of people that she can have at her party so that she doesn't go over her
budget?
Answer:
She can invite 66 people so 66 x 5 = $330 + 120 = $450
Step-by-step explanation:
A typical tip in a restaurant is 15% of the total bill.if the bill is 60$ what would the typical tip be
Answer:
60(.15)= 9
answer is 9
Step-by-step explanation:
Answer:
Step-by-step explanation:
John has a bank account with $7,362. He decides to invest the money at 4.85% interest, compounded annually. How much will the investment be worth after 9 years? Round to the nearest dollar.
The interest compounded after 9 years is $11,271.22
Data;
Principal = $7,362Rate = 4.85% = 0.0485N = 1time = 9Compound InterestTo solve this problem, we have to find the interest compounded at annual interval here;
\(C.I = P(1+ \frac{r}{n})^n^t\)
Let's substitute the values into the equation and solve.
\(c.i = p(1+\frac{r}{n})^n^t\\ c.i = 7362*(1 + \frac{0.0485}{1})^1^*^9\\c.i = 7362 * 1.531\\c.i= 11,271.22\)
The interest compounded after 9 years is $11,271.22
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Answer:
11,274
Step-by-step explanation:
7,362 * (1.0485)^9
11,274
The graph of y=h(x)y=h(x)y, equals, h, left parenthesis, x, right parenthesis is a line segment joining the points (1,9)(1,9)left parenthesis, 1, comma, 9, right parenthesis and (3,2)(3,2)left parenthesis, 3, comma, 2, right parenthesis.
Drag the endpoints of the segment below to graph y=h^{-1}(x)y=h
−1
(x)y, equals, h, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis.
The graph of the linear function and it's inverse is given at the end of the answer.
The inverse function is: \(h^{-1}(x) = -6x + 55\)
How to find the inverse function?To find the inverse function, we exchange x and y in the original function, then isolate y.
In the context of this problem, first we have to find the function h(x), which is a linear function going through points (1,9) and (3,2), hence the slope is given by:
m = (2 - 1)/(3 - 9) = -1/6.
Then:
y = -x/6 + b.
When x = 1, y = 9, hence we can find the intercept b as follows:
9 = -1/6 + b
b = 54/6 + 1/6
b = 55/6.
Then the equation is:
h(x) = -x/6 + 55/6
Then:
y = -x/6 + 55/6
6y = -x + 55
6x = -y + 55
y = -6x + 55.
Hence the inverse function is:
\(h^{-1}(x) = -6x + 55\)
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Solve the following system of equations.
d + e = 6
d – e = 4
infinite number of solutions
infinite number of solutions
(5, 1)
(5, 1)
no solution
no solution
(3, –1)
(3, –1)
Answer: (5,1)
Step-by-step explanation:
Adding the equations gives 2d=10, and thus d=5.
So, it follows e=1.
Therefore, the solution is (5,1).
The solution is (5,1)
Given that d+e =6 and d-e =4
We need to find the solution of the given equations
Elimination method is used to eliminate a variable in an equation to find the value of another variable
Now here ,
We we will solve the equation i.e
d+e = 6
d-e = 4
Solving this equation We get,
2d = 10
Therefore,
d= 5
Now substituting the value of d in equation d+e =6
therefore,
5+e =6
Therefore e = 1
Hence the solution is (5,1)
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Help plssss i only need this side of the paper left
probability that there was an accident = 7.5
probability that there was an no accident when it snowed = 0.28
probability that there was an accident when it snowed = 0.72
probability that there was an accident when it no snowed = 0.846
According to the given information,
We know that,
Probability is the ratio of number of favorable outcomes and total number of outcomes. it deals with finding out the likelihood of the occurrence of an event.
Therefore,
probability that there was an accident = total accident / total event
= 75/100
= 7.5
probability that there was an no accident when it snowed = 21/74
= 0.28
probability that there was an accident when it snowed = 1-0.28
= 0.72
probability that there was an accident when it no snowed = 22/26
= 0.846
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select all that are integers
9, -17, 1/4, 0, -3.6
Answer:
9,-17,0
Step-by-step explanation:
An integer is a whole number
What is the common difference for the arithmetic sequence?
4.7, 6, 7.3, 8.6, 9.9, …
Answer:
1.3 is the common difference.
Step-by-step explanation:
The combined score of James in Geography, economics and science is 194.He scored twice as many marks in economics as in geography and four more marks in science than economics.find his marks in each of the three subjects
In given word problem James scored 38 in geography , 76 into ecomonoics and 80 in Science.
What is word problem?
Choosing whether two provided expressions are comparable with respect to a set of rewriting identities is the task at hand in a word problem in computational mathematics. There are many other instances as well, with the word problem for groups serving as a typical example.
Let us take ,
E= Marks scored in economics
S=Marks scored in Science
G=Marks scored in Geography
And total mark =194.
Here He scored twice as many marks in economics as in geography,
=> E=2G
four more marks in science than economics.
=> S=E+4=2G+4
Here E+S+G=194
=> 2G+2G+4+G=194
=> 5G+4=194
=>5G=194-4=190
=>G = 38.
Now E=2G=2*38=76
And S = 76+4=80.
Hence James scored 38 in geography , 76 into economics and 80 in Science.
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1. Which one of the following is NOT true about polynomial functions f(x) and g(x) if deg (f) = man * d deg * (g) =n?
A. deg (f + g) = max(m, n)
B. deg (f_{g}) <= m + n
C. If g is a factor of f then deg( f )<= m
D. The deg (f ^ 3) = 3m
The option that is not true about polynomial functions is:
Option D. The deg (f ^ 3) = 3m
How to Interpret the degree of Polynomial functions?For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:
Option A: deg(f + g) = max(m, n)
This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.
Option B: deg(f * g) <= m + n
This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.
Option C: If g is a factor of f, then deg(f) <= m
This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.
D. The deg(f ^ 3) = 3m
This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.
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Mr Rodriguez said he drove 15 miles each day his accountant said he drove about 14 miles
Answer:
he drove 15 miles a day
Step-by-step explanation:
in exploration the answer is in the question
A cold water pipe can fill a swimming pool in 4 hours, and a hot water pipe in 6 hours. If cold water pipe is turned on and hot water pipe is turned on 3 hours later then how long will it take them to fill the pool together?
answer = 5
Step-by-step explanation:
A cold water pipe can fill a swimming pool in 4 hours
And a hot water pipe in 6 hours.
If cold water pipe is turned on and hot water pipe is turned on 3 hours later
6-4 = 2
2+3 = 5
5 answer
Answer:
0.6 of an hour
Step-by-step explanation:
A cold pipe takes 4h hours so we can assume ¼ of our job is done in one hour.
After 3 hours go by with the cold pipe on, we have ¼ of the job left.
Now we have our hot pipe, which takes 6 hours for the entire pool, so we can assume that it has a rate of ⅙ per hour. Now since these two pipes are working together we can add them.
⅙ + ¼ = ⁵/₁₂
Now we divide.
Since at the start 3 hours had gone by with the cold pipe that would have been ¾ of our time so, 1 - ¾ = ¼
¼ ÷ ⁵/₁₂ = ⅗ or 0.6 of an hour
Question 1
You can ride a taxi and pay a flat rate of $25 to go anywhere in the city, or you can pay a
base rate of $15 and $1 per mile. For which trip would it make more sense to pay the base
rate and 1$ per mile?
15 mile trip
9 mile trip
25 mile trip
O 12 mile trip
Answer:
9 mile trip
Step-by-step explanation:
$15 + $15 = $30
$15 + $9 = $24
$15 + $25 = $40
$15 + $12 = $27
$30 > $25
$24 < $25
$40 > $25
$27 > $25
6. The sum of 60 and a number is 89
the number = 29
Explanation:
Let the number = y
The sum of 60 and a number is 89:
sum means addition
The equation:
60 + y = 89
collect like terms:
y = 89-60
y = 29
Therefore, the number = 29
PLZ I NEED HELP ANSWER QUICK
Theres always 180 degrees in a flat line angle thingy you need answers fast so im not looking up what its called but 180-125=55 and then you 55-1=54 then 54/3=18!!!!!
The time needed to complete a job is normally distributed with a mean of 1 hour and standard deviation of 10 minutes. Probability to complete the job in hone hour or more, but less than 70 minutes is:
Answer:
The value is \(P(60 < X < 70) = 0.34134\)
Step-by-step explanation:
From the question we are told that
The mean is \(\mu = 1 \ hour = 60 \ minutes\)
The standard deviation is \(\sigma = 10 \ minutes\)
Generally the 1 hour is equivalent to 60 minutes
Generally the probability to complete the job in one hour or more, but less than 70 minutes is mathematically represented as
\(P(60 < X < 70) = P(\frac{60 - 60 }{10 } < \frac{X - \mu}{\sigma } < \frac{70 - 60 }{10 } )\)
=> \(P(60 < X < 70) = P(0 < \frac{X - \mu}{\sigma } < 1 )\)
\(\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )\)
=> \(P(60 < X < 70) = P(0 <Z < 1 )\)
=> \(P(60 < X < 70) = P(Z < 1) - P(Z < 0 )\)
From the z table (Z < 1) and (Z < 0 ) is
\(P(Z < 1) = 0.84134\)
and
\(P(Z < 0 ) = 0.5\)
=> \(P(60 < X < 70) = 0.84134 - 0.5\)
=> \(P(60 < X < 70) = 0.34134\)
At the grocery store, Mr. Arnett allowed each of his
children to fill their own bag with trail mix for their hike.
The table shows the amount of trail mix for each child.
The trail mix costs $4.50 per pound. How much will
Mr. Arnett pay for all the trail mix?
Answer:
where is the table to help solve this question?
what is the mean,median,mode,range of 14,9,20,5,17,13
The sum of two rational number is -3 .If one of them is-15/7 find the other. step explanation
Sum = -3
First no. = -15/7
Second no. = (-3) - (-15/7)
= -3 + 15/7
= -21/7 + 15/7
= (-21 + 15)/7
= -6/7
The second no. is -6/7.
Answer:
\(\frac{-6}{7}\)
Step-by-step explanation:
Let the other number be 'x'
\(x + \frac{-15}{7} = -3\)
x = \(-3 + \frac{15}{7}\)
\(= \frac{-3*7}{1*7} +\frac{15}{7}\\\\=\frac{-21}{7}+\frac{15}{7}\\\\= \frac{-21+15}{7}\\\\= \frac{-6}{7}\)
Question #3
The letters A, B, D, and R are each written on an Index card and then put into a hat.
If each letter is drawn randomly, what is the probability of drawing the letters B-R-A-D in that order?
A1/4
B1/2
C
1//24
D 1/30
The overall probability of drawing B-R-A-D in that order is 1/24.
Option C is the correct answer.
We have,
The probability of drawing the letters B-R-A-D in that order is equal to the product of the probabilities of drawing each letter in that order.
Since we are drawing without replacement, the probability of drawing the first letter B is 1/4.
Then, the probability of drawing the second letter R is 1/3
(since one letter has already been drawn and removed from the hat).
Similarly, the probability of drawing the third letter A is 1/2 and the probability of drawing the fourth letter D is 1/1
(since all the other letters have already been drawn and removed).
The overall probability of drawing B-R-A-D in that order.
= (1/4) x (1/3) x (1/2) x (1/1)
= 1/24
Thus,
The overall probability of drawing B-R-A-D in that order is 1/24.
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simplify to lowest form.
a. 1/2 + 3/2 = ?
b. 2/5 + 3/5 = ?
Answer:
A= 2 B= 1
Step-by-step explanation:
1/2 +3/2= 4/2 than divide 4/2 by 2 it will give you 2/1 so 2/1 equal 2 because 2 is bigger than 1
2/5 + 3/5 = 5/5 it is 1 because if you divide it by 5 you will get a whole number which is 1
I need help :)dndnns
Answer
ahh nvrm i got it wrong and did not wanna mess u up it is 6 thats the correct answer
Step-by-step explanation:
NEED HELP ASAP 100 POINTS AND WILL GIVE BRAINLIEST!!!
Answer:
area of a deck
A= External area - Internal area
A = length x width
A = ( 44ft x 28ft) - ( 32ft x 16ft)
A = 720ft²
PLS PLS HELP! WILL GIVE BRAINLIEST IF ALL QUESTIONS ARE ANSWERED AND IF THEY’RE RIGHT!
Brad made a graph showing how many students were absent from school every day last week.
Use the graph to answer the questions.
1. List the ordered pairs for the graphed points.
Write your answer in the space below.
2. How many students were absent on day 3? Explain how you know.
Write your answer in the space below.
3. On which day were the greatest number of students absent? How many students were absent that day?
Write your answer in the space below.
4. Is the relation represented by the graph a function? Why or why not?
Write your answer in the space below.
Answer:
1. (1,7),(2.10),(3,5),(4,7),(5,9)
2. There were 5 students absent on day 3. I know because it shows on the graph.
3. Day 2 was the greastes number of studnets absent. There were 10 students absent that day.
4. The relation represented is a function becasue for each x-value there is only one y-value.
Step-by-step explanation:
Round 317,675 to the nearest ten thousand
Answer:320000
Step-by-step explanation:
hi im doing homework i hate i-ready so yea can someone answer this please?
Weight of Omar after 4 weeks is 9.4375 pounds.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement.
For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
Weight of Omar at the time of birth = 8 pound 3 ounces
Weight gained by Omar in 4 weeks = 5 × 4 = 20 ounces
New weight of Omar
= (8 lb 3 ounces) + 20 ounces
= 8 lb + 23 oz
As, we know 16 ounces = 1 pound
23 ounces = 1.4375 pound
Now, total weight of Omar after 4 weeks = 8 lb + 23 oz
≈ 8 lb + (1.4375) lb
≈ 9.4375 pounds
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Quarter of 6 hours and 60 minutes
A quarter of 6 hours is 1.5 hours or 90 minutes, and 60 minutes is equivalent to 1 hour. Therefore, a quarter of 6 hours and 60 minutes is equivalent to 2.5 hours or 150 minutes.
what is a Quarter?A quarter is a unit of measurement that represents one-fourth or 25% of a whole. It is commonly used to divide time, money, and other quantities into equal parts. For example, a quarter of an hour is 15 minutes, and a quarter of a dollar is 25 cents. In terms of fractions, a quarter is equivalent to 1/4 or 0.25. The term "quarter" can also refer to a period of time, such as a school term or business quarter, which typically consists of three months or 13 weeks. The word "quarter" comes from the Latin word "quartus," which means fourth.
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Find the exact value under the given conditions.