The sum of two numbers is 85. If four times the smaller number is subtracted from the larger number, the result is 5. Find the two numbers.
The larger number is
The smaller number is

9514 1404 393

Answer:

  sin(tan^-1(x)) = x/√(x² +1)

Step-by-step explanation:

We know that for an angle in a right triangle...

  Tan = Opposite/Adjacent

and

  Sin = Opposite/Hypotenuse

so we can let Opposite = x and Adjacent = 1. The Pythagorean theorem tells us that ...

  Hypotenuse² = Opposite² + Adjacent² = x² +1

Then the sine of the angle is ...

  sin(tan^-1(x)) = x/√(x² +1)

Answer:

a or b

Step-by-step explanation:

the pictures are a little hard to tell apart but im my opinion go for a because its the closest

Answer:

A.)

Step-by-step explanation:

I took the test.

Answer:

The number is 6.

Step-by-step explanation:

[tex]4x-13=x+5\\3x-13=5\\3x=18\\x=6[/tex]

Answer:

Factors are 1,2,3,4,5,6,10,12,15,20,30,60

Step-by-step explanation:

Hope this helps

Factors refers to those numbers which muntiplied that no.here, numbers that muntiply 60 are 1,2,3,4,5,6,10,12,15,20,30,60.

thus these numbers are factors of 60.

Answer:

y=8 and x=8 ✔3. the check is meant to be square root symbol lol

y = 2/3 x - 2

Or

y + 2 = 2/3 ( x )

Answer:

y= 2/3x - 2

hope this helps :)

Answer:

60 cm^3

Step-by-step explanation:

The equation to find the volume for a rectangular prism is length times width time height.

So just multiply 5 times 3 times 4

V=(5)(3)(4)

V=60

Answer:

60cm^3

Step-by-step explanation:

w=3cm

h=4cm

l=5cm

[V=whl]

V=3×4×5=60

9514 1404 393

Answer:

  7/10

Step-by-step explanation:

In order to make the units cancel, they must be the same. There are 4 quarts in 1 gallon, so 40 quarts = 10×4 quarts = 10×(1 gal) = 10 gal.

Then the ratio is ...

  (7 gal)/(10 gal) = 7/10

Answer:

D.To teach a lesson

Step-by-step explanation:

Hope it helps you

Answer:

8.33 hours

Step-by-step explanation:

120-45 = 75

75 ÷ 9 = 8.33

Step-by-step explanation:

the number formed by subtracting 1 from the smallest 7 digit number is largest 6 digit number.

Answer:

8. -2a+14

9. w=3/2

Step-by-step explanation:

8.

The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.

For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as

-2 * a + (-2) * (-7) = final answer

= -2 * a + 14

We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out

9.

Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in

(-2/3)w = 4-5 = -1

Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get

w = (-3/2)

To check this, we can plug (-3/2) for w in our original equation, so

(-2/3) * (-3/2) + 5 = 4

-1 + 5 = 4

4 = 4

This works!

Answer:

Step-by-step explanation:

210=2x3x5x7

280=2x2x2x5x7

360=2x2x2x3x3x5

Answer:

210= 2×3×5×7

280=2×2×2×5×7

360=2×2×2×3×3×5

common factors=2×2×2×3×5×7=840

uncommon factors=3

L.C.M=Common factors× uncommon factors

L.C.M=840×3

L.C.M=2520

Step-by-step explanation:

i hope it will be helpful

plzz mark as brainliest

Answer:

in five (5) ways a committee can be formed from 7 men and 5 women

Answer:

true

Step-by-step explanation:

what else would it be. that is exactly the reason why we have constants.

Step-by-step explanation:

G=2m

m+G=30

m +2m =30

3m=30

m=10

Answer:

AD = 8/3 units

Step-by-step explanation:

Based on the angle bisector theorem, angle bisector BD divides AC into AD and CD such that they are proportional to AB and CB.

This implies:

AB/AD = CB/CD

AB = 8

CB = 10

Set AD equal to x

AD = x

CD = 6 - x

Substitute the values

8/x = 10/(6 - x)

8(6 - x) = 10(x)

48 - 8x = 10x

48 - 8x + 8x = 10x + 8x

48 = 18x

48/18 = 18x/18

8/3 = x

x = 8/3

AD = 8/3 units

Answer:8/3

Step-by-step explanation:

I just took the quiz

Answer: 0, 5

Step-by-step explanation: a translation is just like sliding the object in this case a triangle/point on the triangle. so the point it is at now is -2, 5 because it is 2 to the left and 5 up. and if you go to the right 2. then you are adding 2 to the x value. so -2 +2 = 0. which is how you get 0, 5

Answer:

Devaughn = 31, Sydney = 25

Step-by-step explanation:

(56-6)÷2= 25

So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31

ATQ

[tex]\\ \sf\longmapsto x+x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x=56-6[/tex]

[tex]\\ \sf\longmapsto 2x=50[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto x=25[/tex]

Answer:

Step-by-step explanation:

3

Answer:

y=-3x+4

Step-by-step explanation:

The y intercept is 4 because the line crosses the y axis at the 4 tic mark

The slope will be -3 because the y decreases by 3 every time the x incerases by 1

y=mx+b

y=-3x+4

Answer:

C) (f+g)(x)= 3x^3-2x^2+10x-12

Answer:

Total Distance = 20km = 20 × 1000 = 20,000 m

Distance walked = 800m

Distance travelled by cycle = 20,000 - 800 = 19,200m

Percentage of journey by cycle = (distance travelled by cycle ÷ total distance) × 100

Percentage of journey by cycle = (19200 / 20000) * 100

Percentage of journey by cycle = 96%

9514 1404 393

Answer:

  5.423 miles

Step-by-step explanation:

Let x represent the distance to run. Then the remaining distance to the point that is closest to the island is (6-x) miles. The straight-line distance (d) to the point x from the island is given by the Pythagorean theorem:

  d² = 1² +(6 -x)² = x² -12x +37

  d = √(x² -12x +37)

The total travel time is the sum of times running and swimming. Each time is found from ...

  time = distance/speed

  total time = x/4 + d/2 = x/4 +(1/2)√(x² -12x +37)

__

The total time will be minimized when its derivative with respect to x is zero.

  t' = 1/4 +(1/4)(2x -12)/√(x² -12x +37) = 0

Multiplying by 4 and combining fractions, we can see the numerator will be ...

  √(x² -12x +37) +2x -12 = 0

Subtracting the radical term and squaring both sides, we get ...

  4x² -48x +144 = x² -12x +37

  3x² -36x +107 = 0

The quadratic formula tells us the smaller of the two roots is ...

  x = (36 -√(36² -4(3)(107)))/(2(3)) = (36 -√12)/6 ≈ 5.423 . . . mi

You should run 5.423 miles west to minimize the time needed to reach the island.

__

A graphing calculator solves this nicely. The attached graph shows the time is a minimum when you run 5.423 miles.

Answer:

5(3x+4y)

Step-by-step explanation:

I believe your answer is D

Answer:

option(d)

Step-by-step explanation:

5/12 + 4/12 + 3/12 + 2/12 + 1/12

=> (5+4+3+2+1)/12

=> 15/12 ≠ 10/12

To solve this question, the real rate of return formula is used, and we apply the data given in the exercise into the formula to find the real rate of return.

Formula for the real rate of return:

[tex]R = \frac{1 + N}{1 + i} - 1[/tex]

In which N is the nomial rate and i is the inflation rate, as decimals.

A certificate of deposit offers a nominal interest rate of 2.5 percent annually.

This means that [tex]N = 0.025[/tex]

Inflation is 1 percent

This means that [tex]i = 0.01[/tex]

What is the real rate of return:

Now we apply the formula:

[tex]R = \frac{1 + 0.025}{1 + 0.01} - 1[/tex]

[tex]R = 1.0149 - 1[/tex]

[tex]R = 0.0149[/tex]

0.0149*100% = 1.49%

Thus, the real rate of return is of 1.49%.

For another example of a similar problem, you can check https://brainly.com/question/20164190

Answer: One side could be 18 and the other side will be 33.

Step-by-step explanation:

One way of setting up the inequality is: Side #2 + Side #3 > Side #1

[tex]2x-3+x>18\\3x-3>18\\3x>18+3\\3x>21\\x>7[/tex]

Another way of setting up the inequality is: Side #1 + Side #3 > Side #2

[tex]18+x>2x-3\\18+3>2x-x\\x<21[/tex]

Final way of setting up the inequality is: Side #1 + Side #2 > Side #3

[tex]18+2x-3>x\\15>x-2x\\15>-x\\x>-15[/tex]

Therefore, we have the range for our value of x, which is between 7 and 21. Any possible value between works. Negative measurements are rejected. One of the sides would equal the x-value, while the other side would equal the value of 2x-3.

Answer:

0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.

Step-by-step explanation:

The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Approximation:

We have to use the mean and the standard deviation of the hypergeometric distribution, that is:

[tex]\mu = \frac{nk}{N}[/tex]

[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]

In this question:

88 + 88 = 176 students, which means that [tex]N = 176[/tex]

88 non-history majors, which means that [tex]k = 88[/tex]

44 students are selected, which means that [tex]n = 44[/tex]

Mean and standard deviation:

[tex]\mu = \frac{44*88}{176} = 22[/tex]

[tex]\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88[/tex]

What is the probability that at least 22 of the 44 students selected are non-history majors?

Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21.5 - 22}{2.88}[/tex]

[tex]Z = -0.17[/tex]

[tex]Z = -0.17[/tex] has a p-value of 0.4325

1 - 0.4325 = 0.5675

0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.