All categories

2 years ago

The sum of two numbers is 56 . one number is 3 times as large as the other. what are the numbers?

Mathematics

1 answer:

KatRina [158]2 years ago

6 0

x+y=56

x=3y

3y+y=56

4y=56

y=14

x=14*3 =42

numbers are 14 & 42

You might be interested in

In triangle ABC, a = 9, c = 5, and angle B = 120°. Find the measure of angle A to the nearest degree. Show your work.

slamgirl [31]

<u>Answer:</u>

Angle A = 39°

<u>Step-by-step explanation:</u>

We are given that there is a triangle ABC where a = 9, c = 5 and angle B = 120° and we are to find the measure of angle A.

But first we need to find the side b using the law of cosine:

$b^2 = a^2 + c^2- 2a*c*cos(120)$

$b^2 = 81 + 25 - 2*9*5*(-0.5)$

$b=\sqrt{151}$

Now finding angle A using law of cosine:

$cos(A) = \frac{b^2+c^2-a^2}{2b*c}$

$cos(A) = \frac{151+25-81}{2*12.29*5}$

$cos A=0.7730$

$A=39.38$

Therefore, the measure of angle A = 39°.

7 0

3 years ago

Read 2 more answers

A. Do some research and find a city that has experienced population growth.

horrorfan [7]

A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation $N_{t} =N _{0}e^{rt}$
where:
$N(t)$ is the population after $t$ years
$N_{0}$ is the initial population
$t$ is the time in years
$r$ is the growth rate in decimal form
$e$ is the Euler's constant
We now for our investigation that $N(t)=238300$ , $N_{0} =192157$ , and $t=10$ ; lets replace those values in our equation to find $r$ :
$238300=192157e^{10r}$
$e^{10r} = \frac{238300}{192157}$
$ln(e^{10r} )=ln( \frac{238300}{192157} )$
$r= \frac{ln( \frac{238300}{192157}) }{10}$
$r=0.022$
Now lets multiply $r$ by 100% to obtain our growth rate as a percentage:
$(0.022)(100)$ =2.2%
We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that $N(t)=713777$ , $N_{0} =951307$ , and $t=10$ . Just like before, lets replace those values into our equation to find $r$ :
$713777=951307e^{10r}$
$e^{10r} = \frac{713777}{951307}$
$ln(e^{10r} )=ln( \frac{713777}{951307} )$
$r= \frac{ln( \frac{713777}{951307}) }{10}$
$r=-0.029$
$(-0.029)(100)$ = -2.9%.
We just show that Detroit's population has been declining at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

C. Final equation from point A: $N(t)=192157e^{0.022t}$ .
Final equation from point B: $N(t)=951307e^{-0.029t}$
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.

D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations $N(t)=192157e^{0.022t}$ and $N(t)=951307e^{-0.029t}$ and solve for t:
$192157e^{0.022t} =951307e^{-0.029t}$
$\frac{192157e^{0.022t} }{951307e^{-0.029t} } =1$
$e^{0.051t} = \frac{951307}{192157}$
$ln(e^{0.051t})=ln( \frac{951307}{192157})$
$t= \frac{ln( \frac{951307}{192157}) }{0.051}$
$t=31.36$
We can conclude that if Orlando's population keeps growing at the same rate and Detroit's keeps declining at the same rate, after 31.36 years in May of 2031 Orlando's population will surpass Detroit's population.

E. Since we know that the population of Detroit as 2000 is 951307, twice that population will be $2(951307)=1902614$ . Now we can rewrite our equation as: $N(t)=1902614e^{-0.029t}$ . The last thing we need to do is equate our Orlando's population growth equation with this new one and solve for t:
$192157e^{0.022t} =1902614e^{-0.029t}$
$\frac{192157e^{0.022t} }{1902614e^{-0.029t} } =1$
$e^{0.051t} = \frac{1902614}{192157}$
$ln(e^{0.051t} )=ln( \frac{1902614}{192157} )$
$t= \frac{ln( \frac{1902614}{192157}) }{0.051}$
$t=44.95$
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit.

8 0

3 years ago

Please anyone help

serg [7]

5.46 to 3 sig figs means the range is {5.455,5.465} and 17.74 means the range {17.735,17.745}.
p=q²/r has a maximum value when q=5.465 and r=17.735 and a minimum value when 5.455 and r=17.745.
So the range of p is 1.6769 to 1.6840. When we have 2 decimal places we get p=1.68 which accommodates the maximum and minimum values of the range. So 2 decimal places is a suitable degree of accuracy, or we could say 3 significant figures.

7 0

2 years ago

Read 2 more answers

A researcher conducted a paired sample t-test to determine if advertisements were viewed more in the morning (before noon) or in

Natalija [7]

Answer:

b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).

Step-by-step explanation:

The critical value for one tailed test is t ∝(7) > 1.895

A one tailed test is performed to test the claim that advertisements were viewed more in the morning (before noon) or in the evening (after 5pm)

The null and alternative hypotheses are

H0: μm = μe vs Ha μm > μe

where μm is the mean of the morning and μe is the mean of evening.

The calculated value of t = -1.152587077 which is less than the critical region hence the null hypothesis cannot be rejected .

P(T<=t) one-tail 0.143458126 > 0.05

If two tailed test is performed the critical region is t Critical two-tail 2.364624252

and the calculated t value is -1.152587077 which again does not lie in the critical region .

Hence μm = μe or μm ≤ μe

P(T<=t) two-tail 0.286916252 > 0.025

Therefore

b. No, there was no difference between Morning (M= 32), and Evening (M=40.625), (t [7] = 1.15, p > .05).

Option b gives the best answer.

6 0

2 years ago

Which is a way to break the irregular figure into shapes

STALIN [3.7K]

Answer:

1 parallelogram and 1 rectangle

Step-by-step explanation:

ajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhvdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjhajkdfalksjdfhhsldfjhaskdhflksjdhfaljhfieufhlkjdsfkaljhfkajhlifkajhfalkjh

8 0

2 years ago

Read 2 more answers