======================================================
Explanation:
x and y are the two numbers
The product of those values is 1856, so xy = 1856
The sum is 90, so x+y = 90. Solve for y to get y = 90-x
Plug this into the first equation
xy = 1856
x(90-x) = 1856
90x-x^2 = 1856
0 = x^2-90x+1856
x^2-90x+1856 = 0
Now use the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-90)\pm\sqrt{(-90)^2-4(1)(1856)}}{2(1)}\\\\x = \frac{90\pm\sqrt{676}}{2}\\\\x = \frac{90\pm26}{2}\\\\x = \frac{90+26}{2} \ \text{ or } \ x = \frac{90-26}{2}\\\\x = \frac{116}{2} \ \text{ or } \ x = \frac{64}{2}\\\\x = 58 \ \text{ or } \ x = 32\\\\[/tex]
If x = 58, then,
y = 90-x
y = 90-58
y = 32
So one pair of values is (x,y) = (58,32)
We see that x*y = 58*32 = 1856
If x = 32, then,
y = 90-x
y = 90-32
y = 58
Showing (x,y) = (32,58) is the other solution. But this is just a mirror copy of the first solution. Effectively we're saying the same thing.
The two numbers 58 and 32 multiply to 1856, and they add to 90.
The difference in the two values is 58-32 = 26 which is the final answer.
------------------------
In summary,
58*32 = 1856
58+32 = 90
58 - 32 = 26
Answer:26
Step-by-step explanation:
x+y=90
xy=1856
x*(90-x)=1856
-x^2 +90x -1856=0
or x^2 -90x +1856=0
Using quadratic equation
(x-58)*(x-32)=0
x=58, y=32
58-32=26
Liam solved the equation 72=8⋅b. His work is shown. What error did Liam make?
For which value of p will the equation 6x – 5 = 6x + p have an infinite number of solutions?
A. 5
B. 0
C. -10
D. -5
Answer:
the answer is b
Step-by-step explanation:
Can anyone help me with this i need help quick
Answer:
C
Step-by-step explanation:
y=mx+n m is slope if slopes are perpendicular m1.m2=-1
(2/3) . (-3/2) = -1
m1=2/3
m2=-3/2
y=(2/3)x-3 m=2/3 n= -3
y=(-3/2)x+2 m = -3/2 n = 2
5(x+2) - 3 = 2x + 7 + 3x *
One Solution
No Solution
Infinitely Many Solutions
5x + 27x - 10 = 8(4x +10)
One Solution
No Solution
Infinitely Many Solutions
Divide. Express your answer in simplest form. ○14 ○ 49 ○98 ○28
Answer: 49
see below for work
Answer:
gang gang
Step-by-step explanation:
What is the inequality of y-2x<=-3
(39×5) to siplifiy please help
Answer:
195
Step-by-step explanation:
you just muliply
Answer:
The answer is 175! :)
I recommend searching or creating a times table for yourself, they are incredibly handy! Easy to print off or write down. :))
Step-by-step explanation:
Manny must choose between a pack of four 6.5-ounce containers of yogurt for $3.61 or three 8-ounce containers at $1.27 each. Which is the better buy? Complete the explanation. If necessary, round to the nearest cent.
Answer: Three-8 ounce containers
Step-by-step explanation: 3 x 1.29 divided by 0.6= $6.45 for three 8-ounce containers
4 x 3.77 divided by 0.6= $15.08
12(x-6)and 14(x+14).
plz help
Answer:
138 and 210?
Step-by-step explanation:
Solve the following expression: (9 x 10) - (30 + 30). Show all steps taken.
Answer:
First multiply each brackets
90-60
30
Step-by-step explanation:
Answer:
9 x 3= 27 and 30 + 30= 60.. so 60- 27= 33, but if you want to do 27- 30.. it would be -33.
Step-by-step explanation:
Hope that answers your question!
what is 3 divided by 57.6
Answer:
0.0520833333 is the answer
Answer:
0.05208333333 (reoccurring)
Step-by-step explanation:
Simple bus stop division (:
X - 2
x2-2x + 3
4.
x + 3
x + 3
Answer:
The equation is likely (x2 -2x -3)/(x+2) and to simplify you can do polynomial synthetic division or long division. Using long division because it works in all cases:
________
x+2√x2 -2x -3 how many times does x go into x2 , x times
x - 4 ______
x+2√x2 - 2x -3 multiply x by x + 2 and create the next row
-(x2 )
-4x - 3 bring down the -3 and repeat first step. how many times does x go into -4x, -4 times
-(-4x - 8) multiply x + 2 by -4
5 (this is the remainder but it must be in the form 5/(x+2)
so the answer is x - 4 + 5/(x + 2). Hopefully, this is what your teacher considers "simplified".
Step-by-step explanation:
Copied this from wyzant.com.
Please answer i wanna get this over with h ^-2 / h ^4
Answer:
= h^-6
Step-by-step explanation:
When dividing powers you subtract them (indices rules)
--> -2 - 4 = -6
Hope this helps, please mark as brainliest
A rectangular pool has a length of 200 ft. You're building a model. Using a scale
factor of 1725, what is the scale length of your model? *
Answer:
1.4 inches.
Step-by-step explanation:
Given that the length of the pool = 200 ft.
Scale factor = 1725.
As,
[tex]\text{Scale factor }=\frac{\text{Original length}}{\text{Scaled length}}[/tex]
So,
[tex]\text{Scaled length} = \frac{\text{Original length}}{\text{Scale factor}}[/tex]
By using the given values, we have
{Scaled length} [tex]= \frac{200}{1725} ft.=0.116 ft.[/tex]
As 1 foot = 12 inch,
So, scaled length = 0.116 x 12 = 1.4 inches.
Hence, the scale length of the model = 1.4 inches.
PLEASE HELP!!!!!
What is the result when the number 59 is decreased by 7%?
Answer:
= 59 - (59*0.07)
= 59 - 4.13
= 54.87
Answer:
The result would be 54.87
What is the value of 15/2+I?
Answer:
First, make the denominators
15/2+2/2
Then, add
17/2
If you want it in decimal points
8.5
Step-by-step explanation:
I hope I explained well, please give me brainliest
Examine circle O, where chords AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ are congruent.
Point P lies on AB and point Q lies on CD.
Angles APO and DQO are right angles.
The diagram as described in the problem.
Which congruence statement is true?
A.) QD≅QO
B.) OP≅AB
C.) CD≅AP
D.) OP≅OQ
The answer is D.) OP≅OQ
I hope this is the right graph
Determine the sample size required to estimate a population mean to within 10 units given that the population standard deviation is 60. A confidence level of 90% is judged to be appropriate.
Answer: 98
Step-by-step explanation:
Formula to find sample size if population standard deviation is known:
[tex]n=(\dfrac{z^c\times\sigma}{E})^2[/tex] , where [tex]\sigma=[/tex]population standard deviation, [tex]z^c[/tex] =Critical z-value for confidence level, E= Margin of error.
Given: [tex]\sigma=30,\ \ \ E=10[/tex]
Critical z-value for 90% confidence = 1.645
[tex]n=(\dfrac{1.645\times60}{10})^2\\\\=(1.645\times6)^2\\\\=9.87^2\\\\=97.4169\approx98[/tex]
Required minimum sample size = 98
Sleep habits of New Yorkers. New York is known as the city that never sleeps". A random sample of 25 New Yorkers were asked how much sleep they get per night. Statistical summaries of these data are shown below. The point estimate suggests New Yorkers sleep less than 8 hours a night on average. Is the result statistically signicant? n x s min max25 7.73 0.77 6.17 9.78(a) Write the hypotheses in symbols and in words.(b) Check conditions, then calculate the test statistic, T, and the associated degrees of freedom.(c) Find and interpret the p-value in this context. Drawing a picture may be helpful.(d) What is the conclusion of the hypothesis test?(e) If you were to construct a 90% condence interval that corresponded to this hypothesis test, would you expect 8 hours to be in the interval?
Step-by-step explanation:
1.
the null hypothesis:
H0: u = 8 hours ( new Yorkers sleep for 8 hours)
The alternate hypothesis;
H1: u ≠ 8 hours ( new Yorkers sleep less than 8 hours)
b.
test statistic
t = (barX - u)/s/√n
= 7.73-8/0.77/√25
= -1.7532
degree of freedom = n-1
= 25-1 = 24
c.
p(value)
= p(t < -1.7532)
= 0.046
obviously we can see that the p value is less than 0.05 alpha level so we reject the null hypothesis.
d
The data gives strong evidence that new Yorkers sleep less than 8 hours on average every night.
e.
at 90% level of confidence
we have
7.73-0.26334, 7.73+0.26334
= 7.466, 7.993
please check attachment
thank you!
evaluate the expression for x = 3 y= 1/3 and z= 5. 12 x - 3y / 4 x - Z
Answer:
5
Step-by-step explanation:
12 x - 3y / 4 x - Z
=12×3-3×1/3÷4×3-5
=36-1/12-5
=35/7
=5
So the final answer is 5.
Explain to me in words how you would find the slope of this line and explain answer
Find the missing measure and write your solution on the blank provided
Answer:
5: c=65 d=125 e=60
6: c= 58 d= 121 e=63
7. a=55 b=64 c=61
8. a=61 b=55 c=64
Step-by-step explanation: :)
The proportion of observations from a standard Normal distribution that take values larger than -0.75 is about A) 0.2266 B) 0.7704 C) 0.7734 D) 0.7764 E) 0.8023
Answer:
Option C: 0.7734
Step-by-step explanation:
From z-distribution table attached,
P(Z ≤ -0.75) = 0.2266
However, we are looking for proportion of observations from a standard Normal distribution that take values larger than -0.75.
Thus;
P(Z > -0.75) = P(Z ≤ 0.75) = 1 - 0.2266
P(Z > -0.75) = 0.7734
Option C is the correct answer.
Please help & thank you.
Answer:
2). 79°; 3). 65°; 4). 45°; 5) 73°
Step-by-step explanation:
m∠4 = 180° - (70° + 65°) = 45°
m∠3 = 180° - (45° + 70°) = 65°
m∠2 + m∠3 = 180° - 36° = 144°
m∠2 = 144° - 65° = 79°
m∠5 = 118° - m∠4 = 118° - 45° = 73°
If x is the principal square root of 7, what must be true.
A. x = 7², and x is negative
B. x² = 7, and x is positive
C. x = 7², and x is positive
D. x² = 7, and x is negative
Answer:
B
Step-by-step explanation:
x=√7
squaring
x²=7
-3a - 4(a - 6) = 24 - 7a
Solve the equation
Thanks
-3a-4(a-6)=24-7a
-3a-4a+24=24-7a
-7a+24=24-7a
-7a+24=-7a+24
-7a+24-24=-7a+24-24
Simplify
Subtract the numbers
Subtract the numbers
−7a=-7a
Add 7a to both sides of the equation
-7a+7a =-7a+7a
Simplify
Combine like terms
Combine like terms
0=0
answer is 0=0
I WILL GIVE BRAINLIEST ONLY IF YOU ANSWER WELL
Which expression uses the commutative property to make it easier to evaluate 3/5·1/4·25
A.25·4·3/5
B.5/3·25·1/4
C.3\5·25·1\4
D.3/5·1/25·1/4
Answer:
I dont know im in middle school can you please giva me one i have to get my grades up
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
3
5
(1)
4
(25)
=
3
5
4
(25)
=
3
20
(25)
=
15
4
Guided Practice
CPCTC
Given
KGK
H is the midpoint of GK
Prove:
Side FG - Side JK
Statement
Reason
es
41 divide by 278.8 hi my name chavoria
Which numbers should go in the shaded overlap?
Factors of 30
Factors of 20