1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mestny [16]
3 years ago
10

The difference between the square of two numbers is 11. Twice the square of the first number increased by the square of the seco

nd number is 97 find the numbers
Mathematics
1 answer:
jeyben [28]3 years ago
6 0

Answer:

Below in bold.

Step-by-step explanation:

x^2 - y^2 = 11

2x^2  + y^2 = 97

From the first equation:

y^2 = x^2 - 11

Substituting in the second equation:

2x^2 + x^2 - 11 = 97

3x^2 = 108

x^2 = 36

x = 6, -6.

Substituting  for x in the first equation:

(6)^2 - y^2 = 11

y^2 = 36 - 11 = 25

y = 5, -5.

You might be interested in
I need help with slopes
Lesechka [4]
Slope for E = 2x
Slope for F= 1x
Slope for G=1/2x
8 0
3 years ago
A researcher wants to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual
atroni [7]

Complete question is;

A researcher wants to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual containers are randomly assigned to two different groups. Plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with a kelp extract, while the plants in group 2 are not. After the first frost, 12 of the 50 plants in group 1 exhibited damage and 18 of the 50 plants in group 2 showed damage. Let p1 be the actual proportion of all tomato plants of this variety that would experience damage under the kelp treatment, and let p2 be the actual proportion of all tomato plants of this variety that would experience damage under the no-kelp treatment. Is there evidence of a decrease in the proportion of

tomatoes suffering frost damage for tomatoes sprayed with kelp extract? To determine

this, yo u test the hypotheses H0: p1 = p2, Ha: p1 < p2. The p - value of your test is

A) greater than 0.10.

B) between 0.05 and 0.10.

C) between 0.01 and 0.05.

D)between 0.001 and 0.01.

E) below 0.001.

Answer:

B) between 0.05 and 0.10.

Step-by-step explanation:

We are given;

Number of plants in group that exhibited damage = 12

Number of group 1 plants; n₁ = 50

Number of plants in group 2 that exhibited damage = 18

Number of group 2 plants; n₂ = 50

Proportion of plants in group 1 that exhibited damage; p₁^ = 12/50 = 0.24

Proportion of plants in group 2 that exhibited damage; p₂^ = 18/50 = 0.36

Pooled proportion; p¯ = (12 + 18)/(50 + 50) = 0.3

q¯ = 1 - p¯

q¯ = 1 - 0.3 = 0.7

Z-score will be;

z = ((p₁^ - p₂^) - 0)/√((p¯•q¯)×((1/n₁) + (1/n₂))

Plugging in the relevant values;

z = (0.24 - 0.36)/√((0.3 × 0.7) × ((1/50) + (1/50))

z = -0.12/0.092

z = -1.3

From z-distribution table attached, we have;

p-value = 0.0968

Correct answer is option B.

8 0
2 years ago
what is the unknown number in sequence 2 in the chart? What rule can you write that relates sequence 2 to sequence 1
sergij07 [2.7K]
Answer C. The pattern is that each number in sequence 1 is being doubled to get the number in sequence 2, and 40*2=80
3 0
3 years ago
An object at the top of a building with height 110 feet is thrown upward with an initial speed of 23 ft/s. Find its position z(t
alina1380 [7]

Answer:

Step-by-step explanation:

Given

Height of building is h=110\ ft

Initial upward velocity u=23\ ft/s

height of object is given by

z(t)=ut+\frac{1}{2}gt^2

but building is already at a height of 110 ft so z(t) must be given by

Z(t)=ut+\frac{1}{2}(-g)t^2+110

Z(t)=23\times t-\frac{1}{2}\times 9.8\times t^2

Z(t)=-16t^2+23t+110

Time when it hits is given by when Z(t)=0[/tex]

-16t^2+23t+110=0

t=\frac{-23\pm \sqrt{(23)^2-4\times (-16)\times 110}}{2\times (-16)}

t=\frac{-23\pm 87}{-32}

t=3.43\ s

6 0
3 years ago
The Oregon trail is 2.197 miles long. How long would it take a covered wagon travelling 20 miles a day to complete the trip? Wri
Bess [88]

Answer: It needs 2.4 hours to complete the trip.

Step-by-step explanation:

Since we have given that

Length of Oregon trail = 2.197 miles

Speed at which it travel = 20 miles per day

we need to find the time taken by it ,

As we know that

Time=\frac{Distance}{Speed}

Time=\frac{2.197}{20}\\\\Time=0.10\text{ days}

So,

it will be changed into hours

1\text{ day}=24\text{ hours}\\\\0.1\text{ day}=24\times 0.1=2.4\text{ hours}

so, it needs 2.4 hours to complete the trip.


3 0
3 years ago
Other questions:
  • (01.02) given that f(x) = 2x + 5 and g(x) = x − 7, solve for f(g(x)) when x = −3. (1 point) −15 −8 10 25
    12·1 answer
  • A student government organization is selling Christmas trees as a fundraiser. On Friday, they sold 5 noble fir trees and 3 dougl
    10·1 answer
  • I need help with finding x<br> ANSWER ASAP!!!!!!!!!!
    8·1 answer
  • Solve The equation Pls i need this ASAP! <br><br> y + (–6) = –9
    14·2 answers
  • The point (-2, -1) satisfies which of the following inequalities?
    12·2 answers
  • the measures of two of the angles in a triangle are 126.7 and 19 degrees find the measures of the third angle
    8·1 answer
  • To solve this system of equations by elimination, what operation could be used to eliminate the x-variable and find the value of
    13·2 answers
  • Solve for the two unknown angles in<br> the following isosceles triangle and please show all work!
    6·1 answer
  • Fred flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will show tails, the
    5·2 answers
  • Please help, Don't know the answer
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!