Since a force of 37 N is applied to the spring, the spring stretches by 9.74 cm
To answer the question, we need to know Hooke's law.
What is Hooke's law?This states that the force, F on a stretched spring is directly proportional to its extension, x.
So, F ∝ x
Mathematically, F = kx where k = spring constant
The extension of the spring(How much the spring stretches)Making x subject of the formula, we have
x = F/k
Given that F = 37 N and k = 380 N/m, we have
x = F/k
x = 37 N/380 N/m
x = 0.0974 m
x = 9.74 cm
So, the spring stretches by 9.74 cm
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Can someone please help me with this question? Thank you. No links!
Answer:
I CANT DO IT
Step-by-step explanation:
THE PICTURE IS BROKEN
PLEASE ANSWER 30 POINTS!!!!!
Answer:
E. Point E
Step-by-step explanation:
First, you would move along the x-axis horizontally for 4½ units. Then, you move along the y-axis vertically for 5 units and land on point E.
I hope this helps.
What is the area of this 1/4 circle?
[tex] \frac{1}{4} \times \pi \times ({radius})^{2} = \\ [/tex]
[tex] \frac{1}{4} \times \pi \times {12}^{2} = \\ [/tex]
[tex] \frac{1}{4} \times \pi \times 144 = \\ [/tex]
[tex] \frac{144}{4} \pi = \\ [/tex]
[tex]36\pi[/tex]
The intrest of 3 years on Rs.2400 is Rs 576. Find the rate of intrest...
Answer:
The answer is 8%
Step-by-step explanation:
Given,
Principle=Ra.2400
Time=3 years
Simple Interest= Rs.576
Rate=?
Now,
Rate=100*Simple Interest%P*T
=100*576%2400*3
=57600%7200
=8%
Therefore, the rate of Interest is
8%
(can you give me BRAINLIEST)
If you divide any number by itself, what is the result? How can you apply this result to the expression in part D?
Answer:
1
Step-by-step explanation:
Any number divided by itself is always 1
A cereal box is shaped like a rectangular prism. The box is 20 cm long by 5 cm wide by 30 cm high. What is the surface area of the cereal box?
help me find the area please. the examples in delta math arent helping.
Answer:
Answer 10,006
Step-by-step explanation:
We are Multiplying.
Answer:
157.78
Step-by-step explanation:
Solve each shape individually
For the square, we are given both side lengths so multiply them to find its area
9.8 x 8.7 = 85.26m
For the triangle on the right, we know the base and height lengths, so multiply them and divide by two to find the area
9.8 x 7.2 = 70.56 / 2 = 35.28m
For the triangle on the left, we can find the base by subtracting the side length of the square from the length given on the bottom
16.3 - 8.7 = 7.6
We know the height for this triangle so multiply that by the number you just found and divide by two to find the area
9.8 x 7.6 = 74.48 / 2 = 37.24m
Finally add all of the areas found together to get the total area of the trapezoid
37.24 + 35.28 + 85.26 = 157.78
This year, the sum of Mr Bellini’s age and his son’s age is 28 years. 4years ago, Mr Bellini was 5 times as old as his son
(A) How old is his son this year?
(B) How old is Mr Bellini this year?
Answer:
Let x = son's age
Let 38-x = Mr. Bellini's age (since the sum of their ages must be equal to 38)
Set up the equation using the second statement:
(38 - x) - 4 = 5(x - 4)
Solving,
34 - x = 5x - 20
34 + 20 = 6x
54 = 6x
x = 9 years old (son's age)
38-x = 29 years old (Bellini's age)
Gen ALL in Learning Show Summary Text to Speech (on) Previous Next > 6 Line / is shown on the coordinate grid below. y Q1 Que A A 10 9 8 HNWAUOVO 04 Qu х 05 OL 0 1 2 3 4 5 6 7 8 9 10 wful to photocopy or project without permission QOQI Which ordered pair represents a point that is located above line 1? (5.8C | Lesson 10) Q7 Q F (0,7) G (6, 2) H (1,6) DO O O GA
The ordered pairs of the points F, G and H are their locations on the coordinate plane
The point F is above the line 1
How to determine the coordinate point?
The ordered pairs of the points are given as:
F = (0,7)
G = (6, 2)
H = (1,6)
The line is not given; so, I will provide a general explanation.
Of all the three ordered pairs, the point with the greatest y-coordinate is the point F.
This means that the point F can be above the line 1, while the other points G and H are below the line.
See attachment for the illustration of the line and the ordered pairs
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Find the lateral surface area of the
cylinder 7mm 19mm. Round your answer to the nearest tenth
We can use the lateral surface area equation 2πrh. Assuming π = 3.14 we can plug all of the information into the equation to get 2 * 3.14 * 7 * 19.
multiplying everything you get 835.24, rounded to the nearest tenth is 835.2
can i have some quick help? this is in trinomial method
#1
2x²+x-6ac=6(-2)=-12
2x²+4x-3x-62x(x+2)-3(x+2)(2x-3)(x+2)#2
10a²+3a-110a²+5a-2a-15a(a+2)-1(a+2)(5a-1)(a+2)#3
2c²+5c-12ac=-24
2c²+8c-3c-122c(c+4)-3(c+4)(2c-3)(c+4)Answer:
(a) [tex](2x-3)(x+2)[/tex]
(b) [tex](5a-1)(2a+1)[/tex]
(c) [tex](2c-3)(c+4)[/tex]
Step-by-step explanation:
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]
Find 2 two numbers that multiply to ac and sum to b.Rewrite b as the sum of these 2 numbers.Factorize the first two terms and the last two terms separately, then factor out the common term.Part (a)
Given expression: [tex]2x^2+x-6[/tex]
[tex]\implies ac=2 \cdot -6=-12[/tex]
Factors of -12 that sum to 1: 4 and -3
[tex]\implies 2x^2+4x-3x-6[/tex]
Factor first two terms and last two terms separately:
[tex]\implies 2x(x+2)-3(x+2)[/tex]
Factor out common term [tex](x+2)[/tex]:
[tex]\implies (2x-3)(x+2)[/tex]
Part (b)
Given expression: [tex]10a^2+3a-1[/tex]
[tex]\implies ac=10 \cdot -1=-10[/tex]
Factors of -10 that sum to 3: 5 and -2
[tex]\implies 10a^2+5a-2a-1[/tex]
Factor first two terms and last two terms separately:
[tex]\implies 5a(2a+1)-1(2a+1)[/tex]
Factor out common term [tex](2a+1)[/tex]:
[tex]\implies (5a-1)(2a+1)[/tex]
Part (c)
Given expression: [tex]2c^2+5c-12[/tex]
[tex]\implies ac=2 \cdot -12=-24[/tex]
Factors of -24 that sum to 5: 8 and -3
[tex]\implies 2c^2+8c-3c-12[/tex]
Factor first two terms and last two terms separately:
[tex]\implies 2c(c+4)-3(c+4)[/tex]
Factor out common term [tex](c+4)[/tex]:
[tex]\implies (2c-3)(c+4)[/tex]
is 5.029 less than 5.128
yes
Step-by-step explanation:
After the point the first number of the first number is 0 while the second one is 1
what type of angle is this?
Answer:
This is an acute angle since it measures less than 90 degrees.
Answer Assap need it quick a lot of points!!!!!
HELP ME OR ELSE…
Answer:
Length=12 Width=6 AREA=72 (I think)
Step-by-step explanation:
yea... I didnt know wut the equation was so my small brain did it manually
Cam's tent (shown below) is a triangular prism.
2 m
2 m
1.7 m
3 m
AK
*
1 m 1 m
Find the surface area, including the floor, of his tent.
Answer:
The surface area of the tent is 21.4 m²
Step-by-step explanation:
To find the surface area of a prism you must calculate:
1. The perimeter of the base
2. The area of the base
3. The height of the prism
We have a triangular prism:
Its base is an equilateral triangle of side length 2 m and height 1.7 m
The height of the prism is 3 m
∵ The surface are of the prism is:
S.A = perimeter of the base × height + 2 × area of the base
∵ The perimeter of the equilateral triangle = 3 × length of a side
∵ The length of the side = 2 m
∴ The perimeter of the base = 3 × 2 = 6 m
∵ The area of the triangle = × base × height
∵ The length of the base of the triangle = 2 m
∵ The height of the triangle = 1.7 m
∴ The area of the base = × 2 × 1.7 = 1.7 m²
∵ S.A = perimeter of the base × height + 2 × area of the base
∵ The perimeter of the base = 6 m
∵ The area of the base = 1.7 m²
∵ The height of the prism = 3 m
∴ S.A = 6 × 3 + 2 × 1.7
∴ S.A = 18 + 3.4
∴ S.A = 21.4 m²
The surface area of the tent is 21.4 m²
Determine whether each statement correctly describes the likelihood of an event based on the given number cube. Select True or
False for each statement.
True or False
The statement that correctly descrives the likelilhood of an event based on the given numbered cube is: Option A: It is likely that a number less than 6 is occured.
How to decide the likelihood of an event?Suppose that for a considered sample space, we consider an event E
Then, E is likely to occur if:
[tex]P(E) \geq P(E')[/tex]
where [tex]E_i '[/tex] is complementary event of E (ie, E' occurs whenever E doesn't occur and vice versa)
If so, then we say that E is likely to occur as the outcome of the considered random experiment, else unlikely.
Since we have:
[tex]P(E) = 1- P(E')[/tex] due to E and E' being complement of each other, therefore, we get:
[tex]P(E) \geq 1 - P(E)\\P(E) \geq 0.5[/tex]
Thus, event E is said to be likely if its probability is greater or equal to 0.5, else not.
It is given that the cube is 6 faced (assuming all equally likely), numbered from 1 to 6.
Evaluating likelihood of each event:
It is likely that a number less than 6 is obtained on the number cube.P(Getting a number < 6 on that cube) = [tex]\dfrac{5}{6}[/tex] (since a number out of 6 numbers can occur in 6 ways, but it being < 6 can be done in 5 ways).
Thus, we have:
P(Getting a number < 6 on that cube) =5/6 > 0.5
So it is likely to get a number < 6 on the considered cube. So this statement correctly describes the likelihood of its considered event.
It is unlikely that a number < 4 is obtained on the number cube.Ways to get a number on the considered cube = 6
Ways to get a number < 4 on the considered cube = 3
Thus, we get:
P(Getting a number < 4 on that cube) = 3/6 = 0.5
Thus, it is likely to get a number < 4 on that cube, so this option is wrong.
It is certain that an odd or even number is obtained on the number cubeYes it is certain, but we're considering only those options which correctly describe likelihood instead of certainity.
So, this option is not considerable.
It is unlikely that a number > 1 is obtained on the number cube.Ways to get a number on the considered cube = 6
Ways to get a number > 1 on the considered cube = 5
Thus, we get:
P(Getting a number > 1 on that cube) = 5/6 > 0.5
Thus, it is likely to get a number > 1 on that cube, so this option is wrong.
Thus, the statement that correctly descrives the likelilhood of an event based on the given numbered cube is: Option A: It is likely that a number less than 6 is occured.
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The square of a negative number is 8 more than 2 times the negative number. Find the number. The number =
Answer:
the number = -23 because there are different ways to do this don't bother
if there is a 12 percent chance to get something and you need to get 90 of those things how many tries would it take?
Interval 0 to 10.5 f(x) dx = 9, interval 0 to 3.5 f(x) dx = 2, and interval 7 to 10.5 f(x) dx = 3, how do I find interval 3.5 to 7 (5f(x)-3) dx?
a. The value of the definite integral [tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]
b. The value of the definite integral [tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]
To answer the question, we need to know what definite integrals are.
What are definite integrals?These are integrals which are evaluated between two values of the variable.
a. Integral of [tex]\int\limits^7_{3.5} {f(x)} \, dx[/tex][tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]
Given that [tex]\int\limits^{10.5}_0 {f(x)} \, dx = 9, \int\limits^{3.5}_0 {f(x)} \, dx = 7 and \int\limits^{10.5}_7 {f(x)} \, dx = 3[/tex]
We require [tex]\int\limits^7_{3.5} {f(x)} \, dx[/tex]
So, [tex]\int\limits^{10.5}_0 {f(x)} \, dx = \int\limits^{3.5}_0 {f(x)} \, dx + \int\limits^7_{3.5} {f(x)} \, dx + \int\limits^{10.5}_7 {f(x)} \,dx[/tex]
So, [tex]\int\limits^7_{3.5} {f(x)} \, dx = \int\limits^{10.5}_0 {f(x)} \, dx - \int\limits^{3.5}_0 {f(x)} \, dx - \int\limits^{10.5}_7 {f(x)} \,dx[/tex]
Substituting the values of the variables into the equation, we have
So, [tex]\int\limits^7_{3.5} {f(x)} \, dx = \int\limits^{10.5}_0 {f(x)} \, dx - \int\limits^{3.5}_0 {f(x)} \, dx - \int\limits^{10.5}_7 {f(x)} \,dx[/tex]
[tex]\int\limits^7_{3.5} {f(x)} \, dx = 9 - 7 - 3\\\int\limits^7_{3.5} {f(x)} \, dx = 2 - 3\\\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]
So, [tex]\int\limits^7_{3.5} {f(x)} \, dx = - 1[/tex]
b. Integral of [tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx[/tex][tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]
[tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = \int\limits^7_{3.5} 5{f(x)}\, dx - \int\limits^7_{3.5} 3\, dx\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = 5\int\limits^7_{3.5} {f(x)}\, dx - 3(7.5 - 3)\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx= 5 X (-1 ) - 3 X 4.5 \\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx= -5 - 13.5\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]
So, [tex]\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5[/tex]
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Help please! Thankyou
Answer:
Thus, option A is correct.
Explanation:
match the proportions
$240,000 → 60%x → 100%set up a equation:
[tex]\sf \dfrac{60}{100} = \dfrac{240,000}{x}[/tex]
[tex]\sf x = \$400,000[/tex]
-4y + 14 = 22
-6x + 5 = -1
Answer:
x = 1, y = -2
Step-by-step explanation:
Add. Write the answer as a fraction simplified to lowest terms.
2+1 15 20 =
Answer:
Step-by-step explanation:
LCD (15,20) = 60
[tex]\frac{2}{15}[/tex] + [tex]\frac{1}{20}[/tex] = [tex]\frac{8}{60}[/tex] + [tex]\frac{3}{60}[/tex] = [tex]\frac{11}{60}[/tex]
Answer:
2/15 + 1/20 = 11/60
Step-by-step explanation:
1. Find the least common denominator or LCM of the two denominators:
15 and 20.
Steps to find LCM:
1. Find the prime factorization of 15
15 = 3 × 5
2. Find the prime factorization of 20
20 = 2 × 2 × 5
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 2 × 3 × 5
LCM = 60
2. Next, find the equivalent fraction of both fractional numbers with denominator 60.
For the 1st fraction, since 15 × 4 = 60,
2/15 = 2 * 4 / 15 * 4 = 8/60
Likewise, for the 2nd fraction, since 20 × 3 = 60,
1/20 = 1 * 3 / 20 × 3 = 3/60
Add the two like fractions:
8/60 + 3/60 = 8 + 3/60 = 11/60
Help please. It’s urgent. Right answer gets brainliest
Answer: Please check the image below.
Ilya builds a slide that is 2.9 meters long. It is 1.5 meters above the ground. He wants to determine the distance from the bottom of the slide to the base of the ladder leading up to the slide. Which diagram represents this situation?
A triangle with side length 1.5 meters and hypotenuse 2.9 meters.
A triangle with side length 2.9 meters and hypotenuse 1.5 meters.
A triangle with side length 2.9 meters and hypotenuse 2.9 meters.
A triangle with side length 1.5 meters and hypotenuse 2.9 meters.
Answer:
the first one
Step-by-step explanation:
Answer:Option A is correct. (light blue color in the triangle choices)
3
Find the midpoint M of the line segment joining the points C = (-1, 1) and D - - (5.-7).
M - OD
M =
Answer: (2,-3)
Step-by-step explanation:
if the sum of the two consecutive odd number is 20 find the numbers
a
Answer:
9 and 11
Step-by-step explanation:
let two numbers be X and X+2
so
x+X+2=20
solve for X
x=9
x=20
Answer:
11 + 9 = 20
Step-by-step explanation:
Consecutive odd nymbers are odd numbers that follow each other.
think which two consecutive odd number when added will give 20.
odd numbers = 1 3 5 7 9 11 13 15 17 19
9 follows 11 and when added will equal 20
A bag contains 7 blue cards, 4 green cards, 6 red cards, and 8 yellow cards. You randomly choose a card. a. How many possible outcomes are there? There are possible outcomes. b. In how many ways can choosing a card that is not red occur? Choosing a card that is not red can occur in ways.
Answer:
Step-by-step explanation:
a. 4 outcomes as there are 4 different colours.
b. 3 ways - getting a blue green or yellow card.
Explain in a complete sentence on how you would find the area of a triangle when given the base and height
Geometry. Please Help. Image is attached. Will give brainliest.
Answer:
D
To find the percentage we must first find the area of the circle:
We can find the radius of the circle using the distance formula
Now we calculate the area;
To get the percentage we divide the area of the circle by the square’s are and multiply by 100;
f f(x) = x³ - 2, find f(3)
Answer:
Simply substitute the value of 3 given. In other words, f(3) is the function of f(x) , however, in this case, x is 3. f(3)=3(3)−4.