There are four springs stretched by the same mass.
Spring A stretches 25 cm.
Spring B stretches 10 cm.
Spring C stretches 100 cm
Spring D stretches 1 cm.

Which spring has the largest spring constant?
Ο Α
O B
O C
O D

The outline that that illustrate how k values change so that the solutions are the ones in the question are as follows

(a) The number line solution contains zero

Using algebra, we have;

The given quadratic inequality is; -x² + 4 ≥ x + k

The number line solution is the expression of the solution on the number line.

We have;

-x² + 4 ≥ x + k

-x²  - x + 4 - k ≥ 0

Dividing by (-1), we get;

x² + x - 4 + k ≤ 0

When - 4 + k = -2

k = 2, we get;

x² + x - 4 + 2 ≤ 0

x² + x - 2 ≤ 0

(x - 1)·(x + 2) ≤ 0

Given that the result of the product is less than zero, we have;

((-3) - 1)·((-3) + 2) > 0

Therefore, the solution are;

x ≤ 1, or x ≥ -2

Which gives

-2 ≤ x ≤ 1

The solution of the above inequality includes 0 as shown in the attached number line

The graph of the inequality is plotted using MS Excel, showing the solution set, of -2 ≤ x ≤ 1

(b) There are no solution to the inequality

In the present case, we have;

((-1)² - 4×(-1) × (4 - k) <  0

17 - 4·k < 0

[tex]k > \dfrac{17}{4}[/tex]

Let k = 5, we have;

-x² + 4 ≥ x + k

-x² - x + 4 - 5 ≥ 0

-x² - x  -1 ≥ 0

The discriminant, is (1² - 4×(-1)×(-1)) = -3 < 0, therefore, there are no real

roots to inequality, and -x² - x  -1 is not equal to zero.

Please find attached the graph of the function, which does not intersect with the x-axis, and therefore, has no values at which y = 0

(c) The solution is a single number

-x² + 4 ≥ x + k

When k = x + 5, we have;

0 ≥ x² + 2·x + 1

0 ≥ (x + 1)²

Therefore;

The only solution is; x = -1

Using diagrams:

Please find attached the solution of the function on the number line

The graph of the function showing only one intercept is attached

Learn more here:

https://brainly.com/question/11982012

Answer:

See below.

Step-by-step explanation:

Hi there!

We want to find the equation of the line that has a slope (m) of 1 and that passes through the point (-10, -6)

There are 3 ways to write the equation of the line:

Since we are given both a point and a slope in this situation, it makes sense to write the equation in point-slope form.

Let's label the values of everything we were given to avoid confusion and mistakes:

m=1

[tex]x_1=-10\\y_1=-6[/tex]

Now substitute these values into the equation (note: we have NEGATIVE numbers, while the formula gives SUBTRACTION, which is why we're subtracting a negative)

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y--6=1(x--10)[/tex]

Simplify:

y+6=1(x+10)

The equation can be left as this, or it can be converted into slope-intercept form if you wish.

In that case, we would distribute 1 to each number on the right side.

y+6=x+10

Then, we'll isolate y on one side. Subtract 6 from both sides.

y=x+4

You can also convert it into standard form if you would prefer it that way. To do that, start with slope-intercept form, which we earlier found as y=x+4

In standard form, x and y are on the same side. So subtract x from both sides to move it

-x+y=4

Remember we don't want a (the coefficient in front of x) to be negative. In order to flip the sign, multiply both sides by -1

x-y=-4

Therefore, the answer can be written as y+6=1(x+10), y=x+4, or x-y=4.

Hope this helps!

Answer:

A. 1

B. -1

C. 5

Step-by-step explanation:

A. Using the Formula, we get u sub 2 = 9-9+1, which is just 1

B. Using the Formula, we get u sub 3 = 1-3+1, which is equal to -1

C. Using the Formula, we get u sub 4 = 1-(-3)+1, which is just 1+3+1 = 5

question 1. is 2

question 2 -13

Answer: Question 2 answer is 4        Question 3 answer is 12

Step-by-step explanation:

Question 2: 42*4=168

43*5=210

Answer:

268

Step-by-step explanation:

366 minus 98= 268

CAN I GET BRAINLIEST

Answer:

Answer:

I hope this helps.

Step-by-step explanation:

The quotient of 5 divided by q minus the product of 5 and q.

Answer: (5/q-5q)

The product of 5 and the difference of q minus 5.

Answer: (5(q-5)

The quotient of q divided by 5 plus the product of 5 and q.

Answer: (q/5+5q)

The sum of 5 and the product of 3 times q.

Answer: (5+3q)

Answer:

y=5x

Step-by-step explanation:

y=ax

use any value of x and y from the table

I chose (2,10)

10=2a

10/2=a

a=5

Answer:

312

Step-by-step explanation:

499-187

Answer: Tim needs to save $312 more.

Step-by-step explanation: To find the answer, subtract. $499 minus $187 equals $312. Hope this helps! :>

=================================================

[tex] \rightarrow [/tex]Formula: Amount = P x (1 + R x T)

[tex] \rightarrow [/tex] = 1,400 x (1 + 3.4% x 4)

[tex] \rightarrow [/tex] = 1, 400 x (1 + 0.034 x 4)

[tex] \rightarrow [/tex] = 1,400 x (1 + 0.136)

[tex] \rightarrow [/tex] = 1,400 x 1.136

[tex] \rightarrow [/tex] = 1,590.4

Answer:

9

Step-by-step explanation:

To calculate the value of x we must first understand the total value of all angles in a triangle.

Sum of all angles in a triangle = 180 degrees

That said, we need to write an equation for the total number of degrees in the triangle and solve for x

This will be as follows:

(13x+2)+(5x-7)+(3x-4)=180

The we combine the like terms. This will be as follows:

(13x+5x+3x)+(2-7-4)=180

Simplify further to get

21x-9=180

Simplify further by collecting all like terms on one side of the equal. This will entail the addition of 9 on each side of the equal sign as follows:

21x-9+9=180+9

you will find 21x=189

Simplify further by dividing both sides of the equal sign by 21 to solve for x

21x/21=189/21

Therefore x=9

Answer:

He did not simplify correctly and forgot to place the decimal point correctly.

Step-by-step explanation:

To simplify the equation, one needs to divide both sides of the equal sign by 5.

i.e 5.25/5=5/5

Here we find 1.05=1

Note the placement of the decimal point.

Answer:

d.

took the test

Step-by-step explanation:

Answer:

1[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

17/20 + 7/20

17+7=24

24/20 =1.2

1 [tex]\frac{4}{20}[/tex]

can simplify to be 1[tex]\frac{1}{5}[/tex]

Answer:

1 1/5

Step-by-step explanation:

17/20 + 7/20 is equal to 24/20. Because the denominater (20 in this case) is the same we can leave it there and just add the numerator.

Now to simplify into a proper fraction. We know that only 1, 20 goes into 24 because if there was 2, 20's it would be 40 which is greater than 24. So 24 - 20 is 4. Therefore the answer is 1 4/20 which can be simplified to 1 1/5

Answer:

[tex]m=\frac{2}{3}[/tex]

Step-by-step explanation:

We can see that some of the points that are plotted we can tell what those plots are (-2, 0) (1, 2) (4, 4)

We use the slope formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]  for any of the two plots that are shown on the line

Answer:

2/3

Step-by-step explanation:

P(A n B) = P(A U B) - P(A) - P(B)

= 11/12 - 3/4 - 1/2

= (11 - 9 - 6)/12

= 4/12

= ⅓

Answer:

24 x 12 = 288 hours

Step-by-step explanation:

Answer:

#1

Slope: 1/2

Y Intercept: -3

#2

Slope: -3

Y Intercept: 2

Answer:

slope = 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 7 ) and (x₂, y₂ ) = (3, 10 )

m = [tex]\frac{10-7}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1

Answer:

The independent variable is the week's, the dependent variable is the height in inches.

Step-by-step explanation:

The independent variable is the variable that when changed, something changes because of it. So for example, for plant A, in 2 weeks (independent) thevplant will grow 2 inches (dependent). The dependent variable is the variable that changes because of the independent.

Extra Information is below

Y-intercept: The y-intercept is when the line crosses with the line when the x-axis is 0. For example, plant B is by 0 weeks, it was 4 inches. The y-intercept will be 4 inches because that is where the plant started before any change in the independent variable.

Slope: Y = mx + b. To get the answer for this equation, you first need to find out the constant, the constant if we're using plant A, is 6. The constant is also the y-intercept. The equation will look like Y = mx + 6. The m is the number that when multiplied with the independent variable, then added with the constant, you get y. The m for plant A is 1, the equation should look like y = 1x + 6. Now change the x with the independent variable in the table. The independent variable is 2, so y = 1(2) + 6, y = 2 + 6, y = 8.

Answer:

I am pretty sure the correct answer is never true

Step-by-step explanation:

This is because when,

Δ JKL ≅ Δ MNP

Then, ∠J ≅ ∠M

∠K ≅ ∠N

∠L ≅ ∠P

so ∠L ≠ ∠N

i hope this is right haha

Answer:

For the second one would be 36°

Answer:

2

Step-by-step explanation: