Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 180 newtons stretches a spring 5 cm, how much will a force of 270 newtons stretch the same spring?

Answer:

Option 3

Step-by-step explanation:

[tex]f(x)=4x^2 + 3x-5 \\ \\ f(x+h)=4(x+h)^2+3(x+h)-5 \\ \\ =4(x^2+2xh+h^2)+3x+3h-5 \\ \\ f(x+h)-f(x)=4(x^2+ 2xh+h^2)+3(x+h)-5-(4x^2+3x-5) \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{4(x^2+ 2xh+h^2)+3(x+h)-5-(4x^2+3x-5)}{h}[/tex]

Answer:

-11 F

Step-by-step explanation:

So we need to just add or decrease the temperature.

-5 + 14

9 - 20

-11

Answer:

-5 + 14 = 9

9 - 20 = -11

the answer is -11°f

Answer:

You can make 22 burgers.

Step-by-step explanation:

If you have 312 pounds of ground beef and burgers are 14 pounds, divide 312 by 14 ( 312 / 14).  This gives you an answer of 22.28 You will have leftovers because 14 does not go into 312 perfectly. You can also check the answer by doing multiplication ( 22 * 14) which gives you 308. You cannot have another burger because 308 + 14 = 322 which is over the amount of beef you have.

Answer:

write a semi formal letter to your father's friend

If Latisha has $40 in her checking account and she makes a withdrawal of $20 and then writes a check for $40, then she deposits $30, then the amount she has in her checking account is $10

The amount she has in her checking account = $40

The amount she withdraw from her account = $20

The amount she writes a check = $40

The deposited amount = $30

To find the final checking account balance we have to use the arithmetic operations

The final balance amount = The amount she has in her checking account -The amount she withdraw from her account - The amount she writes a check + The deposited amount

= 40-20-40+30

= $10

Hence, by using arithmetic operations, if Latisha has $40 in her checking account and she makes a withdrawal of $20 and then writes a check for $40, then she deposits $30, then the amount she has in her checking account is $10

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The relative change is 2%.

In contrast to the reference value, the absolute change's size is expressed as a fraction called the relative change: relative change = absolute change reference value = new value reference value reference value. The absolute change is expressed as a percentage of the value of the indicator in the prior period, or "relative change" expresses the absolute change as such. When measuring indicators in percentage terms, such as the unemployment rate, absolute and relative change principles also apply. To determine the absolute change, subtract the starting value from the ending value. Simply deduct 1,000 from 1,100 to arrive at 100 in the example. The student population increased by 100 pupils throughout the course of the year because this is the absolute change.

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Answer:

Step-by-step explanation:

A and C because it asks which word is in the square and pentagon, it is the a and the c

For Roberts the equation is:

to we can write it as slope intercept so:

Now we replace x = 5 so

So the two points are ( 0 , -5) and ( 5 , -4)

Fo Hookthe equation is:

In slope intercept is:

so we replace x = 5 so:

So the two points are: ( 0 , 0) and ( 5 , 2 )

For Elizabeth the equation is:

and slope intercept:

now we replace x = 2 so:

So the coordinates are ( 0 , 5) and ( 2, 6 )

And for Silver the equation is:

In slope intercept is:

now we replace x = 1 so:

So the coordinates are: ( 0, -3) and ( 1, 1 )

So now you can made the graph of the lines and find the message.

Answer:

-3÷8 or -0.375

Step-by-step explanation:

-3÷8÷1=-3÷8×1÷1=-24÷8=-3

The arc angle AC is measured as 55 degrees.

If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.

Therefore, the secants intersect outside the circle at point E.

The arc angle AC can be found as follows:

Therefore,

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

arc angle AC = x

arc angle BD = 23 degrees.

m∠BED = 16 degrees.

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

16 = 1 / 2 (x - 23)

16 = 1 / 2x - 23 / 2

16 + 11.5 = 0.5x

27.5 = 0.5x

x = 27.5 / 0.5

x = 55 degrees.

Therefore,

arc angle AC = 55 degrees.

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Based on the fact that the triangles are similar, the length of x is 7.2 cm and the length of y is 7.4 cm

If the triangles are similar then it means that the difference between their dimensions can be found by a scale factor.

The scale factor is:

= Dimension of larger similar side / Dimension of smaller similar side

= 11.6 / 5.8

= 2

With a scale factor of 2, then x is:

= 3.6 x 2

= 7.2 cm

The value of y would be:

= 14.8 / 2

= 7.4 cm

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Answer:

4 words per minute

Step-by-step explanation:

In 6 minutes Rite typed 24 words, 24 divided by 6 is 4

Answer: y = (1/3)x - 3

Step-by-step explanation:

It passes through -3 at 0, so we know the y = mx + b form will include -3

Next, we want to find the slope:

Change in y = 0 - -3 = 3

Change in x = 9 - 0 = 9

Change in y / Change in x = slope

3/9 = 1/3

The two swimming pools will have same amount of water using this equation, where x represents the time in minutes

3300 - 24x = 3696 - 35x

information given in the question is as follows

the first pool had 3300 liters of water and drains at a rate of 24 liters per minute

the second pool had 3696 liters of water and drains at a rate of 35 liters per minute.

The given information implies that

every minute in x minutes 24x liters of water is drained from the first tank.

3300 - 24x

Similarly, in the second tank in x minutes 35x liters of water in drained from the second tank

3696 - 35x

The tanks will have equal volume of water when the two equations are equal

3300 - 24x = 3696 - 35x

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Answer:

a) 69 b) -11

Step-by-step explanation:

-8 + 77 or 77 - 8 = 69

-21 + 10 = 11

THE VOLUME OF A RECTANGULAR PRISM ID GIVEN BY

[tex]v = l \times b \times h \\ = ( \frac{7}{2} in) \times ( \frac{5}{2} in) \times ( \frac{3}{2} in) \\ \\ v = \frac{35}{2} {in}^{2} \times \frac{3}{2} in \\ v = \frac{105}{2} {in}^{3} \\ v = 52\times \frac{3}{2} {in}^{3} [/tex]

THE FIRST OPTION IS THE ANSWER!!

[tex]9\frac{11}{13}[/tex] is bigger than 9.79

The mixed fraction = [tex]9\frac{11}{13}[/tex]

The mixed fraction is the fraction that expressed with its quotient and remainder. The mixed fraction is the combination of a whole number and a simple fraction

Simple fraction is the fraction that has whole numbers as the numerator and denominator.

The decimal number is a number that has whole and the fractional parts are separated by a decimal point

First we have to convert the mixed fraction into simple fraction

[tex]9\frac{11}{13}[/tex] = 128/13

Next we have to convert the simple fraction into decimal form

Divide 128 by 13

The result will be

128/13 = 9.85

Hence, [tex]9\frac{11}{13}[/tex] is bigger than 9.79

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Flipping and Stretching is the Process for performing the transformation on a coordinate plane using rigid transformations.

A rigid transformation of a geometric object preserves distance between each pair of points of the object. In other words, rigid transformations preserve the shape and size of an object. For example, a rigid transformation of a triangle preserves both the measure of the angles and the lengths of the sides of the triangle. Think of rigid transformations of a shape as being like taking a cardboard cutout of the shape. The shape can be moved around, rotated, and flipped from one side to the other, but the shape itself does not change.

There are rules associated with rigid transformations. A rigid transformation is some function F from a set X to itself such that F preserves the distances between two points. Let d(x ,y) be the distance between two points. Then, to write the definition in mathematical notation, if d(x ,y) = d(F(x),F(y)) for all points x and y, then F is a rigid transformation.

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Answer:

Step-by-step explanation:

Answer:

1.8 = 9

5

= 14

5

as a fraction

(7)^2 +

2nd power means squaring a number and since you need to do that first, it goes in brackets.

answer: 49 + b, or just 7^2 + b

explanation: 7^2 = 7x7, so it is equal to 49. then add b to 49

The domain of f { (x,y) ∈ R²  x² + y² < (3/5)² } is bounded.

What does the math term domain mean?

Given f(x,y) = [tex]\frac{1}{\sqrt{9 - 25x^{2} - 25y^{2} } }[/tex]

a) the domain of f is the value of ( x, y) for which 9 - 25x² -25y² >0

9 - 25x² -25y² ⇒ 9/25 > x² + y² ⇒  x² + y² < (3/5)²

∴ domain of f = [ (x,y) ∈ R² : x² + y² < (3/5)²}

B) Let z = f = [tex]\frac{1}{\sqrt{9 -25x^{2} - 25y^{2} } }[/tex]

 its range is { z ∈ R² : 3z > 1}

c) let f = k ⇒ k = [tex]\frac{1}{\sqrt{9 - 25x^{2} - 25y^{2} } }[/tex]

k² ( 9 - 25x² - 25y²) = 1 =  9 - 25x² - 25y² = 1/k²

⇒ 25x² + 25y² = 9 - 1/k² ⇒ x² + y² = 1/25( 9 - 1/k²)

The level curves are circles for different k values .

d) The boundary of the function's domain

   = { (x,y) ∈ R²  x² + y² = (3/5)²}

e) Since  x² + y² < (3/5)² is the circular open disk , the domain of f is an open set

f) The domain of f { (x,y) ∈ R²  x² + y² < (3/5)² } is bounded.

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Answer:

False

Step-by-step explanation:

It is false when x=1 because

[tex]1^{2} =1[/tex]

Answer: y=-4x-27

Step-by-step explanation:

[tex]y=mx+b[/tex]

Lines are parallel if their slopes are equal

[tex]y=-4x+2[/tex]

⇒ m=-4

⇒ y=-4x+b

A line passes through (-8.5)

⇒ x=-8    y=5

[tex]5=-4(-8)+b\\5=32+b\\5-32=32+b-32\\-27=b[/tex]

So, y=-4x-27

Answer:

85 people were surveyed

Step-by-step explanation:

Let n(X0 represent the number of people who belong in set X

We have 3 sets here
T = set of all people who like tea

C = set of all people who like coffee

M = set of all people who like milk

From the info given

n(T) = 60
n(C) = 45

n(M) = 30

The intersection of the sets are
n(C ∩ T) = 25

n(T ∩ M) = 20

n(C ∩ M) = 15

n(C ∩ T ∩ M) = 10

The number of people who were asked this question is given by

n(T U C U M)

= n(T) +  n(C) + n(M) - n(C ∩ T) - n(T ∩ M) - n(C ∩ M)  + n(C ∩ T ∩ M)

= 60 + 45 + 30 - 25 - 20 - 15 + 10

= 85

Venn Diagram is attached

5

Suppose that $25,200 is invested in a certificate of deposit for 2 years at 11.1 % annual interest to be compounded semi-annually, compound interest will this investment earn is $5,904.8892.

Compound interest, also known as interest on the principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on principal amount plus any accumulated interest. In the finance and economics, compound interest is common.

In contrast to the simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time. The interest per period multiplied by number of periods in a year yields the simple annual interest rate. The nominal interest rate is the another term for the basic annual interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).

It is known that the compound interest is given as

Compound Interest = [total amount of the principal and interest in future]-[total amount of the principal in present]

                                 =[tex]P(1+i)^{2} - P\\P(1+i)^{2} - 1\\[/tex]

where, p= principal, i= nominal annual interest, n= the number of  the compounding period

Given

P = $25,200

i= 11.1% = 0.111

n= 2

compound interest is

C = 25,200 [[tex](1+0.111)^{2}[/tex]-1]

  = $5,904.8892

The investment will earn the interest of $5,904.8892.

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The value of equation is 4,-11

When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement. Let's say James and Natalie were tinkering with matchsticks when they had the idea to arrange the sticks into number patterns. James used four matchsticks to make the numeral 4 in the air. Adding three additional matchsticks allowed Natalie to create a pattern with two 4s. They understood that they may continue to add three matchsticks each round to make a total of four. They deduced from this that, generally speaking, 4+ 3(n-1) sticks are required to create a pattern with n numbers of 4s. The algebraic statement 4+ 3(n-1) is referred to here.

Given that : the equation -6 | 2x+7|=-90

-6 | 2x+7|=-90

|2x +7|=[tex]\frac{-90}{-6}[/tex]

|2x +7|=15

2x + 7 =±15

2x + 7 = 15 ... (i)

2x = 8

x =4

2x + 7 = -15....(ii)

2x = -22

x =-11

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The equation that can be use to find the how many miles, x, Omar ran each day after work is x =  (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days  after work

The total number of days he run = 7 days

Total distance he ran in one week = 63 miles

The distance he run before the work = 3 miles

The total distance he run before the work in one week= 7×3

= 21 miles

The total distance he run after the work = 63 - 21

= 42 miles

The equation that can use to find how many mile x, Omar ran each day after work = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7

Substitute the values in the equation

= 42/7

= 6 miles

Hence, The equation that can be use to find the how many miles, x, Omar ran each day after work is x =  (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days  after work

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