Paloma evaluated the expression 1 3/4 − 5/8. What is a way she can check her work?

Derivatives can be calculated from graphed functions.

The values of the derivatives are:

The given parameter is:

[tex]\mathbf{h(x) = f(g(x))}[/tex]

Start by calculating the equations of f(x) and g(x)

Graph f(x)

The slopes of f(x) are: 3/2 and -3/2

So, the equations are:

[tex]\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}[/tex]

[tex]\mathbf{f(x) = -\frac{3}{2}x,\ x \ge 2}[/tex]

Graph g(x)

The slope of g(x) is: -1/2

So, the equation is:

[tex]\mathbf{g(x) = -\frac 12x}[/tex]

For x = 1 and x = 2, we have:

So, we have:

[tex]\mathbf{h(x) = f(g(x))}[/tex]

Where:

[tex]\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]

[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes

[tex]\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}[/tex]

Open brackets

[tex]\mathbf{h(x) = -\frac{3}{4}x}[/tex]

Differentiate

[tex]\mathbf{h'(x) = -\frac{3}{4}}[/tex]

So:

[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex]

[tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex]

For x = 3, we have:

[tex]\mathbf{h(x) = f(g(x))}[/tex]

Where:

[tex]\mathbf{f(x) = -\frac{3}{2}x\ x \ge 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]

[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes

[tex]\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}[/tex]

[tex]\mathbf{h(x) = \frac{3}{4}x}[/tex]

Differentiate

[tex]\mathbf{h'(x) = \frac{3}{4}}[/tex]

Substitute 3 for x

[tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]

Hence, the values of the derivatives are:

[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex], [tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex] and [tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]

Read more about graphed functions at:

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Answer:

The given average speed =  18 km per hour

Now, as we know from the conversion parameters:

 1000 meters   = 1 km

or 1 meter =  ( 1/ 1000) kilometer

So, we can use the above information to convert average speed into meters per hour.

The given speed =  18 km / hr = 18 x (1000) meters /hr

                            = 18,000 meters / hr

Step-by-step explanation:

Step-by-step explanation:

1.

x = number

x/4 = x/3 - 1

x/3 - x/4 = 1

4x/12 - 3x/12 = 1

x/12 = 1

x = 12

2.

the numerator is the top (it gives the number of the parts of the whole that are combined in the fraction).

the denominator is the bottom (it says in how many and therefore how small parts we split the whole).

x = numerator

y= denominator

fraction is x/y

y = x + 2

(x+3)/(y+3) = 23

x + 3 = 23(y + 3) = 23y + 69

x = 23y + 66

now we use the first equation (y = x + 2) and substitute it into the last equation :

x = 23(x + 2) + 66 = 23x + 46 + 66 = 23x + 112

x = -112/22 = -56/11

y = -68/22 = -34/11

the original fraction is

x/y = -56/11 / -34/11 = -56/11 × -11/34 = 56/34 = 28/17

3.

in 1 hour the large pipe has done 1/3 of the work. and the small pipe 1/6 of the work.

so, in total in 1 hour we get (1/3 + 1/6) done.

what factor do we need to multiply (1/3 + 1/6) to get 1/1 (the whole work) ?

x(1/3 + 1/6) = 1

x(2/6 + 1/6) = 1

x(3/6) = 1

x × 1/2 = 1

x = 2

it takes both pipes together 2 hours to empty the pool.

4.

very similar to 3.

we are just using days instead of hours.

in 1 day Erwin gets 1/2 of the work done and Ana 1/5 of the work. so, together, 1/2 + 1/5 of the total work in one day.

so, how many days to get 1/1 (the whole work) done ?

x(1/2 + 1/5) = 1

x(5/10 + 2/10) = 1

x(7/10) = 1

7x = 10

x = 10/7

it takes them together 10/7 days to mow the whole lawn.

Answer:

c because if the converse is true then the inverse is also logically through

Answer:

Hi please make me brainly

Step-by-step explanation:

please

9514 1404 393

Answer:

  -177146

Step-by-step explanation:

The given formula is useful. The first term is a1 = -2. The common ratio is r = -6/-2 = 3. For n = 11 terms, the sum is ...

  S11 = -2(1 -3^11)/(1 -3) = -2(-177146/-2) = -177146

The sum of 11 terms of the series is -177146.

Answer:

1) 2

2) 1

3) 8

Step-by-step explanation:

brainliest plz

Answer:

14 batches

Step-by-step explanation:

take 5/12 and 1/34 and find the lowest common factor (204) mult 5/12 by 17

85/204 and 1/34 by 6 is 6/204 figure out how many times 6 goes into 85 about 14.17

so 14 full batches

Answer:

UWUWUWUUWUWUWUWUUWUWUW

Step-by-step explanation:

UwU OwO

In coordinates, the first number is the x and the second one is y. In (4,2), 4 is the x and 2 is the y. The x axis goes from left to right and the y axis goes from up to down.

is that all of the question?

Answer:

y = 5

Step-by-step explanation:

Group all y terms on the left side of the equation

Subtract 3y from both sides: 3-y-3y=3y+10-3y

Group like terms: -y-3y+30=3y+10-3y

Simplify the arithmetic: -4y+30=3y+10-3y

Group like terms: -4y+30=3y-3y+10

Simplify the arithmetic: -4y+30 = 10

Group all constants on the right side of the equation

Subtract 30 from both sides: -4y+30-30=10-30

Simplify the arithmetic: -4y=10-30

Simplify the arithmetic: -4y=-20

Isolate the y

Divide both sides by-4: -4y/-4 = -20/-4

Cancel out the negatives: 4y/4 = -20/-4

Find the greatest common factor of the numerator and denominator: y = 5·4/1·4

Factor out and cancel the greatest common factor:

y=5

m=number of miles

A=$110+$0.50m

B=$80+$0.80m

$110+$0.50m=$80+$0.80m Subtract ($80+$0.50m)

$30=$0.30m Divide each side by $0.30

100=m ANSWER: More than 100 miles must be driven per day to make Company A a better deal.

Answer:

0÷3= 0

0/5= 0

Step-by-step explanation:

sorry if I did it wrong

Answer:

The answer is 4

Step-by-step explanation:

2(2/3)2(1/2)3

Answer:

-3

Step-by-step explanation:

we take two points to find slope m

lets take ( 1, 4) and ( 2, 1)

then m=(1-4)/(2-1)

m=(-3)/(1)

m= -3

Step-by-step explanation:

Simple Interest

Discussing interest starts with the principal, or amount your account starts with. This could be a starting investment, or the starting amount of a loan. Interest, in its most simple form, is calculated as a percent of the principal. For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5. The total amount you would repay would be $105, the original principal plus the interest.

four rolled-up dollar bills seeming to grow out of dirt, with a miniature rake lying in between them

SIMPLE ONE-TIME INTEREST

I

=

P

0

r

A

=

P

0

+

I

=

P

0

+

P

0

r

=

P

0

(

1

+

r

)

I is the interest

A is the end amount: principal plus interest

P

0

is the principal (starting amount)

r is the interest rate (in decimal form. Example: 5% = 0.05)

EXAMPLES

A friend asks to borrow $300 and agrees to repay it in 30 days with 3% interest. How much interest will you earn?

Show Solution

The following video works through this example in detail.

One-time simple interest is only common for extremely short-term loans. For longer term loans, it is common for interest to be paid on a daily, monthly, quarterly, or annual basis. In that case, interest would be earned regularly.

For example, bonds are essentially a loan made to the bond issuer (a company or government) by you, the bond holder. In return for the loan, the issuer agrees to pay interest, often annually. Bonds have a maturity date, at which time the issuer pays back the original bond value.

EXERCISES

Suppose your city is building a new park, and issues bonds to raise the money to build it. You obtain a $1,000 bond that pays 5% interest annually that matures in 5 years. How much interest will you earn?

Show Solution

Further explanation about solving this example can be seen here.

Answer:

yes

Step-by-step explanation:

3(8+4)

(3×8)+(3×4)

24+12

36

Answer:

The width of the rectangular yard is 72 inches

Step-by-step explanation:

Let

L -----> the length of the yard

W ----> the width of the yard

we know that

The perimeter is equal to

we have

substitute in the formula and solve for W

Divide by 2 both sides

Subtract 5 both sides

Convert feet to inches

Remember that

1 ft= 12 in

Step-by-step explanation:

The width of the rectangle is 6 feet or 72 inches if the perimeter of the yard is 22 feet, and the length of his yard is 5 feet.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

Perimeter of the rectangle :

P = 2L + 2W

L = 5 feet

22 = 2(5) + 2W

After calculating:

W = 6 feet

1 feet = 12 inches

6 feet = 72 inches

Thus, the width of the rectangle is 6 feet or 72 inches if the perimeter of the yard is 22 feet, and the length of his yard is 5 feet.

Learn more about the rectangle here:

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#SPJ2

Answer: x=1, y=2

Step-by-step explanation:

3(1) - 2(2)=-1

Answer:

the opposite of 1 1/2(1.5) is -1 1/2(-1.5)

Step-by-step explanation:

Step-by-step explanation:

all such triangles inscribed into a circle with their baseline being the diameter of the circle, must be right-angled. the 90 degree angle is at C.

the other thing is that the sum of all angles in a triangle is always 180 degrees.

so,

B = 180 - 90 - 20 = 70 degrees

Answer:

1/3.  To reduce a fraction, divide both the numerator and denominator by the GCF.

Answer:

18, because the number of catalogs is 72/5 ÷ 4/5

Step-by-step explanation:

The answer is the last option because in total, the shelf is 72/5 inches wide. Given each catalog is 4/5 inch wide, and we want to find how many catalogs can fit in the shelf, we have to divide 72/5 by 4/5. When we divide 72/5 by 4/5, we get 18.

Answer:

18

Step-by-step explanation:

Because 72/5 by 4 over 5

72/4

= 18

Hope this helps :) Pls mark brainliest if you want

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x < 1

Interval Notation:

( − ∞, 1)

Answer:

answer is c

Step-by-step explanation:

3x (x-3)=0

than 3x=0 or x-3=0

x=0 or x=3

Answer:

HMMMMMMMMMMMMMMMMMMMMMMMM

Step-by-step explanation:

HMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM

Answer:

23

Step-by-step explanation:

just used a calculator