The sum of two numbers is 59 and the difference is 3. What are the numbers?

A differential equation is an equation that contains one or more functions with its derivatives. The value of h'(3) iss 14.

A differential equation is an equation that contains one or more functions with its derivatives.

Given

h(x) = g(f(x))

Let us differentiate with respect to x by using chain rule we get

h'(x) = g'(f(x))f'(x)

plug the value x =3 in the above equation

h'(3) = g'(f(3))f'(3)

The value of f(3)=4, f'(3)=7 by table given

Plugging in values we get

h'(3) = g'(4)×7

We have g'(4)=2

so h'(3) = 2×7

h'(3) = 14

Hence the value of h'(3) is 14.

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Answer:

y = [tex]\frac{1}{2}x + \frac{29}{4}[/tex]

Step-by-step explanation:

First, we need to rearrange the equation to make it y = mx + c

4x - y = 3

y + 3 = 4x

y = 4x -3

So the slope of the line is 4.

The slope of a line perpendicular to an equation is:

[tex]\frac{-1}{gradient}[/tex]

So the slope of the perpendicular line is:

[tex]\frac{-1}{4}[/tex] = -0.25

Now to find the equation of a line you can use the following equation:

y - y₁ = m(x - x₁)

Where y₁ is the y-coordinate, x₁ is the x-coordinate and m is the gradient. Plug the values in:

y₁ = 6

x₁ = -5

m = [tex]\frac{-1}{4}[/tex]

y - 6 = [tex]\frac{-1}{4}[/tex](x - - 5)

To get rid of the fraction we need to multiply the whole equation by 4:

4y - 24 = -1(x - - 5)

The two negatives cancel out:

4y - 24 = -1(x + 5)

Multiply the brackets out:

4y - 24 = -x + 5

Now, to rearrange the formula back into y = mx + c

Move the -24 over to the other side making it a +24:

4y = 2x + 5 + 24

4y = 2x + 29

Divide everything by 4:

y = [tex]\frac{2}{4}x + \frac{29}{4}[/tex]

y = [tex]\frac{1}{2}x + \frac{29}{4}[/tex]

Answer:

[tex]m<A=125\°[/tex]

[tex]m<B=35\°[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

[tex]m<A+m<B+m<C=180\°[/tex]

substitute the values and solve for x

[tex](6x-1)\°+20\°+(x+14)\°=180\°[/tex]

[tex]7x=180\°-33\°[/tex]

[tex]7x=147\°[/tex]

[tex]x=147\°/7=21\°[/tex]

step 2

Find the measure of angle A

[tex]m<A=(6x-1)\°=6(21)-1=125\°[/tex]

step 3

Find the measure of angle C

[tex]m<C=(x+14)\°=21+14=35\°[/tex]

Answer:

1. c. $450.

2.  22%

Step-by-step explanation:  

1. We will use simple interest formula to find the amount of interest after 2 years on $5,000. As interest is not compounded, so it will not matter if she moves the simple interest earned in separate account or not.

[tex]I=P*r*t[/tex], where,  

I= Amount of interest.

P= Principal amount.

r= Interest rate in decimal form.  

t= Time in years.

[tex]4.5\text{ percent}=\frac{4.5}{100}=0.045[/tex]

Upon substituting our given values in above formula we will get,

[tex]I=5000*0.045*2[/tex]

[tex]I=5000*0.09[/tex]

[tex]I=450[/tex]

Therefore, Tracy will get an amount of $450 as simple interest after 2 years and option c is the correct choice.

2. Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest.

6 months is same as 1/2 year.

[tex]I=P*r*t[/tex]

Upon substituting our given values in above formula we will get,

[tex]209=1900*r*\frac{1}{2}[/tex]

[tex]209=950*r[/tex]

[tex]r=\frac{209}{950}[/tex]

[tex]r=0.22[/tex]

Since interest rate is in decimal form, let us convert it in percent.

[tex]\text{Interest rate}=0.22\times 100=22\text{ percent}[/tex]

Therefore, interest rate of certificate of deposit was 22%.

Answer:

9(5x+7y)

Step-by-step explanation:

Answer:

k > -26

Step-by-step explanation:

To isolate the k, you subtract 6 from both sides to get k < -26.

The correct answer is k > -26

Explanation:

To solve our equation first we need to set out our equation, k + 6 > -20. Next, we have to subtract 6 from both sides of the equation, k + 6 - 6 > -20 - 6 =      k > -26. Finally, we have our answer of k > -26.

Hope This Helps!!!

-AnimeDabGirl

Answer: To solve these types of questions what I always do is get a protractor if you have one and put it up against to where the dot is in the middle of the empty hole and then get a ruler or a pencil and make the line keep going to see what angle. In this case your answer is 65% I think.

Answer: true

Step-by-step explanation: Using the order of operations, 81 / 9 would be first, which is equal to 9. Then, add 2. 2+9 = 11, so the answer is true.

Since division goes before addition we first divide 81:9 and get 9 and to that we add 2 addition goes after division. 9+2 is equal to 11 so the answer is True.

A good way to remember it is:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Hope this helps! <3

Answer:

68

Step-by-step explanation:

Since this is an isosceles triangle the bottom 2 angles are equal.  So both bottom angles are 56 degrees.  The three angles of a triangle add to 180 degrees.

56+ 56+ x = 180

Combine like terms

112 +x =180

Subtract 112 from each side

112-112+x = 180-112

x =68

Answer: 715 Miles

Step-by-step explanation:

Divide 605 miles by 11 hours, which would give you how far he travels in 1 hour. (605/11=55)  Since they give you 13 hours, multiply 13 hours by 55 miles which gets you 715 miles :)

Answer:

B. 6.45

Step-by-step explanation:

So we know that you bought six pounds for $12.90, and you need to know how much it would cost for three pounds. You need to find out what one pound would cost, then multiply that by three.

You would do:

12.90 ÷ 6

Which equals : 2.15

Then take that and multiply it by 3:

2.15 × 3

Giving you 6.45.

Thus leading to, this fish would cost $6.45 for three pounds.

Answer:

height = 5.809

Step-by-step explanation:

l=6m

b=1.5m

l^2=b^2+h^2

36=2.25 +h^2

h^2 = 36 - 2.25

h=[tex]\sqrt{33.75}[/tex]

h = 5.809

Answer:

a₅ = 506.25                   option a

Step-by-step explanation:

Given that,

first term a₁ = 1600

common ratio (r) = [tex]\frac{3}{4}[/tex]

We need to find the fifth term of the geometric progression

We know that the nth term formula

aₙ = a₁rⁿ-¹

where a₁ is first term and r is the common ratio

n is the number of terms

So, n = 5

a₅ = 1600 [tex](\frac{3}{4})^{5-1}[/tex]

a₅ = 1600*[tex](\frac{3}{4}) ^{4}[/tex]

a₅ = 1600*81/256

a₅ = [tex]\frac{2025}{4}[/tex]

a₅ = 506.25                   option a

That's the final answer

Answer:

A. 506.25    

Step-by-step explanation:

Cost per box = $1.28
The cost of each box of crayons can be calculated by dividing the total cost by the number of boxes purchased.

Total cost: $28.16

Number of boxes: 22

Cost per box = Total cost / Number of boxes

Cost per box = $28.16 / 22
=$1.28

Answer:

8a + 2b + c

Step-by-step explanation:

For subtracting polynomials we just need to operate subtracting the terms with same unknown. In our case we sum/subtract the terms that include a between them, the terms that have b between them and the therms with c between them. So we have:

(13a−4b+8c) - (5a−6b+7c) =?

13a−4b+8c - 5a+6b-7c = ?

Lets operate putting together terms with same unknown:

(13a - 5a) + (-4b +6b) + (8c-7c) =

8a + 2b + c

So, if we subtract 5a−6b+7c from 13a−4b+8c we get 8a + 2b + c

I hope it is clear!

y = x + 1   (*)

3x - y = 9   (**)

Substitute (*) to (**):

3x - (x + 1) = 9

3x - x - 1 = 9      add 1 to both sides

2x = 10     divide both sides by 2i

Put the value of x to (*):

y = 5 + 1

Answer:  [tex]\frac{x^2}{10} = -\frac{y^2}{18}[/tex]

Step-by-step explanation:

Since, The degenerate form of an ellipse is always a point.

Thus, the equation that shows only a point will be our answer.

Since [tex]9x^2 + 4y^2 = 1[/tex] is the equation of an ellipse,

Thus, It can not be a point.

[tex]\frac{x^2}{14} + \frac{y^2}{19} =2[/tex] is not a point ( because it is an equation of ellipse)

But, when we plot [tex]\frac{x^2}{10} = -\frac{y^2}{18}[/tex]

We get only a point (0,0).

Thus, equation, [tex]\frac{x^2}{10} = -\frac{y^2}{18}[/tex] shows only one point.

Therefore, it is a generated form of ellipse.

The equation representing a degenerate ellipse would have the sum of the distances from the foci to any point on the curve as a constant.

An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci is constant. So, the equation representing a degenerate ellipse would have the sum of the distances from the foci to any point on the curve as a constant. The correct equation is (b).

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Because this is a parallelogram, we know that the diagonals bisect. This means that AO = DO, and CO = BO

It doesn't matter which two segments we use, but I'm going to use CO = BO for this one.

3x - 7 = x - 1

2x = 6

x = 3

Option B. is the answer.

Answer: d

Step-by-step explanation:

Multiply the probability by the cost of the accident:

14,886.05 x 0.071 = 1056.91

Now add the overhead cost:

1056.91 + 110 = 1166.91

The closest answer to this is number D.

Answer:

D. $1165.49

Step-by-step explanation:

We have that the probability of a driver getting into an accident = 7.1% i.e. 0.071.

Now, the average cost of an accident = $14,886.05

Then, the expected cost of an accident =  $14,886.05 × 0.071 = $1056.91

As, the overhead cost for insurance = $110

Therefore, the driver's insurance premium = $1056.91 + $110 = $1166.91

Since, the closest option to $1166.91 is option D.

Hence, the driver's insurance premium will be $1165.49.

X is greater than negative 20     (-20)

To solve the system of equations, isolate x in the second equation and substitute it into the first equation. Simplify the resulting equation and solve for y. Substitute this value of y back into the second equation to find the value of x.

To solve the system of equations:

50 + 10y + 6y = -14

16y = -64

y = -4

Substitute this value of y back into the second equation to find x:

x - 2(-4) = 10

x + 8 = 10

x = 2

Therefore, the solution to the system of equations is x = 2 and y = -4.

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The correct option is c. The total is calculated incorrectly.

When making a deposit, it is crucial that the total amount being deposited is calculated correctly on the deposit ticket. This total amount should match the sum of the cash and checks being deposited. If there is a discrepancy between the subtotal of the individual amounts and the total, the deposit ticket will not be accepted because it does not accurately reflect the amount of money being handled.

Here's the logic behind why the other options are not the primary issue:

a. The sub total is calculated incorrectly: While this is a potential error, the primary concern for the teller would be the total amount being deposited. The subtotal informs the depositor and the bank of the breakdown of the deposit, but the total is what ultimately needs to be correct for the deposit to be processed accurately.

b. Alissa forgot to sign the deposit ticket for less cash back: While a signature is important for verification purposes, especially if cash back is requested, the absence of a signature would typically result in the teller asking for a signature rather than outright rejection of the deposit ticket. The calculation of the total deposit amount is a more fundamental error that must be corrected before the deposit can be accepted.

d. Alissa forgot to date the deposit ticket: The date on a deposit ticket is important for record-keeping purposes. However, forgetting to date the deposit ticket is usually a minor issue that can be resolved quickly at the teller's window. It would not typically prevent the deposit from being accepted, assuming the total deposit amount is correct.

In summary, the teller's refusal to accept the deposit ticket in its current form most likely stems from an incorrect total calculation, as this directly affects the accuracy of the deposit transaction. Alissa will need to ensure that the total on the deposit ticket correctly reflects the sum of the cash and checks she is depositing. Once the total is corrected, the deposit ticket should be accepted by the teller.

Answer:the value of y is 44

Step-by-step explanation:

Answer:

Area of a parallelogram would be 13.46

Step-by-step explanation:

Since area of a parallelogram is represented by the formula

Area = [tex]\frac{1}{2}[/tex] ([tex](D_{1}*D_{2})[/tex]

Where [tex]D_{1}[/tex] and [tex]D_{2}[/tex] are two diagonals of the given parallelograms.

In the given figure [tex]D_{1}=AC[/tex] and [tex]D_{2}[/tex] = BD

We will find the length of [tex]D_{1}[/tex] and [tex]D_{2}[/tex] first

Since points A and C are (3,6) and (5,1)

So distance AC = [tex]\sqrt{(6-1)^{2}+(3-5)^{2}  }[/tex]

= [tex]\sqrt{5^{2}+(-2)^{2}}[/tex]

= [tex]\sqrt{25+4}=\sqrt{29}[/tex]

Since B and D are the points (6, 5) and (2, 2)

So length of BD = [tex]\sqrt{(6-2)^{2}+(5-2)^{2}}[/tex]

BD = [tex]\sqrt{4^{2}+3^{2}}=\sqrt{25}=5[/tex]

Now we will put these values in the formula

Area of parallelogram = [tex]\frac{1}{2}(\sqrt{29})(5)[/tex]

= [tex]\frac{5}{2}[/tex] × [tex]\sqrt{29}[/tex]

= (2.5) (5.385)

= 13.46

Answer:

Alright well solve by dividing using polynomial division

10 - 60/x + 4 Hope this helps have a nice day :)

Step-by-step explanation:

Step-by-step explanation:

Given blood cholesterol level was measured for each of 8 adults (in mg/dL) are:

264, 191, 160, 148, 262, 212, 268, 246

In order to find the mean, we need to add all those 8 numbers and divide by 8.

Therefore, mean = [tex]\frac{264+191+160+148+262+212+268+246}{8} =\frac{1751}{8} =218.9.[/tex]

In order to find the median, we need to arrange them in ascending order:

148, 160, 191, 212, 246, 262, 264, 268.

The middle most two values are 212 and  246.

Therefore, median = [tex]\frac{212+246}{2} =\frac{458}{2} = 229.[/tex]

[tex]\mathrm{The\:mode\:is\:the\:term\:in\:the\:data\:set\:that\:appears\:the\:most.}[/tex]

[tex]\mathrm{If\:there\:is\:more\:than\:one\:term\:that\:appears\:the\:most,\:then\:there\:is\:no\:mode.}[/tex]

[tex]\mathrm{Count\:the\:number\:of\:times\:each\:element\:appears\:in\:the\:list}[/tex]

[tex]\begin{pmatrix}148&160&191&212&246&262&264&268\\ 1&1&1&1&1&1&1&1\end{pmatrix}[/tex]

[tex]\mathrm{The\:most\:common\:element\:is\:not\:unique,\:so\:there\:is\:no\:mode}[/tex]

Answer: B(APEX)

Step-by-step explanation: