Given the figure below, find the values of x
and z
.

Final Answer:

The equations of the tangents to the curve[tex]\(x = 9t^2 + 6, y = 6t^3 + 3\)[/tex]that pass through the point (15, 9) are [tex]\(y = 2x - 21\)[/tex] and[tex]\(y = -2x + 51\).[/tex]

Explanation:

To find the equations of the tangents, we first substitute (x = 15) and (y = 9) into the parametric equations[tex]\(x = 9t^2 + 6\)[/tex] and [tex]\(y = 6t^3 + 3\)[/tex]. Solving for (t), we get (t = 1) and (t = -1). These values of (t) correspond to the points of tangency.

Next, we find the slopes of the tangents by taking the derivatives of (x) and (y) with respect to (t), resulting in (dx/dt = 18t) and (dy/dt = 18[tex]t^2[/tex]). At (t = 1), the slope is (18), and at (t = -1), the slope is (-18).

Using the point-slope form of a linear equation [tex]\(y - y_1 = m(x - x_1)\)[/tex], where (m) is the slope and [tex]\((x_1, y_1)\)[/tex] is the point of tangency, we obtain the equations of the tangents: (y - 9 = 18(x - 15)) and (y - 9 = -18(x - 15)). Simplifying these expressions yields (y = 2x - 21) and (y = -2x + 51).

[tex]Use\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{14ab^2x^3}{2abx^2}=\dfrac{14}{2}\cdot\dfrac{a}{a}\cdot\dfrac{b^2}{b}\cdot\dfrac{x^3}{x^2}=7\cdot1\cdot b^{2-1}\cdot x^{3-2}=\boxed{7bx}[/tex]

Answer:

[tex]7bx[/tex]

Step-by-step explanation:

[tex]\mathrm{Divide\:the\:numbers:}\:\frac{14}{2}=7 =\frac{7ab^2x^3}{abx^2}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:a =\frac{7b^2x^3}{bx^2}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:b =\frac{7bx^3}{x^2}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}[/tex][tex]\frac{x^3}{x^2}=x^{3-2}=x[/tex]

[tex]=7bx[/tex]

Hope this helps!!!

Answer:

26.

Step-by-step explanation:

You just have to do 22.10 ÷ 0.85.

Final answer:

By dividing the total cost spent on drinks by the cost of each drink ($22.10 ÷ $0.85), we find that 26 people attended the Lopez family picnic.

Explanation:

To determine how many people attended the Lopez family picnic, we need to divide the total cost spent on drinks by the cost of each drink. Since the Lopez family spent $22.10 on drinks and each drink cost $0.85, we perform the following calculation:

Total cost spent on drinks ÷ Cost of each drink = Number of people

$22.10 ÷ $0.85 = 26 people

Therefore, 26 people attended the Lopez family picnic.

Answer:

the answer will be 4/9

Step-by-step explanation:

Answer:

7.3 repeating

Step-by-step explanation:

58-14

=44

44/6

=7.3 repeating

Answer:

Amount of gas that can be hold by Joe's tank = 16 gallons.

Step-by-step explanation:

Given that Joe's gas tank is 1/4 full. After he buys 6 gallons of gas, it is 5/8 full. Now we need to find about how many gallons can Joe's tank hold.

So let's find change that happened after filling the gas.

Change = (5/8 full) - (1/4 full)

Change = (5/8 - 1/4)  full

Change = (5/8 - 2/8)  full

Change = (5 - 2)/8  full

Change = 3/8  full

So that means 3/8 full happens in 6 gallons

then 1 full will happen in 6/(3/8) gallons = 6*(8/3) gallons = 48/3 gallons = 16 gallons

So the amount of gas that can be hold by Joe's tank = 16 gallons.

Answer:

? = 113

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.  Since the lines are parallel, the angles are equal.

? = 113

Answer:

0

Step-by-step explanation:

[tex]f(x)=\sqrt{x}+12  and g(x)=2\sqrt{x}[/tex]

We need to find (f-g)(144)

(f-g)(144) = f(144) - g(144)

[tex]f(x)=\sqrt{x}+12[/tex]

[tex]f(144)=\sqrt{144}+12=12+12= 24[/tex]

[tex]g(x)=2\sqrt{x}[/tex]

[tex]g(144)=2\sqrt{144}=2(12)= 24[/tex]

(f-g)(144) = f(144) - g(144)= 24-24=0

Answer:

o is correct answer

Step-by-step explanation:

f(x)=[tex]\sqrt{x}[/tex]+12

g(x)=2[tex]\sqrt{x}[/tex]

we will find

(f-g)x=[tex]\sqrt{x}[/tex]+12-2[tex]\sqrt{x}[/tex]

(f-g)x=-[tex]\sqrt{x}[/tex]+12

now we  will find

(f-g)(144)

put x=144

(f-g)(144)=- [tex]\sqrt{144}[/tex]+12

(f-g)(144)=-12+12=0

hence proved

Jiri is seventeen years old.

Answer:

J=Jiris

P=2J

P+J-51

Use substitution to solve

2J + J = 51

3J = 51

J=17

Plug 17 into one of the equations

J=17, P + J = 51

P + 17 = 51

P= 34

So Pamela is 34 and Jiris is 17

Answer:

1.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Final answer:

The amount still owed on a loan is called the principal, which is the original amount borrowed minus any repayments made toward it. Interest is charged on this amount, and loans are assets to banks which can be sold in the secondary loan market.

Explanation:

The amount still owed on a loan is referred to as the principal. When you make a payment on a loan, such as a credit card or a mortgage, part of it covers the principal, which is the original amount borrowed, and the rest goes toward paying off interest. Interest is the charge for borrowing the money and is calculated based on the remaining balance of the loan. When a borrower takes out a mortgage loan, for instance, they will repay both the principal and interest over the term of the loan, which often spans many years, such as in a 30-year mortgage.

Banks consider loans as assets because they are legally binding agreements where the borrower must make payments over time. In the banking industry, the value of a loan can also be determined by what another party is willing to pay for it in the secondary loan market, where loans are bought and sold between financial institutions after being originated in the primary loan market.

An example of this can be seen when a borrower owes more on their mortgage than the actual market value of the property, resulting in negative equity. However, as the loan is paid down, the equity typically increases, which is the value of the property minus the remaining loan balance.

Answer:

[tex]V=\frac{1}{3} \pi r^{2} h[/tex]

Step-by-step explanation:

Your r^2 times pi is the area of the base, h is the height, and 1/3 is 1/3 of a cylinder.

Answer:

Step-by-step explanation:

  V=πr2h

_________

       3

Answer:

Distribute

When you have an equation like this, distribute first and then add or subtract like terms to solve for x.

Hope this helps!!

Well, you need to find out what x is equal to, if anything.

The first step to completing it, from what I've learned, is to do the problem that is in parenthesis first.

Hope this helps, sorry if not-

Number of red blood cells = [tex]4.5*10^{6}[/tex]

Number of white blood cells = 5000 or we can write this as [tex]5*10^{3}[/tex]

We have to find how many times more red blood cells are there than white in the sample. so we will divide the two to get the answer.

[tex]\frac{4.5*10^{6}}{5*10^{3}}[/tex]

= [tex]0.9*10^{3}[/tex]

= [tex]9*10^{2}[/tex] = 9*10*10 = 900

Hence, the red blood cells are 900 times more than white blood cells.

Answer:

Red blood cells are 900 times of white blood cells in the blood sample of Laura.

Step-by-step explanation:

Sample of Laura's blood sample contains number of red plus cells = 4.5[tex]10^{6}[/tex] and number of white blood cells = 5×[tex]10^{3}[/tex]

Now we calculate the ratio of red blood cells and white blood cells

= 4.5×[tex]10^{6}[/tex]÷5[tex]10^{3}[/tex]

= 4.5×[tex]10^{3}[/tex]÷5

= 4500÷5

=900

Now scientific representation of data will be

Test                                  Result              Range

White Blood Cells      5×[tex]10^{3}[/tex]per [tex]mm^{3}[/tex]       5-10

Red Blood Cells       4.5×[tex]10^{3}[/tex] per[tex]mm^{3}[/tex]    4.2-6.11            

Answer:

2

Step-by-step explanation:

Final answer:

Assuming a square garden with each side being 8 feet, 50% of the space allocated to daisies would be 32 square feet.

Explanation:

Mr. King is dividing his garden evenly for tulips and daisies, meaning each flower type will occupy 50% of the garden's area. The length of the garden is given as 8 feet, but the width is not mentioned. To determine the actual area for daisies, we need both dimensions of the garden. However, if we assume that the width is also provided or the garden is square (8 feet by 8 feet), then the total area of the garden is 64 square feet (8 feet * 8 feet).

Now, to find the space filled with daisies, we calculate 50% of the total area:

0.50 * 64 square feet = 32 square feet.

Therefore, if the garden is a square and the other dimension equals the given length, the space filled with daisies will be 32 square feet.

Answer:

x=2

Step-by-step explanation:

-2(1 - 4x) = 3x + 8

The first step is to distribute the -2

-2*1 -2(-4x) = 3x+8

-2+8x = 3x+8

Subtract 3x from each side.

-2+8x-3x = 3x-3x+8

-2+5x=8

Add 2 to each side

-2+2 +5x=8+2

5x=10

Divide by 5

5x/5 = 10/5

x=2

Answer:

We have $440 to spend on fliers

Step-by-step explanation:

Budget = supplies + fliers

555 = 115 + fliers

Subtract 115 from each side

555-115 = 115-115 + fliers

440 = fliers

We have $440 to spend on fliers

Answer:

16

Step-by-step explanation:

Since Dean bought 8 postcards during 2 days of vacation, then after 4 days, that would be 16 because multiply by 2.

Answer:

16 postcards

Step-by-step explanation:

So Dean's rate of buying is:

8 postcards/2 days = 4 postcards per day.

Thus, we can find out how many postcards he gets after 4 days by multiplying

4 postcards × 4 days, which equals to 16 postcards.

Hope this is helpful!

Answer:

90 meters/second = rate

Step-by-step explanation:

To find out how fast he ran, we use the equation

distance = rate * time

We know the distance = 270 meters

and we know the time = 3 seconds

Substitute these values in

270 meters = rate * 3 seconds

Divide both sides by 3 seconds

270 meters  / 3 seconds = rate

90 meters/second = rate

Answer:

Step-by-step explanation:

you want to find his speed  so your going to divide the distance he ran by the amount of time which is  270/3 and the answer is 90

Answer:

0.8125

Step-by-step explanation:

See picture!

[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &18800\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ t=\textit{elapsed time}\dotfill &13\\ \end{cases} \\\\\\ A=18800(1-0.12)^{13}\implies A=18800(0.88)^{13}\implies A\approx 3568.0636019[/tex]

Answer:

Domain of y=[tex]\sqrt[4]{x-1}[/tex]: is x>=1

Interval notation: [1,∞)

Step-by-step explanation:

We have y=[tex]\sqrt[4]{x-1}[/tex]

1) The domain of a function is the set of x values for which the function is real and defined.

2) So, x-1 should be positive means x-1>=0, because fourth root of any negative value would be a complex number and not a real number.

3) Now we solve the inequality x-1>=0

4) Adding 1 to both sides of the inequality we get,

x-1+1 > = 0+1

5) Cancel out -1 and +1 from the left side

6) We get x>=1

It concludes that for the domain of the given function, the x value must be greater than or equal to 1

Answer:

Motorcycle will complete the 540 mile trip in 11.25 hr.

The car will complete it 2.25 hours less, or 9 hours.

The speed of the car therefore is 540/9 = 60 mph.

60t + 48t = 540

108t = 540

t = 5

So they will meet in 5 hours, after which time the motorcycle will have traveled 48*5 = 240 miles

and the car will have traveled 60*5 = 300 miles.

Hope this help

Step-by-step explanation:

Answer:

-7 = -3x + b

Step-by-step explanation:

i'm guessing because you have not provided a visual so i can not determine the B.

Answer:

(-11, -5)

Step-by-step explanation:

Use elimination

-2x-4y = 42

2x-8y = 18

-12y = 60

y = -5

Plug it back in

2x-8(-5) = 18

2x+40 = 18

2x = -22

x = -11

(-11, -5)

Answer:

(-11, -5)

Step-by-step explanation:

It's right

Answer:

$25 821.69

Step-by-step explanation:

The formula for the future value (FV) of an investment is

FV =PV(1 + r/n)^nt

FV = 20 000(1 + 0.087/2)^(2×3)

FV = 20 000(1 + 0.0435)⁶

FV = 20 000(1.0435)⁶

FV = 20 000 × 1.291 0847

FV = $25 821.69

i think it is 0.33...i could be wrong.

Answer:

.33 acre  per lot

Step-by-step explanation:

We want to take 25.08 acres and divide them evenly into 76 lots

25.08 /76 = .33 acre  per lot

Answer:

B

Step-by-step explanation:

• A line sloping upwards from left to right has a positive slope

• A line sloping downwards from left to right has a negative slope

The line shown here slopes downwards from left to right, hence has a negative slope → B

Answer:

(a)

Given expression: 49% of 162

we can write 49% as [tex]\frac{49}{100}[/tex]

then;

[tex]\frac{49}{100} \times 162 = \frac{49 \times 162}{100} = \frac{7938}{100}=79.38[/tex]

Therefore, the estimate of the given expression is, 79.38.

(b)

Using mental math to calculate 49% of 162.

Mental math is used as a way to calculate an estimate quickly.

We can write 49% = 50% -1%

(50%-1%) of 162 = 50% of 162 -1% of 162

so,

50% of 162 = [tex]\frac{50}{100} \times 162 = \frac{1}{2} \times 162 = 81[/tex]

and

1% of 162 = [tex]\frac{1}{100} \times 162 = \frac{162}{100} = 1.62[/tex]

Now, subtract these we get;

81 - 1.62 = 79.38

Therefore, by using mental math 49% of 162 is, 79.38