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To find the sum of a finite geometric series, use the formula, Sn=a1(1−rn)1−r,r≠1 , where n is the number of terms, a1 is the first term and r is the common ratio .

hope it helps...!!!

[tex]n=\dfrac 45 (m+7)\\\\\implies 5n = 4(m+7)\\\\\implies 5n = 4m+28\\\\\implies 4m = 5n-28\\\\\implies m = \dfrac{5n-28}{4}[/tex]

Answer:

[tex] - 18 {x}^{2} {y}^{7} [/tex]

Step-by-step explanation:

[tex] - \frac{3}{10} xy(60x {y}^{6} ) = - \frac{3}{10} (60) \times x \times x \times y \times {y}^{6} \\ = - 18 {x}^{2} {y}^{7} [/tex]

We're given a point that the line intersects and its slope.

Let's use Point-slope:-

[tex]\boxed{y-y1=m(x-x1)}[/tex]

y1 = -5

m=-5

x1=-1

[tex]\boxed{y-(-5)=-5(x-(-1)}[/tex]

[tex]\boxed{y+5=-5(x+1)}[/tex]

Convert to slope-intercept:-

[tex]\boxed{y+5=-5x-5}[/tex]

[tex]\boxed{y=-5x-5-5}[/tex]

Finally,

[tex]\bigstar{\boxed{\pmb{y=-5x-10}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

Lindiwe is 18

Step-by-step explanation:

Lindiwe  = L

Preeya = L/2

Sue = L-6

Their combined ages total 39 years

L+(L/2) + L-6 = 39

2.5L = 45

L=18

       Lindiwe=18

       Preeya= 9 (half of Lindiwe)

        Sue = 12 (6 lessthan Lindiwe)

18+9+12 = 39

Answer:

pretty sure its y = 2x +1

Step-by-step explanation:

Answer:

(-2, -36)

Step-by-step explanation:

This is written in Standard Form

[tex]f(x)=5x^{2} +20x-16[/tex]

[tex]ax^{2} +bx+c[/tex]

Convert to vertex form.

[tex]f(x)=a(x-h)^{2}+k[/tex]

[tex]f(x)=5(x+2)^{2}-36[/tex]

Answer:

x = 4 ± [tex]\sqrt{3}[/tex]

Step-by-step explanation:

x² - 8x + 16 = 3 ← the left side is a perfect square

(x - 4)² = 3 ( take square root of both sides )

x - 4 = ± [tex]\sqrt{3}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{3}[/tex]

Answer:

[tex]\text { The volume }=288 \mathrm{ft}^{3}[/tex]

Step-by-step explanation:

let V be the volume of the prism

    B The area of the base which is a triangle

    h is the height of the prism

______

Formula:

V = B × h

________

[tex]\begin{aligned}B &=\frac{9 \times 4}{2} \\&=\frac{36}{2} \\&=18\end{aligned}[/tex]

h = 16

Now we calculate:

[tex]\begin{aligned}V &=B \times h \\&=18 \times 16 \\&=288\end{aligned}[/tex]

Answer:

27

Step-by-step explanation:

So in the triangle, we've got the angle as 64°. And, there's only an opposite value and the hypotenuse value therefore the trig function is sin.

  According to SOHCAHTOA,

sin=opp/ hyp

sin 64°=x / 30

Cross- multiply, then

x= 30 × sin 64°

x= 26.963

x= 27.0(nearest tenth)

The given quadratic equation 3x^2 – 24x + 10 can be written in vertex form that is f(x) = 3(x – 4)2 – 38.

A quadratic equation is an equation of degree 2 and the standard form of a quadratic equation [tex]ax^{2} +bx+c[/tex] where x is the variable and a,b, c are real numbers.

Following the steps already shown to transform the given function into the vertex form,

[tex]f(x) = 3(x^{2} - 8x + 16) + 10 - 3(16)\\f(x) = 3(x - 4)(x - 4) + 10 - 48\\f(x) = 3(x - 4)2 - 38[/tex]

Therefore, the function written in vertex form is f(x) = 3(x – 4)2 – 38.

Learn more about quadratic equations;

https://brainly.com/question/2263981

Answer:

The answer is D!

Step-by-step explanation:

Answer:

4p - 2=7.16 is a formula that can be used to determine the standard price of a pair of socks.

Step-by-step explanation:

The information that we know is...

- Michael purchased four pairs of socks.

-  After utilizing a $2 off coupon, he spent $7.16.

We're expected to figure out what formula we should apply to get the standard price of a pair of socks so...

We start by writing 4p.

4 represents a pair of socks, and p represents the normal price of socks.

4p - 2

Then subtract 2 since he utilized a $2 off coupon.

4p - 2 = 7.16

Lastly, add = 7.16 because he paid in total $7.16.

So, 4p - 2=7.16 is a formula that can be used to determine the standard price of a pair of socks.

Hope this helps! :D

Answer:

[tex]7y=-5x-11[/tex]

Step-by-step explanation:

Since it says the lines are parallel both of their gradients will be same.

so gradient of line 1 = [tex]y=\frac{14-5x}{7}[/tex] = [tex]y=\frac{14}{7}-\frac{5x}{7}[/tex]= [tex]-\frac{5}{7}[/tex]

so equation of line 2 = [tex]y-y_{1}=m(x-x_{1} )[/tex]

                                   = [tex]y-(-3)_{}=\frac{-5}{7} (x-(-2)_{} )[/tex]

                                   = [tex]y +3=-\frac{5}{7}x+\frac{10}{7}[/tex]

                                   = [tex]y =-\frac{5x+10}{7}-3[/tex]

                                   = [tex]7y=-5x-11[/tex]

Step-by-step explanation:

basically a line equation typically looks like

y = ax + b

with a being the slope, and b bent the y-intercept (y value when x = 0).

5x + 7y = 14

7y = -5x + 14

y = -5/7 x + 14/7 = -5/7 x + 2

so, wie know the slope of the original line : -5/7 .

any line parallel to it must have the same slope.

our desired line looks like

y = -5/7 x + b

to get b we use the provided point (-2, -3).

-3 = -5/7 × -2 + b = 10/7 + b

-21/7 = 10/7 + b

-31/7 = b

and the full equation is

y = -5/7 x - 31/7

7y = -5x - 31

5x + 7y = -31

Answer: 2/21

Step-by-step explanation:

6/63= 2/21

Answer:688

Step-by-step explanation:600+(11x8)=x

x=total

600+88=x

x=688

Answer:

I don't understand the question

Answer:

9330

Step-by-step explanation:

6x × 8y + 27x - 6y + 3 = 18 × 536 + 81 - 402 + 3 =

9330

Answer:

The answer is 9330

Hope it helps

✧GHOSTOFSPARTA✧

The cost of the 15 percent of replaced vacuum cleaner which are sold under warranty is $3,681,384. Option b is correct.

Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.

A vacuum cleaner costs $68, and the full-replacement extended warranty costs $22.

The manufacturer sells 360,920 vacuum cleaners under warranty and must replace 15% of them to honor the warranties. Thus, the number of vecuum cleaner replaced by manufacturer is,

[tex]n=\dfrac{15}{100}\times360,920\\n=54138[/tex]

The cost of one vacuum cleaner is $68. Thus the cost of 54138 vcacuum cleaner is,

[tex]C=54138\times68\\C=3681384[/tex]

Hence, the cost of the 15 percent of replaced vacuum cleaner which are sold under warranty is $3,681,384. Option b is correct.

Learn more about the percentage here;

https://brainly.com/question/24304697

Answer:

Step-by-step explanation:

a)

The total amount coffee beans

b)

The total amount of market price

Answer:

a)   750a + 1200r = 1000000

b)   1065a + 876r = 1000000

Step-by-step explanation:

Define the variables:

Part (a)

Given:

If the plantation yields 1,000,000 kg of coffee:

⇒ 750a + 1200r = 1000000

Part (b)

Given:

If the price of Arabica beans is $1.42 per kg, and Arabica yields about 750 kg per hectare, then the price per hectare of Arabica coffee beans is:

⇒ $1.42 × 750 = $1065 per hectare

If the price of Robusta beans is $0.73 per kg, and Robusta yields about 1200 kg per hectare, then the price per hectare of Robusta coffee beans is:

⇒ $0.73 × 1200 = $876 per hectare

Therefore, if the plantation produces coffee worth $1,000,000:

⇒ 1065a + 876r = 1000000

Answer:

[tex]\boxed{\dfrac{y}{x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\dfrac{1}{x} }{\dfrac{1}{y} } \ \text{can also be written as} \ \dfrac{1}{x} \div \dfrac{1}{y}[/tex]

-------------------------------------------

[tex]\rightarrow \dfrac{1}{x} \div \dfrac{1}{y}[/tex]

Simplifying the expression using "a ÷ b = a x 1/b"

[tex]\rightarrow \dfrac{1}{x} \times y[/tex]

[tex]\rightarrow \boxed{\dfrac{y}{x}}[/tex]

Answer:

A

Step-by-step explanation:

[tex]\frac{4}{5} + \frac{2}{5} = \frac{6}{5} \\Simple make it improper, resulting in answer A[/tex]

Hope this helps!

ANSWER:

e. 4 and 2

f. 1 and 3

g. 5 and 6

h. 7 and 8

Ok done. Thank to me >:3

The equation y = 3x - 2 is a linear equation

Points (0,2), (1,1) and (2,4) are on the line y = 3x - 2

The rule is given as:

y = 3x - 2

Set x = 0

y = 3(0)- 2 = -2

Set x =1

y = 3(1)- 2 = 1

Set x = 2

y = 3(2)- 2 = 4

The above means that (0,2), (1,1) and (2,4) are on the line y = 3x - 2

See attachment for the graph of the line y = 3x - 2

Read more about linear equations at:

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Answer:

124

Step-by-step explanation:

4*5*3

+

2*4*8

=124

Formula for volume of a rectangular prism is base x height.

The tangent line DC is perpendicular to the radius of the park

The length of AC is 245 feet

To calculate the distance AC, we start by calculating the length of AB using:

DC^2 = (BC + AB) * BC

So, we have:

105^2 = (45 + AB) * 45

Evaluate the exponent

11025 = (45 + AB) * 45

Divide both sides by 45

245 = 45 + AB

Rewrite as:

AB + 45 = 245

From the figure, we have:

AC = AB + 45

Substitute AB + 45 = 245

AC = 245

Hence, the length of AC is 245 feet

Read more about line of tangents at:

https://brainly.com/question/6617153

~Denki Kaminari here~

Answer:

JGH

Step-by-step explanation:

it can be proven because there is the measurement of "P".

hope this helps :D

Answer:

V=100.5

Step-by-step explanation:

hopes this helps