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2 years ago

line K passes through the point (8,-3) and is parallel to the line y=3x -4. write an equation for line k.

1 answer:

6 0

Parallel lines have the same slope but different y-intercepts. Start with y=mx+b substitute your point given to you for x and y but leave slope alone. Figure out b.
You should get y=3x-27.

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Consider the product (x + y + z)2. If the expression is multiplied out and like terms collected, the result is: x2 + y2 + z2 + 2

VLD [36.1K]

Answer:

Part a: The coefficient of $v^9w^2x^5y^7z^2$ is $1.766 \times 10^{13}$

Part b: The number of terms are 23751.

Step-by-step explanation:

part a

From the given equation the

$(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx$

So the coefficient of any term $x^ny^nz^n$ is given as

$\dfrac{2!}{n!n!n!}$

Similarly for the generic equation of coefficient of the term $x_1^{r_1}x_2^{r_2}x_3^{r_3}......x_k^{r_k}$ in the equation of form $(x_1+x_2+x_3+x_4......x_k)^n$ is given as

$\dfrac{n!}{r_1!r_2!r_3!....r_k!}$

So now the coefficient of $v^9w^2x^5y^7z^2$ is given as

$=\dfrac{25!}{9!2!5!7!2!}\\=1.766 \times 10^{13}$

The coefficient of $v^9w^2x^5y^7z^2$ is $1.766 \times 10^{13}$

Part b:

The number of terms is given as $\left (\ {{m+n-1} \atop {n}} \right )$

where m is the number of variables which are 5 here

n is the power which is 25 so the number of variables is given as

$\left (\ {{5+25-1} \atop {25}} \right )\\\left (\ {{29} \atop {25}} \right )\\\dfrac{29!}{25!4!}=23751$

So the number of terms are 23751.

3 0

2 years ago

Mustafa, Heloise, and Gia have written more than a combined total of 2222 22 articles for the school newspaper. Heloise has writ

Papessa [141]

Answer: $m>8$

Mustafa could have written more than 8 articles for the newspaper.

Step-by-step explanation:

Given: Heloise has written 1/4 as many articles as Mustafa has. Gia has written 3/2 as many articles as Mustafa has.

Let m be the number of articles Mustafa writes.

Then articles written by Heloise= $\frac{1}{4}m$

And articles written by Gia= $\frac{3}{2}m$

The total number of articles = $m+\frac{1}{4}m+\frac{3}{2}m=\frac{4m+m+6m}{4}=\frac{11m}{4}$

Mustafa, Heloise, and Gia have written more than a combined total of 22 articles for the school newspaper.

$\frac{11m}{4}>22\\\Rightarrow\ m>\frac{22\times4}{11}\\\Rightarrow\ m>8$

Hence, Mustafa could have written more than 8 articles for the newspaper.

3 0

2 years ago

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In ΔGHI, the measure of ∠I=90°, IG = 6.8 feet, and HI = 2.6 feet. Find the measure of ∠G to the nearest degree.

Luda [366]

Answer:

$\angle G=20.8\approx 21^{\circ}$

Step-by-step explanation:

Given: In ΔGHI, $\angle I$ =90°, IG = 6.8 feet, and HI = 2.6 feet

To find: $\angle G$

Solution:

Trigonometry defines relationship between the sides and angles of the triangle.

For any angle $\theta$ ,

$tan\theta$ = side opposite to $\theta$ /side adjacent to $\theta$

In ΔGHI,

$tan G=\frac{HI}{GI}$

Put $HI=2.6 \,\,feet\,,\,GI=6.8\,\,feet$

So,

$tan G=\frac{2.6}{6.8}=0.38$

Therefore, $\angle G=20.8\approx 21^{\circ}$

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3 0

2 years ago

Melissa owns a credit card with a 8.9% APR that calculates interest using the ADB excluding new purchases method. The balance af

ira [324]

Answer:

$4.081

Step-by-step explanation:

We have been given that Melissa owns a credit card with a 8.9% APR. The balance after her last billing cycle was $550.

First of all, we will find period rate by dividing APR by 12 as 1 years equals 12 months.

$\text{Period rate}=\frac{8.9\%}{12}=0.74166\%$

The finance charge would be 0.74166% of $550.

$\text{The finance charge}=\$550\times \frac{0.742}{100}$

$\text{The finance charge}=\$550\times 0.00742$

$\text{The finance charge}=\$4.081$

Therefore, the finance charge would be $4.081.

4 0

2 years ago

Question 5 (3 points) The soccer team is planning to sell health bars for a fundraiser. The prices of purchasing health bars fro

Ierofanga [76]

The correct answer is 40 bars.

In order to find this amount we have to find when the y values are worth the same. Since both equations are equal to y, we can set them equal to each other to find a time when the y values are the same.

Company A = Company B
.75x = 10 + .50x ---> Now subtract .50x from both sides.
.25x = 10 ---> Now divide both sides by .25
x = 40

When x = 40 it will cost $30 from both companies.

3 0

2 years ago

Read 2 more answers