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3 years ago

The equation of a line y=2x+14. If the slope is doubled and the y-intercept is reduced by 5, what will be the new equation?

Mathematics

1 answer:

miss Akunina [59]3 years ago

8 0

Answer:

y = 4x + 9

Step-by-step explanation:

Given the linear equation, y = 2x + 14 where:

slope (m) = 2

y-intercept (b) = 14

Doubling the slope: 2 × 2 = 4

Reducing the y-intercept by 5: 14 - 5 = 9

Therefore, the new linear equation is:

y = 4x + 9

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Suppose j varies jointly with g and v, j=1 when g=6 and v=3. Find j when g=8 and v=11

Lady bird [3.3K]

j=4.88 when g=8 and v=11

Further explanation:

When the increase/decrease in one quantity cause increase/decrease in other quantity, it is called direct variation.

Variation is always accompanied by a variation constant.

<u>Given</u>

g and v vary directly with j

IT can be written as:

j∝gv

Putting the variation constant k

j = kgv

Putting g = 6 and v=3

$j = kgv\\1 = k * 6 * 3\\1 = 18k\\k = \frac{1}{18}$

So the value of k is 1/18 which makes the equation

$j = \frac{1}{18}gv\\ Putting\ g=8\ and\ v=11\\j = \frac{1}{18} * 8 * 11\\j = \frac{88}{18}\\ j =4.88$

So, j=4.88 when g=8 and v=11

Keywords: Variation, Direct Variation

Learn more about variation at:

#LearnwithBrainly

8 0

3 years ago

irina1246 [14]

3)
Principal Amount = P = $7200
Interest rate = r = 4% = 0.04
Time = t = 8 years

Formula for compounding is:

$A=P (1+r)^{t}$

Using the values, we get:

$A=7200 (1+0.04)^{8}=9853.70$

Therefore, the compounded amount will be $9853.70

4)
Principal Amount = P = $7200
Compounded Amount = A = $9853.70

Interest Earned = Compounded Amount - Principal Amount
So,
Interest Earned = 9853.70 - 7200 = $2653.70

Therefore, $2653.70 will be earned as interest over a period of 8 years.

5 0

3 years ago

If pis inversely proportional to the square of q, and p is 23 when q is 4, determine p

Misha Larkins [42]

Answer:

$p\ =\ 92$

Step-by-step explanation:

Given

$p\ \alpha\ \frac{1}{q^2}$

$p =23; q=4$

Required

Find p, when $q = 2$

We have:

$p\ \alpha\ \frac{1}{q^2}$

Express as equation

$p\ =\ \frac{k}{q^2}$

Make k the subject

$k =pq^2$

When: $p =23; q=4$

$k =23 * 4^2$

$k =368$

When $q = 2$ , we have:

$p\ =\ \frac{k}{q^2}$

$p\ =\ \frac{368}{2^2}$

$p\ =\ \frac{368}{4}$

$p\ =\ 92$

5 0

3 years ago

Find the solution set of the following quadratic equations using the quadratic formula.

oksian1 [2.3K]

Answer:

<h3> 1) $x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2$ </h3><h3> 2) $x_1=-\dfrac13\,,\quad x_2=-3$ </h3>

Step-by-step explanation:

$x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}2\\\\x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2$

<h3>2)</h3><h3> $3x^2 + 10x=-3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b =10\,,\ c=3\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-10\pm\sqrt{10^2-4\cdot3\cdot3}}{2\cdot3}= \dfrac{-10\pm\sqrt{100-36}}6\\\\x_1=\dfrac{-10+\sqrt{64}}6=\dfrac{-10+8}6=-\dfrac13\,,\qquad x_2=\dfrac{-10-8}6=-3$ </h3>

7 0

3 years ago

P L E A S E H E L P

pychu [463]

Answer:

2100 square cm

Step-by-step explanation:

To find the AREA of a three-dimensional, non-circular figure, you would want to multiply length by width by height ( 20 x 7 x 15). Since we're just looking for area and not volume, this is the equation we'll be going with.

20 x 7 x 15 = 2100

Add in the units, and we get 2100 square cm.

Hope I could help.

3 0

4 years ago