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3 years ago

Solve the inequality: 3(k + 2) -3 < 15

Mathematics

1 answer:

grin007 [14]3 years ago

6 0

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

k < 4

Interval Notation:

(−∞, 4)

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Which graph represents (y-3)^2/25 + (x+1)^2/4 > 1 and y <= square root{x+5}+2

Serjik [45]

Answer: graph №2.

Step-by-step explanation:

$The\ graph\ \frac{(y-3)^2}{25}+\frac{(x+1)^2}{4} > 1\ is\ shown\ in\ fig. 1\ (see \ below).\\The\ graph\ y\leq \sqrt{x+5}+2 \ is\ shown\ in\ fig. 2\ (see\ below).\\$

6 0

2 years ago

On a coordinate plane, 2 lines are shown. Line P Q has points (negative 8, 2) and (4, 2). Line M N has points (8, 6) and (8, neg

DaniilM [7]

Answer:

Slope of PQ = 0

Slope of MN = infinity

PQ and MN are perpendicular to each other

Step-by-step explanation:

for any two points (x1, y1), (x2, y2)given in coordinate plane slope is given by

$y1 - y2/x1-x2\\\\For \ line \ PQ\\slope = 2 - 2/-8-4 = 0\\\\For \ line \ MN \\slope = 6 - (-8)/8-8 = 1/0 = infinity\\\\$

For any line if slope is zero it is parallel to X axis and perpendicular to Y axis

For any line if slope is infinity it is parallel to Y axis and perpendicular to X axis

Also we know X and Y are perpendicular to each other.

Since slope of PQ is zero it is parallel to X axis and perpendicular to Y axis

Since slope of MN is infinity it is parallel to Y axis and perpendicular to X axis.

Thus two lines PQ and MN are perpendicular to each other.

4 0

3 years ago

Read 2 more answers

Matthew invested $3,000 into two accounts. One account paid 3% interest and the other paid 8% interest. He earned 4% interest on

boyakko [2]

Answer:

Mathew invested $600 and $2400 in each account.

Solution:

From question, the total amount invested by Mathew is $3000. Let p = $3000.

Mathew has invested the total amount $3000 in two accounts. Let us consider the amount invested in first account as ‘P’

So, the amount invested in second account = 3000 – P

Step 1:

Given that Mathew has paid 3% interest in first account .Let us calculate the simple interest $(I_1)$ earned in first account for one year,

$\text {simple interest}=\frac{\text {pnr}}{100}$

Where

p = amount invested in first account

n = number of years

r = rate of interest

hence, by using above equation we get $(I_1)$ as,

$I_{1}=\frac{P \times 1 \times 3}{100}$ ----- eqn 1

Step 2:

Mathew has paid 8% interest in second account. Let us calculate the simple interest $(I_2)$ earned in second account,

$I_{2} = \frac{(3000-P) \times 1 \times 8}{100} \text { ------ eqn } 2$

Step 3:

Mathew has earned 4% interest on total investment of $3000. Let us calculate the total simple interest (I)

$I = \frac{3000 \times 1 \times 4}{100} ----- eqn 3$

Step 4:

Total simple interest = simple interest on first account + simple interest on second account.

Hence we get,

$I = I_1+ I_2 ---- eqn 4$

By substituting eqn 1 , 2, 3 in eqn 4

$\frac{3000 \times 1 \times 4}{100} = \frac{P \times 1 \times 3}{100} + \frac{(3000-P) \times 1 \times 8}{100}$

$\frac{12000}{100} = \frac{3 P}{100} + \frac{(24000-8 P)}{100}$

12000=3P + 24000 - 8P

5P = 12000

P = 2400

Thus, the value of the variable ‘P’ is 2400

Hence, the amount invested in first account = p = 2400

The amount invested in second account = 3000 – p = 3000 – 2400 = 600

Hence, Mathew invested $600 and $2400 in each account.

3 0

3 years ago

Read 2 more answers

At the building site there are 16 pallets with sacks of cement the total weight of all the pallets and cement is 4856 pounds eac

inysia [295]

The first thing we must do for this case is to define a variable.
We have then:
x: weight of each pallet with cement
We then have the following equation:
16x = 4856
Clearing x we have:
x = (4856) / (16)
x = 303.5 punds
Answer:
each pallet with cement weigh:
x = 303.5 punds

6 0

3 years ago

Write the equation of the line perpendicular to 3x+2y=-8 that passes through (3,1). Write you answer in slope-intercept form. Sh

Verdich [7]

Answer:

y = (2/3)x - 1, slope-intercept form

Step-by-step explanation:

3x + 2y = - 8

2y = -3x - 8

y = (-3/2) x - 4

Slope of this line is -3/2.

For the perpendicular line slope is 2/3.

Point - slope form is

(y - y1) = m(x - x1)

Point is (3,1). Slope m = 2/3.

y - 1 = (2/3)*(x - 3)

y - 1 = (2/3)x - 2

y = (2/3)x - 1, slope-intercept form

3 0

3 years ago