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1. What is an equation for the line with slope 2/3 and y-intercept 9?

Monica [59]

Question 1:

The generic equation of the line is given by:
$y = mx + b
$
Where,
m: slope of the line
b: cutting point with the y axis
Substituting values we have:
$y = \frac{2}3}x + 9
$
Answer:
an equation for the line with slope 2/3 and y-intercept is:
$y = \frac{2}3}x + 9$

Question 2:

The standard equation of the line is given by:
$y-yo = m (x-xo)
$
Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope of the line is:
$m = \frac{y2-y1}{x2-x1}$
Substituting values:
$m = \frac{1-(-3)}{3-1}$
$m = \frac{1+3}{3-1}$
$m = \frac{4}{2}$
$m = 2
$
We choose an ordered pair:
$(xo, yo) = (3, 1)
$
Substituting values:
$y-1 = 2 (x-3)
$
Rewriting:
$y = 2x - 6 + 1

y = 2x - 5$
Answer:
An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
$y = 2x - 5
$

Question 3:

For this case, since the variation is direct, then we have an equation of the form:
$y = kx
$ Where,
k: constant of variation.
We then have the following equation:
$-4y = 8x
$ Rewriting we have:
$y = \frac{8}{-4}x
$
$y = -2x
$ Therefore, the constate of variation is given by:
$k = -2
$
Answer:
the constant of variation is:
$k = -2$

Question 4:

For this case, since the variation is direct, then we have an equation of the form:
$y = kx
$ Where,
k: constant of variation.
We must find the constant k, for this we use the following data:
y = 24 when x = 8
Substituting values:
$24 = k8
$ Clearing k we have:
$k = \frac{24}{8} 
$
$k = 3
$
Therefore, the equation is:
$y = 3x
$ Thus, substituting x = 10 we have that the value of y is given by:
$y = 3 (10)

y = 30$ Answer:
the value of y when x = 10 is:
$y = 30$

6 0

3 years ago

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3. 4 teammates share 5 granola bars equally. Draw to show how much each person gets. Shade the amount that one person gets. Writ

Andreyy89

I am pretty sure every player would get 0.8 pieces of the 5 granola bar and for the picture you showed us about your question you divide each into 8 pieces (7 lines for each gronala bar) and there you have your answer

3 0

3 years ago

Read 2 more answers

Help will mark brainliest!!!!!

disa [49]

Answer:

D

Step-by-step explanation:

5 0

3 years ago

The scale drawing of an elephant shows a height of 2 cm. The scale for the drawing is 1 cm : 5 ft. This means that for every 1 c

mel-nik [20]

Answer:

10 ft

Step-by-step explanation:

1:5 = 2:x

x = 10

The elephant is 10 ft in real life.

Thenks and mark me brainliest :))

7 0

3 years ago

6. a) Calculate the areas of the three squares. b) Is the triangle a right triangle? Explain. 3 cm 4 cm 2 cm

viktelen [127]

Answer

The total area of the squares = 29 square cm

The triangle is not a right-angled triangle

Step-by-step explanation:

We are given three squares

The first square has a length of 4cm

The second square has a length of 3cm

The third square has a length of 2cm

Part A

Total area = Area of square 1 + Area of square 2 + Area of square 3

Area of a square = l^2

Where l is the length of the square

Area of a square 1 = 4^2

Area of a square = 16 square cm

Area of square 2 = 3^2

Area of square 2 = 9 square cm

Area of square 3 = 2^2

Area of square 3 = 4 square cm

Total area of the square = 16 + 9 + 4

The total area of the square = 29 square cm

Hence, the total square of the figure is 29 square cm

Part B

$\begin{gathered} \text{ To proof if the triangle is a right angled triangle} \\ \text{ We n}eed\text{ to appy Pythagora's theor}em \\ \text{Hypotenus}^2=perpendicular^2+base^2 \\ \text{Hypotenus = 4}cm \\ \text{Perpendicular =3cm} \\ \text{Base = 2cm} \\ 4^2=3^2+2^2 \\ 16\text{ = 9 + 4} \\ 16\text{ }\ne\text{ 13} \\ \text{ Since the hypotenus is not equal to the summation of the perpendicular and base} \\ \text{Hence, the triangle is a not right angled triangle} \end{gathered}$

6 0

1 year ago