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2 years ago

Identify an equation in slope Intercept form for the line parallel to y= -3x+7 that passes through (2,-4)

Mathematics

1 answer:

Montano1993 [528]2 years ago

6 0

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

We have the equation of a line:

$y=-3x+7\to m=-3,\ b=7$

Parallel lines have the same slope. Therefore we have the equation:

$y=-3x+b$

Put the coordinates of the given point (2, -4) to the equation:

$-4=-3(2)+b$

$-4=-6+b$ add 6 to both sides

$2=b\to b=2$

Finally:

$y=-3x+2$

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Find the area of the composite figure.

vivado [14]

So in fig 1 :

L = 14m
W = 9m

Area = L × W
Area = 9 × 14
Area = 126 m²

In fig 2 :

L = 7m
W = 16 - 9 = 7m

Area= L × W
Area = 7 × 7
Area =49m²

TA = 126 + 49
TA = 175 m²

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2 years ago

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2 years ago

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2 years ago

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drek231 [11]

To determine whether 10a-10c are true or false, you first need to know how to find the volume of the shoebox and the volume of the crate.

The equation for volume is l × w × h where l is the length, w is the width, and h is the height.

So, the volume of the shoebox is

V = l × w × h
V = 12 × 6 × 4
V = 288 cubic inches.

To find the volume of the crate, we simply multiply the volume of one shoebox by 20, as the crate holds 20 shoeboxes.

228 × 20 = 4560 cubic inches.

10a. Each shoebox has a volume of 22 cubic inches. False. The volume is 228 cubic inches.

10b. Each crate has a volume of about 440 cubic inches. False. The volume of each crate is 4560 cubic inches.

10c. If the crate could hold 27 shoeboxes, the volume of the crate would be about 7,776 cubic inches.

For this one, let's do some more math. Since we figured out the volume of a crate holding 20 shoeboxes is 4560 cubic inches, let's do the same thing to find the volume of a crate holding 27 shoeboxes.

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11 part A:

Each term above describes the term below, but the term below doesn't necessarily describe the term above.

The choice of terms is : trapezoid, triangle, rhombus, parallelogram

Before we do anything else, let's define our terms, as well as the ones used in the diagram.

Trapezoid - A four sided shape with a pair opposite parallel sides.
Triangle - A shape with three sides.
Rhombus - A shape with four equal straight sides.
Parallelogram - A quadrilateral with two sets of parallel sides.
Quadrilateral - A four-sided shape with four angles.
Square - A four-sided shape with all four sides the same length, and all four angles are the same size.

The first term is quadrilateral. From this, we can determine that the term triangle won't be used at all, as it's a three-sided figure, whereas a quadrilateral is a four-sided figure. This leaves trapezoid, rhombus, and parallelogram as our terms.

A trapezoid is a quadrilateral, because it has four sides, but it can't be a rhombus or parallelogram, so it goes in the first open box.

A parallelogram is a trapezoid, because it has a pair of opposite parallel sides, but it can't be a rhombus, because it doesn't necessarily have all equal sides, so it goes in the second open box.

A rhombus is a parallelogram, because it has two sets of parallel sides, and goes in the third open box.

So, from top box to bottom box, the order the term go is
Quadrilateral
Trapezoid
Parallelogram
Rhombus
Square

3 0

3 years ago

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a rand

SOVA2 [1]

Answer:

Question 1:

(a) P(x<60) = 0.9236

(b) P(x>16) = 0.9564

(c) P(16<x<60) = 0.88

(d) P (x>60) = 0.0764

Question 2:

(a) P(x<3) = 0.0668

(b) P(x>7) = 0.0062

(c) P(3<x<7) = 0.927

Step-by-step explanation:

Question 1:

x = no. of mg of porphyrin per deciliter of blood.

μ = 40

σ = 14

(a) We need to compute P(x<60). We need to find the z-score using the normal distribution formula:

z = (x - μ)/σ

P(x<60) = P((x - μ)/σ < (60 - 40)/14)

= P(z < 20/14)

= P(z<1.43)

Using the normal distribution probability table we can find the value of p at z=1.43.

P(z<1.43) = 0.9236

so, P(x<60) = 0.9236

(b) P(x>16) = P(z>(16-40)/14)

= P(z>-1.71)

= 1 - P(z<-1.71)

= 1 - 0.0436

P(x>16) = 0.9564

(c) P(16<x<60) = P((16-40)/14) < x < (60-40)/14)

= P(-1.71 < z < 1.43)

This probability can be calculated as: P(z<1.43) - P(z<-1.71)

P(16<x<60) = 0.9236 - 0.0436

P(16<x<60) = 0.88

(d) P(x>60) = 1 - P(x<60)

we have calculated P(x<60) in part (a) so,

P(x>60) = 1 - 0.9236

P (x>60) = 0.0764

Question 2:

μ = 4.5 mm

σ = 1.0 mm

In this question, we will again compute the z-scores and then find the probability from the normal distribution table.

(a) P(x<3) = P(z<(3-4.5)/1)

= P(z<-1.5)

P(x<3) = 0.0668

(b) P(x>7) = 1 - P(x<7)

= 1 - P(z<(7-4.5)/1)

= 1 - P(z<2.5)

= 1 - 0.9938

P(x>7) = 0.0062

(c) P(3<x<7) = P(x<7) - P(x<3)

we have computed both of these probabilities in parts (a) and (b) so,

P(3<x<7) = 0.9938 - 0.0668

P(3<x<7) = 0.927

6 0

2 years ago