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3 years ago

A gardener made a scale drawing of a lawn with a scale

Mathematics

2 answers:

stellarik [79]3 years ago

8 0

Answer: I’m pretty sure it’s b?

Step-by-step explanation:

Natali5045456 [20]3 years ago

7 0

Answer: A.

Step-by-step explanation:

I just took the exam

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PLEASE HELP

poizon [28]

Part A
The given line passes through (-2,2) and it is parallel to the line

$4x - 3y - 7 = 0$

We need to determine the slope of this line by writing it in slope -intercept form.

$3y = 4x - 7$

$y = \frac{4}{3} x - \frac{7}{3}$
The slope of this line is
$\frac{4}{3}$

The line parallel to this line also has slope

$m = \frac{4}{3}$

The equation is

$y = \frac{4}{3} x + c$

We substitute (-2,2)

$2 = \frac{4}{3}( - 2) + c$

$c = 2 + \frac{8}{3} = \frac{14}{3}$

The required equation is

$y = \frac{4}{3} x + \frac{14}{3}$

PART B

The given line is

$4x - 3y - 7 = 0$

The slope of this line is
$\frac{4}{3}$

The slope of the line perpendicular to it is

$m = - \frac{3}{4}$

The equation of the line is

$y = - \frac{ 3}{4} x + c$

We substitute the point, (-2,2)

$2= - \frac{ 3}{4} ( - 2) + c$

$2= \frac{ 3}{2} + c$

$c = 2 - \frac{3}{2} = \frac{1}{2}$

The equation of the perpendicular line is

$y= - \frac{ 3}{4} x + \frac{1}{2}$

6 0

3 years ago

HELPPPP 100 points if you help!!!!

nignag [31]

Answer:

Part A)

Chorus:

$c(t)=15(1.12)^t$

Band:

$b(t)=2t+30$

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

$c(t)=a(r)^t$

Where a is the initial population and r is the rate of change.

We will substitute 15 for a and 1.12 for r. Hence:

$c(t)=15(1.12)^t$

This represents the number of people in the chorus after t years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

$b(t)=mt+b$

And by substitution:

$b(t)=2t+30$

This represents the number of people in the band after t years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

$c(9)=15(1.12)^9\approx41.59\approx41$

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

$b(9)=2(9)+30=48$

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for t. So:

$15(1.12)^t=2t+30$

Unfortunately, it is impossible to solve for t using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0

3 years ago

Which mixed number is equal to 18/8 2 6/9 2 5/8 2 1/4 1 2/8

Galina-37 [17]

Answer: 2 1/4

Step-by-step explanation:

4 0

3 years ago

Joy has ₱500.00 to spend for food. She spent ₱98.75 on Monday, ₱73.75 on Tuesday and ₱50.25 on Wednesday. How much money was lef

Alex787 [66]

Answer:

₱277.25

Step-by-step explanation:

₱500.00 - ₱98.75 - ₱73.75 - ₱50.25 = ₱277.25

8 0

3 years ago

Quadrilateral ABCD is dilated by a scale factor of 1 over 2 centered around (2, 2). Which statement is true about the dilation?

Musya8 [376]

Answer:

Option (1)

1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.

Step-by-step explanation:

The rest of the question is the attached figure (1).

The statement options are:

1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.

2) Segment B'D' will run through (2, 2) and will be longer than segment BD.

3) Segment B'D' will parallel to segment BD and will be shorter than segment BD.

4) Segment B'D' will be parallel to segment BD and will be longer than segment BD.

==============================================================

See the attched figure (2), which represents Quadrilateral ABCD and the image A'B'C'D'

As shown:

The quadrilateral ABCD with vertices A(1,2), B(2,3), C(4,2) and D(2,1).

Quadrilateral ABCD is dilated by a scale factor of 1 over 2 centered around (2, 2).

So,

The quadrilateral A'B'C'D' will be with vertices:

A'= (1.5,2), B'= (2,2.5), C'= (3,2), D'= (2,1.5)

Comparing the options with the figure (2):

So, the answer is option (1)

1) Segment B'D' will run through (2, 2) and will be shorter than segment BD.

6 0

3 years ago