2a + b = 20 show your work

If AB is parallel to CD, which statement must be true

Contact [7]

AB and CD do not intersect.

HOPE it helps!!!!!!

8 0

4 years ago

Jordan will hike the trail shown at a rate of mi/h. Write a linear equation to represent the distance Jordan still has to walk

agasfer [191]

Answer:

y = (-mi/h)x + b

y = total distance left to cover

-mi/h = speed at wich he is covering ground

b = the total distance to cover from start to finish

Step-by-step explanation:

Slope Intercept form without other variables filled is shown like this with mx being the slope and b being the y intercept

y = mx + b

all we need to do is fill in known variables with hours multiplied by x represented as m...

y = (-mi/h)x + b

note the negative symbol, this shows that the higher that miles an hour (mi/h) aka speed is, the more distance he will cover REDUCING the distance to cover faster meaning the line will slope DOWNWARD

b would be the the total distance that he has started with, meaning on the point where the line crosses the y axis, the number it crosses at will represent how much he has started with

7 0

2 years ago

In baseball, Shintaro had 4 hits in his last 12 times at bat.

ikadub [295]

For this case we can propose a rule of three according to the Shontaro base performance.

4 hits ------------> 12 times at bat

x -------------------> 36 times at bat

Where "x" represents the number of hits he will have the following week, based on his previous performance.

$x = \frac {36 * 4} {12}\\x = 12$

So, Shintaro will have 12 hits in 36 times at bat

Answer:

Shintaro will have 12 hits in 36 times at bat

OPtion B

3 0

4 years ago

A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associ

lozanna [386]

Answer:

The system of equations representing the situation are

600a + 1200p = 15,000

a + p = 16

with solutions

p = 9

a = 7

Step-by-step explanation:

3 0

3 years ago

According to these three facts, which statements are true?

Yanka [14]

Q1) We have the following statements:

1. Circle W has center (−3, 0) and radius 8.

We can write this statement as the following equation:

 $(x-h)^2+(y-k)^2=r^2 \therefore (h,k)=(-3,0) \ and \ r=8 \\ \\ \therefore (x+3)^2+y^2=64$

The graph of this equation is shown in Figure 1.

2. Circle V is a translation of circle W, 2 units down.

To do this translation we add two units to the y-coordinate, so:

 $(x+3)^2+(y+2)^2=64$

The graph is shown in Figure 2.

3. Circle V is a dilation of circle W with a scale factor of 2.

To do this dilatation we multiply both the center and the radius by the scale factor of 2, thus:

 $(x+3)^2+y^2=64 \\ (h,k)=(-3,0) \\ (h_v,k_v)=2\times (-3,0)=(-6,0) \ and \ r_v=8\times2=16 \\ \\ (x+6)^2+y^2=256$

This circle is shown in Figure 3

So let's analyze each statement.

Q1.1) The center of circle V is (−5, 0).

This is false. From the statement 2 we know that the new center is (-3, -2) and from 3 the new center is (-6, 0).

Q1.2) Circle V and circle W are similar.

Since all circles have the same shape even though they may be different sizes, then all circles are similar. Therefore, it is true that circle V and circle W are similar.

Q1.3) The radius of circle V is 16.

From the statement 3 we can affirm that this is true. By applying the dilatation with a scale factor of 2 we find out that the radius of the new circle is in fact equal to 16.

Q1.4) Circle V and circle W have the same center.

From the statement 2 we know that the new center is (-3, -2) and from 3 the new center is (-6, 0). On the other hand, the center of circle W is (-3, 0). From this, it follows that this statement is false.

Q2) Suppose x is any positive number.

We have two concentric circles as follows:

$x\ \textgreater \ 0 \\ \\ Circle \ 1: Center \ (0,0) \ and \ radius \ 2x \\ \\ Circle \ 2: Center \ (0, 0) \ and \ radius \ 10x$ 

Q2.1) Why is circle 1 similar to circle 2?

If we perform a dilatation, that is, a resizing of one circle, centered on the shared center, until both circles overlap, it will be true that the circles will always overlap no matter what size they are, thus, they are similar. In fact, as we said in above all circles are similar.

Q2.2) Circle 2 is a dilation of circle 1 with a scale factor of 0.2.

Suppose that:

 $x=2$

Then circle 1 is given by the following equation:

 $x^2+y^2=4$

If we dilate this circle with a scale factor of 0.2 then:

 $Circle \ 1: x^2+y^2=4 \\ Diameter \ 1=2r=2\times 2=4 \\ \\ (h,k)=(0,0) \\ (h_v,k_v)=0.2\times (0,0)=(0,0) \ and \ r_v=0.2\times 2=0.4 \\ \\ Circle \ 2:x^2+y^2=0.16 \\ Diameter \ 2=2\times 0.4=0.8 \\ \\ So: \\ \\ Diameter \ 1 \neq Diameter \2$

So the statement both circles have congruent diameters is false.

Q2.3) Circle 2 is a dilation of circle 1 with a scale factor of 5.

We have the same equation for circle 1:

 $x^2+y^2=4$

$Circle \ 1: x^2+y^2=4 \\ \\ Dilatation: \\ (h,k)=(0,0) \\ (h_v,k_v)=5\times (0,0)=(0,0) \ and \ r_v=5\times 2=10 \\ \\ Circle \ 2:x^2+y^2=100$

Two circles have the same area if they have the same radius. Given that this is no applied to our circles, the statement circle 1 and circle 2 have equal areas is false.

8 0

3 years ago