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3 years ago

7

You are given two triangles and the information that the three pairs of corresponding angles are congruent. What other informati

on would guarantee that the triangles are congruent?

1 answer:

ladessa [460]3 years ago

5 0

Congruent pair of corresponding included sides

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a bag of potting soil costs $3 less than a flower pot. Ike paid $41 for 3 flower pots and 5 bags of soil. how much does one bag

Arada [10]

Cost of bag of soil = x-3 where x is the price of a flower pot
41=3x + 5(x-3)
41=3x + 5x -15
41=8x -15
41+15=8x
56=8x
56÷8=x
$7.00=x

5 0

3 years ago

Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.

koban [17]

Answer:

$x^2 + 4x + y^2 +8y = 0$

Step-by-step explanation:

Given

$A = (-1,-2)$

$B = (2,4)$

$AP:BP = 1 : 2$

Required

The locus of P

$AP:BP = 1 : 2$

Express as fraction

$\frac{AP}{BP} = \frac{1}{2}$

Cross multiply

$2AP = BP$

Calculate AP and BP using the following distance formula:

$d = \sqrt{(x - x_1)^2 + (y - y_1)^2}$

So, we have:

$2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

$2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

Take square of both sides

$4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2$

Evaluate all squares

$4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16$

Collect and evaluate like terms

$4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20$

Open brackets

$4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20$

Collect like terms

$4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0$

$3x^2 + 12x + 3y^2 +24y = 0$

Divide through by 3

$x^2 + 4x + y^2 +8y = 0$

3 0

3 years ago

In each of the following scenarios, determine if the data are paired.

zmey [24]

Answer:

1. Can be Paired or Not Paired

2. Paired

3. Not Paired

Step-by-step explanation:

Two sets of observations are paired if each observation in one set has a special correspondence or connection with exactly one observation in the other data set.

1. Can be Paired or Not paired

Reason -

We might look at testing the difference of means using a two sample t-test. However, we may also try running a paired t-test.

But its used in cases where the observations are usually from the same populations at different times or through different sources etc.

Hence can't conclude that it is paired or not paired.

2. Paired

Reason -

Each record is a price of the same item from different stores.

3. Not paired

Reason -

This is again a case of testing the difference of means of two-samples (2 independent samples precisely) that are not paired.

5 0

3 years ago

From her window, Carmella looks up to the top of a neighboring building at an angle of 46°. Her

Vinil7 [7]

Answer:

$270.3\ ft$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle ADE

Find the value of h1

See the attached figure

h1=AD

$tan(25\°)=\frac{h_1}{180}$

Solve for h1

$h_1=(180)tan(25\°)\\h_1=83.94\ ft$

step 2

In the right triangle ABC

Find the value of h2

See the attached figure

h2=BC

$tan(46\°)=\frac{h_2}{180}$

Solve for h2

$h_2=(180)tan(46\°)\\h_2=186.40\ ft$

step 3

Find the height of the neighboring building

we know that

The height of the neighboring building is equal to

$h=h_1+h_2$

substitute the values

$h=83.94+186.40=270.34\ ft$

Round to the nearest tenth of a foot

$h=270.3\ ft$

7 0

3 years ago

5x+4y=-14 <br>3x+6y=6<br> solve the system below by the elimation

lana66690 [7]

Answer:

y = 4

x = -6

Step-by-step explanation:

multiply first equation by 3

3×(5x+4y)= -14 ➡ 15x + 12y = -42

multiply second equation by -5

-5×(3x+6y)= 6➡ -15x -30y = -30

now add both equations up

15x +12y -15x -30y = -42 -30 (15x will eliminate -15x)

-18y = -72

y = 4 use this to find value of x

3x + 6×4 = 6 ➡ ex = -18 ➡ x = -6

8 0

3 years ago