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3 years ago

The proof ABC ≅ DCB that is shown.

Mathematics

2 answers:

miskamm [114]3 years ago

8 0

Solution:

Given: ∠A≅∠D and CD║AB

To Prove: Δ ABC ≅ ΔD CB

Proof:

1. ∠A=∠D→→(Given)

2. As, CD ║AB, ⇒ ∠DCB=∠ABC→→(when lines are parallel, Alternate interior angles are equal.)

3. Segment CB=Segment BC→→Reflection property

⇒Δ ABC ≅ ΔD CB →→(Angle Angle Side or AAS)

Schach [20]3 years ago

4 0

The correct answer is:

AAS

Explanation:

AAS stands for "angle-angle-side." This states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.

In these triangles, we have ∠CAB ≅ ∠CDB given to us to begin with. Throughout the proof, we find that ∠ABC ≅ ∠DCB. We also have that CB is congruent to itself. This is two angles and a side not included, so this is AAS.

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Eamon is arranging 39 books on 3 shelves. If he puts the same number of books on each shelf, how many books will there be on eac

blagie [28]

39 times 3 = 117. Hope this helps

7 0

3 years ago

Find the remainder when f(x) = x3 − 14x2 + 7x − 10 is divided by x − 3. 184 164 −88 −122

Fudgin [204]

Answer:

122

Step-by-step explanation:

For this case we must build a quotient that, when multiplied by the divisor, eliminates the terms of the divide until it reaches the remainder.

It must be fulfilled that:

Dividend = Quotient * Divisor + Remainder

we have that the remainder is 122.

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5 0

3 years ago

Gerardo works at an ice cream shop each flavor of ice cream is stored in a right cylindrical tub that measures approximately 9 i

Leokris [45]

Answer:

Volume left = 404.32 cubic inches

Step-by-step explanation:

volume of a cylinder = $\pi$ $r^{2}$ h

volume of ice cream in the cylindrical tub = $\frac{22}{7}$ x $5^{2}$ x 9

= $\frac{22}{7}$ x 25 x 9

= 707.1429

Volume of ice cream in the cylindrical tub is 707.14 cubic inches.

The ice cream scoop has a spherical volume, so that;

volume of a sphere = $\frac{4}{3}$ $\pi$ $r^{3}$

r = $\frac{2.5}{2}$

= $\frac{5}{4}$ inches

volume of the scoop = $\frac{4}{3}$ x $\frac{22}{7}$ x $(\frac{5}{4} )^{3}$

= $\frac{4}{3}$ x $\frac{22}{7}$ x $\frac{125}{64}$

= 8.1845

volume of the scoop is 8.19 cubic inches.

If he scoops 37 scoops,

volume of the 37 scoops = 37 x 8.1845

= 302.8265

volume of 37 scoops is 302.83 cubic inches.

Volume of ice cream left in the tub = 707.1429 - 302.8265

= 404.3164

Volume of ice cream left in the tub is 404.32 cubic inches.

7 0

3 years ago

a bank charges a simple interest of 3.5% on a loan of $5000 to be paid back over a period of 3 years. How much will the borrower

user100 [1]

Answer: The monthly payments for a $5,000 loan would $146.51.

Step-by-step explanation: How it looks in the TVM Solver formula:

N = 36 ( 3 (years) x 12 (monthly payments) )

I% = 3.5%

PV = $5,000

PMT = 146.51 (or 146.08 if you choose BEGIN)

FV = 0

P/Y = 12 (months)

C/Y = (12 (months)

PMT: END | BEGIN

6 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