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3 years ago

Given AD CB ADB CBD Prove: ∆ADB ≅ ∆CBD

Mathematics

2 answers:

algol [13]3 years ago

8 0

Answer:

<h2>SAS postulate.</h2>

Step-by-step explanation:

Notice that sides AD and BC are congruent, also DB is a common side to both triangles. At this point, we already have two corresponding congruent sides.

Additonally, angles ADB and CBD are congruent. In summary, we have two pair of corresponding sides congruent, and one pair of corresponding angles congruent (which is formed by the congruent sides).

Based on all the given information, by SAS postulate triangles ADB and CBD are congruent.

Andrei [34K]3 years ago

7 0

We will use the SAS (SIDE-ANGLE-SIDE) to prove that two triangles are congruent.

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The diagram shows a length and angle measure in a scale drawing of a triangular roof truss. In the actual roof truss, the length

marishachu [46]

corresponding to AB is 38 feet, the length of the side corresponding to BC is 22 feet, and their included angle measures 115°. For

what length BC is the scale drawing correct?

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3 years ago

The sales tax in Mike's home city is 8.25%. Mike buys a sweater for $49.95, two pair of slacks for $68.59 each, and a suit for $

hjlf

Answer: $50.91

Step-by-step explanation:

The following information can be gotten from the question;

Cost of sweater = $49.95,

Cost of slacks = $68.59 each,

Cost of 2 slacks = $68.59 × 2

= $137.18

Cost of suit = $429.99.

Total cost = $49.95 + $137.18 + $429.99 = $617.12

Sales tax = 8.25%

The sales tax that Mike owe will be:

= 8.25% × $617.12

= 0.0825 × $617.12

= $50.91

Mike will have to pay a sales tax of $50.91

4 0

3 years ago

What is the solution to the following equation?<br><br> 5 + 3 (y - 4) = 4y +10

Umnica [9.8K]

Answer:

5 +3(y-4) = 4y +10

5 + 3y -12= 4y +10

-7 +3y = 4y + 10

3y - 4y = 10 + 7

-y = 17

y= -17

8 0

2 years ago

Read 2 more answers

Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (−1, 2) to (1, 2) (a) find a function f

Korvikt [17]

If there is some scalar function $f(x,y)$ such that

$\nabla f(x,y)=\mathbf f(x,y)=x^2\,\mathbf i+y^2\,\mathbf j$

then we want to find $f$ such that

$\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)$
$\dfrac{\partial f}{\partial y}=y^2=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\dfrac{y^3}3+C$
$\implies f(x,y)=\dfrac{x^3}3+\dfrac{y^3}3+C$

So the vector field $\mathbf f(x,y)$ is conservative, which means the fundamental theorem applies; the line integral of $\mathbf f$ along any path $\mathcal C$ parameterized by some vector-valued function $\mathbf r(t)$ over $a\le t\le b$ is given by

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=a}^{t=b}\mathbf f(\mathbf r(t))\cdot\dfrac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt=f(\mathbf r(b))-f(\mathbf r(a))$

In this case,

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(1,2)-f(-1,2)=\dfrac23$

5 0

3 years ago

A chemist is mixing 45% salt solution with a 30% salt solution to make 60 L of a new solution that will contain 40% salt. How mu

Alinara [238K]

Answer:

30 ml of 45% salt solution and 20 ml of 30% salt solution.

Step-by-step explanation:

Let x be the amount of 45% salt solution and y be the amount of 30% salt solution

the two equation will be:

x+y=60 -- A

0.45x+0.3y=0.4(60) -- B

Solve by substitution

Rewrite Equation A

x+y=60

x=60-y --- C

Substitute C into B

0.45(60-y)+0.3y=24

27-0.45y+0.3y=24

-0.15y=-3

y=20

<u>Substitute</u> the y=20 into equation C

x=60-20

x=30

Therefore, there was 30 ml of 45% salt solution and 20 ml of 30% salt solution.

3 0

2 years ago