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3 years ago

Prove that if AC=DF and AB=DE then BC=EF

1 answer:

8 0

In triangle ABC and DEF
AC =DF, [ given ]
AB =DE, [ given ]
angle A = angle D
by SAS
ABC congruent to triangle DFE
so
BC = EF, [ CPCTC]
hence proved

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Find the solution set of the inequality

Brilliant_brown [7]

Answer:

$\boxed{\textsf{ Hence the solution set is$ \bf{\bigg( \dfrac{33}{4},\infty \bigg) }$}}.$

Step-by-step explanation:

A inequality is given to us and we need to find the solution set. So the given inequality to us is ,

-4x + 35 >2

$\bf\implies -4x + 35 > 2 \\\\\bf\implies -4x > 2-35 \\\\\bf \implies -4x > -33 \\\\\bf \implies x >\dfrac{-33}{-4}\\\\\bf \implies x > \dfrac{33}{4} \\\\\bf\implies \boxed{\pink{\bf x \in \bigg(\dfrac{33}{4}, \infty \bigg) }}$

<h3>★ Hence the solution set is x € ( 33/4 , ∞ ).</h3>

3 0

3 years ago

How long will it take $5,000 to double in an account that pays 5.6% simple interest

Drupady [299]

The answer it should be: 28,000

3 0

4 years ago

7. In the accompanying diagram of right triangle ABC, altitude BD divides hypotenuse

xxMikexx [17]

Answer:

Step-by-step explanation:

5 0

3 years ago

A solid piece of wood shaped as a cylinder with an 8-centimeter diameter is cut as shown. What is the surface area of the figure

aliina [53]

The surface area of the figure is 96 + 64π ⇒ 1st answer
Step-by-step explanation:
* Lats revise how to find the surface area of the cylinder
- The surface area = lateral area + 2 × area of one base
- The lateral area = perimeter of the base × its height
* Lets solve the problem
- The figure is have cylinder
- Its diameter = 8 cm
∴ Its radius = 8 ÷ 2 = 4 cm
- Its height = 12 cm
∵ The perimeter of the semi-circle = πr
∴ The perimeter of the base = 4π cm
∵ The area of semi-circle = 1/2 πr²
∴ The area of the base = 1/2 × π × 4² = 8π cm²
* Now lets find the surface area of the half-cylinder
- SA = lateral area + 2 × area of one base + the rectangular face
∵ LA = perimeter of base × its height
∴ LA = 4π × 12 = 48π cm²
∵ The dimensions of the rectangular face are the diameter and the
height of the cylinder
∴ The area of the rectangular face = 8 × 12 = 96 cm²
∵ The area of the two bases = 2 × 8π = 16π cm²
∴ SA = 48π + 16π + 96 = 64π + 96 cm²
* The surface area of the figure is 96 + 64π

6 0

3 years ago

Solve for t. f(t)=-16t^2+576

IgorC [24]

Answer: t^2=-f-576/16

Step-by-step explanation:

Step 1. Switch the equation around:

-16t^2+576=f

Step 2. Subtract 576 from each side:

-16t^2+576-576=f-576

Step 3. Now simplify:

-16t^2=f-576

Step 4. Divide everything now by -16:

-16t^2/-16=f/-16-576/-16

Step 5. Simplify again:

t^2=-f-576/16

Hope I could help! :)

3 0

4 years ago