Which of the following are mathematical sentences?

What are the domain and range of the function f(x)=5^x-3+1

Hunter-Best [27]

The domain is the set of all possible values of independent variable I.e of x. The range is the complete set of all possible resulting values of the dependent variable of i.e of y

8 0

3 years ago

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A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccol

rjkz [21]

Answer:

27405

Step-by-step explanation:

There are 6 different variants available for each croissant. There are 26 croissants in all out of which 1 is plain. We use combination and permutation technique to identify different ways to choose croissant.

[5 + 26 - 1 ] 26 = 30C26 = 27405.

5 0

3 years ago

Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, l ≥ 20. He h

zhuklara [117]

I added a screenshot of the complete question along with the given choices.

Answers:

w = 10 ft and l = 50 ft ................> second option

w = 20 ft and l = 60 ft ...............> third option

w = 50 ft and l = 40 ft ...............> fifth option

Explanation:

We are given that:

length should be at least 20 ...........> length ≥ 20

equation for perimeter is : 2l + 2w ≤ 200

We will check each option as follows:

Option 1:

w = 50 ft and l = 10 ft

This option is incorrect as the proposed length is less than 20.

Option 2:

w = 10 ft and l = 50 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(10) = 100 + 20 = 120 ≤ 200

The second condition is also satisfied.

This option is correct

Option 3:

w = 20 ft and l = 60 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(60) + 2(20) = 120 + 40 = 160 ≤ 200

The second condition is also satisfied.

This option is correct

Option 4:

w = 90 ft and l = 30 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(30) + 2(90) = 60 + 180 = 240 > 200

The second condition is not satisfied.

This option is incorrect

Option 5:

w = 50 ft and l = 40 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(40) = 100 + 80 = 180 ≤ 200

The second condition is also satisfied.

This option is correct

Hope this helps :)

8 0

3 years ago

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It takes a boat going upstream 5 hours to cover the same distance, as it would cover in 3 hours going downstream. What is the sp

Vaselesa [24]

Answer: 15 kilometers per hour

Step-by-step explanation:

8 0

3 years ago

Given: \overline{AC} \perp \overline{BD} AC ⊥ BD and \overline{BD} BD bisects \overline{AC}. AC . Prove: \triangle ABD \cong \tr

Fofino [41]

Answer:

The Proof for

△ABD ≅ △CBD is below

Step-by-step explanation:

Given:

$\overline{AC} \perp \overline{BD}$

$\overline{BD} \ bisects\ \overline{AC}$

AD = CD .........BD bisect AC

To Prove:

△ABD ≅ △CBD

Proof:

In ΔABD and ΔCBD

BD ≅ BD ....……….{Reflexive Property}

∠ADB ≅ ∠CDB …………..{Measure of each angle is 90°( $\overline{AC} \perp \overline{BD}$ )}

AD ≅ CD ....……….{ $\overline{BD} \ bisects\ \overline{AC}$ }

ΔABD ≅ ΔCBD .......….{By Side-Angle-Side Congruence test} ...Proved

4 0

3 years ago