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sveticcg [70]
1 year ago
5

If m∠NQM=2x+8 and m∠PQR=x+22, find the value of x

Mathematics
2 answers:
Oduvanchick [21]1 year ago
6 0

Answer:

14

Step-by-step explanation:

2x+8=x+22

2x - x= 22 - 8

x=14

Alex777 [14]1 year ago
3 0

Answer:

x = 14

Step-by-step explanation:

∠ NQM and ∠ PQR are congruent ( indicated by the same orange arc within the 2 angles ) , then

2x + 8 = x + 22 ( subtract x from both sides )

x + 8 = 22 ( subtract 8 from both sides )

x = 14

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Find f(-5) and f(12) for each piecewise function f(x){-4x+3 if x<3
Law Incorporation [45]
<h3>Answers:</h3>
  • f(-5) = 23
  • f(12) = 433

==================================================

Explanation:

The given piecewise function is

f(x) = \begin{cases}-4x+3 \ \text{ if } \ x < 3\\-x^3 \ \text{ if } \ 3 \le x \le 8\\3x^2+1 \ \text{ if } \ x > 8\end{cases}

At first piecewise functions may be strange confusing things, but they aren't so bad. I like to think of it like this: f(x) is a function that changes its identity based on what the input x is. We have three situations

  • f(x) = -4x+3 when x < 3
  • f(x) = -x^3 when 3 \le x \le 8
  • f(x) = 3x^2+1 when x > 8

In a sense, we have three different functions but they are combined somehow.

If x is smaller than 3, then we go for the first definition. Or if x is between 3 and 8, then we go for the second definition. Or if x is larger than 8, then we go for the third definition.

-----------------------

f(-5) means f(x) when x = -5. We see that -5 is smaller than 3, so x = -5 makes x < 3 true. We'll use the first definition

f(x) = -4x+3

f(-5) = -4(-5)+3

f(-5) = 20+3

f(-5) = 23

------------------------

Now the input is x = 12. This is larger than 8. In other words, x = 12 makes x > 8 true. We'll use the third definition

f(x) = 3x^2+1

f(12) = 3(12)^2+1

f(12) = 3(144)+1

f(12) = 432+1

f(12) = 433

------------------------

Side notes:

  • We won't use the second definition since we don't have any x inputs between 3 and 8
  • To say "less than or equal to" on a keyboard, you can write "<=" without quotes. For example, x \le 5 is the same as x<=5
3 0
3 years ago
Use the diagram what can be said about angle 7 and 12?
balandron [24]
They are congruent angles
3 0
3 years ago
A recipe for individual chocolate hazelnut tarts calls for ½ cup of hazelnuts per tart. If 1 cup of hazelnuts weighs 4 ounces, w
DerKrebs [107]

Answer:

The amount is sufficient to make 75 tarts.

Step-by-step explanation:

We have been given that a recipe for individual chocolate hazelnut tarts calls for ½ cup of hazelnuts per tart and 1 cup of hazelnuts weighs 4 ounces.

The half cup of hazelnuts will weigh 2 ounces (\frac{4}{2}=2).

1 kg equals 35.274 ounces.

\text{5 kg}=5\times 35.274\text{ ounces}

\text{5 kg}=176.37\text{ ounces}

Since each tart needs  ½ cup of hazelnuts and half cup of hazelnuts will weigh 2 ounces, so we will divide 176.37 ounces by 2 to find number of tarts.

\frac{176.37}{2}=88.185\approx 88

Since we can make 88 tarts from 5 kg hazelnuts, therefore, the 5-kilogram bag of hazelnuts be sufficient to make 75 tarts.

7 0
3 years ago
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katen-ka-za [31]

Answer:

the answer of given question is $400.

6 0
2 years ago
To amend the U.S. Constitution, 3/4 of the 59 states must approve the amendment. If 35 states approve an amendment, will the con
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Answer:

No

Step-by-step explanation:

3/4 of 59 is 44.25. More than 44 states need approve the constitution to be amended

8 0
3 years ago
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