Find the angle measures for each angle.

Answer:

107.5 and 72.5

Step-by-step explanation:

The value of  variable x in the equation is 16.

The equation represented as follows:

x + 14 + x³ = 78

The value x is the variable.

A variable is number represented with a letter in an equation.

Therefore,

x + 14 + 3x = 78

subtract 14 from both sides of the equation

x + 3x + 14 - 14 = 78 - 14

x + 3x = 64

Therefore,

4x = 64

divide both sides by 4

4x / 4 = 64 / 4

x = 16

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The statements that are true are:

3) m∠JKL = 45°

4) m∠MKQ + m∠PKQ = m∠PKM

5) line PK is an angle bisector

1) This statement says that KQ is an angle bisector. This is false because the line KQ does not pass through the diagonal vertex of the right angled symbol at point K.

2) Second statement says that ∠LKQ is bisected. This statement is false because PK is just a perpendicular line to JKM that divides it into 2 equal parts and not a bisector of ∠LKQ

3) The third statement states that m∠JKL = 45°. This statement is true because from the image it is clear that the line KL divides m∠PKJ into two equal parts.

4) Fourth statement says that m∠MKQ + m∠PKQ = m∠PKM. This statement is true. Now, although KQ doesn't bisect m∠PKM into 2 equal parts, nevertheless it divides it into 2 angles namely m∠MKQ and m∠PKQ. This means the sum of m∠MKQ  + m∠PKQ must yield m∠PKM.

5) The fifth statement says that the line PK is an angle bisector. This statement is true because JKM is a straight angle. Thus as PK is perpendicular to it, it has bisected it into two equal parts.

6) The fifth statement says that ∠JKL ≅ ∠QKM. This statement is false because ∠JKL is a bisected angle which is 45° whereas, ∠QKM is not a bisected angle and thus not equal to 45°.

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The time taken by the rock to hit the ground is  3 seconds.

It is given in the question that:-

[tex]t=\frac{\sqrt{h} }{4}[/tex]

Where,

t represents the time (in seconds) taken by the object to reach the ground, and

h represents the height from which the object is falling

We have to find the time taken by a rock to hit the ground after falling from a height of 125 feet.

Using the formula given in the question, we can write,

[tex]t=\frac{\sqrt{125} }{4}=\frac{5\sqrt{5} }{4}[/tex]

We know that,

[tex]\sqrt{5}[/tex] ≈ 2.23

Hence, we can write,

t ≈ (5*2.23)/4 ≈ 2.7875 ≈ 3 seconds (estimated to nearest integer)

Hence, it takes around 3 seconds for the rock to hit the ground after falling from a height of 125 feet.

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GROUP LIKE TERMS TOGETHER.

[tex]3x - 1.79x = 1 - 8 \\ 1.21x = - 7 \\ \frac{1.21x}{1.21} = \frac{ - 7}{1.21 \\ } \\ x = 5.7851239669[/tex]

Answer:

x=[tex]\frac{10}{7}[/tex]

Step-by-step explanation:

8 + 3x = 1 + 7.9x

1. multiply everything by 10 so there is no longer a decimal in the equation

80+30x=10+79x

2. get the x on one side so we -10 and 30x from both side

70=49x

3. divide by 49 on each side as we want to find the value of x

[tex]\frac{70}{49}[/tex]=x

4. the fraction can be simplified to

[tex]\frac{10}{7}[/tex]=x

4. the final answer is

[tex]\frac{10}{7}[/tex]=x

Answer

There are 36 combinations and 181440 permutations

Explanation

The number of combinations of n object taking r at a time is given by the formula;

From the question, n = 9 and r = 7, then substitute these values into the formula

The number of permutations of n object taking r at a time is given by the formula;

Also, n = 9 and r = 7, then substitute these values into the formula to get the number of permutations

Therefore, there are 36 combinations and 181440 permutations

Using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.

As given in the question,

Given: ∠1 ≅ ∠4. Prove ∠2 ≅ ∠3.

(Using angle addition postulate)

    Statements                                              Reasons

1. ∠1 ≅ ∠4           Given

2. ∠1 = 180 - ∠2  Being supplementary angles (angle addition postulate)

3. ∠4 = 180 - ∠3  Being supplementary angles (angle addition postulate)

4. 180 - ∠2 = 180 - ∠3      Substituting Statements 2 & 3 into Statement 1.

5. ∠2 = ∠3                        Simplifying Statement 4 algebraically.

In statement 4, the constants 180 cancel out from either of left hand side (LHS) and right hand side (RHS). Thus the equation gets simplified to Statement 5. It is worthwhile to mention that Supplementary angles or linear pair always sum up to 180° in measure. Additionally linear pair form a straight line together.

Therefore, using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.

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Answer:

a = 240

b = 336

Step-by-step explanation:

To find LCM of 2 number:

To find HCF of 2 numbers:

In this question LCM and HCF is already given but the numbers a and B are unknown.

To find a and B we do the opposite.

Further explanation is in the attached file please open as you will get a clear understanding of the answer.

Answer:

370000

Step-by-step explanation:

So it would go from 962-1000. So 370000

Answer:true

Step-by-step explanation:

because the first one

Answer:

50miles an hour

Step-by-step explanation:

50miles an hour because R = d/t so 500 / 10 is 50

so rate is 50/hour

Answer:

See below:

Explanation:

1.7 dm =  .17 m     assuming  dm is decimeter

.17m  * 10^7  scale  = 1.7 x 10^6 m  = 1.7 x 10^3 km  = 1700 km

Answer: I think that FG and MB are parellel, but I think the way to confirm is to measure with a ruler

Step-by-step explanation:

Answer:

Luana is correct

Step-by-step explanation:

Hello!

According to the question, we are supposed to check whether Luana is right

Oops you made a typo

It's supposed to be -x+2 = --10 not -x+2--10

-x+2 = --10

Add values

When, x = 12

-(+12) + 2 = -10

-12 + 2 = -10

Calculate

-10 = -10

She is correct

When solving

−x+2=−10

Step 1: Subtract 2 from both sides.

−x+2−2=−10−2

−x=−12

Step 2: Divide both sides by -1.

−x/−1 = −12/−1

x=12

So, she's correct

The mean and the standard deviation for the population of products are 2.0 and 0.3329, respectively.

The mean and standard deviation of the population of products produced by the process are 2.0 and 0.3329, respectively.

Start by determining the population mean which use:

μ = (L +  U)/2

Where:

L = 1.9 and U = 2.1

Put the values;

μ = (1.9 + 2.1)/2

μ = 2.0

When p = 5%, the z value from the probability z table is:

z = -1.645

In addition, the z-score is:

z = (x - μ)/(σ/√n)

Put the values;

-1.645 = (1.9 - 2.0)/(σ/√30)

Simplify the equation.

σ = 0.3329

As a result, the mean and standard deviation again for population of products manufactured by the process are 2.0 and 0.3329, respectively.

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The complete question is-

A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights x¯. If test results over a long period of time show that 5% of x¯ the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process?

The construction of the angle bisector of [tex] \angle ABC[/tex], gives the completed statement as follows;

An angle bisector is the ray or line, dividing an angle into two congruent angles.

The steps required to construct the angle bisector of [tex] \angle ABC[/tex] is presented as follows;

The complete statement is therefore;

To construct the angle bisector of.[tex] \angle ABC [/tex], first set the point of the compass on B and draw an arc through BA and BC

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Answer:

56.25

Step-by-step explanation:

We know that, Volume of the cuboid = l × b × h

= 60 cm × 54 cm × 30 cm

= 97200 cm³

Side of the cube = 12 cm

The volume of the cube = side³

= 12³

= 1728 cm³

Required number of cubes = volume of cuboid/volume of the cube

= 97200 / 1728

= 56.25

Thus, 56.25 cubes can be placed in the given cuboid.

The correct description of domain and range for the weight of aeroplane are-

For the given question, the values are-

Function W = 5F + 4000

Full amount of fuel = 200 gallons

No amount of fuel = 0 gallons

Domain : amount of fuel = [0 , 200]

Now, calculate for the range.

If F = 0

W = 5F + 4,000

W = 5(0) + 4,000

W = 4,000

If F = 200

W = 6F + 4,000

W = 6(200) + 4,000

W = 5,200

Range of weight = [4,000 , 5,200]

Thus, the value of range for the total weight of the aeroplane is  [4,000 , 5,200].

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The two factors means that the two value will equate with zero

A) 2x-6

They can be aslo simplified as :

2x-6=0

2x=6

x=3

Thus they gave only one values and cannot be expressed as the factors of two product

B) 2x+6

In this expression

we can simplify as :

2x+6

2x+6=0

2x=-6

x=-3

Thus , they are also not expressed as the factors of the two product

C) 2(x+6)

In this expression

we can simplify as :

2x+12

2x+12=0

2x=-12

x=-6

Thus , they are also not expressed as the factors of the two product

D) (2+x)÷(6+x)

They can express as fraction

Thus, They express as the product of the tewo factors

Answer : D) (2+x)÷(6+x)

The linear equation where m = -4 and passes through (5,9) is y =  - 4x + 29

Linear Equation = an equation between two variables that gives a straight line when plotted on a graph is known as linear equation.

For this statement we need to use the point slope form of linear equation.

The equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form is known as point slope form.

Using point slope form,

y - y1 = m (x - x1)

y - 9 = -4 (x - 5)

y - 9 = -4x + 20

y = -4x + 20 + 9

y = -4x + 29

Therefore, where m = -4 and passes through (5,9) the linear equation will be y = -4x + 29

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The player has a 0.293 percent probability of getting the subsequent number of hits in the subsequent four at-bats.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

In light of the information provided,

designate X as the random variable indicating the player's hit total during his subsequent four at-bats.

Assume that the player hits or misses on each of the following four at-bats in a random order. Consider it a success if the player gets a hit as well.

The probability of "success" is because of the batting average, which is 0.330.

In this case, x can be thought of as the overall success rate across the four at-bats. Inferring that X has a binomial distribution with p=0.330 as its parameters

n=4 p=0.330

Since p denotes the probability of success, the probability of failure is

q=1-0.330

=670

The probability mass function of x here is

f(x)={(4 0)*(0.330)ˣ (0.670)⁽⁴⁻ˣ⁾

The probability that the player will get exactly 2 hits, that is,  is calculated below:

P(2)=F(2)={(4+2)*(0.330)² (0.670)²

              =6[0.04888]

                =0.29328

Thus, the probability that the player will get exactly 2 hits is 0.239.

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An expression which is equivalent to the given expression 18x² +14x + 7 is given by 14x + 18x² + 7.

As given in the question,

Given expression is :

18x² +14x + 7

Simplify all the optional expression to check which one is equivalent to given expression:

a. 7(18x² + 14x)

   = 126x² + 98x

Not equivalent.

b. 14x + 18x²+ 7

Rearrange it

18x²+14x + 7 .

Equivalent.

c. 32x³ + 7

Degree is 3.

Not equivalent.

d. 18x²(14x + 7)

= 252x³ +126x²

Not equivalent.

Therefore, an equivalent expression of 18x²+14x + 7 is 14x + 18x²+ 7.

The complete question is:

Which of the following is an equivalent expression of 18x²+14x + 7?

7(18x² + 14x)

14x + 18x²+ 7

32x³ + 7

18x²(14x + 7)

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Answer: The correct answer is B.

Step-by-step explanation:

To evaluate this expression you must divide x-1 though the expression or factor out the upper half of the equation and cancel out what is necessary.

The division method: attached below :)