Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

If p − 1 is a factor of p4 + p2 + p − k, the value of k is __.

Answer:

Step-by-step explanation:

a^2+b^2=c^2

c^2-b^2=a^2

2^2-1^2=c^2

c^2=3

c=[tex]\sqrt{3}[/tex]

espero que esto te ayude, pero no se si esta correcto lo siento

The federal income tax for this person is $407 per month.

The person qualifies for five personal allowances because they have five children. As of 2021, the standard personal allowance in the United States is $12,550.

As a result, the person can deduct 5 × $12,550 =$62, 750, from their taxable income to account for the five allowance

Their monthly taxable income is 61320 - $62, 750, or $4070. Based on taxable income, the federal income tax is calculated, and the individual's tax rate is determined by their taxable income bracket.

The tax rate on $4070 in taxable income as of 2021 is 10%.

Therefore, the federal income tax for this person is $4070 × 10% = $407 per month.

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By making and solving the respective equation x + 4x + 3 = 63, we can conclude that the age of Adam is 12 years.

According to a mathematical equation, two amounts or values are equivalent to a meaningful term, for example, 6 x 4 = 12 x 2.

When two or more factors must be taken into account together in order to comprehend or describe the entire situation, an equation is used.

So, we know that:

Jeff is 3 years older than four times of Adam.

Now, let Adam be x and Jeff be 4x + 3.

Then, the equation will be:

x + 4x + 3 = 63

5x + 3 = 63

5x = 63 - 3

5x = 60

x = 60/5

x = 12

Adam: = x = 12 years

Therefore, by making and solving the respective equation x + 4x + 3 = 63, we can conclude that the age of Adam is 12 years.

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The value of the equation is A = 1/2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( 1/5 )r + 9/20   be equation (1)

On simplifying the equation , we get

when r = ( 1/4 )

Substituting the value of r in the equation , we get

A = ( 1/5 ) ( 1/4 ) + 9/20

A = ( 1/20 ) + ( 9/20 )

On further simplification , we get

A = 10/20

A = 1/2

Hence , the equation is A = 1/2

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Answer: If a 21.0 kg rock rests on the edge of a cliff 32.0 m high, the gravitational potential energy gained by the rock would be 6585.6 Joules.

Step-by-step explanation:

Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.

As given in the problem a 21.0 kg rock rests on the edge of a cliff 32.0 m high, then we have to calculate the potential energy gained by the rock,

The potential energy of the rock = 21 × 9.8 × 32

                                                     = 6585.6 Joules.

Thus ,If a 21.0 kg rock rests on the edge of a cliff 32.0 m high, the gravitational potential energy gained by the rock would be 6585.6 Joules.

Hope this helps.

Answer:

21.0 kg

Step-by-step explanation:

Answer:

x is undefined

Step-by-step explanation:

[tex]\ln[/tex] is the Natural Logarithm.

The natural log of a negative number is undefined.

The option for the first box is segment addition and the option for the second box is AC does not equal XZ.

Two or more figures are congruent if the dimensions of the one figure is equal to the dimension of the other figure.

Proof of the congruence of two lines are given using the contradiction method.

Given that AC ≅ XZ and BC ≅ XY.

It is proving AB ≅ YZ.

We get by following some steps,

AB + BC ≠ YZ + XY

We know that, AB and BC are the segments joining to form the line AC.

AB + BC = AC

Similarly, YZ and XY are the segments joining to form the line XZ.

YZ + XY = XZ

Substituting in AB + BC ≠ YZ + XY, we get AC ≠ XZ.

So here we are using the segment addition to write AC ≠ XZ

Hence applying segment addition to AB + BC ≠ YZ + XY, AC ≠ XZ

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Answer:

3 3/13 hours

Step-by-step explanation:

you will first find out how many hours it will take for each gardener to do 1 part of the job. gardener 1 is 1/6 and the second is 1/7. you will next add the two fractions. this will equal 13/42. you will then multiply by the reciprocal to get 1, this stands for the whole job done together. The reciprocal is the answer, 42/13. You will then simplify that to 3 3/13 hours.

The number of students who drink coffee with cream is 1800.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that in a recent survey of college students, it was determined that 4 out of 5 students drink coffee. Of those students who drink coffee, 1 out of 8 students adds cream. If a college campus has 18000 students.

The number of students who drink coffee with cream is calculated as:-

Number = ( 4 / 5 ) x ( 1 / 8 ) x 18000

Number = 1800

Therefore, there are 1800 students who like their coffee with cream.

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Correct option is C, A triangle can be formed with these side lengths since 8 cm, which is greater than the third side's 7 cm, is possible.

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilize specific terminology.

Straight angle refers to the angle that is 180 degrees in length.

The side length combinations that can result in a triangle include

2, 7, and 6 centimeters; 2 meters; 5, and 7 meters

6, 6, and 12 feet

According to the triangle inequality theorem, the third side of a triangle is greater than or equal to the sum of any two of its sides.

In other words, in a triangle with sides a, b, and c,

a + b ≥ c

When examining the sets of provided side lengths,

2 cm, 7 cm, and 6 cm in a triangle,

2 + 6 = 8,

Thus, a triangle can be formed with these side lengths since 8 cm, which is greater than the third side's 7 cm, is possible.

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Answer:

x = 40

Step-by-step explanation:

We have to find,

→ the value of x in the equation.

The equation is,

→ (x/2) + 3 = 23

Now the value of x will be,

→ (x/2) + 3 = 23

→ x/2 = 23 - 3

→ x/2 = 20

→ x = 20 × 2

→ [ x = 40 ]

Hence, the value of x is 40.

Note that the tools are matched against the alphabet are given as follows:

A. Drill index - Box that drill bits are stored in

B. Fender cover - Used to protect the vehicle's finish

C. Impact driver - Hand tool that is used to loosen fasteners that are very tight

D. Speed handle - Fits between a socket and a ratchet

F. Flare nut wrench - Tool used to loosen and tighten fuel line fittings

J. Stubby screwdriver - What a very short screwdriver is called

K. 6-point socket - Can be used on a 6-point fastener head

L. 12-point socket - Used on square drive fastener heads

N. Impact driver - An air-powered tool used to remove fasteners

O. Impact socket - Used with air tools

P. Slide hammer - Puller that uses a heavy weight that is slid against its handle

Q. Bearing separator - Used with a puller to pull a bearing from a shaft

R. Torque wrench - Measures the turning effort applied to a fastener

S. Chisel - Hand tool used for quickness when assembling parts

T. Dead blow hammer - A soft-faced hammer that has metal shot in its head

U. Creeper - Used to move around under vehicles

V. Hex wrench/ViseGrips - Commonly called Allen wrenches/Pliers that can be locked to a part

W. Safety goggles - Worn whenever working in the shop

X. Crowfoot wrench/Extension - Wrench used with a ratchet

Y. Coarse tooth hacksaw blade - Hacksaw blade that is the best choice for cutting thick steel

Z. Fine tooth hacksaw blade - Hacksaw blade that is the best choice for cutting Sheet Metal.

The above tools can be classified as hand tools and power tools used in various mechanical and automotive applications.

Their importance lies in their ability to make repair and maintenance tasks efficient and precise, ensuring the proper functioning of machinery and vehicles.

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Answer:

E 1/4 (-8y+6x+7)

Step-by-step explanation:

Tthe the number of smallmouth bass Chelsie caught = 37

and the number of salmon she caught = 15

Here, x represents the number of smallmouth bass Chelsie caught. and y represents the number of salmon she caught.

Chelsie caught 52 fish today.

So we get an equation,

x + y = 52        

Also, for smallmouth bass, she caught seven more than 2 times the amount of salmon she caught.

So we get an equation,

x = 7 + 2y  

So, we get a system of equations:

x + y = 52                      ..........(1)

x = 7 + 2y                .......(2)

Substitute above value of x in equation (1)

(7 + 2y) + y = 52      

7 + 3y = 52

3y = 45

y = 15

Substitute above value of y in equation (2),

x = 7 + 2(15)

x = 37

Therefore, she caught 37 smallmouth bass and 15 salmon.

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The two equations, y = 53x + 10 and y = 55x, represent the cost of x tickets for option 1 and option 2, respectively.

The equation y = 53x + 10 represents the cost of x tickets for option 1, which includes a ticket cost of $53 per ticket plus a shipping fee of $10. So, if Mrs. Curtis buys 1 ticket, the cost would be 53 * 1 + 10 = 63. If she buys 2 tickets, the cost would be 53 * 2 + 10 = 116, and so on.

The equation y = 55x represents the cost of x tickets for option 2, which includes a ticket cost of $55 per ticket and free shipping. So, if Mrs. Curtis buys 1 ticket, the cost would be 55 * 1 = 55. If she buys 2 tickets, the cost would be 55 * 2 = 110, and so on.

By comparing the values of y for different values of x in these two equations, Mrs. Curtis can determine the cost-effective option for buying the tickets.

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Answer:

Step-by-step explanation:

9.5 678 then ada 9.76

"a" can be expressed as a function of "R" as:

[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex].

What are logarithmic properties?

The 4 laws of logarithms are product property, division property, power property and change of base property.

To solve for "a" in terms of "R," we need to isolate "a" on one side of the equation. We can do this by rearranging the equation and applying logarithmic properties.

Starting with the equation R = 3 log(a + 2) + 15, we'll subtract 15 from both sides:

R - 15 = 3 log(a + 2)

Next, we'll divide both sides by 3:

(R - 15) / 3 = log(a + 2)

Finally, we'll use the inverse logarithmic function, denoted as "exp" or "10^," to solve for "a":

[tex]a+2 = 10^{\frac{(R - 15)}{3} }[/tex]

And finally, we'll subtract 2 from both sides to obtain the solution:

[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex]

So, "a" can be expressed as a function of "R" as:

[tex]a = 10^{\frac{(R - 15)}{3} - 2}[/tex]

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We can use the number -5 as:

1. Temperature: If a temperature is measured below 0 degrees Celsius (the freezing point of water), it can be expressed as a negative number. For example, if the temperature is -5 degrees Celsius, it means that it is 5 degrees below the freezing point.

The temperature of 82 degrees above zero is a positive number, and we write it as 82, whereas the temperature of 5 degrees below zero is a negative number, and we write it as -5.

2. Money: In transactions of money, a negative number can be used to represent a debt, or an amount owed. For example, if someone's account balance is -$5, it means they owe $5.

3. Coordinate System: In coordinate system, a point can be located using two numbers, representing its x and y coordinates. If the point has an x coordinate of -5, it means that it is 5 units to the left of the origin (0,0).

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Answer:     212  +-  360 n    

Step-by-step explanation: Everytime you go full circle (360 degrees  )    either positive or negative you will land back at the 212 degree mark.

The value of x is given as follows:

x = 39.3.

Similar triangles share these two features listed as follows:

The equivalent side lengths on the proportional triangles are given as follows:

Hence the proportional relationship relating the side lengths is given as follows:

25/35 = x/55

Applying cross multiplication, the value of x is obtained as follows:

35x = 55(25)

x = 55(25)/35

x = 39.3.

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The percent of the square shaded is 37.5 without including the % sign.

The square is divided into 4 equal parts

1/4 of the square is fully shaded

The other 1/4 is shaded half

Hence,

When the square is divided into 8 equal parts, 3 parts are shaded

Percent of square shaded= Parts shaded/ Total parts × 100

= 3/8 × 100

= 0.375 × 100

= 37.5%

Ultimately, 37.5 is the percent of the square shaded.

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The value of c is zero and a and b can be something else, because the vector are linearly independent.

A set of vectors is linearly independent if no vector can be expressed as a linear combination of the others (i.e., is in the span of the other vectors). A set of vectors is linearly independent if no vector can be expressed as a linear combination of those listed before it in the set.

Assume the following:

[tex]a\left[\begin{array}{ccc}2\\2\\0\end{array}\right] + b\left[\begin{array}{ccc}1\\-1\\1\end{array}\right] +c\left[\begin{array}{ccc}4\\2\\-2\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]

Determine if a=b=c=0

[tex]2a+b+4c =0 (1)\\ 2a-b+2c =0 (2)\\b-2c=0(3)\\[/tex]

Subtract (2) from (1)

[tex]b+c = 0\\b-2c=0[/tex]

Substitute (5) into (4), we get c=0.

So now what do I do with this fact? I'm tempted to say that only c=0, and a and b can be something else.

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Answer:

y = 250x

Step-by-step explanation:

y = 1/[tex]x^{3}[/tex](k)  Solve for k

2 = 1/[tex]5^{3}[/tex](k)

2 = 1/125 (k)  Multiply both sides by 125

250 = k

y = 250x

The addition of the fractions, -3/4 + -5/8 = -11/8.

To add fractions together, ensure you find the common denominator of the fractions you are adding together.

Given the fractions, -3/4 + -5/8, add the fractions as explained below:

-3/4 - 5/8 (i.e. minus times plus is equal to minus)

The common denominator is 8, therefore:

[2(-3) - 1(5)] / 8

(-6 - 5) / 8

= -11/8

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Answer:

if there anything you dont understand ask me

If the length of the model airplane is 12 inches, then the length of the actual airplane is 18 feet.

Rob collects model planes. One of his planes uses a scale in which 1 inch represents 1. 5 feet.

We will use unitary method to find the length of airplane in inches.

This means according to the model,

1 inch in the model = 1.5 feet of the actual

Therefore, if the length of the model airplane is 12 feet

12 inches of the model airplane = 1.5 × 12

                                                     = 18 feet

so, the actual length of airplane is 18 feet.

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The car loses all of its marketable value after 9 years, the x-intercepts represent the points at which the car has lost all of its value, so they are (9, 0) and (0, 22995).

The depreciation equation for the car can be represented as y = mx + b, where y is the value of the car at time x, m is the slope of the line, and b is the y-intercept.

To find the slope, we can use the information that the car loses all of its marketable value after 9 years. The market value of the car will be 0 after 9 years, so we can set y = 0 when x = 9:

0 = m * 9 + b

To find the y-intercept, we can use the information that Jason purchased the car for $22,995. This means that the value of the car at time 0 was $22,995, so we can set y = 22,995 and x = 0:

22,995 = m * 0 + b

Combining these two equations, we can solve for m and b:

0 = m * 9 + b

22,995 = m * 0 + b

b = 22,995

Now that we have found the y-intercept, we can use it to find the x-intercepts by setting y = 0 and solving for x:

0 = m * x + 22,995

0 - 22,995 = m * x

-22,995 = m * x

x = -22,995 / m

Since we don't know the value of m, we can't find the x-intercepts directly. However, since the car loses all of its marketable value after 9 years, the x-intercepts represent the points at which the car has lost all of its value, so they are (9, 0) and (0, 22995).

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A teacher has 60 students in her class and wants to form equal groups for a project. To determine the different groups she can form, we need to find the divisors of 60. The divisors of 60 are the numbers that divide evenly into 60.

The divisors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

These divisors represent the different numbers of students the teacher can form into groups. For example, she could form 60 students into 1 group, 30 students into 2 groups, 20 students into 3 groups, 15 students into 4 groups, and so on.

The teacher could also form more unusual groupings, such as 10 students into 6 groups, 12 students into 5 groups, or 6 students into 10 groups. The important factor is that the number of students must be divisible by the number of groups to ensure that each group has an equal number of students.

In conclusion, a teacher with 60 students in her class can form groups with the following number of students: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. These groupings allow her to balance the workload and provide equal opportunities for students to participate in the project. The choice of grouping size will depend on the specific requirements of the project and the teacher's preferences.

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The classification of the statements are

From the question, we have the following parameters that can be used in our computation:

f(x) = 4(x - 2)³ + 2

First, we calculate the inverse

So, we have

x = 4(y - 2)³ + 2

This gives

4(y - 2)³ = x - 2

Divide by 4

y - 2 = (x - 2)/4

Take the cube roots and add 2

f-1(x) = 2 + ∛[(x - 2)/4]

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If only rate and amount are given, interest can be calculated by multiplying the amount and the rate.

Interest can be found by the formula :

= Interest rate x Amount

This means that finding the interest simply requires multiplying the given interest rate by the amount in question.

For instance:
If you have $100 as the principal, an interest rate of 5% (or 0.05 as a decimal), and a time period of 1 year, the interest would be calculated as follows:

= 100 x 5 %

= $ 5

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