Let f(x) = -3x³ + 9x² - 5x + 15. Use the Factor Theorem to help answer the
following questions.
a) Is a
O Yes
O No
b) Is x + 1 a factor of f(x)?
O Yes
No
1 a factor of f(x)?
c) Is a 3 a factor of f(x)?
O Yes
O No

Using the formula °F = 1.8°C +32°, The temperature in Degrees Celsius of an oven that is 500°F is 260°C.

For everyday purposes, Fahrenheit is used in the United States, its territories, and related states (all of which are covered by the U.S. National Weather Service), as well as in Liberia, the Cayman Islands, and other places. For instance, temperatures for freezing, cooking, and other conditions are typically given in degrees Fahrenheit in the United States.

On the Celsius scale, one of the two temperature scales used in the International System of Units along with the Kelvin scale, the unit of temperature is the degree Celsius. The term "degree Celsius" can be used to describe either a specific temperature on the Celsius scale or a measurement of the difference between two temperatures.

Here,

°F=1.8°C+32°

500°F=1.8°C+32°

1.8°C=468°F

°C=468/1.8

°C=260°C

The temperature in Degrees Celsius of an oven that is 500°F is 260°C by using the formula °F = 1.8°C +32°.

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Answer:

5

Step-by-step explanation:

13

Step-by-step explanation:

i said 36 divide by 3 is 13

Answer:

16

Step-by-step explanation:

Two negatives make a positive:

18-7+5

Solve the problem left to right:

18-7=11

11+5=16

Equation:

A =1/2 * r * C

Replace with the values from the table and check the equation:

First row:

50 = 1/2*4*25

50= 50 TRUE

Second row:

78.5= 1/2*5*31.5

78.5= 78.75 FALSE

Since one equality is false, the equation Doesn't describe the relationship-

Answer : NO

Step-by-step explanation:

Substitute the values

a

=

1

,

b

=

−

2

, and

c

=

−

5

into the quadratic formula and solve for

x

.

2

±

√

(

−

2

)

2

−

4

⋅

(

1

⋅

−

5

)

2

⋅

1

Simplify.

x

=

1

±

√

6

Simplify the expression to solve for the

+

portion of the

±

.

x

=

1

+

√

6

Simplify the expression to solve for the

−

portion of the

±

.

Let's recalll that:

• 1 mile per hour = 1.46667 feet per second

Therefore:

• 10 miles per hour = 1.46667 * 10 feet per second

• 10 miles per hour = 14.6667 feet per second, Khalil!

When a study's findings are highly valid, it means that they accurately reflect the genuine features, traits, and variations in the physical or social reality. The measure of frequency of drinking and driving is: reliable but not valid.

This option contends that although the survey's measure was not valid, it was dependable. This happens when research is constructed in a consistent but ineffective manner. In this instance, a sample of young people from a small town was taken into account; however, despite its consistency and reliability, it does not accurately reflect the findings of data from police records.

How well a method measures what it is supposed to measure is known as its validity. When a study's findings exists highly valid, it indicates that they accurately reflect the genuine features, traits, and variations in the physical or social reality. High dependability exists one sign of a valid measurement.

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Answer:  The correct answer is x=18 and y=59

Step-by-step explanation:

Opposite angles are congruent:

(6x+13) = (7x-5)

Solve for x:

6x+13−7x=7x−5−7x

−x+13−13=−5−13

−x=−18

x=18

Plug x value in for y:

Y=180-(7x-5)

Y=180-(126-5)

Y=180-121

Y=59

The probability that exactly none will graduate is [tex]0.003375[/tex].

What is probability?

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes.

Step-by-step explanation:

Let [tex]X[/tex] be the random variable for the number of students who graduate.

Binomial distribution theorem tells that, [tex]P(X=x)=C(n , x)p^xq^{n-x}[/tex].

Here [tex]p=[/tex]probability of success on a single trial, [tex]q=[/tex]probability of failure on a single trial, [tex]n=[/tex] number of trials.

Given that [tex]p=0.85, q=1-p=1-0.85=0.15[/tex] and [tex]n=3.[/tex]

[tex]P(X=x)=C(3 , x)0.85^x0.15^{3-x}[/tex]

When [tex]3[/tex] students are randomly selected the probability that exactly none will graduate is given by,

[tex]P(X=0)=C(3 , 0)0.85^00.15^{3-0}[/tex]

[tex]P(X=0)=\frac{3!}{0!(3-0)!} 0.15^{3}[/tex]

[tex]P(X=0)=0.15^{3}[/tex]

[tex]P(X=0)=0.003375[/tex]

Hence the probability that exactly none will graduate is [tex]0.003375[/tex].

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Answer:

x=-11

Step-by-step explanation:

Steps are in the attachment, but I couldn't include the last step.

The last step is to divide by -2 on both sides.

The final answer then will be x=-11

Answer:  Choice E

Explanation:

The given inequality means n is between -2 and 6. We exclude -2 itself, but include 6.

The set of integer values is -1, 0, 1, 2, ..., all the way up to 6.

Given the data shown in the table, you can identify that these two points are on the line:

By definition, the Slope-Intercept Form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

You can find the slope of the line using this formula:

Where these two points are on the line:

Answer:

70

Step-by-step explanation:

Answer:

-14.1 kJ

Step-by-step explanation:

We need the specific heat of water, which is 4.184 J/g-K.  It means that 4.184 Joules of energy will raise 1 gram of water by 1 degree Kelvin.  It also means that removing 4.184 Joules of energy will lower the temperature of 1 gram of water by 1 degree Kelvin.

We want to lower the temperature by 15 degrees C (-15C).  That is also -15K.  We have 225 grams of water.

 This can be used in the equation q = mc(T2 - T1),

 where q is the heat, or energy, m is the mass, c is the specific heat, and (T2-T1) is the temperature change, in Kelvin.

 q = mc(T2 - T1)

  q = (225g)(4.184 J/g-K)(10K - 25K)

   q = (225g)(4.184 J/g-K)(-15K)

 q = -14121 J  or -14.1 kJ

It is negative because heat is leaving the system.

7+8x=0

first step -Subtract 7 from both sides.

7+8x-7=0-7

Step 2

8x=-7

Step 3

Divide both side by 8

Instead of dividing the right hand side of equation in step 2 by 8, the right hand side is multiplied by 8 in step 3.

So, the error is in step 3.

The most appropriate choice for percentage will be given by -

Total salary of Marques in a week = $825

If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{x}{10}[/tex])

What is Percentage?

Suppose there is a number and that number has to be expressed as a fraction of 100. The fraction is called percentage. For example 2% means [tex]\frac{2}{100}[/tex]

Here,

Guarantee salary of Marques = $200

Sales made by Marques in a week= $750

Percentage commission on total sales = 10 %

Commission received by Marques = [tex]\frac{10}{100} \times 750\\[/tex]

                                                          = $75

Total salary of Marques in a week = $(750 + 75)

                                                         = $825

If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{10}{100}\times x[/tex])

                                                                                            = $([tex]750[/tex] + [tex]\frac{x}{10}[/tex])

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Hello!

Here are all three solutions to the given equation.

Exact Form:

[tex]w=\frac{21}{20}[/tex]

Decimal Form:

[tex]w=1.05[/tex]

Mixed Number Form:

[tex]w=1\frac{1}{20}[/tex]

Hope this helps!

Answer:

the answer for this question is 35.0

The rate at which the area is increasing is 95cm/sec² .

Let us take the variable a to be the length of the rectangle and take the variable to b be the width of the rectangle.

We know that the area of the rectangle is given by A=a × b

Now differentiating with respect to t we get :

[tex]\frac{dA}{dt} = w\times\frac{da}{dt} +l\times\frac{db}{dt}[/tex]

Substituting the values we get that the rate of increase in the area is :

Rate of increase = (32 + 63) cm/sec² = 95 cm/sec²

A constant function is also regarded as linear in this sense because it is a polynomial of degree zero, or the zero polynomial.

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Answer:

the answer of a question is option A

Neither of the pairs of linear equations has the same slope in both lines, so we don't have parallel lines.

A general linear equation is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

Two linear equations are parallel only if both lines have the same slope and a different y-intercept.

In this case, the lines given are:

y = x + 2 and y = 2.

x = 2 and y = 4

Neither of these are particularly parallel lines (because in both pairs we have different slopes), so we conclude that there is no correct option.

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We want to graph the line:

For doing so, we will choose two different x-values, and we will find its correspondent y-values. This gives us two different points, and when we trace the line that passes through those points, we will have the line we wanted.

In this exercise, we will choose x=0, and x=5.

For x = 0

This gives us the point (0,3).

For x = 5

This gives us the second point: (5,6).

Now, graphing the points on a cartesian plane, and drawing the line between them, we obtain:

when y = 17/4, x= 3/4

then assume y varies directly as x

then y =kx

k = y/x

k= 17/4× 4/3

k= 17/3

when x= 3/4, y = 27/34

A variation is a relation between a set of values of one component and a set of values of other component.

Direct variation is a type of variation in which two variables go line in line with their values

y= kx where k is the proportionality constant

k = 17/3 when y = 17/4 and x= 3/4

using thesame value of k in the expression k=y/x

and x = 3/4, then

y= 27/34

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The proof explained below shows that the triangles are congruent by the AAS congruence theorem.

The AAS congruence theorem states that two triangles can be proven to be congruent to each other if the two angles and a non-included side in one triangle is equal or congruent to two corresponding angles and a corresponding non-included sides in the other triangle.

This implies that, once the criteria needed prove that two triangles are congruent by the AAS congruence theorem are two pairs of congruent angles and a pair of non-included congruent sides.

Using the AAS congruence theorem, the two-column proof that shows each statement and the reason are explained below.

Statement                                   Reason                                        

1. CA bisects angle BAD          1. Given

angle B ≅ angle D                                  

2. Angle CAB ≅ angle CAD     2. Congruent angles formed from bisection

3. Side AC ≅ side CA               3. Reflexive property

4. Triangle ABC ≅ triangle ADC    4. AAS congruence theorem

Thus, the above reasons and statements shows that the two triangles, triangle ABC and triangle ADC, are congruent by the AAS congruence theorem.

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A number is squared when it is multiplied by itself.

Hence, the correct option is Option B

Answer:

Step-by-step explanation:

ABC

ADC