Consider the quadratic function f(x)=8x2−7x+6. What is the constant of the function?

−7
6
7
8

Answer:

r=1

Step-by-step explanation:

x^2 +y^2 =1

We know that x^2 + y^2 = r^2

Replacing that in the equation

r^2 =1

Taking the square root of each side

sqrt(r^2) = sqrt(1)

r =1

The other way is to replace x with r cos theta   and y with r sin theta

(r cos theta)^2 + (r sin theta) ^2 =1

r^2 cos^2 theta + r^2 sin^2 theta = 1

Factor out r^2

r^2 (cos^2 theta + sin^2 theta) =1

We know cos^2 theta + sin^2 theta =1

r^2 (1) =1

r^2 =1

Answer:

  r = 1

Step-by-step explanation:

The usual translation between rectangular coordinates and polar coordinates is ...

Substituting these into your equation, you get ...

  (r·cos(θ))² + (r·sin(θ))² = 1

  r²(cos(θ)² +sin(θ)²) = 1 . . . . . . factor out r²

  r²(1) = 1 . . . . . . . . . . . . . . . . . . use the trig identity cos(θ)² +sin(θ)² = 1

  r = 1 . . . . . . . take the square root

_____

It's that simple. Just as x=1 describes a line in Cartesian coordinates, r=1 describes a circle in polar coordinates.

Answer:

The correct option is D.

Step-by-step explanation:

Given information:

Total number of teams = 3

Total number of members in each team = 3

A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.

It means the points for 1st, 2nd, 3rd, 4th, and 5th place are 5, 4, 3, 2 and 1 respectively.

Total points that can earned = 5+4+3+2+1=15

There were no ties, disqualifications, or withdrawals.

No team earned more than 6 points.

To minimize the score of a team, we have to maximize the score of the other two teams.

Let two teams earn there maximum score. i.e. 6. So the score of third team is

[tex]15-6-6=3[/tex]

The least possible score a team could have earned is 3. Therefore the correct option is D.

The square root property seems to be another name for completing the square

x^2 + 5x + 6 = 0

We move the constant to the other side

x^2 + 5x = -6

We square half the linear coefficient and add that to both sides

x^2 + 5x + (5/2)^2 = -6 + 25/4

Now the left side is a perfect square,

(x + 5/2)^2 = 1/4

Here's the square root property part, we take the square root of both sides, remembering the ±

x + 5/2 = ± 1/2

x = -5/2 ± 1/2

Answer: x = -3 or x=-2

We check by plugging in these values to the original equation, and they work.

------

x^2 + 6x = 16

Again we add half the linear coefficient, squared, to both sides

x^2 + 6x + 3^2 = 16 + 9

(x + 3)^2 = 25

Here comes the square root property, taking the square root of both sides:

x + 3 = ±5

x = -3 ± 5

x = 2 or x = -8

Again we check by substitution, and they both work

Answer: x = 2 or x = -8

Answer:

On a number line, -4 is located to the right of -5

Step-by-step explanation:

Answer:

On a number line, -4 is located to the right of -5

Step-by-step explanation:

The price per pound of apples and cherries can be calculated using a system of linear equations. This is based on the given information about how much Frederick and Wilhelmina spent on these fruits at the farmers' market.

In order to find the price per pound of apples and cherries at the farmers' market, we will use a system of linear equations. We can assume the price per pound of apples is A and the price per pound of cherries is C. Frederick's purchases can be represented as 4A + 15C = 36.93 and Wilhelmina's purchases can be represented as 12A + 9C = 30.51. By using these equations, we can solve for A and C using any method you are comfortable with, such as substitution or elimination.

Note: The information regarding fruit consumption in 2001 and the cost calculation methodology is not directly relevant to the main question, but it provides a context of fun facts.

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Answer:

The correct option is D.

Step-by-step explanation:

In a data set we have three quartiles and the second quartile is known as median.

First quartile Q₁ divides the data set in 1:3. It means [tex]\frac{1}{4}[/tex] of the data set are less than or equal to Q₁ and [tex]\frac{3}{4}[/tex] of the data set are more than or equal to Q₁.

Second quartile Q₂ divides the data set in 1:1. It means [tex]\frac{1}{2}[/tex] of the data values are less than or equal to Q₂ and [tex]\frac{1}{2}[/tex] of the data values are more than or equal to Q₂.

Third quartile Q₃ divides the data set in 3:1. It means [tex]\frac{3}{4}[/tex] of the data values are less than or equal to Q₃ and [tex]\frac{1}{4}[/tex] of the data values are more than or equal to Q₃.

It is given that first quartile of a data set is 2.5. It means [tex]\frac{1}{4}[/tex] of the data set are less than or equal to 2.5 and [tex]\frac{3}{4}[/tex] of the data set are more than or equal to 2.5.

Therefore the correct option is D.

Answer:

D) one-fourth of the values are less than or equal to 2.5, and three-fourths of the values are greater than or equal to 2.5.

Step-by-step explanation:

Answer:

[tex]\large\boxed{\bold{Q1.}\ \overline{WX},\ \overline{XY},\ \overline{YW}}\\\boxed{\bold{Q2.}\ \angle P,\ \angle Q,\ \angle R}[/tex]

Step-by-step explanation:

The longest side is opposite the largest angle, and the shortest is opposite the smallest one.

The largest angle lies opposite the longest side, and the smallest is opposite the smallest side.

Q1.

Calculate m∠Y.

We know: Measures of angles of triangle add up to 180°.

m∠Y + m∠W + m∠X = 180°

Substitute given angles:

m∠Y + 51° + 90° = 180°

m∠Y + 141° = 180°      substitute 141° from both sides

m∠Y = 39°

39° < 51° < 90° → XW < XY < YW

Q2.

RQ < PR < PQ → ∠P < ∠Q < ∠R

Answer:

C.

Step-by-step explanation:

This can be written as

[tex]log_w\frac{(x^2-6)^4}{(x^2+8)^\frac{1}{3} }[/tex]

when you divide log you should subtract the terms

[tex]log_w(x^2-6)^4-log_w(x^2+8)^\frac{1}{3}[/tex]

Rewrite powers in the terms as below

[tex]4log_w(x^2-6)-\frac{1}{3} log_w(x^2+8)[/tex]

Answer:

C. [tex]4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)[/tex]

Step-by-step explanation:

We have been given an expression [tex]log_w\frac{(x^2-6)^4}{\sqrt[3]{x^2+8}}[/tex]. We are asked to choose the equivalent expression to our given expression.  

Upon applying log rule [tex]log_c(\frac{a}{b})=log_c(a)-log_c(b)[/tex], we will get:

[tex]log_w(x^2-6)^4-log_w(\sqrt[3]{x^2+8})[/tex]

Using exponent rule [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex], we will get:

[tex]log_w(x^2-6)^4-log_w((x^2+8)^{\frac{1}{3}}[/tex]

Now, we will apply rule [tex]log_c(a^b)=b\cdot log_c(a)[/tex] to simplify our expression as:

[tex]4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)[/tex]

Therefore, option C is the correct choice.

Answer:

My proof is in the explanation.  

Step-by-step explanation:

This is a two-column proof.

One column for statements and the other for the reason for that statement.

Hopefully it shows up well on your screen. Let me know if it doesn't.

Statement                                          |        Reason

1) CD is the perpendicular                   1) Given

bisector of AB

2) AD=DB                                              2) Definition of bisector

3) CD=CD                                              3) Reflexive property

4) mAngleCDA=90                               4) Definition of perpendicular

5) mAngleCDB=90                               5) Definition of perpendicular

6) mAngleCDA=mAngleCDB               6) Substitution property

7) Corresponding parts of each           7)  SAS

triangle are congruent                                (side-angle-side)

8) AC=CB                                               8) The two triangles are ............................................................................congruent so

                                                                   the corresponding parts ............................................................................are

                                                                   congruent.

Answer:

  C. None of the Above

Step-by-step explanation:

None of the given monomials have all of 4 and x and y as factors.

___

They can all be divided, but the result will be a fraction--which is probably not what is intended. None can be divided "evenly" by 4xy.

Answer:

=20s³+50s²+32s+6

Step-by-step explanation:

We multiply each of the term in the initial expression by the the second expression as follows:

4s(5s²+10s+3)+2(5s²+10s+3)

=20s³+40s²+12s+10s²+20s+6

Collect like terms together.

=20s³+50s²+32s+6

Answer: It's the same thing as multiplication.

Step-by-step explanation:

Answer:

128/3 cubic inches

Step-by-step explanation:

The formula for pyramid volume is (1/3)lwh. Using this we can calculate that the volume of each shape is 320/3 cubic inches and 192/3 inches. When these are subtracted, it reads 128/3 cubic inches.

Answer:

The answer is 42.67 cubic inches.

Step-by-step explanation:

Both the models are in the shape of a square pyramid.

The length of the sides of the base for both the models is 8 inches.

Amy’s model is 5 inches tall and Alex’s model is 3 inches tall.

The volume is given by :

[tex]a^{2}\frac{h}{3}[/tex]

So, Amy's figure volume is :

[tex]8^{2}\times \frac{5}{3}[/tex] = 106.67 cubic inches

And Alex's figure volume is:

[tex]8^{2}\times \frac{3}{3}[/tex] = 64 cubic inches

So, the difference between volumes is = [tex]106.66-64=42.67[/tex] cubic inches.

The answer is 42.67 cubic inches.

Answer:

  D.  1/10

Step-by-step explanation:

The trial results (# who watched TV) are ...

  4 4 3 4 4 4 4 3 3 2

Of the 10 trials, only 1 resulted in 2 in the group of 4 watching TV.

Your probability is 1/10.

Answer:

  1/250 W/m² or 0.004 W/m² or 4 mW/m²

Step-by-step explanation:

The cargo worker is (50 m)/(1 m) = 50 times the reference distance. The intensity varies as the inverse of the square of the distance, so will be ...

  (1/50)²×(10 W/m²) = 10/2500 W/m² = 1/250 W/m²

This might be more conveniently written as 4 mW/m².

Answer:

1/258 *(t^28)

= t^28 / 4^4

= t^28 4^-4

= (t^-7 * 4)^-4

= (4t^-7)^-4

Step-by-step explanation:

Answer:

so the answer is d

Step-by-step explanation:

[tex]\text{lcm}(a,b)=\dfrac{|a\cdot b|}{\text{gcd}(a,b)}\\\\378=\dfrac{|a\cdot b|}{9}\\\\|a\cdot b|=42\\\\a\cdot b=-42 \vee a\cdot b=42[/tex]

So, the least value is -42

Answer:

1/15 or 6.67%.

Step-by-step explanation:

Empirical Probability =  number of red haired people  in the last 60 people  / 60.

= 4/60

= 1/15.

The empirical probability of the next customer at the department store having red hair is approximately 0.0667 or 6.67%, based on the hair color distribution of the previous 60 customers.

The student is asking to determine the empirical probability that the next person to come to the cash register has red hair. Empirical probability is based on actual experiment results and calculated by the number of successful trials divided by the total number of trials.

In this case, the total number of people who went to the cash register is 60. Out of these, 4 people had red hair. Hence, the empirical probability of the next customer having red hair would be 4 out of 60 or 0.0667 when rounded to four decimal places. So, there's approximately a 6.67% chance that the next person to visit the cash register will have red hair assuming that the hair color distribution remains consistent.

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For this case we have that by definition, if two lines are parallel their slopes are equal.

The line given for the following points:

(0,3) and (3, -1). Then the slope is:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-1-3} {3-0} = \frac {-4} {3} = - \frac {4} {3}[/tex]

Then, the requested line will be of the form:

[tex]y = - \frac {4} {3} x + b[/tex]

To find "b" we substitute the given point:

[tex]2 = - \frac {4} {3} (- 3) + b\\2 = 4 + b\\2-4 = b\\b = -2[/tex]

Finally, the line is:

[tex]y = - \frac {4} {3} x-2[/tex]

By manipulating algebraically we have:

[tex]y + 2 = - \frac {4} {3} x\\3 (y + 2) = - 4x\\3y + 6 = -4x\\4x + 3y = -6[/tex]

Answer:

Option D

Answer: last option.

Step-by-step explanation:

 The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

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

Knowing that the given line passes through the points (0,3) and (3,-1), we can find the slope:

[tex]m=\frac{-1-3}{3-0}=-\frac{4}{3}[/tex]

Since the other line is parallel to this line, its slope must  be equal:

 [tex]m=-\frac{4}{3}[/tex]

Substitute the slope and the point (-3, 2) into [tex]y=mx+b[/tex] and solve for "b":

 [tex]2=-\frac{4}{3}(-3)+b\\\\2-4=b\\\\b=-2[/tex]

Then, the equation of the other line in Slope-Intercept form is:

[tex]y=-\frac{4}{3}x-2[/tex]

Rewriting it in Standard form, you get:

[tex]y+2=-\frac{4}{3}x\\\\-3(y+2)=4x\\\\-3y-6=4x\\\\4x+3y=-6[/tex]

Answer:

Step-by-step explanation:

Solving the density equation for mass, we get ...

  D = m/V

  m = DV . . . . . multiply by volume

Substituting the volume formula gives ...

  m = D(4/3π)r³

Alloy A

Substituting D = 7.5 gives ...

  m = 7.5(4/3)πr³

  m = 10πr³ . . . . . simplify

__

Alloy B

Substituting D = 8.5 gives ...

  m = 8.5(4/3π)r³

  m = (34π/3)r³ . . . . . simplify

Answer:

the coordinates of C' = (2,1)

Step-by-step explanation:

The coordinates of point C can be found by looking at the graph.

Coordinates of C are C= (6,3)

If ABCD is dilated by a factor of 1/3 then the coordinates of C' can be found by multiplying the coordinates of C by 1/3

C = (6,3)

C' =(1/3*6,1/3*3)

C' = (2,1)

So, the coordinates of C' = (2,1)

Answer:

The area of the two-dimensional cross section is 30 feet²

Step-by-step explanation:

* Lets explain what is the right triangular prism

- The right triangular prism has five faces

- Two right triangular bases (cross sections)

- Three rectangular faces

- Its volume V = area of its base × its height

- Its surface area SA = the sum of the areas of the five faces

- The area of the triangular bases = 1/2 × base of Δ × height of Δ

* Lets solve the problem

- ABCFED is a right triangular prism

- Its two parallel bases are ABC and DEF

- Its bases are congruent right triangles

∴ AB = DE , BC = EF , AC = DF

∵ AB = 5 feet

∴ DE = 5 feet

- The two-dimensional cross section that is parallel to face ABC

  is the face DEF

∵ Δ DEF is right triangle , where angle E is a right angle

∴ DE and EF are the base and the height of Δ DEF

∵ DE = 5 feet ⇒ proved

∵ EF = 12 feet ⇒ given

∴ The area of Δ DEF = 1/2 × 5 × 12 = 30 feet²

∵ The two-dimensional cross section that is parallel to face ABC

  is the face DEF

* The area of the two-dimensional cross section is 30 feet²

Answer:

The area of the cross section is 30 feet².

Step-by-step explanation:

The area is 30, because you want to multiply 5 and 12, then multiply that by 1/2 to find the area of a right triangle.

For this case we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until reaching the remainder.

It must be fulfilled that:

Dividend = Quotient * Divider + Remainder

Looking at the attached image we have that the quotient is given by:

[tex]x ^ 2 + 7x + 2[/tex]

Answer:

Option C

Answer:

3

Step-by-step explanation:

Answer:

  10^2 . . . . see below for additional information or versions of the answer(s)

Step-by-step explanation:

You seem to want 10^exponent, where exponent is an even single digit, not zero.

We choose exponent = 2, so your expression is ...

  10^2

__

There are several versions of expanded form. One uses exponents. In that form, the expression above is the expanded form.

Another uses multipliers of 1, 10, 100, 1000, and so on. In that form, the expression expands as ...

  10^2 = 1×100

Another expanded form uses individual digits of the expanded form with others set to zero

  10^2 = 100

The standard form is ...

  10^2 = 100.

_____

We suppose your exponential expression might have another multiplier, such as 2.98:

To write an exponential expression with a base of 10 and an even exponent between 1 and 10, we can use 10^2 as an example. By multiplying the base by itself the number of times indicated by the exponent, we find that the expanded form is 10 × 10 = 100. Therefore, the standard form of the expression is 100.

a) The exponential expression with a base of 10 and an even number between 1 and 10 as the exponent would be:

102

b) To write the expression in expanded form, we would multiply the base (10) by itself the number of times indicated by the exponent (2):

10 × 10 = 100

The standard form of the expression would be 100.

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Answer:

[tex]t=0.444\ seconds [/tex]

Step-by-step explanation:

Let

x -----> the number of objects

t ----> the time in seconds

we have

[tex]t=0.003x^{2}+0.001x[/tex]

For x=12 objects

substitute in the formula and solve for t

[tex]t=0.003(12)^{2}+0.001(12)[/tex]

[tex]t=0.444\ seconds [/tex]

To find the time to sort 12 objects, we plug x = 12 into the equation t=0.003x^2 + 0.001x to get t = 0.444 seconds.

The student has asked for the time it will take for a computer to sort 12 objects, according to the function t=0.003x^2 + 0.001x.

Step 1: Plug in the value

The first step is to plug the value x = 12 into the given equation.

t = 0.003(12)^2 + 0.001(12)

Step 2: Calculate squares and products

We calculate (12)^2 which is 144, then multiply it by 0.003, which equals 0.432.

Next, we calculate 0.001 times 12, which equals 0.012.

Step 3: Solve for t

Finally, we sum the two products: t = 0.432 + 0.012, resulting in t = 0.444 seconds.

Answer:

The correct option is a rotation 180° clockwise about the origin followed by a reflection across the line y = x

Step-by-step explanation:

The correct option is missing from the given options:

Option A states that a reflection across the line y = x followed by a reflection across the line yaxis

These transformation map triangle ABC to triangle A'B'C' . So this option is in correct.

Option B states that a reflection across the x-axis followed by a reflection across the y-axis

This option is also incorrect because these transformation map triangle ABC to triangle A'B'C'.

Thus the correct option is a rotation 180° clockwise about the origin followed by a reflection across the line y = x ....

Answer:

A

Step-by-step explanation:

The probability is:

              [tex]\dfrac{9}{38}[/tex]

We need to use the Baye's theorem in order to find the probability .

Jar 1:  has 1 white ball and 4 black balls.

This means that the probability of white ball is: 1/5

( since there are a total of 1+4=5 balls out of which 1 is white)

Jar 2: has 2 white balls and 1 black ball.

This means that the probability of white ball is: 2/3

( since there are a total of 2+1=3 balls out of which 2 are white)

Jar 3 : has 3 white balls and 2 black balls.

This means that the probability of white ball is: 3/5

( since there are a total of 3+2=5 balls out of which 3 are white)

Hence, the probability the ball was drawn from Jar 1​, given that the ball is white is:

Ratio of drawing jar 1 and a white ball from it to the sum of choosing each jar and a white ball from it.

i.e.

[tex]=\dfrac{\dfrac{1}{2}\times \dfrac{1}{5}}{\dfrac{1}{2}\times \dfrac{1}{5}+\dfrac{1}{3}\times \dfrac{2}{3}+\dfrac{1}{6}\times \dfrac{3}{5}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{1}{10}+\dfrac{2}{9}+\dfrac{1}{10}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{2}{10}+\dfrac{2}{9}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{38}{90}}\\\\\\=\dfrac{9}{38}[/tex]

The probability that a drawn white ball came from Jar 1, given the stated conditions, is approximately 0.286 or 28.6%.

This problem can be solved using the concept of conditional probability. Let's define the events as follows:

The question requires us to find P(J1|W), that is, the probability that the ball came from Jar 1 given that it is white. Using Bayes' theorem, we can write this as:

P(J1|W) = [P(W|J1) * P(J1)] / P(W). Here, P(W|J1) is the probability of drawing a white ball from Jar 1, P(J1) is the probability of choosing Jar 1, and P(W) is the total probability of drawing a white ball.

We can find these probabilities as:

Substituting these values into the Bayes' theorem, we find P(J1|W) = [(1/5) * (1/2)] / 0.35 = 0.286 approximately. Therefore, there is approximately a 28.6% chance that the drawn white ball came from Jar 1.

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To solve the problem we will substitute the value of x and C in the given function.

Given to us

The cost​ C, in​ dollars, of renting a moving truck for a day C(x)=0.20x+45,

To find the cost if a person drives x=160 ​miles, simply substitute the value of x in the function of cost c,

[tex]C(x)=0.20x+45\\\\C(160)=0.20(160)+45\\\\C(160)=77[/tex]

Hence, the cost of the moving truck if a person drives x=160 ​miles is $77.

To solve the problem substitute the value of C as 120 in the given function,

[tex]C(x)=0.20x+45\\\\120 = 0.20x+45\\\\x = 375\rm\ miles[/tex]

Hence, If the cost of renting the moving truck is ​$120​, the person​ drives 375 miles.

To solve the problem substitute the value of C as 200 in the given function,

[tex]C(x)=0.20x+45\\\\200 = 0.20x+45\\\\x = 775\rm\ miles[/tex]

Hence, if a person wants the cost to be no more than ​$200. The maximum number of miles a person can​ drive is 775.

Implied Domain is the value of C for which it is defined, since even if the truck is not moving a single mile it will still be costing $45, to a person, therefore, the domain of C is [45, +∞].

If we look at the function it is a function of line therefore, the comparing the two equations,

[tex]y = mx+c\\C=0.20x+45[/tex]

we know that m is the slope of the function,

m = 0.20

therefore, the slope of the function is 0.20.

We know that the intercept of y is the value of y at which it intersect the y axis.

when we put the value of x=0, we get the value of y as 45, therefore, the intercept of y is 45.

Hence, the intercept of y is 45.

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Answer:

  20

Step-by-step explanation:

The sum of (actual - predicted) is ...

  {55, 150, 325, 510, 780, 990} - {40, 150, 300, 500, 800, 1,000}

  = total({15, 0, 25, 10, -20, -10}) = 20

The sum of residuals is 20.

Answer:

10 windows are on the 8th floor

Step-by-step explanation:

1 = 52

2 = 46

3 = 40

4 = 34

5 = 28

6 = 22

7 = 16

8 = 10