The average rate of change of g(x) between x = 4 and x = 7 is 5/6. Which statement must be true?
A. g(7)-g(4)=5/6
B. g(7-4)/7-4=5/6
C. g(7)-g(4)/7-4=5/6 D. g(7)/g(4)=5/6

Answer:

Mean=10

Step-by-step explanation:

To find the mean of a set of numbers, you need to add all of them up and then divide by the amount of numbers that are in the sequence. In this case...

3+8+10+19=40

Then we need to divide by 4 because there are 4 numbers in the sequence. \

40/4=10

Answer:

The mean is 10

Step-by-step explanation:

The mean is just another word for average.

Add the four numbers together and divide by 4

(3+8+10+19)/4

40/4

10

Answer:

I would think that you would want to have the multivitamin and then a placebo, then conduct an experiment testing the results of the multivitamin and observe the effects on both groups taking the medicine.

Step-by-step explanation:

your control group would be the placebo and your experimental group would be the multivitamin...

Answer with explanation:

Objective of the experiment:

       The Multivitamin made by research company is beneficial or not for abolishing short term memory.  

Population

The population can be chosen from the largest city hospital where people are suffering from short term memory loss.

Suppose 100 people are suffering from short term memory loss.

Experimental and control group

  Suppose 40 people are being tested that is in experimental group and 60 people are in Control group.

Sample Procedure

After selecting 40 people in the experimental group , and then providing them Multivitamin for few days ,and then checking whether it is helping them to attain their memory or not is the procedure.

Answer:

D. (2,5)

Step-by-step explanation:

For X:

2+2(5)=12

2+10=12

For Y:

5=2+3

Answer:

D

Step-by-step explanation:

Given the 2 equations

x + 2y = 12 → (1)

y = x + 3 → (2)

Substitute y = x + 3 into (1)

x + 2(x + 3) = 12 ← distribute and simplify left side

x + 2x + 6 = 12

3x + 6 = 12 ( subtract 6 from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

Substitute x = 2 into (2) for corresponding value of y

y = 2 + 3 = 5

Solution is (2, 5 ) → D

Answer:

$31.95

Step-by-step explanation:

The total cost is the initial fee plus the cost of the boxes.

12 + 5×3.99 = 31.95

2354 bdxbdbdbht55675443t35222222222222222222222222

Answer:

He defined variable x as the cost of each fruit bar.

Step-by-step explanation:

6 is the amount of fruit bars Anthony has, so 3y must be for the chocolate-nut bars. So the only thing that makes sense is if variable x is the cost of each fruit bar.

Answer:

A cost a friut bar

Step-by-step explanation:

just finished the test and that was correct have a great day or night!

Answer:

[tex](x+3)(5x^2-2)[/tex]

Step-by-step explanation:

[tex]5x^3+15x^2-2x-6[/tex]

The grouping method means you are going to group some terms together and then factor what you can out of each pair to hopefully make the expression you started with factorable.

Let's try it.

[tex]5x^3+15x^2+-2x-6[/tex]

I like to insert a + in front of the last two terms if it isn't already one.  I think it makes it less confusing.

I'm going to group the first two terms together and I'm going to group the last two terms together like so:

[tex](5x^3+15x^2)+(-2x-6)[/tex]

Now I'm going to factor what I can out of each pairing.

[tex]5x^2(x+3)+-2(x+3)[/tex]

(*I always factor out negative number if the first term in the second pair has a negative on it.)

Now notice in each pairing, there is a common factor of (x+3) so I can factor that out.

The expression then becomes:

[tex](x+3)(5x^2-2)[/tex]

Final answer:

Yes, the grouping method can be used to factor the polynomial 5x³ + 15x² - 2x - 6, resulting in (x + 3)(5x² - 2) as the factored form.

Explanation:

The question is asking if we can use the grouping method to factor the polynomial 5x³ + 15x² - 2x - 6. Factoring by grouping is a technique where we group terms that have common factors and then factor each group individually.

To apply the grouping method to this polynomial, we would look for groups of terms that have common factors and try to factor out those common factors. Let's group the first two terms and the last two terms:

Group 1: 5x³ + 15x²

Group 2: -2x - 6

Factoring out the greatest common factor from each group, we get:

Group 1: 5x² (x + 3)

Group 2: -2 (x + 3)

Now, we can factor out the common binomial factor (x + 3):

(x + 3)(5x² - 2)

This is the factored form of the polynomial using the grouping method.

Answer:

(- 3, 2 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

X has coordinates X(- 2, 3 ), hence

X'(2, 3 ) ← after reflection in the y- axis

Under a rotation about the origin of 90°

a point (x, y ) → (- y, x )

Hence

X'(2, 3 ) → X''(- 3, 2 ) ← final image point

The correct option will be option A: The final image point of X will be (-3,2).

The reflection about an axis is the transformation of the picture about an axis so that distance of every point from the axis before and after reflection will remain the same.

Here the coordinate of point X in triangle XYZ is (-2,3).

First, the triangle XYZ is reflected about the y-axis.

As we know, the reflection of the point of coordination (x,y) after reflection about the y-axis will be (-x,y).

(x,y)→(-x,y)

So the point X of coordination (-2,3) after reflection about the y-axis will be (2,3).

Then the reflected point is rotated about the origin.

As we know the rotation of the point of coordination (x,y) after rotation about origin will be (-y,x).

(x,y)→(-y,x)

So the point of coordination (2,3) after rotation about the origin will be (-3,2).

Therefore The final image point of X will be (-3,2).

Learn more about reflection

here: https://brainly.com/question/1908648

#SPJ2

[tex]\huge{\boxed{4.5}}[/tex]

First, add all the numbers together. [tex]2+2+3+3+3+4+5+6+6+10=\bf{44}[/tex]

Divide by the amount of numbers. [tex]\frac{44}{10}=\boxed{4.4}[/tex]

[tex]4.5[/tex] is the closest, so that is the answer.

Answer:

C. f has a relative maximum at x = 1.

Step-by-step explanation:

A. False.  f(x) is concave down when f"(x) is negative.  f"(x) is the tangent slope of the graph, f'(x).  So f(x) is concave down between x = -1.5 and x = 1.5.

B. False.  f(x) is decreasing when f'(x) is negative.  So f(x) is decreasing in the intervals x < -3 and 1 < x < 2.

C. True.  f(x) has a relative maximum where f'(x) = 0 and changes from + to -.

Answer:

A) function

B) not function

C) not function

D) function

D has domain {1,3,5} and range {2,4,6}.

Step-by-step explanation:

So for a mapping diagram to show a function there can only be at most one line segment coming from a number in the first circle.

So let's look at the problems:

A) There is one segment coming from 2.  (2 to 1)

    There is one segment coming from 4.  (4 to 3)

    There is one segment coming from 6.   (6 ro 5).

So this is a function.

The domain is the first numbers: {2,4,6}.

The range is the second numbers: {1,3,5}.

B)  There is two segments coming from 1. So it is over with, this is not a function.

The domain is the first numbers: {0,1,4}.

The range is the second numbers: {-2,-1,0,1,2}.

C)  There is two segments coming from a. So it is over with, this is not a function.

The domain is the first numbers: {a,b,c}.

The range is the second numbers: {4,5,6,7}.

D) There is one segment coming from each 1, 3, and 5.  So this is a function.

The domain is the first numbers: {1,3,5}.

The range is the second numbers: {2,4,6}.

Answer:

The correct option is A.

Step-by-step explanation:

It is given that Beth makes a scale drawing of her old business card by using the scale factor 5/4.

If the scale factor is less than 1, then it represents compression and if the  scale factor is greater than 1, then it represents enlargement.

Since the scale factor is greater than 1 so the scale drawing is an enlargement.

Let the initial dimension of business card is a by b.

Her scale drawing is [tex]2\frac{1}{2}[/tex] in by 5 in rectangle. Multiply each dimension by reciprocal of scale factor to find the dimension of original card.

[tex]a=2\frac{1}{2}\times \frac{4}{5}=\frac{5}{2}\times \frac{4}{5}=2[/tex]

[tex]b=5\times \frac{4}{5}=4[/tex]

The dimension of original card is 2 in by 4 in.

Therefore the correct option is A.

Answer: A

Step-by-step explanation:

Answer:

[tex]\boxed{\text{3600 mg}}[/tex]

Step-by-step explanation:

Step 1. Calculate the number of capsules

Marilyn takes 2 capsules per day

[tex]\text{No. of capsules} = \text{90 days} \times \dfrac{\text{2 capsules}}{\text{1 day}} = \text{ 180 capsules}[/tex]

Step 2. Convert capsules to milligrams

There are 20 mg in each capsule.  

[tex]\text{No. of milligrams} = \text{180 capsules} \times \dfrac{\text{20 mg}}{\text{1 capsule}} = \textbf{3600 mg}\\\\\text{Marilyn will take } \boxed{\textbf{3600 mg}} \text{ of Pirixocam}[/tex]

Answer:

(7x^2+3)( 3x+5)

Step-by-step explanation:

21x^3 + 35x^2 + 9x + 15.

We will do factor by grouping

Rearranging the terms so I have the terms with a factor of 3 first and 5 last

Factor a 3x from the first two terms and 5 from the last two terms

21x^3  + 9x + 35x^2+ 15

3x(7x^2 +3) +5(7x^2+3)

Now factor out a (7x^2+3)

(7x^2+3)( 3x+5)

Answer:

Cubic = (3x + 5)(7x^2 + 3)

Step-by-step explanation:

If you make up two groups of 2, you might be able to factor this using the distributive property. Let's try it.

First group: 21x^3 +  35x^2          Take out 7x^2 as a common fact

First group: 7x^2(3x + 5)

Second group: 9x + 15                  The HCF is 3

Second group: 3(3x + 5)

Now put your factors together in one long string.

Cubic = group 1 + group 2

Cubic = 7x^2 (3x + 5) + 3(3x + 5)

Note: If you had something like 7x^2 * y + 3 *y then you should see that the factors are y* (7x^2 + 3). So to solve the cubic, you should observe that (3x + 5) is a common factor.

Let y = 3x + 5

y(7x^2 + 3)   Now substitute back for the y.

Cubic = (3x + 5)(7x^2 + 3)

Answer:

343.77°

Step-by-step explanation:

1 radian =  [tex]\frac{180}{Pi}[/tex]°

6 radians will be;

6 ×  [tex]\frac{180}{Pi}[/tex]° =343.7746771 °

Or 343.77° (rounded up to nearest hundredth)

Answer:

343.77

Step-by-step explanation:

Answer:

(-2,12)

Step-by-step explanation:

it is the closest because it is only 2 units away

The coordinates of points on the Cartesian plane, are given by a pair of values

Reason:

The given coordinates are; (-6, 0), (-2, -12), (4, 2), (5, 1)

Method:

A point is close to the y-axis where the magnitude x-coordinate value is low

By observation, the coordinates of the point having the lowest magnitude of the x-value, is the point (-2, -12)

Learn more about the Cartesian plane here:

https://brainly.com/question/16347613

Answer:

=6665

Step-by-step explanation:

The sum of a geometric series is given by:

Sn=a(1-rⁿ)/(1-r)

Sn is the sum of the first n terms, r is the rate and n is the number of terms.

r the quotient between any two consecutive numbers.

r=6/-1= -6

Sn=-1(1-(-6)⁶)/(1--6)

=46655/7

=6665

Sum of the first six terms=6665

Answer:

19 x (42 + 58)

Step-by-step explanation:

The common term is 19

Answer : The expression she use can be, [tex]19\times (42+58)[/tex]

Step-by-step explanation :

Distributive property Law : It says that multiplying a number by the group of numbers added together is the same as doing each multiplication separately.  

For example:

3 × (2 + 4) = 3×2 + 3×4

As we are given the expression:

[tex]19\times 42+19\times 58[/tex]

[tex]\Rightarrow 19\times (42+58)[/tex]

Thus, the expression she use can be, [tex]19\times (42+58)[/tex]

[tex]\dfrac{B_x \sqrt{74_x}}{1D_x}+J_x51_x=4G3_x[/tex]

A=10, B=11, C=12, etc.

[tex]\dfrac{11\cdot x^0\cdot \sqrt{7\cdot x^1+4\cdot x^0}}{1\cdot x^1+13\cdot x^0}+19\cdot x^0\cdot (5\cdot x^1+1\cdot x^0)=4\cdot x^2+16\cdot x^1+3\cdot x^0\\\\\dfrac{11\sqrt{7x+4}}{x+13}+19(5x+1)=4x^2+16x+3\\\\\dfrac{11\sqrt{7x+4}}{x+13}+95x+19=4x^2+16x+3\\\\11\sqrt{7x+4}+95x(x+13)+19(x+13)=(4x^2+16x+3)(x+13)\\\\11\sqrt{7x+4}+95x^2+1235x+19x+247=4x^3+52x^2+16x^2+208x+3x+39\\\\11\sqrt{7x+4}=4x^3-27x^2-1043x-208\\\\121(7x+4)=(4x^3-27x^2-1043x-208)^2[/tex]

[tex]121(7x+4)=(4x^3-27x^2-1043x-208)^2\\\\847x+484=16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433888 x + 43264\\\\16 x^6 - 216 x^5 - 7615 x^4 + 54658 x^3 + 1099081 x^2 + 433041 x +42780=0[/tex]

Now, the "only" thing that remains to do is solving the above equation.

While making this problem I only made sure it has a solution. I didn't try to solve it myself and I didn't know it will end up with such "convoluted" polynomial. Sorry to everyone who tried to solve it... m(_ _)m

I think the best way to approach it is using the rational root theorem since we know that [tex]x\in\mathbb{N}[/tex]. Moreover we can deduce that [tex]x\geq19[/tex] since there is [tex]J[/tex] and [tex]J=19[/tex].

After you succesfully solve it, you should get the answer [tex]x=20[/tex].

Answer:

x(x-5)

Step-by-step explanation:

We cannot solve this expression because there is no equals sign.

We can,however simplify the expression

x^2 -5x

Factor out an x

x(x-5)

Answer:

Step-C. -5x-3y=0 which is the same thing as y= -5/3x + 0.

by-step explanation:

i hope this helps

Answer:

[tex]F'(-3,-5),G'(-2,-5),H'(-2,-2)[/tex]

Step-by-step explanation:

The given points are: F(−5,−3) G(−5,−2) H(−2,−2)

The mapping for reflection in the line [tex]y=x[/tex] is [tex](x,y)\to (y,x)[/tex].

We just have to swap the coordinates of the preimage to obtain the image

[tex]F(-5,-3)\to F'(-3,-5)[/tex].

[tex]G(-5,-2)\to G'(-2,-5)[/tex].

[tex]H(-2,-2)\to H'(-2,-2)[/tex].

Therefore the image points are

[tex]F'(-3,-5),G'(-2,-5),H'(-2,-2)[/tex]

Check the picture below.

Answer:

Option A. will be the answer.

Step-by-step explanation:

It is given in the diagram attached, AB and BC are the tangents to circle O.

We have to find the measure of ∠ABC.

By the theorem,

Measure of ∠ABC which inscribed within the tangents will be [tex]=\frac{1}{2}(arcADC-arcAC)[/tex]

[tex]=\frac{1}{2}(226-134)[/tex]

[tex]=\frac{1}{2}(92)[/tex]

= 46°

Option A. will be the answer.

Answer:

rectangle, square

Step-by-step explanation:

A rectangle always has 4 congruent angles. A square is a rectangle, so a square always has 4 congruent angles.

A parallelogram and a rhombus may or may not have 4 congruent angles.

Answer: rectangle, square

Answer:

Only a square and rectangle

Step-by-step explanation:

Both have angles of only 90 deg.

Answer:

Final direction is 45 degrees south of west or  45 degrees west of south.

Step-by-step explanation:

i) You are facing North

Turn 90 degrees left

ii) 90 degrees left to north is west.

Turn around to reverse your direction

iii) On reversing direction you will be facing east.

Turn 45 degrees left

iv) On turning 45 degrees left, you will be facing north east.

 Turn around to reverse your direction

v) On reversing direction you will be facing south west.

Final direction is 45 degrees south of west or  45 degrees west of south.

Answer:

1/24.

Step-by-step explanation:

Probability(Rolling an even number)

= 3/6 = 1/2.

Probability(Rolling a 3) = 1/6.

Required Probability = 1/2 * 1/2 * 1/6

= 1/24.

The probabilities are multiplied because the 3 events are independent.

Answer:

1/24

Step-by-step explanation:

A die has 6 faces with numbers 1 through 6. Three faces have even numbers, and 3 faces have odd numbers.

Each roll of the die can result in 6 different outcomes.

The total number different outcomes of rolling a die 3 times is 6 * 6 * 6 = 216.

There are 3 possible even number outcomes on the first roll, and another 3 possible even number outcomes on the second roll. The third roll needs to be a 3, so there is one single desired outcome of the third roll.

Total number of desired outcomes: 3 * 3 * 1 = 9

probability(even, even, 3) = 9/216 = 1/24

Answer:

a = -4.

Step-by-step explanation:

If the are perpendicular then the slope of one graph will be - 1 / slope of the other.

Convert each equation to slope-intercept form:

x + 2y + 3 = 0

2y = = -x - 3

y = (-1/2)x - 3/2 (Slope/intercept form)

So the slope of the line perpendicular to this  will be - 1 / (-1/2) = 2.

Consider the other line:

ax + 2y + 3 = 0

2y = -ax - 3

y = (-a/2) x - 3/2 (Slope/intercept form)

So the slope for this line    - a/2 and it equals 2.

-a/2 = 2

-a = 2*2 = 4

a = -4 (answer).

To determine the value of $a$ such that the graph of the equation $ax + 2y + 3 = 0$ is perpendicular to the graph of the equation $x + 2y + 3 = 0$, we'll need to find the slopes of the two lines represented by these equations since two lines are perpendicular if and only if the product of their slopes is $-1$ (the slopes are negative reciprocals of each other).
Let's find the slope of the first line.
The equation of the first line is $x + 2y + 3 = 0$. We can rearrange this to find $y$ in terms of $x$:
\[2y = -x - 3\]
\[y = \frac{-x}{2} - \frac{3}{2}\]
The slope of this line, denoted by $m_1$, is the coefficient of $x$:
\[m_1 = -\frac{1}{2}\]
Now, let's find the slope of the second line.
The equation of the second line is $ax + 2y + 3 = 0$. Rearranging this to solve for $y$ in terms of $x$, we get:
\[2y = -ax - 3\]
\[y = -\frac{a}{2}x - \frac{3}{2}\]
The slope of this line, denoted by $m_2$, is the coefficient of $x$:
\[m_2 = -\frac{a}{2}\]
Now, for the lines to be perpendicular, their slopes must satisfy the following condition:
\[m_1 \cdot m_2 = -1\]
Substituting the known slopes into the equation, we get:
\[-\frac{1}{2} \cdot \left(-\frac{a}{2}\right) = -1\]
\[\frac{a}{4} = -1\]
\[a = -4\]
Therefore, the value of $a$ that ensures the graph of the equation $ax + 2y + 3 = 0$ is perpendicular to the graph of the equation $x + 2y + 3 = 0$ is $a = -4$.

Answer:

A 11

C 9

F 7

Step-by-step explanation:

6x≤ 66

Divide each side by 6

6x/6 ≤ 66/6

x ≤ 11

Any number less than or equal to 11 is a solutions

A 11   yes

B 53  no

C 9  yes

D 12  no

E 50  no

F 7 yes

Answer:

D

Step-by-step explanation:

The answer is anything less than $37,000 because that is how much he has to spend.  D. $34,000 is the only answer less than that, so D is the correct answer.

Answer:

49

Step-by-step explanation:

We are going to use PEMDAS to simplify

[tex]3^3-10+(2 \cdot 4^2)[/tex]

First step is P.

P refers to the parenthesis or anything acting as a grouping symbol.

We notice the following operations there are multiplication and exponents.

According to PEMDAS, after parenthesis we do the exponents so let's do the exponent in the ( ).

[tex]3^3-10+(2 \cdot 16)[/tex]

Now we still have to finish P up. That is we need to do the one last operation in the ( ).

[tex]3^3-10+(32)[/tex]

Nothing left to perform in the () so we can just write:

[tex]3^3-10+32[/tex]

Now there are no more grouping symbols left.

The next letter is E and it stands for exponents so we must evaluate anything we can that has an exponent.

[tex]27-10+32[/tex]

Now after E we have M and D which means to multiply and divide as you the expression from left to right.

There is no multiplication and division so moving on.

A and S means to do the addition and subtraction as it occurs left to right:

[tex]17+32[/tex]

[tex]49[/tex]

Answer:

The coordinates of the midpoint of LN are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]

answer (4)

Step-by-step explanation:

* Lets explain how to find the midpoint of a line

- The coordinates of the midpoint of a line whose endpoints are (x1 , y1)

 and (x2 , y2) are [tex]x=\frac{x_{1}+x_{2}}{2},y=\frac{y_{1}+y_{2}}{2}[/tex]

∵ LMNO is a square

∵ The coordinates of point L are (-6 , 1)

∵ The coordinates of point N are (1 , 8)

- Let the coordinates of point L are (x1 , y1) , the coordinates of point

 N are (x2 , y2) and the coordinates of the midpoint of LN are (x , y)

∴ x1 = -6 , x2 = 1 and y1 = 1 , y2 = 8

- Use the rule of the midpoint above to find the midpoint (x , y)

∵ [tex]x=\frac{-6+1}{2}=\frac{-5}{2}=-2\frac{1}{2}[/tex]

∵ [tex]y=\frac{1+8}{2}=\frac{9}{4}=4\frac{1}{2}[/tex]

∴ The coordinates of the midpoint are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]

* The coordinates of the midpoint of LN are [tex](-2\frac{1}{2},4\frac{1}{2})[/tex]

Answer:

The answer should be D the fourth one

Step-by-step explanation: