According to the Rational Root Theorem, what are all the potential rational roots of fx) = 5x - 7x + 11?

Answer:

2. 10/3.

Step-by-step explanation:

The numerator x/2 + x/ 3

= 3x/6 + 2x / 6

= 5x / 6

Now divide this by x/4

5x / 6 / x/4

= 5x/6 * 4/x .    The x's cancel so this

=  20/6

=  10/3.

Answer:

Lucy bought 4 placemats.

Step-by-step explanation:

Let n be the number of placemats Lucy bought.

1 doormat = $7

1 placemat = $2

n placemats = $2n

Total = $(7+2n)

Total number of objects bought = n+1

Average [tex]=\dfrac{\$(7+2n)}{n+1}[/tex]

So,

[tex]\dfrac{\$(7+2n)}{n+1}=\$3[/tex]

Solve this equation:

[tex]7+2n=3(n+1)\\ \\7+2n=3n+3\\ \\3n-2n=7-3\\ \\n=4[/tex]

Hence, Lucy bought 4 placemats.

Answer:

4

Step-by-step explanation:

is the answer

Answer:

72* 62* & 60* 30* triangles

Step-by-step explanation:

I just remember rhombuses being made with 60 degree triangles from all the examples I did. This may be wrong though. But 90 percent confident lol.

Answer: the triangles marked 75 degrees and 45 degrees

Step-by-step explanation:

A rhombus has equal opposite obtuse angles with equal acute angles.

Answer:

   86 m²

Step-by-step explanation:

It can be convenient to think of the figure as an 8×12 rectangle with a 4×5 triangle cut off the corner.

The rectangle area is the product of its length and width:

  (12 m)×(8 m) = 96 m²

The triangle area is half the product of its base and height:

  (1/2)(4 m)(5 m) = 10 m²

Then the area of the figure is the difference of these:

  96 m² -10 m² = 86 m²

Answer:

12

Step-by-step explanation:

We can count the cubes.

One the right side there are 3 rows of 2 cubes each which is 6

There are 2 sets of identical " sets" of blocks

2*6 = 12

There are 12 blocks

1. Let S represent the cost of the sofa and C represent the cost of the chair.

If the sofa costs $50 less than three times the cost of the chair, then effectively we can write this as:

S = 3C - 50

If the sofa and chair together cost $650, we can write this as:

S + C = 650

2. Now, we can find out how much the sofa and chair cost by solving the two equations we obtained above for C, and substituting S = 3C - 50 into S + C = 650. Thus, we get:

S + C = 650

if S = 3C - 50, then:

3C - 50 + C = 650

4C - 50 = 650 (Add C and 3C)

4C = 700 (Add 50 to both sides)

C = 175 (Divide both sides by 4)

Thus, the cost of the chair is $175. Now, to find the cost of the sofa we need to simply substitute C = 175 into our first equation, S = 3C - 50:

S = 3(175) - 50

S = 525 - 50

S = 475

Thus, the sofa costs $475.

3. Now that we know that the sofa costs $475 and the chair costs $175, all we need to do is to subtract the cost of the chair from the cost of the sofa to find the difference in price:

475 - 175 = 300

Therefor, the sofa costs $300 more than the chair (answer C).

Answer:

figure four

Step-by-step explanation:

this is because 5.5/15 = 6.6/18 which means they are proportional making the two lines parallel.

Answer:

r = 6.40 feet

Step-by-step explanation:

Given line AB is tangent to circle O at point A, this means ∡OAB = 90°

Hence this is a right angle triangle and we can use the Pythagorean theorem.

r² + 20² = 21²

r²  = 21² - 20²

r²  = 441 - 400

r²  = 41

r  = √41 = 6.40 feet

The radius of the tank is = 6.4ft

The radius of the circle can be calculated using the Pythagorean theorem since a distance in of AB and OB where given.

The formula c²= b²+a²

Where b²= AB = 20ft

a²= AO= r

c² = OB = 21ft

Make a² the subject of formula

a² = c²-b²

= 21² - 20²

= 441-400

= 41

a= √41

a= 6.4ft

Therefore, the radius of the tank is = 6.4ft

Learn more about radius of circle here:

https://brainly.com/question/12908707

Answer:

The reflection image of P(0, 0) after two reflections is (8,-6)

Step-by-step explanation:

step 1

Find the coordinates of point P after reflection across x=4

we know that

The distance from point P to the line x=4 is equal to 4 units

so

(0,0) -----> (4+4,0) ----> (8,0)

The reflection image of P is (8,0)

step 2

Find the coordinates of point (8,0) after reflection across y=-3

The distance from point (8,0) to the line y=-3 is equal to 3 units

so

(8,0) -----> (8,-3-3) ----> (8,-6)

Answer:

The correct answer option is C. 1.

Step-by-step explanation:

We are to divide [tex] \frac { 4 0 x } { 6 4 y } [/tex] by [tex] \frac { 5 x } { 8 y } [/tex].

Rewriting them as a fraction in whole:

[tex] \frac { \frac { 4 0 x } { 6 4 y } } {\frac { 5 x } { 8 y } } [/tex]

Changing the division into multiplication by taking the reciprocal of the fraction in the denominator to get:

[tex] \frac { 4 0 x } { 6 4 y } [/tex] × [tex]\frac{8y}{5x}[/tex]

Cancelling out the like terms to get:

1

Answer:

options number four is correct because they are children and they can able to identify the book.

Answer:

The answer is d. q=10 d=28 n=14

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

step 1

Verify if the lines are parallel

we know that

If two lines are parallel, then their slopes are the same

In this problem the slope of f(x) =2/7 and the slope of g(x)=7/2

Compare

2/7≠7/2

therefore

The lines are not parallel lines

step 2

Verify if the lines are perpendicular

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

In this problem the slope of f(x) =2/7 and the slope of g(x)=7/2

Multiply

2/7*7/2=1

1≠-1

therefore

The lines are not perpendicular

Answer:

  55 mph

Step-by-step explanation:

Let x represent Bob's speed. Then John's speed is x+10, and their respective times are found by ...

  time = distance/speed

  330/x = 390/(x+10) . . . . . . . the times are the same

  330(x +10) = 390x . . . . . . .  multiply by x(x+10)

  3300 = 60x . . . . . . . . . . . . . subtract 330x

  55 = x . . . . . . . . . . . . . . . . . . divide by the coefficient of x

Bob is driving at 55 miles per hour.

Bob is driving at a speed of 55 miles per hour.

Let's denote Bob's speed as v miles per hour. Since John is driving 10 miles per hour faster than Bob, John's speed is ( v + 10 ) miles per hour.

 The time it takes to travel a certain distance is given by the formula [tex]\( time = \frac{distance}{speed} \)[/tex]

Bob and John travel for the same amount of time, so we can set their times equal to each other:

[tex]\[ \frac{330}{v} = \frac{390}{v + 10} \][/tex]

Cross-multiplying to solve for (v), we get:

[tex]\[ 330(v + 10) = 390v \][/tex]

Expanding the left side:

[tex]\[ 330v + 3300 = 390v \][/tex]

Now, let's move all terms involving (v) to one side:

[tex]\[ 390v - 330v = 3300 \][/tex]

Simplifying, we find:

[tex]\[ 60v = 3300 \][/tex]

Dividing both sides by 60 to solve for  v :

[tex]\[ v = \frac{3300}{60} \] \[ v = 55 \][/tex]

Answer:

the probability of drawing three consecutive red marbles is based on how many red marbles you have and many marble there is in total.

Answer:

27/512

Step-by-step explanation:

P(3 consecutive red)=P(red)×P(red)*P(red)=3/8*3/8*3/8=27/512.

The reason P(red)=3/8 for each picking of marble us because you are putting the marble back in and there are 3 red while you have 8 marbles in all.

Answer:

B) 67

Step-by-step explanation:

Let’s find the amount of heartbeats for 1 minute, so it’s easier to solve.

Since we divide 4 by 4 to get 1, divide 240 by 4 to get the equivalent.

240/4=60.

Your heart beats 60 times per minute.

Since there are 60 minutes in an hour, multiply the amount of heartbeats per minute (60) by 60.

60*60=3,600

Your heart beats 3,600 times per hour.

Hope this helps!

The answer would be B (the symbol ~ means similar. In other words, that they are the same shape but not the same size).

It can't be A because the symbol ≈ means "approximately"

It can't be C because the symbol = means equal

It can't be D because the symbol ≅ means congruent

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

Our equations are

[tex]y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\[/tex]

Let us understand the term Discriminant of a quadratic equation and its properties

Discriminant is denoted by  D and its formula is

[tex]D=b^2-4ac\\[/tex]

Where

a= the coefficient of the [tex]x^{2}[/tex]

b= the coefficient of [tex]x[/tex]

c = constant term

Properties of D: If D

i) D=0 , One real root

ii) D>0 , Two real roots

iii) D<0 , no real root

Hence in the given quadratic equations , we will find the values of D Discriminant  and evaluate our answer accordingly .

Let us start with

[tex]y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\[/tex]

Hence we have two real roots for this equation.

[tex]y = 2x^2 - 6x + 5\\[/tex]

[tex]y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D<0\\[/tex]

Hence we do not have any real root for this quadratic

[tex]y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\[/tex]

Hence D>0 and thus we have two real roots for this equation.

[tex]y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\[/tex]

Hence we have one real root to this quadratic equation.

Answer:

The first box is "two real solutions," the second box is "no real solution," the third box is "two real solution," and the fourth box is "one real solution".

Step-by-step explanation:

If you live in the United States, then you live in Ohio.

False.

Answer with  explanation:

The converse of conditional statement "if p then q" is given by "if q then p".

The given conditional statement : If you live in Ohio, then you live in the United States.

Then , the converse of the given conditional statement will be :-

If you live in United states , then you live in Ohio.

, which is not true since there are so many states in United states other than Ohio.

Counter-example: If some one lives in Indiana, then he is also lives in United states.

Answer:

Part A:

1/2 base * height

=1/2*4*1.5

=3cm

Part B:

1/2 b * h squared

=1/2*4*1.5

=3cm * 2

=6cm

Part C:

8cm*2.5cm

=20cm

Part D:

Length*Width

=8m*4cm

=32cm

(the comment answers, since someone already did the other ones)
(these are all plato answers btw..)
Part E

area of rectangle i = 20 cm²
area of rectangles i and iii = 2 × 20 cm²= 40 cm²

Part F

total area of the rectangles = 32 cm² + 20 cm² + 20 cm² = 72 cm²

Part G

To find the surface area of the prism, I need to know the areas of its bases and lateral faces, which are triangles i and ii and rectangles i, ii, and iii.

Part H

surface area of the prism = areas of bases and faces =
areas of two triangles + area of one large rectangle + areas of two smaller rectangles =
6 cm² + 32 cm² + 40 cm² =
78 cm2

Part I

This statement is false. Only two rectangles in the figure have equal areas. The third rectangle is larger than the other two.

Part J

This statement is true. The triangles are the bases of the prism, so they are congruent. Congruent triangles have the same area.            

You have a rectangle that is 8 ft by 10 ft

Area = 8 * 10 = 80 square feet.

Then there is a triangle 8 ft high with a base of 4 feet.

Area = /2 x 8 x 4 = 16 square feet.

Add together for total area:

80 + 16 = 96 square feet.

A simple method of calculating Area is multiplying the Length times the Width. It is much harder to calculate the entire thing all at once, so it is easier to rather keep the shapes separate.

10 x 8 = 80. This is the area of your first shape, the Rectangle.

You can do the same with the triangle, although triangles are only half a square. You also only multiply the flat sides, not the slanted side, the side with 8.9.

8 x 4 = 32. Because the shape is a triangle wedge, half a square, you divide your answer, 32, by 2, to get half of 32, which is 16.

Then add the two areas, 16 and 80, which is 96.

(The little box in the bottom right corner of the square is just an angle, it represents that it is a right angle, ignore it if you didn't know what it was.)

Answer:

16c^2+56c+49

Step-by-step explanation:

(4c+7)^2 means (4c+7)(4c+7)

Use foil to multiply:  4c(4c)+4c(7)+7(4c)+7(7)

Simplifying            :   16c^2+28c+28c+49              

                                  16c^2+56c+49

[tex](4c + 7)^2=16c^2+56c+49[/tex]

The answer is:

The equation that is represented by the shown graph is the equation from the option D.

[tex]y=e^{x}-4[/tex]

Since we are given two types of functions, exponential and logarithmic, we need to remember that there is just an option that matches with the graph.

So, from the graph we can see that we are looking for an exponential function which intercepts are located at the point (0,-3) and a point which y-coordinate is equal to 0 and its x-coordinate is located at the x-axis between the number 1 and 2.

From the given options we can see that the only exponential function that intercepts the function at y equal to -3 is the fourth option, so, let's prove that:

Option D,

[tex]y=e^{x}-4[/tex]

Finding the y-intercept, we need to make "x" equal to 0, so:

[tex]y=e^{x}-4[/tex]

[tex]y=e^{0}-4[/tex]

[tex]y=1-4=-3[/tex]

So, we know that the y-intercept point is located at (0,-3)

Finding the x-intercept, we need to make "y" equal to 0, so:

[tex]0=e^{x}-4[/tex]

[tex]e^{x}=4[/tex]

[tex]ln(e^{x})=ln(4)\\x=ln(4)=1.386[/tex]

So, we know that the x-intercept point is located at (1.386,0)

Hence, we have that the axis interception points are (0,-3) and (1.386,0), so, the function that matches with the shown graph is the function from the option D.

[tex]y=e^{x}-4[/tex]

Have a nice day!

Note: I have attached a picture for better understanding.

Answer:

The equation that is represented by the shown graph is the equation from the option D.

Step-by-step explanation:

Answer:

 C)

Step-by-step explanation:

Set each side of the equation equal to y, then rearrange to standard form.

  (1/2)x -5 = y . . . left side of the equal sign

  x -10 = 2y . . . . multiply by 2

  -10 = 2y -x . . . . subtract x

__

  (1/3)x +6 = y . . . right side of the equal sign

  x +18 = 3y . . . . . multiply by 3

  18 = 3y -x . . . . . subtract x

The corresponding system of equations is ...

Answer:x=13

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

Since the polygons are similar, their side lengths will be proportionate.

So, The ratio (x - 3)/2.5 will be proportionate to 16/4 (4).

That said, we can get that (x - 3)/2.5 = 4

Multiply: x - 3 = 10

Add: x = 13

There all log base 3, the base won't matter as long as they're all the same.

log(x^2/y)=2log(x)-log(y)=2(4.5)-3=6

Answer: c. 6

Answer:

  6.2 cm

Step-by-step explanation:

[tex]\dfrac{26.35\,\text{cm}^{3}}{4.25\,\text{cm}^{2}}=6.2\,\text{cm}[/tex]

The height of the box is 6.2 cm.

Answer:

8 batches.

Step-by-step explanation:

Beth made 2.5 batches of blueberry muffins = 15 muffins

Beth needs 60 muffins in total. She already has 15 therefore she only needs 45 more.

45/6 = 7.5

7.5 would not be enough. You need to round up to 8.

Answer:

The answer is E

Step-by-step explanation:

add all the numbers together then count how many numbers there are in tottally then divide

all the numbers added together is 64

there is a total of 16 numbers

64/16=4

Answer:

B)mean of data is closest to number 3.

Step-by-step explanation:

Given  : Histogram .

To find : Which of the following numbers is closest to the mean of this distribution.

Solution : We have given that histogram

We have data 1 , 2, 3, 4, 3, 2, 1.

Total number of data = 7

We need to find mean of the data

Mean = [tex]\frac{1+2+3+4+3+2+1}{7}[/tex].

Mean = [tex]\frac{16}{7}[/tex].

Mean = 2.2

Therefore, mean of data is closest to number 3.