Rewrite the expression in exponential form.

Answer:

Step-by-step explanation:

Let the unknown number = x

[tex]x *\frac{-5}{27}=\frac{-10}{9}[/tex]

x = [tex]\frac{-10}{9}[/tex] ÷ [tex]\frac{-5}{27}[/tex]

[tex]x=\frac{-10}{9}*\frac{-27}{5}\\\\\\x=-2* - 3\\x = 6[/tex]

Answer:

-\frac{7}{6}

Step-by-step explanation:

We can use the slope formula for the segment that joins any two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]:

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

which in our case gives:

[tex]slope=\frac{y_2-y_1}{x_2-x_1} = \frac{-2-5}{3-(-3)}=\frac{-7}{6} =-\frac{7}{6}[/tex]

Answer:

The domain is all values but x=4 and x=2

Step-by-step explanation:

f(x) = (x+1) / ( x^2-6x+8)

Factor the function

f(x) = (x+1) / ( (x-4) ( x-2))

The domain of the function is all values of x except where the function does not exist

This is where the denominator goes to zero

(x-4) ( x-2) =0

Using the zero product property

x-4 =0   x-2 =0

x=4   x=2

The domain is all values but x=4 and x=2

Answer:

Hey there!

This, is the graph of your function:

Thus the domain, or all the possible x values would be all real numbers except 2 and 4, because the lines will only reach 2 and 4 when y is infinity.

Hope this helps :)

Answer:

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Step-by-step explanation:

As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.

Given:

Height of cylinder, [tex]h_1[/tex] = 15 cm

Diameter of cylinder/ cone, D = 26 cm

Slant height of cone, l = 20 cm

Here, we need to find the volume of container.[tex]\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2[/tex]

Here,

[tex]r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm[/tex]

To find the Height of Cylinder, we can use the following formula:

[tex]l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm[/tex]

Now, putting the values to find the volume of container:

[tex]Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3[/tex]

Converting [tex]cm^{3 }[/tex] to litres:

[tex]10613 cm^3 = 10.613\ litres \approx 11\ litres[/tex]

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Answer:

45.

Step-by-step explanation:

100% of a number is the number itself. So, 100% of 45 is 45.

Hope this helps!

Answer:it’s 45

Step-by-step explanation:It’s just the whole number nothing less:)

Answer:

71s

Step-by-step explanation:

The question we have at hand is 7s² + ___ + 13s + 6² = (7s + 6)². We can expand the perfect equation " (7s + 6)² " in order to find our solution. A perfect square consists of 3 terms, and hence the term in the blanks must add to 13s to form another term.

Applying the perfect square formula : ( a + b )² = a² + 2ab + b², let's expand the expression,

(7s + 6)² = ( 7s )² + 2( 7s )( 6 ) + ( 6 )² =  7s² + 84s + 6²

84s - 13s = 71s, which fills in the blank provided.

The correct answer is C. Four pies

Explanation:

Marginal cost refers to an increase in the cost of production as additional units are made. In the case of apple pies, the graph shows the cost for one is $1.00. Moreover, this decreases when two or three pies are produced because the cost is between $0.60 and $0.30. However, if the producer makes four or more units, the cost increases. For example, at four units the cost per unit is $0.60, while at six units the cost is $1.50. Thus, the marginal cost begins to increase at four pies.

Answer: four pies

Step-by-step explanation:

The graph is a marginal cost curve that compares expenses therefore it would equal four pies because the marginal cost rises on the graph starting at 4.

Answer: 0.49 ± 0.0237

Step-by-step explanation: A interval of a 99% confidence interval for the population proportion can be found by:

[tex]p_{hat}[/tex] ± z.[tex]\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]

[tex]p_{hat}[/tex] is the proportion:

[tex]p_{hat}[/tex] = [tex]\frac{1455}{2957}[/tex]

[tex]p_{hat}[/tex] = 0.49

For a 99% confidence interval, z = 2.576:

0.49 ± 2.576.[tex]\sqrt{\frac{0.49(1-0.49)}{2957} }[/tex]

0.49 ± 2.576.[tex]\sqrt{\frac{0.49*0.51}{2957} }[/tex]

0.49 ± 2.576.(0.0092)

0.49 ± 0.0237

For a 99% confidence interval, the proportion will be between 0.4663 and 0.5137 or 0.49 ± 0.0237

Answer:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

First blank: 6a

Second blank: 2/3

Third blank: 21.6

Fourth blank: 3.9

Step-by-step explanation:

Basically, all you need to do is distribute the 2/3 to the stuff inside the parentheses. That means in the first blank, write 6a inside since you're multiplying 2/3 and 6a, and then in the second blank you write 2/3 since you're multiplying 2/3 and 9 together.

2/3*6a+2/3*9 = 21.6 is what you should have.

Now, just solve for a.

4a+6 = 21.6

4a=15.6

a=3.9

Answer:

2/3 * 6a+ 2/3 +9 = 21.6

a = 3.9

Step-by-step explanation:

2/3 ( 6a+9) = 21.6

Distribute

2/3 * 6a+ 2/3 +9 = 21.6

4a + 6 = 21.6

Subtract 6 from each side

4a = 15.6

Divide each side by 4

4a/4 = 15.6/4

a =3.9

Answer:

(-9.6,2)

Step-by-step explanation:

hope i helped

pls can i get brainliest

-Zylynn

Answer:

Step-by-step explanation:

∠OAB is 90 degrees, tangent and a radius met at 90 degree angle

∠OCB=90 degrees, tan and radius meet at 90 degrees angle

OB=12

find angle BOC:

triangle BOA is right angle triangle:

cos(AOB)=adj/hyp=7/12=54.33

angle B= 180-(90+54.33)=35.67

angle COB=54.33 equal to angle AOB

angle AOC=54.33+54.33=108.66

the sum of angles of circle =360

360-108.66= 251.34( exterior angle at the center AOC)

length of the arc= angle (251.34 degrees*7)

convert degrees to radians=4.386 (251.34/π)

length=r*angle in radian=4.386*7=30.71

( i hope this is the answer)

Here is your answer!!!

Cube root of 10648 is 22.

Answer:

22

Step-by-step explanation:

[tex]\sqrt[3]{10648}[/tex] factors into [tex]\sqrt[3]{22^{3} }[/tex]

You then apply the radical rule: [tex]\sqrt[n]{a^{n} }[/tex]=a

In in this case a = 22

Answer:

3x^2 + 3/2 x -9

Step-by-step explanation:

f(x) = x/2 -3

g(x) =3x^2 +x -6

(f+g) (x) =  x/2 -3 + 3x^2 +x -6

   Combine like terms

            = 3x^2 + x/2 +x -3-6

              = 3x^2 + 3/2 x -9

Answer:

see explanation

Step-by-step explanation:

Using the translation rule (x, y ) → (x - 2, y + 4 )

Subtract 2 from the original x- coordinate and add 4 to the original y- coordinate, thus

A(0, 3 ) → A'(0 - 2, 3 + 4 ) → A'(- 2, 7 )

B(- 2, - 4 ) → B'(- 2 - 2, - 4 + 4 ) → B'(- 4, 0 )

C(1, 5 ) → C'(1 - 2, 5 + 4 ) → C'(- 1, 9 )

Answer:

3/4

Step-by-step explanation:

Since, angles θ and α are complementary.

Therefore,

θ + α = 90°

θ = 90° - α

Taking sin both sides.

sin θ = sin (90° - α)

sin θ = cos α (sin (90° - θ) = cos θ)

Since, sin θ = 3/4.....(given)

Hence, cos α = 3/4

Answer:

lateral area

Step-by-step explanation:

examble a cube if you remove the base and the top you remain with the vertical faces and lateral means vertical(we remove the top because it has potential to be a base if you turn it) it applies to any side touching the ground e.g in a cuboid

Answer:

A. Lateral area

Step-by-step explanation:

The lateral surface area is the area of the lateral (vertical) surfaces, it excludes the area of the base and top of a 3D shape.

Answer:

y = 100

Step-by-step explanation:

x = 25

x+y + 55 = 180 since it is a straight line

25+y+ 55 = 180

Combine like terms

80+y = 180

Subtract 80 from each side

y = 180-80

y = 100

Answer:

An example of a prism could be a an amazon box to represent a rectangular prism.  As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.

An example of a cone would be an ice cream cone.  As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.

An example of a cylinder could be a cup.  As the height or the radius of the cup increases, the larger the volume.  More drink for you.

An example of a sphere would be a soccer ball.  As the radius increases, the volume of the ball increases.  Hence, larger soccer balls have a bigger radius than smaller soccer balls.  This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).

Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.

Step-by-step explanation:

Let's simply look at the equations of each shape.

Volume of a prism = base * height

Volume of a cone = Pi * r^2 * (height/3)

Volume of a cylinder = Pi * r^2 * height

Volume of a sphere = (4/3) Pi r^3

Notice that the volumes of prisms, cones, and cylinders directly correlate to height.  As height increases, the volume increases.  The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius.  Consider if you expanded the radius of the sphere, the volume will increase.

Answer:

Increase or decrease the dimensions of objects. See below for an explanation!

Step-by-step explanation:

An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.

A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.

An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.

A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.

You may also shrink the dimensions for each of these objects to make them smaller.

Hope this helps!

Answer:

=-0.809

Step-by-step explanation:

3x^2+5x+7=0 complete the square

3x^2+5x=-7 divide both sides by 3

x^2+5/3 x = -7/3  to complete the square add term(b/2)^2=((5/3)/2)²=25/36

X^+5/3 x+25/36=-7/3 +25/36 factorize

(x+5/6)²= -59/36

x+5/6= + or - √59/36

solution for x= -5/6-√59/6i  (u) OR -5/6+√59/6i (v)

u/v + v/u=(-5/6-√59/6i)/(-5/6+√59/6i) +(-5/6+√59/6i)/(-5/6-√59/6i)=-17/21

=-0.809

Answer:

[tex]\large \boxed{\sf \ \ \ -\dfrac{17}{21}=-0.80952... \ \ \ }[/tex]

Step-by-step explanation:

Hello,

First of all we can verify that 0 is not a solution of the equation so that we can divide by u or v

[tex]\dfrac{v}{u}+\dfrac{u}{v}=\dfrac{u^2+v^2}{uv}=\dfrac{(u+v)^2-2uv}{uv}=\dfrac{(u+v)^2}{uv}-2[/tex]

And we know that

[tex]u+v=-\dfrac{5}{3}\\\\uv=\dfrac{7}{3}\\\\\\as \ \ (x-u)(x-v)=x^2-(u+v)x+uv[/tex]

So it comes

[tex]\dfrac{v}{u}+\dfrac{u}{v}=\dfrac{5^2*3}{7*3^2}-2=\dfrac{25-42}{21}=-\dfrac{17}{21}=-0.80952...[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

hey! it's A and X on edge :)

Answer: A

Step-by-step explanation:

The slope which is also known as gradient can be Mathematically defined as change in dependent variable divide by the change in independent variable.

Slope can rate of increase when it is positive. And rate of decrease when it is negative.

Since the slope of the line through the points is 2. Which is positive, the correct option that describes how the slope relates to the height of the water in the pool is therefore;

The height of the water increases 2 inches per minute. Which is option A

Answer: The Third one is correct

Step-by-step explanation:

Answer:

1,475

Step-by-step explanation:

10 + 50

= 60

60 * 25

= 1,500

1,500 - 25

= 1,475

Answer:

Hey there!

25(10+50)-25

25(60)-25

1500-25

1475

Hope this helps :)

Answer:

x+y = 14

Step-by-step explanation:

x+y+xy = 54

1+x+y+xy = 55

(1+x)(1+y) = 55

(1+x)(1+y) = 5*11

If x and y are integers,

1+x = 5    => x = 4

1+y = 11   =>  y = 10

or

1+x = 11   => x = 10

1+y = 5   =>  y = 4

In either case, x+y = 14

The solution to this system is [tex]x = 4[/tex] and [tex]y = 10[/tex]. Then, [tex]x+y = 14[/tex].

Let be [tex]x + y + x\cdot y = 54[/tex], then we proceed to modify the expression by algebraic means:

The only divisors of 55 is 5 and 11, respectively. Hence, we have the following  system of linear equations:

[tex]x + 1 = 5[/tex] (1)

[tex]y + 1 = 11[/tex] (2)

The solution to this system is [tex]x = 4[/tex] and [tex]y = 10[/tex]. Then, [tex]x+y = 14[/tex].

To learn more on integers, we kindly invite to check this verified question: https://brainly.com/question/1768254

Answer:

b > 9

Step-by-step explanation:

6(b – 4) > 30

Divide each side by 6

6/6(b – 4) > 30/6

b-4 > 5

Add 4 to each side

b-4+4 > 5+4

b > 9

Answer:

[tex]\boxed{b > 9}[/tex]

Step-by-step explanation:

[tex]6(b-4) > 30[/tex]

Resolving Parenthesis

6b - 24 > 30

Adding 24 to both sides

6b > 30+24

6b > 54

Dividing both sides by 6

b > 9

Answer:

Below

Step-by-step explanation:

● a^(-2) *b^3

●(1/a^2) *b^3

● b^3 / a^2

Answer:

a) Vertex b) Maximum c) Axis of symmetry d) Linear e) x-intercept f) Parabola g) Minimum h) Quadratic i) Down

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

d) The first difference of a quadratic sequence will be a linear sequence.

h) The second difference of a quadratic will be constant.

i) image attached

Answer:

D

Step-by-step explanation:

The triangle is an isosceles triangle which means that two sides are the same, A is the same size of the equal side so A is D.

Answer:

The answer is D.

Answer:

{RR,RY,RB,RG,YR,YY,YB,YG,BR,BY,BB,BG,GR,GY,GB,GG}

Step-by-step explanation:

A spinner has four equal-sized sections that are red(R), yellow(Y), blue(B), and green(G).

If the spinner is spun two times, the sample space is given as follows.

{RR,RY,RB,RG,YR,YY,YB,YG,BR,BY,BB,BG,GR,GY,GB,GG}