Estimate the sum by first rounding each mixed number to the nearest whole number and then adding

3 8/9 + 2 5/6

Answer:

D

Step-by-step explanation:

Before the increase, the length is 6 and the width is 5, so the area is 5×6 = 30.

After the increase, the length is x+6, the width is x+5, and the area is tripled: 30×3 = 90.

Therefore:

(x+6) (x+5) = 90

Answer:

x=-1/2

Step-by-step explanation:

Given:

8x^3+12x^2+6x+1=0

Making factors of the given polynomial by using cube formula, given as

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Re-writting the given polynomial:

(2^3.x^3) + 3(2^2.x^2)(1)+3(2x)(1) + (1^3)=0

Hence (2^3.x^3) + 3(2^2.x^2)(1)+3(2x)(1) + (1^3) can be written as (2x+1)^3

(2x+1)^3= 0

2x+1= 0

2x= -1

x= -1/2 !

ANSWER

[tex](-8, - 3)[/tex]

EXPLANATION

Given that: (-8,-8) is on f(x).

Then we can write (-8,f(-8)) is on f(x).

The corresponding point on

[tex]f(x) + 5[/tex]

will be

[tex](-8,f(-8)+5)[/tex]

We substitute f(-8)=-8 to obtain;

[tex](-8, - 8+5)[/tex]

This simplifies to

[tex](-8, - 3)[/tex]

Therefore the corresponding point on f(x)+5 is (-8,-3).

17) 5:6

18) 3:4

19) 4:5

20) 2:3

21) 3:4

22) 2:3

23) 3:5

24) 9:10

These answers are all simplified ratios

Final answer:

The questions involve finding the ratio of two quantities and simplifying them by dividing both numbers by their greatest common divisor. Each ratio gives a comparative relationship between two different counts of items or scores in different subjects.

Explanation:

The questions provided all relate to finding the ratio of two quantities.

In each case, the ratio is found by comparing two quantities and simplifying by dividing both numbers by their greatest common divisor (GCD).

Answer:

B is not necessarily true

Step-by-step explanation:

A) This is always true

B) This is not necessarily true

When two lines intersect, they form angles at the intersection as D says, but that does not mean that the angle will always be 90 degrees as is required for the two intersecting lines to be perpendicular

C) This is always true

D) This is always true

Option B) The lines are not perpendicular is not necessarily true.

When two lines intersect and following are the three different possibilities:

1) They are parallel, if lines are parallel they can never intersect.

2)They cross each at an angle and the point of intersection is unique that is they intersect at only one point.

3) Two lines coincide, that is every point on line 1 is a point on line 2.

Now

In option B it is given that lines are perpendicular that is the specific case of (2) When angle is 90°.

Therefore, it is not necessarily true.

To know more about intersection of lines refer to:

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ANSWER

[tex]y = 3 \pm \sqrt{21} [/tex]

EXPLANATION

The quadratic equation is:

[tex] {y}^{2} - 6y - 12 = 0[/tex]

Group variable terms:

[tex] {y}^{2} - 6y = 12[/tex]

Add the square of half, the coefficient of y to both sides.

[tex] {y}^{2} - 6y + ( - 3) ^{2} = 12 + ( - 3) ^{2} [/tex]

[tex] {y}^{2} - 6y + 9= 12 + 9[/tex]

The LHS us now a perfect square trinomial:

[tex]{(y - 3)}^{2}= 21[/tex]

Take square root:

[tex]y - 3 = \pm \sqrt{21} [/tex]

[tex]y = 3 \pm \sqrt{21} [/tex]

The first choice is correct.

3±√21. The equation [tex]y^{2}-6y-12=0[/tex] has two possible solutions 3+√21 y 3-√21.

If we have a general quadratic equation [tex]ay^{2} +by+c=0[/tex] we can solves the equation by completing the square. First, we divide the quadratic equation by a, we obtain [tex]y^{2} +\frac{b}{a} y+\frac{c}{a} =0[/tex].

For this problem, we have [tex]y^{2}-6y-12=0[/tex]

We can skipped division in this example since the coefficient of [tex]x^{2}[/tex] is 1.

Move the term c to the right side of the equation

[tex]y^{2}-6y=12[/tex]

Completing the square on the left side of the equation and balance this by adding the same number to the right side of the equation, with b = -6.

[tex](\frac{b}{2})^{2} =(\frac{-6}{2})^{2}=(-3)^{2} =9[/tex]

[tex]y^{2}-6y+9=12+9[/tex]

[tex](y-3)^{2}=21[/tex]

Take the square root on both sides of the equation:

y - 3 = ±√21

Add 3 from both sides:

y = 3 ± √21

Answer:

$142500

Step-by-step explanation:

We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.

Assuming [tex]x[/tex] to be the salary of the department head, if the total of the two salaries is $190000, we are to find the salary of the president of the University.

We can write an equation in terms of [tex]x[/tex]:

[tex]3x+x=190000[/tex]

[tex]4x=190000[/tex]

[tex]x=47500[/tex]

Salary of the president of the University = [tex]3(47500)[/tex] = $142500

Hey there! :D

f(-3)= 4(2)^x

Just plug in -3 as x and solve.

4(2)^-3

First do the exponent, and then multiply the four on the outside.

4(1/8)

=1/2

I hope this helps!

~kaikers

Final answer:

To calculate f(-3) for the function f(x) = 4(2)ˣ, substitute -3 into the function, yielding f(-3) = 1/2 after simplifying 4 times 2 raised to the power of -3.

Explanation:

To find f(-3) for the function f(x) = 4(2)ˣ, simply substitute -3 for x in the equation. Here's How:

Start with the original function f(x) = 4(2)ˣ.

Replace every x with -3 to get f(-3) = 4(2)⁻³.

Calculate 2⁻³, which equals 1/8 because negative exponents represent the reciprocal of the base raised to the positive exponent.

Now, multiply 4 by 1/8 to get f(-3) = 4 * 1/8 = 1/2.

Therefore, f(3) for the given function equals 1/2.

Answer:

15. Option A is correct

16. Option B is correct.

Step-by-step explanation:

Question 5:

sin2Ф = 2sinФcosФ

We are given sinФ = 9/13

and we need to find cosФ in order to find sin2Ф

We know that sin^2Ф + cos^2Ф= 1

so, cos^2Ф = 1- sin^2Ф

cos^2Ф = 1- (9/13)^2

cos^2Ф = 88/169

taking √ on both sides:

√cos^2Ф = √88/169

cosФ = (2√22)/13

Now

sin2Ф = 2sinФcosФ

          = 2 (9/13) (( 2√22)/13)

sin 2Ф = 36√22 / 169

Now we find cos2Ф

The formula for cos2Ф = cos^2Ф - sin^2Ф

cos2Ф = ((2√22)/13)^2 - (9/13)^2

cos2Ф = 4*22 /169 - 81/169

cos2Ф = 7/169

So, Option A is correct

Question No 6

We need to find sin2Ф and cos2Ф where cosФ = 6/13

We are given cosФ = 6/13

and we need to find sinФ in order to find sin2Ф and cos2Ф

We know that sin^2Ф + cos^2Ф= 1

so, sin^2Ф = 1- cos^2Ф

sin^2Ф = 1- (6/13)^2

sin^2Ф = 133/169

taking √ on both sides:

√sin^2Ф = √133/169

sinФ = √133/13

Now

sin2Ф = 2sinФcosФ

          = 2 (√133/13) (6/13)

sin2Ф  = 12√133 / 169

Now we find cos2Ф

The formula for cos2Ф = cos^2Ф - sin^2Ф

cos2Ф =  (6/13)^2 - (√133/13)^2

cos2Ф = 36/169 - (133/169)

cos2Ф = -97/169

Since the quadrant is 1st so, cos2Ф will be Positive i.e. 97/169

cos2Ф = 97/169

So, Option B is correct.

Answer:

The missing words

# x ⇒ # y ⇒ # 4 ⇒ # 0

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

∵ f(x) = √(x - 4)

∴ y = √(x - 4) ⇒ switch x and y

∴ x = √(y - 4) ⇒ square the two sides

∴ x² = [√(y - 4)]² ⇒ cancel the root by squaring

∴ x² = y - 4 ⇒ add 4 to the both sides

∴ y = x² + 4

∴ f^-1(x) = x² + 4

* To find the domain of the inverse, find the range of the function

∵ The domain of f(x) is ⇒ x - 4 ≥ 0 (no negative value under√)

∴ the domain is x ≥ 4

- Substitute this value in the function to find the range

∵ x = 4

∴ y = √(4 - 4) = 0

∴ y ≥ 0

- The range of f(x) is y ≥ 0

∴ The domain of the inverse f^-1(x) is x ≥ 0

- The missing words

# x

# y

# 4

# 0

To solve the equation Z + mx = yx for x, we first move 'mx' to the right side to get 'yx - mx = Z'. We then factor out 'x' to get 'x(y - m) = Z'. Finally, we divide by '(y - m)' to get 'x = Z / (y - m)'. This solution holds as long as y ≠ m.

Here, we're going to solve the equation for x: Z + mx = yx.

We can start by grouping the terms with 'x' together. This gives us: yx - mx = Z. Now, we can factor x out of the left side of the equation. This results in: x(y - m) = Z. Finally, to solve for x, we divide both sides of the equation by (y - m). This gives us the solution: x = Z / (y - m).

Note: This solution is under the assumption that y ≠ m because division by zero is undefined.

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Answer:

Step-by-step explanation:

just did the question and got it right.

Hello wendywagor!

Let x = the original price of the sneakers

x - .60x = 22.40

.40x = 22.40

x = $56

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Have A Great rest of Your Day!

Find the circumference:

Circumference = 2 x PI x radius

Circumference = 2 x 3.14 x 19 = 119.32

Divide by 4: 119.32 / 4 = 29.83 rounded to 29.8

The answer is C.

Answer:

C. 29.8 inches

Step-by-step explanation:

Length of complete hula hoop(L)= circumference of hoop

=>[tex]L=2\pi r[/tex]

where radius, r= 19 inches

Therefore length of arc(l) subtending 1/4 of the hoop is

=>[tex]l=\frac{1}{4}\times L=\frac{1}{4}\times2\pi r=\frac{\pi r}{2}[/tex]

=>[tex]l=\frac{\pi \times 19}{2}inches=29.8 inches[/tex]

Thus the length of the arc subtending 1/4 of the hoop is 29.8 inches

Answer:

Step-by-step explanation:

Without a second equation relating x and y, we can solve 3x - 1/2y = 2 ONLY for x in terms of y or for y in terms of x:

x in terms of y:    Multiply all three terms of 3x - 1/2y = 2 by 2, to eliminate the fraction:  6x - y = 4.  Now add y to both sides to isolate 6x:  6x = 4 + y.

Last, divide both sides by 6 to isolate x:

x = (4 + y)/6

y in terms of x:    

y = 6x - 4

If you want a numerical solution, please provide another equation in x and y and solve the resulting system.

Answer:

For the first pic its mode interval and median for the second pic its frequency table.

Step-by-step explanation:

Answer:

w=18 minutes per mile, r=12 minutes per mile

Step-by-step explanation:

Let w and r represent the rates, in minutes per mile, that Carly walked and ran on the treadmill, respectively.

1. On Monday, Carly walked 3 miles and spent 3w minutes, ran 2 miles and spent 2r minutes. In total Carly spent 78 minutes, so

3w+2r=78

2. On Thursday, Carly walked 2 miles and spent 2w minutes, ran 3 miles and spent 3r minutes. In total Carly spent 72 minutes, so

2w+3r=72

Solve the system of two equations:

[tex]\left \{ {{3w+2r=78} \atop {2w+3r=72}} \right.[/tex]

Multiply the first equation by 2, the second equation by 3 and subtract them:

[tex]2(3w+2r)-3(2w+3r)=2\cdot 78-3\cdot 72\\ \\6w+4r-6w-9r=156-216\\ \\-5r=-60\\ \\r=12[/tex]

Substitute it into the first equation:

[tex]3w+2\cdot 12=78\\ \\3w=78-24\\ \\3w=54\\ \\w=18[/tex]

Answer:

17

Step-by-step explanation:

Use the distance equation.

d² = (x₁−x₂)² + (y₁−y₂)²

The order doesn't matter.  If I choose (x₁, y₁) to be (8, 4) and (x₂, y₂) to be (-7, -4), then:

d² = (8−(-7))² + (4−(-4))²

d² = 15² + 8²

d² = 289

d = 17

Final answer:

The distance between the points (8,4) and (-7,-4) on a coordinate plane is 17 units.

Explanation:

In order to find the distance between two points on a coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the points (8,4) and (-7,-4), we can substitute the x and y values into the formula:

d = √((-7 - 8)^2 + (-4 - 4)^2)

d = √(225 + 64)

d = √289

d = 17

Therefore, the distance of the segment formed by joining the two given points is 17 units.

Answer:

see explanation

Step-by-step explanation:

Given a function f(x)

Then at the turning points the derivative of f(x) equals zero, that is

f'(x) = 0 at the turning points

Weird. A period appears above this... huh.

Answer:

[Th]e cube has a greater value.

Step-by-step explanation:

What the word problem really wants us to get [is ]the question of 'Which is greater, A=6a^2 when 'a' [is] 18 or A=4[tex]\pi[/tex]r^2 when r = 9? And here's how to solve that.

Starting with the[ c]ube we have A=6a^2. A bit t[o]o simple, right?

A=6(18)^2 Substitute numbers.

A=6(324) Solve ex[p]onents.

A=1944 Mult[i]ply.

So w[e] know that the cube is 1944 meters cube[d ] in area. But what about the more [f]ormidable sphere? Fo[r] it we need a slightly m[o]re co[m]plicated formula, A=4[tex]\pi[/tex]r^2. However, instead of using the real pi I will be rounding to 3.14, since we have no calculator so anything more would take way too long and fry your[ bra]in.

A=4(3.14)(9)^2 Subst[i]tute numbers.

A=4(3.14)(81) Solve expone[n]ts.

A=12.56(81) Multip[ly].

A=1017.36 Multiply again[.]

Now, since I'm sure all of us can count, we know that 1944 is greater than 1017.36. Or in other words, the cube is bigger than the sphere.

And PLEASE don't copy this guys. Make your own iteration. Change it up!

Answer:

13. 90

14. 43

15. 146

Answer:

7.782352941

Step-by-step explanation:

4.2 divided by 1.02 the multiply the out come of that by 1.89 to get 7.782352941

Answer:

2800 cm^3, or 2.8 liters

Step-by-step explanation:

The base of the tank remains 14 cm × 25 cm. The remaining height is 15 -7 = 8 cm, so the remaining volume is ...

(14 cm)(25 cm)(8 cm) = 2800 cm^3 = 2.8 liters

_____

1 liter = 1000 cm^3

Answer:

First option: (1, 1)

Second option: (-3, 4)

Step-by-step explanation:

Substitute each point into the inequality:

Point (1,1):

[tex]x + 2y \geq3\\\\(1) + 2(1) \geq3\\\\3\geq3[/tex]

(The inequality is satisfied with this point)

Point (-3, 4):

[tex]x + 2y \geq3\\\\(-3) + 2(4) \geq3\\\\5\geq3[/tex]

 (The inequality is satisfied with this point)

Point (-2, 2):

[tex]x + 2y \geq3\\\\(-2) + 2(2) \geq3\\\\2\geq3[/tex]

(The inequality is not satisfied with this point)

Point (5, -2):

[tex]x + 2y \geq3\\\\(5) + 2(-2) \geq3\\\\1\geq3[/tex]

(The inequality is not satisfied with this point)

Answer:

Your answer would be A and B

Step-by-step explanation:

Answer:

[tex]\boxed{\sqrt{65}}[/tex]

Step-by-step explanation:

The radius of circle D is the distance from the origin to (-4, -7).

In math, the distance formula gives us the distance between two points, (x₁, y₁) and x₂, y₂):

[tex]d = \sqrt{(x _{2}-x_{1})^{2} +(y _{2}-y_{1})^{2}}[/tex]

You are really using Pythagoras' Theorem to find the distance. You are building a right triangle whose hypotenuse connects two given points.  

For example, in the blue triangle below, the distance between the points (0,0) and (-4, -7) is

[tex]d = \sqrt{(0 - (-4))^{2} +(0 -(- 7))^{2}}\\\\ = \sqrt{4^{2} +7^{2}}\\ = \sqrt{16 + 49}\\=\sqrt{65}[/tex]

[tex]\text{The radius of the circle is }\boxed{\mathbf{\sqrt{65}}}[/tex]

Answer:

(x + 6)²

Step-by-step explanation:

This is a perfect square of the form

(x + a)² = x² + 2ax + a²

here a² = 36 ⇒ a = 6 and 2ax = 2 × 6x = 12x

Hence

x² + 12x + 36 = (x + 6)²

Answer:

(x+6)(x+6)

Step-by-step explanation:

Answer: the range is 209

Step-by-step explanation: the biggest number minus the smallest will give you the range

The answer is 209. Hope this helps

Answer:

35/5 = 7 Minutes per Window thus: 12*7 = 84 Minutes

Step-by-step explanation:

Answer:

84 minutes or 1 hour and 24minutes

Step-by-step explanation:

12*35=420

420/5=84

Answer:

-65/2

Step-by-step explanation:

I am just a natural genius ;)

Answer:

see explanation

Step-by-step explanation:

Evaluate the parenthesis before multiplication

4² = 4 × 4 = 16 and

( [tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]

Thus 16 + [tex]\frac{1}{4}[/tex] = 16 [tex]\frac{1}{4}[/tex] = [tex]\frac{65}{4}[/tex]

Hence

- 2 × [tex]\frac{65}{4}[/tex] = [tex]\frac{-2(65)}{4}[/tex] = - [tex]\frac{65}{2}[/tex] = - 32 [tex]\frac{1}{2}[/tex]

Answer:

The answer would be A. 1.25