Express y in terms of x if Log 10 x + Log 10 ( Y )= 2 Log 10 (x+1) ​

Answer:

6/3=22/x would be 11

Step-by-step explanation:

hope this is helpful

Answer:

Answer is 11

Step-by-step explanation:

3x22=66

6×X=6X

66/6X=11

The time at which the break started is 10 : 30 am.

The first step is to convert the time between  10:00 a.m. - 11:15 a.m. to minutes.

The time  between  10:00 a.m. - 11:15 a.m. is 1 hour 15 minutes

In order to convert hours to minutes, multiply hour by 60

1 x 60 = 60 minutes

60 minutes +  15 minutes =  75 minutes

The second step is to subtract the time from the break from the duration of the golf lesson

75 minutes -  15 minutes = 60 minutes

The third step is to divide 60 minutes into equal halves by dividing 60 by 2

60 / 2 = 30 minutes

The last step is to add 30 minutes to the time the lesson started : 10 : 00 am + 30 minutes = 10 : 30 am

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Therefore, the missing angle = (1080° - 947°) = 133°

Step-by-step explanation:

Given: Octagon

7 Interior Angles: 122°, 143°, 152°, 107°, 128°, 130° & 165°

Find: The measure of the missing angle:

Plan: Determine total sum of an octagons interior angles and subtract the total of the given angles

Sum of the Interior Angles of an Octagon:S = (n-2) 180°

S = (8 - 2)180° = 6 x 180° = 1080°

Sum of 7 Given Angles: S7IA = 947°

Answer: Exact Form:  4 /5

Decimal Form:  0.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cancel -3

\(\frac{1}{5x4}\)

Simplify  5 x 4 to 20.

​\(\frac{1}{20}\)

Decimal Form: 0.05

Answer:

Step-by-step explanation:

first find seconds in an hour

60(seconds in a minute) *60(minutes in an hour) = 3600 seconds in an hour

then multiply 8 by 3600 to see how many feet per hour

28,800

we need miles so there are 5280 feet in a mile

28800/5280 is 5.45454545 or 5.455 miles per hour

Answer:

1500

Step-by-step explanation:

1/4t=500lbs so 500x3=1500

Answer:

$80

Step-by-step explanation:

Let the number of hours required to make a mailbox = x

Let the number of hours required to make a toy = y

Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.

Each toy requires 1 hour of work from Carlo and 1 hour from Anita.

The table below summarizes the information for ease of understanding.

\(\left|\begin{array}{c|c|c|c}&$Mailbox(x)&$Toy(y)&$Maximum Number of Hours\\--&--&--&------------\\$Carlo&1&1&12\\$Anita&4&1&24\end{array}\right|\)

We have the constraints:

\(x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0\)

Each mailbox sells for $10 and each toy sells for $5.

Therefore, Revenue, R(x,y)=10x+5y

The given problem is to:

Maximize, R(x,y)=10x+5y

Subject to the constraints

\(x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0\)

The graph is plotted and attached below.

From the graph, the feasible region are:

(0,0), (6,0), (4,8) and (0,12)

At (6,0), 10x+5y=10(6)+5(0)=60

At (4,8), 10(4)+5(8)=80

At (0,12), 10(0)+5(12)=60

The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.

The maximum possible revenue is $80.

Answer:

x=-pie/12

sinxcosx=-1/4

multiply both sides by 2

sin2x = 2sinxcosx we know

now equation will be

sin2x = -1/2

2x=-pie/6

x=-pie/12

Answer: 45

Step-by-step explanation:

The total profit in all was \(1040-900=\$ 140\).

The total profit per pizza was \((0.50)(8)=\$4\).

This means they sold \(\frac{140}{4}=35\) pizzas.

Adding this to the 10 pizzas held back, there were \(35+10=45\) pizzas in the original order.

Based on this information we can conclude that in one hour, Oliver and his sister would get all of the windows washed. This means that it would take 5/6 hours which is equal to 50 minutes) for them to get all of the windows washed.

Information is defined as the content of a message which is passed from a source to its receiver.

The number of hours it takes for Oliver to wash the house windows = 2 hours, so in an hour = 1/2

The number of hours it takes his sister to wash the same house windows = 3 hours, so in an hour = 1/3.

To calculate for one hour for both would be addition of the derived fractions;

= 1/2 + 1/3

= 3+2/6

= 5/6

When converter to minutes, multiple by 60;

= 5/6 × 60

= 300/6

= 50 minutes.

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Answer:

If M is the midpoint of AB, then MB is half of AB:

6x + 40 = 2(2x - 30)

6x + 40 = 4x - 60

-4x          -4x

2x + 40 = -60

     -40     -40

2x/2 = -100/2

x = -50

AB = 6(-50) + 40 = -300 + 40 = -260

MB = 2(-50) - 30 = -100 - 30 = -130

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Answer:  \(y= \frac{1}{10}x\)

-------------------------------------------------------------------------------------------------------------

Given: \(\textsf{Slope = 1/10 and goes through (20, 2)}\)

Find: \(\textsf{Slope in slope-intercept form}\)

Solution: First we need to plug into the point slope formula which is \((y - y_1) = m(x - x_1)\).  Let us plug in the values first and then solve for the slope-intercept form.

Plug in the values

Simplify

Answer: Therefore, the final answer in slope-intercept form for the line with a slope of 1/10 that passes through the point (20, 2) is \(y= \frac{1}{10}x\)

Answer:

The second option

x ==> f(x)

-1 ==> 0

0 ==> 3

3 ==> 36

Step-by-step explanation:

Given:

f(x) = 2x² + 5x + 3

{-1, 0, 3}

Required:

Determine the best mapping representing the function

SOLUTION:

First, find f(x) each domain value.

To find f(x), plug in the domain value into the function.

For -1, we have:

f(-1) = 2(-1)² + 5(-1) + 3

f(-1) = 2 - 5 + 3

f(-1) = 0

For 0, we have:

f(0) = 2(0)² + 5(0) + 3

f(0) = 0 + 0 + 3

f(0) = 3

For 3, we have:

f(3) = 2(3)² + 5(3) + 3

f(3) = 18 + 15 + 3

f(3) = 36

The mapping that best represents the function would be:

x (domain) ==> f(x) (range)

-1 ==> 0

0 ==> 3

3 ==> 36

The second option is the answer.

Answer:

equation b the y intercept is the constant which is 1

Step-by-step explanation:

Answer:

7.5 cups pf rice

Step-by-step explanation:

45 divided by 6

The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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Answer:

Step-by-step explanation:4

Step-by-step explanation:

We do the ones that are in parenthesis first. Find out the exponent. 2 to the power of two is 4. 3-4=-1. Then we would add 5. 5+-1 would result of 4.

Answer:

The answer is number 2

Answer:

  (c)  (-∞, -2] ∪ (-1, ∞)

Step-by-step explanation:

You want the range of the piecewise function shown in the graph.

The range is the vertical extent of the graph, the set of possible output values of the function.

This graph shows a gap between y = -2 and y = -1. The value y = -2 is included in the range, but the value y = -1 is not. (That's what the open circle means.)

Hence, the range is ...

  (-∞, -2] ∪ (-1, ∞)

By using the figure below, the value of line segment PT is equal to 54 units.

In Mathematics, the midpoint of a line segment with two endpoints can be calculated by adding each point on a line segment together and then divide by two (2).

Since T is the midpoint of PQ, we have the following:

Line segment PT = Line segment TQ

7x + 5 = 9x - 9

9x - 7x = 9 + 5

2x = 14

x = 14/2

x = 7.

Now, we can determine the value of PT:

PT = 7x + 5

PT = 7(7) + 5

PT = 54 units.

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Complete Question:

Use the figure to the right to find the value of PT. T is the midpoint of PQ PT=7x+9 and TQ=9x-5

Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.\)

\(x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3\)

Answer: Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step-by-step explanation:

Answer:  x = -2/3

Step-by-step explanation:

Bring everything over to the other side that is not in the absolute value, then make a positive and negative version.  You must check your answers.

|3x+2|+3x+2=0                        >Subtract 2 from both sides

|3x+2|+3x = -2                         >Subtract 3x from both sides

|3x+2| = -3x-2                         > Now make 2 equations, one with a + on

                                                 right side and other with negative on right

                                                 side Then you can drop your absolute

                                                 value sign

Positive:

3x+2 = -3x-2                          > Now solve for x by bringing like terms to each

                                                side

6x = -4

x = -4/6                                  >Reduce by dividing top and bottom by 2

x = -2/3

Plug back in to make sure it's a viable solution.

|3x+2|+3x+2=0

|3(-2/3)+2|+3(-2/3)+2=0

|-2 +2| - 2 +2 = 0

0 = 0      so yes x = -2/3 is a solution

Negative:

3x+2 = -(-3x-2)

3x+2 = 3x+2

0 = 0                   The x cancels out so there is no solution from the negative version.  So there is only 1 solution.

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

Answer:

A , B and C

Step-by-step explanation:

evaluate the expressions following the order of operations as set out in PEMDAS

initial expression

note that • indicates multiplication

3 (2 + 6) + 4 × 5 ← evaluate parenthesis

= 3(8) + 20 = 24 + 20 = 44

A

5 × 4 + 3 × (6 + 2) ← evaluate parenthesis

= 5 × 4 + 3 × 8 ← perform multiplication

= 20 + 24 ← perform addition

= 44

B

(6 + 2) × 3 + 4 × 5 ← evaluate parenthesis

= 8 × 3 + 4 × 5 ← perform multiplication

= 24 + 20 ← perform addition

= 44

C

3 × 2 + 3 × 6 + 4 × 5 ← perform multiplications

= 6 + 18 + 20 ← perform addition

= 44

D

3 × 2 + (6 + 4) × 5 ← evaluate parenthesis

= 3 × 2 + 10 × 5 ← perform multiplication

= 6 + 50 ← perform addition

= 56

the expressions equivalent to the initial expression are A , B and C

Answer: d = 14/5

Step-by-step explanation:

14 + d = 6d

14 = 5d

14/5 = d

Check Work:

14 + (14/5) = 6(14/5)

16.8 = 16.8

Answer:

  \(F^{-1}(x)=\dfrac{x-7}{4}\)

Step-by-step explanation:

To find the inverse function, solve for y the relation ...

  F(y) = x

  4y +7 = x

  4y = x - 7

  y = (x -7)/4 . . . . the inverse function

  \(\boxed{F^{-1}(x)=\dfrac{x-7}{4}}\)

Answer:

5(x-1)>5/4x

If you mean (5/4)x, then

Divide by 5

x-1 > (1/4)x

x-1 > x/4

Multiply by 4

4x-4 > x

Add 4

4x > x+4

Subtract x

3x > 4

Divide by 3

x > 4/3

I hope its help u dear

The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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