The length of the flat screen tv is 5 inches less than 3 times it's width. If the perimeter of the tv is 150 inches, find the dimensions

He got $245 for his birthday

The expression simplifies to[tex]\( \left(\frac{2}{3}\right)^8 \), representing \( \frac{2^8}{3^8} \), or \( \frac{256}{6561} \).[/tex]

Sure, here's a detailed stepwise solution with explanation:

1. **Understand the problem**: We're asked to simplify the expression  [tex]\( \left(\frac{2}{3}\right)^2 \cdot \left(\frac{2}{3}\right)^6 \).[/tex]

2. **Apply the exponent property**: According to the exponent property [tex]\(a^m \cdot a^n = a^{m+n}\),[/tex] when multiplying two expressions with the same base, we add their exponents.

3. **Calculate the exponents**:

  - The first expression  [tex]\( \left(\frac{2}{3}\right)^2 \) has an exponent of 2. - The second expression \( \left(\frac{2}{3}\right)^6 \)[/tex] has an exponent of 6.

4. **Add the exponents**:

[tex]- \(2 + 6 = 8\).[/tex]

5. **Combine the expressions**:

  - By applying the exponent property, we get  [tex]\( \left(\frac{2}{3}\right)^{2+6} = \left(\frac{2}{3}\right)^8 \).[/tex]

6. **Final result**:

  - The simplified expression is [tex]\( \left(\frac{2}{3}\right)^8 \), which represents \( \frac{2^8}{3^8} \).[/tex]

  - This can also be expressed as [tex]\frac{256}{656\1} \),[/tex] where 256 is the numerator and 6561 is the denominator.

7. **Explanation of the result**:

  - The simplified expression represents the result of raising  [tex]\( \frac{2}{3} \)[/tex] to the power of 8, which is obtained by multiplying the expression by itself 8 times.

  - It can be interpreted as the fraction [tex]\( \frac{256}{6561} \)[/tex] , which is the result of raising 2 to the 8th power in the numerator and 3 to the 8th power in the denominator.

We are given

nine less than three times a number is forty

we know that

we always start our order of operation from left to right

This sentence represents equality

Let's assume that number as 'x'

Left side is :

3x-9

Right side is :

40

so, we can write as

[tex]3x-9=40[/tex].............Answer

Domain is (5, ∞), {x| x is greater than 5} for all integer n

Range is (-∞, ∞), {y| y belongs to Reals numbers}

[tex]F(x) = log (x - 5)[/tex]

Set up the equation for x

[tex]x - 5 > 0[/tex]

or,

x > 5

So the domain is all values of x greater than 5 to infinity.

Range is set of all correct or valid values of y.

Range = (-∞, ∞), {y| y belongs to Reals numbers}

C

the equation of a parabola in ' vertex form ' is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

the vertex of g(x) = (1, - 3) and a = 1

g(x) = (x - 1)² - 3

Answer:

True.

Step-by-step explanation:

Consecutive square numbers can be written as:

1^2, 2^2, 3^2, 4^2, 5^2 ...

The sequence of the numbers being squared in odd, even, odd, even...

Squaring an odd number yields an odd. Squaring an even yields an even. The difference between an odd and even number is always odd. Since consecutive perfect squares are odd, even, odd... then the difference is always odd.

Answer:

The answer is: True.

Step-by-step explanation:

A perfect square number in math is an integer that can be expressed as the product of a number by itself.

The difference between each square and consecutive number, if it starts with 0, is all odd numbers, in ascending order.

The answer is: True.

Steps:

isolate " x "  for -2x + 2y  + 3z  = 0 ;    x = -  ( - 3z - 2y ) / 2

Subsititute : x = -  ( - 3z - 2y ) / 2

- 2 * (  - ( - 3z - 2y ) / 2 ) - y + z = - 3

2 * ( -  ( - 3z - 2y ) / 2 ) + 3y  + 3z  =5

isolate " z " for  :  - 2  ( -  ( - 3z - 2y ) / 2 ) - y+ z = - 3 ;  z = - ( - 3 +  3y / 2 )

subsititute  z = - ( - 3 + 3y / 2 ) :

2* ( - ( -3* ( - ( - 3 +3y / 2 ) - 2y / 2  ) + 3y  + 3  ( - ( - 3 + 3y / 2 ) = 5

isolate y for 2 ( -( - 3 ) - 3 + 3y / 2 ) - 2y / 2 ) + 3y + 3 ( - ( - 3 + 3y / 2 ) = 5

y = 1

for z =  - ( - 3+ 3y ) / 2

subsititute y = 1

z = - ( - 3 + 3  * 1 ) / 2

z =  0

For x  = - ( - 3z - 2y ) / 2

subsititute y = 1

subsititute z = 0

x = -  ( - 3 *0 - 2 * 1 ) / 2

x =  1

x = 1  , y =  1  , z = 0

I think the answer is 2 (D)   Hope this helps :D

Answer:

6

Step-by-step explanation:

( [72-60] / 72 )*100 =  50 / 3 = 16.7 %

divide every one by m^2

1:m^2+1

Step 1: Subtract 2x from both sides.7x−2x=2x−35−2x5x=−35   Step 2: Divide both sides by 5.‌5x5‌=‌−355‌x=−7 Answer: x = −7

Hope I helped.

1. ∠1 ≅ ∠3                                              1. given

  ∠1 and ∠6 are supplementary angles

  ∠3, ∠4, and ∠5 are supplementary angles

2. m∠1 = m∠3                                        2. definition of congruency

3. m∠1 + m∠6 = 180°                             3. definition of supplementary angles

   m∠3 + m∠4 + m∠5 = 180°

4.  m∠3 + m∠4 + m∠5 = m∠1 + m∠6     4. transitive property

5.  m∠3 + m∠4 + m∠5 = m∠3 + m∠6     5. substitution property

6.  m∠4 + m∠5 = m∠6                             6. subtraction property of equality

S+ST = RT  

3x+1 + 2x-2 = 64  

5x = 65  

x = 13

The answer to this equation would be 7.21

the answer is 7.21.

Final answer:

To find the value of sin10° + tan40° × cos10°, calculate each trigonometric function separately, multiply tan40° by cos10°, then add sin10° to the product. The approximate result is 1.0005, but use a calculator for a precise value.

Explanation:

To solve the expression sin10° + tan40° × cos10°, we first need to calculate the individual trigonometric values. The cosine of 10 degrees (cos(10°)) is approximately 0.9848.

Next, we calculate the tangent of 40 degrees (tan(40°)). According to the provided data, tan(40°) is approximately 0.839.

Using the trigonometric identity for the sine of a sum of angles, we cannot directly simplify the expression because the addition and multiplication involve different angles. Therefore, we perform the multiplication first:

tan40° × cos10° = 0.839 × 0.9848 ≈ 0.8265

Next, we add the value of sine of 10 degrees (sin10°) to this result. Given that sin10° is approximately 0.174:

sin10° + (tan40° × cos10°) = 0.174 + 0.8265 ≈ 1.0005.

However, due to possible rounding in intermediate steps, the actual value might be slightly different when calculated using more precise values or a calculator set to the correct mode.

It will be greater, since there are 16 ounces in a pound. You can say that the new amount will be 16 times the amount of pounds there is.

When you convert pounds to ounces, the number of ounces will always be greater. This is due to the fact that 1 pound equals 16 ounces.

If you convert pounds to ounces, the number of ounces will be greater than the number of pounds. This is because 1 pound equals 16 ounces. For instance, if you have 2 pounds, and you want to convert it into ounces, you would multiply the 2 pounds by 16 (the conversion factor), which would give you 32 ounces. Therefore, the number of ounces is always going to be greater than the number of pounds when you're converting pounds into ounces.

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Answer:

y = m(x - 2)

Step-by-step explanation:

If y over x-2= m and we want to solve for y, multiply both sides of the equation y over x-2= m by (x - 2) first, to remove fractions:

y = m(x - 2)

[tex]f(x)=4x-11\\\\\text{Put the value of x = 5 to the equation of the function}\\\\f(5)=4(5)-11=20-11=9[/tex]

Answer:

6.875

Step-by-step explanation:

We have been given that after a storm Michael measured 6 7/8 inches of snow. We are asked to show this amount  as a decimal.

We can represent our improper fraction as a whole and a part as:

[tex]6\frac{7}{8}=6+\frac{7}{8}[/tex]

Let us convert [tex]\frac{7}{8}[/tex] as a decimal.

[tex]6+\frac{7}{8}=6+0.875=6.875[/tex]

Therefore, the amount as a decimal would be 6.875.

5/6+2 3/4

= 10/12 + 2 9/12

= 2 19/12

= 3 7/12

Hope that helps

Mixed Number Form:[tex]3\frac{7}{12}[/tex]

Step by step: [tex]\frac{5}{6} + 2\frac{3}{4}[/tex]

= [tex]\frac{5}{6} + \frac{11}{4}[/tex]

= [tex]\frac{43}{12}[/tex]

Answer: [tex]3\frac{7}{12}[/tex]

1. The rate of the boat in calm water is 50 miles per hour.

2. The rate of the current is 10 miles per hour.

How the rates are determined:

Let:

[tex]r_b[/tex] be the rate of the boat in calm water (in miles per hour).

[tex]r_c[/tex] be the rate of the current (in miles per hour).

Given:

With the current:

Distance: 120 miles

Time: 2 hours

Speed: [tex]r_b + r_c[/tex] (since the current aids the boat)

So, the equation is:

[tex]r_b + r_c = \frac{120}{2}[/tex] = 60 (Equation 1)

Against the current:

Distance: 120 miles

Time: 3 hours

Speed: [tex]r_b - r_c[/tex] (since the current opposes the boat)

So, the equation is:

[tex]r_b - r_c = \frac{120}{3}[/tex] = 40 (Equation 2)

Step 1: Solve the System of Equations

We have the system:

[tex]r_b + r_c = 60[/tex] (Equation 1)

[tex]r_b - r_c = 40[/tex] (Equation 2)

Step 2: Add the Two Equations

Adding Equation 1 and Equation 2:

[tex]r_b + r_c + r_b - r_c[/tex] = 60 +40

[tex]2r_b[/tex] = 100

[tex]r_b = 50[/tex] (Rate of the boat in calm water)

Step 3: Substitute [tex]r_b[/tex] into one of the Equations

Substitute [tex]r_b[/tex] =50 into Equation 1:

50+[tex]r_c[/tex] = 60

[tex]r_c[/tex] = 10 (Rate of the current)

To solve the equation we have to rearrange the terms i.e. like terms on one side

[tex]-28 = 22 - 5x[/tex]

Subtracting 22 from both sides we get

[tex] -28 -22 = 22-5x - 22[/tex]

[tex] -50 = -5x[/tex]

Divide both sides by -5 we get

[tex]\frac{-50}{-5} = \frac{-5x}{-5}[/tex]

On simplifying we get

[tex] x =10[/tex]

Hence, x= 10 is your answer

Hope this will help

Step 1. Expand

-3x - 4 = 5x + 20

Step 2. Add 3x to both sides

-4 = 5x + 20 + 3x

Step 3. Simplify 5x + 20 + 3x to 8x + 20

-4 = 8x + 20

Step 4. Subtract 20 from both sides

-4 - 20 = 8x

Step 5. Simplify -4 - 20 to -24

-24 = 8x

Step 6. Divide both sides by 8

-24/8 = x

Step 7. Simplify 24/8 to 3

-3 = x

Step 8. Switch sides

x = -3

15.97 as amixed fraction would be 15 97/100

Hope helps! -Aparri

The decimal number  15.97 as a mixed fraction is [tex]15\frac{97}{100}[/tex].

To write 15.97 as a mixed fraction, we need to express it as a whole number combined with a fraction.

The whole number part can be obtained by taking the integer part of 15.97, which is 15.

To determine the fraction part, we need to consider the decimal portion. Since 15.97 has two decimal places.

we can express it as a fraction with a denominator of 100 (since there are two decimal places).

The decimal portion, 0.97, can be written as 97/100.

Putting it together, 15.97 can be expressed as the mixed fraction:

15 + 97/100

Therefore, 15.97 as a mixed fraction is [tex]15\frac{97}{100}[/tex].

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Final answer:

The total bill at Pepe's Pizza Palace was $16.60. Annie paid $6.53, Suz paid $3.32, and Cynthia paid the remaining $8.80.

Explanation:

To determine the total bill and how much each girl paid, we first acknowledge that Cynthia has stated she would pay the remaining $8.80. This gives us a starting point to figure out the portions of the bill that Annie and Suz will pay.

Suz suggests that Annie pays one-third of the bill and offers to pay $1 more than that amount. Suz is to pay 20% of the bill. If Cynthia pays the remaining amount, let's denote the total bill as B.

Using the information given:

Annie pays one-third of the bill plus $1: (1/3)B + $1

Suz pays 20% of the bill: 0.20B

Cynthia pays the remaining $8.80.

Add these up to get the total bill.

(1/3)B + $1 + 0.20B + $8.80 = B

Solving this equation:

0.33B + 0.20B + $8.80 - $1 = B - $1

0.53B + $7.80 = B

B - 0.53B = $7.80

0.47B = $7.80

Dividing both sides by 0.47:

B = 7.80 / 0.47

B = $16.60 (rounding to two decimal places)

Therefore, the total bill amounts to $16.60. Now to find out how much each girl pays:

Annie's portion:

(1/3)*16.60 + $1 = $5.53 + $1 = $6.53

Suz's portion:

0.20*16.60 = $3.32

Cynthia's portion is the amount she agreed to pay:

$8.80

To summarize, the total bill was $16.60. Annie paid $6.53, Suz paid $3.32, and Cynthia paid $8.80.

Answer:

Okay Im going off of my work because we did some in class and then the rest by ourselves but i turned mine in yesterday but didnt recieve a grade yet but i hope these help you...

The number number line it is seven units apart.

The absolute value larger number smaller number would be 2 - (-5). So what you do with that is keep the 2 change the subtraction sign to plus sign and change the negative 5 to positive 5. So your answer would be 7.

And smaller number to larger number would be -5 - 2. And then you do the same steps as the last one. Keep the negative five, change the subtraction sign to addition sign and make the two  negative. And that answer would be -7

2. For the number two problem you would plot the robins nest just below the top of the verticle line. the red squirrel den would be right next to the zero but a tad up. And the groundhog burrow would be below the zero mark and a little before the end of the verticle line.

Next, for groundhog burrow to red squirrel den you put the number 0.3-(-1.2)=1.5    Red squirrel den to Robin’s nest 3.6 – 0.3 = 3.3. And for the last one Groundhog burrow to Robin’s nest 3.6 – (-1.2) = 4.8.

3. you have to turn the 1 1/2 and 3/4 into 8ths. 1/2= 3*4 = 12 and for the denominator 2*4 = 8. So 12/8.

The next one is 3*2 which is 6 and 4*2=8

so now you have 12/8, 6/8, and 1/8

you have to add the points on the chart (i cant really help you on this part because i do not know how to upload picture) but you would make 24 and then you find where 12/8 would go and draw the hops but on mine the hop looks like how you would draw a rainbow but just one for the 12. Then do the same for the 6 and add 1 for the last one to make 19.

On mine I add the 12 + 6 + 1 = 19 so that is how i got mine. (sry if this a bad explination)

it should kinda look like this on the chart.

| | | | | | | | | | | | | | | | | | | | | | | | they should be spaced apart like this.

and for the last one i put cup 3 because it bigger than the amount of ingrident in the recipe. (im not sure if that one was the answer this is the only part we didnt get help on in class)