Are two triangles always congruent if they have the following corresponding parts congruent?
a
Two sides and an angle. Explain your response.

Answer:

x ≤ 8

Step-by-step explanation:

The number of ounces of water x that Will could have poured into each cup is 8 or less than 8. by solving through inequality.

Inequality is just like equation which expresses relationship between two or more variables but it is in greater than or less than form. It is just like:

x+ y<c.

Let the capacity of each cup be x.

According to question

16x+16<=144

16x<=144-16

16x<=128

x<=8.

Hence the number of ounces of water that Will could have poured into each cup is 8 or less than 8.

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Answer:

2(x-7) = 2

Step-by-step explanation:

First, let's look at the first part -- "Twice the difference of a number and 7".  The difference between a number (x) and 7 means x-7.  It also says twice the difference, so we are going to multiply x-7 by 2.  So that ends us with 2(x-7)

The last part -- "equals 2" means we will set what we currently have to 2.  2(x-7) = 2

Answer:

2(x-7)=2

Step-by-step explanation:

The difference of a number and 7 is x-7 (difference means subtract)

Now the question says twice so that is what we do 2(x-7) now equal that to two 2(x-7)=2

Answer: 3753

explanation:  Mean is the average so divide 3753 by 100 to get 37.53.

I do not understand the second half of the question but 2671 in base 3 is 10122221

Answer:

10122221 base 3

Step-by-step explanaUrtion:

Answer:

Every 4 feet in height would be 1 foot in length, so I want to say about 96ft

Step-by-step explanation:

Answer:

$14,800 at 10.5%

$38,850 at 12%

Step-by-step explanation:

Investment at 10.5% (x):

(0.12[$53,650 - x])/0.105x = 3

$6,438 - 0.12x = 0.315x

0.435x = $6,438

x = $14,800

Investment at 12%:

= $53,650 - $14,800

= $38,850

Answer: Investments: @ 10.5%, $14,800; @ 12%, $38,850

Proof: (income from 1st is 1/3 that of the income from the 2nd):

= (0.105[$14,800])/(0.12[$38,850])

= $1,554/$4,662

= 1/3

Let's denote as 'x' the amount of money invested by Ms. Burke at the rate of 10.5%. Given that the total amount of investment is $53,650, it follows that the remaining money invested at 12% is given by $53,650 minus 'x'.

The income from the 10.5% investment is 0.105 multiplied by 'x' and the income from the 12% investment is 0.12 multiplied by the quantity $53,650 minus 'x'.

According to the problem statement, the income from the 10.5% investment is one-third of the income from the 12% investment. Therefore, we can write down the following equation:

0.105*x = (1/3)*0.12*($53,650 - x)

We solve this equation to determine 'x'. The solution for this equation yields 'x' equal to approximately $14,800. This means Ms. Burke invested approximately $14,800 at 10.5%.

Also, we know that the difference between the total amount invested and the amount invested at 10.5% will give us the amount invested at 12%. Hence, by subtracting $14,800 from $53,650, we obtain $38,850.

Therefore, Ms. Burke invested approximately $14,800 at the rate of 10.5% and $38,850 at the rate of 12%.

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To find the width of a 16-inch laptop screen that is 8 inches tall, we can use the 16:9 aspect ratio typical for screens and calculate that the width is approximately 14.22 inches.

Finding the Width of the Laptop Screen

To find out how wide a 16-inch laptop screen is, given that it is 8 inches tall, we can use the Pythagorean theorem assuming the screen has a 16:9 aspect ratio which is typical for laptop screens. To use the Pythagorean theorem, we first need to establish the diagonal (16 inches) as the hypotenuse of a right-angled triangle, with the height and width as the other two sides.

As per the given scale factor for this problem (1/160), it does not seem relevant to finding the width using the Pythagorean theorem. Instead, we can use the aspect ratio to find the width. For a 16:9 aspect ratio:

Height = 9x

Width = 16x

Given the height (8 inches) and assuming it to be 9x:

9x = 8 inches

x = 8 / 9

Now to find the width which is 16x:

Width = 16 * (8 / 9)

Width = 14.222... inches (approximately)

The width of the screen is therefore approximately 14.22 inches.

Answer:

I believe the answer to this question is: -4Y

Question:

Evaluate the expressions 3x - 2 and 4x + 4 for the following values of x. When you have found the value for each expression, write a statement using <, >, or = that shows how the two values are related. a. x = 0 b. x = -6 c. x = 5 d. x = -2

Answer:

Part a: [tex]4x+4>3x-2[/tex]

Part b: [tex]4x+4=3x-2[/tex]

Part c: [tex]4x+4>3x-2[/tex]

Part d: [tex]4x+4>3x-2[/tex]

Explanation:

Part a: Substituting [tex]x=0[/tex], we get,

[tex]\begin{aligned}3 x-2 &=3(0)-2 \\&=-2\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(0)+4 \\&=4\end{aligned}[/tex]

The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]

Thus, [tex]4x+4>3x-2[/tex]

Part b: Substituting [tex]x=-6[/tex], we get,

[tex]\begin{aligned}3 x-2 &=3(-6)-2 \\&=-18-2 \\&=-20\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(-6)+4 \\&=-24+4 \\&=-20\end{aligned}[/tex]

The value of [tex]3x-2[/tex] and [tex]4x+4[/tex] are equal.

Thus, [tex]4x+4=3x-2[/tex]

Part c: Substituting [tex]x=5[/tex], we get,

[tex]\begin{aligned}3 x-2 &=3(5)-2 \\&=15-2 \\&=13\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(5)+4 \\&=20+4 \\&=24\end{aligned}[/tex]

The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]

Thus, [tex]4x+4>3x-2[/tex]

Part d: Substituting [tex]x=-2[/tex], we get,

[tex]\begin{aligned}3 x-2 &=3(-2)-2 \\&=-6-2 \\&=-8\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(-2)+4 \\&=-8+4 \\&=-4\end{aligned}[/tex]

The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]

Thus, [tex]4x+4>3x-2[/tex]

Final answer:

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Explanation:

Part a: 4x+4>3x-2

Part b: 4x+4=3x-2

Part c: 4x+4>3x-2

Part d: 4x+4>3x-2

Part a: Substituting x=0, we get,

[tex]\begin{aligned}3 x-2 &=3(0)-2 \n&=-2\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(0)+4 \n&=4\end{aligned}[/tex]

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Part b: Substituting x=-6, we get,

[tex]\begin{aligned}3 x-2 &=3(-6)-2 \n&=-18-2 \n&=-20\end{aligned}\begin{aligned}4 x+4 &=4(-6)+4 \n&=-24+4 \n&=-20\end{aligned}[/tex]

The value of 3x-2 and 4x+4 are equal.

Thus, 4x+4=3x-2

Part c: Substituting x=5, we get,

[tex]\begin{aligned}3 x-2 &=3(5)-2 \n&=15-2 \n&=13\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(5)+4 \n&=20+4 \n&=24\end{aligned}[/tex]

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Part d: Substituting x=-2, we get,

[tex]\begin{aligned}3 x-2 &=3(-2)-2 \n&=-6-2 \n&=-8\end{aligned}[/tex]

[tex]\begin{aligned}4 x+4 &=4(-2)+4 \n&=-8+4 \n&=-4\end{aligned}[/tex]

The value of 3x-2 is less than 4x+4

Thus, 4x+4>3x-2

Answer:

12.3 + 0.61 +100= 112.91

Step-by-step explanation:

All you have to do is make all the values have two place values and then add.

Answer:

x = ± 2

Step-by-step explanation:

Given

3x² - 6 = 10 - x² ( add x² to both sides )

4x² - 6 = 10 ( add 6 to both sides )

4x² = 16 ( divide both sides by 4 )

x² = 4 ( take the square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2

b {+2}

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Answer:

X=5 and y=-6

Step-by-step explanation:

Positive five cancels out -5 and—6 cancels out positive six, so you are left with 0 which equals 0.

Check the picture below.

The simplified form of n-6p³ is n-6p³.

To simplify the expression n-6p³, we need to combine like terms. Since n and 6p³ do not have any common factors, the simplified form of the expression is n-6p³.

Answer:

The answer to your question is A = 648 u²

Step-by-step explanation:

I attach the solution because it said that I was writing improper words.

Answer:

Eqn of the problem: 2(3x + x) = 30

Solution: Width = 3.75 inches  and Length= 11.25 inches

Step-by-step explanation:

We are given;

We are required to represent the equation of the problem;

The formula for getting the perimeter of a rectangle is;

Perimeter = 2 (l+w)

In this case;

2(3x + x) = 30

Therefore;

The equation for the problem is;

2(3x + x) = 30

8x=30

Thus;

8x = 30

  x = 3.75 inches

 3x = 11.25 inches

Hence, the with is 3.75 inches while the length is 11.25 inches

For this case we have the following equation:

[tex]p + 2p + 3p = 12[/tex]

To solve we follow the steps below:

We add similar terms from the left side of the equation:

[tex]6p = 12[/tex]

We divide between 6 on both sides of the equation:

[tex]p = \frac {12} {6}\\p = 2[/tex]

Finally, we have to:

[tex]5p-1 = 5 (2) -1 = 10-1 = 9[/tex]

Answer:

[tex]p = 2\\5p-1 = 9[/tex]

Answer:

12 m apart

Step-by-step explanation:

Final answer:

To find the distance between Ernie and Trevor in the camping scenario, trigonometry principles utilizing the law of sines can be applied effectively, resulting in a distance of approximately 15.54m between them.

Explanation:

To find the distance between Ernie and Trevor, we can use trigonometry. Let's focus on the triangle formed by Bert, Ernie, and Trevor. Since Bert and Ernie are 10m apart with a 30-degree angle at Bert, we can use the law of sines to find Ernie and Trevor's distance. By the law of sines:

Answer:

60(if you sell all)

Right now you have: 41 dollars

Step-by-step explanation:

Answer: you will have 41 dollars.

Step-by-step explanation:

because if you had 60 chocolate and now you had 19 left you sold 41 chocolate bars and you multiply that by how much there are which is 1 dollar and 41 time 1 is 41.

The weight of 4 screws is 0.1 ounces

Step-by-step explanation:

The problem can be solved by setting up a proportion.

In fact, we know that:

- The weight of 80 screws is 2 ounces

- So we want to find the weight of 4 screws

We can write the following proportion:

[tex]\frac{80}{2}=\frac{4}{x}[/tex]

where

x is the weight of 4 screws

Solving the equation, we find:

[tex]x=\frac{4\cdot 2}{80}=0.1[/tex]

So, the weight is 0.1 ounces.

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Answer:

Answer is √7 ( not A, not B)

Step-by-step explanation:

BD/AB = sin 60°

BD/2 = √3/2

BD = √3

AD/AB = cos 60°

AD/2 = 1/2

AD = 1

CD = 3 -1 = 2

BC = √BD² + CD² = √(3 + 4) = √7

Answer:

k = 4

Step-by-step explanation:

The constant of proportionality is found by starting with y = kx, then finding k.

We can just use one point (such as the first one, (1,4) ) and substitute these values of x and y into the equation  y = kx, to get:

4 = k x1

k = 4.

So y = 4x

(we can also check that all the other points also satisfy this equation - which they do, as each y value is 4 times the corresponding x value)

Answer:

4

Step-by-step explanation:

The total amount is $ 780

Solution:

Let the total amount be "x"

Given that,

First person gets $ 268

Second person gets $ 200

Third person gets 40 %

This means, third person gets 40 % of total amount

Third person = 40 % of x

[tex]Third\ person = 40 \% \times x\\\\Third\ person = \frac{40}{100} \times x\\\\Third\ person = 0.4x[/tex]

We know that, total amount is equal to sum of amount got by all three persons

Total amount = first person + second person + third perosn

[tex]x = 268 + 200+ 0.4x\\\\x - 0.4x = 268 + 200\\\\0.6x = 468\\\\x = \frac{468}{0.6}\\\\x = 780[/tex]

Thus the total amount is $ 780

Answer:

Step-by-step explanation:

132,874,015 rounded to the nearest hundred thousand....

132,900,000 <===

Answer:

The plumber worked for 43 minutes.

Step-by-step explanation:

A plumber charged $70 for the first 30 minutes of each house call plus $4 for each additional minute he works.

Now, the total amount to be paid to the plumber C(x) as a function of x number of minutes that he works can be modeled by the equation

C(x) = 70 for x ≤ 30 minutes and C(x) = 70 + (x - 30)4 for x > 30 minutes.

Now, the plumber charges Hayden $122 for the house visit. In that case, x must be greater than 30 minutes.

So, we can write

122 = 70 + (x - 30)4

⇒ 122 = 70 + 4x - 120

⇒ 4x = 172

⇒ x = 43 minutes.

Therefore, the plumber worked for 43 minutes. (Answer)

3.5 belongs to Rational number sets mainly and also belongs to Real Numbers.

Step-by-step explanation:

Number Sets are nothing but group of number classified into groups.

They are Natural, Whole, Integers, Rational, Irrational and Real numbers.

Natural number set = {1,2,3...},

Whole number set= {0,1,2,3...},

Integers = { ....-2, -1, 0, 1, 2, ....},

Rational numbers = { Integers, Decimals, Fractions},

Irrational numbers = { non fractional numbers eg: π,[tex]\sqrt{2}[/tex] etc.}

Real = { Natural, Whole, Integers, Rational, Irrational }.

Any number which is a fraction resulting in a decimal value is Rational Number sets.

3.5 is a decimal number so it can be Rational Number sets also Real Number sets.

Answer:

d = 5t + 20

Step-by-step explanation:

d represents the distance and t represents the time, in hours

Let he equation which model this situation ⇒ d = a t + b

Where a and b are constant.

Let the gas station is the starting point

So, at gas station t = 0 , d = 20

∴ 20 = 0 * a + b ⇒ b = 20

When he reaches home 2 hours later notes that he has traveled 30 miles.

and with substituting with b = 20

∴ 30 = 2 * a + 20

2a = 30 - 20 = 10  ⇒ a = 10/2 = 5

∴ d = 5t + 20

The equations that can be used to model this situation d = 5t + 20

Answer:

7 tiles

Step-by-step explanation:

91/13=7

Answer:

7

Step-by-step explanation:

if 91 tile = 13 hot plate

X tile = 1 hot plate

(let X represent the number of tiles for one plate)

cross miltiply: 91×1 =13×X

X = 91/13

X =7 tiles