Convert the length 7 centimeters to meters. Compare the numerical values when both numbeers are written in scientific notation

Any rational number added to 0.6 will produce a rational number.

Adding any rational number to 0.6 will produce a rational number. Rational numbers include whole numbers, fractions, and terminating or repeating decimals.

The question asks which number, when added to 0.6, produces a rational number. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since 0.6 is already a rational number (it can be expressed as 6/10 or 3/5), adding any other rational number to it will also produce a rational number. Examples of rational numbers include whole numbers, fractions, and terminating or repeating decimals.

Therefore, any number that is rational (such as 0, 1/2, 3, 4.5, etc.) will produce a rational number when added to 0.6.

Here, we are required to find the value of Q in the following system so that the system to the solution is {(x,y) : x-3y=4}

x-3y=4

2x-6y=Q

Therefore, Q = 8.

By comparison between equations: x-3y=4 and 2x - 6y = Q.

We need to multiply equation x - 3y = 4 by 2 so that it somewhat resembles 2x-6y=Q;

Ultimately, we have;

Therefore, the two equations now resemble one another and therefore, Q = 8

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The value of Q that makes the system have the same solution as {(x, y) : x - 3y = 4} is Q = 8.

To find the value of Q in the given system so that the solution is {(x, y) : x - 3y = 4}, you need to make sure that the second equation, 2x - 6y = Q, is equivalent to the first equation, x - 3y = 4.

This means that the two equations have the same solution.

To do this, we can start by simplifying the second equation to be equivalent to the first one:

2x - 6y = Q

We can simplify this equation by dividing both sides by 2:

x - 3y = Q/2

Now, we want this equation to be the same as the first equation, x - 3y = 4.

To make them equal, we need to have Q/2 equal to 4.

Therefore:

Q/2 = 4

To solve for Q, multiply both sides of the equation by 2:

Q = 2 * 4

Q = 8

For similar question on equation.

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The answer is B: 4.5 cm, 7.5 cm

Here's why: 7.5 is 3 cm more than 4.5, and when added together, 7.5 + 7.5 + 4.5 + 4.5 = 24.

The formula of a perimeter of a rectangle: P = 2(w + l)

w - width, l - length

We have:

P = 24cm and l = (w + 3)cm

Substitute:

24 = 2(w + w + 3)

24 = 2(2w + 3)     |use distributive property

24 = (2)(2w) + (2)(3)

24 = 4w + 6      |subtract 6 from both sides

18 = 4w     |divide both sides by 4

w = 18/4

w = 9/2

w = 4.5 cm

l = 4.5 + 3 = 7.5cm

Without additional information correlating the number of hats sold to the number of scarves sold, it is impossible to determine how many hats the knitter sold.

Based on the question, there isn't enough information provided to determine how many hats the knitter sold. The information given tells us only about the number of scarves sold, which is 5. If any relationship between the number of hats and scarves sold was provided, then the solution could be possible. For example if the knitter sells an equal amount of hats and scarves then we could say she sold 5 hats. However, without any such information, it is impossible to ascertain the number of hats sold.

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There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

1. SSS   (side, side, side)

SSS Triangle

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.

For example:

triangle is congruent to:   triangle

(See Solving SSS Triangles to find out more)

If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

2. SAS   (side, angle, side)

SAS Triangle

SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.

For example:

triangle is congruent to: triangle

(See Solving SAS Triangles to find out more)

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA   (angle, side, angle)

ASA Triangle

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

For example:

triangle is congruent to: triangle

(See Solving ASA Triangles to find out more)

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

4. AAS   (angle, angle, side)

AAS Triangle

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal.

For example:

triangle is congruent to: triangle

(See Solving AAS Triangles to find out more)

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

5. HL   (hypotenuse, leg)

This one applies only to right angled-triangles!

triangle HL   or   triangle HL

HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")

It means we have two right-angled triangles with

the same length of hypotenuse and

the same length for one of the other two legs.

It doesn't matter which leg since the triangles could be rotated.

For example:

triangle is congruent to: triangle

(See Pythagoras' Theorem to find out more)

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Caution! Don't Use "AAA"

AAA means we are given all three angles of a triangle, but no sides.

AAA Triangle

This is not enough information to decide if two triangles are congruent!

Because the triangles can have the same angles but be different sizes:

triangle is not congruent to: triangle

Without knowing at least one side, we can't be sure if two triangles are congruent.

The five postulates and theorems that can prove triangles are congruent are Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), and Hypotenuse-Leg (HL). These are based on comparing angles and sides of the triangles.

In geometry, congruent triangles are triangles that have the same size and shape, meaning they have equal side lengths and angles. There are several postulates and theorems that can be used to prove that triangles are congruent. They include:

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y = f(x) + n  moves it n units up

y = f(x) - n  moves it n units down

y = f(x + n) moves it n units left

y = f(x - n) moves it n units right

y = nf(x) stretches it in the y-direction

y = 1/n f(x) compresses it

y = f(nx) compresses it in the x-direction

y = f(1/n x) stretches it

y = −f(x) Reflects it about x-axis

y = f(−x) Reflects it about y-ax

Look at the picture.

Answer: y = 3cos(x - 0.5π) + 2

Answer:Total number of side pieces [tex] = 14[/tex]

Step-by-step explanation:

To find the number of side pieces we use formula = [tex] \frac{Area of wooden plank}{Area of 1 side piece} [/tex]

Area of wooden plank [tex]= length \times width[/tex]

Length of wooden plank [tex] =\frac{77}{8}feet =\frac{77}{8} \times 12 [/tex] inches

Length [tex] = \frac{231}{2} [/tex] inches

Width of plank [tex] = \frac{9}{16} foot = \frac{9}{16} \times 12 =\frac{27}{4}[/tex] inches

Area of plank[tex]= \frac{231}{2} \times \frac{27}{4} [/tex] sq inches

Area of 1 side piece [tex]= \frac{33}{4} \times \frac{27}{4}[/tex] sq inches

Now using formula

Number of pieces [tex]= \frac{Area wooden plank}{Area of 1 side piece} [/tex]

[tex] =(\frac{231}{2} \times \frac{27}{4} )\div (\frac{33}{4} \times \frac{27}{4}) [/tex]

Converting division into multiplication we get,

[tex] =(\frac{231}{2} \times \frac{27}{4} )\times (\frac{4}{27} \times \frac{4}{33} )[/tex]

On solving we get

[tex]= 14[/tex]

Total number of side pieces [tex] = 14[/tex]

The answer is A. 85/4=21 with 1 left over. They will need 22 golf carts.

Answer:

On 4/5 gallon of gasoline, hybrid car will travel 36 miles of distance.

Step-by-step explanation:

Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline

then, hybrid will travel " 1 4/11* x" distance in 1 gallon of gasoline

Given that, non hybrid car travel, x = 33 miles per gallon

Then, hybrid car travel, 1 4/11*x = 1 4/11* 33 = 45 miles per gallon

On 1 gallon of gasoline hybrid car travel= 45 miles

On 4/5 gallon of gasoline hybrid car will travel= 4/5*45= 36 miles

On 4/5 gallon of gasoline, hybrid car will travel 36 miles of distance.

slope (m) = rate.    $40 per hour is the rate, so m = 45

y-intercept (b) = one time fee.   $45 is the flat rate which is the one time fee, so b = 45

y = mx + b

y = 40x + 45

Answer: A

Answer:

17.30 dollars

Step-by-step explanation:

Given that Payton and James mow the lawns.

They do this during summer.

The amount they spend are:

Gas  cost  = 3.50

Leaf bags =  1.20

Add these to get total costs

Total cost  = 4.70

Charge they get per lawn = 22.00

Profit = Revenue - cost

Here revenue per lawn = 22 and cost per lawn = 4.70

Hence profit = 22-4.70 = 17.30 dollars.

Answer is they make 17.30 dollars per lawn.

Answer:

The answer is B

Step-by-step explanation:

2 : 2.5 = 3 : w

w = 2.5 * 3 : 2

w = 3.75

Answer:

the answer is p=5.75t

Step-by-step explanation:

The slope-point formula:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (0, 6) and (1, 3),

Substitute:

[tex]m=\dfrac{3-6}{1-0}=\dfrac{-3}{1}=-3\\\\y-6=-3(x-0)[/tex]

[tex]-8x + x + 15 = -7x + 12\\\\-8x+x+7x=12-15\\\\0=-3\\\\x\in\emptyset[/tex]

There are no solutions to this equation. Hence, the solution to the given linear equation is the empty set (Ø) because simplification results in an untrue statement.

This is a linear equation, and we can solve it step by step. The first step is to simplify the equation. If we combine similar terms, we get -7x + 15 = -7x + 12. Then we can cancel the -7x from both sides of the equation, which gives us 15 = 12.

However, this statement is not true. Therefore, there are no solutions to this equation, making the solution set Ø (empty set).

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Seth:

Equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.

Karen:

Equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.

Part A: Converting it in function for by solving for y first.

Solving 7.50x + 15y = 750, equation we get

7.50x + 15y = 750

15y = -7.50x + 750

Solving 6x + 4y = 700 for y, we get

6x + 4y = 700

4y = -6x + 700

On comaring with slope-intercept form y=mx+b, we got slope for Seth equation is -1/2 and slope for Karen is -3/2.

If we take absolute of those -1/2 and -3/2 we get 1/2 and 3/2.

Therefore, Karen has the higher slope. We can see the graph that blue line has greater slope as it's increasing/decreasing with greater rate.

In function form we could write equation as

Part B : y-intercept of Karen equation is 175 and y-intercept of Seth equation is 50.

Part C: If both students work 80 hours for the month.

Let us plug x =80 in each of the equations.

Seth would earn $10 from mowing lawn.

Therefore, the number of lawns Seth has to mow = 10/15 = 0.67 that is approximately 1 lawn.

Karen would earn $50 from walking dog.

So, the number of dogs Karne has to walk = 55/4 = 13.75 that ia approximately 14 dogs.

Part D: If Karen begins charging $8 per hour for babysitting and Seth begins earning $8 per hour.

The equations would become : 8x + 15y = 750, 8x + 4y = 700.

Answer:

Seth:

Equation 7.50x + 15y = 750, where x is the number of hours Seth works and y is the number of lawns he mows.

Karen:

Equation 6x + 4y = 700, where x is the number of hours Karen works and y is the number of dogs she walks.

Part A: Converting it in function for by solving for y first.

Solving 7.50x + 15y = 750, equation we get

7.50x + 15y = 750

15y = -7.50x + 750

y = -1/2x + 50

Solving 6x + 4y = 700 for y, we get

6x + 4y = 700

4y = -6x + 700

y= -3/2x + 175.

On comaring with slope-intercept form y=mx+b, we got slope for Seth equation is -1/2 and slope for Karen is -3/2.

If we take absolute of those -1/2 and -3/2 we get 1/2 and 3/2.

Therefore, Karen has the higher slope. We can see the graph that blue line has greater slope as it's increasing/decreasing with greater rate.

In function form we could write equation as

f(x) = -1/2x + 50 and

f(x) = -3/2x + 175.

Part B : y-intercept of Karen equation is 175 and y-intercept of Seth equation is 50.

Therefore, Karen has greater y-intercept.

This means Karen earns $175 by just walking dogs.

Part C: If both students work 80 hours for the month.

Let us plug x =80 in each of the equations.

y = -1/2x + 50  => y = -1/2(80) + 50 = -40 +50 = $10.

Seth would earn $10 from mowing lawn.

Therefore, the number of lawns Seth has to mow = 10/15 = 0.67 that is approximately 1 lawn.

y = -3/2x + 175  => y = -3/2(80) + 175 = -120 +175 = $55.

Karen would earn $50 from walking dog.

So, the number of dogs Karne has to walk = 55/4 = 13.75 that ia approximately 14 dogs.

Therefore, the number of lawns Seth has to mow is less than the number of dogs Karen has to walk.

Part D: If Karen begins charging $8 per hour for babysitting and Seth begins earning $8 per hour.

The equations would become : 8x + 15y = 750, 8x + 4y = 700.

It would not effect the graph much. Even the y-intercepts would remain same.

There would be a slightly change in slopes.

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Step-by-step explanation:

Answer:

The answer is B sweetheart.

Step-by-step explanation:

A unit rate is a rate with one in the denominator, an example being 55 mph where the 'per hour' is based on one hour. Proportions are the equality of two ratios, while unit scales represent ratios used in scaled models or drawings and do not require a value of 1. Option C) is the correct answer.

A unit rate is a type of rate that expresses the comparison of two different quantities, where one of the quantities is fixed at a value of 1. When looking at the options provided, a unit rate is best described as: A. a rate with one in the numerator.

This definition is not accurate because the unit rate refers to having 1 in the denominator. So, the correct answer to what a unit rate is: C. a rate with one in the denominator. An example of a unit rate would be traveling 55 miles in one hour, which can be written as (55/1) miles per hour or simply 55 mph.

A proportion on the other hand is an equivalence between two ratios. For instance, if we say 1/2 = 3/6, we're explaining that these two fractions, or ratios, are proportionate because they represent the same value when simplified. In contrast, a unit scale, like those often found on maps, does not necessarily have a value of 1 in its ratio.

Answer:

Option C: x=7

Step-by-step explanation:

We are given an equation in x and asked to solve for x

The given equation is

[tex]\frac{x+3}{5} =2[/tex]

To solve for x, we have to have only x on the left side.

So multiply the equation both sides by 5 first

We get x+3 =2(5) =10

Subtract 3 to get

x =10-3 =7

Hence 7 is the answer.

We can verify the answer by substituting for x in the given equation.

Substitute x=7 we get (7+3)/5 = 2

Thus answer is right.

You want to use the distributive property, i.e. the possibility to distribute a multiplication to both terms of an sum/subtraction.

In this case, if you think of 395 as of 400-5, you have

[tex] 5 \times 395 = 5 \times (400-5) [/tex]

And you can use the distributive property to write

[tex] 5 \times (400-5) = 5\times 400 - 5\times 5[/tex]

Both of these multiplications are easy to perform in your mind:

[tex] 5\times 400 - 5\times 5 = 2000 - 25 = 1975[/tex]

The solution to 5×395=5×(_ - _) is found by calculating the multiplication, 5 x 395 = 1975. Then we find two numbers that result in 1975 when multiplied by 5 and subtracted; one example could be 396 and 1. Thus, the equation can be 5×395=5×(396 - 1).

In order to solve the problem 5×395=5×(_ - _) using mental math, we first compute the multiplication of 5 and 395, which is 1975. Now, we need to find two numbers that, when multiplied by 5 and subtracted, give us 1975. As there can be multiple possible pairs, one potential solution could be 5×(395+1) = 5×396 = 1980. So, the two numbers are 396 and 1, and the complete equation would be 5×395=5×(396 - 1).

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The answer is 65! Just took the test

Factor each one to see what they have in common:

15x² = 3 * 5 * x * x

42x³ = 2 * 3 * 7 * x * x * x

They both have: 3, x, x

When multiplied together, 3 * x * x = 3x²

Answer: 3x²

In order to check if a comparison such as this is true, you can use this logical equivalence:

[tex] \dfrac{a}{b} > \dfrac{c}{d} \iff ad > bc,\quad \dfrac{a}{b} < \dfrac{c}{d} \iff ad < bc [/tex]

Anyway, it's not always necessary to make this check. We know that every proper fraction represents a number between 0 and 1, and any improper fraction represents a number greater than 1. So, every proper fraction is less than every improper fraction.

So, the first two options are surely wrong, because they ask for a proper fraction to be more than an improper fraction.

The third option compares two proper fractions, so we actually have to check:

[tex] \dfrac{16}{26}>\dfrac{30}{31} \iff 16 \cdot 31 > 26 \cdot 30 \iff 496 > 780[/tex]

which is false.

Last option:

[tex] \dfrac{35}{30}<\dfrac{22}{12} \iff 35 \cdot 12 < 30 \cdot 22 \iff 420 < 660[/tex]

Which is true.

The answer I believe is Linear Pair

Answer: Linear Pair

Two angles that are adjacent and supplementary form a linear pair.

Answer:

The standard form like [tex](a+bi)[/tex] will be:  [tex]15+8i[/tex]

Step-by-step explanation:

Given expression is:   [tex]2\sqrt{-16}+\sqrt{225}[/tex]

First factoring out -16 as (-1×16) , we will get....

[tex]2\sqrt{-1}*\sqrt{16}+\sqrt{225}[/tex]

Now, replacing [tex]\sqrt{-1}[/tex] as  [tex]i[/tex] .......

[tex]2i\sqrt{16}+\sqrt{225}[/tex]

Finally, simplifying the radicals in the above expression, we will get......

[tex]2i*4+15\\ \\ =15+8i[/tex]

Thus, the standard form like [tex](a+bi)[/tex] will be:  [tex]15+8i[/tex]

Answer:

tttgtgt

Step-by-step explanation:

gtgtggtt

[tex]-2-\dfrac{3}{4}x=10\ \ \ \ |+2\\\\-\dfrac{3}{4}x=12\ \ \ \ |\cdot(-4)\\\\3x=-48\ \ \ \ |:3\\\\\boxed{x=-16}\\\\Answer:\ a.)\ -16[/tex]

Final answer:

To solve the equation -2 - 3/4x = 10, you first add 2 to both sides of the equation, then multiply both sides by -4/3 to get x alone. The solution to the equation is x = -16, which is option (a).

Explanation:

To solve the equation −2 − 3/4x = 10, we need to isolate x. First, we can add 2 to both sides of the equation:

−3/4x = 10 + 2

−3/4x = 12

Next, we multiply both sides by the reciprocal of −3/4, which is −4/3 to get x alone:

(−4/3)*(−3/4)x = 12(−4/3)

x = −16

Therefore, the solution is −16, which corresponds to option (a) −16.

Answer:

Step-by-step explanation:

As per the problem, we are given that

Toy store owner gave 47 balloons to his customers.

And there are 7 balloons left.

So we can find the total number of balloons the Toy store owner start with by adding the given numbers.

Hence total number of balloons the Toy store owner start with[tex]=47+7=54[/tex]

Final answer:

The toy store owner had 54 balloons originally. This is found by adding the 7 balloons left to the 47 given away.

Explanation:

The question is asking to find the total number of balloons the toy store owner originally had. To solve this, we use simple addition. If the owner gave away 47 balloons and has 7 left, you would add the two numbers together to find the original amount.

Step-by-Step Explanation:

Therefore, the toy store owner originally had 54 balloons.

The fromula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

a) (-1, -8), (-7, -4)

substitute

[tex]m=\dfrac{-4-(-8)}{-7-(-1)}=\dfrac{-4+8}{-7+1}=\dfrac{4}{-6}=-\dfrac{2}{3}[/tex]

b) (2.1, 3.8), (3.1, 7.6)

substitute

[tex]m=\dfrac{7.6-3.8}{3.1-2.1}=\dfrac{3.8}{1}=3.8[/tex]