Part II: What is 5,290,000,000,000 written out in words? What is it in scientific
notation?

x = –5 or x = 3

Solution:

Given expression:

[tex]|-1-x|=4[/tex]

[tex]\Rightarrow |-x-1|=4[/tex]

⇒ –x – 1 = 4 or –x – 1 = 4

First take –x – 1 = 4.

Add 1 on both side of the equation.

⇒ –x – 1  + 1 = 4 + 1

⇒ –x = 5

Divide by –1 on both side of the equation, we get

⇒ x = –5

Now take –x – 1 = –4.

Add 1 on both side of the equation.

⇒ –x – 1  + 1 = –4 + 1

⇒ –x = –3

Divide by –1 on both side of the equation, we get

⇒ x = 3

x = –5 or x = 3

Hence the two values of x are –5 or 3.

Answer:

1. 60 miles per hour

2. Yes, linear

3. Y=60x

Step-by-step explanation:

1. Speed is 60 miles per hour.

2. A function relationship is a relationship between two variables.

3. The rule to represent the function is Distance = 60t.

1. What is the speed?

The speed of the car is the rate at which it is traveling. It is calculated by dividing the distance traveled by the time taken to travel that distance.

Speed = Distance / Time

From the graph, we can see that the car travels 120 miles in 2 hours. Therefore, the speed of the car is:

Speed = 120 miles / 2 hours = 60 miles per hour

2. Is this a function relationship?

A function relationship is a relationship between two variables where each input value has only one output value. In other words, for every value of the independent variable (in this case, time), there is only one corresponding value of the dependent variable (in this case, distance).

We can see from the graph that the distance traveled by the car increases linearly with time. This means that there is a one-to-one relationship between the two variables, and therefore the relationship is a function.

3. If this is a function, write a rule to represent it.

A rule for a function is a mathematical expression that shows how the dependent variable is related to the independent variable. In this case, the rule for the function would be:

Distance = Speed * Time

Substituting the speed of the car into the rule, we get:

Distance = 60 miles per hour * Time

Therefore, the rule to represent the function is:

Distance = 60t

where t is the time in hours.

Answer:

the answer is c

Step-by-step explanation:

see picture

Answer: the measure of SQR is 53°

Louise’s answer is not correct

Step-by-step explanation:

Let us revise how to solve (ax + b)²

The answer of square a binomial contains three terms: (1st)² + 2(1st)(2nd) + (2nd)²

∵ The bracket is (5x³ + 3)²

- Square the first term

∴ The first term of the answer = (5x³)² = (5)²(x³)² = [tex]25x^{6}[/tex]

- Multiply the 1st , the 2nd term and 2

∴ The second term of the answer = 2(5x³)(3) = 2(5)(3)x³ = 30x³

- Square the 2nd term

∴ The third term of the answer = (3)² = 9

∴ (5x³ + 3)² =  [tex]25x^{6}[/tex] + 30x³ + 9

∵ Louise’s answer is (5x³)² + (3)² =  [tex]25x^{6}[/tex] + 9

- By comparing the his answer with the answer above, he did

   not find the middle term

∴ Louise’s answer is not correct

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Answer:

Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.

Step-by-step explanation:

Sample Response ^^^

Answer:

The man's son

Step-by-step explanation:

"Brothers and sisters I have none, but that man's father is my father's son" the part where he says "that man's father is my father's son" implies that he is looking at his son.

Answer:

VW=30, WX=20, YW=30,ZX=20

Step-by-step explanation:

The expression [tex]8x^2 + 10x[/tex] factors to [tex]2x(4x + 5)[/tex] and has solutions x = 0 and x = -5/4.

We first need to understand what it represents. In this expression, [tex]x[/tex] is the variable, and the terms [tex]8x^2[/tex] and [tex]10x[/tex] are polynomial terms where:

[tex]8x^2[/tex] indicates that the variable [tex]x[/tex] is raised to the power of 2, meaning it is multiplied by itself ([tex]x \times x[/tex]) and then scaled by a factor of 8.

[tex]10x[/tex] means that the variable [tex]x[/tex] is multiplied by 10.

The first term is [tex]8x^2[/tex].

The second term is [tex]10x[/tex].

In this case, the terms are not like terms because one is [tex]x^2[/tex] and the other is [tex]x[/tex]. Therefore, they cannot be combined further. The expression is simplest as it stands, which is:  [tex]8x^2 + 10x[/tex]

Factoring out [tex]2x[/tex] gives us:

[tex]2x(4x + 5)[/tex]

Thus, [tex]8x^2 + 10x[/tex] can also be expressed as [tex]2x(4x + 5)[/tex]. This is useful if you are trying to find the roots of the equation (setting it equal to zero) since it can help identify the values of [tex]x[/tex] that satisfy the equation [tex]8x^2 + 10x = 0[/tex].

This gives two possible solutions for x:

2 * x = 0 which leads to x = 0

4 * x + 5 = 0 which leads to x = -5/4

Answer:

3x+2

Step-by-step explanation:

We want to find an expression that is equivalent to:

[tex]x+1-x+2x+x+1[/tex]

We regroup similar terms to get:

[tex]x-x+2x+x+1+1[/tex]

We now combine the similar terms to obtain:

[tex]3x+2[/tex]

Therefore the expression that is equivalent to:  x + 1 − x + 2x + x + 1 is [tex]3x+2[/tex]

Answer:

3x + 2

Step-by-step explanation:

3x + 2

Solve by simplifying the given expression OR substitute 1 for x in each expression.

x + 1 − x + 2x + x + 1 → x − x + 2x + x + 2 → 3x + 2

OR

x + 1 − x + 2x + x + 1 → 1 + 1 − 1 + 2(1) + 1 + 1 = 5

3x + 2 → 3(1) + 2 = 5

Answer:

n = - 4

Step-by-step explanation:

Given

6n - 2(4n + 7) + 4 = - 2 ← distribute and simplify left side

6n - 8n - 14 + 4 = - 2

- 2n - 10 = - 2 ( add 10 to both sides )

- 2n = 8 ( divide both sides by - 2 )

n = - 4

To solve the equation 6n - 2(4n + 7) + 4 = -2, we apply the distributive property and combine like terms to simplify. The solution is n = -4.

To solve the equation 6n - 2(4n + 7) + 4 = -2, we need to apply the distributive property and combine like terms to simplify.

Therefore, the value of n that makes the equation true is n = -4.

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Answer:

[tex]\large \boxed{\text{21.86 ft}^{2}}[/tex]

Step-by-step explanation:

Area of shaded region = area of square - area of semicircle

1. Area of square

A = s² = (6 ft)² = 36 ft²

2. Area of semicircle

Area of circle = πr²

Area of semicircle = ½πr²

r = 3 ft, so

A = ½π(3 ft)² = ⁹/₂π ft³

3. Area of shaded region

A = area of square - area of semicircle

[tex]\begin{array}{rcl}A & = & \mathbf{\left(36 - \dfrac{9}{2} \pi \right )} \textbf{ ft}^{\mathbf{2}}\\\\ &\approx & \left (36 - 14.1372\right)\text{ ft}^{2}\\ & \approx & \mathbf{21.86}\textbf{ ft}^{\mathbf{2}} \\\end{array}\\\text{The area of the shaded figure is approximately $\large \boxed{\textbf{21.86 ft}^{\mathbf{2}}}$}[/tex]

Answer:

Mikhail's age is 25 years old

Step-by-step explanation:

Let's make an equation: Say Mikhail is x, so Gabby would be 2*x=2x

If the sum of their ages equals 75, then x+2x=75, and x=2x=3x, so 3x=75.

75/3=25

Final answer:

Gabby's age is twice Mikhail's age, and the sum of their ages is 75. By setting up and solving a system of equations, we can determine that Mikhail's age is 25.

Explanation:

To solve this problem, we can set up a system of equations using the information given. Let's say Gabby's age is represented by 'G' and Mikhail's age is represented by 'M'. We know that G = 2M and the sum of their ages is 75, so we can write the equation G + M = 75. Now we have a system of equations:

G = 2M and G + M = 75.

To solve this system, we can substitute the value of G from the first equation into the second equation: 2M + M = 75. Combine like terms: 3M = 75. Divide both sides by 3: M = 25. So Mikhail's age is 25 years old.

================================================

Explanation:

If points F and E are the midpoints of segment VU and segment ST respectively, then segment FE is the midsegment of the trapezoid. The midsegment is parallel to the bases, and the midsegment's length is found by adding up the bases VS and UT, then dividing by 2.

(VS + UT)/2 = FE

(29 + x+17)/2 = 23 ... plug in given info; isolate x

(x+46)/2 = 23

x+46 = 23*2 ... multiply both sides by 2

x+46 = 46

x = 46-46 ... subtract 46 from both sides

Answer:

2.2r

Step-by-step explanation:

3.7r - 1.5r =

= r(3.7 - 1.5)

= r×2.2

= 2.2r

Yo sup??

given expression: 3.7r-1.5r

3.7r-1.5r

=3.7r+(-1.5r)

=2.2r

Hope this helps.

Answer:4.21,4.22,4.23, 4.24

Step-by-step explanation:

4 1/5 is 4.2 as a decimal and the numbers between 4.2 and 4.5 as numbers with 2 places past the decimal place are the ones above.

The number with two decimal places that are bigger than 4(1/5) and smaller than 4.25 is 4.22.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4(1/5)

= 21/5

= 4.2

Now,

Two decimal numbers between 4.2 and 4.25.

4.21, 4.22, 4.23, and 4,24.

Thus,

The number is 4.22.

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Given data:

m∠P = m∠R and TP = SR

To prove that ΔQTP ≅ ΔQSR:

Consider ΔQTP and ΔQSR,

m∠P = m∠R (given angle)

TP = SR (given side)

m∠Q = m∠Q (common angle)

∴ ΔQTP ≅ ΔQSR (by ASA congruence rule)

Hence ΔQTP and ΔQSR are congruence triangles by Angle - Side - Angle congruence rule.

Answer:

Mary reached the airport in 40 minutes

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Time it takes John to go from home to the train station = 30 minutes

Time it takes John to go from the train station to the airport = 55 minutes

Mary left 25 minutes later and reached the airport 20 minutes earlier than John

2. How long did it take Mary to get to the airport?

Total time it takes John to reach the airport = Time it takes John to go from home to the train station + Time it takes John to go from the train station to the airport

Total time it takes John to reach the airport = 30 + 55

Total time it takes John to reach the airport = 85 minutes

Now, let's calculate the time it takes Mary to reach the airport, this way:

Total time it takes John to reach the airport - minutes Mary left later - minutes Mary got to the airport earlier than John

85 - 25 - 20 = 85 - 45 = 40

Mary reached the airport in 40 minutes

Answer: Mary got to the airport in 40 Minutes.

Amount of tax on the book (s) is $0.72

Step-by-step explanation:

⇒ 6 × 12 = 100 × s

⇒ 72 = 100s

⇒ s = 72/100 = 0.72

Answer:

Set #9 are congruent triangles.

Step-by-step explanation:

They are the same shape and size. If I were to flip them over, they would mach up.

Answer:

cap its only 10

Step-by-step explanation:

To divide 64 students into small groups greater than 2 with no remainder, you would use the concept of combinations, specifically 62C3, resulting in 3,992 possible ways.

A teacher has 64 students to divide into small groups greater than 2 with no remainder. To solve this, we can use the concept of combinations, denoted as nCr, where n is the total number of students and r is the size of each group. In this case, the calculation would be 62C3, which equals 3,992 ways of dividing the students into groups.

Answer:

x=-13

Step-by-step explanation:

1. Divide both sides by -0.4

2. Subtract -3 on both sides.

3. -10-3=-13

Answer:

In mathematics, a function (f) is a relationship between a given set X (called domain) and another set of elements Y (called codomain) so that each element x of the domain corresponds to a single element f (x) of the domain (the that form the route, also called scope ranking).

See: Relations and functions

In everyday or simpler language, we will say that mathematical functions are equivalent to the common logical process that is expressed as "dependent on."

Mathematical functions can refer to everyday situations, such as: the cost of a phone call that depends on its duration, or the cost of sending a parcel that depends on its weight.

As an example, what would be the rule that relates the numbers on the right with those on the left in the following list ?:

1 --------> 1

2 --------> 4

3 --------> 9

4 --------> 16

The numbers on the right are the squares of those on the left.

The rule is then to "square":

1 --------> 1

2 --------> 4

3 --------> 9

4 --------> 16

x --------> x 2.

To refer to this rule we can use a name, which is usually the letter f (of function). So, f is the rule "square the number".

Usually two notations are used:

x --------> x 2 or f (x) = x 2.

Thus, f (3) means applying the rule f to 3. Doing so results in 3 2 = 9.

Then f (3) = 9. Similarly f (2) = 4, f (4) = 16, f (a) = a 2, etc.

Answer:

value of x is greater than -8.

Step-by-step explanation:

5-(x+5)>-2(x+4)

we need to find value of x.

consider

5-(x+5)>-2(x+4)

using distributive property, we get

5-x-5>-2x-2×4

5-x-5>-2x-8

nowsimplify both side

-x+2x>-8

transfer -2x form RHS To LHS

-x+2x-8

x>-8

therefor, value of x is greater than-8.

Answer:if u I simplified then 17x

Step-by-step explanation:

Like terms are 10+7=17+x=17x

Answer:

1/14

Step-by-step explanation:

2/7 to 4 means 2/7 to 4/1

This gives

2/7

4/1

rearranging, we have;

2/7 * 1/4

2 * 1

7 * 4

= 2/28

to reduce to the simplest form, we'll divide the numerator and denominator by 2 ( the HCF of both)

1/14

To write the ratio 2/7 to 4 as a fraction in simplest form, multiply both the numerator and denominator of 2/7 by 4. Simplify the resulting fraction by dividing both the numerator and denominator by their common factor, which is 4. The simplest form of the ratio is 2/7.

To write the ratio 2/7 to 4 as a fraction in simplest form, we need to multiply both the numerator and denominator of 2/7 by 4. This gives us (2 * 4) / (7 * 4) = 8/28. Since both 8 and 28 have a common factor of 4, we can simplify the fraction further.

Dividing both the numerator and denominator by 4, we get 8/28 = 2/7.

Therefore, the ratio 2/7 to 4 as a fraction in simplest form is 2/7.

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Answer:

One piece of candy costs $0.52.

Step-by-step explanation:

5.2/10=0.52

Answer:

5,12,13

Step-by-step explanation:

i think thats what the other person meant to say, either way, these numbers are correct

Answer: 5, 12, 13

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The diagonals of a rectangle are congruent, thus

DB = AC = 48

The diagonals also bisect each other, thus

DE = 0.5DB = 0.5 × 48 = 24 → B

Answer:

2.4 kg

Step-by-step explanation:

Given

dog eats 0.3 kg of dog food each day

hence we can say that  the unit rate is 0.3 kg per day

1 day ------> eats 0.3 kg

8 days -------> eats 0.3 kg x 8 = 2.4 kg

Answer:

2.4 kilogram

Step-by-step explanation:

If

1 day = 0.3kg

8day =

0.3 multiply by number of days

0.3kg * 8= 2.4kg