Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.

Which equation can be used to find m, the midpoint of the two numbers?

(m – 5)(m + 5) = 99
(m – 10)(m + 10) = 99
m2 – 25 = –99
m2 – 100 = –99

Answer:

2.12

Step-by-step explanation:

I'm takingit rn :/

The estimated sum of 521,370 and 26,839, when rounded to the nearest hundred, is 548,200.

To find the estimated sum, you first need to round each number to the nearest hundred before adding them. For the given numbers 521,370 and 26,839, we round them as follows:

521,370 rounds to 521,400 (because the number after the hundreds place, 7, is 5 or greater, so we round up).

26,839 rounds to 26,800 (because the number after the hundreds place, 3, is less than 5, so we round down).

Now we add the rounded numbers:

521,400 + 26,800 = 548,200

So, the estimated sum of 521,370 and 26,839 is 548,200.

Answer:

100 cm3

Step-by-step explanation:

To find the solution to this problem, we have to use the formula for volume, which is Length x Width x Height. So, we have to do 5cm x 10cm x 2cm, which is 100. Finally, we have to square the centimeters, which gives us

100 cm3

Hope this helped!

Since f(x) is an even function, the statement which is true is the graph of f(x) has a line of symmetry about the y-axis.

To answer the question, we need to know what an even function is.

An even function is a function f(x) such that f(x) = f(-x). That is f(x) is single valued for both positive and negative values of x.

Now, for an even function, since f(x) = f(-x), both positive and negative values of x give a single value of f(x).

For this to be true, the graph of f(x) is symmetric about the y-axis.

So, since f(x) is an even function, the statement which must be true is graph of f(x) has a line of symmetry about the y-axis.

Learn more about even functions here:

https://brainly.com/question/4711998

#SPJ2

Final answer:

To evaluate 10⁻⁷, it is understood as 1 divided by 10 to the seventh power, or 0.0000001. This notation is used in scientific measurements, for instance in expressing the hydronium ion concentration based on pH.

Explanation:

To evaluate 10⁻⁷, we must understand the notation of negative exponents.

10 raised to the power of -7 can be written as 1 divided by 10 raised to the power of 7:

10⁻⁷ = 1 / 10⁷

Since 10 raised to any positive power results in a large number, 10 raised to the power of 7 is a very large number (10,000,000). Dividing 1 by this large number is very close to zero:

1 / 10⁷≈ 0.000 000 1

Therefore, 10⁻⁷ is approximately equal to 0.000 000 1. This value is incredibly small, representing one divided by ten million.

This type of notation is commonly used in scientific measurements, such as expressing the concentration of hydrogen ions in a solution with a certain pH level.

Daniel can go on 14 rides at the fair.

To find out the greatest number of rides Daniel can go on, we need to calculate the cost of admission and the cost of the rides. The admission to the fair is $4 and each ride costs $1.50. To determine the number of rides, we subtract the cost of the admission from the total amount Daniel has to spend and then divide that by the cost of each ride. So, Daniel can go on (25 - 4) / 1.50 = 14 rides. Therefore, the greatest number of rides Daniel can go on is 14.

https://brainly.com/question/28703160

#SPJ2

Answer:

Given: [tex]\frac{x}{6} + 2 = 15[/tex]                             ......[1]

To prove : x =78

Subtraction property states that you subtract the same number to both sides of an equation.

Subtract 2 from both sides of an equation [1];

[tex]\frac{x}{6} + 2 - 2= 15 -2[/tex]

Simplify:

[tex]\frac{x}{6} = 13[/tex]                                             ......[2]

Multiplication property states that you multiply the same number to both sides of an equation.

Multiply 6 to both sides of an equation [2];

[tex]\frac{x}{6} \times 6 = 13 \times 6[/tex]

Simplify:

[tex]x = 78[/tex]                      proved!

Statement                                           Reason

1.  [tex]\frac{x}{6} + 2 = 15[/tex]                 Given

2.  [tex]\frac{x}{6} = 13[/tex]                 Subtraction property of equality

3. [tex]x = 78[/tex]                              Multiplication property of equality

Final answer:

To solve for x, subtract 2 from both sides of the equation, then multiply both sides by 6. This yields that x equals 78, completing the proof.

Explanation:

To complete the two-column proof, we start with what is given and use algebraic manipulation to prove that x equals 78. Here are the steps formatted into a proof:

Answer: 22

Step-by-step explanation:

Given : The data set represents the number of snails that each person counted on a walk after a rainstorm.

The given data :  12, 13, 22, 16, 6, 10, 13, 14, 12

Arrange in order :  6,10 , 12, 12, 13, 13, 14, 16, 22

We can see that all data values are closer to each other except 22.

22 is an extreme value as compare to the entire data values.

Therefore, the outlier of the data set is 22 .

To find the 7th term in the geometric sequence, determine the common ratio using given terms, a2 and a4, then use the formula for the nth term to calculate a7. The common ratio is 1/4, and the 7th term is 0.75.

The student is asking to find the 7th term (a7) of a geometric sequence for which the 2nd term (a2) is 768 and the 4th term (a4) is 48. To solve for the 7th term, we must first determine the common ratio of the sequence.

We know that in a geometric sequence, each term is the product of the previous term and the common ratio (r). The formula for the nth term of a geometric sequence is an = a1 * r^(n-1), where a1 is the first term and n is the term number.

Since a4 is the 4th term and a2 is the 2nd term, we can write these equations:
a4 = a2 * r^(4-2)48 = 768 * r^2
By solving this equation, we get:
r^2 = 48 / 768 = 1 / 16, which means r = 1 / 4.

Now that we know the common ratio, we can find the 7th term (a7) by using the formula from above with n = 7:
a7 = a2 * r^(7-2) = 768 * (1/4)^(7-2) = 768 * (1/4)^5 = 768 * 1/1024 = 0.75

Hence, the 7th term of the given geometric sequence is 0.75.

Answer:

[tex]\frac{16}{25} =0.64[/tex]

Step-by-step explanation:

Given : A spinner used for a game is divided into 4 sections: Yellow, Brown, Red and Orange. The spinner is spun 50 times and lands on brown 18 times

To Find: What is the experimental probability that the spinner does NOT land on brown

Solution :

Since we are given that the spinner is spun 50 times .

Ans the spinner lands on brown 18 times

Probability of landing on brown = [tex]\frac{18}{50} =\frac{9}{25}[/tex]

Since we know that the sum of probabilities is 1

So, probability that the spinner does NOT land on brown is :

⇒ 1 - prob. of landing on brown

⇒[tex]1-\frac{9}{25}[/tex]

⇒[tex]\frac{25-9}{25}[/tex]

⇒[tex]\frac{16}{25}[/tex]

Thus probability that the spinner does NOT land on brown is 16/25=0.64

The solutions of the given system of equations: y = x2 – 7x + 16 and y = x - 1 is 4 + i and 4 - i.

A quadratic equation in the variable x is an equation of the form

ax² + bx + c= 0, where a, b, c are real numbers, a * 0.

Given equations are:

y= x²-7x+16 and y=x-1

So, x-1= x²-7x+16

or, x²-8x+17=0

or, x²-8x+17  =0

a=1, b=-8, c=17

Using discriminant method,

x= [tex]-b\pm\sqrt{b^{2}-4ac } /2a[/tex]

x= -(-8) ± [√(-8)²- 4*1*17]/2*1

x=8±√(√64-68)/2

x= 8±√(-4)/2

x= 4 ± i

x= 4 + i and x= 4 - i

Learn more about quadratic equation here:

https://brainly.com/question/2263981

#SPJ2

Answer:

256

Step-by-step explanation:

Answer:

Surface Area of Design = 256 in.²

Step-by-step explanation:

Given: a Shape which is made by placing two cuboid on one another.

To find: Surface area of shape.

Figure is attached.

Surface Area of Design

= Lateral Surface Area of Base Cuboid + Lateral Surface area of Top Cuboid + Area of rectangle CDLJ + Area of rectangle EFNM + Area of rectangle ABHG

Dimensions of Base Cuboid:

Length, CJ = 8 in.

Width, CD = LJ = MN = 5 in.

Height, AD = 4 in.

Dimensions of Top cuboid:

Length, HI = BI - BH = 8 - 4 = 4in.

Width, GH = KI = MN = 5 in.

Height, FH = JN - JI = 8 - 4 = 4 in.

Length of rectangle ABHG, AB = 5 in.

Width of rectangle ABHG , BH = 4 in.

Length of rectangle DCJL, DC = 5 in.

Width of rectangle DCJL , CJ = 8 in.

Length of rectangle EFNM, EF = 5 in.

Width of rectangle EFNM , FN = 4 in.

Lateral Surface Area of Base Cuboid = 2 × Height ( length + Width )

                                                              = 2 × 4 ( 8 + 5 )

                                                              = 8 ( 13 )

                                                              = 104 in²

Lateral Surface Area of Top Cuboid = 2 × Height ( length + Width )

                                                              = 2 × 4 ( 5 + 4 )

                                                              = 8 ( 9 )

                                                              = 72 in²

Area of rectangle DCJL = length × breadth

                                        = 5 × 8

                                        = 40 in.²

Area of rectangle ABHG = length × breadth

                                        = 5 × 4

                                        = 20 in.²

Area of rectangle EFNM = length × breadth

                                        = 5 × 4

                                        = 20 in.²

⇒ Surface Area of Design = 104 in.² + 72 in.² + 40 in.² + 20 in.² + 20 in.²

                              = 256 in.²

Therefore, Surface Area of Design = 256 in.²

(5X-6)(5X+6) THIA IA THE ANSWER TO THE problem

The value of the tabular function at x = –15 will be –2. Then the correct option is C.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given in the form of a table.

x        –15              –2              –1               0              13             16          22

y         –2             –15               0               3               5              12          13

The value of y corresponds to x is the value of the function.

The value of the tabular function at x = –15 will be –2. Then the correct option is C.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

The value of 'a' is determined from the horizontal asymptote y=2, which gives a=2. The value of 'b' is derived from the vertical asymptote x=-1, leading to b=1. Hence, the function with the given asymptotes is f(x) = 2x+3 over x-1.

To find the values of a and b for the function f(x) = ax+3 over x-b, given the horizontal and vertical asymptotes, we need to consider the general behavior of rational functions. A vertical asymptote occurs where the denominator of a rational function is zero, while a horizontal asymptote is determined by the relationship between the degrees of the numerator and the denominator.

Since the vertical asymptote is x = -1, we know that the denominator of the function must be zero when x = -1. Thus, we can determine that b = 1, since the denominator is x - b and -1 - b = 0.

The horizontal asymptote is given by y = 2. This indicates the value that the function approaches as x goes to infinity. For the function f(x) = ax+3 over x-b, the degrees of the numerator and denominator are both one. Therefore, the horizontal asymptote is determined by the ratio of the leading coefficients of the numerator and the denominator, which means a / 1 = 2, so a = 2.

Therefore, the values of a and b are 2 and 1, respectively.

salesperson earns $300.50 per week plus 7% of her weekly sales .To have the sales necessary for the salesperson to earn at least $900.85 in one week we can form an inequality equation. Let x denote his weekly sales.

300.50+7% x ≥ 900.85

Subtracting 300.50 both sides:

7%x≥ 600.35

0.07x ≥ 600.35

Dividing both sides by 0.07

x≥8576.428

Option B . x is greater then or equal to 8576.43 is the right answer.

First, let's write 65% as a decimal. We can do this by moving the decimal point 2 places to the left. When we do this, we will get 0.65.

Next, the word of means "multiply" so we have to multiply 0.65 by 40.

(.65) × (40) = 26.00

To calculate 65 percent of 40, convert 65% to a decimal (0.65) and then multiply by 40 to get the answer, which is 26.

To find what 65 percent of 40 is, you can convert the percentage to a decimal and then multiply by the number. To convert a percentage to a decimal, divide it by 100. In this case, 65% becomes 0.65.

Next, multiply 0.65 by 40 to get the answer.

The calculation process looks like this:
0.65 (converted percentage) × 40 (the number) = 26

Therefore, 65 percent of 40 is 26.