How many solutions exist for each system of equations?
x + 2y = –1
2x + 3y = 0

Answer:

x = ± 10

Step-by-step explanation:

to solve the equation let y = 0 , that is

100 - x² = 0 ( add x² to both sides )

100 = x² ( take square root of both sides )

± [tex]\sqrt{100}[/tex] = x , that is

x = ± 10

Answer:

$3705.60

Step-by-step explanation:

1969/85=23.16

23.16x160=3705.6

The statement that is false is 15% of her students are in biology, the correct option is A.

Suppose two dimensions are there, viz X and Y. Some values of X are there as X_1, X_2, ... , X_n and some values of Y are there as Y_1, Y_2, ... , Y_n

List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  X_i  and Y_j  (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

We are given that;

The relative frequency table

Now,

This is because the relative frequency table shows that 0.15 of her students are freshmen in biology and 0.2 of her students are sophomores in biology. Therefore, the total percentage of her students in biology is 0.15 + 0.2 = 0.35, which is 35%, not 15%.

The other statements are true based on the relative frequency table.

Therefore, by the two-way table the answer will be 15% of her students are in biology.

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By the remainder theorem of polynomial division, the complete equation is f(-3) = 11

The equation is given as:

f(x)/x + 3

Set the divisor to 0

x + 3 = 0

Solve for x

x = -3

Given that the quotient has a remainder of 11.

It means that:

f(-3) = 11

Hence, the complete equation is f(-3) = 11

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The number of potential customers that the company has reached is 10,000  e--mail addresses.

A word problem is a real-life problem and it can be approached with the use of a mathematical model, interpretation into variables, and arithmetic operations usage.

Given that:

The number of potential customers that the company has reached is:

= 2500  3500 + 4000 e--mail addresses.

= 10,000  e--mail addresses.

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Answer:

False

Step-by-step explanation:

Protons have positive charge.

Answer:

Protons have a positive charge.

Step-by-step explanation:

[tex]\text{Apply Pythagorean theorem,}\\\\~~~~~~~~\text{Hypotenuse}^2=\text{Base}^2 + \text{Perpendicular}^2\\\\\implies 9^2 = \text{Base}^2 + \left(2\sqrt{14} \right)^2\\\\\implies 81 = \text{Base}^2 + 56\\\\\implies \text{Base}^2 = 81-56\\\\\implies \text{Base}^2 = 25\\\\\implies \text{Base} = \sqrt{25}\\\\\implies \text{Base} = 5\\\\\text{The length of the third side is 5 units.}[/tex]

The bus at an angle of sight of 75 degrees from the man is at a distance of 541 feet

The distance function is given as:

d = 140 sec(x)

Where x represents the angle of sight.

In this case,

x = 75

So, we have:

d = 140 sec(75)

Evaluate the product

d = 541

Hence, the bus at an angle of sight of 75 degrees from the man is at a distance of 541 feet

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Answer:

d

Step-by-step explanation:

if 2 chords of a circle intersect , then the product of the parts of one chord is equal to the product of the parts of the other chord, that is

KN × JN = LN × MN

(x - 4)(x + 23) = (x + 14)(x - 1) ← expand factors on both sides using FOIL

x² + 19x - 92 = x² + 13x - 14 ( subtract x² from both sides )

19x - 92 = 13x - 14 ( subtract 13x from both sides )

6x - 92 = - 14 ( add 92 to both sides )

6x = 78 ( divide both sides by 6 )

x = 13

The measure of angle that is coterminal with 425° is 425° + (1440n)°

Coterminal angles are angles in multiples of the angles in standard positions examples(360°).

It is mostly gotten by adding  360° or multiples of 360 to the angle.

One of the unique behavior of coterminal angles is that their sine, cosine and tangent are equal.

Analysis:

From the options, the only one with an addition of 360 or multiples of 360 is 425 + 1440n

If we put n = 1, the coterminal angle gotten is 1865.

if we find the sine of 425°, we get 0.9063 which is same as the sine of 1865°.

In conclusion, the coterminal angle to 425° is 425° + (1440n)°.

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Answer:

B. 425° – (840n)°, for any integer n

The answers of the given geometrical shapes are:

1. 226.29 cubic yard

2. 46.1 cubic inches

3. 2413.71 cubic inches

4. 234.67 cubic millimeter

5. 340.48 cubic yards

6. 113.14 cubic feet

7. 528 cubic centimeter

8. 905.14 cubic centimeter

9. 56.57 cubic feet

Mensuration is the branch of geometry that deals with measurement of volumes and areas of geometrical shapes.

Analysis:

1. volume of cylinder =π [tex]r^{2}[/tex]h. where r = 6/2 = 3 yard, h = 8 yard

                                  =  [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 8 = 226.29 cubic yard

2. volume of cone = [tex]\frac{1}{3}[/tex] x π  [tex]r^{2}[/tex]h. where r = 2inches, h = 11

                              =  [tex]\frac{1}{3}[/tex] x [tex]2^{2}[/tex] x   [tex]\frac{22}{7}[/tex]  x 11 = 46.1 cubic inches

3. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 8, h = 12

                                   =   [tex]\frac{22}{7}[/tex] x [tex]8^{2}[/tex] x 12 = 2413.71 cubic inches

4. volume of cone =  [tex]\frac{1}{3}[/tex] x π  [tex]r^{2}[/tex]h. where r = 4, h = 14

                               =  [tex]\frac{1}{3}[/tex]  x  [tex]\frac{22}{7}[/tex] x [tex]4^{2}[/tex] x 14 = 234.67 cubic millimeter

5. volume of cone =  [tex]\frac{1}{3}[/tex] x π  [tex]r^{2}[/tex]h. where r = 5, h = 13

                              =  [tex]\frac{1}{3}[/tex] x  [tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex] x 13 = 340.48 cubic yards

6. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 3, h = 4

                                   = [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 4 = 113.14 cubic feet

7. volume of cone = [tex]\frac{1}{3}[/tex] x π  [tex]r^{2}[/tex]h.  r = 6, h = 14

                               =  [tex]\frac{1}{3}[/tex] x  [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 14 = 528 cubic centimeter

8. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 6, h = 8

                                   =   [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 8 = 905.14 cubic centimeter

9. volume of cylinder =  π [tex]r^{2}[/tex]h. where r = 1.5, h = 4

                                    =   [tex]\frac{22}{7}[/tex]  x [tex]1.5^{2}[/tex] x 4 = 56.57 cubic feet

In conclusion, the volume of cylinders and cones for the given dimensions are:

1. 226.29 cubic yard

2. 46.1 cubic inches

3. 2413.71 cubic inches

4. 234.67 cubic millimeter

5. 340.48 cubic yards

6. 113.14 cubic feet

7. 528 cubic centimeter

8. 905.14 cubic centimeter

9. 56.57 cubic feet

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Answer:

x is all real numbers

Step-by-step explanation:

This means that the graph is continuous from negative infinity to positive infinity.

Answer:

x = 3

Step-by-step explanation:

2x + 12 = 18

2x = 18-12

2x = 6

x = 3

give brainliest please!

hope htis helps :)

Answer:6

Step-by-step explanation:

0x+12+x=18

0x+x=18-12

x=6

The amount of metal needed to make the metal stud for the costume is 12 unit²

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the meatal stud does not have a base, hence:

Amount of metal needed = sum of area of triangular faces = 4(1/2 * 2 * 3) = 12 unit²

The amount of metal needed to make the metal stud for the costume is 12 unit²

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Answer:

Never

Step-by-step explanation:

If p is true and ~ q is false, then p -> ~ q is ____ false

This translates to:

true -> true

So it will never be false.

Answer:

Step-by-step explanation:

Step-by-step explanation:

-x^2+6x+55=0

x^2-6x-55=0

x^2-6x+(3)^2-55-(3)^2=0

(x-3)^2-64=0

Answer:

(4, 2)

Step-by-step explanation:

the midpoint of points (x1, y1) and (x2, y2) is ([tex]\frac{x_{1} + x_{2}}{2}[/tex],[tex]\frac{y_{1} + y_{2}}{2}[/tex])

plug in points (-2, -4) and (10, 8) to get ((10+(-2))/2), (8+(-4))/2) = (4, 2)

Answer: I think that the answer would be B. This is what i got after doing the work

Answer:

18

Step-by-step explanation:

Mode =  modal class (Recurring)
The number/value that appears the most which in this case is 18 because it can be seen twice.

Answer:

Yes.

Step-by-step explanation:

When [tex]x=15[/tex],

[tex]x+9=15+9=24 > 21[/tex].

Answer:

Yes this is true

Step-by-step explanation:

24 is greater than 21; which means this statement is always true.

The equation that could be used to find the number of flowers purchased if the total bill was $9 is:0.50n + 1.50 = $9.

Since each flower costs $0.50, multiplying the cost per flower by the number of flowers (n) gives the total cost of the flowers then 0.50n represents the cost of the flowers.

and, 1.50 represents the fixed cost for placing the order.

and $9 represents the total bill, which includes the cost of the flowers and the fixed cost.

By adding the cost of the flowers (0.50n) to the fixed cost (1.50), the equation sets the total bill equal to $9 we get the Equation as

0.50n + 1.50 = $9

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Answer:

284.3

Step-by-step explanation:

Trapezoid Formula:

A=a+b/2*h

plug in the numbers

Using an exponential function, it is found that the multiplier used to predict the amount of medication remaining 2 hours after the peak level is of 0.6889.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, we have that the decay rate is of r = 0.17, hence:

[tex]A(t) = A(0)(0.83)^t[/tex]

After 2 hours, the multiplier is given by:

[tex]A(2) = A(0)(0.83)^2 = 0.6889A(0)[/tex]

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Answer:

h(x) = 3x(x - 2) - 4

Step-by-step explanation:

A quadratic function is a polynomial having a degree of 2.

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

On expanding h(x) :

⇒ h(x) = 3x (x - 2) - 4

⇒ h(x) = 3x² - 6x - 4

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

Hence, h(x) is a quadratic function.

Answer:

h(x) = 3x(x - 2) - 4

Step by-step explanation

A quadratic function has a degree of 2.

Firstly, we expand h(x):

h(x) = 3x (x - 2) - 4

OR h(x) = 3x squared - 6x - 4
Therefore, it is h(x)

Answer:

The Ganges

Step-by-step explanation:

Answer:

Ganga

Step-by-step explanation:

Answer:

-22

Step-by-step explanation:

h-3h-8=14

-2h=14+8

-2h=22

h=-11

The initial step that must be taken before solving almost any problem is to understand what the problem is asking for us to do and what is provided to us to complete that goal.  Looking at the problem statement, we can see that we are being requested to solve for h and we are provided an expression to do so.  Let's begin solving the expression by combining like terms.

Combine like terms

Just a quick explanation on what combine like terms means, it basically just means to combine the coefficients of the numbers associated with the same variables.  Like in this example we can combine h and -3h because they have have the variable h associated with them.

Add 8 to both sides

Divide both sides by -2

Simplify the expression

Therefore, after completing the steps above we were able to determine that the value of h is equal to -11.

Answer:

65

Step-by-step explanation

Just did it on egde