Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. y < c - 1 y > x -4

If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered. 12x2 + x + 20 is the same as the given expression.

6/10, 9/15, 12/20, etc. are fractions that are identical to 3/5. The value of equivalent fractions remains unchanged when lowered. Explanation: The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.

The given quadratic expression 12x^2+x-20

now, 12x^2 + 16x - 15x - 20

4x (3x+4) - 5(3x+4)

(4x-5) (3x+4)

the root of the equation is (4x-5) (3x+4)

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Answer:

Ron killed 8 times as many spiders as Harry: R = 8 * H

Step-by-step explanation:

This expression represents the situation in which Ron killed 8 times as many spiders as Harry.

A proof competition is held annually by Contradiction Club, with special prizes awarded for first, second, third, and fourth place. If 16 students participate in the competition this year, the awards can be allocated among the students in 120 different ways.

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Answer: the cost for Internet increase by 5/4 per minute

Step-by-step explanation:

The difference between the two polynomials (9x²+8x)-(2x²+3x) is 7x²+5x.

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here,

The difference between the two polynomials (9x²+8x)-(2x²+3x) is 7x²+5x.

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Answer:

1/100, or 0.01, or 10^-2

Step-by-step explanation:

Simplify to get 1/10^2

and evaluate to get 1/100 or some the alternative forms (see above)

Kaj bought 3 bananas and 5 apples.

From these three pieces of information, we can set up the following two equations:

We can substitute the third equation into the first equation and get:

y+2 + y = 8

So we know that y = 3

Now we can substitute this value into the second equation and get:

x + 0.5(3) = 8

So we know that x = 5

So Kaj bought 3 bananas and 5 apples.

And also we can substitute y = 3 into the third equation and get:

x = y + 2

So we know that x = 5

So Kaj bought 3 bananas and 5 apples.

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The number of real solution varies according to the degree of the equation and the nature of the equation, The answer is dependent on degree and nature.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

example:

A linear equation (degree 1) has one real solution.

A quadratic equation (degree 2) can have either two real solutions, one real solution or no real solutions, as it depends on the discriminant of the equation, as I explained in my previous answer.

A cubic equation (degree 3) can have one to three real solutions, depending on the coefficients of the equation.

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The length of the side of the table top as calculated from the given data will be 6x⁴y².

To calculate the area of the table top we will have to square of the sides given .

area =(36x.16y^4 )²

side =√(36x.16y^4 )²

= 6x⁴y².

In mathematics the product of a number multiplied by itself is considered to be its square. Eg.) 6 multiplied by 6 gives 36 which is known as its square.

The given table is square in shape and hence its area will be given my multiplying its side with itself.

Area of a square = side x side.

To find its length we can simply find the square root of the number.

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log 30+ log 6 is not equivalent to log 36

Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).

The original phrase is as follows

Log 36

Following that, we write the alternatives (a) log 2+ log 18

Apply the logarithmic rule log 2+ log 18 log (218)

Log 2 plus log 18 log (36)

Remove the bracket

Log 2 plus log 18 log36

(a) Log 2+ Log 18 is the same as log 36.

(b) Log 30 plus log 6

Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)

Log 30 plus log 6 Equals log (180)

Remove the bracket

Log 30-plus log 6-log180

Hence,

(c) Log 30+log 6 does not equal log 36.

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Answer:

see explanation

Step-by-step explanation:

A

for the triangles to be similar by the AA postulate then 2 angles in both triangles must be congruent.

In this case we are only given 1 pair of congruent angles.

Thus not able to say similar by AA postulate, therefore Sharon is incorrect in her assumption.

B

the sides are of different lengths but the ratios of corresponding sides are equal, that is

[tex]\frac{JK}{GH}[/tex] = [tex]\frac{8}{4}[/tex] = 2 and [tex]\frac{JL}{GI}[/tex] = [tex]\frac{10}{5}[/tex] = 2

If the ratios of 2 pairs of corresponding sides of 2 triangles are equal and the included angles are congruent , then the triangles are similar, so

Δ GHI and Δ JKL are similar by the SAS postulate

C

the ratios of corresponding sides are equal , then

[tex]\frac{KL}{HI}[/tex] = [tex]\frac{JL}{GI}[/tex]

[tex]\frac{KL}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )

KL = 14

Hassan can paint maximum 11 bookcases with 10 gallons of paint.

A fraction represents a numerical value, which defines the parts of a whole.

Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.

The basics of fractions explain the top and bottom numbers of a fraction.

Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x. Hence, 1/4 is the fraction here.

Given,

Hassan has 10 gallons of paints.

1 bookcase requires 7/8 gallons of paint

Let Hassan paints x bookcases.

According to the question

7/8x = 10

7x = 80

x = 80/7

x = 11.43

But no. of bookcases should be in whole.

Number of bookcases painted with 10 gallons of paint = 11.

Hence, Maximum 11 bookcases can be painted by Hassan with 10 gallons of paint

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"Thickness of two boards = Thickness of first board + Thickness of second board" would be the closely estimated equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, separated by the 'equal' sign.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

The thickness of the two boards together can be represented by the sum of the thickness of each individual board. Therefore, the equation that most closely estimates the thickness of the two boards stacked together is:

Thickness of two boards = Thickness of first board + Thickness of second board

So in this case, the equation would be:

Thickness of two boards = inch + inch

This equation gives the total thickness of two boards stacked together and it's the closest estimation.

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The area of the floor in the scale drawing is 60 inches²

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Actual rectangular floor.

Length = 24 feet

Width = 40 feet

Scale rectangular floor.

Length = 6 inches

Width = 40/4 = 10 inches

The area of the scale rectangular floor.

= Length x Width

= 6 x 10

= 60 icnhes²

Thus.,

The area of the floor is 60 inches².

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The area occupied by the semicircle, rectangle, and right-angled triangle in the figure is 51.63 m3.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.

given

Three shapes—a rectangle, a triangle, and a semicircle—make up the figure.

Triangle + rectangle + semicircle together make up the figure's surface area.

Triangle's area is equal to 1/2 * 3 * 5.

Triangle's surface area is 15/2.

Triangle's surface area is 7.5 m3.

Rectangle area equals length times width

Rectangle's area is equal to 6 x 5.

30 m2 is the rectangle's area.

Semicircle area equals πr²/2

Semicircle's area is equal to π(3)²/2

Semicircle's area is equal to 3.14(9)/2.

Semicircle's area is equal to 3.14 x 4.5.

Semicircle's surface area is 14.13 m2.

Area: 30 + 14.13 + 7.5

The area occupied by the semicircle, rectangle, and right-angled triangle in the figure is 51.63 m3.

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The probability that the bead taken from the bag is purple or red is total is 0.75 or 3/4.

The total number of beads in the bag is 12.

Out of these, 3 are purple and the rest are red (12-2-1-3 = 6). So, the probability of drawing a purple bead is 3/12 and the probability of drawing a red bead is 6/12.

To find the probability of drawing either a purple or red bead, we add the individual probabilities together: (3/12) + (6/12) = 0.25 + 0.5 = 0.75. This means that there is a 75% chance that the bead taken from the bag will be purple or red.

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The complete question is -

Write down the letter of the event that is likely. bag contains 12 beads_ 2 of the beads are blue: of the beads are green: 3 of the beads are purple: The rest of the beads are red: Julia takes a bead from the bag at random c) Show the probability that this bead is purple Or red is Totulmen.

We employ the following equation to get the normal monthly cost:

4m - 8 = 64

Regular monthly expenses amount to $18.

Irma paid for her cats' subscription in advance for a 4-month period.

She saved $8 overall when she utilized a one-time discount.

Irma totaled $64 in payment.

We must identify the equation that can be utilized to calculate m, the average monthly cost.

Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.

When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.

Irma paid a total of $64 according to the problem, thus we can create the following equation:

4m - $8 = $64

We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.

4m = $64 + $8

4m = $72

Finally, divide both sides by 4 to solve for m:

m = $72 / 4

m = $18

So, the regular cost per month, m, is $18.

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To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Let's begin with a straightforward equation: x + 2 = 7.

How do you obtain X on your own?

Take away two from both sides.

⇒ x + 2 - 2 = 7 - 2\s⇒ x = 5

Check the solution, x = 5, by reentering it into the equation. We get 5 + 2= 7.

R.H.S. L.H.S.

Utilizing triangle properties or the Pythagorean theorem, we can get a solution for the unknown side or angle of a triangle.

With the aid of an example, let's clarify how to solve for x in a triangle.

Two of ABC's legs, which measure 7 units and 24 units respectively, are right-angled at B. Look for the hypotenuse X.

By using the Pythagorean theorem to ABC,

We obtain AC2 = AB2 + BC2, where x2 = 72 + 242, 49 + 576, and 625 where x2 = 625.

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Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Here,

Given : The parallelogram  has M angle  =100 degree

And to Find :L angle

In a parallelogram sum of the adjacent angle is 180°, So

So ,

Using this parallelogram property ,

we find :

=>100 + L =180

=> L = 80

Thus,

We get the L value using parallelogram properties.

Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

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Answer:

This is how you graph it

Step-by-step explanation:

As seen in the equations above, this equation can fit into the equation y=mx+b. M = slope, where is how we will be able to plot the points. Since the slope for both is two, we would go up 2 then right 1, from the y intercept. Which is the point we will be starting at. Plot two points directly on the y-axis at (0,3) and (0,1). Then go back to the slope and go up 2 and right 1. I hope I helped!

This situation can be represented with an equation as y = mx + b. The constant of proportionality (m) is a number that represents how much flour is needed for each additional batch of cookies. If the equation is in the form y = mx + b, then the relationship is proportional.

Shiloh needs to make multiple batches of cookies from a recipe that calls for 2 2/3 cups of flour to make two regular batches. To represent this situation in an equation, the equation is y = mx + b, where y is the amount of flour needed for the number of batches (x) Shiloh is making, m is the constant of proportionality, and b is the initial amount of flour needed (2 2/3 cups).

The constant of proportionality (m) in the situation above is the measure of how much flour is needed for each additional batch of cookies. For example, if the constant of proportionality is 0.75, that means Shiloh would need to add 0.75 cups of flour for each additional batch of cookies.

Therefore, if Shiloh is making three batches of cookies, the equation would be y = 0.75x + 2 2/3, and the total amount of flour needed would be 4 1/8 cups (2 2/3 + 0.75 + 0.75).

By using an equation to represent this situation, it is easy to determine if a relationship is proportional.

If the equation is in the form y = mx + b, then the relationship is proportional.

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Answer:

Step-by-step explanation:

Answer:

6,532

Step-by-step explanation:

ixl

Therefore, the measures of those two angles are 33° and 24°.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle."

Geometry is a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.

We know, the sum of the angles in a triangle is always 180 degrees.

126 + x + y = 180

x + y = 54

Given that the two angles are in a ratio of 11:16, the proportion:

x/y = 11/16

Solving for x and y, we get:

x = 11y/16

We substitute this equation into the equation x + y = 54 and we get:

11y/16 + y = 54

Solving for y we get y = 24. Then we can use the proportion to find x:

x = 11 * 24 / 16 = 33.

So the two angles are 33° and 24°.

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Answer: D

Step-by-step explanation:

Since we are given 2 points, we can use that to find slope, convert to slope-intercept form, and then manipulate it to be standard form. Standard form is ax+by=c.

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-12-8}{1-(-9)} =\frac{-20}{10} =-2[/tex]

With m=-2, we can plug it into slope-intercept form to find the y-intercept.

[tex]y=-2x+b[/tex]         [plug in point]

[tex]8=-2(-9)+b[/tex]    [multiply]

[tex]8=18+b[/tex]             [subtract both sides by 18]

[tex]b=-10[/tex]

With m and b, we can plug in the equation.

[tex]y=-2x-10[/tex]        [add both sides by 2x]

[tex]2x+y=-10[/tex]

This gives D as the answer.

On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).

Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]

Area = 1/2| 60 |

Area of pentagon  = 30 sq unit

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Answer: 1.

Step-by-step explanation:

[tex]\displaystyle\\sin^2x(cot^2x+1)=\\\\sin^2x(\frac{cos^2x}{sin^2x}+1)=\\\\\frac{sin^2xcos^2x}{sin^2x}+sin^2x=\\\\cos^2x+sin^2x=\\\\1.[/tex]

Step-by-step explanation:

x² - 32 = 4x

x² - 4x - 32 = 0

with a little bit experience we see immediately that this is

(x - 8)(x + 4) = 0

the positive x for this to be true is x = 8.

formally, the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (4 ± sqrt((-4)² - 4×1×-32))/(2×1) =

= (4 ± sqrt(16 + 128))/2 = (4 ± sqrt(144))/2 =

= (4 ± 12)/2 = 2 ± 6

x1 = 2 + 6 = 8

x2 = 2 - 6 = -4

we were right at the beginning.

the positive solution is x = 8.

Answer:

I think you do know how because where the point is now is correct!!