16 January aca it class Factorist the followsing.

1. 2l+2w
2. -2ab²-4a²b
3. 9x²-4
4. y²+7x+12
5. 3x²+6x-18​

Given:

Graph them and transform as described.

1. A(1, 2), B(1, 5), C(5, 5)

Reflection: in the x-axis

2. A(4, -3), B(-1, -1), C(1,3)

Reflection: in the y-axis

3. A(2, 1), B(2, -3), C(4, -2)

Reflection: in the line y = 1

See attached for each. It should be self-explanatory.

Answer:

Question 1:

Question 2:

Question 3:

Step-by-step explanation:

Given vertices of the pre-image:

If the pre-image is reflected in the x-axis, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is reflected in the y-axis, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is reflected in the line y = 1, the transformation rule is:

Therefore the vertices of the image are:

Answer:

2nd option

Step-by-step explanation:

[4    -7] * [a    b] *  = [1    0]

[-1    2]    [c    d]       [0    1]

4 * a + (-7) * c = 1

4 * b + (-7) * d = 0

-1 * a + 2 * c = 0

-1 * b + 2 * d = 1

4a - 7c = 1  ==> equation 1

4b - 7d = 0  ==> equation 2

-a + 2c = 0  ==> equation 3

-b + 2d = 1  ==> equation 4

(-b + 2d = 1) * 4  ==> make -b into -4b

   -4b + 8d = 4

+   (4b - 7d = 0)

-4b+4b + 8d-7d = 4+0  ==> add equations 2 and 4 to cancel the variable b

8d-7d = 4 ==> -4b+4b=0 and adding anything by 0 will result in itself: 0+3=3

d = 4

-b + 2d = 1

-b + 2(4) = 1  ==> substitute 4 for d

-b + 8 = 1   ==> simplify

-b = -7  ==> subtract 8 on both sides

b = 7  ==> simplify

Since we got the values of b and d, the matrix now looks like this:

[4    -7] * [a    7] *  = [1    0]

[-1    2]    [c    4]       [0    1]

Now solve for a and c using equations 1 and 3:

4a - 7c = 1  ==> equation 1

-a + 2c = 0  ==> equation 3

(-a + 2c = 0) * 4  ==> make -a into -4a

   -4a + 8c = 0

+   (4a - 7c = 1)

-4a+4a + 8c-7c = 0+1  ==> add equations 1 and 3 to cancel the variable b

8c-7c = 1 ==> -4a+4a=0 and adding anything by 0 will result in itself: 0+3=3

c = 1

-a + 2c = 0

-a + 2(1) = 0  ==> substitute 1 for c

-a + 2 = 0   ==> simplify

-a = -2  ==> subtract 2 on both sides

a = 2  ==> simplify

Since we got the values of a and c, the matrix now looks like this:

[4    -7] * [2    7] *  = [1    0]

[-1    2]    [1    4]       [0    1]

Hence, the answer is the 2nd option.

Answer:

option A

Step-by-step explanation:

The slope intercept form of a linear equation is expressed as: [tex]y=mx+b\text{ where }m\ne0[/tex]

The slope described how the y value changes as x changes. If it's positive then that means as x increases, y increases and if it's negative then that means as x increases, y decreases.

Knowing this information, there is only one reasonable option in this case. Given the equation: [tex]y=x+6[/tex], we know that it has a slope of positive one, meaning it's increasing. Given the equation: [tex]y=-\frac{3}{4}x+4[/tex], we know that it has a slope of negative three fourths, meaning it's decreasing.

The graph shown is increasing so option A is the only reasonable option in this case.

Answer:

100,000,000,000cm

Step-by-step explanation:

there are one hundred billion cm in one billion meters.

The equation perpendicular to the line is y= −1/2 x. Therefore, option B is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

In the given graph, the coordinates are (2, 3) and (0, -1)

Slope m=(-1-3)/(0-2)

= -4/(-2)

m=2

Substitute m=2 and (x, y)=(2, 3) in y=mx+c, we get

3=2(2)+c

c=-1

Substitute m=2 and c=-1 in y=mx+c, we get

y=2x-1

Find any equation perpendicular to the line.

y= −1/2 x

Therefore, option B is the correct answer.

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The number of zeroes that the product has at the end 50 x 49 x 48 x ... x 3 x 2 x 1 will be 12.

The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as

n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1

The expression is given below.

⇒ 50 x 49 x 48 x ... x 3 x 2 x 1

⇒ 50!

Then the number of zeroes in the product at the end will be given as,

⇒ 50 / 5 + 50 / 5²

⇒ 50 / 5 + 50 / 25

⇒ 10 + 2

⇒ 12

The number of zeroes that the product has at the end 50 x 49 x 48 x ... x 3 x 2 x 1 will be 12.

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Answer:

6

Step-by-step explanation:

85 +12.5*x visits =155

12.5x≥70

x must be greater than 5.6 so she need to go 6 times & then she'll get her free ticket

Answer:

C is irrational--6 is not a perfect square.

The term that represents the cost of the shoes after the discount is (1 - 0. 025)s. Option D

Algebraic expressions are described as mathematical expressions that consist of factors, constants, variables, terms and coefficients.

They are also made up of arithmetic operations, which includes;

From the information given, we have that there was a 25% discount on all the shoes Declan bought

Given the expression;

c + ( 1 - 0.25)s + 0. 08[c + (1 -0.25)s ]

expand the bracket

c + s - 0. 25s + 0. 08( c - s - 0. 25s)

expand the parentheses

c + s - 0. 25s + 0. 08c - 0. 08s - 0.02

But for the cost of the shoes after the 25% discount, we have;

(1 - 0. 025)s

Hence, the expression is (1 - 0. 025)s

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Answer: [tex]5 \text{ cm}^2[/tex]

Step-by-step explanation:

[tex]4 \times 1 \frac{1}{4}=4 \times \frac{5}{4}=5[/tex]

Therefore, the answer is [tex]5 \text{ cm}^2[/tex].

Using the given information, the measure of angle AEB is 62

From the question, we are to determine the measure of angle AEB

From the given information, we have that

Angle A = 86°

Angle C = 110°

Angle D = 40°

First, we will calculate the measure of angle B

A + B + C + D = 360°

86 + B + 110 + 40 = 360 (Sum of angles in a quadrilateral)

B + 236 = 360

B = 360 - 236

B = 124

∴ Angle ABC = 124

Then,

Angle ABC is bisected

Therefore,

Angle AEB = 1/2 × 124

Angle AEB = 62

Hence, angle AEB is 62

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The pair of parallel lines intersected by a transversal so at least one angle is 45 degrees has an angle B'EB as 45 degrees.

In terms of geometry, parallel lines are two separate lines that never cross each other and are located in the same plane. They may be vertical or horizontal.

They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

The pair of parallel lines intersected by transversal is as shown:

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Using the provided conditions and values, This is solved with the concept of word problem, The answer is first, second and third aircrafts have 576,512 and 864 seats.

A word problem in mathematics is a problem that is written in natural language (i.e., words) rather than in mathematical notation. It presents a real-world scenario that requires the use of mathematical concepts and skills to solve. Word problems often involve finding unknown quantities based on given information, and they can be challenging because they require students to understand the problem and translate it into mathematical equations or formulas. They are often used in primary and secondary education to help students apply their math skills to real-world situations and develop critical thinking skills.

A mathematical expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that represents a mathematical statement or equation. Mathematical expressions can be evaluated to find a numerical value. They can also be simplified by applying the order of operations (PEMDAS) to combine like terms or to remove unnecessary parentheses. Additionally, mathematical expressions can also be used to represent the relationship between different variables.

Let x be the number of seats on the second aircraft. Then, the first aircraft has x+64 seats and the third aircraft has 2x-152 seats.

We know that the total number of seats for all three aircraft is 1900, so we can set up the following equation:

x + (x+64) + (2x-152) = 1900

Solving this equation gives us x = 512, which means the second aircraft has 512 seats. We can then use this information to find the number of seats for the other two aircraft:

First aircraft: 512 + 64 = 576 seats

Third aircraft: 2(512) - 152 = 864 seats.

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Answer:

2 miles

Step-by-step explanation:

Distance = speed x time

= 10mph x 1/5

= 2 miles

Answer:

B)  x + y ≤ 30,000

     x ≥ 8,000

     x ≥ 3y

Step-by-step explanation:

Definition of the variables:

If Tamara has $30,000 and part or all of which she wants to invest into a combination of corporate bonds and municipal bonds, then the sum of the investments in the two bonds will be less than or equal to $30,000:

If Tamara wants to invest no less than $8,000 into corporate bonds, then the amount invested in corporate bonds (x) will be greater than or equal to $8,000:

If Tamara wants to invest at least three times as much into corporate bonds than into municipal bonds, then the amount invested in corporate bonds (x) will be greater than or equal to 3 times the amount invested in municipal bonds (y):

The solution to the expression 5 2 (3x4) divided by 3-5 is -312

Fractions are simply described as part of a whole number or variable.

There are different types of fraction which includes;

PEMDAS is a mathematical acronym used to give the order of operations to be followed in solving expressions.

It stands for;

Given the expression;

52(3×4)/3 - 5

expand the parentheses

52(12)/-2

624/-2

Divide the values

-312

Hence, the values is -312

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Sara's average speed for the entire race is

3.6 meters per second

The first 50 meters of the race is ran at a constant speed of 4.6 m/s.

Let's compute the time taken for this portion

distance = rate*time

time = distance/rate

time = 50/(4.6)

time = 10.869

It takes approximately 10.869 seconds to run the first 50 meters (at a constant speed of 4.6 m/s).

Add on the other time values from the other sections (10 and 23) to get 10.869+10+23 = 43.869

The entire 200 m race takes about 43.869 seconds.

So Sara's average speed over the entire race is about 200/43.869 = 4.559 which rounds to 4.6 m/s when rounding to one decimal place.

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Answer : 165/2

To do this, we just have to add 82 and 1/2. However, the question asks for an improper fraction, so we turn 82 into 164/2. Now, we add 1/2 to 165/2 which equals 164+1/2 = 165/2.

Answer:

Here are the true statements:

The false statement is:

The G-intercept of G(t) represents the total distance the vehicle traveled. The t-intercept of G(t) represents the time it takes the vehicle to run out of gas. (This is not the case, the y-intercept represents the initial amount of gas and the x-intercept represents the time it takes the vehicle to run out of gas)

The percentage of  mass of Cs in the sample is 25%

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. A percentage, indicates hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

To calculate the percentage of  Cs in the sample

100/400 x 100

=25%

To calculate the percentage of cesium (Cs) in the sample

300/400 x 100

=75%

Hence, 25% is the percentage of  Cs in the sample

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The ordered pairs that satisfies the linear inequality x < - 3 are (-4, -3) and (-3, -3)

A linear inequality is a mathematical statement that describes a relationship between two or more variables that are not necessarily equal. It is similar to a linear equation, but instead of an equal sign, it uses one of the inequality signs: <, >, ≤, or ≥.

A linear inequality can also be represented graphically on a coordinate plane, by shading the region of the plane that satisfies the inequality. The solution set of a linear inequality is the set of all points that make the inequality true.

A linear inequality can also have infinitely many solutions, no solution or a unique solution. The solution set will be a region in a coordinate plane which is a half-plane, a line or a point depending on the inequality.

In the problem, the inequality x < -3 will have an ordered pair of solution of

(-∞, -3).

This implies that all values of x must lies from negative till infinity while y lies up to - 3.

In the options given, only (-4, -3) and (-3, -3) satisfies this criteria.

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The value of trig in ratios as fraction are, sin X = 45/24 , cos W = 17/8

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now, we can find all the values as;

⇒ sin X = Perpendicular / Hypotenuse

⇒ sin X = 45 / 24

And, we get;

⇒ cos W = Base / Hypotenuse

⇒ cos W = 51 / 24

⇒ cos W = 17 / 8

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Answer:

To solve for x in this equation, you can follow these steps:

Subtract 5 from both sides: 2/3x = -4

Multiply both sides by 3/2 to cancel out the denominator on the left side: x = -6

So the solution for x is -6

So, 2/3x + 5 = 1 becomes 2/3(-6) + 5 = -4 + 5 = 1

I think it is the third answer.

Because your problem says 'no more than' so it can't be the fourth one,because it has '≤' which means that the number is lower or equal.

So it is the third one.

Hope I helped you!

The amount that would be covered by the Insurance Plan would be and the amount that is billed to the patient is  $ 9. 75

The amount that would be covered by the insurance plan in a 85 / 15 coinsurance plan is 85 % of the bill. The amount to be covered by the insurance plan is:

= 85% x 65

= $ 55. 25

The amount billed to the patient is:

= Total bill - covered by insurance plan

= 65 - 55 .25

= $ 9. 75

In conclusion, the amount that would be covered by the insurance plan is $ 55. 25 and the amount to be billed to the patient to be paid by them is $ 9. 75.

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The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The line's equation is x=-2.5.

The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).

This intersection represents the point on the triangle's perimeter. Distance d = (a - ax)2 + (b - bx)2 is the geometry formula for distance. "d" represents the separation between a vertex and the circumference, where x = 1, 2, 3.

The junction of the perpendicular bisectors of each side of the triangle, or the lines that are perpendicular to each side's midpoint, is where the triangle's circumcenter can be located.

To determine it, we locate the intersection of the circumcenter and the first name of the triangle, which is the point at which each line intersects the other

(-4,0) B=(-4,-4) C=(-1,-4) (-1,-4) (-4, -2),

y=-2 is the perpendicular line to AB's midpoint.

The intersection of the line at (-2.5,-2) and (-5/2,-2)

where BC's midpoint is located.

The line's equation is x=-2.5.

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Answer:

First choice

y = 3ˣ

Step-by-step explanation:

It is easier if you examine the obviously wrong choices

Choice 2, y = 9x is incorrect because at x = 0, y = 9x should be 0, instead it is 1

Choice 3 , y = 3x is incorrect for the same reason

Choice 4 y = x³ is incorrect because at x = 0, x³ should be 0, instead it is 1

Correct choice is the first one: y = 3ˣ

Let's check:

x = 0,  y = 3⁰  = 1 because any number raised to the power 0 is 1

x = 1, y = 3¹ = 3; because any number raised to the power 1 is 1itself

x = 2; y = 3² = 9 ; so fts

You can test out the rest of the entries yourself

For the graph of the function F(x), when x goes from 0 to 1, F(x) is a negative number with large absolute value. Option D is correct.

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.

When the value of x goes from 0 to 1 the function shifts and the value is decreased gradually, thus giving F(x) as negative number with a large absolute value.

Hence, option D is the correct answer.

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