Solve the inequality for x and identify the graph of its solution.
|x + 3| < 2

Area of the shape formed by joining triangle , trapezium and rectangle with height 3.5cm is equal to 6.25cm².

As given in the question,

Height of the shape = 3.5cm

length of the rectangle =3cm

Base of a triangle= 8mm

                           = 0.8cm

Parallel sides of the trapezium

side1 = 0.8cm

side 2= 3cm

Let x represents the height

Ratio of the height of rectangle ,trapezium and triangle =2:3:2

2x +3x+2x =3.5

⇒7x =3.5

⇒x =0.5

Height of rectangle =2×0.5

                             = 1cm

Height of trapezium =3×0.5

                               = 1.5cm

Height of the triangle =2×0.5

                                 = 1cm

Area of triangle = (1/2)× 0.8 ×1

                        = 0.4cm²

Area of trapezium = (1/2) ×(0.8+3)×1.5

                            = 2.85cm²

Area of rectangle = 3 ×1

                            =3cm²

Area of the shape =0.4 +2.85 +3

                            = 6.25cm²

Therefore, area of the shape formed by joining triangle , trapezium and rectangle with height 3.5cm is equal to 6.25cm².

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Answer:

[tex]\frac{x}{3}\sqrt{\frac{x}{3}}[/tex]

Step-by-step explanation:

[tex]g(h(x))=g(x/3)=\sqrt{x/3} \\ \\ f(g(h(x)))=f(\sqrt{x/3}) \\ \\ =(\sqrt{x/3})^3 \\ \\ =\frac{x}{3}\sqrt{\frac{x}{3}}[/tex]

Step-by-step explanation:

follow the steps and apply the rules of geometry

The measure of angle AXY based on the information will be A. 70°.

It should be noted that the value of a right angle is equal to 90°.

In this case, we will add the angles that are given and equate them to 90°. This will be:

6x + 40 + 10 + 2x = 90°

8x + 50 = 90°

Collect like terms

8x = 90° - 50°

8x = 40°

Divide

x = 40° / 8

x = 5°

Therefore, the value of angle AXY will be:

= 6x + 40

where x = 5.

= 6(5) + 40

= 30 + 40

= 70°

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Answer:

D

Step-by-step explanation:

We can add the two functions.

[tex]j(x)+k(x)=(17+0.05x)+(4+0.03x)=21+0.08x[/tex]

The rectangle MATH is translated by using the transformation rule P'(x, y) = (x - 7, y - 4) to create the rectangle M'A'T'H'.

In this problem we have the case of a rectangle, a geometric locus, that is translated both horizontally (7 units to the left) and vertically (4 units down). Vectorially speaking, a translation is represented by the following vector sum:

P'(x, y) = P(x, y) + T(x, y)     (1)

Where:

If we know that P(x, y) = (x, y) and T(x, y) = (- 7, - 4), then the transformation rule is derived below:

P'(x, y) = (x, y) + (- 7, - 4)

P'(x, y) = (x - 7, y - 4)

The rectangle MATH is translated by making use the transformation rule P'(x, y) = (x - 7, y - 4).

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The difference between 2/5(d-10)-2/3(d+6) is -56.

Firstly simplifying the terms to find the difference. Simplifying the first part -

Rewriting the expression

Expression 1 = 2/5(d - 10)

Multiplying the terms with the bracket

Expression 1 = 2d/5 - ((2×10)/5)

Multiplying the terms on Right Hand Side

Expression 1 = 2d/5 - 2×2

Performing multiplication

Expression 1 = 2d/5 - 4

Simplifying the second part -

Rewriting the expression

Expression 2 = 2/5(d + 6)

Multiplying the terms with the bracket

Expression 2 = 2d/5 + ((2×6)/5)

Multiplying the terms on Right Hand Side

Expression 2 = 2d/5 - 12×5

Performing multiplication

Expression 2 = 2d/5 - 60

Subtracting expression 2 from expression 1

Difference = 2d/5 - 60 - (2d/5 - 4)

2d/5 will be subtracted to give 0

Difference = - 60 + 4

Performing subtraction

Difference = - 56

Therefore, the difference between mentioned expressions is -56.

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The table of values showing the relationship between the number of cakes the bakery makes and the number of bags of four the bakery uses is:

Cakes           |   3    6     9     12      15

Bags of flour|   1     2     3      4        5

A bakery made 9 cakes using 3 bags of flour.

We can introduce a relation between the number of cakes and the bags of flour in the form of a ratio.

Then, cakes : bags of flour = 9 : 3

We can simplify this ratio into 3:1.

So the ratio between the number of cakes and bags of flour = 3:1

We take values for number of bags of flour from 1 to 5 and found the corresponding values for number of cakes using the ratio 3:1.

For each value of number of bags of flour, we just needed to multiply 3 with it to get the number of cakes made.

So using this relationship between cakes made and the amount of flour used to make all their cakes, we can makes table with values:

Cakes           |   3    6     9     12      15

Bags of flour|   1     2     3      4        5

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Answer:

x = 55

Step-by-step explanation:

61+3×X=226

61+3x=226-61

3x=165

x= 165/3

x= 55

Answer: D

Step-by-step explanation:

The x-intercepts are where the graph meets the y-axis.

The y-intercepts are where the graph meets the x-axis.

Answer: D x-intercepts: (-10,0) and (2,0)

y-intercept (0,-5)

[tex] \sqrt{4x} = 3a - y \\ \sqrt{4} \times \sqrt{x} = 3a - y \\ 2 \sqrt{x} = 3a - y \\ \frac{2 \sqrt{x} }{2} = \frac{3a}{2} - \frac{y}{2} \\ \sqrt{x} = \frac{3a}{2} - \frac{y}{2} \\ ( { \sqrt{x} })^{2} = {( \frac{3a}{2} - \frac{y}{2} })^{2} \\ x = ( \frac{3a}{2} - \frac{y}{2} ) ^{2} [/tex]

ATTACHED IS THE SOLUTION

Answer:

y = - x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x + 9 ← is in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation of the parallel line

to find c substitute (7, - 13 ) into the partial equation

- 13 = - 7 + c ⇒ c = - 13 + 7 = - 6

y = - x + 6 ← equation of parallel line

Answer:

Step-by-step explanation:

Parallel lines have the same slope. So the slope of the line that's parallel to

Now, plug that into the Point-slope formula:

Where:

Plug in the values:

I hope this helps!!

If the rows are  perpendicular to the footpath, then the gardener ensure that that the rows are parallel.

Parallel:

Any two lines are said to be parallel if the Corresponding angles so formed are equal.

Given,

The head gardener at a botanical garden wants to plant rosebushes in parallel rows on either side of an existing footpath.

Here we need to find how can the gardener ensure that that the rows are parallel.

To know the answer, we have to consider the following,

Let us consider,

If the gardener digs every row at a 90° angle to the footpath, then each row will be exactly perpendicular to the foot path of the garden.

Which means,

If the rows are  perpendicular to the footpath, then the rows are parallel.

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The linear graph of y = 2x + 3 is shown below.

To graph the linear equation, plot each points from the table of values on a coordinate plane then connect the points to each other as a straight line.

Given the table, to fill it, substitute each value of x into y = 2x + 3:

For x = -2:

y = 2(-2) + 3

y = -4 + 3

y = -1

For x = -1:

y = 2(-1) + 3

y = -2 + 3

y = 1

For x = 0:

y = 2(0) + 3

y = 3

Thus, plot the points, (-2, -1), (-1, 1), (0, 3), (1, 5), and (2, 7) on a graph. The graph is shown below.

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The postulate that can be used to prove that the triangles are congruent is: AAS.

The AAS congruence postulate states that if two angles and one non-included side of one triangle are congruent to corresponding two angles and one non-included side of another triangle, it can be proven that both triangles are congruent triangles.

From the image, we know that triangles RST and UVT have:

Two pairs of congruent angles, which are angle RST ≅ angle UVT and angle RTS ≅ UTV (vertical angles)

One pair of non-included congruent sides, which are RT ≅ UT.

Thus, we can conclude that they are congruent triangles based on the AAS congruence postulate.

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Answer:

The correct answer is B) Option B has a higher present value at time zero.

Step-by-step explanation:

We use spreadsheets to compare both options.

We have to calculate

future value

present value

Option A

Net Present Value (NPV) 10534,87

Future value  12.547

Option B

Net Present Value (NPV) 10692,05  is higher than option A

Future value  12.734 is higher than option A

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The function which contains non-negative real number is y = (x - 1)² and the domain is [0, ∝).

What is real number?

In mathematics, real number are those numbers which contain negative numbers, whole numbers as well as natural numbers. And all the positive real number lies in the first quadrant in the graph. The set of real numbers (denoted by R) includes both rational numbers (positive, negative and zero) and irrational numbers.

According to the question, the given functions whose domain consists of all non-negative real numbers.

Non-negative real numbers lie in the first quadrant. Therefore, the function(d) contains all non-negative real numbers.

Given function: y = (x - 1)²

The domain for this function is: [0, ∝)

Hence, the function which contains non-negative real number is y=(x - 1)² and the domain is [0, ∝).

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Answer:

first choice in the image.

numerator: 12

denominator: 30

Step-by-step explanation:

"Name the numerator and denominator of the fraction that represents the number of trucks that he has loaded out of the total needing to be loaded"

so numerator = "number of trucks that he has loaded"

and denominator = "total needing to be loaded"

Joaquin was asked to load 30 trucks today. So his/her total would be 30.

thus the denominator is 30.

Joaquin has finished loading 12 already, which means he/she has loaded 12. so, the numerator is 12.

Answer: 244.92 square inches

Step-by-step explanation:

The radius is half the diameter so is 3 inches

Substitute r=3 and pi= 3.14 into the equation:

SA= (2x3.14x9) + (2x3.14x3x10)

Put that into your calculator and you get 244.92

Answer

Step-by-step explanation:

When one dice is rolled, the total sample space = 6 When two dice is rolled, total sample space = 6*6=36 A) P(sum less than 9) = 1 - P(sum greater than or equal to 9) Sample outcomes for sum greater than or equal to 9 = {(3,6),(4,5),(5,4),(6,3),(4,6), (5,5),(6,4), (5,6), (6,5),(6,6)} P(sum greater than or equal to 9) = 10/36 = 5/18 or 0.2778 P(sum less than 9) = 1-5/18 = 13/18 or 0.7222 B)Sample outcomes for sum greater than or equal to 10 = {(4,6),(5,5),(6,4), (5,6),(6,5),(6,6)} P(sum greater than or equal to 10) = 6/36 = 1/6 or 0.1667 C) sample outcomes for event 3 on one die or both = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),(1,3),(2,3), (4,3),(5,3),(6,3)} P(3 on one die or both die) = 11/36 or 0.3056

Answer:

$60.20

Step-by-step explanation:

7.5 percent of 56 can be found by multiplying 56 times .075, which equals 4.2. Add that to 56 and you get the total cost, which is $60.20

Answer:

9/20

Step-by-step explanation:

3/5 is the same as 12/20, so 12 fish are guppies, now 3/4 is also 9/12, so 9 of the fish are red guppies, 9/20 is in the simplest form

The number of books Henry read each number is 3 or 6/2 in a fraction.

A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

As given in the question,

The number of books read in 2 months is 4.

Henry read books at a constant rate.

The Number of books read by Henry in 1 month is ( 6/2 ) = 3 books.

Therefore, the number of books read by Henry as per the given condition of reading 6 books in 2 months at a constant rate is equal to 6/2.

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Answer:

1. e

2. c

3. f

4. b

5. a

6. d

Step-by-step explanation:

Addition - Subtraction

Subtraction - Addition

Multiplication - Division

Division - Multiplication

x^2 = square root X

square root x = x^2

Answer:

A to 5. B to 3. C to 1. D to 6. E to 2. F to 4.

Step-by-step explanation:

It makes sense.

Sam's score percentage for the whole year was  15 %

This  is a simple question of average,

Sam improved his score by 20% in the 1st semester, and in the 2nd semester, his score improved by 10%.

let 20  in out of 100 and 10 out of 100.

then, the total percentage score is equal to 20+10=30.

and, the total percentage in which out of getting is 100+100 =200

we have to find sam's score percentage for the whole year

which is equal to the total percentage score by sam's divided by percentage which is out of getting and whole multiplied by 100 Because we are finding the percentage.

=>30*100/200=>15 percentage.

So, Sam's score percentage for the whole year= is 15 %

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Both conclusion are correct and the second conclusion is RS = RQ + QS.

The midpoint is halfway between the two end points, Its x value is halfway between the two x values. Its y value is halfway between the two y values.

Given that,

Part 1, If B is between A and C then AB + BC = AC

Then, we need to find the conclusion in Part 2 if Q is between R and S.

The required conclusion can be find out by using the concept of deductive reasoning.

Deductive reasoning involves a pattern which is followed in one argument and by following the same pattern we reach to a conclusion for some other argument.

Now, If we see in Part 1 if B is between A and C then the length of line segment AC is equal to sum of its mid segments AB and BC

⇒ AB + BC = AC

Similarly, if Q is between R and S, then the length of line segment RS is equal to sum of its mid segments RQ and QS

⇒ RS = RQ + QS

Hence, The required Conclusion is RS = RQ + QS.

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1. Yes. There is a proportional relationship between the cost of items before tax and the price after tax because they share a constant of proportionality.

2. The constant of proportionality refers to the relative ratio that establishes the proportional relationship between two values.

Other descriptions of the constant of proportionality include:

Two variables possess a proportional relationship when their ratio or product produces a constant.

We can use the equation, k = y ÷ x, to find the constant of proportionality.

For instance, let the cost of items before tax be $100 with a 7% sales tax. The cost of the articles after tax is $107.

Therefore, the constant of proportionality is 1.07 ($107/$100).

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Answer:2x+ 24

Step-by-step explanation:

6x-4x=2x+ 24

Answer:

✨hello mark as branlist pls x=3

Step-by-step explanation:

6x+24−4x=30

6x+24−4x=30

6x+24+−4x=30

(6x+−4x)+(24)=30

2x+24=30

2x+24=30

2x+24−24=30−242x=6

2x

2

=

6

2

x=3