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Knowledge Check
In the figure below, j Il n. Find the values of y and z.
شکر
60°
y4z-20)
Question 5
A
11
Z =
0

The inequality representing the graph shown in figure is -

y < 6x + 3.

[Refer to the graph plotted at the end for confirmation]

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. The L.H.S and R.H.S of an inequality are not equal.

Given is a graph of an inequality plotted on graph paper.

The following steps are to be followed in order to find the inequality -

STEP 1 - Determining inequality type.

From the graph, it can be seen that the the border line dividing the green shaded area from the remaining graph is uniform i.e. not dashed. Therefore, the inequality is a strict inequality which means that, either inequality sign is '>' or '<'. The sign cannot be ≤ or ≥.

STEP 2 - Determining the inequality equation.

From the graph, it can be seen that the y - intercept of line is (0, 3). The line cuts the x - axis at coordinates (- 0.5, 0). Therefore, it can be concluded that -

y - intercept = 3

x - intercept = - 0.5

Then, the slope of line will be = [m] = | 3 - 0/0 -(- 0.5) | = |3/0.5| = 6

The general equation of line with slope 'm' and y - intercept is -

y = mx + c

y = 6x + 3

Therefore, y = 6x + 3 is the equation of straight line.

STEP 3 - Determining the side to be shaded.

For this, take the origin (0, 0) and test it with both the inequalities '>' and '<'.

For inequality → greater than ' > ' -

y > 6x + 3

Put (x, y) as (0, 0), we get -

0 > 6 x 0 + 3

0 > 3

Which is false.

For inequality → less than ' < ' -

y < 6x + 3

Put (x, y) as (0, 0), we get -

0 < 6 x 0 + 3

0 < 3

which is true.

So our final inequality is → y < 6x + 3.

Therefore, the inequality representing the graph shown in figure is -

y < 6x + 3.

[The graph for this inequality is attached below]

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Answer:11/57

Step-by-step explanation:

The point at 1/5 of the coordinate points is (-11/5, -7/5)

The coordinates are given as:

(-3, -2) to (1, 1)?

The location 1/5 can be represented as

m : n = 1 : 4

The location of the point is then calculated as:

P = 1/5 * (mx2 + nx1, my2 + ny1)

This gives

P = 1/5 * (1 * 1 + 4 * -3, 1 * 1 + 4 * -2)

Evaluate

P = 1/5 * (-11, -7)

This gives

P = (-11/5, -7/5)

Hence, the point at 1/5 of the coordinate points is (-11/5, -7/5)

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Answer:

Step-by-step explanation:

B.

The simplification of the number 2√15 is 7.74.

Squaring a number would be the inverse operation of square rooting it.

The given expression is;

= 2√15

For finding the value of √15; use long division method.

√15 = 3.87

Put the value;

=  2 × 3.87

=  7.74.

Thus, the value of the expression is found as 7.74.

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The inequality will be 50x ≤ 25000 - 11000 and the value of x will be x ≤ 402.

From the information, the shipping container will be used to transport several 50-kilogram crates across the country by rail and the greatest weight that can be loaded into the container is 25000 kilograms.

Let the number of 50-kilogram crates that can be loaded into the shipping container be represented by x.

This will be:

50(x) + 11000 ≤ 25000

50x+11000 ≤ 25000

Collect like terms

50x ≤ 25000 - 11000

50x ≤ 14000

Divide

50x/50 ≤ 14000 / 50

x ≤ 402

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As given the sum of squares of three consecutive integers,  four digits which never occur in the ones place are 1,3,6,8.

As given,

Let x -1 , x , x +1 are three consecutive integers.

Sum of the squares of three consecutive integers

= (x -1)² +x² + (x+1)²

= x² -2x +1 +x² +x² +2x +1

=3x² +2

Now substitute x = 0,1,2,3,4,5,6,7,8,9

Sum = 2, 5,14,29, 50, 77, 110, 149, 194, 245

Four digit never occur at ones place = 1,3,6,8

Therefore, as given the sum of squares of three consecutive integers,  four digits which never occur in the ones place are 1,3,6,8.

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The cost for using the hair dryer for 10 minutes is $0.05

We know that the hair is rated at 1850 watts, meaning that it uses 1850 watts per hour of usage.

We know that 10min = (10/60) hours = 1/6 hours.

And we can rewrite:

1850 watts = 1.850 kW

Then the wattage used in these 10 minutes is:

1.850 kW*(1/6 hours) = 0.31 kWh

And the cost is $0.15 per kWh, then the cost here is:

C = $0.15*0.31  = $0.05

The cost for using the hair dryer for 10 minutes is $0.05

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Answer:x=20

Step-by-step explanation:You would keep x by itself and you would add 17+3 which would equal 20.So therefore the answer would be x=20.

Answer:

Step-by-step explanation:

It means she made a rectangle. 2cm wide, 5cm high.

Answer:

x [tex]\geq[/tex] -40.6

Step-by-step explanation:

9/5x + 23 [tex]\geq[/tex] -50 (subtract 23 over to other side)

9/5x [tex]\geq[/tex] -73 (multiply by 5)

9x [tex]\geq[/tex] -365 (divide by 9)

x [tex]\geq[/tex] -40.6

Answer:

Step-by-step explanation:

the answer is B

[tex]\bold{H \: e \: y \: o \: !}[/tex]

__________________

[tex]\mathtt{\sqrt{\frac{9x^3}{4y^2}}}[/tex]

__________________

Apply radical rule: [tex]\mathtt{=\sqrt{\frac{a}{b}}} \: = \: \mathtt{\sqrt{\frac{a}{b}}},[/tex] assuming [tex]\mathtt{a \geq 0, \: b \: \leq 0}[/tex]

[tex]\mathtt{=\sqrt{\frac{9x^3}{4y^2}}}[/tex]

__________________

Simplify: [tex]\mathtt{\sqrt{9x^3}} \: : \: \mathtt{3x\sqrt{x}}}[/tex]

[tex]\mathtt{=\sqrt{\frac{3x\sqrt{x}}{4y^2}}}[/tex]

__________________

Simplify: [tex]\mathtt{\sqrt{4y^2}} \: : \: \mathtt{2y}[/tex]

[tex]\mathtt{\frac{3x\sqrt{x}}{2y}}[/tex]

Hope It Helps!

A n s w e r e d : -  ᴀᴅʀɪᴀɴɴᴏɪʀ

Two expressions with an equal sign is equation.-12/7  is the solution for

7/4q-2=-5

Two expressions with an equal sign is called as equation.

The given equation is

7q/4-2=-5

Shift -2 from left to right,

7q/4=-5+2

Add -5+2 in RHS

7q/4=-3

Cross multiply

7q=-12

Divide both sides by 7

q=-12/7

Therefore required solution is -12/7.

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Cost of posting 3 small, 9 medium and 2 large parcels = $94.45

Let the cost of a small parcel be x

Let the cost of a medium parcel be y

Let the cost of a large parcel be z

Cost of 6 small, 8 medium and 9 large parcels:

6x + 8y + 9z = 173.20------(1)

Cost of 7 small, 13 medium and 17 large parcels:

7x + 13y + 17z = 291.5-------(2)

Also, a large parcel costs twice as much as a small parcel, therefore

z = 2x

Substituting z = 2x in equation (1) and (2) we get:

24x + 8y = 173.20------(3)

41x + 13y = 291.5--------(4)

Multiplying equation (3) with 13 and equation (4) with 8 we get

312x + 104y = 2251.6

328x + 104y = 2332

By solving the equations we get

16x = 80.4

x = 5.02

Putting x = 5.02 in equation (3) we get:

y = 6.59

z = 10.04

Cost of posting 3 small, 9 medium and 2 large parcels: 3*5.02 + 9*6.59 + 2*10.04 = 15.06 + 59.31 + 20.08 = $94.45

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Julia have to pay $2.57 as sales tax on purchase of headphones.

Given,

The cost of headphones which Julia wants to purchase on sale = $ 42.79

The sales tax in Julia's country = 6%

We have to calculate the amount of sales tax Julia will pay on the purchase:

That is,

Sales Tax Value = Percentage of sales tax × Price of headphones

Sales Tax Value = (6 / 100) × 42.79

Sales Tax Value = 0.06 × 42.79

Sales Tax Value = 2.5674

Sales Tax Value ≈ 2.57

Therefore, Julia have to pay $2.57 as sales tax on purchase of headphones.

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Answer:

look it up

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

Pi 9/25 = 1.131

Decimals are usually rational

Answer:

9. In banking, the account balance is the amount of money you have available in your checking or savings account. Your account balance is the net amount available to you after all deposits and credits have been balanced with any charges or debits.

10 . The temperature of water in a glass if room temperature is 21 degrees Celsius if a glass is standing one in that room, because room temperature is commonly given as 20 to 22 degrees Celsius, however, if the air in the room goes through temperature variations,then a body of water will heat up or cool down,then the temperature of

the water in the glass tends to average out those temperature variations.

Answer:

20%

Step-by-step explanation:

Answer:

you will need 23 square feet because if you add it all up that's what you get

Answer:

-80

Step-by-step explanation:

This question involves order of operations.

Since all operators are multiply, we will evaluate them from left to right.

5 × -8 × 2

= - 40 x 2

= - 80

Answer:

-80

Step-by-step explanation:

Cross sectional data are collected from several entities at the same point in time.

In statistics and econometrics, cross-sectional data, often known as a cross section of a research population, is a type of data gathered by watching numerous participants all at once. It's also possible that the analysis disregards variations in time.

You evaluate a data set at a certain point in time when you conduct a cross-sectional data analysis. Cross-sectional data is frequently sourced from surveys and public records. The datasets document observations of various variables at a specific time.

In conclusion, the correct option is A.

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0.45  is the probability someone who studies very hard for the bar passe.

What is probability?

Odds of passing = 1.22  = p ( passing)/ P(not passing)

P(Pass)/P( fail)  = 1.22

p (pass) = 1.22 p (fail)

P(pass) + P(fail) = 1

1.22 p (fail) + p(fail) = 1

2.22 p(fail) = 1

P (fail) = 0.4505   ≅ 0.45

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Answer: (4, -4)

Step-by-step explanation: In the fourth quadrant, x = positive and y = negative, if you count the squares, 4 would be on the top and four would align to T on the bottom. Since x goes first, it would result in (4, -4)

According to the given statement  the perimeter of triangle xyz  = P = (3√5 + 5) units.

The analysis of geometry involving coordinate points is known as coordinate geometry (also known as analytical geometry). Finding this same distance between two points, dividing lines in the m:n ratio, locating a line's midpoint, and calculating the area of a triangle throughout the Cartesian plane are all feasible using coordinate geometry.

The distance of ZY

Z(1,0)

Y(3,1)

Substituting the the value if formula we get:

d = √((1 - 0)² + (3 - 1)²)

dZY = √5 units

Now ,

distance between XY

X(-1 , 4)

Y(3 , 1)

d = √((1 - 4)² + (3 + 1)²)

dZY = √25 units

      = 5 units.

The perimeter of the triangle:

P = ZX + ZY + XY

adding all that value we get:

P = (2√5 + √5 + 5)

P = (3√5 + 5) units.

According to the given statement  the perimeter of triangle xyz  = P = (3√5 + 5) units.

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Answer:

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

The options that are not functions from those given are; Options B and C.

The vertical line test is a method that is used to determine given relation is a function or not.

A) This table can be classified as a function because the input x-values have independent y-values as output. The only repeated output value is 7. Thus, we can say that it is likely a quadratic function with x-intercept as x = 2.

B) This cannot be a function because the same input values which is 6 has 2 different output values.

C) Similar to B above, this curve cannot be a function because some input values have 2 output values which is not a property of a function.

D) This is a function because of the wave and it is likely a trigonometric function.

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