The coordinate grid shows points A through K. Which points are solutions to the
system of inequalities listed below? (2 points)
2x + y < 10
2x - 4y > 8

EFGHJ

EFG

ACDM

AEF

The Coordinate Grid Shows Points A Through K. Which Points Are Solutions To Thesystem Of Inequalities

Answers

Answer 1

Answer:

E is the solution of the inequality

Coordinates of points A = (-5,4)B = (4,7)C= (-2,7)D= (-7,1)E= (4, -2)F = (1 , -6)G= (-3, -10)H= (-4 , -4)I= (9, 3)J= (7 , -4)K= (2 ,3)

putting the values of coordinates in equation to check for the solution.

For A

2x + y < 10

2(-5) + 4 < 10.

-10 - 4 < 10

-14 < 10 ( true)

2x - 4y > 8

2(-5) - 4(4) > 8

-10 - 16 > 8

-26 > 8

false..

it is not the solution of the equation.

similarly we can find for other coordinates.

E is the solution


Related Questions

En una tienda comercial anuncia descuentos sucecivos del 30% y 20% en todos los electrodomésticos, ¿Que descuento único equivale?

Answers

Answer:

0

Step-by-step explanation:

A farmer has only goats and hens in his farm,on a particular day,he sold 12 animals (goats and hens) and the total number of their legs was 32. how many goats and how many hens did he sell that day?

Answers

The number of goats sold is 4 and hens sold is 8.

What is an Equation ?

An equation is a mathematical statement which equates two algebraic expression with an equal sign.

Let the total number of goats sold be g

Let the total number of hens sold is h

g + h = 12

The total no. of legs of a goats sold will be 4g

and the total number of legs of a hens sold will be 2h

and it is given that

4g +2h = 32

The system of equation formed is

g + h = 12

4g +2h = 32

Multiplying equation (1) by 2 and then (1) - (2)

-2g = -8

g = 4

Therefore the number of goats sold is 4 and hens sold is 8.

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If 10% off is 20 what is 23% off?

Answers

23% off is 46 because 10%is 20 so 20% is 40 and 1% is 2 because 20/10 is 2 so the answe is 46
It would be 46
The person who answered is correct

Omar is going to an amusement park. The price of admission into the park is $25, and once he is inside the park, he will have to pay $5 for every ride he rides on. How much money would Omar have to pay in total if he goes on 8 rides? How much would he have to pay if he goes on r rides?

Cost with 8 rides:
Cost with r rides:
Need answer quickly!

Answers

Cost with 8 rides: 65
Cost with r rides: 25+(r x 5)

The cost of 8 rides will be equal to $65 and the equation for the r rides will be equal to $25 + $5(r).  

What is an equation?

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Price of admission into the park = $25

Price to pay for every ride in the park = $5

(a)

Then, the price to pay for 8 rides will be,

$25 + $5(8)

= $25 + $(40)

= $65

(b)

Then, the equation for the price to pay for r rides will be equal to,

$25 + $5(r)

Here, r is the number of rides.

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On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). a point is at (negative 3, 1). what is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)? y – 1=negative three-halves(x 3) y – 1=negative two-thirds(x 3) y – 1= two-thirds(x 3) y – 1= three-halves(x 3)

Answers

The equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)

Equation of a line

A line is the distance between two points. The equation of a line in point-slope form is expressed as:

y - y0 = m(x-x0)

Given the coordinates (-2, -4) and (2, 2) on the line, the slope is expressed as:

Slope = 2-(-4)/2-(-2)

Slope = (6)/4

Slope = 3/2

Find the equation of the line

y -(1) = 3/2(x-(-3))

y - 1 = 3/2(x+3)

Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)

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Answer:

d

Step-by-step explanation:

find the new prices after the given percentage increases.
a] £35 increased by 10%
b} £105.99 increased by 12%

Answers

Answer:

a] 38.5$
b] 118.71$

Step-by-step explanation:

A)35$ was increased by 10%
So:
10% of 35$
10/100 x 35 ($)
3.5$
So 35$ was increased by 3.5$ and the new price is 38.5$
B)105.99$ was increased by 12%
So:
12% of 105.99$
12/100 x 105.99$
=12.7188$
Let's round it to the nearest hundredths:
12.72$

So 105.99$ was increased by 12.72$ and the new price is 118.71$

HOPE IT HELPS :D
Tip: "of" means multiplication in Maths.

Expand & simplify
3(t+5)+5(t−6)

Answers

Answer:

8t - 15

Explanation:

⇒ 3(t+5)+5(t−6)

distribute inside parenthesis

⇒ 3(t) + 3(5) + 5(t) + 5(-6)

multiply the variables

⇒ 3t + 15 + 5t - 30

collect like terms

⇒ 3t + 5t + 15 - 30

add/ subtract like terms

⇒ 8t - 15

Solution: 8t-15

Detailed explanation:

First the problem asks us to expand

[tex]\tt 3(t+5)=3\cdot t +3\cdot5=3t+15[/tex]

Similarly

[tex]\tt 5(t-6)=5\cdot t -5\cdot 6=5t-30[/tex]

Therefore

[tex]\tt 3t+15+5t-30[/tex]

Upon combining like terms

[tex]\tt 8t+15-30[/tex]

Upon doing this further

[tex]\tt 8t-15[/tex]

Choose the correct simplification of the expression (2x7y)2(y5)3.

Answers

The correct simplification of the expression is  4x¹⁴y¹⁷

Given,

The expression is (2x⁷ y)² (y⁵)³

To distribute the exponent, apply the power rule (ab)ⁿ = aⁿbⁿ

Implement the product rule to (2x⁷y)².

Here, we have a = 2x⁷ , b = y and n = 2

=(2x⁷)² y²(y⁵)³

= 2²(x⁷)² y²(y⁵)³

= 4(x⁷)² y²(y⁵)³

Now exponents should be multiplied while using the product rule.

The product rule is (aˣ)ⁿ = aˣⁿ

We apply this to (x⁷)² and (y⁵)³

So the expression becomes,

=4x⁷·² y² (y⁵·³)

= 4x¹⁴ y² y¹⁵

∵ In exponents we have a rule that if bases are same then powers are added i.e, aˣ aⁿ = aˣ⁺ⁿ

∴ 4x¹⁴ y¹⁵ ⁺ ²

= 4x¹⁴ y¹⁷

Hence we get the answer as 4x¹⁴ y¹⁷

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In 20 years charlie will be three times as old as he is now.how old is charlie is he now

Answers

Answer:

10 years old

Step-by-step explanation:

let his age be x , then in 20 years

x + 20 = 3x ( subtract x from both sides )

20 = 2x ( divide both sides by 2 )

10 = x

Charlie is 10 years old

The solution to an inequality is graphed on the number line.

A number line going from negative 5 to positive 5. A solid circle appears between positive 4 and positive 5. The number line is shaded from the circle to negative 5.
What is another way to represent this solution set?

{x | x < 4.5}
{x | x ≤ 4.5}
{x | x > 4.5}
{x | x ≥ 4.5}

Answers

The correct answer is option B which is {x | x ≤ 4.5}

What is a number line?

A number line is a representation of a graduated straight line used to represent real numbers in introductory mathematics.

Because the arrow is pointing to the left, the answer to the solution set needs to be less than the number the dot is on.

A solid dot on a number means that that number is included in the solution set.

In the picture the solid dot is on 4.5, so the solution set needs to be equal to or less than 4.5.

Therefore the correct answer is option B which is {x | x ≤ 4.5}

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i need help i don’t know how to solve these!

Answers

Its actually pretty simple, all you do is graph both inequalities and wherever both of the shaded areas overlap is where all of the solutions will be. Hope this helps

Please help me I am stuck

Answers

so the answer to one is simply 132, because all you have to do it replace t with 0.5, and then evaluate.

the answer to the first part of second question is -64/32 or -2 because all you have to do is find the vertex, which is the point of maximum height. the formula for this -b/2a.
the answer to the second part is 160 because to find the height at the vertex just plug the x coordinate of the vertex in and evaluate. this will give you the maximum height

I WILL GIVE BRAINIEST
Line AB and Line CD bisect each other at point E. If AE = 3x - 10y + 123, BE = -2x - 7y + 122, CE = 9x + 10y - 171, and DE = 3x + 20y - 249, what are the values of x and y?

Answers

The values of x and y are 7 and 12 respectively

Solving simultaneous equations

From the question, we are to determine the values of x and y

From the given information,

Line AB and Line CD bisect each other at point E

Then, we can conclude that

AE = BE

and

CE = DE

From the given information,

AE = 3x - 10y + 123

BE = -2x - 7y + 122

CE = 9x + 10y - 171

DE = 3x + 20y - 249

Then, we can write that

3x - 10y + 123 = -2x - 7y + 122

Simplifying

3x +2x -10y + 7y = 122 -123

5x -3y = -1 ----------- (1)


Also,

9x + 10y - 171 = 3x + 20y - 249

Simplifying

9x -3x +10y -20y = -249 + 171

6x -10y = -78 --------- (2)

Now, solve equations (1) and (2) simultaneously

5x -3y = -1 ----------- (1)

6x -10y = -78 --------- (2)

Multiply equation (1) by 10 and equation (2) by 3

10 × ( 5x -3y = -1

3 × ( 6x -10y = -78

50x -30y = -10 ----------- (3)

18x -30y = -234--------- (4)

Then, subtracting equation (4) from equation (3), we get

50x -18x -30y-(-30y) = -10-(-234)

32x -30y + 30y = -10 + 234

32x = 224

∴ x = 224/32

x = 7

Put the value of x into equation (1), to find y

5x -3y = -1

5(7) -3y = -1

35 -3y = -1

35 + 1 = 3y

36 = 3y

∴ y = 36/3

y = 12

Hence, the values of x and y are 7 and 12 respectively

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The first step in determining the solution to the system of equations, y = -x2 - 4x - 3 and y = 2x + 5, algebraically is to set the two equations equal as -x2 - 4x -3 = 2x + 5. What is the next step?

Answers

Answer:

See below

Step-by-step explanation:

Next step is to gather 'like' terms

-x2 - 4x -3 = 2x + 5.

x^2 + (4x + 2x)   + (3+5)    = 0       then simplify

x^2 + 6x + 8     = 0        then factor

(x+4)(x+2) = 0  

so either of these terms = 0

x+4 = 0    means   x = -4

x+ 2 = 0 means  x = - 2          

Answer:

d

Step-by-step explanation:

Combine like terms onto one side of the equation.

Match each pair of equivalent values.

1 .
1
square root of 16
2 .
12
square of 8
3 .
4
4 2
4 .
64
1 2
5 .
16

6 .
2

Answers

Answer:

1 - [tex]1^{2}[/tex]

12 - ?

4 - square root of 16

64 - [tex]8^{2}[/tex]

16 - [tex]4^{2}[/tex]

2.828 - square root of 8

Step-by-step explanation:

I need more terms to match

Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.

What are mathematical values?

A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42. Every integer or even other mathematical object set to a variable or constant is that object's value.

A mathematical expression's value is the outcome of a computation it describes when its variables and constants are given values. The amount that the function assumes for these argument numbers is the result of a function, assuming the value(s) provided to its argument(s).

Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.

Therefore, Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.

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What are the roots of the polynomial equation x cubed minus 5 x 5 = 2 x squared minus 5? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth.

Answers

The solution to the equation of the polynomial function x³-5x+5 = 2x²-5  is (c) –2.24, 2, 2.24.

What is Polynomial Equation?

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here, The function is given as:

         x³-5x+5 = 2x²-5

Split the function.

So, we have:

   y = x³-5x+5

   y = 2x²-5

Using a graphing calculator, we have the x coordinate at the point o intersection of both equations to be

x = –2.24, 2, 2.24

Hence, the solution to the equation is (c) –2.24, 2, 2.24

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Raya buys a van for £9500 plus VAT at 20%
Raya pays a deposit for the van.
She then pays the rest of the cost in 12 equal payments of £665 each month.
Find the ratio of the deposit Ray pays to the total of the 12 equal payments.
Give your answer in its simplest form.

Answers

Step-by-step explanation:

yo thara bhai joginder tu he ek bndr

assume that y varies inversely with x. If y= 1.6 when x= 0.5, find x when y= 3.2

Answers

Answer:

x = 0.25

Step-by-step explanation:

If y varies inversely with x, then:

[tex]y \propto \dfrac{1}{x} \implies y=\dfrac{k}{x} \quad \textsf{(for some constant k)}[/tex]

Given:

y = 1.6 when x = 0.5

Substitute the given values into the found equation and solve for k:

[tex]\implies 1.6=\dfrac{k}{0.5}[/tex]

[tex]\implies k=1.6(0.5)[/tex]

[tex]\implies k=0.8[/tex]

Therefore:

[tex]y=\dfrac{0.8}{x}[/tex]

To find the value of x when y = 3.2, substitute y = 3.2 into the found equation and solve for x:

[tex]\implies 3.2=\dfrac{0.8}{x}[/tex]

[tex]\implies x=\dfrac{0.8}{3.2}[/tex]

[tex]\implies x=0.25[/tex]

How many complex roots does the equation 0=3x5−x4−5x2+1 have?

Answers

the equation has 5 complete roots

5

The given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.

What is a polynomial?

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The given polynomial equation below is:

0 = 3x⁵ − x⁴ − 5x² + 1

3x⁵ − x⁴ − 5x² + 1 = 0

The given polynomial equation is a polynomial of degree 5.

The simplest method is to solve it graphically using a graphing program.

Clearly, the polynomial equation is a degree 5 equation, hence it has a maximum of 5 roots.

We may now locate the roots of the equation using the graph.

Since there are 3 real roots, the remaining are two complexes, so there are 2 complex roots

Hence, the given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.

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The​ _____ _____, denoted ​, is given by the formula ​_____, where x is the number of individuals with a specified characteristic in a sample of n individuals.

Answers

The sample proportion denoted [tex]\hat{p}[/tex] is given by the formula [tex]\hat{p} = \frac{x}{n}[/tex], where, x is the number of individuals with a specified characteristic in a sample of n individuals.

What is a sample proportion?

A sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

Mathematically, sample proportion can be calculated by using this formula:

[tex]\hat{p} = \frac{x}{n}[/tex]

Where:

x is the number of individuals with a specified characteristic.n is the total number of individuals in a sample.

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The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete two rotations every minute.

Write a sine model, y = asin(bt) + k, for the hight (in feet) of the end of one blade as a function of time t (in seconds). assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.

Options are displayed in the picture

Answers

Answer:

D: y= 10sin([tex]\frac{\pi }{15}t[/tex]) + 30

Step-by-step explanation:

30 feet above the ground is the k value.

10 feet long is how long the blades reach up and down which is also known as the amplitude.

The rest is given in all answers.

a recursive formula for the sequence 18,9,4.5,... is

Answers

Answer:

A1 = 18

A(n) = A (n-1) -2

Step-by-step explanation:

N represents the number in a sequence and the difference in the sequence is -2 since each time the number is listed in the sequence it is divide by 2.

How many factors does 16 have

Answers

Answer:

5

Step-by-step explanation:

1,2,4,8,16 total 5 factors

there are 4 factors of 16 and those are 1, 2, 4, and 8

Graph the function.
For the function whose graph is shown below, which is the correct formula for the function?

Answers

Answer:

[tex]\displaystyle{y=-3x-1}[/tex]

Step-by-step explanation:

I have two methods: standard-learning which will explain overall mathematically - basically formula, etc. - while the other one trick-tips method will rely on choices rather mathematical calculations but with explanation on why and how.

Standard-Learning

First, let’s pick two points that are integers since they are easily to be found via graphs. We see that (-1,2) and (0,-1) is a part of the graph so now we finally have picked two points for our calculations.

When we have finally picked two points, we will be using them for slope calculation. This part is crucial for finding an equation of a line because a line has to contain slope in its equation.

To calculate the slope, we use rise over run formula which is:

[tex]\displaystyle{\dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Note that [tex]\displaystyle{\Delta}[/tex] is delta - in both mathematic and physics, it means changes in.

So, we will be using those two points that we have picked to substitute in the slope formula. Let’s determine that [tex]\displaystyle{(x_2,y_2)=(-1,2)}[/tex] and [tex]\displaystyle{(x_1,y_1)=(0,-1)}[/tex].

Therefore, our slope will be:

[tex]\displaystyle{m=\dfrac{2-(-1)}{-1-0}}\\\\\displaystyle{m=\dfrac{2+1}{-1}}\\\\\displaystyle{m=-3}[/tex]

Next, find the y-intercept. From the graph, we see that the graph intercepts at (0,-1) which is y-intercept so we will only use y-value. Hence, b = -1.

From the slope-intercept form:

[tex]\displaystyle{y=mx+b}[/tex]

Substitute m (slope) = -3 and b (y-intercept) = -1. Hence, the equation of line is:

[tex]\displaystyle{y=-3x-1}[/tex]

Fast Way (Trick-Tips)

Relying on choices and knowledge of graph, notice that there are slopes of 3 and -3.

Keep in mind that if slope is negative, it will decrease down and if slope is positive, it will increase up.

Therefore, cut off all choices with positive slopes which are 1 and 3. We are now left with 2 and 4.

Next, look at the graph and tell its y-intercept. It intercepts y at y = -1 so we take value of -1.

So choice 4 is cut off and now we have choice 2 as the answer.

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Gerald purchased a rectangular plot of land. the length of the plot is 20 feet more than the width. the cost of the land was $12 per square foot. gerald also had a fence put around the entire perimeter of the plot, at a cost of s8 per linear foot. the total amount he spent on both the land and the fence was $10,560. part a write an equation in two variables for the perimeter, p, and an equation in two variables for the area, a, of the plot of land where x is the width of the plot in feet. provide evidence to support your equations

Answers

Answer:

P =2(x+ y) [tex]ft[/tex].

A =xy [tex]ft^{2}[/tex]

Step-by-step explanation:

perimeter of rectangle (P)= 2(L+B

Area of rectangle (A)        =    L×B

Given,

width = 'x'

length = y = x+20

therefore using above formula

P = 2(x+20 + x) = 2(2x+20)

A = (x+20)(x)

cost of land per square foot = $12

cost of land per linear foot   = $8

total cost of land                   = $10560

now,

P×8 + A×12   = 10560

2(2x+20)×8 +  (x+20)(x)×12 = 10560

32x + 320 + 12x²+ 240x     = 10560

12x² + 272x                         = 10240

12x² + 272x - 10240           = 0

solving this quadratic equation using Discriminant method

x = [-b ±√(b² - 4ac)]/2

where b is the coefficient of x

a is the coefficient of x²

and c is the constant term

by replacing values in the above formula

x = 19.5  , x = -42.24

as the area cannot be negative therefore -42.24 is neglected

hence x = 19.5ft

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In AABC, what is the value of x?

Answers

Answer:

x = 6.5

Step-by-step explanation:

* since it's a triangle ALL the angles inside should give you 180° * Equate everything to 180°

8x + 10x - 10°+ 10x + 8° = 180°( sum of angles on a triangle)

28x - 2° = 180° * group like terms*

28x = 182°

x = 6.5



15. 3x-5=3
16. 3(x-2) = 4(x + 3)
17. +3=
18. 2==
19. 4-2-3
X+2
20.-2-3-3
21. 쭉 = 큭
22. 2x-5-1=3-x
3. 2x + ==3(x-1)
4. 10x-1=x+4
5. k=8k-2
6. -x + 2 = 3x-27
4
7. 1-6x = -x +
B.
9. 2-(x + 1) = 2 + 5x
D. 2(1-x) = 10 - (x + 2)
. 9x - (4x - 5) = 3x - 11
x-9=3(x + 1)
-xx-2)-4=x+6▸
+ 2x
6(5-4x) = -4(5x + 11)

Answers

Answer:

tgnjfgznjE XVNJ

Step-by-step explanation:

rtjtejWEJAREfnndzjt

Answer:

15. 2.66

16. - 18

17. Impossible

18. Impossible

19. - 1

20. - 8

21.

Use the fraction model to multiply: three multiplied by five sevenths. Leave your answer as an improper fraction. (1 point)

three fraction models, each model is partitioned into seven equal parts, with five parts shaded in each model
eight sevenths
eight tenths
fifteen twenty ones
fifteen sevenths

Answers

The product of three and five-sevenths is given by (D) Fifteen sevenths.

In fraction multiplication, we multiply the corresponding position like we multiply numerator with numerator and denominator with another denominator.

The denominator for a whole number is always 1.

Here given the numbers are three and five-sevenths, that is [tex]3,\frac{5}{7}[/tex].

So here since 3 is a whole number then the denominator of it is 1.

We can write 3 as [tex]\frac{3}{1}[/tex].

So product [tex]=\frac{5}{7}\times\frac{3}{1}=\frac{5\times3}{7\times1}=\frac{15}{7}[/tex]

Using the fraction model we get,

Here we can see that there are three bars with seven divisions in which fives are shaded.

So in multiplication with three we have to take the shaded region as the numerator and have to all the shaded and total bar for once.

here a total number of divisions in one bar is 7, so the denominator of the product is 7.

A total number of shaded divisions is 15, so the numerator of the product is 15.

So the product is [tex]\frac{15}{7}[/tex], that is fifteen sevenths.

Hence the correct option is (D) Fifteen sevenths.

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What statement is true for f(x) = 3.2^x?

Answers

Answer:

Step-by-step explanation:

A 4-digit combination lock can be opened only if a correct combination of digits from 0-9 is chosen. Find the probability of guessing the correct combination if: none of the digits are repeated, any of the digits can be repeated, any of the digits can be repeated but the 3 and 8 are not in the combination.

Answers

The probabilities are as follows:-

if none of the digits is repeated 0.504If any of the digits can be repeated 1If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The probability will be calculated as follows:-

Total combinations are = 10⁴ = 10000

A) if none of the digits are repeated:-The combinations will be 10 x 9 x 8 x 7 = 5040

Probability =  5040 /  10000

Probaility = 0.504

B) If any of the digits can be repeated:- The combinations will be 10 x 10 x 10 x 10 = 10000

Probabilityy = 10000 / 10000 = 1

C )If any of the digits can be repeated but the 3 and 8 are not in the combination the combinations will be 7 x 7 x 7 x 7 = 2401

Probability = 2401 / 10000 = 0.24

Therefore if none of the digits is repeated 0.50.If any of the digits can be repeated 1.If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.

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