Which linear inequality represents the solution set graphed?
A) 2y + 3x < 10
B) 2y + 3x > 10
C) 2y − 3x < 10
D) 2y − 3x > 10

Answer:

On her 60th birthday, she would have earned $83048.5.

Step-by-step explanation:

The formula to calculate the compound interest is:

[tex]A=P(1+\frac{r}{100} )^{n}[/tex]  --- (1)

where A is Principal and interest, r is the rate of interest and n is the number of years compounded.

For our problem,

P = 25000,

r = 0.05 and

n = 60 - 30 = 30

Substitute these values in (1), we get,

[tex]A=25000(1+0.05)^{30}[/tex]

[tex]=25000(1.05)^{30}[/tex]

= 25000(4.32194)

= 108048.5

Compound Interest = Amount - Principal

= 108048.5 - 25000

= 83048.50

Hence, on her 60th birthday, she would have earned $83048.5.

Answer:

The interest in 30 years be 8305000 cent.

Step-by-step explanation:

Formula

[tex]Amount = P(1+r)^{t}[/tex]

Where P is the principle , r is the rate of interest in the decimal form and t is the time.

As given

On her 30th birthday, Ann Marie opened a new compound interest account with $25,000.

The account pays 5% interest annually.

If Ann Marie retires on her 60th birthday and close the account at that time .

P = $25000

5% is written in the decimal form.

[tex]= \frac{5}{100}[/tex]

= 0.05

r = 0.05

As  Ann Marie open account on his 30 th birthday and close it at its 60 th birthday .

Thus

t = 60 - 30

t = 30 years

Put all the value in the formula

[tex]Amount = 25000(1+0.05)^{30}[/tex]

[tex]Amount = 25000(1.05)^{30}[/tex]

[tex]Amount = 25000\times 4.322 (Approx)[/tex]

[tex]Amount = \$ 108050[/tex]

As

Amount = Principle + Interest

Putting the value

$108050 = $25000+ Interest

$108050 - $25000 = Interest

Interest = $83050

As 1 dollar = 100 cent

Convert $83050 convert into cent .

$83050 = 83050 × 100

             = 8305000 cent.

Therefore the interest in 30 years be 8305000 cent.

Answer:

13 3/4 servings

Step-by-step explanation:

Stephen has  1  1/10 kg of tofu.

He uses 2/25 kg in each serving.

We will divide to figure out how many servings he can make

1 1/10 ÷ 2/25

We need to change the mixed number 1 1/10 to an improper fraction

1 1/10 = (10*1 + 1) /10 = 11/10

11/10 ÷2/25

Copy dot flip

11/10 * 25/2

275/20

Divide the top and bottom by 5

55/4

We will change this back into an improper fraction

4 goes into 55   13 times   with 3 left over

13 3/4

He can make 13  3/4 servings

Answer:

Harry is 2 years old and Jim is 6 years old.

Step-by-step explanation:

set up the equations. let harry be h and jim be j.

h+4=j

j+2=2(h+2)

plug in the j from the first equation.

you should get h=2 (harry is two years old)

if h+4=j, 2+4=j. so j=6 (jim is six years old)

Answer:

Harry is 2 years old and Jim is 6 years old.

Step-by-step explanation:

Let x years be Harry's age now and y years be Jim's age now.

1. In 4 years, Harry’s age will be x+4 years. If in 4 years, Harry’s age will be the same as Jim’s age is now, then

[tex]x+4=y.[/tex]

2. In 2 years, Jim's age will be y+2 years and Harry's age will be x+2 years. If in 2 years, Jim will be twice as old as Harry will be, then

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

Solve the system of two equations:

[tex]\begin{array}{l}x+4=y\\y+2=2(x+2).\end{array}[/tex]

Substitute y=x+4 into the second equation:

[tex]x+4+2=2(x+2),\\ \\x+6=2x+4,\\ \\6-4=2x-x,\\ \\x=2[/tex]

and [tex]y=2+4=6.[/tex]

Answer: 4 tickets

Step-by-step explanation: If $15.25 is Salar’s total and each ticket costs $3.50, we need to use division to figure out how many tickets Salar can purchase. When we divide 15.25/3.50, we get 4.35 (approximately). Salar can’t have .35 of a ticket, so we round down to 4 whole tickets.

The answer is C, -6, -√225, 4 7/8.

Rational means that the number can be expressed as a fraction and integer numerators and denominators. -6 and 4 7/8 can clearly be expressed as a fraction. -6 can be expressed as -6/1 and 4 7/8 can be expressed as 39/8.

-√225 is equivalent to -15, which is rational.

A is wrong because the number includes Pi.

B is wrong because -3.0541 never ends and √99 is irrational.

D is wrong because √21 is also irrational.

The Set C.  -6, -√225, 4 7/8 is the only set that contains all rational numbers.

The set of rational numbers consists of numbers that can be expressed as a fraction of two integers. To determine which set of numbers contains all rational numbers, we need to check if all the numbers in each set can be expressed as a fraction.

In set A, only 1/2 is a rational number.

In set B, -3.0541... and 0.14363 can be expressed as fractions, but √99 cannot.

In set C, -6, -√225, and 4 7/8 can all be expressed as fractions.

In set D, √21 is not a rational number, while 0 and 0.75 are rational numbers.

Therefore, set C is the only set that contains all rational numbers.

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Answer:

- 2  1/10

Step-by-step explanation:

-2/5 -x -9/10

Let x = 4/5

-2/5 - 4/5 - 9/10

Combine like terms

-6/5 - 9/10

Get a common denominator of 10

-6/5 * 2/2 - 9/10

-12/10 - 9/10

-21/ 10

Change this to a mixed number

10 goes into 21   2 times with 1 left over

-2 1/10

Answer:

- 2  1/10

Step-by-step explanation:

Answer:

Mean = £1.8 million

Step-by-step explanation:

The MEAN is the sum of all the numbers divided by the number of numbers.

Hence the mean is [tex]\frac{9}{5}=1.8[/tex] million

Answer:

A. x > 0

Step-by-step explanation:

As long as the number (x) is a number greater than 0, the inequality would be correct. Take for example, 1 (a number greater than 0)

4^1 = 4; 2^1 = 2; 4 > 2

Another example is 2

4^2 = 16; 2^2 = 4; 16 > 4

etc.

~

Answer:

A. x > 0

Step-by-step explanation:

see graph

4^x > 2^x

Replace 4 with 2^2

2^2^x > 2^x

a^b^x = a^(b*c)   so

2^ 2x > 2^x

If the bases are the same, the exponents must keep the same ratio

2x>x

This is true if x>0

I think, it's the symbol of the inches.

3" = 3 inches

or it's the second derivative of the function

[tex]\dfrac{d^2y}{dx^2}=f''(x)[/tex]

Answer: The second option represents a slope of 1/4

Step-by-step explanation:

To find slope, select two points along the line and plug them into this equation: (y2-y1)/(x2-x1)

We'll take the two points in the second graph and plug them into the equation above: (4-3)/(4-0)= 1/4

Therefore, the second option represents a slope of 1/4. Hope this helps:)

Answer:

(B) would be the best answer choice

Step-by-step explanation:

Answer:

x = 2 or x = 1 or x = -1 or x = 3/2   thus from the answers given only A: applies

Step-by-step explanation:

Solve for x over the real numbers:

2 x^4 - 7 x^3 + 4 x^2 + 7 x - 6 = 0

The left hand side factors into a product with four terms:

(x - 2) (x - 1) (x + 1) (2 x - 3) = 0

Split into four equations:

x - 2 = 0 or x - 1 = 0 or x + 1 = 0 or 2 x - 3 = 0

Add 2 to both sides:

x = 2 or x - 1 = 0 or x + 1 = 0 or 2 x - 3 = 0

Add 1 to both sides:

x = 2 or x = 1 or x + 1 = 0 or 2 x - 3 = 0

Subtract 1 from both sides:

x = 2 or x = 1 or x = -1 or 2 x - 3 = 0

Add 3 to both sides:

x = 2 or x = 1 or x = -1 or 2 x = 3

Divide both sides by 2:

Answer:  x = 2 or x = 1 or x = -1 or x = 3/2

Answer:

The answer is 2.4

Step-by-step explanation:

Divide 1.2x10^5 by 4.9x10^3 and you should get the answer of 2.44.

Hope this helps

Answer:

Please, see the answers in the attached files.

Step-by-step explanation:

Please, see the attached files.

Thanks.

Answer:

If there are 31 days in this month, it is January

Step-by-step explanation:

The converse of a statement is when you switch the conclusion with the hypothesis. If you do this, you get:

If there are 31 days in this month, it is January.

This is false btw. December has 31 days, and it's not January

The converse of the statement 'If it is January, then there are 31 days this month' is 'If there are 31 days this month, then it is January'. This is done by reversing the order of the 'if' (antecedent) and 'then' (consequent) parts of the statement.

The converse of the conditional statement 'If it is January, then there are 31 days this month.' is 'If there are 31 days this month, then it is January.'

In a conditional statement, the order of the 'if', known as the antecedent, and the 'then', known as the consequent, makes up the statement's direction. The converse of a conditional statement simply flips or reverses this order. It's important to note that the truth of the original statement does not guarantee the truth of its converse.

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The x in the formula is the depth.

You are given two different depths, replace x with the depths, solve for T, then subtract the to find the difference:

At 1200 meters the temperature is:

T = 4500/1200 = 3.75 degrees

At 3750 meters the temperature is:

T = 4500 / 3750 = 1.20 degrees.

The difference in temperature between the two depths is:

3.75 - 1.20 = 2.55 degrees C.

Answer:

a = 59

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable (a). Add 17 to both sides

a - 17 = 42

a - 17 (+17) = 42 (+17)

a = 42 + 17

Simplify. Combine like terms

a = 42 + 17

a = 59

59 is your answer

~

Solve for a (this means they want you to get "a" by itself in the equation)

So:

a - 17 = 42     Add 17 on both sides to get "a" by itself

a - 17 + 17 = 42 + 17

a = 59

Answer: His smallest age could be 16 years.

Step-by-step explanation:

Since we have given that

Four-fifths of his current age is greater than three-quarters of his age one year from now.

Let his present age be x

So, According to question,

[tex]\frac{4}{5}x>\frac{3}{4}(x+1)[/tex]

Take the equality,

[tex]\frac{4}{5}x=\frac{3}{4}(x+1)\\\\\frac{4}{5}x=\frac{3}{4}x+\frac{3}{4}\\\\\frac{4}{5}x-\frac{3}{4}x=\frac{3}{4}\\\\\frac{16x-15x}{20}=\frac{3}{4}\\\\\frac{x}{20}=\frac{3}{4}\\\\x=\frac{3\times 20}{4}\\\\x=15[/tex]

So, [tex]x>15[/tex]

Hence, Nearest and smallest integer greater than 15 is 16 .

Therefore, His smallest age could be 16 years.

Answer:

Answer: His smallest age could be 16 years.

Step-by-step explanation:

Since we have given that

Four-fifths of his current age is greater than three-quarters of his age one year from now.

Let his present age be x

So, According to question,

Take the equality,

So,

Hence, Nearest and smallest integer greater than 15 is 16 .

Therefore, His smallest age could be 16 years.

Answer: if talking square root, it is sqrt3/2. if talking decimals, it is about 0.87.

Answer:

Sine 60°= √3/2

=1.732/2

0.8660

Step-by-step explanation:

In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse).

From the triangle shown in the attachment

The sine of an angle =

Opposite/hypotenuse

Sine 60°= √3/2

=1.732/2

0.8660

Answer:c

Step-by-step explanation:

Answer: Hey he got it right it's C

Step-by-step explanation:

Answer:

[tex]p(x)=-x^3-2x^2+5x+6.[/tex]

Step-by-step explanation:

If a cubic polynomial has zeros [tex]x_1,\ x_2,\ x_3,[/tex] then it has a form

[tex]p(x)=a(x-x_1)(x-x_2)(x-x_3).[/tex]

In your case, zeros are -3, -1 and  2, then the polynomial is

[tex]p(x)=a(x-(-3))(x-(-1))(x-2),\\ \\p(x)=a(x+3)(x+1)(x-2).[/tex]

If [tex]p(0)=6,[/tex] then

[tex]p(0)=a(0+3)(0+1)(0-2)=6,\\ \\-6a=6,\\ \\a=-1[/tex]

and

[tex]p(x)=-(x+3)(x+1)(x-2)=-x^3-2x^2+5x+6.[/tex]

Answer:

B 2 < x < 6

Step-by-step explanation:

six times an integer is between 12 and 36.  Between does not include so we use <   not ≤

12 < 6x < 36

Divide all sides by 6

12/6 < 6x/6 < 36/6

2 < x < 6

Answer:

57

Step-by-step explanation:

6x?=5/8x15 3/4

Answer:

B $13

Step-by-step explanation:

Julie has 16.73  That is approximately 17 dollars

She buys a purse that is 4.12.   That is approximately 4 dollars

17 -4 = 13

She will have approximately 13 dollars left

Answer:

y = [tex]\frac{-2}{3} + 10[/tex]

Step-by-step explanation:

A line perpendicular to 2x = 1 - 3y has the same gradient (or slope). To find this we must isolate the y:

Move the -3y over to the other side making it a +3y:

3y + 2x = 1

Move the +2x over to the other side making it a -2x:

3y = -2x + 1

Divide everything by 3:

y = [tex]\frac{-2}{3}x + \frac{1}{3}[/tex]

So the gradient is [tex]\frac{-2}{3}[/tex]

Now as the points are given, (9 , 4)

The equation of the line so far is:

y = mx + c

4 = [tex]\frac{-2}{3}[/tex](9) + c

4 = -6 + c

Move the -6 over making it a +6:

4 + 6 = c

c = 10

So that means the full equation is:

y = [tex]\frac{-2}{3} + 10[/tex]

Answer:

C < A < B

Step-by-step explanation:

Answer:

Step-by-step explanation:The answer is C<A<B and the reason is is because angle A and C are the same and angle B is the largest.

Answer: y > x, y > 2

The horizontal line goes through 2 on the y axis. This boundary line is represented by the equation y = 2, since every point on this line has a y coord of 2. The shading above it means that the inequality is y > 2. Every point in the shaded region of y > 2 has a y coord that is larger than 2.

The other inequality is y > x because we shade above the dashed boundary line y = x, which is that slanted dashed line.

Combining the two regions of y > 2 and y > x leads to what is shown.

Final answer:

The question regarding systems of inequalities is incomplete, but linear inequalities like y < x or y > 2 can be graphically represented. The same is true for linear equations, with options A, B, and C all depicting linear forms.

Explanation:

The question which system of inequalities is shown seems to be missing some context or parts, but in general, inequalities can be represented on a graph and used to describe the relationship between variables. When dealing with linear inequalities, such as y < x or y > 2, these can be shown graphically with a line dividing the plane into two regions: one where the inequality is true and the other where it is false. For instance, y < x would be represented by a line that slopes upward to the right, and the region below this line (where y is less than x) is shaded. Similarly, for y > 2, a horizontal line is drawn at y=2, and the area above this line is shaded, indicating where y is greater than 2.

When looking at linear equations, all the options A. y = -3x, B. y = 0.2 + 0.74x, and C. y = -9.4 - 2x are indeed linear, as they can all be written in the form y = mx + b, where m and b are real numbers and represent the slope and y-intercept of the line, respectively.

Answer:

x =7

Step-by-step explanation:

Remark

Equation

(x + 2)/(x - 4) = (3x + 6)/ (x + 2)

Solution

I would begin this problem by taking out the common factor on the top right term. You'll see why in a second.

(x + 2)/(x - 4) = 3(x + 2)/ (x + 2)   Notice the two binomials on the right cancel.

Answer:

In the attachment.

Step-by-step explanation:

Rewrite [tex]x\geq-3y-6[/tex] as a [tex]y\geq -\frac{1}{3}x-2[/tex]. Then mark each set with different color and take the intersection of these.