Examine the following system of inequalities.
{y > −x + 4 and y ≤−(1/2)^x + 6
Which graph shows the solution to the system?

Dotted linear inequality shaded below passes through (negative 4, 0) and (0, 4). Solid exponential inequality shaded above passes through (negative 1, 8) & (0, 7).

Dotted linear inequality shaded below passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5).

Dotted linear inequality shaded above passes through (negative 4, 0) and (0, 4). Solid exponential inequality shaded below passes through (negative 1, 8) & (0, 7).

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5).

Answer:

40

Step-by-step explanation:

6*6/6*-2i/2i*6/2i*-2i

Answer:

40

Step-by-step explanation:

Answer:

X=1

Step-by-step explanation:

1. You subtract 6x with 9x so it should equal 2=3x-1

2.You add 1 to the 2 so it should be 3=3x

3.You divide 3 on both sides so it should be 3/3=3x/3

4.After you divide you finally get the answer 1=x or x=1

6x + 2 = 9x - 1

6x - 9x = - 1 - 2

-3x = -3

x = -3/-3

x = 1

Prove:

Let x = 1

6x + 2 = 9x - 1

6(1) + 2 = 9(1) - 1

6 + 2 = 9 - 1

8 = 8

It checks to be true.

The answer is x = 1.

Answer:

A. (x - 10)(x - 4)

Step-by-step explanation:

The product is 0 if one of the factors is 0.

(4 - 10)(4 - 4)

= (4 - 10)*0

= 0

Answer:

A. (x - 10)(x - 4)

Step-by-step explanation:

Let x=4

O A. (4 - 10)(4 - 4) = -6 * 0 = 0

OB. (4 + 4)(4 - 10) = 8* -6 = -48

O C. (4 + 6)(4 - 2) = 10 * 2 = 20

OD. 4*4(4-6)=16*-2 = -32

1,2

1,3

1,4

1,5

2,1

2,3

2,4

2,5

3,1

3,2

3,4

3,5

4,1

4,2

4,3

4,5

5,1

5,2

5,3

5,4

20 looks like the number.

Please Vote my answer brainliest. thanks!

Answer:

This is an acute triangle

Step-by-step explanation:

Pythagoras theorem is used to determine if a triangle is right, acute or obtuse

If the sum of squares of two shorter lengths is greater than the square of third side then the triangle is an acute triangle.

If the sum of squares of two shorter lengths is less than the square of third side then the triangle is an obtuse triangle.

If the sum of squares of two shorter lengths is equal the square of third side then the triangle is a right triangle.

so,

[tex](40)^2 = (37)^2 + (24)^2\\1600 = 1369+576\\1600<1945[/tex]

As 1600<1945, the given triangle is an acute triangle ..

Answer:

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Step-by-step explanation:

We have with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.

We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).

So,

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Answer:

74mm

Step-by-step explanation:

296 divided by 4 sides is 74 mm each side

Answer:

Difference = 2.25°

Step-by-step explanation:

Here we are given that at depth the Temperature T is inversely proportional to the depth x.

[tex]T[/tex] ∝ [tex]\frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{x}[/tex]

Where 4500 is constant

Now we have to find the difference in the temperature at 1200 mts and 3750 mts

1. x=1200

[tex]T= 4500 \times \frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{1200}[/tex]

[tex]T= 3.75[/tex]

2. x=3750

[tex]T= 4500 \times \frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{3750}[/tex]

[tex]T=1.2[/tex]

Hence Difference is

T = 3.75 -1.20

= 2.25

Therefore The difference of the temperature at 1200 mts and 3750 mts is T=2.25°

Answer:

66 in^2.

Step-by-step explanation:

We  can use the formula for the area of a trapezoid:

Area = (h/2) (a + b) where h = the height and a and b are the lengths of the opposite parallel lines.

so the Area of ABCD = (6/2)*(10 + 12)

= 3 * 22

= 66 in^2.

For this case we have that the area of the figure is given by the sum of the area of a rectangle plus the area of a triangle.

By definition, the area of a reactangle is given by:

[tex]A = a * b[/tex]

Where:

a, b:they are the sides of the rectangle.

According to the figure we have:

[tex]a = 10\\b = 6[/tex]

Substituting we have:

[tex]A = 10 * 6\\A = 60[/tex]

Thus, the area of the rectangle is [tex]60in ^ 2[/tex]

On the other hand, the area of a triangle is given by:

[tex]A = \frac {b * h} {2}[/tex]

Where:

b is the base and h is the height of the triangle.

According to the figure we have to:

[tex]b = 12-10 = 2\\h = 6[/tex]

Substituting in the formula:

[tex]A = \frac {2 * 6} {2} = \frac {12} {2} = 6[/tex]

Thus, the area of the rectangle is[tex]6in ^ 2[/tex]

Then, the total area of the figure is:

[tex]A_ {T} = 60in ^ 2 +6in ^ 2 = 66 \ in ^ 2[/tex]

Answer:

[tex]66 \ in ^ 2[/tex]

Answer:

Definition of Point by Gray:

    A point is a location in a region.

→A point is smallest and simplest representation of any location or any thing or an object in two, three, or n-dimensional plane.

This can be explained in following way.

For a large enclosed room , Lighting a small bulb will represent a point.Similarly , stars in the sky appear as a point with respect to earth.Sun in the Universe can be  called as a point.

Answer:

A

Step-by-step explanation:

The statement uses the terms location and region that are defined based on an understanding of a point.

Brainliest Please

Have a nice day *smiley face emoji

Answer:

The other coordinate for the given equation is 34.

Step-by-step explanation:

We are given the following equation and we are to fin the value of the y coordinate given that the value of the x coordinate is [tex] 8 [/tex]:

[tex] y = \frac { 7 } { 2 x + 6 } [/tex]

Substituting the given value of x in the above equation to find y:

[tex]y = \frac { 7 } { 2 } ( 8 ) + 6 [/tex]

y = 34

(8, 34)

[tex]3x^2 - x+ 7 =0\\\Delta=(-1)^2-4\cdot3\cdot7=1-84=-83\\x\in\emptyset[/tex]

no real solutions

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = 4(x - 10) ← is in point- slope form

with slope m = 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex]

The perpendicular line passes through (- 3, 7), hence

y - 7 = - [tex]\frac{1}{4}[/tex](x - (- 3)), that is

y - 7 = - [tex]\frac{1}{4}[/tex](x + 3) → D

Answer:

[tex]\large\boxed{B.\ x=1,\ C.\ x=-\dfrac{5}{3}}[/tex]

Step-by-step explanation:

[tex]2x-5=-3x^2\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2+2x-5=0\\\\3x^2+5x-3x-5=0\\\\x(3x+5)-1(3x+5)=0\\\\(3x+5)(x-1)=0\iff3x+5=0\ \vee\ x-1=0\\\\3x+5=0\qquad\text{subtract 5 from both sides}\\3x=-5\qquad\text{divide both sides by 3}\\x=-\dfrac{5}{3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]

M= 1488

This is how many number of minutes Justin has used his phone in a month.

I solved this by first subtracting 24 from 113.28, which is 89.28.

Next I knew multiplication would have to be involved.

I had to figure out 0.06 times what equals 89.28.

Well that would be 1488.

Please Vote my answer brainliest. thanks!

Based on the given monthly fee and per-minute charge for Justin's phone, if the minimum monthly charge is $113.28, this indicates that he has used his phone for at least 1488 minutes in that month.

To solve this question, we can start by setting up an inequality because we want to find the possible numbers of minutes Justin can use his phone. Given that Justin pays a monthly fee of $24 and $0.06 per minute of use, the total charge (T) in a month is given by the equation:

T = 24 + 0.06m

It is stated that the least he has been charged in a month is $113.28. To find the possible number of minutes, we need to solve this inequality for m:

113.28 <= 24 + 0.06m

If we subtract $24 from each side, it becomes:

89.28 <= 0.06m

Then by dividing each side by 0.06, we get:

m >= 1488

So, Justin has used his phone for at least 1488 minutes in a month.

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Answer:

X = 21

Step-by-step explanation:

X- 12 = 9

Add 12 to each side

X- 12+12 = 9+12

X = 21

Answer:

The function is defined along the x-axis. Yes the equations y = 0 is a function

Step-by-step explanation:

It means that  y  is  0  in all values of  x

The graph y = 0 would be a horizontal line that overlaps the x-axis. This would be a function because the y-value (zero) never has the same x-value.  This means that it would pass the vertical line test since the graph would only pass through it once.

Hope this helped!

~Just a girl in love with Shawn Mendes

Denise has conducted an observational study to learn about different influences that affect which colleges students choose to attend. Denise surveyed 400 students at her new college and found that 80% of the students chose their college based on a friend who also attends that college.

What conclusion can Denise make from her study?

A. There may be a link between knowing current students and choosing a college, and she can draw a cause-and-effect conclusion from an observational study.

B. There may be a link between knowing current students and choosing a college, but she cannot draw a cause-and-effect conclusion from an observational study.

C. Knowing a current student enrolled at a college causes incoming students to choose that college, but she cannot draw a cause-and-effect conclusion from an observational study.

D. Knowing a current student enrolled at a college causes incoming students to choose that college, and she can draw a cause-and-effect conclusion from an observational study.

The conclusion that Denise can make from her observational study is B. There may be a link between knowing current students and choosing a college.

An observational study is a study that observes individuals and measures variables of interest but doesn't influence the responses.

In this case, Denise has conducted an observational study to learn about different influences that affect which colleges students choose to attend.

Here, the conclusion that Denise can make from her study is that there may be a link between knowing current students and choosing a college even though she cannot draw a cause-and-effect conclusion from the study.

Learn more about an observational study on:

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Answer:

a -1.8

Step-by-step explanation:

f(x)=y=0

when y = 0, x=-1.8

Answer:

A. [tex]-1.8[/tex]

Step-by-step explanation:

We have been graph of a function. We are asked to find the value of x, when [tex]f(x)=0[/tex].

We know that [tex]f(x)=0[/tex] stands for x-intercept. [tex]f(x)[/tex] stands for value of y. We know that y is zero on x-axis.

Upon looking at our given graph, we can see that our function has only one x-intercept that is at point [tex](-1.8,0)[/tex].

This means that [tex]f(-1.8)=0[/tex], therefore, the value of x is [tex]-1.8[/tex] and option A is the correct choice.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y+2=\frac{1}{5}(x-1)[/tex]  

This is the equation of the line into point slope form

The point is (1,-2) and the slope  is m=1/5

we know that

To correctly identify the graph find out the x and y intercepts of the graph

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

[tex]y+2=\frac{1}{5}(0-1)[/tex]

[tex]y=-\frac{1}{5}-2[/tex]

[tex]y=-\frac{11}{5}=-2.2[/tex]

The y-intercept is the point (0,-2.2)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0+2=\frac{1}{5}(x-1)[/tex]

[tex]10=x-1[/tex]

[tex]x=11[/tex]

The x-intercept is the point (11,0)

To graph the line plot the intercepts and join the points

see the attached figure

The absolute value of  I-32I = 32

For given question,

We need to find the absolute value of -32

We know that, for any number 'a',

the absolute value of a is |a| = a (positive value)

|-32| = 32

Therefore,  the absolute value of  I-32I = 32

Learn more about the absolute value here:

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Answer:

2750

Step-by-step explanation:

5500 ÷ 2 (multiplying by 50% is the same as dividing by 2)= 2750

50% of 5500 commuters is calculated as 2750. Hence, 2750 commuters carpool to work.

To find the number of commuters who carpool, we'll use a very basic principle in mathematics: percentage calculation. The problem states that 50% of the 5500 commuters carpool to work. To find the number of commuters carpooling, we multiply the total number of commuters by the percentage of those who carpool. In mathematical terms, it looks like this:(50/100) * 5500 = 2750. Therefore, 2750 commuters carpool to work.

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Answer:

x = 50.9

Step-by-step explanation:

35.6 = √(15.3²) + √(x²)

35.6 = 15.3 + x

x = 35.6 + 15.3

x = 50.9

Answer:

When the hot tub is half full, there are 400 gallons of water in it.

Step-by-step explanation:

If 75% or 3/4 of the hot tub is 600 gallons and you need to find 50% or 1/2. Divide 600 by 3 to get 200 then simply multiply by 2 to get 400.

When the hot tub is half full, it would contain 400 gallons of water.

To find out how many gallons are in the hot tub when it's half full, calculate the total capacity of the hot tub using the information that 75% equals 600 gallons. Then, take 50% of that total capacity to find that when the hot tub is half full, it contains 400 gallons.

If a hot tub is 75 percent full with 600 gallons of water, that means the hot tub's total capacity when it's 100% full is larger than 600 gallons. To find out how many gallons are in the hot tub when it's half full, we must first determine the hot tub's total capacity. We can set up a proportion to find the total capacity (T) since 75% of T is 600 gallons.

75% of T = 600 gallons

0.75  imes T = 600 gallons

Now, to find the total capacity (T), divide both sides by 0.75:

T = 600 gallons / 0.75

T = 800 gallons

So, the hot tub's total capacity is 800 gallons. To find the amount of water when the hot tub is half full, simply take 50% of the total capacity:

50% of 800 gallons = 0.5  imes 800 gallons

50% of 800 gallons = 400 gallons

Therefore, when the hot tub is half full, it would contain 400 gallons of water.

Answer:

C. 10,4

Step-by-step explanation:

Using the Law of Cosines [Solving for Angle Measures → cos<A = -a² + b² + c²\2bc, cos<B = a² - b² + c²\2ac, cos<C = a² + b² - c²\2ab; Solving for Sides → a² = b² + c² - 2bc cos<A, b² = c² + a² - 2ac cos<B, c² = b² + a² - 2ab cos<C], set up your triangle with your angles and sides OPPOSITE from each other.

Suggestion: make Side b 12 and Side a 6, leaving you with Side c to find. According to the problem and how you set up your triangle, <C can be 60°. This is how you should set it up:

c² = 36 + 144 - 144 cos 60°; 108 = c²

The reason being is because 6² is 36, 12² is 144, 2ab → 2[12][6] is 144, and cos 60° is ½. Putting this altogether will give you 108 = c². Obviously, the final step is to take the square root of 108, which rounded to the nearest tenth, is 10,4.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

**Whenever you are solving for an angle using the Law of Cosines, towards your final answer, use the cos⁻¹ function to cancel the cos to isolate your angle measure.

Final answer:

Using the law of cosines with the given sides 6 cm and 12 cm and included angle of 60 degrees, the length of the third side is approximately 10.4 cm, corresponding with answer choice C.

Explanation:

To calculate the length of the third side of a triangle when two sides and the included angle are known, we can use the law of cosines. The law of cosines states that c² = a² + b² - 2abcos(C), where a and b are the lengths of the sides, C is the included angle, and c is the length of the third side opposite to angle C.

In this question, we have been given two sides of lengths 6 cm and 12 cm with an included angle of 60 degrees. Plugging these values into the law of cosines formula, we get c² = 6² + 12² - [tex]2\(\cdot\)6\(\cdot\)12\(\cos(60^\circ)\)[/tex].

Since [tex]\(\cos(60^\circ)\)[/tex] equals 0.5, the calculation simplifies to c² = 36 + 144 - 72 = 108. Taking the square root of both sides, we find that c ≈ 10.4 cm, which aligns with answer choice C.

Answer:

A) h(x)=9x-13

Step-by-step explanation:

f(x) = 2x - 1  

g(x) = 7x -12

Add them together

f(x) = 2x - 1  

g(x) = 7x -12

-------------------------

f(x)+g(x) = 9x-13

h(x) = 9x-13

Answer:

A

Step-by-step explanation:

I took the test

The answer is D!!!

y=6x^2-24x+16

Answer:

Option 4 - [tex]y=6x^2-24x+16[/tex]

Step-by-step explanation:

Given : The vertex form of the equation of a parabola is [tex]y=6(x-2)^2-8[/tex]

To find : What is the standard form of the equation?

Solution :

The vertex form of the equation of a parabola is [tex]y=6(x-2)^2-8[/tex]

We solve the equation to get standard form,

[tex]y=6(x^2-2^2-2(x)(2))-8[/tex]

[tex]y=6(x^2+4-4x)-8[/tex]

[tex]y=6x^2+24-24x-8[/tex]

[tex]y=6x^2-24x+16[/tex]

The standard form of the equation is [tex]y=6x^2-24x+16[/tex]

Therefore, Option 4 is correct.

Answer:

$70

Step-by-step explanation:

10.50/ 3 = 3.5

3.5 times 20 =70

Answer:

A line parallel to this line will have slope 4/5.

Step-by-step explanation:

2 parallel lines will have the same slope.

y = mx + c is the general form of the slope-intercept formula of a line, the slope is given by m.

y = 4/5 x - 3

-we see by comparing the 2 equations that the slope of this line (m) is 4/5.

Final answer:

The slope of a line parallel to the one given by the equation y = 4/5x - 3 is 4/5. This maintains the definition that parallel lines have identical slopes.

Explanation:

The slope of a line that is parallel to the line represented by the equation y = 4/5x - 3 is 4/5. This is because parallel lines have the same slope. In the context of algebra and straight lines, the slope of a line is a measure of its steepness, commonly identified as 'm' in the slope-intercept form y = mx + b, where 'b' is the y-intercept. Each of the provided figures and examples illustrate that the slope of a straight line remains constant regardless of other changes.

Looking specifically at the equation y = 4/5x - 3, this is in slope-intercept form where the coefficient of 'x' is the slope, which is 4/5. Therefore, any parallel line would have the same slope of 4/5.

Answer:

[tex]\large\boxed{D.\ \dfrac{-4x+9}{2x(x-2)}}[/tex]

Step-by-step explanation:

[tex]\dfrac{1}{2x^2-4x}-\dfrac{2}{x}=\dfrac{1}{2x(x-2)}-\dfrac{2}{x}=\dfrac{1}{2x(x-2)}-\dfrac{(2)(2)(x-2)}{2x(x-2)}\\\\=\dfrac{1-4(x-2)}{2x(x-2)}\qquad\text{use the distributive property}\\\\=\dfrac{1-4x+8}{2x(x-2)}=\dfrac{-4x+9}{2x(x-2)}[/tex]

Answer:

The correct option is D.

Step-by-step explanation:

Consider the provided expression.

[tex]\frac{1}{2x^2-4x}-\frac{2}{x}[/tex]

Now take the LCM of the denominator and solve the above expression as shown:

[tex]\frac{x-2(2x^2-4x)}{x(2x^2-4x)}[/tex]

[tex]\frac{x-4x^2+8x}{x(2x^2-4x)}[/tex]

[tex]\frac{9x-4x^2}{x(2x^2-4x)}[/tex]

Cancel out the x as it is common in numerator and denominator.

[tex]\frac{9-4x}{2x^2-4x}[/tex]

[tex]\frac{-4x+9}{2x(x-2)}[/tex]

Hence, the correct option is D.