This table defines function f:

Answer:

Step-by-step explanation:

3x + 1 < 7...subtract 1 from both sides

3x < 7 - 1

3x < 6 ...divide both sides by 3

x < 6/3

x < 2

which means the second answer choice is correct!

Answer: Second Graph

Step-by-step explanation:

Given inequality

3x + 1 < 7

Subtract 1 on both sides

3x + 1 - 1 < 7 - 1

3x < 6

Divide 3 on both sides

3x / 3 < 6 / 3

x < 2

Apply the inequality to the graph

Since it is less than, the circle should be hollow

Since it is less than 2, the line should point to the left

Therefore, it should be the Second Graph

Answer:

c^2 = a^2 + b^226^2 = 10^2 + b^2 676 = 100 + b^2 576 = b^2 shortest side length = 24 units

Step-by-step explanation:

100–pound earthling's weight on Saturn using the proportion is (B)

15/4 = 100/x.

To find the 100–pound earthling's weight on Saturn using the proportion:

Therefore, 100–a pound earthling's weight on Saturn using the proportion is (B) 15/4 = 100/x.

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The correct question is given below:
A bowling ball weighs 15 pounds on earth and weighs 4 pounds on the planet Saturn. you could determine a 100–pound earthling's weight on Saturn using the proportion:

a. start fraction 15 over 4 end fraction = start fraction x over 100 end fraction

b. startfraction 15 over 4 endfraction = 100 over x endfraction

c. startfraction 4 over 15 endfraction = startfraction 100 over x endfraction

d. either a or c

Answer:

x=10

Step-by-step explanation:

x-3(+3)=7+3

We need to add 3 to both sides to isolate x.

x=10

Answer:

Step-by-step explanation:

x - 3 = 7

x = 7 + 3

x = 10

Answer:

First answer lol

Step-by-step explanation:

is the domain by any chance x ≥-2?

This real-world problem has the limitations 75< x <110 and 0< y[tex]\leq[/tex] 50, hence:

option (C) is the best choice.

The term "inequality" refers to a mathematical expression in which both sides have mathematical signs that are either less than or greater than one another, and the expression is one where the two sides are not on equal footing.

We have:

Your senior vacation is scheduled to include a class trip to a beach. Only when it's between 75 and 110 degrees do guests at the resort get access to the pool. 50 passengers can go with you.

Let y be the number of passengers and x be the temperature

75 to 110 degrees are the range of the temperature.

75 < x < 110

50 passengers can go with you.

0 < y ≤ 50

In order to illustrate this real-world issue, the limitations are 75 <x <110 and 0< y [tex]\leq[/tex]50.

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To estimate that table given in Option (4) will define the quadratic relationship.

Therefore, the table of Option (5) will describe the quadratic relationship.

By estimating the second difference, if the second difference in a table exists equivalent, the table will define the quadratic relationship.

In the given option, we estimate that table given in Option (4) will define the quadratic relationship.

x       y      I st difference       II nd difference

0      4           -                               -

1      -4      -4 - (4) = -8                    -  

2     -4      -4 - (-4) = 0                0 - (-8) = 8

3      4       4 - (-4) = 8                 8 - 0 = 8

The second difference between the terms in y exists exactly as 8.

Therefore, the table of Option (4) means the quadratic relationship.

Similarly, in Option (5) we will estimate the second distinction of y terms.

x        y             I st difference       II nd difference

0      -4                     -                          -

1       -8               -8 - (-4) = -4              -

2     -10             -10 - (-8) = -2      -2 - (-4) = 2  

3     -10             -10 - (-10) = 0       0 - (-2) = 2

Here the second difference exists identical to 2.

Therefore, the table of Option (5) will describe the quadratic relationship.

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The height of the box would be = 30cm.

The volume of the box = 6900 cm3

The base of the box = 23 cm

The depth of the box = 10cm

Therefore the height of the box can be gotten from the formula used to calculate the volume of the box. That is;

Volume = base×depth×height

6900 = 23×10×h

make h the subject of formula;

height = 6900/230

= 30cm

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Applying the angle of intersecting chords theorem, the value of z is: D. 100.

According to the angle of intersecting chords theorem, in a circle like the one shown in the image above, where two chords intersect to form vertical angles, the theorem states that the angle formed equals half of the sum of the measures of the arcs intercepted by the angles.

Applying the angle of intersecting chords theorem, let's find x first:

73 = 1/2(96 + x)

Multiply both sides by 2

2 × (73) = 1/2(96 + x) × 2

146 = 96 + x

Subtract both sides by 96

146 - 96 = 96 + x - 96

50 = x

x = 50°

Therefore:

x + z + 96 + 114 = 360° [full circle measure]

Plug in the value of x

50 + z + 96 + 114 = 360

z + 260 = 360

Subtract both sides by 260

z + 260 - 260 = 360 - 260

z = 100°

The answer is: D. 100°.

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By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

Herein we find the case of a rectangular tank being filled with water at constant flow are, which is dimensionally speaking, volume by time. We know that dimensions of the tank are described in centimeters, whereas flow rate is described in liters per minute. Please notice that a liter is equal to 1000 cubic centimeters:

t = [(80 cm) · (60 cm) · (50 cm) · (1 L / 1000 cm³)] / (24 L / min)

t = 10 min

By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

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f(x) = 2x² + 7x + 6 and g(x) = 2^x + 5 have -

The equation of the functions are given as:

f(x) = 2x² + 7x + 6  &

g(x) = 2^x + 5

Next, we plot the graph of both functions (see attachment)

From the graph, we have the following highlights

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3435 were children visited the India gate.

What is a linear equation in math?

Given,

             men = 1265

            women = 1150

Total women and men -

        men + women = 2415

         = 5450-2415  ⇒ 3435

Therefore,  3435 were children visited the India gate.

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6) For the inverse to be a function, f(x) needs to be one to one. To accomplish this, restrict the domain to one side of the axis of symmetry

7) The y-intercept of the inverse is when x=0. This means we want to find when f(x)=0.

[tex]4(1/3)^x = 16 \\ \\ (1/3)^x= 4 \\ \\ x=\log_{1/3}(4) \approx -1.26[/tex]

Answer:B

Step-by-step explanation:

Answer:

(a + b)(a + b - 2)

Step-by-step explanation:

(a + b)² - 2(a + b) ← factor out (a + b) from each term

= (a + b)(a + b - 2)

Answer:

  x = 3√3

  y = 6

Step-by-step explanation:

The geometric mean relations between segments intersecting the long hypotenuse and its parts can be used to find the values of interest.

  x = √(9·3) = 3√3

  y = √((9+3)·3) = 6

__

Additional comment

These right triangles are all similar, so corresponding sides are proportional. When the proportions are solved for a missing side, a geometric mean relation results. (The geometric mean of 'a' and 'b' is √(ab).)

Identify the segments above the horizontal line as w, x, y. (x and y are already identified in this figure.)

The ratio of short side to long side is ...

  x/9 = 3/x   ⇒   x² = 9·3   ⇒   x = √(9·3)

The ratio of short side to hypotenuse is ...

  y/(9+3) = 3/y    ⇒   y² = (9+3)·3   ⇒   y = √((9+3)·3)

Likewise, the ratio of long side to hypotenuse is ...

  w/(9+3) = 9/w   ⇒   w² = (9+3)·9   w = √((9+3)·9) = 6√3

The point with the greatest distance to the origin is given by:

B. (-3, 3).

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The origin is given by point (0,0), hence the distance of a point (x,y) to the origin is given by:

D = sqrt(x² + y²).

Hence the distances for each point given in the problem are:

Hence option B has the greatest distance.

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Answer:

x = 30° and y = 52°

Step-by-step explanation:

angles on the circle subtended by the same arc are congruent

x and 30° are on the same arc, then x = 30°

y and 52° are on the same arc, then y = 52°

Answer:

4

Step-by-step explanation:

h(x) = -1/3x+2 where we need to find -4h(9)

h(9): x = 9

h(x) = -1/3(9) + 2

h(x) = -3 + 2

h(x) = -1

-4h(9) is -4h(x):

-4(-1) = 4

Answer:

a. 3x^3 + 2x^2 - 3x +10

Step-by-step explanation:

(x+2)(3x^2-4x+5)

x(3x^2-4x+5) +2(3x^2-4x+5)

3x^3-4x^2+5x+6x^2-8x+10

3x^3-4^2+6x^2+5x-8x+10

3x^3+2x^2-3x+10

Answer:

Assunming that the equation is y = -16x² +85x, I suggest Dario find a new profession.  He kicks the ball 133 feet high, but it only travels 2.7 feet downfield at that point.  It will have travelled 2*2.7 feet or 5.4 feet horizontal when it returns to ground.

Step-by-step explanation:

We can answer the question of how hiogh and far the ball travels (in feet) by either of two methods.  The first is to differentiate the equation and set it equal to 0, and the second is the graph it and look for the vertex and x intercept.

Differentiate

y = -16x² +85x

The first derivative produces an equation that gives us the slope of the line at any point x.  At the ball's top height, it stops and reverses direction, a point at which the slope is zero.

y = -16x² +85x

d(y)/d(x) = -32x + 85

0 = -32x + 85

32x = 85

x = 2.66 feet horizontal distance when the ball reaches its peak.

At x = 2.66, y is 112.9 feet high

When the ball returns, it adds amnother 2.66 feet to the horizontal distance, for a total of 5.4 feet.

Graph:

See attached plot of the function.

Horizontal distance is 2.66 feet and height is 133 feet. The x-intercept is at 5.4 feet.

After all that, the ball only travelled downfield (we hope downfield) a total of 5.4 feet.

Answer:

Below in bold.

Step-by-step explanation:

9t^2 - u^2     (the difference of 2 squares)

= (3t - u) (3t + u).

2c - 4d - pc + 2pd

= 2(c - 2d) - p(c - 2d)

c -2d is common to both parts so the factors are:

(2 - p)(c - 2d)

Answer:

1. No

2. No

3. Yes

4. No

5. Yes

6. No

Step-by-step explanation:

If you want to check if a graph is a function, do a vertical line test. For every vertical line, there should be only 1 point on the line if the graph is a function.

The measurements that are correct for the given triangle are

sin C = 9/15

B ≈ 53.13°

From the question, we are to determine which of the given trigonometrical ratios for the given triangle are correct

The given triangle is a right angle triangle

Using SOH CAH TOA

sin C = 9/15

∴ The option sin C = 9/15 is correct

Also,

Using SOH CAH CAH

tan B = 12/9

∴ The option tan B = 9/12 is NOT correct

To determine the measure of angle B (m ∠B)

From tan B = 12/9

Then,

tan B = 1.33333

B = tan⁻¹(1.33333)

∴ B ≈ 53.13°

Thus, the option B ≈ 53.13° is correct

Hence, the measurements that are correct for the given triangle are

sin C = 9/15

B ≈ 53.13°

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The number of ways there are to move from (0, 0) to (7, 7) in the coordinate plane with movements of only one unit right or one unit up accordingly is; 49 while that such that y =x is; 7.

It follows from the task content that the movement intended on the coordinate plane is; from (0, 0) to (7, 7).

The number of ways to move such that movements of only one unit right or one unit up is; 7 × 7 = 49.

The number of ways for which y= x is therefore is; 7 as the movement is diagonal.

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The perimeter of a given shape implies the sum of all its sides. While the area of a given shape is the total value of space it would cover on a 2-dimensional plane.

The perimeter of the shape is 104 cm.

The area of the shape is 640 [tex]cm^{2}[/tex].

The perimeter of a given shape implies the sum of all its length of sides., such that the value of each individual side is summed to a total value.

The area of a given shape is the total value of space it would cover on a 2-dimensional plane. The area of shapes depends on the type of shape.

In the given question, the given shape has 12 sides. Some of these sides can sum up to a given length as shown in the diagram.

So that;

perimeter = 2 + 32 + 10 + 10 + 2 + 32 + 8 + 8

                 = 104 cm

Thus, the perimeter of the shape is 104 cm

ii. The area of the shape = length x width

                                         = 32 x 20

                                         = 640 [tex]cm^{2}[/tex]

Therefore, the area of the given shape is 640 [tex]cm^{2}[/tex].

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The solution to the inequalities 3x + 5 < 6x + 8 and 4x + 3 < 7x + 5 is x > -1 and x > -2/3 respectively

Inequality signs are;

3x + 5 < 6x + 8

3x - 6x < 8 - 5

-3x < 3

x > 3/-3

The inequality sign is flipped from < to greater than because of the division with negative value.

x > -1

2. 4x + 3 < 7x + 5

4x - 7x < 5 - 3

-3x < 2

The inequality sign is flipped from < to greater than because of the division with negative value.

x > -2/3

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Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

To find the order of matrix:

To prove:

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

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Answer:

24 dollars.

Step-by-step explanation:

1/4 + 1/3 = 3/12 + 4/12 = 7/12

7/12 a + 8 = 22

7/12 a = 14

a = 14 x 12/7

a = 24

Answer:

The bottom graph.

Step-by-step explanation:

The asymptote ( in between the 2 curves) on the bottom graph is  at x = 1, because when x = 1 the denominator = 0.