Please, fill in the blanks.

Answer:

96

Step-by-step explanation:

2 x 6=12

12 x 4= 48

48 x 2=96

Answer: y int is 8 the slope of the line is -1/2 and the equation of the line is y=-1/2x +8

Step-by-step explanation:

you can get slope by using the the points (6,5) and (8,4) to use y2-y1/x2-x1 and your y int is just where the line intersects the y axis which is 8. 8 then equals b in the equation y=mx+ b and you get m by using the first equation.

The value of the function P(8) given that P(x) = 3.5(1.4)ˣ is (c) 51.65 million

From the question, we have the following parameters that can be used in our computation:

An exponential function

The equation of the exponential function is then given as

P=3.5(1.4)x

Express properly

So, we have

P(x) = 3.5(1.4)ˣ

where x represents the amount of decades since 1800

From the question, we have

x = 8

Substitute the known values in the above equation, so, we have the following representation

P(8) = 3.5(1.4)⁸

Evaluate the expression

P(8) = 51.65261696

Approximate

P(8) = 51.65

Hence, the value of P(8) is (c) 51.65 million

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Answer:

700 + 50x ≥ 1200

where x represents the number of weeks needed to save.

Step-by-step explanation:

Check the picture below.

whatever those savings are on week "x", they have to be at least $1200

The point estimate of the population mean is 21.

The point estimate of the population mean is the midpoint of the confidence interval.

To find the midpoint, add the lower and upper bounds of the interval and divide by 2. In this case, the lower bound is 17 and the upper bound is 25, so the point estimate of the population mean is (17 + 25) / 2 = 21.

On the other hand, the margin of error is a measure of the precision of the estimate. It is the amount by which the estimate could be off and still be considered accurate. The margin of error is typically expressed as a percentage of the point estimate. In this case, the margin of error would depend on the level of confidence you have in the estimate and the size of the sample you used to generate the interval. Without more information, it is not possible to determine the margin of error.

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On using the scale value of 2 : 1, the area of green parallelogram is obtained as 120 in².

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

Height of blue parallelogram = 6 inches

Base of blue parallelogram = 10 inches

The scale value is given as = 2 : 1

Height of green parallelogram = 6 × 2 = 12 inches

Base of green parallelogram = 10 × 1 = 10 inches

It is known that area of parallelogram = base × height

So, area of green parallelogram is -

= 12 × 10

= 120 in²

Therefore, the area value is obtained as 120 in².

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The statements which are correct about the inequalities in each case as required are as follows;

It follows from the task content that the statement which is correct about each of the inequalities is to be matched accordingly.

It is noteworthy to know that the underlying perspective is such that;

If the coefficient of a variable upon isolation on one side of the inequality is negative, it follows that the inequality sign must be flipped while multiplying or dividing both sides of the inequality by a negative number.

On the other hand, if the coefficient of the variable is positive, the inequality sign is not to be flipped.

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All the mathematical expressions are,

1) 11 - k

2) p + 9

3) 16h

4) f < 12

5) 16 < m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

All the algebraic expression are,

1. Eleven decreased by k

2. p increased by 9

3. Sixteen multiplied by a number h

4. f less than twelve

5. Sixteen less than m

Now,

We can write all the expression as,

1. Eleven decreased by k

⇒ k - 11

2. p increased by 9

⇒ 9 + p

3. Sixteen multiplied by a number h

⇒ 16 × h

⇒ 16h

4. f less than twelve

⇒ f < 12

5. Sixteen less than m

⇒ 16 < m

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The linear function in the table is given as follows:

g(x) = 4x - 1/2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

When x increases by 0.5, y increases by 2, hence the slope m is obtained as follows:

m = 2/0.5

m = 4.

When x = 0, y = -0.5, hence the intercept b is given as follows:

b = -1/2.

The function is then defined as follows:

g(x) = 4x - 1/2.

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The required point is W.

What is the co-plaer and non co-planer?

Co-planar refers to a set of objects that lie in the same plane or lie on the same flat surface. They have the same elevation and do not intersect each other.

Non-coplanar refers to a set of objects that are not in the same plane or do not lie on the same flat surface. They have different elevations and may intersect each other.

W is a point that is not co-planar with R, S, and T.

Consider the provided plane.

We need to find the point that is not co-planar with R, S, and T.

Co-planar: Two object or points are said to be co-planer if they lie in the same plane.

Non co-planar: Two object or points are said to be non co-planer if they don't lie in same plane.

Now consider the provided plane, the point W is not lie in the plane V.

While point R, S and T lie in the plane V.

Hence, the required point is W.

W is a point that is not co-planar with R, S, and T.

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The area and the perimeter of the figure are given as follows:

The figure is composed as follows:

Applying the Pythagorean Theorem, the diameter of the circle is given as follows:

d² = 2 x 12²

[tex]d = \sqrt{2 \times 12^2}[/tex]

d = 16.97 cm.

Then the radius of the circle is given as follows:

r = 0.5d

r = 0.5 x 16.97

r = 8.485 cm.

The area of a circle of radius r is given by the multiplication of π and the square of the radius, as follows:

A = πr².

Hence, considering that the figure is a semi circle, we have that:

Ac = 0.5 x π x (8.485)²

Ac = 36π

The area of the right triangle is of:

At = 0.5 x 12 x 12

At = 72 cm².

Meaning that the area of the shape is given as follows:

A = Ac + At.

A = 36π + 72

A = 36(π + 2) cm².

The perimeter of the shape is obtained by the sum of 2 times 12 cm and the circumference of the semi circle.

The circumference of a semicircle of diameter d is given as follows:

C = 0.5πd.

Hence:

C = 0.5π x 8.485

C =  4.2425π.

Meaning that the perimeter of the shape is given as follows:

P = (24 + 4.2425π) cm.

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Answer:

Area: T = 24

Perimeter: p = 24

Semiperimeter: s = 12

Step-by-step explanation:

We know the lengths of all three sides of the triangle, so the triangle is uniquely specified.

a=6

b=8

c=10

The triangle perimeter is the sum of the lengths of its three sides

p=a+b+c=6+8+10=24

The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.

Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.

By writing and evaluating an exponential equation, we can see that the value of the car now is $9,216.

We know that the initial value of the car is $18.000, and the value depreciates at a rate of 20% per year.

If we define x as the number of years since the car was bought, we can write the value equation as:

V(x) = $18,000*(1 - 20%/100%)^x

V(x) = $18,000*(1 - 0.2)^x

V(x) = $18,000*(0.8)^x

The value of the car after 3 years is what we get if we evaluate the exponential equation in x = 3.

V(3) = $18,000*(0.8)^3

V(3) = $9,216

That is the value of the car now.

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The type of function that is shown in the given graph image is called a; Cubic Function

The vertical line test is a tool in graph functions that is very important when we are trying to determine the function that a specific graph represents. Now, we can further say that the vertical line is typically one that includes all points alongside a specific x-value with the y-value of a point that a vertical line will intersect a graph to represent an output for that particular input x value.

Now, there are different types of graphs and they all depend on the particular type of function that is being graphed. The eight most popular graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each of the types of graphs are usually unique which means that is easy to visually differentiate from the rest.

In this given graph, we can see that the graph shows an image that corresponds to a cubic function because of the classical infinite branches, then the three real roots and then the two extrema values

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The expression -5 (8x + 9) - 7x is equivalent to the expression - 47x - 45

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ -5 (8x + 9) - 7x

Simplify the expression, then we have

⇒ -5 (8x + 9) - 7x

⇒ - 40x - 45 - 7x

⇒ - 47x - 45

The expression -5 (8x + 9) - 7x is equivalent to the expression - 47x - 45

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(37.5, 42, 43.5} is the set of numbers that makes the inequality true

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given that:

Amanda uses the inequality below to calculate how many minutes, m, it takes her to swim at least 1,500 meters.

40m ≥ 1, 500

To determine which set of numbers makes the inequality true, solve for m and check the pick that contains the values greater than or equal to m:

40m ≥ 1, 500

m  ≥ 1, 500/40

m  ≥ 37.5

Thus, the set of numbers that makes the inequality true is (37.5, 42, 43.5}

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Answer:

13 dollars

Step-by-step explanation:

The limit lim x → ∞ (2/3)ˣ = ∞

A limit is the value of a function as the independent variable tends to a particular value.

Since we have lim x → ∞ (2/3)ˣ, to find this limit, using the fact that lim x → a ㏑f(x) = ㏑[lim x → a ㏑f(x) ]

So, since  lim x → ∞ (2/3)ˣ, taking natural logarithm of both sides, we have that

lim x → ∞ (2/3)ˣ

㏑[lim x → ∞ (2/3)ˣ] = lim x → ∞ ㏑(2/3)ˣ

= lim x → ∞ x㏑(2/3)

So, substituting x = ∞ into the equation, we have that

lim x → ∞ x㏑(2/3) = ∞㏑(2/3)

= ∞

So, lim x → ∞ (2/3)ˣ = ∞

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Answer:

7.9

Step-by-step explanation:

The  time that the rocket will hit the ground to the nearest tenth of a foot is 17 secs.

We were given the equation as y=-16x^2+261x+130 , thene we can equate this to zero. as

0=-16x^2+261x+130

from this we can see that this is a quadratic equation, where a= -16, b=261, c =130

Then input into the quadratic formular we have:

[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]

Then if we input the values we have [tex]x=\frac{-261+-\sqrt{261^{2}-4*-16*130} }{2*-16}[/tex]

Then the value of x are: -0.49 and 16.79

The positive value is the time that the rocket will hit the ground. Therefore, the rocket will hit the ground after 16.79 secs.

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Answer: 600km

Step-by-step explanation:

Using the concept of proportion, with the same average rate,

3 hours -> 200 km

9 hours -> A km

Hence,

9/3 = A/200

A = 200 x 9/3 = 200 x 3

                        = 600

Answer: 600 km

Step-by-step explanation:

We need to apply the concept of Time speed distance here.

When speed is constant, T ∝ D

D = S*T

200 km = 3hrs

X km = 9hrs

X = 200*9/3

  = 200*3

  = 600km

Time spent in class per week is 6 × 52 × 5 = 1560 minutes.

Time spent in class per day is 6 × 52 = 312 minutes.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Since Stephanie has 6 classes a day. Each class is 52 minutes. She goes to school 5 days a week.  The time she spend in class can written as:

time in class = 6 × 52 × 5 = 1560 minutes per week

The time can also be written in form of the time spent per day:

time in class = 6 × 52 = 312 minutes per day

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Answer:

Option a) 6x+6 is correct.

Step-by-step explanation:

Option a) 6x+6 is correct.

The given expression 6x+6 represents a linear expression.

Step-by-step explanation:

Definition: Linear expression  is a mathematical statement defining an equality. It is usually a polynomial equation having degree 1. It can be written as linear relationship with variables and a constant.

6x+6 expression represents a linear expression

Because it has degree 1.

Therefore Option a) 6x+6 is correct.

The given expression 6x+6 represents a linear expression.

a) 6x+6

The given expression 6x+6 represents a linear expression.

Definition:

Linear expression is a mathematical statement defining equality. It is usually a polynomial equation having a degree of 1. It can be written as a linear relationship with variables and a constant.

6x+6 expression represents a linear expression.

Because it has degree 1.

Therefore, a) 6x+6 is correct.

The given expression 6x+6 represents a linear expression.

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Distance: 19

Steps:

Distance (d) = √(16 - -3)2 + (8 - 8)2

= √(19)2 + (0)2

= √361

=          19

The length of third side of the triangle will be A. x + 13.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

In this situation, triangle has a perimeter of 9x+6. The first side of the triangle has a length of 5 x and the second side has a length of 3x-7.

The length of third side of the triangle will be:

= 9x + 6 - (3x - 7 + 5x)

= x + 13

The correct option is A.

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The solutions of the quadratic equation:

(x+ 2)*(x + 8) = 0

are:

x = -2

x = -8

Here we have the following quadratic equation:

(x + 2)*(x + 8) = 0

And we want to solve it for x.

Remember the zero property, for any real number A, the product with zero gives:

A*0 = 0

Then:

(x + 2)*(x + 8) = 0

If either (x + 2) = 0 or (x + 8) = 0

Solving these two we get:

x + 2 = 0

x = -2

x + 8 = 0

x = -8

The two solutions of the quadratic equation are x = -2 and x = -8

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The  Distance between B to C = 58 km,

distance between C to D = 30 km

Average speed between B to C = 59.79 km/h

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.

Given  A commuter train moves from station A to D via B and C,

distance from A to C via B = 70 km

distance from B to D via C = 88 km

av. speed of the train from A to B = 48 km/h

av. speed of the train from C to D = 45 km/h

time taken by train to reach B = 15 min = 15/60  = 0.25 hour

distance between A to B = speed x time from A to B

distance between A to B = 48 x 0.25

distance between A to B = 12 km

A. Distance between B to C = distance from A to C - distance between A to B

Distance between B to C = 70 - 12 = 58 km

B. distance between C to D = distance from B to D -  Distance between B to C  

distance between C to D = 88 - 58 = 30 km

C. let av. speed from B to C is x

total distance covered by train  = 12 + 58 + 30 = 100 km

av. speed for journey = 50 km/h

time taken to complete journey = 100/50 = 2 hours

time is taken from A to  B = 0.25 hour

time is taken from B to C = 58/x

Time is taken from C to D = 30/45 = 0.66 hour

halt at b = 3 minute and halt at C = 4 minute

total halt = 3 + 4 = 7 minute = 7/60 = 0.12 hour

Total time  = time taken from(A to B + B to C + C to D) + total hault

2 = 0.25 + 58/x + 0.66 + 0.12

58/x = 0.97

x = 59.79 km/h

Hence The  Distance between B to C = 58 km,

distance between C to D = 30 km

Average speed between B to C = 59.79 km/h

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Angel should increase the dimensions of the deck by 5 feet each

From the question, we have the following parameters that can be used in our computation:

Length = 20 feet

Width = 25 feet

So, the area is

Area = 20 * 25

Evaluate

Area = 500

When increased by 50%, we have

(20 + x) *(25 + x) = 500 * 1.50

Evaluate

(20 + x) * (25 + x) = 750

Express 750 as 25 * 30

So, we have

(20 + x) * (25 + x) = 25 * 30

This means that

20 + x = 25

25 + x = 30

Solve for x

x = 5 and x = 5

This means that

Increment = 5

Hence, the lengths should be increased by 5 feet

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