A car travels at an average speed of 64 miles per hour. how many miles does it travel in 4 hours and 45 minutes?

The english alphabet contains 2121 consonants and 55 vowels. How many strings of 66 lowercase letters of the English alphabet contain

The linear equation can be represented as a straight line on a graph. The equation for the given case is v = 0.05 + 0.01m.

A linear equation is a equation that has degree as one.

To find the solution of n unknown quantities n number of equations with n number of variables are required.

Given that,

The value of stock at the beginning is $0.05,

And, its rate of increase for each month is 0.01.

Suppose the value of stock be v and the month be m,

Then, the increment in its value for any month m  is $0.01m.

Now, the equation for the value of stock v at any month m can be written by summing its initial value to its increment value obtained for each month as,

v = 0.05 + 0.01m.

Hence, the equation representing the value of the stock v in any months m is given as v = 0.05 + 0.01m.

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The value of the integers can be obtained by solving the equation as 5 and 6 respectively.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

Suppose the smaller integer be x.

Then, the larger one is x + 1.

As per the question, the following equation can be formed as,

x + 3(x + 1) = 23

⇒ 4x + 3 = 23

⇒ x = 5

Thus, the larger integer is 5 + 1 = 6.

Hence, the integers are obtained as 5 and 6 respectively.

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Answer:

The length of BC is 48 units.

Step-by-step explanation:

Given information: Line g bisects line segment BC at Point H. BH = 4x and HC = 24.

It is given that line g bisects line segment BC at Point H. It means point H divides the line BC in two equal parts BH and HC.

[tex]BH=HC[/tex]

[tex]4x=24[/tex]

Divide both sides by 4.

[tex]x=6[/tex]

The value of x is 6.

[tex]BH=4x=6\times 4=24[/tex]

The length of BC is

[tex]BC=BH+HC[/tex]             (Segment addition property)

[tex]BC=24+24=48[/tex]

Therefore the length of BC is 48 units.

The expression could be used to find the area of the isosceles triangle above is  [tex]\sqrt{40} \cdot \sqrt{40} /2[/tex]

The length of the base is the distance between the points 4+2i and 10+4i, so

Base= |10+ 4i (4+2i)| = |10+4i-4-2i|= |6 + 2i| = [tex]\sqrt{6^2 +2^2}[/tex] = [tex]\sqrt{36+4}[/tex]= √40

The middle point of the base is placed at point

4+2i+ 10 + 4i/2 =  6i +14/2 = 7+ 3i

The length of the height is the distance between the points 5+9i and 7+3i

Height = 5 +91 (7+3i)| =|5+ 9i −7 - 3i| = |−2+6i| = [tex]\sqrt{(-2)^2 + 6^2} = \sqrt {4+36}[/tex] = √40

So, the area of the triangle is

[tex]A= 1/2 \cdot Base \cdot Height= \sqrt{40} \cdot \sqrt{40} /2[/tex]

Therefore, The expression could be used to find the area of the isosceles triangle above is  [tex]\sqrt{40} \cdot \sqrt{40} /2[/tex]

The probable question may be:

An isosceles triangle’s altitude will bisect its base. Which expression could be used to find the area of the isosceles triangle above?

Points on the graph of the triangle are (5+9i), (10+4i), and  (4+2i).

A. \sqrt{40} \cdot \sqrt{40} /2

B. \sqrt{40} \cdot \sqrt{68} /2

C. \sqrt{232} \cdot \sqrt{288} /2

D.  \sqrt{232} \cdot \sqrt{164} /2

Final answer:

To find the area of an isosceles triangle when given the length of the base and the altitude, you can use the formula A = ½ × base × height. The altitude of an isosceles triangle will bisect its base, so you can divide the base in half to find the length of the base above the altitude.

Explanation:

An isosceles triangle's altitude will bisect its base. To find the area of the isosceles triangle, we can use the formula A = ½ × base × height. Since the altitude bisects the base, we can divide the base in half to find the length of the base above the altitude. Let's say the length of the base is 2x and the length of the altitude is h. So, the expression to find the area of the isosceles triangle is A = ½ × (2x) × h = xh.

if interior angle is 170, subtract 170 from 180 to find exterior angle:

180-170 = 10 = exterior angle

the sum of exterior angles is 360 so divide by exterior angle to find sides:

360 /10 = 36 sides

A counterexample showing the conclusion 'All the marbles in the bag are black' as false.

A counterexample is a scenario where the premises are true but the conclusion is false, demonstrating the invalidity of an argument. In this case, to prove invalidity, a counterexample could be a situation where there is at least one marble in the bag that is not black. For instance, if there are three black marbles and one red marble inside the bag, the selection of three black marbles is still possible, but the conclusion that all marbles are black is false.

Answer:

Notice that the given line is vertical, which means its slope is undetermined.

We can demonstrate that using the slope definition:

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

[tex]m=\frac{1-0}{2-2}=\frac{1}{0}=IND[/tex]

Which is undetermined because null denominators cannot be determined.

Now, the Point-Slope form of a line refers to expressin the equation with one point and its slope. So, if we cannot determine the slope, we cannot determine the point-slope form neither. In other words, we need to have a determined slope to express it in this form.

The function d = 10t signifies that you cover 10 miles of distance per hour.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

You ride your bicycle at a rate of 10 mi/h. the distance d (in miles) that you ride is given by the function d=10t.

We have the distance [d] as the function of time as -

d = 10t

The given equation id d = 10t. The slope of the line is 10. This means that you cover 10 miles of distance in 1 hour. The graph representing the function is plotted.

Therefore, the function signifies that you cover 10 miles of distance per hour.

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The number can be arranged from least to greatest as 2.03<2.3<2.303<2.33.

A decimal is a number with a whole and a fractional portion. Decimal numbers are between integers and indicate numerical value for a whole plus some fraction of a whole. In fraction form, we may say there is one and one-half pizzas. This is represented in decimal form as 1.5 pizzas.

Let's write the numbers to the third decimal point. Therefore, we can write the numbers as,

Now, the numbers can be arranged as,

2.030 < 2.300 < 2.303 < 2.330

2.03 < 2.3 < 2.303 < 2.33

Hence, the number can be arranged from least to greatest as 2.03<2.3<2.303<2.33.

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