9/3 write the fraction as a whole number

Answer:

  d = (c -4)² +7 = c² -8c +23

Step-by-step explanation:

Both 'c' and 'd' are expressed in terms of the variable k. In general, that variable is eliminated by writing k in terms of 'c' or 'd', then substituting for k in the other equation.

We recognize that the 9k² term in the expression for 'd' is the square of the 3k term in the expression for 'c'. That means we don't have to solve for k; we only need to solve for 3k. The equation for 'c' gives an easy way to do that.

  c = 3k +4

  c -4 = 3k . . . . . . . subtract 4 to get an expression for 3k

Substituting into the equation for 'd', we have ...

  d =7 +9k²

  d = 7 +(3k)² . . . . . writing 9k² in terms of 3k

  d = 7 +(c -4)² . . . . substituting for 3k. This is d in terms of c.

This can be simplified to ...

  d = c² -8c +23 . . . . another form of d in terms of c.

To express 'd' in terms of 'c', solve the first equation for 'k' and substitute this value into the second equation. This yields: d=7+((c-4)^2)/3.

To express d in terms of c, we first need to make k the subject of c=3k+4. We do this by subtracting 4 from both sides, getting c-4=3k, and then dividing both sides by 3, which gives us k=(c-4)/3. Next, we substitute this value of k into the second equation: d=7+9k^2. Substituting, we get d=7+9*((c-4)/3)^2, which, when simplified, gives the result d=7+((c-4)^2)/3. This is the expression for d in terms of c.

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Answer:

c

Step-by-step explanation:

The correct function is,

⇒ y = x + 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The following points for a function are graphed in the coordinate plane: (0, 4), (1, 5), (2, 6), and (3, 7).

Now, We know that;

All the points are satisfy the function.

Hence, By options c;

y = x + 4

Put x = 0, y = 4

y = x + 4

4 = 0 + 4

4 = 4

Hence, The correct function is,

⇒ y = x + 4

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Answer:

[tex]a=3[/tex] and [tex]b=5[/tex]

Step-by-step explanation:

We have been given an equation [tex]\frac{3}{x}+\frac{5}{x^2}=\frac{ax+b}{x^2}[/tex]. We are asked to find the value of 'a' and 'b'.

Let us make a common denominator:

[tex]\frac{3*x}{x*x}+\frac{5}{x^2}=\frac{ax+b}{x^2}[/tex]

[tex]\frac{3x}{x^2}+\frac{5}{x^2}=\frac{ax+b}{x^2}[/tex]

Add numerators:

[tex]\frac{3x+5}{x^2}=\frac{ax+b}{x^2}[/tex]

Therefore, [tex]a=3[/tex] and [tex]b=5[/tex] for the given equation.

Answer:

p(x) = 19+15

Step-by-step explanation:

The length of QR in rectangle PQRS is 12 cm, found by setting up the proportional relationship 14/21 = 8/QR, where 14 cm and 8 cm are the lengths of sides AB and BC of rectangle ABCD, respectively, and 21 cm is the length of side PQ of rectangle PQRS.

Since rectangle ABCD is similar to rectangle PQRS, their corresponding sides are proportional. To find the length of QR, we will set up a proportion using the given lengths:

AB/PQ = BC/QR

Substituting the given lengths:

14/21 = 8/QR

Now, solve for QR:

QR = (21  * 8) / 14

QR = 168 / 14

QR = 12 cm

So, the length of QR in rectangle PQRS is 12 cm.

Given is a Right triangle LMN with right angle at M i.e. angle M = 90 degrees.

Given are the sides LM = 15, MN = 36, and LN = 39.

It says to find cos(N) = ?

So opposite side would be LM, adjacent side would be MN, and LN is the hypotenuse.

We know about the "Soh-Cah-Toa" rule in which cosine ratio is given by :-

[tex] cos(N) = \frac{Adjacent}{Hypotenuse} \\\\
cos(N) = \frac{MN}{LN} \\\\
cos(N) = \frac{36}{39} \\\\
cos(N) = \frac{12}{13} [/tex]

Hence, final answer is [tex] cos(N) = \frac{12}{13} [/tex].

The shortest column of the line plot

The  least common test score from the graphs is 70.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A line plot shows the frequency of data, in short it shows how many times something has occurred or the number of times data occurs in a group of data.

The number of data is represented by markers or in this case "x"s. The more x's along the column, the more times it occurred.

The bar graph there does not show the frequency of the different scores. This shows the relationship between the test number and the percentage of the scores obtained. It does not tell you the individual scores obtained.

The least common test score is 70

Hence, the  least common test score from the graphs is 70.

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Approximately 5,700 more people attended the concert in the second city.

To estimate how many more people attended the concert in the second city, we can round the attendance numbers to the nearest hundred and then subtract the smaller number from the larger one. For the first city, 3,546 people rounds off to 3,500 people, and for the second city, 9,238 people rounds off to 9,200 people. Now we subtract the rounded number of the first city from the rounded number of the second city.

So, 9,200 (rounded attendance in the second city) minus 3,500 (rounded attendance in the first city) equals 5,700.

Therefore, approximately 5,700 more people attended the concert in the second city.

The value of the exponent number in standard from is A = 903

The exponential form is an easier way of writing repeated multiplication involving base and exponents. It has a base and a power

The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1.

It is often used in mathematics and science to represent large or small numbers more efficiently. It can also be used to simplify certain mathematical operations, such as multiplication and division, by using the properties of exponents.

Given data ,

Let the exponential form of the number be A

Now , the value of A = 9.03×10²

To convert 9.03×10² to standard form, we need to multiply the number by the appropriate power of 10 so that it is expressed as a number between 1 and 10.

Starting with 9.03×10² , we can move the decimal point two places to the right to get:

9.03×10^2 = 903

So the standard form of 9.03×10² is simply 903

Hence , the standard form is A = 903

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Answer

13.1 millimeters

Explanation

The volume of any regular object is found by;

Volume = base area × length.

In the question, the base is a triangle of height  12 millimeters and a base length L.

The length of the prism is  14.3 millimeters.

∴ Volume = base area × length.

   1,123.98 = (1/2 × 12 × L) × 14.3

   1,123.98 = 85.8 L

   L =  1,123.98/85.8

       = 13.1 millimeters

Answer:

4182 is ur answer

Step-by-step explanation:

Answer:

V + F = E + 2

The statement correctly shows the relationship found in Euler's formula is   F + V - E = 2.

For any real value θ, we have:

[tex]e^{i\theta} = \cos(\theta) + i\sin(\theta)[/tex]

where 'e' is the base of the natural logarithm, and 'i' is iota, the imaginary unit.

We are given that;

Euler's formula states that for any convex polyhedron (a 3-dimensional solid with flat faces and straight edges), the number of faces (F), vertices (V), and edges (E) are related by the formula:

F + V - E = 2

One possible statement that correctly shows the relationship found in Euler's formula is:

"The number of faces, vertices, and edges in a convex polyhedron are related by Euler's formula, which states that F + V - E = 2."

Therefore by euler's formula the answer will be F + V - E = 2.

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