Work out the equation of the straight line
shown below.
Give your answer in the form y = mx + C,
where m and c are integers or fractions in
their simplest forms.
Y
6
5
4
3
2-
1
-6 -5 -4 -3 -2 -1 0
-14
-2-
-3+
-4-
-5-
-6-
1 2 3 4 5 6
X

Answer:

y is > 7

Step-by-step explanation:

Any y value greater than 7 would make the product greater than 5. This can be looked at as y > 7. So y/7 can be rthough of as y divided by 7. 5 x y/7 can be though of as y * 5 divided by 7. Or 5y/7. To make this value 5, y must be 7. Since 7/7 is 1, and 1*5 is 5. If the number is greater than this it would have to be >7/7, since this would make it >1*5. So y must be >7. Hope this helps!

Answer:

9 (or anything above)

Step-by-step explanation:

5 x 9/7 = 45/7 = 6 3/7. Anything above would also work. Also, 8 and 7 work too

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We know,

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[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

Answer: Commutative property.

Step-by-step explanation: Basically, the commutative property can be expressed as a + b = b + a, which matches this scenario pretty well. You are correct.

Let me know if this is right! :)

Answer: 25% of 40 is 40 times 25 divided by 100 which is 10 (number of children in the club)

there:)

Answer: 160 children

Step-by-step explanation: 25% times 4 is 100%. So, you'd multiply 40 by 4.

Answer:

[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)[/tex]

Step-by-step explanation:

We want to simplify:

[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}[/tex]

Recall the Pythagorean Identity:

[tex]\sin^2(A)+\cos^2(A)=1[/tex]

So:

[tex]\cos^2(A)=1-\sin^2(A)[/tex]

Substitute:

[tex]\displaystyle =\frac{1-\sin^2(A)}{1+\sin(A)}[/tex]

Factor. We can use the difference of two squares pattern:

[tex]\displaystyle =\frac{\left(1-\sin(A))(1+\sin(A))}{1+\sin(A)}[/tex]

Cancel. Hence:

[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)[/tex]

The explicit formula for an arithmetic sequence whose common difference is 8 and the first term is -2 is

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

The sequence is given by the formula

nth term = a + (n - 1) * d

where a = first term

n = the term

d = common difference

In the problem, d = -2 and a = 8, because of this we have

= a + (n - 1) * d

= 8 + (n - 1) * -2

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Answer:

(4.6, 4)

Step-by-step explanation:

Given the coordinates (3,2) and (7, 7) partitioned between 3:2

M(X,Y) = [(ax1+bx2/a+b, ay1+by2/a+b)]

X = 3(3)+2(7)/3+2

X = 9+14/5

X = 23/5

X = 4.6

Similarly;

Y = 3(2) + 2(7)/3+2

Y = 6+14/5

Y = 20/5

Y = 4

Hence the required coordinate is (4.6, 4)

Answer:

44

Hope this helps.  :)

Answer:

Step-by-step explanation:

See the difference in y-values:

Next level difference is 4, so add 4 to 16:

Now add 20 to the last number:

The next number is 48

The statement that is correct about the behavior of the given graph is; D:

The range of the function is all real numbers greater than or equal to 0.

The graph of the function  is as shown in attached diagram.

The function is;

y = √-x

1. The domain of the function is defined the set of all possible input values for x. Therefore, upon close inspection of the graph, we can say that the domain of this function is;

x ∈ (-∞, 0]

2. The range of the function is defined as the set all possible output values for y. By closely inspecting the attached graph, we can say that  the range of this function is; y ∈ [0, -∞)

From the above, we can tell that the range of the function is all real numbers greater than or equal to 0.

Looking at the options, only option D can be said to be correct about the behavior of the given graph.

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The missing options are;

The domain of the function is all real numbers greater than 0.

The range of the function is all real numbers less than or equal to 0.

The domain of the function is all values less than 0.

The range of the function is all real numbers greater than or equal to 0.

Answer:

22. acute triangle

23. right triangle

24. equilateral triangle

25. right triangle

Step-by-step explanation:

let me know if any of these are wrong

Answer: The greatest of the three is 10.

Step-by-step explanation:

27/3=9 so the numbers will be around nine.

8+9+10=27

Answer:

Let x represent the value of the smallest of the three consecutive integers.

Then, the value of the middle integer is x+1, and the value of the greatest integer is x+2.

Since the sum of the three integers is 27, we have:

x + (x+1) + (x+2) = 27

Combining like terms, we have:

3x + 3 = 27

Subtracting 3 from both sides, we have:

3x = 24

Dividing both sides by 3, we have:

x = 8

Therefore, the value of the smallest integer is 8, the value of the middle integer is 8+1 = 9, and the value of the greatest integer is 8+2 = 10.

Thus, the value of the greatest integer is 10.

Step-by-step explanation:

The coefficient of the variable x² in the expression 3x² is 3 and 4x^2 is 4

The expression is 3x²

To find : The coefficient of the variable x² in the expression

Coefficient is the number that is beside the variable in the equation.

The coefficient of x in 3x²  is 3

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

As we can see that the term that is in multiplication with x²  is 3.

Hence, the coefficient of x²  in the equation 3x²  is 3.

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Answer: 28 years

Step-by-step explanation:

Given

The equation showing the value of the bag after x years is [tex]C=25(1.025)^x[/tex]

If the price of the bag increased by 2.5%, from the equation, we can deduce that

Initial cost of the bag is 25

Double of the initial value is 50

Insert it in the equation

[tex]\Rightarrow 50=25(1.025)^x\\\Rightarrow 2=1.025^x\\\text{Taking natural log}\\\Rightarrow \ln 2=x\ln (1.025)\\\\\Rightarrow x=\dfrac{\ln 2}{\ln 1.025}\\\\\Rightarrow x=28.07\approx 28[/tex]

It will take 28 years

Answer:

D. The points seem to be clustered around a line.

Step-by-step explanation:

The scatterplot points are spread out and forming a line, not around a point.

There are two outliers.

Answer:

f(6) = - 50

Step-by-step explanation:

substitute x = 6 into f(x) , that is

f(6) = - 6² - 14 = - 36 - 14 = - 50

Answer:

-50

Step-by-step explanation:

f ( x ) = - x² - 14

Accordingly, to find the value of f ( 6 ) you have to replace x with ( 6 ).

f ( 6 ) = - (6)² - 14

f ( 6 ) = - 36 - 14

f ( 6 ) = -50

Answer:

try the diamond see if that works sorry if its wrong

Triangle is  most likely the next step in the series, option D is correct.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The first polygon is hexagon which has 6 sides

The second polygon is Pentagon which has 5 sides

The third polygon is square which has 4 sides

As we observe one side is decreasing from the each polygon from 1st to 3

So the fourth polygon will have three sides which is triangle

Hence, triangle is  most likely the next step in the series, option D is correct.

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Answer:

2*2*3*3*5

When these numbers are multiplied, the answer is 180.

Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.

1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.

2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).

3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.

4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.

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Answer:

121 feet

Step-by-step explanation:

By graphing the equation we can see the maximum y value is 121

Answer:

The value of x is 12.

i think it is correct.

Answer:

80 I THINK, SORRY IF NOT RIGHT

Step-by-step explanation:

Answer:

The approximate area by Riemann Sum of the curve is represented by [tex]A = 0.4\cdot \Sigma\limits_{t = 1}^{n} [2\cdot (2+0.4\cdot t)^{3} - 4][/tex].

Step-by-step explanation:

The area below the curve is estimated by the concept of Riemann Sum with right endpoint rectangles, which is defined by the following formula:

[tex]A = \left(\frac{\Delta x}{n} \right) \cdot \Sigma \limits_{t = 1}^{n} g\left (x_{o} + \frac{\Delta x}{n}\cdot t \right)[/tex] (1)

Where:

[tex]A[/tex] - Area below the curve, in square units.

[tex]n[/tex] - Number of rectangles, no units.

[tex]x_{o}[/tex] - Lower bound of the interval, in units.

[tex]\Delta x[/tex] - Length of the interval, in units.

[tex]t[/tex] - Summation index.

If we know that [tex]g(x) = 2\cdot x^{3} - 4[/tex], [tex]n = 10[/tex], [tex]x_{o} = 2[/tex] and [tex]\Delta x = 4[/tex], then the area below the curve is represented by the following equation:

[tex]A = 0.4\cdot \Sigma\limits_{t = 1}^{n} [2\cdot (2+0.4\cdot t)^{3} - 4][/tex]

Answer:

b. 2 feet

Step-by-step explanation:

The formula for volume of a cylinder is: V=πr^2h

Start by plugging in what they give you

V=πr^2h

314 =π(r)^2(25)

314 = 25π(r)^2

divide both sides by 25π, which is 78.5

4 = r^2

take the square root of both sides

r = 2

The smallest positive integer that is both a multiple of 7 and a multiple of 4, is 28 .

To find the smallest positive integer that is both a multiple of 7 and a multiple of 4, first find the multiples of both 4 and 7 to see which multiples are common between them and which are the lowest.

The multiples of 4 and 7 are:

Multiples of 4 :

4, 8, 12, 26, 20, 24, 28, 32, 36, 40,

Multiples of 7 :

7 , 14 , 21 , 28 , 35 , 42 , 49

The smallest positive integer that is both a multiple of 7 and a multiple of 4 is therefore 28.

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Applying it's formula, the surface area of the given cylinder is:

B. S = 250pi cm²

The surface area of a cylinder with radius r and height h is given by the following formula:

S = 2pi(r + h)

For this problem, the dimensions are given as follows:

r = 5 cm, b = 20 cm.

Hence we apply these measures to the given formula, and the surface area in square centimeters is given as follows:

S = 2pi(r + h)

S = 2pi x 5(5 + 20)

S = 250pi cm²

Hence option B is the correct surface area.

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Answer:

2·x^5·y

Step-by-step explanation:

2x^5y

Answer:

Step-by-step explanation:

122121