MN= cm
Help me please!! Stuck on this thanks:)

Answer:

B

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

(x + 1)² + (x + 3)² = (x + 5)² ← expand all factors using FOIL

x² + 2x + 1 + x² + 6x + 9 = x² + 10x + 25 , that is

2x² + 8x + 10 = x² + 10x + 25 ← subtract x² + 10x + 25 from both sides

x² - 2x - 15 = 0 ← in standard form

(x - 5)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 3 = 0 ⇒ x = - 3

however, x > 0 , then x = 5

Answer:

B. 5

Step-by-step explanation:

[tex] \sf{C = \sqrt{ A {}^{2} + B {}^{2} }}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(x + 3)}^{2} + {(x + 1)}^{2} }}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(x {}^{2} + 6x + 9)} + {(x {}^{2} + 2x + 1)}}}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(2x {}^{2} + 8x + 10)}}}[/tex]

[tex]\sf{(x + 5) {}^{2} = { {2x {}^{2} + 8x + 10}}}[/tex]

[tex]\sf{ {x}^{2} + 10x + 25= { {2x {}^{2} + 8x + 10}}}[/tex]

[tex]\sf{0= { {2x {}^{2} \red{ { - x}^{2} } + 8x \red{ - 10x} + 10 \red{ - 25}}}}[/tex]

[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]

[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]

[tex]\sf{0= (x - 5)(x + 3)}[/tex]

[tex] \sf{x_{1} - 5 = 0 }[/tex]

[tex] \sf{x_{1} = 0 + 5 }[/tex]

[tex] \sf{x_{1} = \boxed{5 }}[/tex]

[tex] \sf{x_{2} + 3 = 0 }[/tex]

[tex] \sf{x_{2} = 0 - 3 }[/tex]

[tex] \sf{x_{2} = \boxed{- 3 }}[/tex]

Option B. 5

The number of teams that can be made is 10.

In order to determine the number of teams he can make, divide the number of friends by the total number of people that must be in the team. Division is the process of grouping a number into equal parts using another number.

31 / 3 = 10 remainder 1

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Answer:

[tex]x=\frac{35}{9} .[/tex]

Step-by-step explanation:

[tex](3\sqrt{3})^{-x+1} =\frac{1}{3}*27^{x-5}\\( \sqrt{3^2*3}) ^{1-x}=\frac{1}{3} *((3)^3)^{x-5}\\(\sqrt{27} )^{1-x}=\frac{1}{3}*3^{3*(x-5)}\\ (\sqrt{3^3})^{1-x} =\frac{1}{3}*3^{3x-15}\\ 3^{\frac{3 }{2}*(1-x)}=\frac{1}{3}*3^{3x-15}\ |*3\\ 3*3^{\frac{3}{2}-\frac{3}{2}x}=3^{3x-15}\\ 3^{1+1,5-1,5}=3^{3x-15}\\ 3^{2,5-1,5x}=3^{3x-15}\ \ \ \ \Rightarrow\\2,5-1,5x=3x-15\\4,5x =17,5\ |*2\\9x=35\ |:9\\x=\frac{35}{9}.[/tex]

Answer:

y = sin3x

Step-by-step explanation:

the equation is of the form y = sinbx

the period of the sine wave is

period = [tex]\frac{2\pi }{b}[/tex] ( b is the coefficient of x )

here period = [tex]\frac{\pi }{3}[/tex] × 2 = [tex]\frac{2\pi }{3}[/tex] , then

[tex]\frac{2\pi }{3}[/tex] = [tex]\frac{2\pi }{b}[/tex] ⇒ b = 3

y = sin3x ← equation of graph

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is D.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

For a function to be even, the graph of the function should be such that it should be symmetrical about the x-axis. Therefore, the points of the graph will be the opposite.

The 7 points of option D can be plotted as shown below, which is symmetrical about the X-axis. Hence, the correct option is D.

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(a) The gradient is [tex]\frac{40}{5}=\boxed{8}[/tex], and represents the cost of buying one book in dollars.

(b) Draw the line through (0,0) and (20, 130).

(c) Since the gradient of the line representing company B is less (6.5 vs 8), it is better to buy books from company B because they are cheaper.

The locus of the point represented by the equation y = 3•x + 2, indicates that the point (1, 5) is on the locus of the point.

The distance from the x-axis is the y-value

The distance from the y-axis is the x-value

Therefore;

The equation of the locus of the point is presented as follows;

When x = 1, y = 3 × 1 + 2 = 5

When x = 1, y= 5

Therefore;

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The loan amount is given as $76521

We first have to calculate the total amount of tuition

6970 x 4 + 11320 x 4

= 73160

[tex]73160 (1+\frac{\frac{4.5}{100} }{12} )^1^2[/tex]

= 73160 x (1 + 0.00375)¹²

= 76520.95

Hence the new loan amount after  agrace period of 1 year = $76521

b. PV = $76521

i = [tex]\frac{4.5/100}{12}[/tex]

= 0.00375

t = 10 years

[tex]PMT[\frac{1-(1+0.00375)^-^1^2^0}{0.0375} ]= 76521[/tex]

pmt = 793. 05

The monthly payment is  $793. 05.

In ten years the total payment is 793.05 x 10 x 12

= 95166

Difference = 95166 - 76521

= $18645

In ten years her ,monthly payment on the loan would be  $18645.

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Answer:

30000 milliliters

0.03 liters

Step-by-step explanation:

The volume of the box is 2.5 x 3.0 x 4.0 = 30 cc

There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml

There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters

The volume of the box is 30 mL or 0.03 L.

Volume is a metric magnitude that is defined as the extension in three dimensions of a region of space. Volume is defined as the amount of space occupied by the object or figure in three-dimensional space. Volume is measured in cubic units.

The volume of this prism depends on its three dimensions and is calculated as the multiplication of these dimensions,

Volume= Dimension 1× Dimension 2× Dimension 3

The volume of the box = 2.5 x 3.0 x 4.0 = 30 cc

There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml

There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters

Hence, the volume of the box is 30 mL or 0.03 L.

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Step-by-step explanation:

the whole forest is 4920 km².

4/5 if that was destroyed with salvageable wood :

4/5 × 4920 = 3,936 km²

there is 30 tons of salvageable wood per km², so in total :

3936 × 30 = 118,080 tons.

the wood can be removed at av rate of 53.5 tons per day.

how many days until cleaned up ?

as many days as 53.5 fits into the total amount of 118,080 :

118080 / 53.5 = 2,207.102804... days.

so, it will take about 2,207 days to remove all the salvageable wood.

The additive inverse of the polynomial is 6x³-4x²+4x.

Given The polynomial is -6x³+4x²-4x.

A polynomial is an expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It consists of indeterminates and coefficients.

The number that results in zero when a number is added to it is said to be a number's additive inverse. The opposite, a shift in the sign, and negation are other names for this number.

The given polynomial is -6x³+4x²-4x.

To find the additive inverse of the polynomial, multiply the polynomial with minus sign, we get

-(-6x³+4x²-4x)=6x³-4x²+4x.

Hence, the additive inverse of the polynomial -6x³+4x²-4x is 6x³-4x²+4x.

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Answer:

(6,2)

Step-by-step explanation:

If you are looking for the coordinates then that is the correct answer.

Answer:

(6,2)

Step-by-step explanation:

Because the Y axis is vertical so you would move down and subtract 5 from the 7. Your X would stay the same. So the answer will be (6,2)

Answer:this is all I could find

Step-by-step explanation:

Answer:

1.  A(-8,3) B(-8,-2) C(-4,-2)

2. A'(8,3) B'(8,-2) C'(4,-2)

3. A"(-12,1.5) B"(-12,-3) C"(-6,-3)

4. they give you the coordinates, haha. Just graph and connect the dots.

5. Coordinates of ABC: A(-8,3) B(-8,-2) C(-4,-2)

   Coordinates of A'''B'''C''': A'''(-3,10) B'''(-3,5) C'''(1,5)

The correct coordinates for a 90 degree rotation is: A''''(3,8) B''''(-2,8) C''''(-2,4)

Most of these are formulas so I hope you have this memorized in preparation for tests! Good luck!

Based on the given texts in the table about the graph of the function, the true statements are:

The function, 4x - 15 shows that 15 is the y-intercept which means that the graph will cross the y-axis at (0,15).

The point of discontinuity is x = - 2 and we see this with the gap created at x < -2 and -2 ≤ x ≤ 4.

The graph is indeed increasing over the interval (4, ∞o) because any value of x that is greater than 4 will increase f(x) = [tex]3^x^-^4[/tex].

The domain of the function is also all real numbers as it begins at negative infinity and ends at infinity, (-∞, ∞).

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Answer:

about 1920

step by step explanation:

40×50weeks=2000hours per year.

40×2weeks(the weeks off) = 80

2000-80= 1920hours per year

Answer: [tex]|f(x)-8| < 0.03[/tex]

Answer:

-12.8 %

Step-by-step explanation:

-3200 / 25 000   x 100%  =  -  12.8 %

Answer:

Your answer is -12.8%

Step-by-step explanation:

To calculate the percent decrease, we:

Find the difference between the new value and the original

Divide the number by the original

Multiply by 100 and the % symbol.

The population of the town originally had 25,000. 3,200 people moved away. This means that the new population is 21,800.

21,800-25,000=-3,200

-3,200/25,000=-0.128

-0.128(100)=-12.8%

The towns population decreased by 12.8%.

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Required probability is 0.8990

Given that,

p = 0.44

1 - p = 0.56

n = 736

[tex]\mu_\hat{p}} = p = 0.44\\\sigma_\hat{p}} = \frac{p*(1-p)}{n} = \sqrt(\frac{0.44*0.56)}{736} ) =[/tex]0.01830

Converting Normal distribution to standard normal because  A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. Hence it's easy to work with standard normal distribution.

P(0.14<[tex]\hat{p}[/tex]<0.47) =  P((0.41-0.44)/0.01830) < [tex]\frac{\hat{p} - \mu _{\hat{p}} }{\sigma _{\hat{p}} }[/tex]<(0.47-0.44)/0.01830

Using normal algebra we get:

= P(-1.64 < z < 1.64)

= P(z < 1.64) - P(z < -1.64)

= 0.9495 - 0.0505

= 0.8990

Thus, required probability is 0.8990

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Step-by-step explanation:

310/100 × 72

= 223.2

using fraction × total

hope you understand.

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The number b is b > -5/9

The statement is given as:

a number b times 18 is greater than -10

This can be represented as:

b * 18 > -10

Divide both sides by 18

b > -10/18

Simplify

b > -5/9

Hence, the number b is b > -5/9

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The longest possible integer length of the third side of the triangle is 6 < x < 28

The sum of any two sides must be greater than the third side for a triangle to exist

let the third side be x

x + 11 > 17 and x + 17 > 11 and 11 + 17 > x

x > 6 and x > - 6 and x < 28

The longest possible integer length of the third side of the triangle is 6 < x < 28

The length of the 3 sides of a triangle needs to always be among (however no longer the same) the sum and the difference of the opposite two sides. As an example, take the instance of two, 6, and seven. and. consequently, the third side period should be extra than 4 and less than 8.

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Answer:

27

Step-by-step explanation:

Let the third side length be s. Then, by the Triangle Inequality, we know that s satisfies the inequalities

[tex]s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.[/tex]

[tex]\begin{align*} s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.\end{align*}[/tex]

The first two inequalities hold as long as s > 6 and the third holds if s < 28. The largest possible integer s that satisfies all of these is 27.

The system of linear inequalities which satisfy the region R are:

Mathematically, the standard equation of a straight line is given by y = mx + b.

In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which the lines passes through.

For the broken line, we have:

y-intercept = 3.

x-intercept = -3.

Points (x, y) = (0, 3) and (-3, 0).

Since the line is broken (not equal to), the inequality is given by:

y < x - 3.

For the other line, we have:

y-intercept = 5.

x-intercept = -5/2.

Points (x, y) = (0, 5) and (-5/2, 0).

(x/-5/2) + y/5 ≤ 1

-2x + y ≤ 5

y ≤ -2x + 5

For the line passing through the origin, we have:

y - x ≥ 0

y ≥ x.

In conclusion, the system of linear inequalities which satisfy the region R are:

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The statements about the function that are true include:

g(0) = 0

g(1) = -1

g(-1) = 1

From the information, the points include:

(x1, y1) = (-2, 2, 5).

(x2, y2) = (0, 0)

(x3, y3) = (2, 3, 5).

It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in ten graph.

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Answer: the answer is b, d, and e.

g(0) = 0

g(1) = 1

g(-1) = 1

Step-by-step explanation:

Answer:

The equation for the line which passes through the points given as (a, b) and (a, b+1), is x=a, which represents a vertical line.

Step-by-step explanation:

It is given that a line passes through the points whose coordinates are (a, b) and (a, b+1).

It is asked to find the linear equation which passes through the given points.

To do so, first determine the slope of the given line using the coordinates and the formula for the slope. Accordingly, proceed to find the equation of the given line.

Step 1 of 2

Determine the slope of the line.

The points through which the line passes are given as (a, b) and (a, b+1). Next, the formula for the slope is given as,

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

Substitute b+1&b for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and a&a for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]m=\frac{b+1-b}{a-a}$\\ $m=\frac{1}{0}$[/tex]

b+1. So the equation of the line cannot be found using the general point-slope form equation.

Step 2 of 2

Write the equation of the line.

So, by definition, the line that passes through the given points is a vertical line. Now, as its x- coordinate is a, so the equation of the line is given as x=a.

Recall that the area of a trapezoid is equal to the average of its bases times its height.

For the trapezoids shown here, each base corresponds to the value of [tex]y=2x^2[/tex] when [tex]x[/tex] is one of the endpoints of some interval, while the height is the length of that interval.

On the interval [-2, -1], the trapezoids has bases 2(-2)² = 8 and 2(-1)² = 2, and "height" -1 - (-2) = 1. Then its area is (8 + 2)/2 × 1 = 5.

On the interval [-1, 0], one of the bases is 2(-1)² = 2 and the other is 2(0)² = 0, and the height is again 0 - (-1) = 1. Then the trapezoid's/triangle's area is (2 + 0)/2 × 1 = 1.

Then the total area under the curve [tex]y=2x^2[/tex] on the interval [-2, 0] is approximately 5 + 1 = 6.

Compare this to the actual value of the area given by the definite integral,

[tex]\displaystyle \int_{-2}^0 2x^2 \, dx = \frac{16}3 \approx 5.333\ldots[/tex]

Answer:

c.) 6 1/2

Step-by-step explanation:

Volume = length × width × height

2 1/6 × 1 1/5 × 2 1/2

13/6 × 6/5 × 5/2

13/5 × 5/2

13/2 = 6 1/2

The proportion that solves for the distance between D and E is  x/15 = 6/9

An equation is an expression that shows the relationship between two or more numbers and variables.

Triangle ABC and CDE are similar triangles, hence the ratio of their corresponding sides are in the same proportion.

Hence:

x/15 = 6/9

The proportion that solves for the distance between D and E is  x/15 = 6/9

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