Solve the simultaneous equations
y=2-5x
y = x² – 2x – 8

Answer:

n - 4 = - 15

Step-by-step explanation:

Hope this helps :)

Answer:

32

Step-by-step explanation:

[tex]5\cdot \:5+7[/tex]

The annual interest rate is 6.69%  for 3 years at compound interest.

What does the term "compound interest" mean?

[tex]A = P.( 1 + \frac{r}{n} )^{n.t}[/tex]

p = 5600

t = 3

I = 1200

n = 1

The interest  earned I is

I = [tex]P. ( 1 + \frac{r}{n} )^{n.t} - P[/tex]

1200 = [tex]5600 . ( 1 + \frac{r}{1} )^{1.3} - 5600[/tex]

[tex]1200 = 5600 .( 1 + r )^{3} - 5600[/tex]

[tex]\frac{1200}{5600} = ( 1 + r)^{3} - 1[/tex]

[tex]\frac{3}{14} = ( 1 + r )^{3} - 1\\[/tex]

[tex]\frac{17}{14} = ( 1 + r)^{3}[/tex]

Take the log base 10 of both sides

log17 - log14 = 3.log( 1 + r)

1.23045 - 1.14613 = 3.log( 1 + r)

3.log( 1 + r) = 0.084322

log( 1 + r) = 0.028107

1 + r = [tex]10^{0.28107}[/tex]

1 + r = 1.06686

r = 0.06686

The annual interest rate is 6.69%.

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All real numbers x more than 2 units from 0 will be |x - 2| ≤ 0.

What does "real number" mean?

All real numbers x at most 2 units from 0

This means if x is centered at 2 then it can move at the max 2 units on either side (i.e. 4 units after 2 and 0 units before 2)

This will be |x - 2| ≤ 0

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A triangle is a 2-dimensional shape that has 3sides and 3 interior angles. The height of the isosceles triangle is approximately 49.5cm

The theorem states that the square of the hypotenuse is equal to the sum of the square of other two sides.

From the given question, the hypotenuse is 50cm and the base of the triangle is 14cm

Determine the height using the expression

h² = 50² - (14/2)²

h² = 2500 - 7²

h² = 2500 - 49

h = √2451

h = 49.5cm

Hence the height of the triangle is approximately 49.5cm

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Answer:

Where exactly is the "the following" you are talkibg about.

Answer:40 miles

Step-by-step explanation:

Answer:

-4/7, 1/19, 7/4

Step-by-step explanation:

-4/7 is less then zero, and the only negative number so it is first

1/19 is the second lowest

7/4 is the highest because it is the only one that is greater then 1. (simplified, 7/4= 1 3/4)

Answer:

150pi

Step-by-step explanation:

The formula for the volume of a cone is one-third the volume of a cylinder.

It is   [tex]V=\frac{1}{3} Bh[/tex]   where B is the area of the circle base and h is the height of the cone.

To find the base of the cone, use the formula for the area of a circle. So, the radius is 5. So, the area of the base is pi × radius².

[tex]5^{2} =25[/tex]

[tex]\frac{1}{3}[/tex] × 25pi × 18 = 150pi

Answer:

SHOWN BELOW!!!!

Step-by-step explanation:

KEEP IN MIND ----> *Square root of a number is a value, which on multiplication by itself gives the original number. The square root is an inverse method of squaring a number.*

Alright so the first equation C^2 - 49 = 0

Step 1 : Add 49 to both sides

C^2 - 49 + 49 = 0 + 49

C^2 = 49

Step 2 : Take the square root

(squ root) C^2 = (squ root)49

C = +/- (squ root) 49

Final answer ---> C = 7 OR C = -7

2.) 4S^2 - 100 = 0

Step 1 : Add 100 to both sides

4S^2 - 100 + 100 = 0 + 100

4S^2 = 100

Step 2 : Divide both sides by 4

4S^2/4    =   100/4

S^2 = 25

Step 3 : Take the square root

(squ root) S^2 = (squ root) 25

S =  +/- (squ root) 25

Final answer ---> S = 5 OR S = -5

3.) 9x^2 = 324

Step 1: Divide both sides by 9.

9x^2/9 = 324/9

x^2 = 36

Step 2: Take the square root

squ root) x^2 = (squ root) 36

x = +/- (squ root) 36

Final answer ---> x = 6 OR x = -6

The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]

To find the equation:

When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:

[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]

The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:

As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]

Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]

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The correct question is given below:

Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.

Answer: x=5+[tex]\sqrt{15}[/tex]

Step-by-step explanation:

x² - 10x+10=0

x² - 5x - 5x+10=0

x² - 5x - 5x+25-15=0

(x-5)^2 -15=0

(x-5)^2=15

x-5=[tex]\sqrt{15}[/tex]

x=5+[tex]\sqrt{15}[/tex]

Answer:

$1,820

Step-by-step explanation:

The math problem is $35 times 52 weeks

Answer: the slope=0

Step-by-step explanation:

[tex]\displaystyle\\(7,-2)\ and\ (7,5)\\[/tex]

                        [tex]\displaystyle\\\boxed {the \ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]

[tex]x_1=7\ \ \ \ \ x_2=7\ \ \ \ y_1=-2\ \ \ \ \ y_2=5\\Hence,\\\displaystyle\\the slope=\frac{7-7}{5-(-2)} \\\\the\ slope=\frac{0}{5+2} \\\\the\ slope=\frac{0}{7}\\\\ the\ slope=0[/tex]

Answer:

y-intercept : 3

x-intercepts are 1 and 2

Vertex is at (2,-1)

Axis of symmetry is at x = 2

Step-by-step explanation:

See attached graph.

The equation y = x² – 4x + 3 represents a parabola

y-intercept at is at B(0,3); y-intercept is 3

x-intercept points at C(1,0) and D(3,0) so x-intercepts are 1 and 3

The vertex is the lowest point on this parabola (2-1)

Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line x = 2

The equation of the line shown in the diagram is y = 0.5x+0.5.

A line is a mark connecting two points.

To calculate the equation of the line, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the equation of the line shown in the diagram is y = 0.5x+0.5.

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The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.

Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be

V = π r²h cubic units

A cylindrical tube 14.5 cm high and 4.5 cm in diameter is used to collect blood samples. Then the radius of the cylinder will be

r = d / 2

r = 4.5 / 2

Then the volume of the cylinder will be

V = π r²h

V = 3.14 (4.5 / 2)² × 14.5

V = 3.14 × 20.25 × 14.5 / 4

V = 921.98 / 4

V = 230.5 cubic cm

V = 0.23 cubic dm

The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.

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Answer:  onever

Step-by-step explanation:

4x-8>1+4(x+3)

4x-8>1+4(x)+4(3)

4x-8>1+4x+12

4x-8>4x+13

4x-8-4x>4x+13-4x

-8>13

Hence, inequality is never true

Answer:

1 and 1/6 or 7/6

Step-by-step explanation:

Answer:

7/6

Step-by-step explanation:

=5/6+2/6

=5/6+1/3

7/6

She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.

The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.

Since the race is 21 miles in total, x and y together must add up to 21.

Hence,

x + y = 21

The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation

d = st, or t = d/s.

Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:

x/8 + y/12 = 2

Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24

3x + 2y = 48

And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:

3x + 2(21 - x) = 48

3x + 42 - 2x = 48

x = 6

Use y = 21 - x again:

y = 21 - (6) = 15.

Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.

Obviously, 15 + 6 = 21, thus the overall distance is correct.

In terms of time, 6 miles at 8 mph takes

6/8 =.75 hours = 45 minutes, whereas

15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.

As stated in the question, the total time to complete would be.

75 + 1.25 = 2 hours.

As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.

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Answer: -15.5 or -31/2

Step-by-step explanation:

it may look weird but if that's what the equations says then your gonna do it.

-5(3/10) -> (5/1)(3/10) = 15/10 = -3/2 or -1.5
-1.5 - 14 = -15.5

:

() =-5-14 (=3/10)

(3/10)= -5 (3/10) -14

f(3/10) = -15/10 -14

= -15-140

----------

10

= -195/10

=- 19.5

The standard deviation is provided by this. = 6.7528

Because it aids in comprehending measurements whenever the data is distributed, the standard deviation is significant. The standard deviation of the data will be higher the more evenly distributed the data is.

sample data = ( 32, 41, 36, 24, 29, 30, 40, 22, 25, 37)

To find mean of the given data:

Mean = Sum of items/ Count items

Mean = (32 + 41 + 36 + 24 + 29 + 30 + 40 + 22 + 25 + 37 / 10)

          = 31.6

now finding the variance:

First we  Add All the sample:

32 + 41 + 36 + 24 + 29 + 30 + 40 + 22 + 25 + 37 = 316

make Square of the solution:

316*316 =99856

and multiply by how many items there are. We have 10 items.

=99856/10

= 9985.6

For the time being, put this number aside.

Take your original set of numbers from Step 1 and square each one this time on its own.

32² + 41² + 36² + 24² + 29² + 30² + 40² + 22² + 25² + 37² = 10396

Subtract the sum from Step 2 from of the sum from Step 3.

10396 - 9985.6 = 410.4

The items in someone data set is reduced by 1 by.10 - 1 = 9

Divide the result of Step 4 even by result of Step 5. You get the variation from this.

410.4 / 9 = 45.6

Your response from Step 6 should be squared. The standard deviation is provided by this.

6.7528

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I understand that the question you are looming for is:

For the following sample data, compute the variance and the standard deviation. 32, 41, 36, 24, 29, 30, 40, 22, 25, 37

You can just try out all the answers but I'll give you a solution.

We will expand out the middle term to 5x^2 - 30x - 6x + 36, then we group the first 2 terms together, and the last 2 terms together.

= 5x (x - 6) - 6(x - 6)

And we put x-6 out : (x-6)(5x-6) = 0

Now, we can just set the value of one bracket to 0 and find out the value of x, and do the same for the other one

x - 6 = 0 -> x = 6
5x - 6 = 0 -> x = 6/5

Because 6 is not a possible option, the answer is x = 1.2

Answer:

it's x+3

Step-by-step explanation:

it seems to go up by one so if you go down by you the input of 1 would be the output of 4 also known as (1,4)

and go again down by 1 and get (0,3)

so we know we have to add 3 each time so it is x+3

MBND is a parallelogram as BN=MD and BN║MD.

A parallelogram is a quadrilateral whose both pair of opposite side are equal and parallel. Few examples of parallelograms are square, Rhombus  and rectangle.

Given ABCD is a parallelogram and ∠A=90°

Now we have to prove that MBND is a parallelogram

Given BN⊥AC and DM⊥AC

Since BN and DM are both perpendicular to the same straight line AC then we cam say that BN║DM.

Again we know  from the properties of parallelogram that the diagonal divides a parallelogram into two equal triangles.

Therefore the diagonal AC divides the parallelogram into two equal triangles ΔABC and ΔADC.

Now we know that the area of a triangle is given by [tex]\frac{1}{2}[/tex] ×base ×height .

Area of  ΔABC =Area of ΔADC

Since BN⊥AC and DM⊥AC

∴[tex]\frac{1}{2}[/tex]×BN×AC=[tex]\frac{1}{2}[/tex]×DM×AC

This above equation can be simplified as

BN=MD

Hence BMND is a parallelogram as we know from the properties of parallelogram that when a pair of opposite sides are equal and parallel in a quadrilateral it is a parallelogram.

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Answer:

C

Step-by-step explanation:

539/3 = 179.666

85/3 =28.3333

9285/ 3 = 3095

640/3=213.3333

Answer:

C

Hope this helps :)

Step-by-step explanation:

All the others numbers equal a decimal when divided by 3. However, C equals a whole number so it's C.

9,285 ÷ 3 = 3,095

The height of the tower is approximately 46.765 feet

Step-by-step explanation:

The given parameters are;

The distance from the foot of the tower where the angle of elevation is

measured = 27 feet

The angle of elevation to the top of the tower from a point 27 feet from the foot of the tower, θ = 60°

Therefore, by trigonometric ratio, we have;

tan 60= the height of tower / distance from foot of tower

[tex]\sqrt{3}[/tex]= height of tower /27

1.73205 *27 = height of tower

46.765 feet is the height of tower

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An angle is denoted by the angle symbol ∠ and the three letters representing the name of the angle.

An angle is denoted by the angle symbol ∠ which is then being followed by three letters that will represent the points that form an angle.

Lets say for example, the expression ∠ABC will mean that “the angle is formed by the points A, B and C”

where the vertex of the angle is at the point B as it is in the middle.

Angles can also be of different types like:

An Acute Angle which means an angle is less than 90 degrees.

A Right Angle which means an angle which is exactly 90 degrees.

An Obtuse Angle which is an angle more than 90 degrees and less than 180 degrees.

A Straight Angle which is an angle that is exactly 180 degrees.

And a Reflex Angle which is an angle greater than 180 degrees and less than 360 degrees.

Therefore, an angle is denoted by the angle symbol ∠ and the three letters representing the name of the angle.

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Answer: A=-2

Step-by-step explanation:

AB=11

B=9

B-11=A

9-11=A

A=-2