Compare the graphs f(x)=(x-10)^2+8 with the graph of f(x)=x^2

Answer:

All 3 are right triangles.

Step-by-step explanation:

In a right triangle c^2 = a^2 + b^2   where c is the longest side.  ( by Pythagoras).

a) 3^2 = 9, 6^2 = 36 and √27 ^ 2 = 27

36 = 9 + 27

So this is a right triangle.

b)

17^2 = 289, 15^2 = 225 and 8^2 = 64

289 = 225 + 64

Also right triangle.

c) √50 ^ 2 = 50, 5^2 = 25 and 5^2 = 25

So also right triangle.

The result of the subtraction of the vectors is: [706 -3 0].

To subtract two vectors, we subtract the corresponding elements.

In this problem, the vectors are given as follows:

The subtractions of the corresponding elements are:

Hence the result is:

[706 -3 0].

More can be learned about vector operations at https://brainly.com/question/26963744

#SPJ1

Answer:

Below.

Step-by-step explanation:

It's the Alternate Angle Theorem.

The opposite sides of the quadrilateral are parallel.

Answer:

The LCM is 20

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the LCM of 4, 10

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The lcm stands for the least common multiple.

Using our times tables, let's find the lcm of 4 and 10.

[tex]\bf{Which\;is\;20}[/tex]. 40 is indeed a common multiple of 4 and 10, but it's not the least common multiple. The lcm is 20.

We can also list some multiples of 4 and 10 and find the lcm.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...

10: 10, 20, 30, 40, 50, 60...

As you can see, we end up with the same answer: the lcm of 4 and 10 is indeed 20.

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{=Lcm=20}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]

The sum of angles of a triangle equals 180°.

Therefore:

|∠EAB| + |∠ABE| + |∠BEA| = 180°

Susbtitute

|∠EAB| = 14°

|∠ABE| = 45°

|∠BEA| = x°

14° + 45° + x° = 180°

59° + x° = 180°    |subtract 59° from both sides

∠BEA and ∠CED are vertical angles. Vertical angles are congruent, meaning that they have the same angle measure.

Therefore

In ΔCDE:

|∠CED| + |∠DCE| + |∠EDC| = 180°

Substitute:

|∠CED| =121°

|∠DCE| = 27°

|∠EDC| = y°

121° + 27° + y° = 180°

148° + y° = 180°    |subtract 148° from both sides

Let

[tex]S_N = \displaystyle \sum_{n=1}^N -7 \left(\frac38\right)^n = -7\left(\dfrac38 + \dfrac{3^2}{8^2} + \dfrac{3^3}{8^3} + \cdots + \dfrac{3^N}{8^N}\right)[/tex]

Then

[tex]\dfrac38 S_N = -7\left(\dfrac{3^2}{8^2} + \dfrac{3^3}{8^3} + \dfrac{3^4}{8^4} + \cdots + \dfrac{3^{N+1}}{8^{N+1}}\right)[/tex]

[tex]S_N - \dfrac38 S_N = -7 \left(\dfrac38 - \dfrac{3^{N+1}}{8^{N+1}}\right)[/tex]

[tex]\dfrac58 S_N = -\dfrac{21}8 \left(1 - \left(\dfrac38\right)^N\right)[/tex]

[tex]S_N = -\dfrac{21}5 \left(1 - \left(\dfrac38\right)^N\right)[/tex]

As [tex]N\to\infty[/tex], the exponential term will converge to zero, so the infinite sum converges to

[tex]\displaystyle \sum_{n=1}^\infty -7 \left(\frac38\right)^n = \lim_{n\to\infty} S_N = \boxed{-\dfrac{21}5}[/tex]

Answer:

Option C: y=-1/2x + 8

Step-by-step explanation:

So we have the options:

A) y=2x+5

B) y=-1/2x+4

C)y=-1/2x+8

D)y=-2x+5

But first let's define what parallel even is. When two lines are parallel it means that there slope is the same value and the same sign, while there y-intercepts are different, because if they were the same, then they wouldn't be parallel, they would just be the same exact line.

So we're given the equation in standard form. To find the slope we can change it so it's in the form of y=mx+b. This can be done by simply isolating y. The reason we want it in the slope-intercept form is because m represents the slope and b represents the y-intercept. m is the slope because as x increases by 1 the y-value will increase by m. So the "rise" will be m and the "run" will be 1, thus the slope will be m/1 or in other words m because the slope is defined as rise/run. So let's start the steps to isolating y

Original equation

2x+4y=16

Subtract 2x from both sides

4y=-2x+16

Divide both sides by 4

y = -1/2x + 4

Here we have it in slope-intercept form. In this case the slope, or m, is -1/2 and the y-intercept or b is 4. So now let's look at the other equations.

Option A: This equation has a slope of 2, which is not the same as -1/2 so it is not parallel

Option B: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. But look at the y-intercept it's 4, that's the same y-intercept as the original equation. This means the two equations are equal and not parallel

Option C: This equation has a slope of -1/2 which is the same as -1/2 so it might be parallel. It has a y-intercept of 8 which is not the same as 4, so the two lines are parallel and not equal! This is the answer

Answer: [tex]55^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line add to [tex]180^{\circ}[/tex].

We have been able to prove that the area of the triangle formed by the joining midpoints of triangle ABC is 1/4 the area of triangle ABC.

Area of triangle joining the points A, B & C is;

A₁ = ¹/₂[tex]\left[\begin{array}{ccc}1&1&1\\3&-2&5\\4&0&0\end{array}\right][/tex]

A₁ = ¹/₂(-1 * -20) + (1 * 8)

A₁ = 14

Thus;

Midpoint of AB is (¹/₂, 2)

Midpoint of BC is (³/₂, 0)

Midpoint of AC is (4, 2)

A₂ = [tex]\frac{1}{2} \left[\begin{array}{ccc}1&1&1\\\frac{1}{2} &\frac{3}{2} &4\\2&0&2\end{array}\right][/tex]

A₂ = ¹/₂(3 - 1(-7) + (1 * -3))

A₂ = ⁷/₂

Since A₁ = 14, we can equally say that;

A₂ = ¹/₄A₁

Read more about area of triangle at; https://brainly.com/question/13938833

#SPJ1

Answer:

3.57 taps

Step-by-step explanation:

14/5 = 10/x hours (divide both sides by 10)

50/14 = x (3.57 taps)

Brainliest, please :)

Answer:

7 taps

Step-by-step explanation:

rate =    1 tank / 5 taps = 14 hr

1 tank = 70 tap-hr

70 tap -hr  / x tap  = 10 hr

x = 7 taps

There's no "whole" number that gets exactly to 2230 (but the question that you are asking is the square root of 2230 I believe) but the answer would essentially be about 47.22.

The value of x is

1. x= -37/48

2. x=0

3. x = 33/4

4.  x= -20/7

A mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

1.  6(8 x + 6) + = - 1

   48x + 36 = -1

 x= -37/48

2.  9x/7 + 6 = 6

9x/7= 6-6

9x/7 =0

x= 0*7/9

x= 0

3. 2x/11 (11 - 7) = 6

    x * 4= 6*11/2

    4x= 33

    x = 33/4

4. 11x/4 (4 - 2) = 9x + 10

 11x/4 * 2 = 9x +10

11/2*x = 9x +10

-7/2x = 10

x= -20/7

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ1

The probability that the 2-digit number is prime is 3/8

The sets are given as:

First digit = {1, 2}.

Second digit = {1, 2, 3, 4}

When the 2-digit is formed, we have:

Numbers = {11, 12, 13, 14, 21, 22, 23, 24}

In the above set, there are 3 prime numbers out of the 8 numbers.

Hence, the probability that the 2-digit number is prime is 3/8

Read more about probability at:

https://brainly.com/question/11234923

#SPJ1

Answer:

  D)  Hungary

Step-by-step explanation:

You are being asked to compare 4 pairs of numbers. The population will have decreased if the number in the 2005 column is less than the number in the 1985 column.

Whenever you compare numbers, you start with the most-significant digit. If the most-significant digit has a higher place value, the number is larger. If the digits have the same place value, the number with the larger digit is larger. If no determination can be made by these comparisons, then the digits to the immediate right are compared.

  27,... > 19,...  2 > 1 in the 10-millions place

  10,... > 9,...  1 has a greater place value

  29... > 24...  comparison shifts to the 10-thousands place: 9 > 4

  10,058,... < 10,649,... . . . . the population decreased (0 < 6)

The "population decreased" result is found on the last line of the table, identified by the Country name "Hungary."

Hungary's population decreased from 1985 to 2005.

Answer: B. X = [tex]4\sqrt{6}[/tex]

Step-by-step explanation:

sec(45) = hyp/12

12sec(45) = hyp

hyp = 16.9

cot(60) = x/16.9

16.9cot(60) = x

x = 9.7

B. X = [tex]4\sqrt{6}[/tex]

Answer:

Irrational number

Step-by-step explanation:

  Prime factorize the number and then simplify.

[tex]\sf \sqrt{5}*\sqrt{5}*\sqrt{8}=\sqrt{5*5*8}[/tex]

                     [tex]\sf = \sqrt{5*5*2*2*2}\\\ = 5* 2* \sqrt{2}\\\\= 10\sqrt{2}[/tex]is an irrational number.

Answer:

m>35

Step-by-step explanation:

We have to find the least m for 65 + 0.8m > 93.

subtract 93 from each side of the inequality: 0.8m > 28

divide both sides of the inequality by 4: 0.2m > 7

multiply both sides of the inequality by 5 to find m: m>35.

The required range of the x in the inequality [tex]\left|x+3\right|-2\le0[/tex] is [-1, -5]
and the graph is attached below

Inequality, can be define as when the equations contain [≤ , ≥   <, >] is called inequalities.

Simplifying

[tex]\left|x+3\right|-2\le0[/tex]
[tex]|x+3|\leq 2\\-2\geq x+3\leq2 \\-5\geq x \leq-1[/tex]

Thus, the required range of x in inequality  [tex]\left|x+3\right|-2\le0[/tex] is [-5, -1].

learn more about Inequality here:
https://brainly.com/question/20383699

#SPJ1

Answer: The answer to the question is Answer Choice "B"

where it says x=-1

Step-by-step explanation:

Proof that It's actually correct as you can see it on the screenshot :)

Answer:  69m^2

Step-by-step explanation:

we can find the area of shaded region by  subtracting the area of removed region.

so,

area of rectangle= length*width

for area of removed region

=4m*2m=8m^2

for area of  larger region

=11m*7m=77m^2

Now final destinaltion

area of shaded region=area of lareger region-area of smaller region

                                     =77m^2-8m^2

                                    =69m^2

The simplification of each form of expression is;

(6r + 7) + (13 + 7r)

= 6r + 7 + 13 + 7r

= 13r + 20

(13 - 3/2r) - (1 - r)

= 13 - 3/2r - 1 + r

= 12 - 3/2r + r

= 12 -3r+2r/ 2

= 12 - 1/2r

(-8 - r) + (2r - 4)

= -8 - r + 2r - 4

= -12 + r

(7r - 3/2) - (2/3 + 6r)

= 7r - 3/2 - 2/3 - 6r

= r -9-4/6

= r - 13/6

Learn more about simplification:

https://brainly.com/question/723406

#SPJ1

Using proportions, it is found that Paula Radcliffe's World Record time was of 2h 15 min 25s.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In seconds, Dale Grieg's time is of:

3 x 3600 + 27 x 60 + 45 = 12,465s.

The Womens' World Record Marathon time has improved by 34.82%, that is, it was reduced by 34.82%, which means that the time is 65.18% of what it was, hence Paula Radcliffe's time is seconds is given by:

P = 0.6518 x 12465 = 8,125s.

In hours, minutes and seconds, we have that:

8,125s = 2h 15 min 25s.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

D : (0 ≤t ≤6)

R : (-2 ≤d ≤0)

Step-by-step explanation:

your domain is your x and your range is your y.

this means that you start by looking at your x axis. in this problem, x goes from 0 to 6, so 0 ≤t ≤6

this is the same for y.

y goes from -2 to 0 (remember that you read the y axis down and up, so you need to have the negative number written first)  

so -2 ≤d ≤0

Answer:

(domain: 0 ≤ t ≤ 6)

(range: -2 ≤ d ≤ 0)

Step-by-step explanation:

domain of a function: all possible x-values

range of a function: all possible y-values

here, we know that we can't have negative time (note: time is along the x-axis and is x-variable; it is describing the domain)

(and yes, while time still goes on forever, this graph does not have an arrow on the end of it, meaning that is where we are considering time to stop--and because its an ≤ sign, it wouldn't be infinity)

so, time goes from 0 to 6

(domain: 0 ≤ t ≤ 6)

here, we also know that our submarine won't go above the water level (it's not going to keep floating up into space forever), so the maximum value of our range (depth) is going to be 0

we also won't be going any lower than where the toy starts--which we can see to be -2

so, the depth goes from -2 to 0

(range: -2 ≤ d ≤ 0)

hope this helps!! have a lovely day :)

Angles around a point equal 360°, so n = 360 - 291 = 69°

Thus, as angles in a triangle add to 180°, m = 180 - 31 - 69 = 80°

Answer:

Actually this question is easy. Mutual angles are equal to each other. Then 152-90=62

The height of the building to the nearest foot is 121.5 ft.

The height of the building can be found using trigonometric ratios.

Therefore,

tan 59° = opposite / adjacent

tan 59°= h / 73

cross multiply

h = 73 tan 59°

h = 73 × 1.66427948235

h = 121.492402212

h = 121.5 ft

Therefore, the height of the building to the nearest foot is 121.5 ft.

learn more on height here: https://brainly.com/question/10393131

#SPJ1

The strategy that Lucy uses to recall her phone number is what is known as Chunking.

This refers to the place where information is stored for future use and can either be a short or long-term memory.

Hence, we can see that based on the breaking down of her phone numbers of Lucy into a particular format that separates them using country/state code, she is making use of chunking.

This method of chunking is effective because it would help Lucy to recall her number quite easily.

Read more about memory here:

https://brainly.com/question/24688176

#SPJ1

Original function involved multiplication by 4 and then subtraction of 2.

Inverse function involves addition of 2 and then division by 4.

So the inverse represents the reverse of the given process.

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

According to the function,

Let the function be represented by f(x).

Step 1- Multiplying the number x by 4 results in 4x.

Step 2 - Subtracting 2 from results give 4x - 2.

So the function becomes:

f(x) = 4x - 2

We will find the inverse function by Replacing f(x) by y, and isolate x on one side of the equation and find the inverse:

[tex]y=4x-2\\\\ < br/ > y+2=4x\\ < br/ > x =\frac{1}{4} (y+2)\\ < br/ > f^-^1(y) = \frac{1}{4} (y+2)\\ < br/ > f^-^1(x) = \frac{1}{4} (x+2)[/tex]

Here,

The inverse function represents the reverse process.

Here, Original function involved multiplication by 4 and then subtraction of 2.

Inverse function involves addition of 2 and then division by 4.

So the inverse represents the reverse of the given process.

Learn more about Function here:https://brainly.com/question/12431044

#SPJ1

Answer:

(x+5)² + (y+5)² = 18

Step-by-step explanation:

Since the outline of the circle intersects with the point (-8,2), you can substitute to find the equation of the circle in the form (x-h)² + (y-k)² = r². First the center of the circle is given in the form (h,k). So (-5, -5) → (x – (-5))² + (y – (-5))² = r² → (x + 5)² + (y + 5)² = r².

Then to find r², substitute the given point with x and y.

((-8) + 5)² + ((-2) + 5)² = r²

(-3)² + (3)² = r²

18 = r²

r² = 18.

Answer:

√41, or about 6.4 units

Step-by-step explanation:

[tex] \sqrt{ {5}^{2} + {4}^{2} } = \sqrt{25 + 16} = \sqrt{41} [/tex]

√41 is about 6.4 units