complete the square to solve the equation below. check all that apply.

x^2 + 8x - 1 = 19

There's a neat trick to finding the rational form of a repeating decimal number. Take for instance [tex]x=0.123123123\ldots[/tex]. Then

[tex]x = 0.123123123\ldots \\\\ \implies 1000x = 123.123123\ldots \\\\ \implies 1000x - x = 123.123123\ldots - 0.123123\ldots \\\\ \implies 999x = 123 \\\\ \implies x = \dfrac{123}{999}[/tex]

It's easy to reverse this method to find the repeating decimal form of [tex]\frac7{11}[/tex]. Let

[tex]x = \dfrac7{11}[/tex]

Multiply the numerator and denominator by 9,

[tex]x = \dfrac{63}{99}[/tex]

It follows that

[tex]x = \dfrac{63}{99} \\\\ \implies 99x = 63 \\\\ 100x - x = 63.6363\ldots - 0.6363\ldots \\\\ \implies x = 0.636363\ldots[/tex]

The first 20 digits after the decimal are made up of 10 each of 3 and 6, so the sum is 10 × (3 + 6) = 90.

Answer:

90

Step-by-step explanation:

Using long division, we find that  Every group of two digits after the decimal point has a sum of 9 so the sum of the first 20 digits after the decimal point is 10*9=90

The expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.

Given that, the length of the rectangle is [tex]\frac{5}{2}[/tex] units greater than twice its width.

We need to determine the expression that gives the perimeter of the rectangle in terms of w.

Given, width = w units, then length= 2w + [tex]\frac{5}{2}[/tex] units.

The perimeter of the rectangle is the sum of all the sides of the rectangle.

That is, perimeter of a rectangle = 2 (length+width).

Now, perimeter of a rectangle = 2 (2w + [tex]\frac{5}{2}[/tex]+w)=6w+5 units.

Hence, the expression that gives the perimeter of the rectangle in terms of w is 6w+5 units.

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Answer:

first blank: 3

second blank: 4

Step-by-step explanation:

The completed equation should say:

y = -3x + 4

This is slope-intercept form of the equation. It's a fill-in-the-blank equation. You put the slope in the first blank and the y-intercept in the second blank. Your math program put the negative sign in and it does need to be there. To find the slope, look at the points on the line. To get from one point to the next you go DOWN3 and over 1. DOWN3 and OVER1 is the slope -3/1, which is -3. This number goes beside (in front of) the x. The line crosses the y-axis at 4, fill that in at the end of the equation (the second blank).

The equation for the line is

y = -3x + 4

Step-by-step explanation:

please mark me as brainlest

Answer:

3. Definition of Midpoint

4. VAT, Vertical Angles Theorem

5. ASA, Angle-Side-Angle Theorem

If two lines intersect, then their opposite angles are equal. Then the value of  x is 25°.

The missing graph is given below.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Then the value of x will be

 75° = (4x - 25)°​

100° = 4x

   x = 25°

Then the value of  x is 25°.

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Vivian is traveling at 6 Noelle per hour and Noelle is traveling at  x+5 = 11 Noelle per hour.

Speed can be calculated as the ratio of distance traveled to the time taken.

Vivian and Noelle both leave the park at the same time, but in opposite directions, their total distance is the 136

Let Vivian's speed be = x

Let Noelle's speed be = x+5

They each can travel for 8 hours  

so time = 8 hours

Distance = speed × time

136 = x(8) + (x+ 5) 8

136 = 8x + 8x + 40

96 = 16x

x = 6

So, Vivian is traveling at 6 Noelle per hour and Noelle is traveling at  x+5 = 11 Noelle per hour.

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Answer:

See below

Step-by-step explanation:

The question is garbled.  I don't see a graph nor can I interpret the list of numbers.  

g(x) = 2x-1+3 can be simplified to:

g(x) = 2x+2

This line is shown in the attached graph.  It has a slope of 2 and a y-intercept of 2.

The missing blanks have been filled.

A function is a mathematical statement used to relate a dependent and an independent variable.

It is given that

Total time taken to hike is 8 hours

Let the time taken in hours is represented by t

and the elevation is represented by h

Every hour, the hikers gain 250 feet in elevation.

The independent variable is t , time taken to hike , in hours .

The dependent variable is h , increased elevation in feet or elevation the hikers have gained .

A possible verbal description is Elevation at any given time equals 250 times the time taken to hike.

The equation h = 250 t corresponds to the relationship.

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Answer: Choice D) set of even integers

=======================================================

Explanation:

U = universal set = {all positive integers} = {1, 2, 3, 4, 5, ...}

A = {stuff in set U that is odd} = {1, 3, 5, 7, 9, ...}

[tex]A^c[/tex] = {stuff in set U but NOT from set A} = {2, 4, 6, 8, ...}

[tex]A^c[/tex] = {set of even numbers from set U}

In set theory, the complement is simply the complete opposite. If the number 7 is found in set A for instance, then 7 is not going to live in the complement [tex]A^c[/tex]

The opposite of the odd numbers is the set of even numbers.

Therefore, we go for choice D as our final answer.

Side note: if we union set A with its complement [tex]A^c[/tex] then we get the universal set as a result. [tex]A \cup A^c = \text{universal set} = \text{set of all positive integers}[/tex]

The solution is Option D.

Ac =  {x|x ∈ U and is an even positive integer} where Ac represents the complement of set A

What is union and intersection of sets?

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set U be = {all positive integers}

So , the values of set U = { 1 , 2 , 3 , 4 , 5 .. }

And , let the set A = {x|x ∈ U and x is an odd positive integer}

So , the value of set A = { 1 , 3 , 5 , 7 , ... }

And , the complement of set  A is Ac

The value of set Ac is all the even positive odd integers

So , the value of set Ac = { 2 , 4 , 6 , 8 .. }

Therefore , the value of set Ac = { 2 , 4 , 6 , 8 .. }

Hence , the set Ac = {x|x ∈ U and is an even positive integer}

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Answer:

y = 5

Step-by-step explanation:

Since the lines are parallel, same side interior angles are supplementary.

That allows us to solve for x.

7x + 17 + 5x - 5 = 180

12x = 168

x = 14

The angles 23yand 5x - 5 are supplementary, so the sum of the measures equals 180°.

23y + 5x - 5 = 180

We already know that x = 14.

23y + 5(14) - 5 = 180

23y = 115

y = 5

The value of m will be; m  = (-∞ , - 15/4) ∪ ( 1 , ∞ ).

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given: line y = mx  + 3 intersects the line 3x + 4y + 12 = 0 at two distinct points.

To find the set of values of m.

The system of equations are;

y = mx  + 3

3x + 4y + 12 = 0

The intersection point are (1, −15/4)

So, the value of m will be

m  = (-∞ , - 15/4) ∪ ( 1 , ∞ )

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The correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that:-

We have the data from the question that the temperature of Bangkok is hotter than cape town.

Bangkok > Cape town

And the temperature of Cape town is hotter than Moscow.

Cape town > Moscow

Now for both the statements, the inequality will be given as:-

Bangkok's temperature < Cape Town's temperature < Moscow's temperature.

Therefore the correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.

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Answer:

333.333 Tiles and 333.333 Square Foot

Step-by-step explanation:

3X <= 1000

X <= 1000/3

X <= 333.333 Tiles

Then

333.333* 1sqt2 = 333.333 Square Foot

Answer:

(3, -2)

Step-by-step explanation:

 We can view slope as: [tex]\frac{rise}{run}[/tex] (rise / run)

"rise" is the change in y from one point to another

"run" is the difference in x from one point to another

So, if the slope of a line is 2, it rises 2 every time it runs 1 (2 = 2/1)

So, we can find another point on the line by adding 2 to the y-value, and adding 1 to the x-value.

(x, y)  

          (2, -4)

         + 1  + 2

           (3, -2)

So, another point on this graph is (3, -2)

The line that passes through (-2, 1) and (8, 2) is:

y = (1/10)*x + 12/10

I assume you want to find the equation of the line that passes through (-2, 1) and (8, 2).

A general linear equation is written as:

y = a*x + b

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we know that it passes through (-2, 1) and (8, 2), then:

[tex]a = \frac{2 - 1}{8 - (-2)} = 1/10[/tex]

Then the line is:

y = (1/10)*x + b

To find the value of b, we use one of the given points, for example if we use (8, 2), it means that when x = 8, we must have y = 2.

2 = (1/10)*8 + b

2 - 8/10  = b

20/10 - 8/10 = b

12/10 = b

Then the linear equation is:

y = (1/10)*x + 12/10

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The equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r

See attachment for the complete question

From the complete question, we have:

The angle is given in radians.

So, the arc length is calculated using

Arc length = Angle * Radius

Substitute known values

s = Θ * r

Hence, the equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r

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Answer:

A

Step-by-step explanation:

On Edge

Using the given information, the width of the river is 505.96 m

From the question, we are to determine the width of the river

Consider the given diagram,

Let F be the first position of the biker

S be the second position

and C be the position of the church

First, we will determine the distance covered from F to S

Speed = 160m/min

Time = 4 minutes

Using the formula,

Distance = Speed × Time

Distance covered = 160 × 4

Distance covered = 640 m

That is, /FS/ = 640 m

Now, consider ΔFSC

∠F = 90° - 70° = 20°

∠S = 90° + 56° = 146°

and ∠C = 180° - 20° - 146° = 14°

By the Law of Sines

[tex]\frac{/FC/}{sin\ S}= \frac{/FS/}{sin\ C}[/tex]

∴ [tex]\frac{/FC/}{sin\ 146^\circ}= \frac{640}{sin\ 14^\circ}[/tex]

[tex]/FC/ =\frac{640 \times sin \ 146^\circ}{sin \ 14^\circ}[/tex]

/FC/ = 1479.33 m

Now,

By SOH CAH TOA

[tex]cos \ 70^\circ = \frac{d}{/FC/}[/tex]

NOTE: d is the width of the river

∴ d = /FC/ × cos70°

d = 1479.33 × cos70°

d = 505.96 m

Hence, the width of the river is 505.96 m

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Answer: If Peter bought 8 toys, the cost of the toys will be 29.

From the equation, y = 3x + 5, they have given the value of x as eight. So if we put eight in the equation and solve it, we will get the value of y. I believe there are some errors in the question as it doesn't specify that y is the cost. Also cost requires some sort of unit, which is not given in the context. I can't really tell if it is dollars or rubles or pounds etc. So I just gave it as the way it is. Since no other clues are given, this is most likely it.

y = 3x + 5

y = 3(8) + 5

y = 24 + 5

y = 29

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Answer:

1. 85 people were surveyed

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for y and z ~

[tex]\qquad \sf  \dashrightarrow \: z + 61 = 180[/tex]

[ Co- interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \: z = 180 - 61[/tex]

[tex]\qquad \sf  \dashrightarrow \: z = 119 \degree[/tex]

now,

[tex]\qquad \sf  \dashrightarrow \: 5y + 14 = 119[/tex]

[ by Alternate interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \: 5y = 119 - 14[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5y = 105[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 21 °[/tex]

The angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.

For the given figures we need to find the unknown angles.

In the first figure to find angle p first apply the angle sum property to the triangle.

That is, 82°+31°+p=180° (∵ Sum of interior angles of a triangle is 180°)

⇒p=67°.

p=67° is a vertically opposite angle to the other triangle.

To find q:

67°+98°+q=180°

⇒q=15°.

In the second figure to find angles x and y apply the angle sum property to the triangle.

That is, 28°+(53°+x)+17°=180°

⇒98°+x=180°

⇒x=82°.

To find y:

x+y+17°=180°

⇒82°+y+17°=180°

⇒y=81°

In the third figure to find angles x and y apply the angle sum property to the triangle.

That is, 100-x+30+4x+7x=180°

⇒10x=80°⇒x=10°.

Now the angles of the triangle are 100-10=90°, 30+4x=70°

y=90°+70°=160° (∵Exterior angle is equal to the sum of two opposite interior angles).

In the 4th figure, to find angle 's' use the isosceles triangle concept.

That is, s+76°+76°=180° (∵In isosceles triangle base angles are equal)

⇒s=28°

In the 5th figure, to find angle 'm' use the isosceles triangle concept.

That is, 35°+m+m=180° (∵In isosceles triangle base angles are equal)

⇒2m=145°

⇒m=72.5°

Hence, the angles are p=67°, q=15°, x=82°, y=81°, s=28° and m=72.5°.

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Answer:

y = 47

Step-by-step explanation:

All of the angles in a triangle must add up to 180. The angle marked 3y can help us find the missing angle of the triangle: 180-3y
Then you can make an equation to help solve for y:
50 + (2y-3) + (180-3y) = 180
Combine like terms:
227-y=180
y = 47

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: y=47 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \:(2y - 3) + 50 = 3y[/tex]

[tex]\qquad \tt \rightarrow \:2y - 3 + 50 - 3y = 0[/tex]

[tex]\qquad \tt \rightarrow \:2y - 3y + 47 = 0[/tex]

[tex]\qquad \tt \rightarrow \: - y = - 47[/tex]

[tex]\qquad \tt \rightarrow \:y = 47 \degree[/tex]

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Answer:

6) B

7) D

Step-by-step explanation:

6)

The surface area of a cylinder is 2 * pi * r * (r + h)

SA = 2 * 3.14 * 3.6 * (3.6 + 8.5) = 2 * 3.14 * 3.6 * 12.1 = 273.6 cm^2

7)

The volume of a cylinder is pi * r^2 * h

V = 3.14 * (3.6)^2 * 8.5 = 345.9 cm^3

Answer:

6. surface area= 2πrh

where r=radius of the base

h=height of the cylinder

π=pie

π=22/7, r=3.6, h=8.5

2×22/7×3.6×8.5= 192.3cm²

square root of 192.3 is 13.9, the one whose square root is closest to that of 192.3 in the options is 178 whose square root is 13.3. A

7. volume=product of the height and its base area

volume=πr²h

22/7×3.6²×8.5 = 346.2. D

The percentage discount on the item will be equal to 8%.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The percentage of the discount will be calculated as:-

Percentage discount = ( 17 - 16.64 ) / ( 17 )

Percentage discount= ( 1.36 ) / ( 17 )

Percentage discount = 0.08 x 100 = 8%

Therefore the percentage discount on the item will be equal to 8%.

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The value of angle x is 67 degree.

A right angled Triangle is a triangle with one angle as 90 degree.

It is given that the for the angle x , the base of the triangle is 28 ft.

The hypotenuse = 72ft.

The trigonometric ratios can be used to find the value of x

cos x = 28 /72

x = cos⁻¹ (28/72)

x = 67 degree (Rounded off to nearest tenth)

Therefore the value of angle x is 67 degree.

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Answer: p=2, q=-1

Step-by-step explanation:

[tex]\frac{\sqrt{3}-1}{\sqrt{3}+1} \left(\frac{\sqrt{3}-1}{\sqrt{3}-1} \right)=\frac{3+1-2\sqrt{3}}{2}=\frac{4-2\sqrt{3}}{2}=2-\sqrt{3}\\\\\therefore p=2, q=-1[/tex]

The total amount of snowfall on the two days combined is 4 3/8 cm

From the question, we are to determine the amount of snowfall on the two days combined

From the given information,

the amount of snowfall was 1/8 cm on Thursday

The amount of snowfall was 4 1/4 cm on Wednesday

Then,

The total amount of snowfall on the two days combined will be

[tex]\frac{1}{8}+4\frac{1}{4}[/tex] cm

= [tex]\frac{1}{8}+\frac{17}{4}[/tex]

= [tex]\frac{1+34}{8}[/tex]

= [tex]\frac{35}{8}[/tex]

= [tex]4\frac{3}{8} \ cm[/tex]

Hence, the total amount of snowfall on the two days combined is 4 3/8 cm

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