complete the square to solve the equation below. check all that apply.
x^2 + 8x - 1 = 19
Answers
Answer:
B and D
Step-by-step explanation:
First take the equation and subtract 19 on both sides. You get x^2+8x-20=0
using the quadratic formula you get x= (-8 + or - root (8^2 -4(1)(-20)))/ 2(1)
simplify it and you get x= (-8 +or- 12) / 2
Separate the equation into two and you get (-8 + 12) / 2 and (-8 - 12) / 2
first one gives: 4/2=2
second gives -20/2=-10
answer x=-10,2
Related Questions
Which is the graph of g(x) = 2x-1+3?
O
-12
-8
-4
8-
4
-8
-12+
8
X
Answers
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.
When 7/11 is written as a decimal, what is the sum of the first 20 digits after the decimal point? Pls Help
Answers
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
Avani has a loyalty card good for a discount at her local hardware store. The item she wants to buy is priced at $17, before discount and tax. After the discount, and before tax, the price is $15.64. Find the percent discount.
Answers
The percentage discount on the item will be equal to 8%.
What is the percentage?
The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
Price of the item before tax and discount = $17After discount and before tax price is = $15.64The 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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In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s?
Circle O is shown. Line segments A O and B O are radii with length r. Angle A O B has a measure of theta. Arc A B has a measure of s.
s = Θ · r
r = Θ · s
s = Θ + r
r = Θ + s
Answers
The equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r
How to determine the arc length?See attachment for the complete question
From the complete question, we have:
Θ represents the central angler represents the circle radiusThe 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
please help me with my math
Answers
[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]
Vivian and Noelle both leave the park at the same time, but in opposite directions. If Noelle travels 5 mph faster than Vivian and after 8 hours, they are 136 miles apart, how fast in mile per hour is each traveling
Answers
Vivian is traveling at 6 Noelle per hour and Noelle is traveling at x+5 = 11 Noelle per hour.
What is speed?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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Determine the Angle Measures
Answers
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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Find the equation of the line passing through the points -2x+1 (8,2)
Answers
The line that passes through (-2, 1) and (8, 2) is:
y = (1/10)*x + 12/10
How to find the equation of the line?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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−3(a−8)+4a=−8(a+3)+3
Answers
Reason
Distribute multiply parentheses first
-3(a-8) +4a= -8(a+3)+3
-3a +24 +4a = -8a -24 +3
Now combine like terms to isolate “a”
-3a +4a +8a = -24 +3 -24
9a = -45
Now divide both sides by 9 to solve for “a”
a= -5
) How long does he travel at 30 km/h, if he travels 1.2 h at 20 km/h?
Answers
Step-by-step explanation:
please mark me as brainlest
On Thursday, the amount of snowfall was 1/8 cm. On Wednesday, the amount of snowfall was 4 1/4 cm. What was the amount of snowfall on the two days combined?
Answers
The total amount of snowfall on the two days combined is 4 3/8 cm
Addition of fractionsFrom 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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HELP WITH THIS PLSSS ITS CYLINDERRR
Answers
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 cost of the toy is expressed by the function y = 3x + 5, where x is the number of toys. If Peter bought 8 toys, find the cost of the toys.
Answers
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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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Answers
The value of angle x is 67 degree.
What is a Right Angled Triangle ?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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Venn diagrams ! 3rd times a charm….
Answers
Answer:
1. 85 people were surveyed
Henry leads a team of hikers for a full-day hike that takes 8 hours. Every hour, the hikers gain 250 feet in elevation. • The independent variable is ____, ________ in ________. • The dependent variable is _____, increased elevation in feet, or __________. A possible verbal description is “____ equals 250 times ____.” The equation ______ = ___________ corresponds to this relationship.
Answers
The missing blanks have been filled.
What is a Function ?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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A line with slope 2 passes through the point (2, -4). Find the coordinates of another point on the line.
Answers
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)
Select two ratios that are equivalent to 2 : 9.
Choose 2 answers:
9:2
1881
12:54
18:4
20:45
Answers
A contractor is purchasing some stone tiles for a new patio, each tile costs $3 and he wants to spend less than $1000 the size of each tile is 1 square foot, write and inequality that represents the number of tiles he can purchase with a $1000 limit, and the figure out how large the stone patio can be
Answers
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
The line with equation y = mx + 3 intersects the line with equation 3x + 4y + 12 = 0 at the point (1, −15/4) Find the value of m.
Answers
The value of m will be; m = (-∞ , - 15/4) ∪ ( 1 , ∞ ).
What is a system of equations?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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You are riding along a straight river from east to the west at speed of 160m/m. At a given time, you will see the bearing of a church on the other parallel road is N 70 degrees W, and 4 minutes later the bearing is N 56 degrees W. What is the width of the river? (Round your answer to two decimal points)
Answers
Using the given information, the width of the river is 505.96 m
Bearing and DistancesFrom 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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3. Find x 75° (4x 25)°
Answers
If two lines intersect, then their opposite angles are equal. Then the value of x is 25°.
The missing graph is given below.
What is an angle?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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Find p and q if, √3 −1 /√3 +1 = p + q√3
Answers
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]
someone help me with rest please asap!!
Answers
Answer:
3. Definition of Midpoint
4. VAT, Vertical Angles Theorem
5. ASA, Angle-Side-Angle Theorem
In January, Bangkok is hotter than Cape Town while Cape Town is hotter than Moscow. Which inequality correctly compares the temperatures of the three cities?
Which Answer-
A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature
B.
Bangkok's temperature < Moscow's temperature < Cape Town's temperature
C.
Bangkok's temperature > Moscow's temperature > Cape Town's temperature
D.
Bangkok's temperature > Cape Town's temperature > Moscow's temperature
Answers
The correct answer is option A which is A.Bangkok's temperature < Cape Town's temperature < Moscow's temperature.
What is inequality?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:-
In January, Bangkok is hotter than Cape Town while Cape Town is hotter than Moscow.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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The length of a rectangle is units greater than twice its width. If its width is w, which expression gives the perimeter of the rectangle in terms of w?
A.
2(w) + w
B.
w + w
C.
3w +
D.
6w + 5
Answers
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.
What is the perimeter of the rectangle?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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PLEASE HELP ASAP
(Picture shown)
Answers
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
If the set U = {all positive integers} and set A = {x|x ∈ U and x is an odd positive integer}, which describes the complement of set A, Ac?
Ac = {x|x ∈ U and is a negative integer}
Ac = {x|x ∈ U and is zero}
Ac = {x|x ∈ U and is not an integer}
Ac = {x|x ∈ U and is an even positive integer}
Answers
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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Can somebody help me and tell me if i’m right or not because I don’t know how to do this
Find the value of y.
Answers
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
Find y.
Help me please:))
Answers
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]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
