The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.
The given quadratic equation is [tex]x^{2}[/tex] - 20 = 8 x . To get the solutions of the given quadratic equation we need to simplify the quadratic equation. The step wise simplification of the given quadratic equation is,
[tex]x^{2}[/tex] - 20 = 8 x
[tex]x^{2}[/tex] - 8x -20 =0
on breaking -8x in two parts as -10x + 2x , we will get
[tex]x^{2}[/tex] -10x + 2x -20 = 0
x (x - 10) + 2 (x - 10) = 0
On taking (x-10) as common, we get
(x-10) (x+2) = 0
x = -2 , 10
The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.
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CCSS ARGUMENTS Determine whether each statement is true or false. If false, give a counterexample. If true, explain your reasoning.
Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent.
Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent: Always TRUE
What exactly does the term "triangle congruency" mean?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).The statement states that:
Two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent.So, the statement is always true as it satisfies two conditions of congruency which are the SSS condition and AA condition.Therefore, the statement "two triangles with two pairs of congruent corresponding angles and three pairs of congruent corresponding sides are congruent" is Always TRUE.
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Type the correct answer In each box. Use numerals Instead of words. If necessary, use / for the fraction bar(s).
Triangle ABC is defined by the points A(2,9), B(8,4), and q-3,-2}.
Complete the following equation for a line passing through point C and perpendicular AB.
Answer:
bStep-by-step explanation:
In this problem, you will investigate the location of the points of concurrency for any equilateral triangle.
a. Concrete Construct three different equilateral triangles on tracing paper and cut them out. Fold each triangle to locate the circumcenter, incenter, centroid, and orthocenter.
Fold the triangles to find their circumcenter (by making perpendicular bisectors), incenter (by making angle bisectors), centroid (by constructing medians), and orthocenter (using a different piece of patty paper for each equilateral triangle) (by making the altitudes of each side).
What points of concurrency are always inside the triangle?A triangle's three angle bisectors are concurrent in a point equidistant from its sides. The incenter of a triangle is the point where the angle bisectors of a triangle intersect. The incenter is always found within the triangle.
The circumcenter of a triangle is the point where the three perpendicular bisectors meet. It is the circumcenter of the circle circumscribed around the triangle, which is equidistant from the triangle's three vertices.
Fold the triangles to find their circumcenter (by making perpendicular bisectors), incenter (by making angle bisectors), centroid (by constructing medians), and orthocenter (using a different piece of patty paper for each equilateral triangle) (by making the altitudes of each side).
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What did Alexander Fleming discover that helped solve a societal problem?
an antibiotic
bacteria
infections
mold
Answer:
Antibiotic
Step-by-step explanation:
Alexander Fleming discovered penicillin, the most important drug that destroys bacteria within the human body. This discovery has led to the prevention of many diseases and untimely deaths in society. He was a pharmacologist, botanist, and biologist that won a Nobel Prize in Physiology for his major contributions in developing antibiotic substances.
Evaluate each logarithm. log₁₀₀ 100
In mathematics, the logarithm is the reciprocal of a power. This means that the logarithm of a given number x is the exponent by which another fixed number (the base b) must be increased to get that number x. The simplest logarithm counts the number of times the same element occurs when multiplying repeatedly. The logarithm of x to base b is denoted by log b (x), or log b x without parentheses. Also, if confusion is impossible or the base doesn't matter, log x shows that even without an explicit base: B. In big O notation.
Logarithm base 100 of 100 is 1.
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Precipitation for the month of march was 4 3/4 inches less than average. In April the precipitation was 1 1/2 inches Lea than average. How many inches below average was the precipitation for both march and April
The value of fraction is 6 1/4 inches are equal to 19+6/425mm.
Given that the precipitation in March was 4 3/4 inches below average and the precipitation in April was 1 1/2 inches below average.
We must determine how many inches the precipitation in March and April fell short of typical.
Add 4 3/4 inches and 1 1/2 inches to get the answer. So,
4 3/4 + 1 1/2
19+6 / 4
= + 4 312
6 1/4 inches are equal to 19+6/425mm.
six inches Therefore, the precipitation was 4 less than usual for both March and April.
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Find the number of possible outcomes for following situation.
Blanca chooses from 5 different flavors of ice cream and 3 different toppings.
15 is the number of possible outcomes.
What exactly are permutation and combination?A permutation is a process of arranging objects or numbers in a specific order.Combinations are a method of selecting objects or numbers from a collection or group of objects without regard for their order.We, for example, are made up of four letters: P, Q, R, and S.Every possible configuration is a combination.The combinations of P, Q, R, and S, on the other hand, are permutations.To find the possible outcomes:
Given: 5 flavors and ice cream of 3 different toppings.
5 × 3 = 15Therefore, the number of possible outcomes is 15.
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Which relation is a function
Binary relation is a function .
Functions are relationships where each input has a single output. There is one output for each input in a relation that passes the vertical line test.
How can I tell if a relationship serves a purpose?
A relation is considered to be a function if each element in the domain is mapped to a distinct element in the codomain.
What are the characteristics of a binary relation?
Binary relationship A subset of P x Q from the set P to Q is defined as R. If (a, b) R and R P x Q, then a and b are connected by R, or aRb. When sets P and Q are equal, we say that R is a relation on P, for example.
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The measure of one angle is 3 degrees more than 1/2 the measure of its supplement. Identify and solve an algebraic equation.
Answer: x+(x/2 + 3)=180 ==> 1st option
62 degrees ==> smaller angle
118 degrees ==> Larger angle
Step-by-step explanation:
x=one angle
y=1/2 x + 3
x+y=180 ==> supplementary angles add up to 180 degrees.
x+(1/2 x + 3)=180
x+(x/2 + 3)=180 ==> 1st option
x+x/2 + 3=180
2x/2 + x/2 + 3=180
(2x+x)/2 + 3=180
3x/2 + 3=180
3x/2=177
3x=354
x=118 degrees ==> Larger angle
x/2 + 3=
118/2 + 3=
59+3=62 degrees ==> smaller angle
find L in the cone
please hurry
Answer:
12
Step-by-step explanation:
Answer:
can you maybe explain it a little more?
Step-by-step explanation:
A store owner mixes 2 lb of candy that costs x dollars per pound with 3 lb of candy
that costs $1.50 per pound. She sells the mix for $2.50 per pound.
How much did the 3 lb of the second type of candy cost the owner?
Considering the definition of an equation and the way to solve it, the cost of 2 pounds(lb) of the first type of candy is $4 per pound.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it (this is, the equality must be true).To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Cost of the 2 pounds of candyKnowing that:
A store owner mixes 2 lb of candy that costs x dollars per pound with 3 lb of candy that costs $1.50 per pound. She sells the mix for $2.50 per pound.the equation in this case is:
2x + 3×1.50 = 2.50×(2 + 3)
Solving:
2x + 4.5= 12.5
2x= 12.5 - 4.5
2x= 8
x= 8÷ 2
x=4
Finally, the cost of 2 pounds(lb) of the first type of candy is $4 per pound.
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Lauren is saving up. she alright has $40 and can save an additional $5 per week using money from her after school job. How much money would Lauren have after 9 weeks of saving?
Answer:
$85
Step-by-step explanation:
y=5x+40
x=weeks
y=total money
y=5(9)+40
y=45+40
y= 85
A studio engineer charges a flat fee of 450 for equipment rental and 42 an hour for recording and mixing time. Write the equation that shows the cost to hire the studio engineer as a function of time. How much would it cost to hire the studio engineer for 17 hours?
Slope-intercept form, y = mx + b, of linear equations, emphasizes the slope and the y-intercept of the line.
The cost to hire the studio engineer for 17 hours is $ 1164.
What is slope-intercept form?Let x be the time measured in hours and y be the total cost in dollars if two different costs are provided. This problem has been solved with the help of slope-intercept form, y = mx + b.
The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given exists even the y-intercept (0, b). In the formula, b represents the y value of the y-intercept point.
Slope-intercept form, y = mx + b, of linear equations, emphasizes the slope and the y-intercept of the line.
From the given information, we get
W = 450 + 42 [tex]*[/tex] 17
= $ 1164
The cost to hire the studio engineer for 17 hours is $ 1164.
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Find the value of each variable
The Value of 3-5c is 1 less than the value of 1-c.
Answer:
½ < C
Step-by-step explanation:
that is the answer above
-2 2/3 * (-4 3/7) help me please. thanks
:)
Answer:
11.8
Step-by-step explanation:
I simply just did multiplication
I multiplied the whole numbers alone and did the same with the fraction
Example: -2*-4=8
2/3*3/7
then you add the two products and get your answer
i need help solving this angle problem
Answer:
Step-by-step explanation:
42=8x+10
42+10=8x
52=8x
x=52/8
x=6.5
Please help! Due in 5 mins!
Answer:
It's the first option, if you simplify 6 by 4, its 1 1/2 and first option is also 1 1/2 the last option is also equivalent
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
The first side of a triangle is 3 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 27 m. Find the length of the 1st side.
Answer: the length of the 1st side is 4 m
Step-by-step explanation:
P=a+b+c
b=a+3
c=4a
Hence,
27=a+(a+3)+4a
27=a+a+3+4a
27=6a+3
27-3=6a+3-3
24=6a
Divide both parts of the equation by 6:
4=a
Thus,
a=4 m
the measure of a supplement of an angle exceeds 10 times the measure of its complement by 9. Find the measure of the angle
Answer:
81°
Step-by-step explanation:
Let the angle be x. Then,
complementary angle = 90 - xsupplementary angle = 180 - xAccording to question,
=> 180 - x - 10(90 - x) = 9
=> 180 - x - 900 + 10x = 9
=> 9x - 720 = 9
=> 9x = 729
=> x = 81
The measure of the angle is 81° (ans)
Answer:
81°
Step-by-step explanation:
Definitions
Complementary angles: Two angles whose measures sum to 90°.
Supplementary angles: Two angles whose measures sum to 180°.
Define the unknown angle
Let x be the unknown angle.Therefore:
Complement of x = 90° - x°Supplement of x = 180° - x°If the measure of the supplement exceeds 10 times the measure of its complement by 9:
⇒ supplement = 10 × complement + 9
⇒ (180 - x) = 10(90 - x) + 9
⇒ 180 - x = 900 - 10x + 9
⇒ 180 - x = 909 - 10x
⇒ 180 - x + 10x = 909 - 10x + 10x
⇒ 180 + 9x = 909
⇒ 180 + 9x - 180 = 909 - 180
⇒ 9x = 729
⇒ 9x ÷ 9 = 729 ÷ 9
⇒ x = 81
Therefore, the measure of the angle is 81°.
Solve for x:
1/3 |x-3|+ 4 = 10
Answer:
x=-15 and x=-15
Step-by-step explanation:
We try to move everything from the left to the right starting with the number that is further away from x, so 4. We subtract it from both sides.
1/3|x-3|+4-4=10-4
1/3|x-3|=6
Next, we have the fraction so basically, 1 is being divided by 3 so we are going to multiply both sides by three.
1/3|x-3|×3=6×3
|x-3|=18
We get rid of the absolute value signs to get
x-3=18
But we are not sure if 18 is negative so we put it like this.
x-3=-18
x-3=18
Then we add 3 from both sides.
x-3+3=-18+3
x-3+3=18+3
Which equals:
x=-15
x=21
Hope this helped! :)
Hot dogs come in packs of 10, while buns come in packs of eight. What are the least numbers of packs you should buy in order to have the same numbers of hot dogs and buns?.
Solving for the least common multiple (LCM), the least numbers of packs you should buy in order to have the same numbers of hot dogs and buns is 4 packs of hotdogs and 5 packs of buns.
A common multiple is defined as a whole number, that is a shared multiple of each set of numbers. The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both numbers.
If hot dogs come in packs of 10, while buns come in packs of eight, solving for their LCM,
10 : 10, 20, 30, 40, 50, . . .
8 : 8, 16, 24, 32, 40, 48, . . .
LCM = 40
Considering 40 hotdogs and 40 buns, dividing each by 10 and 8, the number of packs of each will be:
packs of hotdogs = 40/10
packs of hotdogs = 4
packs of buns = 40/8
packs of buns = 5
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a. What is the solution of the system? Use elimination.
x-2y+3 z = 12
2x-y-2z = 5
2x+2 y-z = 4
By elimination, the solution of the system of equations, x - 2y + 3z = 12, 2x - y - 2z = 5 and 2x + 2y - z = 4, is (4 , -1 , 2).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Given:
x - 2y + 3z = 12 (equation 1)
2x - y - 2z = 5 (equation 2)
2x + 2y - z = 4 (equation 3)
Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.
Adding equations 1 and 3 will eliminate the variable y.
x - 2y + 3z = 12 (equation 1)
2x + 2y - z = 4 (equation 3)
3x + 2z = 16 (equation 4)
Multiply equation 2 by 2 and add with equation 3.
2x - y - 2z = 5 (equation 2)
⇒ 4x - 2y - 4z = 10
+ 2x + 2y - z = 4 (equation 3)
6x - 5z = 14 (equation 5)
Multiply equation 4 by 2 and subtract with equation 5.
3x + 2z = 16 (equation 4)
⇒ 6x + 4z = 32
- (6x - 5z = 14) (equation 5)
9z = 18
z = 2
Substitute the value of z to either equation 4 or 5 and solve for x.
3x + 2z = 16 (equation 4)
3x + 2(2) = 16
3x = 16 - 4
3x = 12
x = 4
Finally, substitute the value of x and z to any of the first three equations, and solve for y.
x - 2y + 3z = 12 (equation 1)
4 - 2y + 3(2) = 12
-2y = 12 - 4 - 6
-2y = 2
y = -1
Hence, the solution of the system of equations is (4 , -1 , 2).
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A die is rolled. Find the probability of the outcome. P(1 or 6 )
The required probability is 1/3
Rolling a die is an equally likely event which means that probability of getting any number on rolling a die is same. When a die is rolled, there are total six outcomes in sample space which are 1, 2, 3, 4, 5, and 6 .
If a die is rolled once, then the probability of getting 1 is 1/6, and the probability of getting 6 is also 1/6.
These two events are mutually exclusive.
Thus, the probability of getting either 1 or 6 in a single throw is,
P(A or B) = P(A) + P(B)
P(A or B) = 1/6 + 1/6 = 2/6
P(A or B) = 1/3
The required probability is 1/3
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10. Determine the value of x if RY = 11x + 46 and RW = 3x + 58.
The value of x is 3/2.
What is a Line Segment?A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.
The figure given below shows a line segment YW, where the length of line segment YW refers to the distance between its endpoints, Y and W.
Given that R is the midpoint of YW
RY = 11x + 46 and RW = 3x + 58.
Y______________R______________W
⇒ YW = RY + RW
Since R is the midpoint of YW,
So RY = RW
Substitute the values of RY = 11x + 46 and RW = 3x + 58,
⇒ 11x + 46 = 3x + 58
Rearrange the terms of the above equation and solve for x,
⇒ 11x - 3x = 58 - 46
⇒ 8x = 12
⇒ x = 12/8
⇒ x = 3/2
Hence, the value of x is 3/2.
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The question seems to be incomplete the correct question would be
If R is the midpoint of YW.
Determine the value of x if RY = 11x + 46 and RW = 3x + 58.
Use a two-dimensional model and the dimensions provided to calculate the circumference and area of the flower. Round to the nearest tenth,
if necessary.
circumference:
area:
in2
in.
5 in-
The circumference and area of the flower are 15.7 and 19.6 respectively
How to calculate the circumference and area of the flower?The image that completes the question is added an attachment
From the image, we have
Diameter = 5 inches
The circumference is calculated as
C = π * Diameter (d)
So, we have
C = πd
This gives
C = 3.14 * 5
Evaluate
C = 15.7
The area is calculated as
A = π(d/2)^2
This gives
A = 3.14 * (5/2)^2
Evaluate
A = 19.6
Hence, the circumference and area of the flower are 15.7 and 19.6 respectively
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The diagram shows a triangle. What is the value of b?
Answer:
b=95
Step-by-step explanation:
180=34+(b-30)+(b-14)
190=2b
b=95
34+(95-30)+(95-14) = 180
Answer:
b-30+b-14+34=180
2b+4-14=180
Step-by-step explanation:
2b=190 ,b=95
how do you graph y=1x+6
Answer:
6 is the y intercept and 1 is the slope, so it goes up 1 unit right 1 unit
Step-by-step explanation:
Is -15/3 a irrational or rational number
Answer: rational
Step-by-step explanation:
Which lines are parallel to the graph of 4x – y = 6? Check all that apply.
x – 4y = –12
y – 2 = –4(x + 1)
y + 1 = 4(x – 2)
y = 4x + 11
y = x – 3
8x – 2y = 6
Answer: Options 3, 4, 6
Step-by-step explanation:
[tex]4x-y=6 \\\\-4x+y=-6\\\\y=4x-6[/tex]
This means are looking for lines with a slope of 4 (since parallel lines have the same slope).
x – 4y = –12: This rearranges to y=0.25x+3, so the slope is 1/4.y – 2 = –4(x + 1): This has a slope of -4.y + 1 = 4(x – 2): This has a slope of 4.y = 4x + 11: This has a slope of 4.y = x – 3: This has a slope of 1.8x – 2y = 6: This rearranges to y=4x-3, so the slope is 4.The 8s in 88,000 value
80 thousand and 8 thousand.
What is a place value chart?Using place value diagrams, we can check that the digits are in the right positions. Writing the digits in the place value chart first, followed by writing the numbers in their customary and standard form, can help you precisely determine the positional values of numbers.
Given that: we have given 88,000.
The number 88000 has two 8s, as can be seen.
One of them is located at 10,000 places, while the other is at 1,000 places.
Value of first 8 from right is
8 thousand
Values of second 8 from right is
80 thousand.
Therefore, 80 thousand and 8 thousand
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