Answers
Angles <6 and <12 are alternate interior angle.
What are angles <6 and <12?An interior angle is an angle that is inside a shape. It can also be described as an angle that lie in the area bounded between two parallel lines that are intersected by a transversal. In the given image, angles 6 and 11 are interior angles. The sum of interior angles is 180 degrees.
An alternate interior angle is an angle that is formed when two parallel lines are crossed by a transversal. The angle formed on the inner side of the parallel lines, and on the opposite sides of the transversal are called alternate interior angles. The alternate interior angles are angles 6 and 12.
A corresponding angle is an angle that is on the same side of one of two lines cut by a transversal and on the same side of the transversal. Angle 4 and 12 are corresponding angles.
An alternate exterior angle is the two angles that is formed the outer side of the two parallel lines but on the opposite side of the transversal. Angles 4 and 14 are alternate exterior angle.
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Related Questions
Find all the zeros of each function. f(x)=x⁴-5 x²+6
Answers
According to the question, to calculate the zeros of each function. The given function is f(x) = [tex]x^{4}-5x^{2} +6[/tex]
Now, let us assume [tex]a=x^{2}[/tex]. Therefore, the above equation can be written as:
[tex]f(x)=a^{2}-5a+6[/tex]
Calculate the factors of the given equation and it can be re-written as:
[tex]f(x) = (a+2)(a+3)[/tex]
To calculate the final solution, equate it to zero.
[tex](a+2)(a+3)=0\\a=-2,-3[/tex]
Now, substitute these values in the original assumed equation:
The zeros function values are [tex]-\sqrt{2i};\sqrt{2i},-\sqrt{3i} ,\sqrt{3i}[/tex]
What is zero functions?
A zero function is a function which is almost zero everywhere on the graph. It is also known as a constant function.
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Simplify. Rationalize all denominators. 4+√12 / 4-√12
Answers
The simplification of 4+√12 / 4-√12 after rationalizing all denominators
is 7+4[tex]\sqrt{3}[/tex]
We are given the equation;
[tex]\frac{4+\sqrt{12} }{4-\sqrt{12} }[/tex]
The above equation can also be written as;
[tex]\frac{4+\sqrt{4*3} }{4-\sqrt{4*3} }[/tex]
Since our question requires us to rationalize the denominator, we will use the initial equation to rationalize the denominator. That is;
[tex]\frac{4+\sqrt{12} }{4-\sqrt{12} }[/tex] * [tex]\frac{4+\sqrt{12} }{4+\sqrt{12} }[/tex]
We then simplify;
4(4+[tex]\sqrt{12}[/tex])+[tex]\sqrt{12}[/tex](4+[tex]\sqrt{12}[/tex]) / 4(4+[tex]\sqrt{12}[/tex])- [tex]\sqrt{12}[/tex](4+[tex]\sqrt{12}[/tex])
= 16+4[tex]\sqrt{12}[/tex]+4[tex]\sqrt{12}[/tex]+[tex]\sqrt{12*12}[/tex] / 16+4[tex]\sqrt{12}[/tex]-4[tex]\sqrt{12}[/tex]-[tex]\sqrt{12*12}[/tex]
= 16+8[tex]\sqrt{12}[/tex]+12 /16-12
=28+8[tex]\sqrt{12}[/tex] / 4
=28+8[tex]\sqrt{4*3}[/tex] /4
= 28+8*2[tex]\sqrt{3}[/tex] /4
=28+16[tex]\sqrt{3}[/tex] /4
Divide all sides by 4;
= 7+4[tex]\sqrt{3}[/tex]
The final answer is therefore; 7+4[tex]\sqrt{3}[/tex]
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Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total of
$
1215
.
$
445
was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?
Answers
Joy was charged the labor of 11 hours
Joy was charged a total of $1215 from the landscaper for listed parts and labor
He was charged $445 for listed parts
He was charged the rest for labor
The hourly rate for labor is $ 70
Let the number of hours worked by labor be x
so, we can form a linear equation here as 445 + 70x = 1215
Now we have to solve this linear equation
445 + 70x = 1215
70x= 1215 - 445
70x = 770
x = 770/ 70
x = 11
Therefore, 11 hours of labor was needed to complete the job.
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Find the y-intercept and x-intercept of the line.
-x+2y=2
Answers
y intercept: (0,1)
Complete the table and then graph the function.
Answers
summing-up the values for equation of line y = x/2 + 1 in table :
x y
-10 -4
-6 -2
-2 0
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here, the given equation is :
y = x/2 + 1
Now, computing the value of y corresponding to values of x by substituting values in above equation :
when x = -10 :
y = x/2 + 1
y = -10/2 + 1
y = -5 +1
y = -4
similarly, for :
x = -6 , y = -2
x = -2 , 0
summing-up the above values in table that is attached below :
x y
-10 -4
-6 -2
-2 0
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Now to draw the line graph of above equation taking any two coordinates let us say (-2,0) and (-2,-6). Now drawing the line joining these two points as shown in figure attached below.
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what is nine plus ten
Answers
The value of nine plus ten is 19
What are Mathematical operations?Mathematical operations are simply known as arithmetic operations used in solving algebraic problems and other mathematical calculations.
These operations include;
AdditionSubtractionMultiplicationDivisionBracketExponents, etcIn this case, we have;
nine plus ten
This is expressed as;
9 + 10
The sum is 19
Thus, the value of nine plus ten is 19
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Meghan needs to create a 4-digit password. The digits cannot repeat in the password and cannot start with the digit 0. What is the probability , to the nearest hundredth of a percent, the the password starts with a 9 and ends with a 6?
Answers
The probability to the nearest hundredth of a percent, the the password starts with a 9 and ends with a 6 is 1%.
A four digit password will have number ranging from 0-9.
There are four spots in total.
The first spot can not be taken by zero, so only 9 options can take the place of first spot. As the number can not be repeated, the second spot has only options a 0-8. The third spot will eventually have 8 options only. The Fourth spot will have 7 options available to fill the spot.
Hence total number of 4-digit passwords combinations can be calculated by multiplying the options,
= 9 x 9 x 8 x 7
= 10206.
A total of 10206 passwords are possible.
The number of passwords starting from nine and ending with six can be found as,
= 1 x 9 x 8 x 1
= 72
A total of 72 passwords starting from 9 and ending with 6.
The probability that a password chosen is starting from 9 and ending with 6 is,
P(E) = 72/10206
P(E) = 0.007
Probability in percent,
= 0.007 x 100
= 0.7
Rounding it off, we get nearly 1%.
So, the probability is nearly 1%.
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lily’s age is 2 years and 4 months hugo’s age is 1 year and 8 months
write lily’s age in months as a fraction of hugo’s age in months
give your fraction in its simplest form
Answers
Step-by-step explanation:
lily's in months=4/12
hugos in months=8/12
4/12+8/12
1/3+2/3
lily's month in simplest form=1/3
hugos month in simplest form=2/3
PLEASE HELP ME MARKING BRAINLYYYYY
Answers
Answer:
i think it c im not sure though I tried my best to figure the answer out. pls dont get mad if its wrong.
Answer:
A
Step-by-step explanation:
20xday will help determine how many she reads, the +52 will allow us to account for the 52 she a;ready read.
The sum of thirty six and fourteen and divided by the sum of one and three
Answers
we can simplify this into
50 divided by 4
50/4
the answer is 12.5
Yong Quan was trying to access his email account when he could not remember the 4 digit password to the email account. He clicked on the button to reveal a hint. The hint: The biggest even number which can be formed by the numbers 1, 3, 8, 6. What was Yong Quan's password to the email account?
Answers
Suppose that x and y vary inversely. Write a function that models each inverse variation and find y when x=-5 . x=2 when y=12
Answers
A function that models each inverse variation is y = 24. 1/x and y when x=-5 is -24/5
What precisely is the inverse of a function?Those with inverse properties cancel each other out. In other words, f(g(x)) = g(f(x)) = x if g(x) is f's inverse (x). We have a great approach we can use to achieve this given an equation for which we desire the inverse.
Not every action has an equivalent. It is obvious that f(x) will never again have the same value if it has an inverse. We designate a unique name for this resource.
Inverse variation is y = k. 1/x
given y = 12
x = 2
So, 12 = k. 1/2
So, the value of k = 24
We can conclude that the value of constant variation is 24
when x = -5, the value of y will be -
y = k.1/x
y = 24 . 1/-5
y = -24/5
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Rationalize the denominator of each expression. Assume that all variables are positive. ∛x / ∛y
Answers
The rationalization of the given expression is (xy²)¹/³ /y .
Rationalization can be thought of as the process used to remove the base or imaginary number from the denominator of an algebraic fraction. That is, remove the radical of the fraction so that the denominator contains only rational numbers.Radicals are expressions that use roots such as: B. Square root or cube root. For example, an expression of the form: √(a + b) is a root.The mathematical conjugate of any binomial means another exact binomial with opposite signs between the two terms.We have to rationalize the denominator of the expression ∛x / ∛y ,
where x and y are positive.
∛x / ∛y
= (∛x / ∛y) × (∛y / ∛y)
= ∛(x × y) / ∛(y × y)
= (∛xy)/ ∛y²
= (∛xy)/∛y²
= (xy²)¹/³ /y
The answer is (xy²)¹/³ /y .
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What percent of
140 is 175?
Answers
Answer:
125%
this is the answer in percent form
if we take 140 as the 100%, what is 175 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 140 & 100\\ 175& x \end{array} \implies \cfrac{140}{175}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{4}{5}=\cfrac{100}{x}\implies 4x=500\implies x=\cfrac{500}{4}\implies x=125[/tex]
I can type 400 words per hour. How many minutes will it take me
to write a report with 2,000 words
Answers
Writing 2,000 words will take about 50 minutes for the average writer typing on a keyboard and 1.7 hours for handwriting.
Answer:
5 hours. the response has to be 20 characters long.
Write an equation in slope-intercept form of the line that passes through (-9, -3) and (-7, 5)
Answers
The slope-intercept form of the line passing through the two points is
y = 4x + 33
Slope-intercept equation is one of the special forms of the linear equation.
To find the slope,
The point-slope formula is used to find the slope
y₂-y₁ = m (x₂-x₁)
where (x₁,y₁) and (x₂,y₂) are (-9,-3) and (-7,5), Then
5 - (-3) = m [-7 - (-9)]
5 + 3 = m (-7+9)
8 = m(2)
m = 8/2
m = 4
Therefore, the slope of the line passing through two points is 4
To find the intercept,
We can use the slope intercept formula to find the intercept
y = mx + b
where (x,y) be (-9,-3) abd m = 4 , Then
-3 = 4(-9) + b
-3 = -36 = +b
b = 36-3
b = 33
Therefore, the intercept of the line passing through two points is 33
Thus, the slope intercept form of the line passing through the two points
(-9, -3) and (-7, 5) can be written as
y = 4x + 33
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100 points top anyone who can answer these questions.
Answers
in the given figure the value of x is 45°.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given:
<PQR= x+7
<SQR=x+3
<PQR+<SQR=<PQS=100°
According to given question we have
<PQR+<SQR=<PQS
Put the value we get
x+7+x+3=100
Compare like terms we get
2x+10=100
Substract 10 from both sides we get,
2x=90
Divide 2 on both sides we get,
x=45°
Therefore, in the given figure the value of x is 45°.
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A 99-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
Answers
Answer: 8.25 inches per hour
Step-by-step explanation: 99/12 = 8.25
which statement is true about the system of linear equations graphed in the coordinate plane below
Answers
Answer:
Step-by-step explanation:
The system of equations does not have one solution because the lines will never intersect.
if g(x)=x^2-7x find g(-2)
Answers
The value of the function at g(-2) is 18.
A function is defined a relation between two variables in such a way that the dependent variable y is related to the independent variable x.
Functions are normally denoted by f, g or h and g(x) denotes a function whose independent variable is x.A value of x is called the domain The resultant value of y for every x in the domain is called the range of the function.To calculate a specific value of a function we substitute the given value in the expression of x thereby calculating the value of the function at that point.
Given function : g(x)=x²-7x
At x=-2 , written as g(-2) we put the value -2 in the expression of x.
∴g(-2)=(-2)²-7(-2)
or, g(-2)=4+14
or, g(-2)=18
Hence the value of the function at g(-2) is 18.
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Find the degree measure of an angle of 3 π/4 radians.
Answers
Answer: 135°
Step-by-step explanation:
Since π = 180°
(3 × π)/ 4
Substitute 180° for π
= (3 × 180)/4
Simplify
= 540/4
= 135°
Four-thirds of a number is decreased by 12. The result is eight
Answers
Answer:
The number is 15
Step-by-step explanation:
x = a number
4/3 x - 12 = 8
Rearrange the equation so that the integers are on one side - in the format Ax = B
4/3 x - 12 = 8
4/3 x = 8 + 12
4/3 x = 20
Simplify the equation - in the format x = A - then solve for x
4/3 x = 20
4 x = 20 * 3
4 x = 60
x = 60 / 4
x = 15
[tex] \large \bf \implies{A\: number\: is\:15}[/tex]
Step-by-step explanation:A number is x
then we have [tex]\frac{4}{3}[/tex]x - 12 = 8
[tex] \bf \longrightarrow \frac{4}{3}x - 12 = 8 \\ \\ \bf \longrightarrow \frac{4}{3}x = 8 + 12 \\ \\ \bf \longrightarrow \frac{4}{3}x = 20 \\ \\ \bf \longrightarrow 4x = 20 \times 3 \\ \\ \bf \longrightarrow4x = 60 \\ \\ \bf \longrightarrow x = \frac{ \cancel{60}}{ \cancel{4} } \\ \\ \bf \longrightarrow \: x = 15[/tex]
'Four thirds of the number is [tex]\frac{4}{3}x[/tex] then decreased by 12 is [tex]\frac{4}{3}x - 12[/tex] then gives the result 8. That is [tex]\bf\frac{4}{3}x - 12 = 8[/tex]'
Jaycee has already saved $75 for an upcoming vacation. Every week, she adds another $15 to her vacation savings. The relationships between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings, is a linear relationship. Write an equation to describe the linear relationship.
Answers
Answer:
it adding
Step-by-step explanation:
the length of time for $5000 to earn $1000 if invested at 10% per annum
Answers
3) Find the length of the line on the grid below. Hint: you need to draw a
right triangle with the given line as the hypotenuse!
Answers
right side of the triangles length is: 3
using pythagoras:
4^2 + 3^2 = 25
(sqrt)25 = 5
length of line: 5
An athlete is training for a triathlon by running each day. After 3 1/2 days, they ran a total of 12 3/5 miles. On average, how many miles did this athlete run per day? This is a division question. The mixed number 3 1 2 is the divisor. pls help asap
Answers
On average, the number of miles the athlete ran per day is; 18/5 or 3.6 miles per day
How to calculate the average distance?We are given;
Number of days the athletes ran = 3¹/₂ days = 7/2 days
Total distance ran in the given time = 12³/₅ miles = 63/5 miles
Now, the average distance will simply be given by the expression;
Average Distance = Total Distance/Number of days of running
Now, let us convert the fractions to improper fraction for easy division. Thus, we have;
Number of days the athletes ran = 7/2 days
Total distance ran in the given time = 63/5 miles
Thus;
Average Distance = (63/5)/(7/2)
Average distance = 63/5 * 2/7 = 18/5 = 3.6 miles per day
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HELP ME PLEASE
Your friend invites you to go to an indoor skateboard park. you'd like to go, but since you dont have a helmet or knee pads, you'll have to pay to rent them. You'll also need to buy a day pass to enter the park.
Write a formula that will help you determine your total cost. h=helmet rental
k=knee pad rental
p=cost of day pass
c=total cost
Answers
Answer:
C=h+k+p
Step-by-step explanation:
You just add all of the variables and it equals your total cost. if it was by hour the equation would be slightly different
Written in simplest exponential form the product (3x¹)(-2x¹)
(1) –5r2
(3) x¹
(2) -6x¹0
(4)-6x²1
is?
Answers
A nutrition label indicates that one serving of apple crisp
oatmeal has 2.5 grams of fat. How many grams of fat are t
there in 3.75 servings? Justify your answer. (Example 5) Ex
Answers
9.375 grams of fat are there in 3.75 servings.
A Nutrition Facts label lists the nutritional content, the serving size, and the calories for a recommended serving of a food product. This helps consumers make the best decision on how much to eat, maybe when they want to eat this food, or how they can better balance their food choices throughout the day.
Given the statement:
A nutrition label indicates that one serving of Apple crisp oatmeal has 2.5 grams of fat.
Determine the grams of fat in 3.75 servings.
In order to determine the grams of fat in 3.75 servings, we simply needed to multiply 2.5 grams by 3.75.
= (2.5 grams)×( 3.75)
= 9.375 grams of fat.
Thus , 3.75 servings contain 9.375 grams of fat ,if 1 serving contain 2.5 grams of fat .
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Patrick grated 2/3 of a block of cheese to make macaroni. What fraction of the block is left
Answers
——
3/3 - 2/3 = 1/3