Angle A is a right angle in △ABC.
Which side is opposite to angle A?
side BC
side AB
side AC
Answers
Option 1 is correct. The side opposite to angle A is side BC, which is the hypotenuse.
In a triangle, the side opposite the right angle is known as the hypotenuse. Since angle A is given as a right angle in △ABC, the side opposite this right angle will be the hypotenuse.
In △ABC:
Side AB is adjacent to angle A, forming one leg of the right triangle.
Side AC is also adjacent to angle A, forming the other leg of the right triangle.
Side BC is opposite angle A and is the longest side of the triangle, making it the hypotenuse.
Therefore, side BC is opposite to angle A in △ABC.
Complete question:
Angle A is a right angle in △ABC.
Which side is opposite to angle A?
1. side BC
2. side AB
3. side AC
Related Questions
Sarah deposits $600 in a savings account that pays 2.5% per year. What is the minimum number of years it would take for the amount in her account to be more than $800, provided no more money is deposited in the account?
Answers
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = {log(800) - log(600)} ÷ log(1.025)
Years = {2.903089987 -2.7781512504} / 0.010723865392
Years = { 0.1249387366 } / 0.010723865392
Years = 11.6505319708
That's how many years it takes for the $600 to become exactly $800.00
The question specifically asks how long for the money to be MORE than $800.00?
So, if we enter 800.01 into the equation, then the answer is
Years = {log(800.01) - log(600)} ÷ log(1.025)
Years = {2.9030954156 -2.7781512504} / 0.010723865392
Years = 0.1249441652 / 0.010723865392
Years = 11.6510381875
It will take at least 12 years for Sarah's $600 deposit at a 2.5% annual interest rate to grow to more than $800, assuming the interest is compounded annually.
To determine how long it will take for Sarah's $600 deposit at a 2.5% annual interest rate to grow to over $800, we can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for in years.Since the problem doesn't specify the compounding frequency, let's assume it's compounded annually for simplicity:
[tex]A = 600(1 + 0.025)^t[/tex]. We need A to be greater than $800.
To find the minimum number of years (t), we solve for t:
[tex]800 < 600(1 + 0.025)^t[/tex]
Solving for t gives us: t > ln(800/600) / ln(1.025).
Using a calculator, we find that t > 11.89.
Therefore, it will take at least 12 years for the amount in Sarah's account to exceed $800.
Using the similar triangles which equation could be used to find the slope of line AB
Answers
The equation that could be used to find the slope of line AB is m = p/q.
What are similar triangles?Two triangles are said to be similar if they have congruent corresponding angles and their corresponding sides are in equal proportion.
Given that, is a graph showing two similar triangles, we need find the equation of the slope of the line AB.
So,
The slope = rise / run = Δy / Δx
Here, Δy / Δx = m/n
Since, the triangles are similar so, m/n = p/q
Therefore,
Δy / Δx = p/q
Hence, the equation that could be used to find the slope of line AB is m = p/q.
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△ABC has interior angles with measures x°, 100°, and 70°, and △DEF has interior angles with measures y°, 70°, and 20°. Using the given information, which statement is true? The triangles are similar because they each have an interior angle with a measure 70°. The two triangles are not similar because x≠y . The two triangles are not similar because y=90 so it is impossible to have three congruent angles. The two triangles are not similar because the interior angles are congruent but the side lengths are different.
Answers
△ABC has interior angles with measures x°, 100°, and 70°.
By using angle sum property, which states that the sum of measures of all three angles is 180 degrees.
[tex] x^{\circ}+100^{\circ}+70^{\circ}=180^{\circ} [/tex]
[tex] x^{\circ}=10^{\circ} [/tex]
Now, △DEF has interior angles with measures y°, 70°, and 20°.
By using angle sum property,
[tex] y^{\circ}+70^{\circ}+20^{\circ}=180^{\circ} [/tex]
[tex] y^{\circ}=90^{\circ} [/tex]
Now, we can say that,
"The two triangles are not similar because x≠y"
As one angle of measure 70 degree is common in both the triangles.
If 'x' would be equal to 'y' , then we could say that the triangles are similar by AA criteria.
Therefore, the two triangles are not similar because x is not equal to y.
A group consists of five five men and eight eight women. seven seven people are selected to attend a conference.
a. in how many ways can seven seven people be selected from this group of thirteen thirteen?
b. in how many ways can seven seven women be selected from the eight eight women?
c. find the probability that the selected group will consist of all women.
Answers
a) 116 ways to select seven people.
b) ways to select 7 women.
c) The probability is 0.004662
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
a) Number of ways can seven people be selected from this group of thirteen
C( 13, 7)
= 13! /6! 7!
= 1716
b) Number of ways seven women selected from Eight women
C(8 ,7)
= 8!/ 7! 1!
= 8
c) The probability that the selected group will consist of all women
= 8 / 1716
= 0.004662
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How do the areas of the parallelograms compare?
The area of parallelogram ABCD is 4 square units greater than the area of parallelogram EFGH.
The area of parallelogram ABCD is 2 square units greater than the area of parallelogram EFGH.
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
The area of parallelogram ABCD is 2 square units less than the area of parallelogram EFGH.
Answers
A = b * h
Where,
b: base
h: height
We have then:
ABCD parallelogram:
A = (3) * (3)
A = 9 units ^ 2
EFGH parallelogram:
A = (3) * (3)
A = 9 units ^ 2
Answer:
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
What would be the next number in pattern 1/324, 1/108, 1/36, 1/12 answers are 1/3, 1/5, 1/4, 1
Answers
The next number in pattern 1/324, 1/108, 1/36, 1/12 would be 1/4
Further explanationFirstly , let us learn about types of sequence in mathematics.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
[tex]\boxed{T_n = a + (n-1)d}[/tex]
[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.
[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]
[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
r = common ratio between adjacent numbers
Let us now tackle the problem!
Given:
This problem is about Geometric Sequence. Let's see why.
[tex]\frac{1}{324} , \frac{1}{108} , \frac{1}{36} , \frac{1}{12} , . . .[/tex]
T₁ = [tex]\frac{1}{324}[/tex]
T₂ = [tex]\frac{1}{108}[/tex]
T₃ = [tex]\frac{1}{36}[/tex]
T₄ = [tex]\frac{1}{12}[/tex]
[tex]\large {\boxed {\frac{T_2}{T_1} = \frac{T_3}{T_2} = \frac{T_4}{T_3} = r = 3} }[/tex]
From the above results it can be concluded that this is Geometric Sequence.
The next number will be the fifth term and can be calculated as following.
[tex]T_n = a ~ r^{n-1}[/tex]
[tex]T_5 = \frac{1}{324} \times 3^{5 - 1}[/tex]
[tex]T_5 = \frac{1}{324} \times 3^4[/tex]
[tex]T_5 = \frac{1}{324} \times 81[/tex]
[tex]\large {\boxed {T_5 = \frac{1}{4} } }[/tex]
Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
a shop made a profit of £23500 in 2009. in 2010 the profit increased to £28000.work out the percentage increase in profit, to the nearest 1%
Answers
now, if we take 23500 to be the 100%, what is 4500 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 23500&100\\ 4500&p \end{array}\implies \cfrac{23500}{4500}=\cfrac{100}{p}\implies p=\cfrac{4500\cdot 100}{23500}[/tex]
Write a recursive definition for the set of odd positive integers.
Answers
a[n+1] = a[n] +2
Final answer:
A recursive definition for the set of odd positive integers starts with a base case of 1 and uses a recursive step where each subsequent odd integer is obtained by adding 2 to the current odd integer.
Explanation:
To write a recursive definition for the set of odd positive integers, you can define a base case and a recursive step. The base case is the smallest odd positive integer, which is 1. The recursive step will then generate the next odd integer by adding 2 to the current odd integer. Here's how you can express it:
Base case: Let O1 = 1, which establishes that 1 is the first odd positive integer.
Recursive step: For every odd positive integer On, there exists an On+1 = On + 2. This means that if you have an odd positive integer, the next one in the set can be found by adding 2 to the current one.
This definition ensures that every number generated by the recursive step will be odd since adding 2 to an odd number always results in another odd number, and starting from 1, guarantees that all numbers will be positive.
Which situation best represents a proportional relationship?
a. sandra sold 2 bracelets for $3 and 3 bracelets for $6.
b. jeff ran 4 miles in 20 minutes and 6 miles in 24 minutes.
c. lamont packed 27 glasses in 9 cases and 81 glasses in 27 cases.
d. fernanda placed 8 pencils in 2 boxes and 16 pencils in 8 boxes?
Answers
y = mx
where y and x are the 2 variables and m is a constant value
directly proportional means when one variable increases or decreases the other variable too increases or decreases by the same amount.
a)
2 bracelets sold for $3
1 bracelet costs - 3/2
therefore 3 bracelets would cost 3/2 * 3 = $4.5
but the cost of 3 bracelets in this case is $6 therefore this is not a proportional relationship
b)
time taken for 4 miles - 20 minutes
time taken for 1 mile - 20/4
Therefore 6 miles time taken = 20/4 * 6 = 30 minutes
but it has taken only 24 minutes to run 6 miles therefore this is not a proportional relationship
c)
number of glasses in 9 cases - 27
glasses in 1 case - 27/9
therefore glasses in 27 cases - 27/9 * 27 = 81 glasses
in the given scenario , 81 glasses were packed in 27 cases therefore this is a proportional relationship
d)
number of pencils in 2 boxes - 8
number of pencils in 1 box - 8/2
number of pencils in 8 boxes - 8/2 * 8 = 32
however in this case only 16 pencils in 8 boxes so this too is not a proportional relationship
correct answer with a proportional relationship is C
??? quadrilateral abcd ??? is inscribed in this circle. what is the measure of angle c? enter your answer in the box. ?? a quadrilateral inscribed in a circle. the vertices of the quadrilateral lie on the edge of the circle and are labeled as a, b, c,
d. the interior angle a is labeled as left parenthesis 2 x plus 3 right parenthesis degrees. the angle b is labeled as left parenthesis 2 x minus 4 right parenthesis degrees. the angle d is labeled as left parenthesis 3 x plus 9 right parenthesis degrees.
Answers
When, you have a quadrilateral inscribed in a circle, measure of the opposites sides are supplementary (they add to 180). Therefore, we can write and solve the following equation with angles D and B to find the value of x in the problem.
3x + 9 + 2x - 4 = 180
5x + 5 = 180
5x = 175
x = 35
Now, input x = 35 into the expression for A to find that the measure of angle A is 73.
Since A and C are supplementary:
A + C = 180
73 + C = 180
C = 107
Answer:
∠C = 107°
Step-by-step explanation:
Quadrilateral ABCD is inscribed in a circle, and a quadrilateral inscribed in a circle is known as cyclic quadrilateral.
So, ABCD is cyclic quadrilateral.
∠A = 2x + 3
∠B = 2x - 4
∠D = 3x + 9
Also. the sum of opposite angles of the cyclic quadrilateral is supplementary.
⇒ ∠B + ∠D = 180
⇒ 2x - 4 + 3x + 9 = 180
⇒ 5x = 175
⇒ x = 35
Now, ∠A = 73
Also, ∠A + ∠C = 180
⇒ ∠C = 180 - 73
⇒ ∠C = 107°
Removing which point from the coordinate plane would make the graph a function of x?
(–4, 3)
(–2, 1)
(0, 4)
(1, 1)
Answers
can someone check my work. I don't know what I did wrong
Answers
m∠2 = 34 - the sum of the interior angles of all triangles is 180 degrees. If you set the sum of all three interior angles equal to 180 and solve for the missing interior angle measure, you will get 34.
180 = 51 + 95 + x
180 = 146 + x
34 = x
m∠3 = 95 - you're correct.
m∠4 = 38 - you're correct.
m∠5 = 47 - you're correct.
To find m∠6, first find m∠7.
m∠7 = 59 - angle 7 is supplementary with the 121° angle; together they are 180 degrees. If you solve 180 = 121 - x for x, you see that m∠7 is 59°.
m∠6 = 74 - 180 (the sum of the interior angles of every triangle) minus the other two angle measures yields the measure of angle 6.
what two numbers multiplies to -90 and add to -8
Answers
Final answer:
The two numbers that multiply to -90 and add up to -8 are -10 and 2. This is found by factoring -90 and checking different factor pairs until the correct one is identified.
Explanation:
The student is asking for two numbers that when multiplied result in -90, and when added result in -8. This is a factorization problem that can be addressed by setting up a system of equations or by using intuition to guess and check pairs of factors. We are looking for a pair of numbers that have one positive and one negative number, because the product is negative (-90), and the sum is also negative (-8).
By listing out the factors of 90, we can test which pair of numbers, with one being negative, would multiply to -90 and add up to -8. After some trial and error, we find the pair that works are -10 and 9. -10 × 9 = -90 and -10 + 9 = -1. However, since the sum needs to be -8, then the correct pair is -10 and 2, because -10 × 2 = -20 and -10 + 2 = -8.
a 12-ft-long ladder is leaning against a wall and makes an 80 degree angle with the ground.how high up the wall does the ladder reach, and how far is the base of the ladder from the base of the wall? round to the nearest inch.,
Answers
Answer:
The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.
Step-by-step explanation:
Let us draw a diagram for the given situation.
In the attached figure,
AB = the height of wall where the ladder reaches
AC = ladder
BC = distance of base of ladder from the base of the wall
In triangle ABC,
[tex]\sin C=\frac{AB}{AC}\\\\\sin80=\frac{AB}{12}\\\\AB=12\sin80\\\\AB=11.82[/tex]
And
[tex]\cos C=\frac{BC}{AC}\\\\\cos80=\frac{BC}{12}\\\\BC=12\cos80\\\\BC=2.08[/tex]
Now, 1 feet = 12 inches
Hence, 11.82 ft = 141.84 inches
and 2.08 feet = 24.96 inches
Therefore, in the nearest inches, we have
The ladder reaches 142 inches and the base of ladder is 25 inches far from the base of the wall.
Is this done correctly or incorrectly??
PLEASE LET ME KNOW
PLZ HELP ASAP
Answers
A collection of quarters and dimes is worth $6.75. The number of dimes is 4 less than three times the number of quarters. How many quarters and dimes are in the collection?
Answers
Hope this helps!!:)
Have a good day!!:D
Plz mark brainliest!!XD
A rental company charges $9.50 per hour for a scooter plus a $15 fee. Write an equation in slope- intercept form for the total rental cost C of renting a scooter for h hours
Answers
C=$9.50h+15
The inverse of x -> y is:
Answers
The inverse of the statement is if both terms are negated:
"not x" implies "not y"
We have cases where the statement is true (Rain implies clouds) but the inverse is false (not rain does not imply not clouds; it can be cloudy while it does not rain).
3. If the volume of a cube of wood is15.625 cm3 and its mass is 10.00 grams, show the calculation for the density of the wood. @ganeshie8 @SolomonZelman,
Answers
density of wood = 0.64 gm/cm³
Explanation:
Density of a substance can be calculated as follows:
density = [tex] \frac{mass}{volume} [/tex]
We are given that:
mass of wood = 10 grams
volume of wood = 15.625 cm³
Substitute with the givens in the above equation to get the density as follows:
density = [tex] \frac{10}{15.625} [/tex] = 0.64 grams / cm³
Hope this helps :)
Answer:
The density of the wood is, 0.64 [tex]g/cm^3[/tex]
Step-by-step explanation:
Using the density formula:
[tex]\text{density} = \frac{\text{mass}}{\text{Volume}}[/tex] .....[1]
As per the statement:
If the volume of a cube of wood is 15.625 cm3 and its mass is 10.00 grams.
⇒Volume = 15.625 cubic cm and mass = 10 gram
Substitute the given values in [1] we have;
[tex]\text{density} = \frac{10}{15.625}[/tex]
Simplify:
density = 0.64 [tex]g/cm^3[/tex]
Therefore, the density of the wood is, 0.64 [tex]g/cm^3[/tex]
So I tried to answer this the best that I can but I keep getting wrong answers can someone help me I will award brainliest .
Answers
[tex]2*\sqrt{3}*\dfrac{cos(x)}{sin(x)}+4*cos(x)- \dfrac{3}{sin(x)} +2*\sqrt{3}\\ =2*cos(x)*(\dfrac{\sqrt{3}}{sin(x)}+2)-\sqrt{3}(\dfrac{\sqrt{3}}{sin(x)}+2)\\ =(\dfrac{\sqrt{3}}{sin(x)}+2)*(2*cos(x)-\sqrt{3})\\\\ cos(x)=\dfrac{\sqrt{3}}{2} -\ \textgreater \ x=\dfrac{\pi}{6}\ or\ x=\dfrac{11*\pi}{6}\\ or\\ \dfrac{\sqrt{3}}{sin(x)}+2=0-\ \textgreater \ sin(x)=-\dfrac{\sqrt{3}}{2}-\ \textgreater \ x=\dfrac{5*\pi}{3}\ or\ x=\dfrac{4*\pi}{3}\\\\ [/tex]
Which of the following are characteristics of the graph of the quadratic parent function?
A. It has one intercept.
B. It opens down.
C. It has a vertex at (0, 0).
D. It is U-shaped.
Answers
Answer:
The correct options are A, C and D.
Step-by-step explanation:
The quadratic parent function is
[tex]f(x)=x^2[/tex]
The properties of quadratic parent function are:
1. It has one intercept, i.e, x- and y-intercept are at origin.
2. It has a vertex at (0, 0).
3. It is U-shaped.
4. Each image y has two preimage, except 0.
5. It opens up.
From the given option one the option B is incorrect because the quadratic parent function opens upward.
Therefore the correct options are A, C and D.
1. Simplify (4xy^2)^3(xy)^5
2. Simplify (2t^–3)^3(0.4r)^2
Thank you whoever answers so much!,
Answers
multiplication=add the exponents
x^2.x^3=x^5
power=multiply the exponents
(x^2)^3=x^6
1. (4xy^2)^3(xy)^5
(64x^3y^6)(x^5y^5)
64x^8y^11
2. (2t^-3)^3(0.4r)^2
(8t^-9)(0.16r^2)
0.16r^2/8t^9 or r^2/50t^9
Note main rules:
[tex]1.\quad (a\cdot b)^n=a^n\cdot b^n,\\ \\2.\quad a^m\cdot a^n=a^{m+n},\\ \\3.\quad (a^m)^n=a^{mn}.[/tex]
1. Consider expression [tex](4xy^2)^3(xy)^5.[/tex] Using previous rules:
1 step: [tex](4xy^2)^3=4^3\cdot x^3\cdot (y^2)^3=64x^3y^{2\cdot 3}=64x^3y^6;[/tex]2 step: [tex](xy)^5=x^5\cdot y^5;[/tex]3 step: [tex](4xy^2)^3(xy)^5=64x^3y^6x^5y^5=64x^{3+5}y^{6+5}=64x^8y^{11}.[/tex]2. Consider expression [tex](2t^{-3})^3(0.4r)^2.[/tex] Using previous rules:
1 step: [tex](2t^{-3})^3=2^3\cdot (t^{-3})^3=8t^{-3\cdot 3}=8t^{-9};[/tex]2 step: [tex](0.4r)^2=0.4^2\cdot r^2=0.16r^2;[/tex]3 step: [tex](2t^{-3})^3(0.4r)^2=8t^{-9}\cdot 0.16r^2=8\cdot 0.16t^{-9}r^2=1.28t^{-9}r^2.[/tex]Answer:
[tex]64x^8y^{11};[/tex][tex]1.28t^{-9}r^2.[/tex]write 4x - 2y = -8 in slope-intercept form
Answers
( 4x - 2y = -8)
--------------------
Then find the Y-intercept and X-intercept which is 4 and -2
(4x - 2y = -8)
(4x - 2y = -8)
----------------------
Since we already have the slope our equation so far is
y = 2x + M
And since we have out Y-intercept you replace 4 for m
y = 2x + 4 is your answer
PUTTING MAX POINTS
Find all polar coordinates of point P where P = (6, -π/5)
Answer choices:
(6, -π/5 + 2nπ) or (-6, -π/5 + 2nπ)
(6, -π/5 + 2nπ) or (-6, -π/5 + (2n + 1)π)
(6, -π/5 + (2n + 1)π) or (-6, -π/5 + 2nπ)
(6, -π/5 + 2nπ) or (6, π/5 + (2n + 1)π)
Answers
Your answer should be d
the weight of a goat increased by 12 pounds is 38 pounds.write an equation to represent the situation.
Answers
x+12=38
4. Name a pair of corresponding angles
1. Angle 1 and angle 6
2. Angle 2 and angle 6
3. Angle 3 and angle 5
4. Angle 4 and angle 5
~
5.Use the figure. Assume that lines JL and MP are parallel
If m angle 4 =105°, then what is m angle 8?
1. 105°
2. 75°
3.175°
4.25°
Answers
(5) is 1. Angle 4 and 8 are corresponding giving them the same angle
For the given case the pair of angles are consecutive angles, corresponding angles, consecutive interior angles and alternate interior angles respectively and ∠8 = 105°. The correct option is (1).
What are parallel lines?The parallel lines are a group of straight lines that never intersect with one another. The distance between two parallel is always the same.
The given problem can be solved as follows,
(4) The pair of angles can be named as below,
(1) The angles ∠1 and ∠6 are called consecutive angles.
(2) The angles ∠2 and ∠6 are called corresponding angles.
(3) The angles ∠3 and ∠5 are called consecutive interior angles.
(4) The angles ∠4 and ∠5 are called alternate interior angles.
(5) The measure of ∠8 is given as below,
Since ∠4 and ∠8 are corresponding angles.
∠4 = ∠8 = 105°.
Hence, the names of the pair of angles are consecutive angles, corresponding angles, consecutive interior angles and alternate interior angles respectively and ∠8 = 105°.
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An artist wants to reduce the size of a drawing using a scale factor of 3:1 . The original drawing has an area of 720 square inches. What is area of the new drawing? Enter your answer in the box. in²
Answers
3/1=720/x
Cross multiply you get 3x=720
Solve for x which is 720/3
New area is 240 square inches
Answer: The area of the new drawing is 240 in².
Step-by-step explanation:
Hi, to answer this we have to use ratios:
Since the ratios is 3:1, it means that 3 units are equal to 1: 3/1
So, 720 units will be equal to x : 720/x
3/1 = 720/x
Solving for x:
x = 720/ (3/1)
x = 720/3
x = 240 in²
The area of the new drawing is 240 in².
Feel free to ask for more if needed or if you did not understand something.
PLEASE HELP!!! 100 POINTS!!! WILL GIVE BRAINLIEST!!!!
Graph the two lines:
2x + 3y = 18
3x -4y > 16.
Give the Domain and Range, Slope, and Y-intercept for each line.
Graph each equation above on the graph below and show all work.( Or tell me how to graph it)
Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer.
2x + 3y = 18 3x -4y > 16
Slope-Intercept Form: Slope-Intercept Form:
Domain: Domain:
Range: Range:
Slope: Slope:
Y-intercept: Y-intercept:
Answers
[tex]2x + 3y = 18[/tex]
DOMAIN IS ALL REAL NUMBERS
RANGE IS ALL REAL NUMBERS
SLOPE IS -2/3
Y INTERCEPT IS (0,6)
SLOPE INTERCEPT FORM
[tex]y = \frac{ - 2}{3} x + 6[/tex]
for the equation
[tex]3x - 4y > 16[/tex]
DOMAIN IS ALL REAL NUMBERS
RANGE IS ALL REAL NUMBERS
SLOPE IS 3/4
Y INTERCEPT IS (0,-4)
SLOPE INTERCEPT
[tex]y < \frac{3}{4} x - 4[/tex]
[tex]2x + 3y = 18[/tex]
[tex]3x -4y \ \textgreater \ 16[/tex]
They are written in standard form, [tex]ax+by=c[/tex], so our first step is to convert them into slope-intercept form, [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
We rearrange to basically solve for y in each function.
1) [tex]2x + 3y = 18 \\ 3y = -2y+18 \\ y= \frac{-2}{3}y+6[/tex]
2) [tex] -4y\ \textgreater \ -3x+16[/tex]
We divide by –4 to isolate y, but remember when multiplying or dividing with a negative number in an inequality, we flip the sign of the inequality.
[tex]y \ \textless \ \frac{3}{4}x-4[/tex]
This gives us our slope-intercept forms for each.
For the domain, each function is defined for all real x. This is a property of linear (and polynomial) functions. The inequality does not affect this.
The range, however, is a bit tricky. The range of a linear or polynomial function is always all real numbers y. It might be tempting to restrict it for an inequality, however, the range is still all reals.
In set-builder notation, we write for the domains of both functions: {[tex]x \ | \ all \ real \ numbers[/tex]}. For the ranges, we write {[tex]y \ | \ all \ real \ numbers[/tex]}.
In interval notation, we write [tex](- \infty, \infty)[/tex] for both the domain and range.
To obtain the slope and y-intercept, we look back to the functions in slope-intercept form, [tex]y=mx+b[/tex], again where m is the slope and b is the y-intercept.
For the equation, we have
[tex]m= \dfrac{-2}{3} [/tex]
and [tex]b=6[/tex].
For the inequality, we have
[tex]m= \dfrac{3}{4} [/tex]
and [tex]b=-4[/tex].
We can use the slope and y-intercept to graph each function. Remember that an inequality with less than or greater than (i.e., no "equal to" part) is represented with a dotted line.
To find where you shade the inequality, think about its sign. Since y is less than the expression, we shade below the line. We can also verify this by plugging in a test-point above or below the line and shading the region where the test-point is a valid solution.
See the graphed solution set attached.
MATH HELP LEASE WILL GIVE BRAINLIEST!!!
What is the value of θ for the acute angle in a right triangle?
sin(θ) = cos(58°)
Question 4 options:
32°
58°
122°
29°
Answers
The 1st selection is appropriate.
1.
(05.08 MC)
Given the equation 1 over x−1 + 2 over x =x over x−1
Part A: What values of x that would make the equation no solution? Why?
Part B: What is the solution of the equation. Show all of your steps.
Max and Maggie have to clean the house. It takes Max 10 hours to clean the house, while Maggie can complete the task in 6 hours. How long will it take for them to work together? Explain each step in solving this equation.
Answers
Part B) x=2 or x=1.
Together they could clean the house in 3.75 hours.
Explanation:
Part A is explained with the answer.
Part B)
[tex]\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}[/tex]
We will first multiply each term by (x-1) to cancel those denominators:
[tex]\frac{1}{x-1} \times \frac{x-1}{1}+\frac{2}{x} \times \frac{x-1}{1}=\frac{x}{x-1} \times \frac{x-1}{1} \\ \\ \frac{x-1}{x-1}+\frac{2(x-1)}{x}=\frac{x(x-1)}{x-1} \\ \\ 1+\frac{2(x-1)}{x}=x[/tex]
Now we multiply everything by x to cancel that denominator:
[tex]1(x)+\frac{2(x-1)(x)}{x}=x(x) \\ \\x+2(x-1)=x^2 \\ \\x+2*x-2*1=x^2 \\x+2x-2=x^2 \\3x-2=x^2[/tex]
We want all of the variables to be on the same side of the equation, so subtract 3x from both sides:
3x-2-3x=x²-3x
-2=x²-3x
To solve quadratics, we set them equal to 0. Add 2 to both sides to make this happen:
-2+2=x²-3x+2
0=x²-3x+2
To solve this by factoring, we want factors of 2 that sum to -3. -2(-1)=2 and -2+-1=-3:
0=(x-2)(x-1)
The zero product property tells us that either x-2=0 or x-1=0; therefore x=2 or x=1.
Max cleans 1/10 of the house in an hour, since it takes him 10 hours to clean the whole house. Maggie cleans 1/6 of the house in an hour, since it takes her 6 hours to clean the whole house. Our equation is then:
1/10x+1/6x=1 (one whole, since it is one house; x is the number of hours)
Find a common denominator. 60 is the first thing that 10 and 6 both evenly divide into:
6/60x+10/60x=1
16/60x = 1
Divide both sides by 16/60:
16/60x ÷ 16/60 = 1 ÷ 16/60
x = 1/1 ÷ 16/60
x = 1/1 ×60/16
x = 60/16 = 3.75.
Answer:
a
Step-by-step explanation: