Answer:
(Some textbooks describe a proportional relationship by saying that " y varies proportionally with x " or that " y is directly proportional to x .") This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.
10:4 = 5:2
6:2 = 3:1
Not equal.
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 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
During a certain 3 month period, a company reported a 3,500 profit. I cover the next 3 month period, the company period a 6000 profit for those months. By approximately what percent did the company profit increase?
A) 25%
B) 32%
C) 42%
D) 55%
E) 70%
The company profit approximately increased by E) 70%.
What is an approximation?An approximation is an equivalent value or number obtained by rounding off to the required significant figure.
The result obtained through approximation is not an exact value but is the nearest rounded value.
For instance, 71.4% can be approximated to 71% or 70%. 58 minutes can be rounded off or approximated to 1 hour.
Data and Calculations?Profit in 3 months = $3,500
Profit in 6 months = $6,000
Increase in profit = $2,500 ($6,000 - $3,500)
Percentage increase in profit = 71.43% ($2,500/$3,500 x 100)
71.43% ≈ 70%
Thus, the company profit approximately increased by E) 70%.
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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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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 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°.
how is 4 divided by 2/3 = 6 ?
Here are some steps in the photo.
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Source of the photo: Calculator Soup
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.
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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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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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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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 :)
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
HELP ME PLEASEeeeeee
Answer:
7.2
Step-by-step explanation:
7.4-0.2=7.2
Identify the pattern and find the next three terms. 100,117,134,151,168, ...........
The given sequence 100,117,134,151,168, ........... is in AP. The next three terms are 185, 202, 219..
What is the AP arithmetic progression sequence?The difference between two numerical orders is a constant value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.
We'd emerge across a few fundamental words in AP that have been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be described in terms of common differences, as shown below.
The procedure for appraising an AP's n-th term is as follows: an = a + (n − 1) × dThe following is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the given sequence is; 100,117,134,151,168, ...........
The series comprises of five given terms.
Let the initial term be 'a₁' = 100.
The second term be 'a₂' = 117.
The third term be 'a₃' = 134.
And, the fourth term is 'a₄' = 151.
The AP must have the equal common difference. So,
d = a₃ - a₂
Substitute the values.
d = 134 - 117
d = 17
Thus, the computed common difference is 17.
or d = a₄ - a₃ (Substitute the values)
d = 151 - 134
d = 17
Since, a₃ - a₂ = a₄ - a₃
Thus, we can get to know that the given sequence is in AP.
Now, the 6th term is estimated as; a₆ = a₅ + d = 168 + 17
a₆ = 185
Similarly, the 7th term will be; a₇ = a₆ + d = 185 + 17
a₇ = 202
And, the 8th term will be calculated as; a₈ = a₈ + d = 202 + 17
a₈ = 219.
Therefore, it can be said that the given sequence is in AP next three terms be 185, 202, 219.
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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! :)
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:
1)the local park measure 60m by 50m. part of the park is torn to install a sidewalk of uniform width about it, reducing the area of the park itself by 321m2. what quadratic equation represents the situation?
2)the length of a rectangle is 1m less than twice the width. The area of the rectangle is 120 m2. what quadratic equation illustrates the situation?
1)The neighborhood park is 60m by 50 m. The park is reduced in size by 321m2 as a portion of it is ripped up to create a uniform-width sidewalk around it. What quadratic equation best captures the circumstances?
2)A rectangle's length is 1 m less than twice its width. The rectangle has a 120 m2 area. What quadratic equation best describes the circumstances?
Answer for the first question is the quadratic equation is [tex]4x^{2} -220x+321=0\\[/tex].
Answer for the second question is The quadratic equation is [tex]x^{2} -x-120=0[/tex].
1)Let 'x' stand in for the sidewalk's width.
The area of the park is: [tex]A_{1} =60\times50[/tex]
The reduced area of the park measures
60-2x by 50-2x with area of [tex]A_{2} =(60-2x)(50-2x)[/tex]
[tex]A_{1} -A_{2} =321[/tex]
[tex]60\times50-(60-2x)(50-2x)=321[/tex]
[tex]3000-(60-2x)(50-2x)=321\\3000-(3000-120x-100x+4x^{2} )=321\\220x-4x^{2} =321\\4x^{2} -220x+321=0\\[/tex]
Therefore, the quadratic equation is [tex]4x^{2} -220x+321=0\\[/tex].
2) Given that,
Width=x.
length=2x-1
Area=120[tex]m^{2}[/tex]
We know area=length[tex]\times[/tex]width
120=x(x-1)
[tex]x^{2} -x=120\\x^{2} -x-120=0[/tex]
Therefore, The quadratic equation is [tex]x^{2} -x-120=0[/tex].
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Is -15/3 a irrational or rational number
Answer: rational
Step-by-step explanation:
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
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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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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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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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.
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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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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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:
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.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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