For the area of triangle, the constant of variation is 1/2.
What is variational constant?
The link between the independent (x) and dependent (y) variables is shown by a constant of variation. A continuous relationship between the variables indicates to the user that there is one; it does not alter regardless of how the scenario changes.
It can be employed to ascertain how the dependent variable will alter in response to changes in the independent variable. For instance, if a person drives continuously at the same pace, they may calculate their distance by multiplying the number of hours they spent driving by the speed they were moving at. In this instance, the speed is the constant since it remained constant regardless of how long or how far they travelled during the journey.
A triangle's area is equal to (1/2) * (base) * (height).
It fluctuates in tandem with both the base length and the height.
The (1/2) represents the variational constant.
To learn more about constant of variation from given link
https://brainly.com/question/116551
#SPJ4
simplify this algebraic expression
y - 3/3 + 12
A.y - 11
B.y + 13
C.y + 11
D.y - 5
a -90 degree rotation is the same as
Answer:
Step-by-step explanation:
A 270 degrees anticlockwise rotation is the same result as the rotation of the 90 degrees.
You can choose between two tennis courts at two university campuses to learn how to play tennis. One campus charges 25 per hour. The other campus charges 20 per hour plus a one-time registration fee of 10 .
c. If you want to practice for a total of 10 hours, which university campus should you choose? Explain.
I should choose second or other campus, as it is cost effective.
We will begin with forming the equation according to the information provided in question. Let us represent the number of hours with t.
Cost on choosing first or one campus to play tennis-
Cost = 25 × t
Cost on choosing second or other campus to play tennis -
Cost = 10 + 20 × t
Now finding cost on each campus for duration of ten hours.
First campus -
Cost = 25 × 10
Cost = 250
Second campus -
Cost = 10 + 20 × t
Cost = 10 + 20 × 10
Cost = 10 + 200
Cost = 210
Therefore, to practice for a total of 10 hours, I should choose second or other campus, as it is cost effective.
Learn more about calculations on time -
https://brainly.com/question/26714672
#SPJ4
Find the measure. (Lesson 5-1)
TQ
If TQ = 2x - 6 and RQ = x + 3 then the measure of TQ = 12.
What is Perpendicular Bisector Theorem?The perpendicular bisector theorem states that if a point is on a segment's perpendicular bisector, it is equidistant from the segment's endpoints.
According to the perpendicular bisector theorem, any point on the perpendicular bisector is equidistant from both ends of the line segment on which it is drawn. If a pillar stands at an angle in the center of a bridge, all of its points will be equidistant from the bridge's end points.
Where, TQ = 2x - 6 and RQ = x + 3
By the Perpendicular Bisector Theorem, RQ = TQ.
2x - 6 = x + 3
x = 9
Substitute the value of x in TQ, we get
TQ = 2(9) - 6
= 18 - 6
= 12
Therefore, the value of TQ = 12.
To learn more about Perpendicular Bisector Theorem refer to:
https://brainly.com/question/4137998
#SPJ4
Rosita runs every day in preparation for a marathon. If she runs 8.7 miles a day, how many
miles will she run in 26 days?
Answer:
226.2 miles
Step-by-step explanation:
8.7 x 26 = 226.2
Which equation represents a line with slope -2 and y -intercept 3 ?
f. 3 y=x-2
g. 3 y=-2 x+1
h. y=2 x-3
i. y=-2 x+3
Answer: Maybe f I'm not sure
Step-by-step explanation:
Zach found four consecutive odd integers such that 5 times the sum of the first and the third was 22 greater than the product of 8 and the sum of the second and the fourth. What were the integers?
Answer:
3, 5, 7, 9
Step-by-step explanation:
Give Brainliest if I helped!
The four consecutive odd integers that Zach found are x, x + 2, x + 4, and x + 6 are -11, -9, -7, and -5.
To solve this problem, set up equations based on the given information.
"5 times the sum of the first and the third":
[tex]5(x + x + 4)[/tex]
"the product of 8 and the sum of the second and the fourth":
[tex]8((x + 2) + (x + 6))[/tex]
According to the problem, the first equation should be 22 greater than the second equation:
[tex]5(x + x + 4) = 8((x + 2) + (x + 6)) + 22[/tex]
Next, simplify and solve the equation:
[tex]5(2x + 4) = 8(2x + 8) + 22[/tex]
Remove the bracket by multiplying the terms:
[tex]10x + 20 = 16x + 64 + 22[/tex]
Take the variables to LHS and constants to other side and solve it:
[tex]6x = -66[/tex]
On dividing by 6 on both sides:
x = -11
Now that the value of x, and find the four consecutive odd integers:
x = -11
On substituting x value in the following terms:
[tex]x + 2 = -11 + 2 \\= -9\\x + 4 = -11 + 4\\ = -7\\x + 6 = -11 + 6 \\= -5[/tex]
Therefore, the four consecutive odd integers are -11, -9, -7, and -5.
Learn more about consecutive integers here:
https://brainly.com/question/180332
#SPJ4
two cars travel down the highway at the same speed. if the first car travels 10 kilometers per hour faster than its current speed and the second car travels 10 kilometers per hour slower than its current speed than the first car would travel in two hours the same distance the second car would travel in thee hours. what is the original speed of the cars?
Answer:
The original speed of the cars is 50 km/hStep-by-step explanation:
Let the original speed of the cars be x.
The first carWhen speed is x + 10 the distance in two hours is:
2(x + 10)The second carWhen speed = x - 10 the distance in three hours is:
3(x - 10)Since the distance is same in both cases, set them equal and solve for x:
2x + 20 = 3x - 303x - 2x = 20 + 30x = 50The original speed of the cars is 50 km/h
Answer:
Original speed = 50 km/h
Step-by-step explanation:
Given that,
→ first car travels 10 km faster than its current speed. It would travel in two hours the same distance.
→ second car travels 10 km per hour slower than its current speed. It would travel in 3 hours the same distance.
Then the equation will be,
→ 2(x + 10) => 1st car
→ 3(x - 10) => 2nd car
→ 2(x + 10) = 3(x - 10)
Now the original speed of the cars is,
→ 2(x + 10) = 3(x - 10)
→ 2x + 20 = 3x - 30
→ 2x - 3x = -30 - 20
→ -x = -50
→ [ x = 50 km/h ]
Hence, the original speed is 50 km/h.
Evaluate the functions
F(-2)
F(3)
F(5)
F(e+4)
Answer:
F(5)
Step-by-step explanation:
its right very sorry if its late
Given: AB || CD-i AB ≅ DC
Prove: Δ A B E ≅ ΔC D E
We have proved that , the ΔABE is congruent to ΔCDE i.e., ΔABE ≅ ΔCDE
It is given that AB║ CD and AB ≅ DC.
We have to prove that ΔABE is congruent to ΔCDE i.e., ΔABE ≅ ΔCDE.
What is the SAS rule of congruency of triangles ?
SAS axiom states that if two sides and the included angle of one triangle are equal to two sides and included angle of other triangle, then triangles are congruent.
As per the question ;
AB║ CD and AB ≅ DC
The two triangles are ΔABE and ΔCDE
So ,
AB = CD (from given data)
also ;
Included angles of two triangles are equal ;
∴
∠ABE = ∠CDE (from given data)
and
BE = BE (common)
∴ Both triangles are congruent to each other ;
i.e.,
ΔABE ≅ ΔCDE.
by SAS axiom.
Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX
To learn more about congruency rules click here ;
https://brainly.com/question/13525673
#SPJ4
geometry
through: (1,4), slope=6
Answer:
Step-by-step explanation:
Point slope form y-y₁ = m(x-x₁)
y-4 = 6(x + 1)
y-4 = 6x + 6
y = 6x + 10
Twelve is greater than the sum of 6 and a number.
012>6+n
O 12<6n
012<6+n
12 >6n
Answer:
12<6+n
this is the answer
Anne and Katherine are both saving money from their summer jobs to buy bicycles. If Anne had $150 less, she would have
exactly as much as Katherine. And if Katherine had twice as much, she would have exactly 3 times as much as Anne. How
much money have they saved together?
$300
$400
$450
$625
$750
If f(x)=7-3 x and g(x)=3 x-7 , what is the value of f(1)+g(1) ?
If f(x)=7-3 x and g(x)=3 x-7 , the value of f(1)+g(1) is 0
What is function composition?A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
f(x)=7-3 x and g(x)=3 x-7
For, f(1) = 7 - 3(1)
= 7 - 3
= 4
For, g(1) = 3x - 7
= 3(1) - 7
= -4
f(1) + g(1) = 4 - 4
= 0
To learn more about function composition from given link
https://brainly.com/question/10687170
#SPJ4
Given that 32 √ 2 = 2ª, find the value of a.
The value of 'a' in the given expression is 11/2.
Elaborate about the square root.The square root formula can be used to calculate the square root of any number. The square root of any number is the value that, when multiplied by itself, yields the original number. Each number has two square roots, one positive and the other negative. For example, the number four has two square roots, -2 and 2.
Given [tex]$32 \sqrt{2}=2^a$[/tex]
We can write 32 as:
32 = 2 × 2 × 2 × 2 × 2
32 = [tex]2^{5}[/tex]
We can write [tex]$\sqrt{2}=2^{1 / 2}$[/tex].
Now,
[tex]$$\begin{array}{r}32 \sqrt{2}=2^a \\2^5 \cdot 2^{1 / 2}=2^a \\2^{5+1 / 2}=2^a \\2^{1 / 2}=2^a \\\end{array}$$[/tex]
Therefore, the value of a = 11/2.
To know more about square roots visit:
https://brainly.com/question/1387049
#SPJ9
Find the circumference of circle described. Round to the nearest hundredth.
a. radius =2.5 centimeters
Answer:
15.71 cm
Step-by-step explanation:
circumference is [tex]\pi[/tex]d
diameter is 2r
radius = 2.5 cm so the diameter is 2.5*2 = 5 cm
circumference = [tex]\pi[/tex] (5) -> 15.707
rounded to the nearest hundredth is 15.71 cm
The company in Problem 2 has an alternative bonus plan. It pays a $ 5000 bonus if a new salesperson makes 10 sales in the first week and then improves by one sale per week each week thereafter. One salesperson qualified for this bonus with the minimum number of sales. How many sales did the salesperson make in week 50 ? In all 50 weeks?
The given situation shows an arithmetic sequence and the number of sales in the week 50 can be determined by using the nth term formula of arithmetic sequence. The sales in all 50 weeks can be determined by using the formula for sum of finite arithmetic sequence.
An arithmetic sequence is an ordered set of numbers that have a constant difference called a common difference between consecutive terms. Each term is obtained by adding the common difference to the previous term.
In the given situation, the first term (a) is the number of sales to be made in the first week. Hence, a = 10
The common difference (d) is the number added to get the number of sales in the next week. Hence,
d = 1
Hence, in the 2nd week the number of sales should be 11 and in 3rd week it should be 12.
Using the formula for nth term and n = 50,
an=a+(n-1)d
a50=10+(50-1)1
a50=10+(49)1
a50=10+49=59
The formula of finding the sum of the finite arithmetic sequence:
Sn=(n/2)(a1+an)
S50=(50/2)(10+59)
S50=25(69)=1725
Hence, the number of sales in the 50th week is 59 and the total number of sales made in the 50 weeks is 1725.
Learn more about arithmetic sequence:
https://brainly.com/question/6561461
#SPJ4
Somerville has a population of 38,400 people. The town has been seeing its population decline by 3% every year. If this trend continues, what will the population be in 3 years?
The population of Somerville is approximately 35047 after a depreciation of of 3% every year .
Depreciation is economics refers to two different aspects of the same idea: first, the actual decline in an asset's fair value as it is used and worn, such as the annual decline in value of factory equipment; and second, the allocation in accounting statements of the asset's original cost to the periods during which it is used.
Here depreciation is the gradual decline in population each year in the town.
The rate of depreciation or decline is the percentage amount of population that decreases every year.
The formula used to calculate depreciation is given by:
[tex]A=P(1-r)^t[/tex]
Given the rate of depreciation as 3%.
Population at present = 38400
Population after 3 years:
= 38400 (1 - 0.03 )³
= 38400 ( 0.97 )³
= 35046.6432
≈ 35047
Hence the population after 3 years will be approximately 35047.
To learn more about depreciation visit:
https://brainly.com/question/8321101
#SPJ1
Answer: =35047
Step-by-step explanation:
Dexter's family buys tickets every year for a concert. Last year they were in seats C3, C4, C5 , and C6 . This year, they will be in seats D16, D17, D18 , and D19 . Write a translation in words and using vector notation that can be used to describe the change in their seating.
A translation in words and using vector notation that can be used to describe the change in their seating as-
In words: Dexter's family move 13 seats to the right and one row back.In vector notation: < 13, -10>.What is meant by translation?In geometry, translation refers to a function which moves an object a specified distance. The object isn't otherwise altered. It has not been rotated, mirrored, or resized.
Each point of a object must be relocated in the same direction and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, and also the object after the translation is referred to as the image.Now, as per the stated question.
In the previous year the seats given to Dexter's family were C3, C4, C5 , and C6.
Now, for current year, seats are at D16, D17, D18 , and D19.
Choose a seat from the new row & compare it to the seat with the previous row. Seat D16 is 13 seats to the right and 1 row back from C3.
As a result, the translation vector could be written as < 13, -10>.
To know more about the translation vector, here
https://brainly.com/question/24766817
#SPJ4
Determine whether the given measures define 0,1,2 , or infinitely many triangles. Justify your answers. a=10, b=15, m
We can construct an unlimited number of triangles when given only two sides and no indication of the angle, such as a = 10m and b = 15m
Consider this:
With 10m and 15m side lengths and an angle value ranging from 0 to 360 degrees, how many distinct triangles are possible?
Make one of the triangles with sides of 10 meters, 15 meters, a 30 degree angle, and a third side that may be adjusted to your preferred length using a protractor. A triangle has been built by you.
By changing the length and angle of the third side, we can produce a completely different triangle that is similar to this one.
Keep in mind that you choose the side lengths and angle. This suggests that you might make a different decision. Using the same angles, you can make an infinite number of different triangles.
As a result, using just one angle and one side length, we can create an unlimited number of triangles.
To learn more about, Triangles here
brainly.com/question/2773823
#SPJ4
y varies directly with x .
If y=5 when x=-3 , find x when y=-1 .
Using direct variation, the value of x for equation y = 5/-3 (x) is 3/5 when y = -1
What is direct and inverse variation?When x is not equal to zero, an equation of the form y = kx describes the linear function known as direct variation. When x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.
Using direct variation,
y = kx
⇒ 5 = k(-3)
⇒ k = 5 / -3
for y = -1
y = 5/-3 (x)
⇒ -1 = 5/-3 × x
⇒ x = 3/5
To learn more about direct and inverse variation from given link
https://brainly.com/question/493649
#SPJ4
What is the product of a number and 14 plus 10, written as an algebraic expression?
10(x + 14)
10x − 14
14 ÷ x − 10
14x + 10 please give me the answer i need help
Answer:
14x+10
Step-by-step explanation:
The product means multiplication
Answer:
D 14x+10
Step-by-step explanation:
will give you EXTRA BRAINLIEST POINTS
i don't understand this and need to submit asap please help thanks :D
whatis the answer to 4.5x=18
[tex] \large \bf \implies{x = 4}[/tex]
Step-by-step explanation:Let's solve your equation step-by-step[tex] \bf \longrightarrow{4.5x = 18}[/tex]
Divide both sides by 4.5[tex] \bf \frac{ \cancel{4.5}x}{ \cancel{4.5}} = \frac{18 }{4 \cancel{.}5} = \frac{18 \times 10}{45} = \frac{180 \div 3}{45 \div 3} = \frac{60 \div 3}{15 \div 3} = \frac{20 \div 5}{5 \div 5} = \frac{4}{1} = 4 \\ [/tex]
[tex] \large \bf \implies \boxed{x = 4} \: ans.[/tex]
You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $ 50, $ 52, $ 55 , and $ 59 . If this pattern continues, how much will you receive in the tenth month?
a. Write a formula to describe this sequence.
Money received in tenth month: $104.
A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
Money received in first four months: $50, $52, $55, %59.
To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
A formula that describes this arithmetic sequence: [tex]a_n=a_{n-1}+n[/tex], n > 1., where n = number of month.
To learn more about arithmetic Progressions, refer to the link: brainly.com/question/6561461
#SPJ4
Latasha is baking cookies. The radius of each cookie is 9 centimeters.
What is the area of each cookie?
Use 3.14 for pi and round your answer to the nearest tenth.
PLEASE HELP!!!!
Answer:
The area of each cookie is 254.3
Suppose you make a 4-minute local call using a calling card and are charged 7.6 cents. The cost of a local call varies directly with the length of the call. How much more will it cost to make a 30 -minute local call?
a. Which quantity is the dependent quantity?
For the linear equation C = kl, where c, cost is the local variable and it takes 49.4 cents more for a 30 min local call. The dependent variable is the price of a local call.
What is a linear equation?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.
The equation representing the situation
C = kl
where c depicts the cost and l is the length of call.
The dependent variable is the price of a local call.
The term "mord more" denotes that we are searching for the price difference between a 4 minute call and a 30 minute call, or the price of a 26 minute call.
The cost for 26 minutes will be 49.4 cents.
To learn more about linear equations from given link
https://brainly.com/question/2284852
#SPJ4
Two factory plants are making TV panels. Yesterday, Plant A produced 6000 fewer panels than Plant B did. Five percent of the panels from Plant A and 4% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 1410 defective panels?
Plant P produced 15333 numbers of panels when the two plants together produced 1410 defective panels using unitary method.
What is unitary method?It is a method for figuring out a single unit's value, then multiplying that value by itself to get the required value.
Given data
Plant produces defective panels = 1140
Plant A produce = 5%
Plant B produce = 4%
Assume,
Number panels Plant B produce = x
Number panels Plant A produce = x - 6000
[tex]\frac{5}{100}[/tex](x) + [tex]\frac{4}{100}[/tex](x-6000) = 1140
0.05x + 0.04x - 240 = 1140
0.09x = 1380
x = 15333
Plant P produced 15333 numbers of panels when the two plants together produced 1410 defective panels using unitary method.
To learn more about unitary method, visit
https://brainly.com/question/17355857
#SPJ9
Meals with a Purpose are selling to-go charcuterie boards. You can purchase a small board or a medium board. On Thursday, Meals with a Purpose sold 10 small charcuterie boards and 12 medium charcuterie boards for a total of $144. On Thursday, Meals with a Purpose sold 5 sold charcuterie boards and 9 medium charcuterie boards for a total of $93.
What is the cost of each small charcuterie boards and one medium charcuterie boards?
The cost of each small charcuterie boards is $6 and one medium charcuterie boards is $7.
How to illustrate the information?A mathematical statement known as an equation is made up of two expressions joined together by an equal sign. It is a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Let small charcuterie boards = c
Let medium charcuterie boards = m
Therefore, the equation will be:
10c + 12m = 144
5c + 9m = 93
Multiply equation i by 5
Multiply equation ii by 10
50c + 60m = 720
50c + 90m = 930
Subtract
30m = 210
m = 210/30
m = 7
Therefore, 5c + 9m = 93
5c + 9(7) = 93
5c + 63 =93
5c = 93 - 63
5c = 30
Divide both sides by 5
c = 30 / 5
c = 6
Therefore, based on the information the cost of each small charcuterie boards is $6 and one medium charcuterie board is $7.
Learn more about equations on:
brainly.com/question/13763238
#SPJ1
A dance group of 17 teenagers had a mean mass of 44.5kg. to enter a competition there needs to be 18 people in the group with an average mass of 44.4kg or less. what is the maximum mass that the 18th person could be
Answer:
Step-by-step explanation:
so first it would be -0.1 but that means you need to remove the 17th person and get 2 really light people because one can not be negative hope this helps
