Answer:
when the sum of the squares of the sides are equal to the square of the hypotenuse
Step-by-step explanation:
we use Pythagoras, 97 is the hypotenuse, 65 and 72 the sides.
97² = 65² + 72²
97² = 97²
it is a right triangle
A popular social networking website wants to upgrade its webpage design, but it is unsure how its audience would respond to the change. what is the best step for the website to take in order to gauge the target audience’s response if it wants to limit the risk of alienating the entire target audience?
To limit the risk of alienating the entire target audience it needs to release the design to a small number of randomly chosen members .
Who are the target audience?target audience serves as a term that describes the people that a particular work or a product is been directed to.
Therefore, as a popular social networking website who want to limit the risk of alienating target audience, it should work randomly.
Learn more about target audience at;
https://brainly.com/question/1462532
#SPJ4
65. show that of all the isosceles triangles with a given perimeter, the one with the greatest area is equilateral.
Answer:
Below.
Step-by-step explanation:
I can do this using calculus but the algebra will be a bit messy.
Let the 2 equal sides of isosceles triangle be x and the base be y units long.
Then perimeter p = 2x + y.
Area A = 0.5yh where h is the altitude of the triangle.
h = sqrt [x^2 - (0.5y)^2]
= [x^2 - (0.5y)^2]^0.5
So A = 0.5y * [x^2 - (0.5y)^2]^0.5
From the perimeter formula y = p - 2x so:
A = 0.5(p-2x) * [x^2 - (0.5(p-2x)^2]^0.5
A = 0.5(p-2x) * [x^2 - 0.25(p^2 - 4xp + 4x^2)]^0.5
A = 0.5(p-2x) * [x^2 - 0.25p^2 + xp - x^2]^0.5
A = (0.5p-x) * [xp - 0.25p^2]^0.5
We now find the derivative and equate it to zero to find the value of x which corresponds to a maximum area.
We use the product rule:
dA/dx = (0.5p-x)* 0.5(xp - 0.25p^2)^(-0.5) * p - 1(xp - 0.25p^2)^0.5 = 0
p(0.5p - x) / (2((xp - 0.25p^2)^0.5 - (xp - 0.25p^2)^0.5 = 0
p(0.5p - x) / (2((xp - 0.25p^2)^0.5 = (xp - 0.25p^2)^0.5
Now multiplying though by (2((xp - 0.25p^2)^0.5 :-
p(0.5p - x) = 2 (xp - 0.25p^2)
0.5p^2 - px = 2px - 0.5p^2
p^2 = 3px
x = p^2/3p = p/3
So for a maximum value of the area x = p/3.
But y = p - 2x
= p - 2(p/3)
= p - 2/3p
= p/3
- but we've just shown that x = p/3
That means that x = y and the triangle is Equilateral.
a tv studio has brought in 4 boy kittens and 5 girl kittens for a cat food commercial. the director is going to choose 5 of these kittens at random to be in the commercial.
what is the probability that the director chooses 3 boy kittens and 2 girl kittens? round your answer to three decimal places.
The probability that the director chooses 3 boy kittens and 2 girl kittens is 0.32.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have total number of kitten = 4+5 = 9
Total number of outcomes if the director is going to choose 5 of these kittens at random to be in the commercial:
= C(9, 5) = 126
The director chooses 3 boy kittens number of ways:
= C(4, 3) = 4
The director chooses 2 girl kittens number of ways:
=C(5, 2) = 10
Total favourable outcomes = 10×4 = 40
The probability = 40/126
= 0.317 ≈ 0.32
Thus, the probability that the director chooses 3 boy kittens and 2 girl kittens is 0.32.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
Mason has a business selling perfume at the mall. Currently his business has a
balance of -$20.
Which amounts of sales would give Mason's business a positive balance?
Choose ALL that apply.
$15 $35 $21 $29 $30 $19
Answer:
21, 29, 30, 35
Step-by-step explanation:
anything greater than 20 would break even and then give a position balance
Can someone please answer this, ill give you brainliest Would be very appreciated.
Explanation:
Expression: d = 16t² where d is distance. t is time.
1)
Here t = 2
d = 16(2)²
d = 64 feet
2)
h = 906-t²
h = 906 - 16(2)²
h = 842 feet
3)
expression of height: y = 906 - 16t²
Answer:
64842y = 906 - 16t²Step-by-step explanation:
Q1
Distance travelled in 2 second 16(2)²64 feetQ2
Height of object after 2 seconds906 - 64842 feetQ3
height of object t seconds after it is droppedy = 906 - 16t²
Peter is planting a rectangular garden. The length is 15 yards longer than the width. Jorge is planting a square garden. The sides of Jorge's garden are equal to the width of Peter's garden. What is the ratio of the area of Peter's garden to the area of Jorge's garden? Use this ratio to find the ratio of the areas if the width of Peter's garden is 32 yards.
x + 32/x ; 32/15
x-32/x ; 32/15
x+15/x ; 47/32
x-15/x ; 47/32
If the width of peter's garden is 32 yards, the ratio of the areas is 47: 32
Area of a rectangle.area of rectangle = lw
where
l = lengthw = widthTherefore,
Peter rectangular garden
l = 15 + xJorge is planting a square garden. The sides of Jorge's garden are equal to the width of Peter's garden.
Therefore,
x = side of Jorge gardenThe ratios are as follows;
(15 + x)x : x²
Therefore, if the width of peter's garden is 32 yards, the ratio of the areas is as follows:
(15 + 32)32 : 32²
1504: 1024
752: 512
376: 256
94:64
47: 32
learn more on rectangle here: https://brainly.com/question/23881202
#SPJ1
Answer:
(x+15)/x; 47/32
Given: RT || SP, RQ ≅ QP, RP bisects ST at Q
Prove: ΔRQT ≅ ΔPQS
Triangles R Q T and P Q S are connected at point Q. Lines R T and S P are parallel. The lengths of lines R Q and Q P are congruent.
Tamir is working to prove the triangles congruent using SAS. After stating the given information, he states that TQ ≅ QS by the definition of segment bisector. Now he wants to state that ∠RQT ≅ ∠PQS. Which reason should he use?
alternate interior angles theorem
corresponding angles theorem
linear pair postulate
vertical angles theorem
Answer: vertical angles theorem
Step-by-step explanation:
HELP ASAP PLSSSSSSS
Clara surveyed the students at her school to find out if they like pies and/or sandwiches. The results of her survey are shown in the two-way table below:
Like Pies
Do Not Like Pies
Total
Like Sandwiches
25
43
68
Do Not Like Sandwiches
26
6
32
Total
51
49
100
If a student does not like sandwiches, what is the probability that student also does not like pies?
81.3%
26.0%
23.1%
18.8%
Answer:
18.8%
Step-by-step explanation:
For calculating this, focus on one part of the table :
The row where students do not like sandwichesThere are 32 students who do not like sandwiches, and 6 of them do not like pies. Take this a proportion :
P (does not like pies, do not like sandwiches) = 6/32P = 3/16P = 18.8%Students who don't like sandwiches also don't like pie is the 2 nd box on 2 nd line
Probability
P(E)=6/32P(E)=6/32×100=3/16×100=18.8%Option D
A diner is serving a special lunch combo meal that includes a drink, a main dish, and a side. Customers can choose among 5 drinks, 4 main dishes, and 5 sides. How many different combo meals are possible? Select from the drop-down menu to correctly complete the statement Customers can create Choose... different lunch combo meals. 4 A 1 2 3 4 5. oc 9
Since the customers can choose among 5 drinks, 4 main dishes, and 5 sides. there 100 different combo meals are possible.
Since order is not important we use combination to solve the problem
What is combination?This is the number of ways in which x objects can be selected out of n objects. It is given mathematically as ⁿCₓ = n!/x!(n - x)!
The number of different combo mealsNow, given that the customer can choose among 5 drinks, 4 main dishes, and 5 sides.
There are ⁵C₁ ways of choosing the drinks.
So, ⁵C₁ = 5!/1!(5 - 1)!
= 5!/1!/4!
= 5
There are ⁴C₁ ways of choosing the main dishes.
So, ⁴C₁ = 4!/1!(4 - 1)!
= 4!/1!/3!
= 4
There are ⁵C₁ ways of choosing the sides.
So, ⁵C₁ = 5!/1!(5 - 1)!
= 5!/1!/4!
= 5
So, total number of ways of choosing the combo meals is
⁵C₁ × ⁴C₁ × ⁵C₁ = 5 × 4 × 5
= 100 ways.
So, there 100 different combo meals are possible.
Learn more about combination here:
https://brainly.com/question/26852614
#SPJ1
Answer: The answer is 100
Step-by-step explanation:
Find the measure of each side of a square
that has an area of 225 square centimeters.
chef johnson used 4 1/2 of flour to make 4 fruitcakes. How many cups of flour are needed for 1 fruitcake
Answer:
1 1/8 cups of flour
Step-by-step explanation:
hi!
If Chef Johnson needs 4 1/2 cups of flour to make 4 fruitcakes and he wants to make one, he has to divide the recipe by 4. 4 1/2 / 4= 1 1/8
Which statement BEST describes the graph of f(x - 6)?
A. The graph of f(x) is shifted up 6 units.
6
B. The graph of f(x) is shifted left 6 units.
C. The graph of f(x) is shifted right 6 units.
D. The graph of f(x) is shifted down 6 units.
Answer:
B. f(x) is shifted left by 6 units
Step-by-step explanation:
when we talk about translations, we know they happen along the X axis, y axis or sometimes both, in this case we see that were subtracting x by six units, so we are moving left along the x axis
ways to remember this is:
-you count up x the RIGHT way going right
-you count UP y
and of cource by process of ellimination we know that decreasing X goes left and decreasing y goes down
ALSO NOTE: x always goes horizontally and y always goes vertically
The figures below are similar. What is v?
Answer:
v = 16 mm
Step-by-step explanation:
since the figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{v}{20}[/tex] = [tex]\frac{28}{35}[/tex] ( cross- multiply )
35v = 560 ( divide both sides by 35 )
v = 16
Find two positive consecutive odd integers such that the square of the large integer is one less than twice the square of the smaller integer.
Step-by-step explanation:
x, x+2 are the two positive consecutive of integers (x + 2, because the minimum distance between 2 odd numbers is always 2, as there can never be 2 odd numbers directly following each other; and neither can even numbers, by the way).
(x+2)² = 2×x² - 1
x² + 4x + 4 = 2x² - 1
0 = x² - 4x - 5
we can solve this by factoring.
that means we need to find a and b so that
(x - a)(x - b) = x² - 4x - 5 = 0
and x = a and x = b are the 2 solutions of the quadratic equation.
x² - ax - bx + ab = x² - 4x - 5 = 0
x² - (a+b)x + ab = x² - 4x - 5 = 0
a+b = 4
ab = -5
that means that either a or b has to be 5 and the other -1.
so, the result is
(x - 5)(x + 1) = 0
x = 5
or
x = -1
are the possible solutions.
since we are only looking for positive integers, x = -1 is not a valid solution.
and only x = 5 remains as valid solution.
therefore, the 2 positive consecutive odd integers are
5, 7
Alejandro was picked by this teacher to find the integer that has the square root closest to 7, without going over. he wrote 52 on the bored. was he correct? explain your reasoning.
Considering that the square root of 49 is 7, and 52 > 49, Alejandro was not correct, as the correct integer is of 48.
What is the integer that has the square root closest to n, without going over?The integer that has square root n is given by:
S(n) = n².
Hence the closest is given by:
C(n) = n² - 1.
In this problem, we have n = 7, hence:
C(7) = 7² - 1 = 48.
Which means that Alejandro was not correct.
More can be learned about square roots at https://brainly.com/question/27678604
#SPJ1
PLEASE HELP ME IF YOU DO you will get the most loyal friend and honest and nicest
Answer:
Below:
Step-by-step explanation:
1. 2 15/28
2. 2 7/10
3. 5/6
4. 1 5/12
5. 2 1/12
Match the mortgage types with their descriptions. it requires the buyer to make a 20% down payment. a large portion of principal is paid in a single payment at the end of the loan. it has the same interest rate for the life span of the loan. it requires a lower down payment and allows buyers to have a lower credit score. it initially has a fixed rate for three to five years and then adjusts at a predetermined time. it starts with a low interest rate and then adjusts throughout the duration of the loan.
The types of mortgages and their descriptions are:
Government insured - it requires the buyer to make a 20% down payment.Balloon mortgage - a large portion of principal is paid in a single payment at the end of the loan.Fixed rate - it has the same interest rate for the life span of the loan.Coventional - it requires a lower down payment and allows buyers to have a lower credit score.Hybrid - it initially has a fixed rate for three to five years and then adjusts at a predetermined time.Adjustable - it starts with a low interest rate and then adjusts throughout the duration of the loan.What are some types of mortages?There are various types of mortgages to take care of the people of different economic situations.
For instance, government insured mortgages help reduce mortgage rates but require a down payment of 20% of the mortgage and fixed rate mortgages allow for the same payment for the mortgage's life.
Find out more on mortgage types at https://brainly.com/question/15272867.
#SPJ4
Which expression represents the sixth term in the binomial expansion of (5y 3)10?
The expression in the 6th term in the binomial expression is [tex]265781250y^6[/tex]
How to determine the expression in the sixth term?The expression is given as:
(5y + 3)^10
The above expression is a binomial expression, and the xth term can be represented using:
[tex]^nC_x (a)^x * (b)^{n-x}[/tex]
So, we have:
[tex]^{10}C_6 * (5y)^6 * (3)^4[/tex]
Evaluate the combination expression
[tex]210 * (5y)^6 * (3)^4[/tex]
Evaluate the exponents
[tex]210 * 15625y^6 * 81[/tex]
Evaluate the product
[tex]265781250y^6[/tex]
Hence, the expression in the 6th term is [tex]265781250y^6[/tex]
Read more about binomial expressions at:
https://brainly.com/question/13602562
#SPJ4
What is the median of this data set?
{12, 8, 9, 12, 10, 13,8}
Enter your answer in the box.
Answer:
10
Step-by-step explanation:
IMPORTANT HELP PLEASE ANSWER IMMEDIATELY!!!!!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the following equation. Show all your work.
(x/(x−2))+((x−1)/(x+1))=−1
Answer:
Step-by-step explanation:
PLEASE HELP ASAP!!
Describe the transformations from the parent function, and define the function of the following graph.
Answer:
-x^2-4x+2
Step-by-step explanation:
(-2,6) (0,2) (2,-4)
sin(-17pi/6)
How do I solve this
Answer:
if you have a graphing calculator you can just plug the whole equasion in. the anser I got was -0.1547307191
Step-by-step explanation:
to get pie you have to hit second and then ^
Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
Answer:
a) None
b) (0, -2)
Step-by-step explanation:
The x-intercept is the point at which the line cuts through the x-axis, while the y-intercept in the point at which the line cuts through the y-axis.
a) The line does not cut through the x-axis, thus it has no x-intercept.
b) The line cuts through the y-axis at y= -2, making its y-intercept (0, -2).
Does anybody know how to solve this?
The area of the rectangle in the form of a polynomial is 40(x² + 6x + 5). If the width is 160 ft, then the area of the rectangle is 57,600 square ft.
What is a rectangle?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.
If the length and width of the rectangle are (10x + 10) and (4x + 20). Then the area of the rectangle will be
Area = (10x + 10)(4x + 20)
Area = 40x² + 200x + 40x + 200
Area = 40x² + 240x + 200
Area = 40(x² + 6x + 5)
If the width is 160 feet then the value of x will be
4x + 20 = 160
4x = 140
x = 35
Then the area of the rectangle will be
Area = 40(35² + 6 × 35 + 5)
Area = 40(1225 + 210 + 5)
Area = 40 (1440)
Area = 57,600 square ft
More about the rectangle link is given below.
https://brainly.com/question/10046743
#SPJ1
HELP ASAP PLSSSS!!!!
If you need an image im putting it down below
Which line best represents the line of best fit for this scatter plot?
Graph shows numbers from 0 to 10 at increments of 1 on the x axis and numbers from 0 to 18 at increments of 2. Scatter plot shows ordered pairs 1, 1 and 2, 4 and 3, 12 and 4, 6 and 5, 8 and 6, 8 and 7, 12 and 8, 10 and 9, 14 and 10, 18. A line labeled P joins ordered pair 0, 1 and 9, 18. A line labeled Q joins ordered pairs 0, 1 and 10, 16. A line labeled R joins ordered pairs 0, 1 and 10, 10. A line labeled S joins ordered pairs 0, 1 and 10, 6.
Line P
Line Q
Line R
Line S
This line is fairly close to the majority of the points shown. Unfortunately there's an outlier left out, but it isn't too far from the main cluster. The further the outlier is, the more pull it will drag the line away from the main cluster.
Line Q
The suitable line should contain most dots near itQ contains atleast 4 around it.No other has soQ is correct
Solve the equation.
7x2 + 5 - x = 6x2 + 10
X =
20
It
Answer:
1 +√21 + 1 - √21
2 2
Step-by-step explanation:
A car starts from an office building, which is 5 miles east and 2 miles south of the town center. The car travels 6 miles north, makes a left turn and then travels 8 miles. What is the car’s final position? What single translation vector moves the car from its starting position to its final position?
Answer:
[tex]\displaystyle \binom{-8}{6}[/tex]
Step-by-step explanation:
The car's starting position is 2 miles south of the town center. If it travels 6 miles north, then it will be 4 miles north of the town center.
The car's starting position is 5 miles east of the town center. If it travels 8 miles west, it will be 3 miles west of the town center.
Therefore, its final position is 4 miles north and 3 miles west of the town center.
If the car travels 6 miles north from it's starting position, the y-value of the vector will be 6, as the car is moving in a positive direction along the y-axis.
If the car travels 8 miles left, the x-value of the vector will be -8, as the car is moving in a negative direction along the x-axis.
Therefore, the single translation vector that moves the car from its starting position to its final position is:
[tex]\displaystyle \binom{x}{y}=\binom{-8}{6}[/tex]
tim has 4 quarters and 5 pennies. how many cents does tim have?
Answer: $1.05
Step-by-step explanation:
quarters= 25 cents
4 x 25=100 cents
pennies=1 cent
5 x 1 = 5 cents
100+5=$1.05 or 105 cents
The base of a ladder is placed 2.8m away from a tree that is 4.5m tall. The end of the ladder touches the top of the tree. Calculate the length of the ladder.
Answer:
The length is 7.3m
Step-by-step explanation:
The end of the ladder touches the top of the tree when kept at 2.8m away from the tree.
The Tree is 4.5m tall
The length of the ladder will be: 2.8+4.5 = 7.3
ou toss a coin (heads or tails), then spin a three-color spinner (red, yellow, or blue). Complete the tree diagram, and then use it to find a probability.
1. Label each column of rectangles with "Coin toss" or "Spinner."
2. Write the outcomes inside the rectangles. Use H for heads, T for tails, R for red, Y for yellow, and B for blue.
3. Write the sample space to the right of the tree diagram. For example, write "TY" next to the branch that represents "Toss a tails, spin yellow."
4. How many outcomes are in the event "Toss a tails, spin yellow"? (1 point)
5. What is the probability of tossing tails and spinning yellow? (1 point)
The tree diagram that represents the events is an illustration of probability and combination
The tree diagramTo draw the tree diagram, we make use of the following representations:
H for heads, T for tails, R for red, Y for yellow, and B for blue.See attachment for the tree diagram.
The sample space and the outcomesFrom the tree diagram, the sample space is as follows:
S = {HR, HY, HB, TR, TY, TB}
The number of outcomes that represents "Toss a tail, spin yellow"This is represented as: TY
From the sample space above, we have:
TY = 1
Hence, the number of outcomes that represents "Toss a tail, spin yellow" is 1
The probabilityWe have:
TY = 1
Sample size = 6
Hence, the of tossing tails and spinning yellow is 1/6
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
