The value of c is given as follows:
a) Radical form: [tex]c = \sqrt{80}[/tex]
b) Rounded to the nearest hundredth: 8.94.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
For this problem, we have that:
a and b are the sides.c is the hypotenuse.Applying the Pythagorean Theorem, the value of c is obtained as follows:
c² = a² + b²
c² = 4² + 8²
c² = 80
[tex]c = \sqrt{80}[/tex]
c = 8.94 -> nearest hundredth = two decimal digits.
More can be learned about the Pythagorean Theorem at brainly.com/question/30203256
#SPJ1
Sara pays a total of $322 for her car insurance. The total is made up of a basic charge plus 15% sales tax.
Calculate the amount of sales tax that Sara pays.
state where in the ty plane the hypothesis of theorem are satisfied
The ty plane the hypothesis of theorem are satisfied
The hypothesis of a theorem is a statement or assumption that is made in order to prove a mathematical result.
The hypothesis of the Tychonoff theorem is satisfied in a variety of different spaces, including compact spaces and metrizable spaces.
This theorem is important because it provides a useful tool for understanding the properties of topological spaces, which are spaces that have certain structures that allow for the study of continuous functions and mappings.
In summary, the hypothesis of the Tychonoff theorem is a necessary condition for the theorem to be proven and is satisfied in a variety of different spaces.
Understanding the hypothesis and the spaces in which it is satisfied is crucial for understanding the theorem and its applications in mathematics.
Complete Question:
State where in the ty-plane the hypotheses of Theorem
To know more about hypothesis here.
https://brainly.com/question/29576929
#SPJ4
The graph above is a graph of what function?
Answer:
The graph of the function is a parabolic function graph
Step-by-step explanation:
Formula for a parabolic function: ( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the graph be represented as A
Now , a parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax² + bx + c.
The value of the graph increases and decreases in a format according to the quadratic equation.
So , the graph of the function goes downward when value of a < 0 and the graph of the function goes upward when the value of a > 0
The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0
Therefore , the graph is a parabolic graph
Hence , The graph of the function is a parabolic function graph
22. last year for sales of units, hurst ltd had sales of £ , variable expenses of £ , and fixed costs of £ . what would be the break-even point in units?
The break-even point in units can be calculated if the sales price per unit (P) is known. In conclusion, the break-even point in units is an essential calculation that helps companies understand their financial performance and determine the minimum level of sales they need to achieve to cover their costs and start generating a profit.
Break-even point in units = Fixed costs / (P - Variable expenses per unit)
= Fixed costs / (P - Variable expenses / Sales)
The break-even point is a crucial calculation in the field of business and finance, as it represents the level of sales at which a company's expenses and revenue are equal, and there is no profit or loss. In this scenario, Hurst Ltd's break-even point in units can be calculated based on its sales, variable expenses, and fixed costs.
Here you can learn more about the break-even point
https://brainly.com/question/29063970#
#SPJ11
What is the equation of a line that passes through (4,-1) and is parallel to
y = 1/4x +7?
PLEASE ANSWER ASAP THIS IS FOR MY FINAL
Answer:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Since the line given in the question is parallel to y = 1/4x + 7, we know that the line has a slope of m = 1/4.
To find the equation of the line that passes through (4,-1), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
Therefore, the equation of the line passing through (4,-1) and parallel to y = 1/4x + 7 is:
y - (-1) = 1/4(x - 4)
y + 1 = 1/4x + 1
This is the equation of a line passing through (4,-1) and parallel to y = 1/4x + 7.
Find the scalar and vector projections of b onto a.
a=⟨−5, 12⟩, b=⟨4, 6⟩
The scalar projection is 42/13, and the vector projection is 42/169⟨-5,12⟩.
The scalar projection of b onto a can be calculated using the formula [tex]\frac{a.b}{|a|}[/tex], and the vector projection of b onto a can be calculated using the formula [tex]\frac{a.b}{|a|^{2} } .a[/tex]. The formula for finding the magnitude of a is |a| = √c²+d² if a = ⟨c,d⟩.
a = ⟨−5, 12⟩, b = ⟨4, 6⟩
a⋅b = ⟨−5, 12⟩⟨4, 6⟩
= -20 + 72
= 42
|a| = √[(-5)² + (12)²]
= √25 + 144
= √169
= 13
The scalar projection is
[tex]\frac{a.b}{|a|}[/tex] = [⟨−5, 12⟩⟨4, 6⟩]/√[(-5)² + (12)²]
= [-20 + 72]/√25 + 144
= 42/√169
= 42/13
The vector projection is
[tex]\frac{a.b}{|a|^{2} } .a[/tex] = [42/(13)²] ⟨−5, 12⟩
= 42/169⟨−5, 12⟩
To know more about scalar projection, here
https://brainly.com/question/12924145
#SPJ4
HELPPPPPPPPP 10 poingts
Answer:45
Step-by-step explanation: So the total measure of an exterior would be 360 so you divide the number of sides on the polygon be 360 and you get 45. (I hoped that helped.)
Answer:
45 degrees
Step-by-step explanation:
A octagon is 360 degrees total and since there is 8 sides you would do 360/8 which gives you 45 degrees
HOPE THIS HELPS
6. Emma's cake recipe requires three large eggs to make two dozen slices of cake. how many large eggs are needed to make 144 slices of cake? (A) 16 (B) 8 (C) 9 (D) 12(E) Other
(E) Other
To make 144 slices of cake, Emma will need 18 large eggs.
To solve this problem, we need to know how much 2 dozen is.
1 dozen = 122 dozen = 24So, for every 24 slices of cake, 3 eggs are needed.
To figure out how many slices of cake 1 egg can make, we can divide 24 by 3.
24 ÷ 3 = 83 ÷ 3 = 1Now, for every 8 slices of cake, 1 egg is needed.
Now, taking 144, we can divide that by 8 to get the number of eggs needed.
144 ÷ 8 = 18Therefore, 18 eggs will be needed to make 144 slices of cake.
[HELP FAST WILL GIVE BRAINLIEST] Identify the explicit formula for the sequence given by the following recursive formula:
Answer:
f(n) = 4n - 6
Step-by-step explanation:
the explicit formula for an arithmetic sequence is
f(n) = f(1) + (n - 1)d
where f(1) is the first term and d the common difference
given the recursive formula
f(n) = f(n - 1) + 4
this allows a term in the sequence to be found by adding the common difference d to the previous term.
here f(1) = - 2 and d = 4 , then explicit formula is
f(n) = - 2 + 4(n - 1) = - 2 + 4n - 4 = 4n - 6
Consider the following parametric equations. Answer parts a through d. x=t^2, y=t+4, - 4 ≤ t ≤4 Upward DownwardRight Left
The parametric equation x = t^2, y = t + 4, -4 ≤ t ≤ 4 is open at right side.
Therefore the answer is Right.
A parametric equation is a set of equations that describes the position of a point in the xy-plane in terms of a third variable, usually called a parameter. In this case, the parametric equations x = t^2 and y = t + 4 describe the position of a point on the xy-plane in terms of the parameter t.
y = t + 4
So t = y - 4
x = t²
So x = (y - 4)²
This is of the form x = 1(y - 4)²
x = a(y – k)2 +h is the sidewise form of a parabola with vertex (h, k). So this parametric form represents a parabola with vertex (0, 4) open at right side.
To know more on parametric equation
https://brainly.com/question/29168942
#SPJ4
Yesterday the temperature at noon was 28.6°F. By midnight, it had dropped by 30.7°F. What was the temperature at midnight?
special right triangle
Your are to receive $2007 in 5 years, or you can opt to receive an equivalent amount today. At 6% nominal interest, what amount should you receive today? a. $1300 b. $1400 c. $1500 d. $1600
At 6% nominal interest, the amount should you receive today is (d) $1600.
The word "total" refers to the addition of numbers or the destruction of something, and a total is a whole or complete sum.
The present value of $2007 received in 5 years can be calculated using the formula:
PV = FV / (1 + r)^t
Where:
PV is the present value
FV is the future value ($2007)
r is the nominal interest rate (6%)
t is the time period (5 years)
So, PV = $2007 / (1 + 0.06)^5 = $1600
Therefore, you should receive $1600 today if you want an equivalent amount.
To learn more about interest here:
https://brainly.com/question/19291527
#SPJ4
for which value(s) of the constant k does the system have no solutions? exactly one solution? infinitely many solutions? explain your reasoning.
The three possibilities for a linear system, in terms of free variables, rank and nullity, are
Three possibilities for a linear system.
No solution Signal equation 0 = 1
Infinitely many solutions One or more free variables nullity ≥ 1
Unique solution Zero free variables nullity = 0
No Solution. There is no solution to a system of equations exactly when a signal
equation 0 = 1 occurs during the application of swap, multiply and combination
rules. We report the system inconsistent and announce no solution. Infinitely Many Solutions. The situation of infinitely many solutions occurs when
there is at least one free variable to which an invented symbol, say t1, is assigned.
Since this symbol takes the values −∞ < t1 < ∞, there are an infinity of solutions.
The condition rank less than n can replace a reference to the number of free variables.
Unique Solution. There is a unique solution to a system of equations exactly when
zero free variables are present. This is identical to requiring that the number n of
variables equal the number of lead variables, or rank = n.
To know more about Rank Symbol visit brainly.com/question/29811883
#SPJ4
Lucy runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes
PLS HELP NEED THIS NOW!
a. 8cm ( AD=BD)
b. 8cm ( BD=BC) , Triangle BCD is equilateral
c. 8 cm ( DC = BD)
d Perimeter of ABCD is AD+DC+BC+AB= 8+8+8+11=35
Definition of TriangleA triangle is a two-dimensional plane shape formed by three sides in the form of straight lines and has three angles. Besides having 3 sides or ribs and angles, the properties of a triangle have an angle of 180°.
The Nature of the equilateral TriangleThe following are the properties of an equilateral triangle, including:
Has three sides that are the same length. It has the same angles, which are 60° each. It has three axes of symmetry that intersect at exactly one point. Can be placed on the frame in exactly six ways.Learn more about triangle at https://brainly.com/question/25813512
#SPJ1
Blaine is two years older than three times a jillion’s age Jillian is also 16 years younger than Blaine. How old is Blaine
Answer:
SLAY
Step-by-step explanation:
UWU
A triangle having area of √135 square meter and perimeter 18 meter has a side 4 meter. Find the measurement of the remaining two sides.
The measurement of the remaining two sides of the triangle be 4cm and 6cm.
How to find the measurement of the remaining two sides of the triangle?Given :- Perimeter of triangle = 18m.
Area of triangle = √135m².
One side of triangle = 8m.
Triangle is a plane figure with three straight sides and three angles.
Let the equation be Area of ∆ = 1/2bh
= 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B
= √( s(s-a)(s-b)(s-c) ) [ where s = (a + b + c)/2 ]
By using Heron's formula to get the Area of triangle,
s = (Perimeter /2) = (18/2) = 9m.
Putting values now we get :-
√(s(s-a)(s-b)(s-c) ) = √135
substitute the values in the above equation, we get
√[9(9-8)(9-b)(9-c)] = √135
Squaring Both sides we get,
9 × 1 × (9-b)(9-c) = (√135)² = 135
Dividing both sides by 9, we get,
(9-b)(9-c) = 15
81 - 9c - 9b + bc = 15
simplifying the above equation, we get
81 - 9(b + c) + bc = 15
9(b + c) - bc = 81 - 15
9(b + c) - bc = 66 -------- (1).
Also, if Rest two sides are b and c, we get,
→ 8 + b + c = 18
→ (b + c) = 18 - 8 = 10 cm. ------ (2).
Putting value of (2) in (1) , we get,
→ 9 × 10 - bc = 66
simplifying the above equation, we get
→ bc = 90 - 66
→ bc = 24 ------------ (3).
We do Factors of (3), we just have to check now, which satisfy Equation (2) also . (sum of Factors will be 10).
24 = ( 1, 24) , (24, 1), ( 2,12), (12,2) , (3,8) ,(8,3) , (4,6),(6,4)
We can see (4,6) or (6,4) Satisfy the (2).
Therefore, the measurement of the remaining two sides of the triangle be 4cm and 6cm.
The complete question is:
the perimeter of a triangular garden is 18 m. if its area is under root 135 m^2 and one of the tree sides is 8 m, find the remaining two sides
To learn more about triangle refer to;
https://brainly.com/question/1058720
#SPJ1
This is an example of an isosceles triangle. An isosceles triangle is a triangle with two equal sides and two equal angles.
Find the measurement of the remaining two sides?In this particular triangle, the side with a measurement of 4 meters is one of the two equal sides, meaning the remaining two sides must also have a measurement of 4 meters. To calculate the area and perimeter of the triangle, we can use the following formulas: Area = 1/2 x base x height Perimeter = a + b + c Given that the area of the triangle is √135 square meter and the perimeter is 18 meter, we can plug these values into the formulas to solve for the remaining measurements of the triangle.For the area, we can solve for the height by rearranging the formula: Height = 2 x area / base Height = 2 x √135 / 4 Height = 3√3 For the perimeter, we can solve for the remaining two sides by rearranging the formula: a + b + c = 18 a + b = 18 - 4 a + b = 14 Therefore, the two remaining sides of the triangle have a measurement of 4 meters, and the remaining height of the triangle has a measurement of 3√3 meters.To learn more about isosceles triangle refer to:
https://brainly.com/question/1475130
#SPJ1
Identify the action verb(s) in the sentence.
People in church prayed, and an angel woke Peter.
The bolded words represents the verbs in the statement as -
People in church prayed, and an angel woke Peter.
What is a verb?Verbs are words that show an action (sing), occurrence (develop), or state of being (exist).
Given is the statement as -
People in church prayed, and an angel woke Peter.
The verbs in the given statement are {bolded words} -
People in church prayed, and an angel woke Peter.
Therefore, the bolded words represents the verbs in the statement as -
People in church prayed, and an angel woke Peter.
To solve more questions on verbs, visit the link below -
https://brainly.com/question/1946818
#SPJ1
How many ways can the letters in the word world be arranged?
There are 120 ways that the letters from the word "world" can be arranged
What is permutation?It is the ordered arrangement of members belonging to a set with no repeats.
To solve this problem the formula and the permutation procedure we must use is:
nPr = n! / (n-r)!
Where:
nPr = permutationn = total number of objectsr = number of selected objects! = factorial of the numberInformation about the problem:
n = 5 (world)r = 5 (letters)5P5 =?Applying the permutation formula we have:
nPr = n! / (n-r)!
5P5 = 5! / (5-5)!
5P5 = 5! / 0!
5P5 = 5*4*3*2 / 1
5P5 = 5*4*3*2
5P5 = 120
Learn more about permutation at: brainly.com/question/1216161
#SPJ4
There are counters of four different colours in a bag. A counter is taken out at random.
This table shows the probabilities of different colours.
Colour gold silver bronze white
Probability 0.05 0.15 0.55
Find the probability that the counter is
a. gold or silver
b. not gold
c. silver or bronze
a)
P (gold or silver) is 0.20
b)
P (not gold) is 0.95
c)
P (silver or bronze) is 0.70
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Color gold silver bronze white
Probability 0.05 0.15 0.55 0.25
Now,
The probability that the counter is
a)
P (gold or silver)
= 0.05 + 0.15
= 0.20
b)
P (not gold)
= 1 - 0.05
= 0.95
c)
P (silver or bronze)
= 0.15 + 0.55
= 0.70
Thus,
The probabilities are given above.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ1
differentiate. f(t) = 3 t t − 6
Basically in this question we will apply product rule of diffrentiation .
f(t) = 3t (t-6)
f'(t) = (3t)'.(t-6) +(t-6)'.(3t)
f'(t) = 3(1). (t-6) + (1).3t
f'(t) = 3t-18 +3t
Final Answer - f'(t) = 6t -18
Differentiating the given function. f(t) = 3 t (t − 6) gives f'(t) = 6t - 18 using the product rule of differentiation.
Given that, f(t) = 3t.(t-6)
To differentiate the given function we use product rule in order to simplify the differentiation.
Divide the function into two different products and then differentiate :
f(t) = 3t (t-6)
f'(t) = (3t)'.(t-6) +(t-6)'.(3t)
f'(t) = 3(1). (t-6) + (1).3t
f'(t) = 3t-18 +3t (or)
expand the given f(t) = 3t.(t-6)
= 3t^2 - 18 t
we have , f'(x) = n.x^(n-1) if f(x) = x^n
differentiating f(t) = f'(t) = 2(3t) - 18
= 6t - 18
Learn more about the differentiation here :
https://brainly.com/question/24898810
#SPJ4
mahek owns a holiday tree farm. there are currently 800 trees on the property. each year 20% of the trees are harvested and sold, and 200 seedlings are planted. write a recursive definition for the number of trees on the farm at the beginning of the nth year.
aₙ = 0.20aₙ₋₁ + 200 is the recursive formula for the above sequence.
Therefore, choice A is the right one.
Given:
A holiday tree farm is owned by Mahek.
Currently, the site has 800 trees.
200 saplings are planted together with the 20% of the trees that are harvested and sold each year.
a₁ = 800
The recursive formula is,
aₙ = 0.20aₙ₋₁ + 200
Hence, the correct formula is aₙ = 0.20aₙ₋₁ + 200
To learn more about the sequence;
brainly.com/question/21961097
#SPJ12
You went to Sweet Spot to get some candy. The cost is $5.00 per pound. You have a coupon that gives you a discount of $0.20 off per pound. If you buy $4 pounds of candy, what will your total cost be, excluding tax?
Answer:
$19.20
Step-by-step explanation:
The discount per pound is $0.20, so the cost per pound after the discount is $5.00 - $0.20 = $4.80 per pound.
You want to buy 4 pounds of candy, so the total cost before tax is 4 * $4.80 = $19.20
So, your total cost for 4 pounds of candy will be $19.20.
Answer:
total cost be, excluding tax = $19.20
Step-by-step explanation:
DISCOUNT: $0.20 x 4 pounds = $ 0.80
Cost of 4 pounds $5 x4 = $20
$20 - $0.80 = $19.20
What is unique about Pythagorean triples?
The unique property of Pythagorean triplets is the square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.
Here,
Pythagorean triplet's unique property is that,
The square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base for a right-angled triangle.
hypotenuse² = perpendicular² + base²
Thus, the unique property of Pythagorean triplets is the square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ1
4) ABC is a triangle. 6 cm 60° C 7 cm (a) Work out the area of triangle ABC. Give your answer correct to 3 significant figures. (b) Work out the length of the side AB. Give your answer correct to 3 significant figures. B Diagram Not drawn accurately
Answer:
A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. Please select the best answer from the choices provided A B C D
Which of the following statements is not true concerning the comparison of the bag weights for the two brands?
Almost 25% of the weights for brand B are less than the lowest weight for brand A.
About 50% of the weights for brand A are within the top 25% of the weights for brand B.
More than 75% of the weights for brand A are within the top 50% of the weights for brand B.
More than 75% of the weights for brand A are higher than the top 25% of the weights for brand B.
The statement "Almost 25% of the weights for brand B are less than the lowest weight for brand A" is not true concerning the comparison of the bag weights for the two brands, 1st option.
How does inequality work?Inequalities are mathematical expressions in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is replaced by a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In comparison to Brand B's box plot display, Brand A's rectangular box, as well as the length of the whiskers, are shorter. As a result, Brand A's bag weights are less variable than Brand B's bag weights.
Find out more on inequalities here: https://brainly.com/question/24372553
#SPJ1
The full question is:
Which of the following statements is not true concerning the comparison of the bag weights for the two brands?
Almost 25% of the weights for brand B are less than the lowest weight for brand A.
About 50% of the weights for brand A are within the top 25% of the weights for brand B.
More than 75% of the weights for brand A are within the top 50% of the weights for brand B.
More than 75% of the weights for brand A are higher than the top 25% of the weights for brand B.
Write the numbers 2001, 2002, 2003, 2004, 2005, and 2006 into the circles so that the
sum of the numbers on a side of the triangle is always the same, and this sum is as
great as possible.
20 POINTS
Answer:
To find the numbers 2001, 2002, 2003, 2004, 2005, and 2006 into the circles so that the sum of the numbers on a side of the triangle is always the same, we can start by finding the average of the numbers:
(2001 + 2002 + 2003 + 2004 + 2005 + 2006) / 6 = (12,016) / 6 = 2004
Next, we can place the numbers around the average so that the sum of the numbers on a side of the triangle is as great as possible:
2004
2006 2005
2003 2002 2001
In this configuration, the sum of the numbers on each side of the triangle is 6021.
you throw 3 fair six-sided dice at the same time, what is the expected sum of faces?
For three fair six-sided dice, the possible sum of the faces rolled can be any digit from 3 to 18.the number of sums will be greater than 16 and the minimum number greater than 16 is 17.
For instance the minimum sum occurs when all three dices shows 1 (i.e. 1 + 1 + 1 = 3) and the maximum sum occurs when all three dces shows 6 (i.e. 6 + 6 + 6 = 18).
Thus, there are 16 possible sums when three six-sided dice are rolled.
Therefore, from the pigeonhole principle, the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice is 16 + 1 = 17 times.
The pigeonhole principle states that if n items are put into m containers, with n > m > 0, then at least one container must contain more than one item.
That is for our case, given that there are 16 possible sums when three six-sided dice is rolled, for there to be two same sums, the number of sums will be greater than 16 and the minimum number greater than 16 is 17.
learn more about of sum here
https://brainly.com/question/4176440
#SPJ4
which of the following represents the lowest speed in miles per hour?
6 miles in 1/8 hour
11 miles in 1/4 hour
16 miles in 3/8 hour
20 miles in 1/2 hour
Answer:
20 miles in 1/2. That would be 40 miles per hour
Step-by-step explanation:
6 ÷ 1/8 is the same at 6 x 8 = 48
11 ÷1/4 is the same as 11 x 4 = 44
16 x 3/8 is the same as 16 x 8/3 = 42 2/3
20 ÷ 1/2 is the same as 20 x 3 = 40
