We found the length of the other leg by using Pythagoras’ theorem y is equal to 21.0 centimeters when the length of one of its legs is 20.0 centimeters.
In this question we have to make an equation by using the right triangle's value which is given in the question,
by putting these values in the Pythagoras’ theorem.
As given, the hypotenuse of a right triangle = 29.0 centimeters.
The length of one of its leg = 20.0 centimeters
Now, by using Pythagoras’ theorem we will find the length of the other leg:
hypotenuse^2 = base^2 + perpendicular^2,
We put the value according as given in question:
29^2 = 20^2 + y^2
After finding the square of number of both side:
841 = 400 + y^2
Now we will rearrange this equation:
y^2 = 841 - 400
y = 21 centimeters is the length of the other leg.
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Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4;
zeros: -4-5i; - 5
multiplicity 2
Let a represent the leading coefficient. The polynomial is f(x) = a(________)
(Type an expression using x as the variable. Use integers or fractions for any
numbers in the expression. Simplify your answer.)
Answer: [tex]x^4 +2x^3 -14x^2 +210x+1025[/tex]
Step-by-step explanation:
By the conjugate root theorem, -4+5i is also a root.
[tex]f(x)=a(x+4-5i)(x+4+5i)(x+5)^2\\\\=a(x^2 -8x+41)(x+5)^2\\\\ =a(x^2 -8x+41)(x^2 +10x+25)\\\\=a(x^4 +2x^3 -14x^2 +210x+1025)[/tex]
Hi please help me if you do I would be happy
A photo collage consists of seven equal-sized square photos arranged in a row to form a rectangle. If the total area of the collage is 567 square inches, what is the length of the collage?
The length of the square collage will be 63in.
In the question, It is stated that a photo collage is made by arranging 7 square shaped photos in a row. The arrangement is done in such a way that it forms a rectangle. The total area of the collage is 567 square inches. We have to find out the length of the Collage.
Given that, the photos arranged are of square shape then their length and breadth must be equal. So,
Side of square photo: x
Now, seven photos were arranged, So,
Length of collage = 7x
Breadth of collage = x
We know the Area of the Rectangle is Length*Breadth
Putting Area A = 567, l = 7x, and b = x, we get:
=> Area = l*b
=> 567 = 7x*x
=> 567 = 7x²
=> x² = 81
=> x = 9
We get x = 9, We know length = 7x so l = 63in
Hence, the Length of the Collage will be 63 inches.
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Which ordered pair could you remove from the relation {(–1, 0), (1, 3), (2, 2), (2, 3), (3, 1)} so that it becomes a function
Answer:(3,1)
Step-by-step explanation:
Because you cant have (1,3) and (3,1).
Answer:
(2,3)
or (2,2) if the function does not need to be continuous.
Step-by-step explanation:
For a set of points to be considered a function, it must be true that for every X value, you have only a single Y value solution.
In other words, looking through your points listed, you would remove any point where an X value appears twice with different Y values.
[tex](X,Y)\\(-1,0)\\(1,3)\\(2,2) < -\\(2,3) < -\\(3,1)\\\\[/tex]
Notice the two points with arrows, both have 2 as their X value, but different Y values. Removing either one of them would make this a function. Although, by removing (2,3) the function has the potential to also be continuous, because having two of the same Y value for different X values would cause a piece-wise function which is generally non-continuous.
Counterexamples
Instructions: Show that the conjecture is false by finding a counterexample. Change the value of n below in order to make it a counterexample.
"For every integer n, n3 is positive."
n=1
n=−3
n=2
n=5
n= Answer
Counterexample
A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion. It is used to check the validity of an argument.
We have been given the conjecture:-
"For every integer n, [tex]n^3[/tex] is positive."
We have to show that the conjecture is false by finding a counterexample.
Let us take an integer n = - 5
Finding its cube we, get
[tex]n^3[/tex] = -125
We know that,
-125 is not positive, it is negative.
Hence, the conjecture "For every integer n, [tex]n^3[/tex] is positive." is proven wrong by finding a counterexample which states otherwise.
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HELP PLS LAST ONE
Simplify (4y³ – 2y +9) − (2y³ − 3y² + 4y + 7).
Answer the questions in the photo ( will mark brainliest if correct )
Angles of a polygon add to 360 degrees. To find the measure of each exterior angle of a regular n-gon. divide 360 by n.
18) 27.719) 36020) 12021) 36022) 4523) 20Nora and her little brother, Finn, spent all afternoon raking leaves. They filled b bags with leaves. When Nora wasn't looking, Finn emptied 4 of the bags to make a leaf pile! Luckily, Nora caught Finn before he got to the remaining 7 bags
Based on the number of bags of leaves that Finn emptied and the number of bags remaining, the total number of bags that Nora and Finn filled up is 11 bags.
How to find the number of bags?Finn and his sister, Nora, have been racking leaves and they raked enough to fill up a certain number of bags.
Out of these bags, Finn emptied 4 bags to be able to make a leaf pile. Nora then stopped him from emptying the other 7 bags.
The total number of bags of leaves raked by Nora and Finn is:
= Number of bags remaining + Number of bags emptied by Finn
= 7 + 4
= 11 bags of leaves
Remaining part of question:
How many bags of leaves were raked by Finn and Nora?
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Enola bought 14 chicken wings for $29.40. How much would it cost for 5 wings?
Answer:
x=10.50
Step-by-step explanation:
14 = 5
________
29.40 = x
cross multiply - 29.40 x 5 = 147
Then u would divide like this
14/14=1 147/14=10.5
Which graph does not represent a function?
hler
Intro
Done
Answer:
The third one (the elliptical shape) is not a function
Step-by-step explanation:
Every x value of a function must be paired to a single y value. One really easy way to tell of a graph is a function is called the "vertical line test." This says that if a vertical line drawn anywhere in the graphed area passes through more than one point, it is not a function.
The Tiny family is purchasing a coat for $ 1.3 x10-5 a pair of boots for $ 2.1 x 10-5 and a pair of gloves for $ 7.6 x 10-6. The Tiny family paid with $5.0 x 10-4
What is the Total:______________________________________________________
How much change :
___________________________
The total cost for the items which the Tiny family purchased is $41.6 × 10⁻⁶ while their change is equal to $45.84 × 10⁻⁵.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to determine the total cost, we would add all of the costs incurred by Tiny family as follows:
Total cost = 1.3 × 10⁻⁵ + 2.1 × 10⁻⁵ + 7.6 × 10⁻⁶
Total cost = (1.3 + 2.1) × 10⁻⁵ + 7.6 × 10⁻⁶
Total cost = 3.4 × 10⁻⁵ + 7.6 × 10⁻⁶
Total cost = $41.6 × 10⁻⁶
Next, we would calculate the change as follows:
Change = Amount paid - Total cost
Change = $5.0 x 10⁻⁴ - $41.6 × 10⁻⁶
Change = $45.84 × 10⁻⁵
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A theater group made appearances in two cities. the hotel charge before tax in the second city was $500 higher than in the first. the tax in the first city was 6.5% and the tax in the second city was 6% the total hotel tax paid for the two cities was $748.7. how much was the hotel charge in each city before tax?
Using algebraic expression and equation, the hotel charge before tax in each city is $5749.60 and $6249.60, respectively.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Let x = hotel charge before tax in the first city
If the hotel charge before tax in the second city was $500 higher than in the first, then
hotel charge before tax in the second city = $500 + x
If the tax in the first city was 6.5% and the tax in the second city was 6% and the total hotel tax paid for the two cities was $748.7, then
x(0.065) + ($500 + x)(0.06) = $748.7
Solving for x,
x(0.065) + ($500 + x)(0.06) = $748.7
0.065x + $30 + 0.06x = $748.7
0.065x + 0.06x = $748.7 - $30
0.125x = $718.7
x = $5749.60
hotel charge before tax in the first city = $5749.60
hotel charge before tax in the second city = $500 + x
hotel charge before tax in the second city = $500 + $5749.60
hotel charge before tax in the second city = $6249.60
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The distance remaining to a destination after t minutes is given by d(t) = 340-0. 85t, measured in miles. The graph of d(t) is shown below.
After how many minutes is the destination reached?
In 400 minutes, it will reach the destination.
What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over"). The term is also frequently used metaphorically to refer to a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation, as spatial thinking is a rich source of conceptual metaphors in human thought (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalise the majority of these notions of distance, both literal and figurative.
Distance is equal to speed × time. Time is equal Distance/Speed.
we have given, d(t)=340-0.85t
where, t is the time and d(t) is the distance.
when t = 0 we get,
d(t)=340
If we set d(t)=0 we get, 0= 340- 0.85t
add with 0.85t on both side
0.85t=340
t= 340/0.85
t= 400 minutes
Hence, the time taken to reach the destination is 400 minutes.
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Math translation/shrink problem
The rule of g(x) after the transformation is g(x) = 3(x + 4)^2 + 3(x + 4)
How to determine the image of the transformation?The function is given as
f(x) = x^2 + x
The transformations are given as:
Translation 4 units leftHorizontal shrink by 1/3The rule of the above transformations are :
Translation 4 units left: (x + 4, y)Horizontal shrink by 1/3: (3x, y)When the above transformations are combined, we have
Translation 4 units left: (x + 4, y)Horizontal shrink by 1/3: (3(x + 4), y)This means that
g(x) = 3f(x + 4)
So, we have
g(x) = 3(x + 4)^2 + 3(x + 4)
Hence, the function g(x) is g(x) = 3(x + 4)^2 + 3(x + 4)
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the length of a rectangle is given by 6t 5 and its height is √t, where t is time in seconds and the dimensions are in centimeters. find the rate of change of the area with respect to time.
Answer:
I am stuck on it too can some one help me please.
Which graph represents the solution set of the system of inequalities?
{y>−2x−2y≤x+4
The graph represents the solution set of y > -2x - 2 and y ≤ x + 4 is graph (a)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the system of inequalities graphically?The system of inequalities is given as
y > -2x - 2
y ≤ x + 4
Next, we plot the system of inequalities on a graph (see attachment)
From the attached graph, we have both lines of the graph intersect at (-2, 2)
Also, we can see that the graph has two lines (one shaded and one closed line)
By comparing the attached graph and the graphs in the list of options, we can see that the graph represents the solution set of the system of inequalities is graph (a)
Hence, the graph represents the solution set of the system of inequalities is graph (a)
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2. What is the value of x when y = 17 for the quadratic function
f(x) = x² + 6x + 10?
A. -7 only
B. 1 only
C. 7 only D. -7 and 7
E. -7 and 1
Value of x when y = 17 for the quadratic function f(x) = x² + 6x + 10 is -7 and 1. That is option E.
Given, y=17 :
17 = x² + 6x + 10
Move 17 to RHS (right-hand side) :
0 = x² + 6x - 7
Using the Middle Splitting method:
0 = x² + (7x - 1x) - 7
0 = x(x + 7) - 1(x+7)
0 = (x - 1) (x + 7)
Now, equate both the equations (x-1) and (x+7) separately with 0.
The first value of x is
(x - 1) = 0
x = 1
The second value of x is
(x + 7) = 0
x = -7
∴ The values of x are -7 and 1. According to the question, that is option E.
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⚠URGENT!!!⚠Find the volume of the figure shown.
Volume=_________cm^3
By using the concept of composite solid, the volume of the entire figure is equal to 566 cubic centimeters.
What is the volume of the figure shown in the picture?
In this question we find a composite solid formed by the following components:
Two prisms with a rectangular base.Two prisms with a right triangular base.Please notice that the volume of a prism is equal to the product of the area of the transversal area and the height of the prism. Now we proceed to determine the volume of the entire figure:
V = V₁ + V₂ + 2 · V₃
V = (19 cm) · (2 cm) · (7 cm) + (10 cm) · (4 cm) · (7 cm) + 2 · [(1 / 2) · (5 cm) · (4 cm)]
V = 566 cm³
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kumon level C pages please i dont want to waste my time
Answer:
Image result for kumon level C
This award is presented to a student who has completed Level C10 or higher during or before their 1st-grade year. Math Level C covers multiplication and division.
Step-by-step explanation:
Make x the subject of the equation. Y=2x-a
Answer:
1/2y+1/2a=x
Divide both sides by2, then but the a value on the other side.
If m = 8 and 3m + 72=4y – 56, then by the Substitution Property of Equality, 3(8) + 72 = 4y − ???
Answer:
56
Step-by-step explanation:
3m + 72 = 4y - 56
3(8) + 72 = 4y - 56
24 + 72 = 4y - 56
96 = 4y - 56
4y = 152
y = 38
3(8) + 72 = 4y - x
24 + 72 = 152 - x
96 = 152 - x
-56 = -x
x = 56
I would like to cover a box with contact paper. The box is 18in X 1'1 in x ain How much square in of Contact paper will be used.
The total amount contact paper required will depend on total surface area of the box which will be 778 square inches.
As per the question statement, we are given a box with dimensions
(18in x 1ft 1in x 5 in) and we are supposed to find the total amount contact paper required to cover it.
The total amount contact paper required to cover it will depend on the total surface area of the box.
Given length(L) = 18 inches
Given width(W) = 1 ft 1 in = 13 inches
Given height(H) = 5 inches
Total Surface Area of the box is given by the formula
Area = 2(LW + WH + HL)
Area = 2(18*13 + 13*5 + 5*18)
Area = 2*389
Area = 778 square inches
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find the 6th term of the sequence 4, 6, 9,...
Answer:
30.375
Step-by-step explanation:
this is a geometric sequence, meaning it has a common growth factor
to find the growth factor, you divide a term by the previous term (example: 9/6)
so for this problem:
9/6 = 1.5
6/4 = 1.5
so 1.5 is the common growth factor
then you just multiply so:
9 • 1.5 = 13.5
13.5 • 1.5 = 20.25
20.25 • 1.5 = 30.375
4, 6, 9, 13.5, 20.25, and 30.375
so 30.375 is your 6th term
hope this helps :)
mcdonald's sells the big mac for $2.50 in 1998, while a competing restaurant, burger king, sold the whopper for $0.75. The management of Mcdonalds develops a business plan for future growth that projects an increase in the price of big macs of $0.25 per year, while the management of burger king develops a plan aimed at increasing the price of the whopper by 15% each year.
What would be the function of both burger king and mcdonalds
The function of both burger king and mcdonalds cost are respectively; C(n) = 0.75(1.15)ⁿ and C(n) = 2.5 + 0.25n
How to find the function sequence?The formula for the nth term of an arithmetic sequence is given as;
aₙ = a + (n - 1)d
where;
a is first term
n is position of term
d is common difference
For McDonald's, we are told that the initial price is $2.50 and the common difference is $0.25. Thus, the function will be;
C(n) = 2.5 + 0.25n
where n is number of years after 1998
We are told that the cost in burger king increases by 15% each year. Thus, using formula for geometric progression, the function is;
C(n) = 0.75(1 + 0.15)ⁿ
C(n) = 0.75(1.15)ⁿ
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write an equation that passes through the point -9, 4 and is parallel to y=2/3x+19
The equation of the line that is parallel to y = 2/3x + 19 and passes through (-9, 4) is: y = 2/3x + 10.
How to Write the Equation of Parallel Lines?Two lines that are parallel have equal slope (m).
In the slope-intercept form of the equation of given line, y = mx + b:
m = slope of the lineb = y-intercept of the line.Given:
A point (-9, 4)
Equation, y = 2/3x + 19.
The slope (m) = 2/3.
The line that passes through (-9, 4) and is parallel to y = 2/3x + 19 would also have a slope (m) = 2/3.
Substitute (x, y) = (-9, 4) and m = 2/3 into y = mx + b to find the value of b:
4 = 2/3(-9) + b
4 = -6 + b
4 + 6 = b
b = 10
To write the equation, substitute m = 2/3 and b = 10 into y = mx + b:
y = 2/3x + 10.
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Theodora had practiced playing table tennis for hours by the end of the week. If each day the practice lasted for of an hour, how many days did she practice during the week?
Answer:
7 hours
Step-by-step explanation:
each day she practices 1 hour and there are 7 days in a week so 7 hours by the end of the week
Jason's square bedroom has an area of 112 square feet. The length of one
of his room is between what two whole numbers?
Multiplying Radicals.
HELP ME PLEASE !!!!!!
5. The value of x = 15
6. The converse that must be used is: C. Same-side exterior ∠s converse.
7. The proof is completed in the explanation part.
8. Slope of AB = 7/4; Slope of CD = -4/7, they are perpendicular.
What is the Same-Side Exterior Angles Theorem?The same-side exterior angles theorem states that same-side exterior angles that are on the same side of a transversal are supplementary to each other. Its converse states that if same-side interior angles are supplementary, then the lines they lie on are parallel to each other.
5. 10x - 22 + 3x + 7 = 180 [same-side exterior angles theorem]
13x - 15 = 180
13x = 180 + 15
13x = 195
x = 15
6. The converse that must be used to show that lines y and x are parallel to each other is: C. Same-side exterior angles converse.
7.
Statements Reasons
1. ∠6 ≅ ∠8 1. Given
2. y║z 2. Corresponding ∠s converse
3. ∠2 and ∠3 are supplementary 3. Same Side Interior ∠s
8. Given:
A(-3, 8)
B(1, 15)
C(10, -9)
D(3, -5)
Slope = change in y / change in x
Slope of AB = (8 - 15)/(-3 - 1) = -7/-4 = 7/4
Slope of CD = (-9 -(-5))/(10 - 3) = -4/7
-4/7 is the negative reciprocal of 7/4. Perpendicular lines have slope that are negative reciprocals of each other.
Therefore, CD and AB are perpendicular.
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Which equation compares the number of computers in b to the number a?
Answer:
3 × 5 = 15
Step-by-step explanation:
5 is the common number
Bonjour, je vous demande de l'aide pour ce gros exercice de maths niveau seconde merci d'avance.
Answer:
type in english
Step-by-step explanation:
english please