The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.
Given,
The exponents; 3^6 and 3^5.
We have to simplify this into a single power of 3.
In multiplication;
For exponents with same base, simply add the exponents.That is,
aᵇ . aⁿ = a^(b + n)
For exponents with different base, multiply the base and add the exponents.a^b . c^d = a x c ^ (b + d) = ac^bd
So,
3⁶ . 3⁵ = 3^(6 + 5) = 3¹¹
That is,
The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.
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A triangular boat's sail has a total area of 7 square inches.
If the height of the sail is 3 inches less than twice the
length of its base, then find the length of the base and
height.
Answer: b = 3.5, h = 4
Step-by-step explanation: a = 1/2bh, area of a triangle formula
7 = 1/2((b)(2b-3)) state h in terms of b
7 = 1/2(2b^2-3b) simplify
7 = b^2 - 1.5b simplify
b = 3.5 final answer
Then, solve for h.
h = 7 - 3 substitute
h = 4 final answer
hope this helps!
Step-by-step explanation:
area of a triangle
base × height / 2
in our case
base × height / 2 = 7
base × height = 14
height = 2×base - 3
we can use the last identity in the area equation and get
base × (2×base - 3) = 14
2×base² - 3×base - 14 = 0
the solution to a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
base = (3 ± sqrt((-3)² - 4×2×-14))/(2×2) =
= (3 ± sqrt(9 + 112))/4 = (3 ± sqrt(121))/4 =
= (3 ± 11)/4
base1 = (3 + 11)/4 = 14/4 = 7/2 = 3.5 in
base2 = (3 - 11)/4 = -8/4 = -2
negative numbers for sizes of physical objects don't make sense, so, base = 3.5 in is our solution.
height = 2×base - 3 = 2×3.5 - 3 = 7 - 3 = 4 in
base length = 3.5 in
height = 4 in
Which number sentence is true?
A.1/3x(-2/5)=-2/15
B.-1/3x2/5=2/15
C.-1/3x(-2/5)=-2/15
D.1/3x2/3=-2/15
The number sentence that is true is 1/3 x (-2/5)=-2/15 . Option A
What is a fraction?A fraction is simply defined as the subset of a whole set or the part of a whole element.
The several types of fractions includes;
Simple fractionsProper fractionsMixed fractionsImproper fractionsComplex fractionsExamples of simple fractions: 1/2, 1/8
Examples of proper fractions: 3/4, 8/10
Examples of mixed fractions: 3 1/6, 2 1/8
Examples of improper fractions: 7/4, 8/5
Given the fraction;
a. 1/3 x (-2/5)
The product of the fraction is = - 2/15
b. -1/3 x 2/5 = 2/15
The product is = -2/15
c. -1/3 x (-2/5)
The product is 2/15
d. 1/3 x 2/3
The product is 2/9
Hence, the sentence is option A
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Determine if 0.868668666866668666668...0.868668666866668666668... is rational or irrational and give a reason for your answer.
The numbers given as 0.868668666866668666668... and 0.868668666866668666668... are irrational numbers
How to categorize the numbers?From the question, the numbers are given as
0.868668666866668666668... and 0.868668666866668666668...
As a general rule.
Numbers that end in three dots are irrational numbers
The above is true because
These numbers are non-terminating decimals (i.e. theu do not end)These numbers cannot be represented as a fraction of integersWhen numbers cannot be represented as a fraction of integers, then such numbers are irrational numbers
Hence, the numbers are irrational numbers
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Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.
What are irrational numbers?An irrational number is a type of real number which cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.
Here,
Both numbers are irrational numbers, because
Thus, Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.
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1. (01.01 LC)
Which of the following is a flat surface that extends infinitely, has length and width, but does not have depth?
Angle
O Circle
O Plane
Segment
Answer:
plane
Step-by-step explanation:
The plane is flat like a wall or the floor. It has infinite length and infinite width but has no thickness (as thick as a line--which has no thickness) basically a line is one-dimensional and a plane is two-dimensional.
See image.
suppose 9 people arrive at a bank at the same time. in how many ways can they line up to wait for the next available teller? a) 40,320 b) 362,880 c) 9 d) 5,040 e) 81 f) none of the above.
The number of ways in which they can line up to wait for the next available teller is 362880.
What is termed as the permutation?We occasionally want to understand how many different ways we can order a set of items. A permutation is the number of different ways this may be done.We want to know how many different ways there are to line up 9 people.
We can choose one of the nine people in line to take the first spot. There are just eight people left to select from once we've decided who will fill this position. This means that only eight people can fill this same second position in this line. Now that the first two spots are filled, there are just seven people left to fill the third, and this line of thought can continue until the last spot is filled.= 9×8×7×6×5×4×3×2×1
= 362880
Thus, the number of ways in which they can line up to wait for the next available teller is 362880.
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55
1. Given the sequence: 10, 5,
10,5, 2'4"
(a) Write the explicit formula for the sequence.
(b) Generate the next 3 terms. Label appropriately.
81 PI 01
10 to the 3d power + 10 to the 2nd power + 10 to the 1st power
Answer: 1110
Step-by-step explanation:
Answer:
1,110
Step-by-step explanation:
1. Multiply to the powers(?)
10 x 10 x 10 = 1000
10 x 10 = 100
10 = 10
2. Add
1000 + 100 + 10 = 1110
Which graph represents the solution set for p − 3.6 < −5.8?
The solution for the given inequality is p < -2.2. The graph that represents the solution is attached below.
Graph of linear inequalitiesFrom the question, we are to determine the graph for the solution set for the given inequality
The given inequality is p - 3.6 < -5.8
First, we will solve the inequality
Solving the inequality
p - 3.6 < -5.8
Add 3.6 to both sides
p - 3.6 + 3.6 < -5.8 + 3.6
p < -2.2
The solution is p < -2.2
The graph of the inequality is shown below
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Answer: number line with an open circle on point negative 2.2 and arrow shaded to the left
Step-by-step explanation:
If this guy is correct
Mohal has a loyalty card good for a discount at his local pharmacy. To find the total he has to pay, before tax, he multiplies the prices by 0.96. What percent discount does the card give?
The percent discount the card gives can be:
4% or 96%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Royal card for discount.
Multiplying the total price to pay with 0.96 means two cases.
0.96 = 96/100 = 96%
Cases 1:
If the percent discount is 96% we will multiply the total prices to pay by 0.96 and subtract the value from the total price.
Example:
Total price to pay = 100
0.96 x 100 = 96
Total price to pay = 100 - 96 = 4
Cases 2:
If the percent discount is 4% we will multiply the total prices to pay by 0.96 after subtracting 4% from 100%.
Example:
Total price to pay = 100
Discount = 4%
100% - 4% = 96%
96% = 0.96
Total price to pay = 0.96 x 100 = 96
Thus,
The percent discount the card gives can be:
4% or 96%.
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X=
/////////////////////
Answer:
x = 60
Step-by-step explanation:
(2x + 15)° and 135° are corresponding angles and are congruent , then
2x + 15 = 135 ( subtract 15 from both sides )
2x = 120 ( divide both sides by 2 )
x = 60
Answer:
x = 60
Step-by-step explanation:
The two angles are corresponding. This means that both of the angles are congruent (same). So, you set both of them equal to each other. That means to do 2x + 15 = 135. You do basic algebra and then you get 60 for x. Hope this helps!
MARKING BRAINLEIST PLS HELP ME OUT HERE
316 is value of circle's arc BC .
What is an arc in maths?
A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length perfectly divides the circumference of the circle.A circle's circumference forms an arc. An arc length is the length of the arc, whereas an arc measure is the measurement of the angle the arc makes at the center of a circle. This measurement can be expressed in radians or degrees. Using the fact that pi radians = 180 degrees, we can quickly convert between the two.Short arc BC is the difference between 360° and long arc BAC
arc BC = 360 - arc BAC
= 360 - 44
= 316
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What is the
range?
Help meeeeeee
Aiden is preheating his oven before using it to bake. The initial temperature of the oven is 70° and the temperature will increase at a rate of 25° per minute after being turned on. What is the temperature of the oven 13 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
HURRY PLEASE!
after the given information, at least how many more steps are necessary to solve this proof
The following steps would be:
• TP and TP (for both triangles) are congruent by the reflexive property.
,• The triangles are congruent by the SAS theorem.
,• Angle S and angle O are congruent.
Helpppp please , fast
The coordinates of the orthocenter of triangle DEF are given as follows:
(6.67, -2).
How to find the orthocenter of a triangle?The orthocenter of a triangle is the point of intersection of the three altitude lines of the triangle.
Hence, we need to find two of the lines, and them find the intersection point between them, as the third line will necessarily intersect these lines at this point.
The midpoint of segment DE is:
(6, 1).
Which is the mean of the coordinates.
Vertex F is at point (8, -8), hence the slope of the line with these two points is:
m = (-8 - 1)/(8 - 2) = -9/2 = -4.5.
Hence:
y = -4.5x + b.
When x = 6, y = 1, hence we can find b as follows:
1 = -4.5(6) + b
b = 28.
Hence one line is:
y = -4.5x + 28.
The midpoint of segment EF is:
(8, -1.5).
Which is the mean of the coordinates.
Vertex D is at point (4, -3), hence the slope of the line with these two points is:
m = (-1.5 - (-3))/(8 - 4) = 0.375.
Hence:
y = 0.375x + b.
When x = 8, y = -1.5, hence we can find b as follows:
-1.5 = 0.375(8) + b
b = -4.5.
Hence the two lines that we have to find the intersection point is:
y = -4.5x + 28.y = 0.375x - 4.5.Then the x-coordinate of the orthocenter of the triangle is:
-4.5x + 28 = 0.375x - 4.5
4.875x = 32.5
x = 32.5/4.875
x = 6.67.
The y-coordinate of the orthocenter of the triangle is:
y = 0.375(6.67) - 4.5 = -2.
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What is the x ponet of y
;-;
The variable y is shown with no exponent. Any term with no exponent is understood to have an exponent of 1, so y has an exponent of 1.
10. Find the area of the shaded region.
17 yd
5 yd
7 yd
6 yd
7 yd
4 yd
Answer:
176 yd
Step-by-step explanation:
UNSHADED REGION (white rhombus): A=(s1+s2)/2 * H
s1=7
s2=1+7=8
H=6
A=(7+8)/2*6=45
SHADED + UNSHADED REGION (big parallelogram): area of parallelogram A=B*H
B=17
H=7+6 = 13
A=17*13=221
SHADED REGION: big parallelogram area - rhombus area
221 - 45 =176 yd
What is the y-intercept of f(x) = -2 (1/2)^x?
Answer:
-2
Step-by-step explanation:
f(x) = -2 (1/2)^x
you find the y-intercept where x = 0
= -2 (1/2)^0
= -2 *1
= -2
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar sign, 3, point, 25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most \$30$30dollar sign, 30 before tax. The restaurant only sells pancakes in stacks of 444 pancakes for \$5.50$5.50dollar sign, 5, point, 50.
Let SSS represent the number of stacks of pancakes that Benjamin buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
3.25+S \leq 303.25+S≤303, point, 25, plus, S, is less than or equal to, 30
(Choice B)
B
3.25+S \geq 303.25+S≥303, point, 25, plus, S, is greater than or equal to, 30
(Choice C)
C
3.25+5.50S \leq 303.25+5.50S≤303, point, 25, plus, 5, point, 50, S, is less than or equal to, 30
(Choice D)
D
3.25+5.50S \geq 303.25+5.50S≥303, point, 25, plus, 5, point, 50, S, is greater than or equal to, 30
2) What is the largest number of pancakes that Benjamin can afford?
The correct option is D that is bill is equal to or greater than $30
3.25 + 5.5s < =30
The first step in building the inequality is modelling Benjamin's spendings.
He buys a chocolate milk that costs $3.25, plus S stacks of pancakes, each at $5.50. Thus, in total, his spendings are of:
3.25 + 5.25s
He wants the bill to be of at most $30, that is, his spending has to be at most $30, thus:
T < 30
3.25 + 5.5s < =30
Thus the correct inequality is option D which is 3.25 + 5.5s < =30
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find x
please and thank you
Answer: x = 65
Step-by-step explanation:
1) First find the mini triangles, left and right angles
We will be calling the left one A and the right one B.
2) Next use triangle sum to find B.
62 + 50 + b = 180
b = 68
3) Use triangle sum again to find A.
53 + 80 + a = 180
a = 47
4) Use triangle sum to find the top mini angle.
47 + 68 + c = 180
c = 65
5) Since x is in the vertical angle of c, they are equal
c = x
65 = x
Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due?
Next, you decide to pay with a $20.00 bill. How much change will you receive after paying for your video game?
Using simple linear equations we calculate that the change left will be $6.24 .
The equals sign is used to indicate that two expressions on each side of the equal sign are equal in the many mathematical formulas that are utilized to form an equation.
Depending on the language, the definition of the word equation and its cognates may change slightly.The first step in solving a variable equation is to determine the precise values of the unknown variables that lead to the provided equality. The equation's solutions, often referred to as the variables for which the equation must be solved, are the values of the unknowable variables that satisfy the equality.Let the change received be x.
Therefore let us construct an equation for the situation
cost of game + tax + change = 20
or, 12.98 + 0.78 + x = 20
or, 13.76 + x = 20
or, x = 6.24
Therefore he will receive 6.24 after solving the equation.
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Question 4 of 5
Compare -2 and 5. Which statement is not true?
OA. 5 is farther to the right on a number line.
OB. 151>1-21
C. -2 has a greater absolute value.
O D. 5 is farther from zero on a number line.
write the polynomial in standard given the following zeros: x=0,i\sqrt(2),-i\sqrt(2)
The polynomial is x³ + 2x
If the zeros or roots of the polynomial are given, then the standard form of the polynomial can be found.
That is, a, b and c are roots of the polynomial, then the polynomial will be of degree 3 since 3 zeros are there and the factors of the polynomial will be , x-a, x-b and x- c.
Then the polynomial is, (x-a)(x-b)(x- c) = x³-(a+b+c)x-abc
Here the zeros of the polynomial are x = 0, x = i√2 and x = -i√2.
So the factors of the polynomial are (x-0), (x - i√2) and (x +i√2).
Hence the polynomial is , (x-0) (x - i√2)(x +i√2) = x(x²+2) = x³ + 2x
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Eric is buying food for an upcoming holiday party. He can get pizzas for $7 each using a coupon he found online, and he wants to figure out the cost of buying 12 pizzas so he can plan his budget. Please provide answers to each of the following questions:
What is the direct variation equation that represents this situation? (worth 2
points)
How much will Eric spend if he buys 12 pizzas? (worth 2 points)
Explain how you calculated his total cost for pizzas. (worth 2 points)
Answer:
The answer would be 7 times 12
Eric will spend $84
I calculated it by seeing how much each of the pizzas cost-$7 the I figure out how many pizzas he need-12 Now what we need to do is multiply 7 and 12 because if one pizza is $7 (Stated in the written problem) then I know that it would be 7+7+7+7+7+7+7+7+7+7+7+7 12 times, one time for each pizza needed. The simpler version would be 7 time 12 which then we would get a value of $84.
Step-by-step explanation:
Hope this helps!!
Answers to all the subparts using equations are:
(A) Equation: 7x = C(B) Cost of 12 pizzas: C = $84(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.So, the answers to all the subparts are as follows:
(A) Equation that can be formed is:
Let, the cost be C.x be the number of pizza buying.Equation: 7x = C(B) Cost of 12 pizzas:
Let, x = 12.
Then,7x = C7(12) = CC = $84(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.
Therefore, answers to all the subparts using equations are:
(A) Equation: 7x = C(B) Cost of 12 pizzas: C = $84(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.Know more about equations here:
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Correct question:
Eric is buying food for an upcoming holiday party. He can get pizzas for $7 each using a coupon he found online, and he wants to figure out the cost of buying 12 pizzas so he can plan his budget. Please provide answers to each of the following questions:
(A) What is the direct variation equation that represents this situation? (worth 2
points)
(B) How much will Eric spend if he buys 12 pizzas? (worth 2 points)
(C) Explain how you calculated his total cost for pizzas. (worth 2 points)
Malik had a checking account balance of $92.18. His bank will fund the first debit card purchase that creates a negative balance up to a limit of $100.00, but charges a
$28.00 fee for that overdraft. Malik made a purchase of $36.12 yesterday, and another purchase of $76.50 today. He used a debit card for each purchase. What is Malik's
account balance after the two purchases and any overdraft fees?
negative $140.62
negative $20.44
O negative $112.62
O negative $48.44
Can someone please help me
In accordance with analytic geometry, the equation that represents the line is y = - (1 / 4) · x - 6.
What is the equation for a line shown on a graph?
Herein we find the representation of a line set on a Cartesian plane. According to analytic geometry, line are represented by equations of the form y = m · x + b, where m, b are the slope and the y-intercept, respectively.
Both the values of the slope and the y-intercept can be found by knowing the location of two points lying on the line. If we know that (x₁, y₁) = (0, - 6) and (x₂, y₂) = (4, - 7), then we find the following system of linear equations:
b = - 6 (1)
4 · m + b = - 7 (2)
By (1) in (2):
4 · m - 6 = - 7
4 · m = - 1
m = - 1 / 4
The equation that represents the line is y = - (1 / 4) · x - 6.
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3 1 1 / 5 + 1 /
2 =
Answer:
5 7/10
Step-by-step explanation:
first you multiply five by the three, then add the eleven. so now you have a improper fraction, 26/5 plus 1/2. find the Least common denominator which is 10, and whatever you do to the denominator you do to the numerator which makes 57/10 simplify and you'll get 5 7/10
Answer:
Step-by-step explanation:
1. Find the lcm(least common denominator)
(5 x 2 = 10)
2. Multiply the numerators by the same number as the denominator(you multiplied 5 by 2 to get 10 so you multiply 311 by 2. You multiplied 2 by 5 to get 10 so you multiply 1 by 5.)
311 x 2 = 622
1 x 5 = 5
3. Add
622/10 + 5/10 = 627/10
4. Simplify
627 ÷ 10 = 62 [tex]\frac{7}{10}[/tex] (it can also be written as: 62.7)
20$ startup fee and a $5 monthly fee write an equation in slope intercept form that models
The slope intercept form of equation that models $20 startup fee and $5 monthly fee is y = 5x +20 , y is total fee and x is number of months
What is slope intercept form?The slope intercept form of an equation is y = mx + c
where y is y coordinate, x is x coordinate, m is the slope of the line and c is y intercept.
Let the total fee after x months be y
Then y is sum of startup fee and sum of all month's fee
For x months total monthly fees = 5(x)
Therefore the total fee after x months , y = 5x +20 which is same as slope intercept form y=mx+c
when x= 0 ⇒ y = 20 , startup fee
Thus, the equation in slope intercept form is y = 5x +20 ,where y is total fee and x is number of months.
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resuelve la siguiente ecuación con el metodode suma y resta x + y = 5
2x + y = 4
La solucion del sistema de ecuaciones es x = 1, y = 4, o (1, 4) en notación standard.
¿Como resolver el sistema de ecuaciones?Aqui tenemos el sistema de ecuaciones:
x + y = 5
2x + y = 4
Si tomamos la segunda ecuación, y a esta le restamos la primera, obtendremos:
(2x + y) - (x + y) = 5 - 4
(2x - x) + (y - y) = 1
x = 1
De esta forma encontramos el valor de x, para encontrar el valor de y, deberemos reemplazar x = 1 en una de las ecuaciones. Yo usare la primear.
x + y = 5
1 + y = 5
y = 5 - 1
y = 4
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Create a quadratic inequality with the roots -5 and 2.
Answer:
y=x^2+3x-10
Step-by-step explanation:
.........