Answer: 36.902 Seconds
Step-by-step explanation:
(1) --> To find the time that the rocket is at a height of more than 100 feet, you need to find the time when the height of the rocket is equal to 100 feet.
(2) --> do this by setting your equation equal to 100
[tex](-\frac{1}{2} )t^2 + 15t = 100[/tex]
[tex](-\frac{1}{2}) t^2 + 15t - 100 = 0[/tex]
(3) --> From here, use the quadratic formula to solve for t
Quadratic formula:
[tex]t = - \frac{-b+-\sqrt{b^2 - 4ac} }{2a}[/tex] (solving the b+ first)
[tex]t = \frac{(-15 + \sqrt{225 - 4(-\frac{1}{2}) (-100)}}{-1}[/tex]
[tex]= \frac{(-15 + \sqrt{475})}{-1}[/tex]
[tex]= \frac{(-15 + 21.902)}{-1}[/tex]
[tex]= \frac{6.902}{-1}[/tex]
[tex]= -6.902[/tex]
(solving b-)
[tex]t = \frac{-15 - \sqrt{475}}{-1}[/tex]
[tex]= \frac{-15-21.902}{-1}[/tex]
[tex]= \frac{-36.902}{-1}[/tex]
[tex]= 36.902[/tex]
HENCE: The first solution, -6.902, is not a valid time because it is negative. The second solution, 36.902, is the time when the rocket is at a height of 100 feet. Since the rocket is at a height of more than 100 feet for the entire time after it reaches a height of 100 feet, the rocket will be at a height of more than 100 feet for 36.902 seconds.
Write 250 beads in total on 8 necklaces as an algebraic expression.
The algebraic expression that represents the number of beads per necklace is given as follows:
250/8.
How to write the algebraic expression?The algebraic expression representing the number of beads per necklace is obtained applying the proportion in the context of the problem.
The proportion is given by the division of the total number of beads by the total number of necklaces, as follows:
Beads per necklace = Number of beads / Number of necklaces.
The parameters for this problem are given as follows:
Number of beads: 250.Number of necklaces: 8.Hence the algebraic expression that represents the number of beads per necklace is given as follows:
250/8.
(dividing the number of beads by the number of necklaces given in this problem).
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find the value of jk for this problem
The measure of JK from the given similar quadrilaterals is 30 units.
What are similar figures?Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar when they both have a lot of the same properties but still may not be identical.
Given that, JKLM and PQRS are similar figures.
MJ=21, JK=4y-2, KL=6x+3, LM=36, PQ=10, QR=11, and RS=12.
Since, given quadrilaterals are similar, we get
JK/PQ =LM/RS
4y-2/10 =36/12
4y-2/10=3
4y-2=30
4y=32
y=8
So, JK=4y-2
JK=30 units
Therefore, the measure of JK is 30 units.
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Mike bought 15 baseball cards.Rookie players are featured on 3/4 of the cards. How many cards featured rookie players?
The number of cards that featured rookie players is given as follows:
11 cards.
How to obtain the number of cards with rookie players?The number of cards with rookie players is obtained applying the proportion, which is a fraction of the total amount in the context of a problem.
To find the desired amount, the proportion is multiplied by the total number of cards, hence obtaining the number of cards with rookie players.
The parameters for this problem are given as follows:
Proportion of rookie players: 3/4 of the cards.Total number of cards: 15 cards.Hence the number of cards featuring rookie players is calculated as follows:
3/4 x 15 = 45/4 = 11.25 cards.
Rounding to the nearest integer, 11 cards.
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What is the median of the data? 30, 29, 16, 11, 16, 20, 21, 13, 15, 15, 23, 30
A. 26
B. 15
C. 16
D. 18
Answer:b a
Step-by-step explanation:
Unit 2, Lesson 7 - Homework
1. One batch of meatloaf contains 2 pounds of beef and cup of breadcrumbs.
Complete the double number line diagram to show the amounts of beef and bread
crumbs needed for 1, 2, 3, and 4 batches of meatloaf.
2.
beef (pounds)
bread crumbs (cups)
Write a sentence that describes this situation and that uses the word per.
Place Aprwer Here
Answer:
3 batches of meatloaf requires 6 pounds of beef
and 3 cups of bread crumbs.
Step-by-step explanation:
For pounds of beef
1 batch meatloaf = 2 pounds of beef
3 batches of meatloaf = x
Cross Multiply
x = 3 x 2 pounds of beef
x = 6 pounds of beef
3 batches of meatloaf requires 6 pounds of beef
For bread crumbs
1 batch meatloaf = 1 cup of bread crumbs
3 batches of meatloaf = x
Cross Multiply
x = 3 × 1 cup of bread crumbs
x = 3 cups of bread crumbs
3 batches of meatloaf requires 3 cups of bread crumbs.
Therefore, 3 batches of meatloaf requires 6 pounds of beef and 3 cups of bread crumbs.
Line a is parallel to line b and goes through the point (1,2). Line b goes through the point (3,1) and is perpendicular to line c whose equation is y = -2x+3. Find the y-intercept of line a.
Line a is parallel to line b and goes through the point (1,2). Line b goes through the point (3,1) and is perpendicular to line c whose equation is y = -2x+3.The y-intercept of line a is -7
given that
Line a is parallel to line b and goes through the point (1,2)
Line b goes through the point (3,1) and is perpendicular to line c
equation of line c is y = -2x+3
To find y-intercept of line a.
we need to find the slope of the equation
slope(m) = [tex]\frac{y2 - y1}{x2 - x1}[/tex] =[tex]\frac{1 - (-3)}{2 - 1}[/tex] = [tex]\frac{4}{1}[/tex] = 4
now , we need to write equation in slope intercept form
y = mx + b
1 = (4)2 + b
1 = 8 + b
b = -7
The y-intercept of line a is -7
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A segment has endpoints at (−9,5)
-
9
,
5
and (34,5)
34
,
5
. How many units long is the segment?
The distance between the points (-9, 5) and (34, 5) will be 43 units.
What is the distance between two points?It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
The points are given below.
(-9, 5) and (34, 5)
Then the distance between the points is given as,
D² = (34 + 9)² + (5 - 5)²
D² = (43)²
D = 43 units
The distance between the points (-9, 5) and (34, 5) will be 43 units.
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Angela went to the farmers' market to buy some vegetables She wanted some yelow squash and zucchini which were both on sale for 1.146 per pound. Angela bought 2 pounds of yellow
pounds of zucchini. To the nearest cent, what was the total cost of the vegetables?
The total cost of the vegetables to the nearest cent is $3.44
Define Unitary Method.The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.
Define ratio and proportion.Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.
Angela bought 2 pounds of yellow squash and 1 pound of zucchini. The yellow squash and the zucchini were both on sale for $1.146 per pound.
To find the total cost of the yellow squash, we can multiply 2 pounds by $1.146 per pound:
2 pounds * $1.146/pound = $2.292
To find the total cost of the zucchini, we can multiply 1 pound by $1.146 per pound:
1 pound * $1.146/pound = $1.146
To find the total cost of the vegetables, we can add the cost of the yellow squash and the zucchini:
$2.292 + $1.146 = $3.438
The total cost of the vegetables to the nearest cent is $3.44
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Graph the solution to this inequality on the number line.
−8 + x < −3
(Please answer this question by taking a screenshot of the number line and drawing a number line where it needs to go)
A graph of the solution to this inequality (x < 5) is shown on the number line in the image attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for the comparison of two (2) or more numerical data, numerals, and variables that are contained in an algebraic equation, especially based on the following inequality symbols:
Less than (<).Greater than or equal to (≥).Greater than (>).Less than or equal to (≤).Generally speaking, a number line is a type of chart which primarily decreases in numerical value towards the right from zero (0) and increases in numerical value towards the left from zero (0).
Next, we would solve the given inequality by adding eight to both sides as follows;
−8 + x < −3
−8 + x + 8 < −3 + 8
x < 5
Therefore, the solution is x is less than five.
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helppp me please i need help
y=6x+11
2x-3y=7
Need Step by Step Solution
The solution of the system of equations:
y = 6x + 11
2x- 3y = 7
is (-5/2, -4).
How to solve the system of equations?Here we want to solve the following system of equations:
y = 6x + 11
2x- 3y = 7
We can see that y is already isolated on the first equation, so we can substitute this on the second equation.
We will get:
2x - 3*(6x + 11) = 7
2x - 18x - 33 = 7
Now we can solve that equation for x:
2x - 18x - 33 = 7
-16x - 33 = 7
-16x = 7 + 33
-16x = 40
x = 40/-16 = -10/4 = -5/2
And the value of y is what we get if we evaluate one of the functions in x = -5/2.
I will use the first one.
y = 6x + 11
y = 6*(-5/2) + 11
y = -15 + 11
y = -4
So the solution of the system of equations is (-5/2, -4).
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6. Higher Order Thinking Helen makes
the rectangle on the right from tiles.
Each tile is 1 unit square. Helen says the
white tiles cover more area than the
black tiles. Do you agree? Explain.
On solving the provided question we cans ay that - the area of the rectangle will A = 121 cm sq.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
So we have been provided with,
L = 11 cm and B = 11 cm
so, A = L X B = 11 X 11 = 121 cm sq.
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You need to multiply 44.8 by 0.22.
How many numbers will fall after the decimal point in your solution?
a.) 1
b.) 2
c.) 3
d.) 4
Answer:3
Step-by-step explanation:
44.8 times 0.22 is 9.856 so 3 numbers will fall after the decimal point. You can also determine the answer by simply adding the number of decimal places in the numbers multiplied.
1. in several sentences, explain the right triangle drawings you need to model the shadow scenarios. make sure it answers the following: a. what does each side length signify? in particular explain what does the hypotenuse in your drawing signify in the real world?
The right triangle drawings are used to model the shadow scenarios. Each side length of the triangle represents a different part of the scenario.
Modeling Shadow Scenarios Using Right Triangle DrawingsThe hypotenuse represents the distance from the sun to the object casting the shadow, the side adjacent to the hypotenuse represents the length of the shadow, and the side opposite the hypotenuse represents the height of the object casting the shadow. In the real world, the hypotenuse is used to calculate the angle of the sun relative to the object casting the shadow.
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The diagram below shows Zainab observing a kite. Given that the angle of inclination of the kite from Zainab's sight is 35⁰ and the distance between Zainab's eyes and the kite is 120 meters. Calculate the horizontal distance, d in meters. State the correct answer to three significant figures.
The distance that is covered is 98.3 m.
What is the distance in meters?We know that in this case now, we would need to obtain the distance that has been traveled as it has been shown. We can see from the diagram, that the angle of inclination of the kite from Zainab's sight is 35⁰ and the distance between Zainab's eyes and the kite is 120 meters.
Using the trigonometric ratios for the right angled triangles we have;
Cos θ = adjacent /hypotenuse
adjacent = d
hypotenuse = 120 m
cos 35 = d/120
d = 120 cos 35
d = 98.3 m
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Gualberto has a barrel that collects rainwater. As the rainwater evaporates,
the height of the rainwater changes from 24.83 in. to 18.08 in. over a period of
5 days. What is the average change in the height of the rainwater each day?
Show your work.
The average change in height of the rainwater each day is 1.35 inches.
What is average change?The rate at which one value in a function changes in proportion to another is known as the average rate of change. The slope of a graphed function is typically calculated using the average rate of change.
Given, Gualberto has a barrel that collects rainwater. As the rainwater evaporates, the height of the rainwater changes from 24.83 in. to 18.08 in.
Thus,
The change of height in 5 days = 24.83 - 18.08
The change of height in 5 days = 6.75
Hence,
The Average change of height in 5 days = 6.75 / 5
The Average change of height in 5 days = 1.35
Therefore, Every day, the rainwater's height changes by 1.35 inches on average.
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A measure of a person's ability and willingness to pay debts on time.
ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.
What is an equation?There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.
X now has 300 mg of sodium in it.
[tex]x = 300[/tex]
Y also has 450 mg of sodium in it.
[tex]y = 450[/tex]
Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.
Let the number of frozen dinners be "b," and the number of soup cans be "a."
ax + by = 6000
a(300) + b(450) = 6000 .
Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation
[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]
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A clothing store is having an anniversary sale. Every piece of clothing in the store is
marked down 15%. What is the sale price of a belt that has a regular price of $23?
Answer:
$19.55
Step-by-step explanation:
$23-15%=$19.55
Match the y-coordinate with the given x-coordinate for the equation y = log₁0x.
1. 100
2. 1/10
3. 10
4. 1
5. 1/100
-2
1
0
-1
2
The y-coordinate matched with the given x-coordinate:
x = 100 → y = 3
x = 1/10 → y = 0
x = 10 → y = 2
x = 1 → y = 1
x = 1/100 → y = -1
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
Given:
Logarithmic function,
y = log(10x).
(1).
x = 100
So,
y = log{(10)(100)}.
y = log(1000)
y = 3
(2).
x = 1/10
So,
y = log{(10)(1/10)}.
y = log(1)
y = 0
(3).
x = 10
So,
y = log{(10)(10)}.
y = log(100)
y = 2
(4).
x = 1
So,
y = log{(10)(1)}.
y = log(10)
y = 1
(5).
x = 1/100
So,
y = log{(10)(1/100)}.
y = log(1/10)
y = -1
Therefore, the y-coordinate matched with the given x-coordinate
x = 100 → y = 3
x = 1/10 → y = 0
x = 10 → y = 2
x = 1 → y = 1
x = 1/100 → y = -1
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Please help!!! Algebra 2
The area of the sum of all the center triangles in the sequence of figure can not be determined; since the series has an indefinite number of terms, the series does not have a sum. Option D
Area of a triangle.The area of a given triangle is the space that it occupies on a 2 dimensional plane. So that the major formula that can be used to determine the area of a triangle is;
Area of a triangle = 1/2 * base * height
The sum of area of given triangles implies the mathematical addition of the values of area for each of the triangles.
In the given question, it was given that the pattern continues indefinitely. Thus it is impossible to determine the area of the sum of all center triangles in the sequence of figure.
Therefore the appropriate answer is option D. Since the series has an indefinite number of terms, the series does not have a sum.
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If 3 less than 4 times a certain number is 9 more than the number, find the number.
Answer:
okay now I really think that doing or solving any question like this will start first by solving out Earth I mean x okay by solving it out and after solving it and I'm really sorry cuz I'm using a voice note that's why I'm having all this misinterpretation so when you sort out x you begin to sort out all the questions nowhere for them to settle number the certain number will be x know where the four times a number will be no where the 903 will be and I really think that is it
a) Work out the nth term rule for the sequence of cube numbers.
Therefore , the solution of the given problem of sequence comes out to be T = 5832.
A sequence is what?The phrase "sequence" refers to a grouping of numbers, or "terms." 2, 5, and 8 are examples of terms. By making advantage of a specific pattern some sequences follow, it is possible to make some sequences infinitely long. To continue the sequence, use the sample of 2,5,8, and then add 3. There are equations that show where to seek for words in a list of words. In mathematics, a sequence is a group of items that are all in some kind of order . The length of the series is the total number of ordered objects, which may be limit . arranging two or more things in a sensible order. Chronological.
Here,
Given :
to determine the nth term norm for the members of the cube in order.
1, 8, 27, 64, and... are
the cube numbers.
The 18th term
=> T(18) = 183
=> T(18) = n³
=>T(n) = n³ = 5832
Therefore , the solution of the given problem of sequence comes out to be T = 5832.
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A dump truck normally carries 10 cubic yards of gravel. A cubic yard of gravel
weighs 1.35 tons. Road bans in the spring specify that the truck can only be
loaded to 85 percent of normal capacity.
How many tons of gravel can the truck carry when road bans are in effect?
The quantity of gravel in tons which the truck can carry when the road bans are in effect as required to be determined is; 11.475 tons.
What quantity in tons of gravel can the truck carry when road bans are in effect?It follows from the task content that the quantity of gravel which the truck in discuss can carry when road bans are in effect be determined.
First, since the truck normally carries 10 cubic yards of gravel and each cubic yard weighs 1.35 tons.
Therefore, the truck can carry; 10 × 1.35 = 13.5 tons of gravel.
On this note, since the truck can only be loaded 85 percent of normal capacity when road bans are in effect.
The quantity which the truck can carry when road blocks are in effect is therefore; ( 85 / 100 ) × 13.5 = 11.475 tons of gravel.
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Which ordered pairs represent points on the graph of this equation? Select all that apply.
2y= –3x–4
All the ordered pairs that represent points on the graph of this equation include the following:
A. (-4, 4).
C. (-2, 1)
E. (2, -5)
F. (0, -2)
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
How to determine the ordered pairs that represent points on the graph?In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.
By critically observing the graph of the given function (see attachment), the solutions are include following;
Ordered pair = (-4, 4).
Ordered pair = (-2, 1).
Ordered pair = (2, -5).
Ordered pair = (0, -2).
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Complete Question:
Which ordered pairs represent points on the graph of this equation? Select all that apply.
2y= –3x–4
(-4, 4)
(7, 6)
(-2, 1)
(0, 7)
(2, -5)
(0, -2)
A lighthouse, which is 18 feet high, stands on a cliff that is 150 feet above sea level. The distance from the top of the lighthouse to a sailboat on the ocean is 360 feet.
What is the angle of elevation (x) from the sailboat to the top of the lighthouse? Round the answer to the nearest degree.
Therefore, using the supplied numbers, we may convert this data into a bar graph.
A graph is what?
A graph is a non-linear data structure made up of nodes, or vertices, and edges. In a graph, the nodes, also known as vertices, are joined together by any two edges. This graph's edges (E) are 1, 2, 1, 3, 2, 4, 2, 5, and 4, 50, while its vertices (V) are 1, 2, 3, 5, and 1.
given
[tex]P(A) = 0.70\\P(C|A) = 0.30\[/tex]
So we are to find
[tex]P(C|A) = P(A|C) * P( C) / P(A)\\[/tex]
As here as we are to find conditional probability .
As a result, option a) is accurate since p (c vertical line a) equals fraction numerator p (a vertical line c)p (a)over denominator p (c)end fraction.
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Find the length of the midsegment of the trapezoid with the vertices S(0, 0), 7(2, 7), U(6, 10), V(8, 6).
The length of the midsegment is
Answer:
7.5
Step-by-step explanation:
A trapezoid is a quadrilateral where the bases are parallel, but the legs are not parallel.
Given vertices of trapezoid STUV:
S = (0, 0)T = (2, 7)U = (6, 10)V = (8, 6)The parallel bases of the trapezoid are TU and SV.
Find the lengths of TU and SV using the distance formula.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}TU&=\sqrt{(x_U-x_T)^2+(y_U-y_T)^2}\\&=\sqrt{(6-2)^2+(10-7)^2}\\&=\sqrt{(4)^2+(3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}SV&=\sqrt{(x_V-x_S)^2+(y_V-y_S)^2}\\&=\sqrt{(8-0)^2+(6-0)^2}\\&=\sqrt{(8)^2+(6)^2}\\&=\sqrt{64+36}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]
The midsegment of a trapezoid is the segment parallel to the bases that connects the midpoints of the legs.
[tex]\boxed{\begin{minipage}{6.5cm}\underline{Midsegment of a Trapezoid}\\\\$M=\dfrac{b_1+b_2}{2}$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the length of the midsegment. \\\phantom{ww}$\bullet$ $b_1$ and $b_2$ are the parallel bases. \\\end{minipage}}[/tex]
Substitute the found lengths of the bases into the midsegment formula:
[tex]\implies M=\dfrac{5+10}{2}[/tex]
[tex]\implies M=\dfrac{15}{2}[/tex]
[tex]\implies M=7.5[/tex]
The length of the midsegment is 7.5.
A diagram that represent 4/5 divided by 2/3
The value of the diagram represented by 4/5 divided by 2/3 is 6/5
What is fraction ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
A numerical number that designates a portion of a whole is used to represent fractions. A fraction is a component or segment taken from a whole, which can be any number, a certain amount, or an object. Let's use an illustration to better comprehend this idea. The pizza in the accompanying image has been sliced into 8 equally sized pieces. Now, if we wish to refer to a single portion of the pizza, we can do so by using the notation 1/8, which indicates that we are talking about one portion out of 8 equally sized portions.
The fractions are 4/5 and 2/3
Now 4/5 divided by 2/3 is given by
[tex]\frac{\frac{4}{5} }{\frac{2}{3} }[/tex] = [tex]\frac{4}{5}*\frac{3}{2} = \frac{6}{5}[/tex]
The value of the diagram represented by 4/5 divided by 2/3 is 6/5
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1 x _ = 1.66
thank you for answering
this helps!!
Answer:
1.66
Step-by-step explanation:
1x1.66=1.66
q/10 + 71 = 75
what is "q"
Answer:
q=40
Step-by-step explanation:
q/10+71=75
-71. -71
q/10=4
x10 x10
q=40
hopes this helps
Answer:
What the guy above me says!
Step-by-step explanation:
What is the measure of angle 2?
130⁰
142⁰
38⁰
90⁰
Answer:
142 degrees
Step-by-step explanation:
they are vertical angles!