1.9 × 10^3 is 215 times smaller than 4.085 × 10^5.
The basic formula for the area of a rectangle is length x width, but the basic formula for volume is length x width x height. The calculation does not change depending on how you refer to different measurements. For example, you can use depth instead of height.
Every 3D object occupies a certain space. This space is measured by its volume. Volume is defined as the space occupied within the bounds of an object in three-dimensional space. Also called the capacity of the object. The volume of an object is the amount of space it fills. Large capacity is measured in cubic meters m3. Smaller volumes are measured in cubic centimeters cm3 or cubic millimeters mm3.
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Collect like terms: 3x(exponent of 2) + 2x + 3x -1
The like terms in the expression are 2x and 3x, and the solution is 3x^2 + 5x - 1
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to collect the like terms?The expression is given as
3x(exponent of 2) + 2x + 3x -1
Rewrite the expression properly
So, we have
3x^2 + 2x + 3x -1
The like terms are the expressions that have the same variables
In this expression, the like terms are 2x and 3x
When evaluated, we have
3x^2 + 5x - 1
Hence, the equivalent expression is 3x^2 + 5x - 1
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how much less than 6 is the sum of 2 3/4 and 2 4/5
Answer: 9/20 or 0.45
Step-by-step explanation:
simplify the expression.
Write the EXPLICIT rule for the arithmetic sequence
-10, -3, 4, 11,...
The difference between the following term is 7 and explicit rule is
[tex]a_{n}=-17+7n[/tex]
What is Explicit rule?Explicit rule is a rule that you can solve without needing the previous term.
How Should Explicit Formula Be Written?The nth term in the series is where the explicit formula can be expressed. The explicit formula of the sequence for the arithmetic progression a, a + d, a + 2d, a + 3d,...a + (n - 1)d is formed by the nth term. An = a + (n - 1)d is the explicit formula for this arithmetic series. The explicit formula can also be calculated for the harmonic and geometric sequences.
Here, [tex]a_{n}=-17+7n[/tex]
put n = 1
[tex]a_{n}[/tex]= =-17+7(1)
= -17+7
=-11 which is the first term
similarly for n = 4
-17+7(4)
= -17+ 28 =11 which is the fourth term.
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Find the length and width of the greatest rectangular area that the farmer can enclose with 100 m of fencing. the length is m and the width is m.
Answer:
25 length and 25width
Step-by-step explanation:
we need to find the biggest area with a perimeter of 100 and all sides need to be the same. So you divide 100 by 4 and you get 25 for width and 25 for length
Can anyone assist me?
please
How to solve for number 3
Answer: m<F = 134
EF = 18in
Step-by-step explanation:
Since both angles FEG and FGE are equal, we could make out that lines EF and FG are equal measures making an isosceles triangle. Therefore we just add up both 23 to get 46 and subtract it by 180 getting 134
Jonathan wants to buy a lid for his frying pan. The diameter of the pan is 9 inches. What is the approximate circumference of a lid that will fit his frying choices are A 28.26 in B 56.52in C 14.13in D 254.34in
A 28.26
The approximate circumference of a lid that will fit his frying is 28.26.
Circumference of circle
In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
Formula of circumference if a circle is 2[tex]\pi[/tex]r.
Given that the diameter of the pan is 9 inches.
Radius of pan = 4.5 inches
Therefore circumference of pan = 2 × (22/7) × 4.5
= 28.28 inches
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In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
Formula of circumference if a circle is 2r.
Given that the diameter of the pan is 9 inches.
Radius of pan = 4.5 inches
Therefore circumference of pan = 2 × (22/7) × 4.5
= 28.28 inches
A random sample of students were asked whether they preferred to sweep the floor or to do the dishes, and whether they preferred to hear music or have silence while doing the chore. The results of the survey are summarized in the table. Sweep Dishes Total Music 60 96 Silence 62 104 Total 78. 122 200 What is the probability that a student prefers to do the chore in silence? O A 0.21 OB. 0.31 Ос 0.39 OD. 0.42 E. 0.52
this is:
[tex]P=\frac{\text{silence}}{\text{total}}=\frac{104}{200}=0.52[/tex]answer: E
Which equation represents a line which is perpendicular to the line y=2x-4?
Answer:
y = -1/2x - 4
Step-by-step explanation:
The perpendicular line always changes with the negative reciprocal of the slope.
Given m
n, find the value of x and y.
(5x+20) (y-18)
(6x-4)°
The values of x and y are: 24° and 58° respectively.
We know that vertically opposite angles are equal, so:
(5x+20) = (6x-4)
5x-6x = -4-20
-x=-24
x=24
hence x=24°
also, angles on a straight line adds up to 180°, so:
5x+20+y-18=180°
using x=24
5(24)+20+y-18=180°
120+20+y-18=180
140+y-18=180
y+122=180
y=180-122
y=58°
Hence the values of x and y are 24° and 58° respectively.
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Cici likes to collect shoes, but she only has half the number of pairs of shoes that her friend Aubree has. If Cici has 42 pairs of shoes, how many pairs of shoes does Aubree have?
Answer:
84 pairs of shoes
Step-by-step explanation:
Since Cici has pairs of shoes, use this equation to solve for the number of pairs of shoes Aubree has
What is 4+4 I’m feeling generous “I know what it is I’m not that yak bc I can’t say it but have a nice day :)
Answer:
thx for the points have a nice day too
Step-by-step explanation:
Answer: 8
Step-by-step explanation:
Double 4 and add
or
4x2.
( ik this is a joke ;] )
A shop sells cola in three different size bottles.
2 Litre
£1.99
600ml
62p
Which size bottle is the best value for money?
You must show all your working.
1.5 Litre
£1.53
You have 270 ft^2 of carpet. You want to install carpeting in a room that is 20 ft long and 15 ft wide. Do you have enough carpet? Explain how you know. (1pt)
Answer: No, there isn't enough carpet
Explanation:
The room is 20 feet by 15 feet. The floor area is length*width = 20*15 = 300 square feet, which is larger than the 270 sq ft of carpet you have available. Therefore, you don't have enough carpet. The amount needed is 300-270 = 30 sq ft
Answer:
No
Step-by-step explanation:
20 ft*15 ft=300 ft^2
you need to cover 300 ft^2
you only have 270 ft^2
so you can't cover it
Carly is saving money babysitting on the weekends. last month, she saved $120. this month, carly saved 30% more than she saved last month. how much did she save this month?
Question: Carly is saving money babysitting on the weekends. last month, she saved $120. this month, carly saved 30% more than she saved last month. how much did she save this month?
Answer: Goodmorning: } It's $156.
Step-by-step explanation: you would change the 30% to a decimal by moving the decimal point two spaces to the right.
this would get you .30 or .3
you would then multiply the $120 by .3
you would get 36
then since she saved 30% MORE you would add the 36 to the 120 and get 156.
Have a nice day !!!
If f(x) = 4x – 6, then f-1(x) =
Answer:
(x+6)/4
Step-by-step explanation:
We are given the following function:
f(x) = 4x-6
It can also be written as:
y = 4x - 6
Finding the inverse:
We have to exchange y with x, and then isolate y. It becomes:
[tex]x=4y-6[/tex]Isolating y:
[tex]4y=x+6[/tex][tex]y=\frac{x+6}{4}[/tex]The inverse function is:
[tex]f^{-1}(x)=\frac{x+6}{4}[/tex]equation that is perpendicular to 5x +3y=-21 and passes through (-5,1)
The equation of line perpendicular to the line 5x + 3y = -21 will be;
⇒ y = 3x/5 + 4
What is Equation of line?
The equation of line with slope m and passes through the point
(x₁, y₁) is;
⇒ y - y₁ = m (x - x₁).
Given that;
The equation of perpendicular line is,
⇒ 5x + 3y = -21
And, The point on the line will be (-5 , 1)
Now,
The product of the slopes of the perpendicular line will be -1.
Slope of the perpendicular line 5x + 3y = -21 is;
5x + 3y = -21
y = - 5x/3 - 21/3
y = -5x/3 - 7
dy/dx = m₁ = -5/3
So, The slope of line which is perpendicular to the line is;
m₁ m₂ = -1
m₂ = -1/m₁
m₂ = 3/5
So, The equation of line perpendicular to the line 5x + 3y = -21 and passes through the point (-5, 1) is;
⇒ y - y₁ = m (x - x₁).
⇒ y - 1 = 3/5 (x - (-5)).
⇒ y - 1 = 3/5 (x + 5)
⇒ 5 (y - 1) = 3 (x + 5)
⇒ 5y - 5 = 3x + 15
⇒ 5y = 3x + 15 + 5
⇒ 5y = 3x + 20
⇒ y = 3x/5 + 4
Thus, The equation of line perpendicular to the line 5x + 3y = -21 will be;
⇒ y = 3x/5 + 4
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How do I graph the function y = -2/3
The graph for the function y = -2/3 is shown in the image below.
How to Graph the Function of a Horizontal Line?The function of a horizontal line is expressed as y = b, where b is the point on the y-axis where the line intercepts the y-axis.
This means that, the graph of y = b would be a graph that has its line cutting across the y-axis at point b on the y-axis, showing a horizontal line.
Given the function, y = -2/3, this shows that b, which is -2/3, is the value of the y-coordinate where the line intercepts or cuts the y-axis. The graph of this function would be a graph that is horizontal and passes through the point, y = -2/3 on the y-axis.
The graph of y = -2//3 is given in the diagram attached below.
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the answer for y-3=-3y-43
Natalie is competing in the javelin throw event at her school. in order to qualify for the final round, the mean length of her javelin throws in the first round must be at least 195 feet. she has 1 more throw left in the first round. this list shows the length, in feet, of natalie's first 7 javelin throws. 188, 204, 194, 195, 187, 201, 199 question what is the minimum length, in feet, that natalie must throw the javelin on her next throw in order to qualify for the final round? enter the answer in the box.
The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.
Based on the given conditions,
The length of her javelin throws in the first round must be at least 195 feet.
She has 1 more throw left in the first round.
This list shows the length, in feet, of Natalie's first 7 javelin throws.
= 188, 204, 194, 195, 187, 201, 199
The minimum length is,
= 188 + 204 + 194 + 195 + 187 + 201 + 199
= 1368
Let us assume,
Final length = x
So,
We can write,
( x + 1368 ) / 8 ≥ 195
x + 1368 ≥ 195 * 8
We can multiply the coefficient,
x + 1368 ≥ 1560
x ≥ 1560 - 1368
We can sum or difference the coefficient,
x ≥ 192
This is Inequality function.
Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤ or ≥.
Therefore,
The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.
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2.10 guessing on an exam: in a multiple choice exam, there are 7 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers. what is the probability that: (please round all answers to four decimal places)
A person can burn 120 calories in 15 minutes of running. Calculate how many
calories the person will burn in 1,5 hours.
Question 5.2 [2 marks]
So, if in 15 minutes, a person can burn 120 calories. In 1 minute, a person can burn 8 calories.
120 ÷ 15
8
15 | 120
120
0
8 CALORIES.NOW, how many calories a person burn in 1.5 hours?
FORMULA (HOURS TO MINUTES)60 × 1.5
60
X 1.5
300
60
90.0
90 MINUTES15 minutes x 8 calories = 120 calories (GIVEN)
90 minutes × 8 calories
90
x 8
720
ANSWER = A person can burn 720 calories in 1.5 hours.Answer correctly for 50 points.
Dont lie or i will report you.
Answer: 36 5/9
Step-by-step explanation:
12% of Cu in a 11.5 g coin
If a coin weighing 11.5 grams, has 12 Percentage of Cu content by mass in it, then the exact quantity of Cu in the coin in grams will be 1.38 grams.
As per the question statement, a coin weighing 12 grams, has 12 % of Cu content by mass in it.
We are required to calculate the exact quantity of Cu present in the coin in grams, from the above mentioned data.
To solve this question, we will simply need to calculate 12% of 11.5, and we will obtain our desired answer, that is,
12% of 11.5 = [(12/100) * 11.5] = (0.12 * 11.5) = 1.38 grams.
Hence, a coin weighing 11.5 grams, having 12 Percentage of Cu content by mass, will have 1.38 grams of Cu inside it.
Percentage: In mathematics, a percentage is a number or a ratio expressed as a fraction of 100 and often denoted using the percent sign, "%", to determine a certain part of one whole.Grams: As per the International System, the gram is a metric unit of mass being equal to one one thousandth of a kilogram.To learn more about Percentage and Grams, click on the link below.
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Twice a number plus 6 times the
number is 72. Find the number.
Answer:
The number is 9
Explanation:
So, the first thing you have to do is write out the problem. 2x+6x=72
Then, you combine like terms. 8x=72
Then, you have to isolate the variable, so you divide by 8 on both sides. 8x/8=72/8
Then, you have x=9, which is your answer.
Answer:
The number is 9.
Step-by-step explanation:
Framing the expression and solving:
Let the number be 'x'.
Twice a number = 2x
6 times the number = 6 *x = 6x
2x + 6x = 72
Combine the like terms,
8x = 72
Divide both sides by 8,
x = 72 ÷ 8
x = 9
Identify the correct equation of a line that passes through the points \displaystyle \left(-6,-10\right)(−6,−10) and \displaystyle \left(6,-2\right)(6,−2).
The equation of the line that passes through the points ( -6,-10 ) and ( 6,-2 ) is y = (2/3)x - 6.
How to determine the equation of a line from two points?The equation of line is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the data in the question;
Point 1( -6,-10 )
x₁ = -6y₁ = -10Point 2( 6,-2 )
x₂ = 6y₂ = -2First, we determine the slope "m" of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -2 - (-10) ) / ( 6 - (-6) )
m = ( -2 + 10 ) / ( 6 + 6 )
m = 8 / 12
Slope m = 2/3
Next, we determine the y-intercept "b"
y = mx + b
-10 = (2/3)(-6) + b
-10 = -12/3 + b
-10 = -4 + b
b = -10 + 4
b = -6
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (2/3)x + (-6)
y = (2/3)x - 6
Therefore, the equation of the line is y = (2/3)x - 6.
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Make and test a conjecture about the quotient of two negative integersThe quotient of two negative integers is anumber.= =14 =-21 =--21-5
Answer:
The conjecture is;
"The quotient of two negative integers is a positive rational number"
Explanation:
Recall that negative divided by negative is equal to positive;
[tex]\frac{-1}{-1}=1[/tex]for the given question;
[tex]\begin{gathered} \frac{-4}{-5}=\frac{-1\times4}{-1\times5}=1\times\frac{4}{5} \\ \frac{-4}{-5}=\frac{4}{5} \end{gathered}[/tex]secondly;
[tex]\begin{gathered} \frac{-14}{-7}=\frac{14}{7}=2 \\ \frac{-14}{-7}=2 \end{gathered}[/tex]Thirdly;
[tex]\frac{-21}{-5}=\frac{21}{5}[/tex]we can observe that all the quotient of two negative integers solved in the three questions above gave a positive rational number.
Therefore, The conjecture is;
"The quotient of two negative integers is a positive rational number"
6. Trapezoid ABCD with vertices A(-3, 6), B(0, 7),
C(1, 4), and D(-5, 2): (x,y) → (x + 4, y - 1)
A' (
B (
CC.
D’______
The new vertices of the trapezoid after translation:
A'( - 7, 8 ), B'( 7, 2 ), C'( - 1, 0 ), and D'( - 3, 4 ).
Consider the trapezoid ABCD with vertices as:
A( - 3, 6 ), B( 0, 7 ), C( 1, 4 ), and D( - 5, 2 )
When a figure is relocated from one place to another without changing its size, shape, or orientation, a transition known as translation takes place.
For example: ( x, y ) → ( x + 4, y - 1 )
Consider the point ( - 3, 6 ),
Point A when translated 4 units horizontally to the left and 2 units upward will be:
A( - 3, 6 ) → A'( - 3 - 4, 6 + 2 ) = A'( - 7, 8 )
Point B when translated to the right by 7 units and downwards by 5 units will be:
B( 0, 7 ) → B'( 0 + 7, 7 - 5 ) = B'( 7, 2 )
Point C when translated to the left by 2 units and downwards by 4 units will be:
C( 1, 4 ) → C'( 1 - 2, 4 - 4 ) = C'( - 1, 0 )
Point D when translated to the right by 2 units and upwards by 2 units will be:
D( - 5, 2 ) → D'( - 5 + 2, 2 + 2 ) = D'( - 3, 4 )
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Does this graph show a function? Explain how you know.
O A. Yes; there are no y values that have more than one x-value.
B. No; there are y values that have more than one x-value.
C. Yes; the graph passes the vertical line test.
D. No; the graph fails the vertical line test.
If a vertical line exists moved across the graph and, at any time, touches the graph at only one point, then the graph exists a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
What is meant by vertical line test?The vertical line test is a visual approach for assessing whether a curve in the plane accurately depicts the graph of a function by counting the points on the curve where vertical lines cross it. Consequently, any vertical line in the plane can only ever cross the graph of a function once.
Use the vertical line test to define whether or not a graph represents a function. If a vertical line exists moved across the graph and, at any time, touches the graph at only one point, then the graph exists a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Therefore, the correct answer is option D. No, the graph fails vertical line test.
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Cary's dad gave her $20.00 to spend on shoes at the mall. Cary spent 85% of the money onone pair of shoes. How much money does Cary's dad get back from his $20.00?
Answer:
$3
Step-by-step explanation:
20 - 20 (85%)
= 20 - 17
= 3
