Yes, the rate 4.8 laps every 8 minutes; 3.6 laps every 6-minute form a proportion.
A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:
1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
4.8 lap every 8 minutes will be equal to (4.8/8) = 0.6 lap a minute.
3.6 lap every 6 minutes will be equal to (3.6/6) = 0.6 lap in a minute.
Here, as the value of the ratio of both the quantities are same so the given values are said to be in Proportion.
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What are the 3 possible solutions when solving a system of equations?
Three possible solutions when solving a system of equation are: one solution, no solution, and infinite solutions.
The 3 possible solutions of a system of equations are:
- Unique or one solution
- Infinite solutions
- No solution
In case of a system of linear equations, we can determine the type of its solution as follows:
- If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.
- If the slopes are the same but the equation of the lines are different, the lines are parallel, hence they will not intercept. Therefore, there is no solution.
- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
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Does 3 3 have a solution?
Given equation 3 = 3 is an identity, so it has infinite solutions.
Consider the given mathematical equation 3 = 3
We need to check whether the given mathematical equation has solution or not.
We know that a statement 3 = 3 's true no matter what.
We can observe that for given statement 3 = 3, there's no variable in sight.
This means, 3 = 3 must has infinite solutions.
We know that an equation which is always true, no matter what values we substituted is called as an identity.
This equation is an identity, all real numbers are solutions.
Therefore, the equation 3 = 3 have infinitely many solutions.
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If an object is propelled upward from ground level with an initial velocity of 80. 1 feet per second? It’s height h in feet t seconds later is giving by the equation h= -16ft+ 80. 1t after how many seconds does the object hit the ground
The object will hit the ground after 5.01 seconds.
When an object is propelled upward from ground level with an initial velocity of 80.1 feet per second then its height h in feet t seconds later is giving by the equation,
h= -16t^2+ (80.1)t
When the object hit the ground, the height of the object h would be zero.
To find: time (t) when h = 0
Substitute h = 0 in given equation.
h = -16t^2+ (80.1)t
0 = -16t^2+ (80.1)t
16t^2 - (80.1)t = 0
t (16t - 80.1) = 0
t = 0 or 16t - 80.1 = 0
t = 0 OR t = (80.1)/16
t = 0 OR t = 5.01
Therefore, it will hit the ground after 5.01 seconds.
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I need to factor completely to get an answer for
r²+3r-28
I need to get factors in parenthesis like (r +/- #) (r +/- #)
I need it before tomorrow
Answer:
(r + 7)(r - 4) = 0
Step-by-step explanation:
r² + 3r - 28 = 0
(r + 7)(r - 4) = 0
r = -7, 4
How do you find the hypotenuse of a 45 45 90 triangle?
The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.
The hypotenuse of a 45 45 90 triangle is calculated as the square root of the length of the leg.
We plug the known length of the leg into our 45-45-90 theorem formula:
Hypotenuse = leg * (√2)
Properties of 45-45-90 triangles :
To point out the 45-45-90 special right triangle, check for these three identifying properties:
The polygon is an isosceles right triangle.The two side lengths are congruent, and their opposite angles are also congruent.The hypotenuse (longest side) is the length of either leg times the square root (sqrt) of two, √2.Read more about the isosceles triangle:
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Latifa writes down a number
She says
If i find the cube root of that number and then quadruple the answer,I get 16
What number did Latifa write down?
Answer:
64?
Step-by-step explanation:
Basically the idea is we suppose the number she thinks of is "x"
She says that if she cube roots the number and then quadruples it (means multiply by 4 I think) she gets 16. We set this up as equation below:
[tex]4\sqrt[3]{x} = 16\\\sqrt[3]{x} = 4\\x = 4^{3}\\ x= 64[/tex]
This is my best guess, not totally sure sorry
a. Kiran tried to double this recipe. He used 2 cups of
yogurt, 6 tablespoons of peanut butter, 5 teaspoons of
chocolate syrup, and 4 cups of crushed ice. He didn't
think it tasted right. Describe how the flavor of Kiran's
recipe compares to Clare's recipe.
Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.
Define unitary method.A single or distinct variable is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
Here,
Given :This recipe was doubled by Kiran. He used 4 cups of crushed ice, 6 tablespoons of chocolate syrup, 6 tablespoons of peanut butter, and 2 cups of yogurt.
1. Kiran's smoothie would be more chocolatey than Clare's. All ingredients are doubled, but there is an extra teaspoon of chocolate syrup in his smoothie.
2. Answers vary. Sample response: he should use 4 teaspoons of chocolate syrup instead of 5.
Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.
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The area of the triangle is no more than 30 square inches. Right and solve inequality that represents a.
(HELP ASAP!)
The answer is a ≤ 30.
An inequality is a mathematical expression that compares two values or expressions using an inequality operator. In this case, the inequality would be a ≤ 30. This means that the area of the triangle must be less than or equal to 30 square inches.
This can be solved by finding the area of the triangle. To do this, we need to know the lengths of the sides of the triangle. Suppose we have sides p, q, and r. Then the area of the triangle can be found using the formula:
a = 1/2 × b × h
where q is the base of the triangle and r is the height. To ensure that the area of the triangle is no more than 30 square inches, the inequality must be satisfied. That is, 1/2 × b × h ≤ 30. This inequality can be rewritten in terms of the side lengths by substituting 1/2 × q × r for h. This gives us a ≤ 30.
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You have a circle-shaped mirror in your bedroom. To figure out where to hang it, you must find the diameter of the circle. You know the radius is 34 centimeters. How long is the diameter in inches? (Diameter = 2xradius) ( 1in = 2.54cm)
A. 26.8 inches
B. 86.4 inches
C. 172.7 inches
D. 13.4 inches
The diameter of a given circle, measured in inches, is 26.8 inches, according to the solution.
The correct option is A.
What makes it called a circle?A circle is a circular shape that can be created by tracing a moving point in a plane so that its distance from thea specified point remains constant. From the Greek word kirks, which means hoop or ring, comes the term circle.
How can a circle be so strong?Circular shapes give us a feeling of completion, assurance, and harmony from a psychological perspective. They stand for the concepts of oneness, integration, and wholeness. In addition to lacking angles, they also lack a beginning and an end. Because of this, a circle is a strong, yet secure, kind, and benign element.
According to the given information:Given,
Radius of circle= 34cm=13.36 inches
Diameter= 2x radius
Diameter = 26.8 inches
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What should be done to these equations in order to solve a system of equations by elimination?
To solve the problem of a system of equations by elimination, we can start with both equations in standard form. Then we can decide which variable will be easier to eliminate.
How can we decide? We want to have the coefficients of any one of the variables be opposites so that we can put the equations together and eliminate that variable.
To solve a simultaneous equation by using the elimination method, you eliminate any one variable first.
Before you can do that, the coefficient of one of the variables in the two equations must be the same.
From the given questions, for the coefficient of one variable in the two equations to be the same, we multiply the first equation by 3.
If we can do this, the coefficient of Y in the two equations will now be 3.
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A certain library charges a late fee of $0.05 for each day that a book is
late. Last month, 158 people returned books that were 7 days late.
This month, 40 less people than last month will return books that are 7
days late. How much will the library collect in late fees this month for
returned books that are overdue by 7 days?
Answer: $41.3
Step-by-step explanation:
this month late = 158 - 40 = 118
7× $0.05 = $0.35
118 × $0.35 = $41.3
What is the value of 5 by 2?
The value of 5 divided by 2 is 2.5.
Therefore the answer is 2.5.
When dividing 5 by 2, we are trying to find out how many times 2 can fit into 5. The answer is 2 with a remainder of 1, this is why it can also be written as 2 and 1/2.
When dividing 5 by 2, we can also write the result as a fraction, in this case, it is 2 and 1/2 or 2.5 in decimal form. It is the exact same thing as 2.5, just represented in a different way.
It's important to note that, in general, dividing integers will give a decimal number. If you want the result to be a fraction, you will have to express it as such.
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Select all questions that depicts one of the properties of exponents
Answer: 1st, 4th, and 5th choices
HELPPP 1. Write an equation of the ellipse with foci (0,14) and co-vertices at (±4,0).
The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].
Define ellipse.An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.
[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]
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Is maths hard or easy?
Maths can be hard or easy, depending on the level of difficulty and the individual's experience and understanding numbers.
Maths is a subject that can range in difficulty depending on the level of complexity and the individual's experience and knowledge. Some people may find it easy, while others may find it difficult. In the end, it all depends on the level of understanding and the amount of effort put into learning and practicing.
Maths can be hard or easy, depending on the level of difficulty and the individual's experience and understanding numbers
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Answer:
BOTH!
Step-by-step explanation:
See math can be easy or hard. It all depends on YOU. The equation itself isn't hard at all. Mybe a little more work to put in. but its your brain that tells you comething is too challenging or too hard. Now if you are a straight A students and you love math then ofcource your going to be like this is easy!
Rewrite in simplest rational exponent form. Show each step of your process
The final answer is 4x, which is the simplest form of expression.
What is the rational exponent?
A rational exponent is an exponent that is in the form of a ratio of two integers, such as a/b where a and b are integers and b is not equal to zero.
To rewrite the expression in simplest rational exponent form, we can first simplify the radicals and then combine any like terms. Here are the steps to simplify the given expression:
4√x* √x = 4 * 1 √x * √x = 4 * x^(1/2) * x^(1/2) = 4 * x^( (1/2)+(1/2) ) = 4 * x^(1)
x^(1) = x
So, the expression in simplest rational exponent form is 4x
x * 4x = 4x
Notice that 4 and x are in the same radical which means 4 is a coefficient of x.
Therefore, 4√x * √x can be written as 4x, which is in the simplest form.
hence, the final answer is 4x, which is the simplest form of expression.
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As a 11 1/3 inch candle burns down, its height decreases 1/6 inch each hour. How many hours does it take for the candle to burn completely?
SHOW YOUR WORK
The number of hours after which the candle is burned completely is
68 hours.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Candle height = 11(1/3) inches
Each hour the height decreases by 1/6 inch.
Now,
The equation to find the number of hours x after which the candle is burnout is 11(1/3) - (1/6)x = 0
Solve for x.
11(1/3) - (1/6)x = 0
11(1/3) = (1/6)x
34/3 = (1/6)x
x = (34 x 6) / 3
x = 34 x 2
x = 68
Thus,
After 68 hours the candle is completely burnt.
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What is a 69 sided shape called?
A 69 sided shape called"Hexacontakaienneagon".
Naming a polygon by its number of sides requires that we know the appropriate:
3=tri, 4=tetra, 5=penta, 6=Hexa, 7=hepta, 8=octa, 9=Nona or ennea, 10=deca,11=hendeca,12=dodeca,13=triskaideca,14=tetradeca,15=pentadeca,16=hexadeca,17=heptadeca,18=octadeca,19=enneadeca,20=icosa
For polygons with 3 through 20 sides, simply add "gon" to the prefixes at the left.
For more than 20 sides, we "construct" the name by using so-called combining prefixes:
For Tens Digit:
20=icosi,30=triaconta,40=tetraconta,50=pentaconta,60=hexaconta,70=heptaconta,80=octaconta,90=enneaconta
for One's Digit:
1=hena,2=di,3=tri,4=tetra,5=penta,6=hexa,7=hepta,8=octa,9=ennea
60 and 9
hexaconta kai ennea
As per the given information, 69 is defined as "Hexacontakaienneagon".
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What does 5a+10a equal to?
Answer:
15a
Step-by-step explanation:
5a + 10a = 15a
Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren
By probability, she will not receive a phone call from any of her grandchildren after 146 days
How does probability affect our lives?In those circumstances, probability helps in assessing the likelihood of an event. Probability plays a significant role in daily life. political strategy analysis, blood type determination, sports and gaming strategies, insurance buying or selling, online shopping, and online gaming.
There is a [tex]\frac{2}{3}[/tex] chance that the first child won't call, a [tex]\frac{3}{4}[/tex] chance that the second child won't call, and a [tex]\frac{4}{5}[/tex] chance that the third child won't call on any given day. There is a [tex]\frac{2}{3} *\frac{3}{4} * \frac{4}{5} = \frac{2}{5}[/tex] chance that no child calls her on a randomly selected day.
When we consider a sample of 360 days, in particular, this "unrigorous" reasoning becomes rigorous due to linearity of expectation; over the first 360 days, 360 * 2/5 = 144 days will pass without a phone call. Now, we just check the remaining days. On days $361 and $362, no one calls her. On days 363 and 364, she receives calls from children every three and four days, respectively. On day 365, she receives calls every five days. Therefore, to get our answer of 146, we two more days in 144.
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Don’t know just need help with answer
The length AB is 15.
What is length ?
Distance is measured by length. The quantity of length has the dimension of distance in the International System of Quantities. Most measurement systems choose a base unit for length from which all other units are derived. The metre serves as the fundamental unit of length in the International System of Units.
The definition of length is the measurement or extent of something from end to end. In other terms, it is the largest of the two or the highest of the three dimensions of geometrical forms or objects.
In contrast to width, which is used to gauge an object's width from side to side, length is used to gauge an object's length from one end to the other.
As it is a isosceles the two sides are equal
5x = 4x + 3
x = 3
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4. Write an equation of the circle that has a diameter with endpoints (12, 3) and
(-18, 3). (Lesson 6-4)
x² + y² + 6x - 6y - 207 = 0 is the equation for the circle whose circumference has endpoints at (12, 3), and (-18, 3).
What is the equation of a circle?We are aware that a circle's general equation is (x - h)2 + (y - k)2 = r2, where (h, k) is its center and r is its radius.
Therefore, to bring the constant term to the righthand side of the equation, add 21 to both sides.
So, the midpoints of the diameter are determined by the coordinates of the circle's center since the endpoints of the diameter are (x1, y1) = (12,3) and (x2, y2) = (-18,3).
The midpoints are so:
x = (x₁ + x₂)/2 = (12 + (-18))/2 = (12 - 18)/2 = -6/2 = -3 and
y = (y₁ + y₂)/2 = (3 + 3)/2 = 6/2 = 3.
Consequently, the circle's center's coordinates are (-3, 3)
The circle's diameter:
The circle's radius is [(x1 - h)2 + (y1 - k)2], where:
(x₁, y₁) = coordinates of end of diameter = (12, 3) and
(h, k) = coordinates of center of circle = (-3, 3)
As a result, when we enter the values of the variables into r, we get:
r = √[(x₁ - h)² + (y₁ - k)²]
r = √[(12 - (-3))² + (3 - 3)²]
r = √[(12 + 3)² + 0²]
r = √[15² + 0²]
r = √15²
r = 15
The formula for the circle:
The formula for a circle with a center (h,k) is: (x - h)² + (y - k)² = r²
By changing the variables' values in the equation, we arrive at:
(x - h)² + (y - k)² = r²
(x - (-3))² + (y - 3)² = 15²
(x + 3)² + (y - 3)² = 15²
x² + 6x + 9 + y² - 6y + 9 = 225
x² + 6x + y² - 6y + 9 + 9 - 225 = 0
x² + y² + 6x - 6y - 207 = 0
Therefore, x² + y² + 6x - 6y - 207 = 0 is the equation for the circle whose circumference has endpoints at (12, 3), and (-18, 3).
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A pair of shoes is on sale for 20% off they now cost 50$
The original price of the pair of shoes is $62.5.
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
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Original price = 100%
Offer price = $50
Offer = 20%
Now,
80% = 50
Multiply 100/80 on both sides.
100% = 100/80 x 50
100% = $62.5
Thus,
The original price is $62.5.
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The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?
When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.
Properties of 9-divisible numbersA number is itself divisible by nine if the total of its digits is also nine digits.
Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine.
By utilizing the aforementioned attribute, we can
3 + A +A +1 = 9, OR 18, OR 27
4 + 2A = 9, OR 18, OR 27
using 18
2A = 18 - 4
2A = 14
A = 7
therefore we can say that the number is 3771
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If Mr. Brust can bambam 8 jamjams in 12 whamwhams, the how many jamjams can he bambamin 33 whamwhams? (Yes, I know this is weird)
Answer: 22 jamjams in 33 whamwhams
Step-by-step explanation:
33 ÷ 12 = 2.75 = 12 x 2.75 = 33
2.75 x 8 = 22
Answer:
Mr. Brust can bambam 22 jamjams in 33 whamwhams.
Step-by-step explanation:
Mr. Brust can bambam 8 jamjams in 12 whamwhams.
Mr. Brust can bambam x jamjams in 33 whamwhams.
Use a proportion.
8/x = 12/33
12x = 8 × 33
x = 8 × 33/12
x = 12
Answer:
Mr. Brust can bambam 22 jamjams in 33 whamwhams.
lamar bought v vanilla cupcakes and 8 chocolate cupcakes for the party write an expression that shows how many cupcakes lamar bought in all
Answer:
8 + v
Step-by-step explanation:
assuming Lamar didn't buy any other cupcakes outside of the chocolate and vanilla ones mentioned, the expression that gives you the total amount of cupcakes bought for the party is 8 + v. since you don't know the number of vanilla cupcakes Lamar bought, it is represented as the variable v in this problem. Then just add 8 and the variable v together. hope this helped :]
4 Siobhan and Ralph shared £700 in the
ratio 2:3.
Siobhan gave a quarter of her share to Karen.
Ralph gave a fifth of his share to Karen.
What fraction of the £700 did Karen receive?
Therefore ,the solution to the given problem of proportion comes out to be karen got £70.
What is a proportion?The rule of three is used to link the measures because a proportion is a fraction of a total amount. It is possible to construct equation or relations between variables that are either direct (when both rise or decrease) or inverse proportional (when one increases and the other declines, or vice versa) in order to determine the necessary measures in the situation.
Here,
Given :
Siobhan and Ralph shared £700 in the
ratio 2:3.
Thus,
280 / 420 = 2/3
Thus,
Siobhan and Ralph has £280 and £420 respectively.
and Siobhan gave a share of quarter to karen :
So,
280/4 =70
Therefore ,the solution to the given problem of proportion comes out to be karen got £70.
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How do you check whether 7 3x is a factor of 3x3 7x?
7 + 3x is not a factor of expression 3x^3 + 7x
Consider given expression 3x^3 + 7x
Let f(x) = 3x^3 + 7x
Assume that 7 + 3x is a factor of 3x^3 + 7x
This means, 7 + 3x = 0 would be the root.
x = -7/3
If x = -7/3 is root of polynomial f(x) = 3x^3 + 7x then f(-7/3) must be equal to 0
We find the value of given polynomial for x = -7/3
f(x) = 3x^3 + 7x
f(-7/3) = 3(-7 / 3)^3 + 7 (-7 / 3)
f(-7/3) = (3 × (-343)) / 27 + (-49 / 3)
f(-7/3) = [(-343) - 147] / 9
f(-7/3) = -490 / 9
f(-7/3) ≠ 0
Since f(-7/3) ≠ 0, x = -7/3 is not root of polynomial f(x) = 3x^3 + 7x
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Can you help me with this
Han says that the value of the 7 in 735,208 is 10 times the value of the 7 in 137,342. Do you agree with Han
Han is wrong , we do not agree with him. The value of the 7 in 735,208 is not the 10 times the value of the 7 in 137,342.
The value of 7 here refers to the place value of 7 , in 735,208 7 is at lakhs place whereas in 137,342 , 7 is in thousandth place .
Therefore , Han is wrong as because if we will the 7 in 137,342. when multiplied by 10 will go to the ten thousandth place and not the lakh place.
The place value is a measure which is used to represent the position of each digit in a number . Based on their position in the number, digits are assigned place values such as ones, tens, hundreds, thousands, ten-thousands, and so on. For example, 1 in 512400 has a place value of ten thousands, i.e. 10000.
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