The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]
To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.
When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:
[tex]$x = ky^3$[/tex]
where k is the constant of proportionality.
Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:
[tex]$y = \frac{m}{\sqrt{z}}$[/tex]
where m is the constant of proportionality.
Substituting the second equation into the first equation gives:
[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Since the value of x is 3 when z is 12, the equation can be written as:
[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]
Rearranging gives:
[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]
Substituting this value of k into the original equation gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Substituting z as 75 gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]
Simplifying gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]
Therefore, the value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].
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2. Rabbit Problem
When rabbits were first brought to Australia last
century, they had no natural enemies so their numbers increased
rapidly. Assume that there were 60,000 rabbits in 1865, and that by
1867 the number had increased to 2,400,000. Assume that the num-
ber of rabbits increased exponentially with the number of years that
elapsed since 1865.
Write the particular equation for this function,
b. How many rabbits would you predict in 1870?
c. According to your model, when was the first pair of rabbits in-
troduced into Australia?
According to the exponential function,
a) The function that models the given situation is f(rabbits) = 65000(√500/13)ˣ
b) The number of rabbits in 1870 is 6.5
c) According to your model, the first pair of rabbits introduced into Australia is 19th century
Here we have given that during the 19th century, here rabbits were brought to Australia.
And here we also know that the rabbits had no natural enemies on that continent, their population increased rapidly.
And we have given that there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.
Then according to the exponential function that could be used to model the rabbit population y in Australia in terms of x, the number of years since 1865 is to be determined.
Then the exponential function can be written as,
=> f(rabbits) = 65000(√500/13)ˣ
When we plot these on the graph then we get the graph like the following.
Through the graph we have identified that the value of rabbits in 1870 is 6.5
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SA triangle has side lengths of 11, 60, and 61. When using the converse of the Pythagorean theorem to determine if this is a right triangle, what is the value of c in the formula a² +b²=c²?
61
11
11²
60
Value of c is determined 61 unit.
What is right-angled triangle?
Triangle that has one angle 90 degree is called right-angled. In case of a right triangle the square of the largest side length is equal of the sum of the square of the other two side length.
what is the value of c in the above formula?
SA triangle has three side length 11-unit, 60 unit and 61 unit respectively.
The triangle is verified as a right-angled triangle by Pythagorean theorem.
And as the properties of a Pythagorean theorem the sum of the square of two side length is equal to the square of the largest side length.
if we say, one side length, a = 11 unit
second side length, b = 60 unit
the largest side length, c
now we will check,
√(11²+60²) = c² =√3721 = 61
the value of c = 61 unit.
hence, the SA is right-angled triangle.
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What does ∠ABC mean?
The measure of angle ABC means, vertex B lies in between A and C, whose value is to be obtained.
Explain the term angles?Whenever two straight lines as well as rays intersect at a single endpoint, an angle is created. The vertex of the an angle is the location where two points come together.
Measure or "the measure of" are indicated by the "m." Consequently, m1 and m2 stand for "the measure for angle one" and "this same measure of angle two," respectively.The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.A closed shape with both inner and exterior angles, a triangle is created by three line segments.When the values of the remaining two angles are known, then angle sum property is utilised to determine the measure of an uncertain interior angle.Thus, the measure of angle ABC means, vertex B lies in between A and C, whose value is to be obtained.
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How can these models be used to find the sum 2. 3 + 1. 94?
Enter your answers in the boxes.
The models show a total of 3 wholes,
tenths, and
hundredths. After regrouping 10 tenths into 1 whole, there are
wholes,
tenths, and
hundredths. Therefore, the sum of the numbers is
The sum of 2.3 and 1.94, that is 2.3 + 1.94 is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.
Therefore the answer is 4.24.
The first number, 2.3, can be broken down into 2 wholes and 3 tenths.
The second number, 1.94, can be broken down into 1 whole, 9 tenths and 4 hundredths.
To add the two numbers together, we first add the wholes: 2 + 1 = 3.
Next, we add the tenths: 3 + 9 = 12
Since we cannot have more than 9 tenths in a whole, we must regroup 12 tenths as 1 whole and 2 tenths.
We add the regrouped tenths to the number of wholes: 3 + 1 = 4
After regrouping, we have 4 whole and 2 tenths.
Now we add the hundredths: 0 + 4 = 4
Thus the sum is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.
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A correlation coefficient of is the amount of the variance in the dependent variable unexplained by the levels of the independent variable alleged to produce the effect under study. A correlation coefficient of 0.3 leaves what percent of the variance in the dependent variable unexplained by the independent variable
The percent of the variance in the dependent variable unexplained by the independent variable is 81%
What does correlation coefficient mean?A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.
9 percent of the variance is explained by the independent variable if the correlation coefficient is 0.3.
The correlation coefficient is therefore represented as follows:
[tex]r = 0.3[/tex]
The explained variance is found using the following formula:
[tex]R^{2} = r^{2} \\R^{2} = (0.3)^{2} \\R^{2} = (0.3)*(0.3)\\R^{2} = 0.9[/tex]
Thus, 81% of the variance remains unexplained by variations in the independent variable.
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A 40-liter fish tank is being filled with a faucet at a constant rate of 2 liters per minute. Before the faucet is turned on, the fish tank has a volume of 3 liters. The volume of water V in the fish tank is a function of time t. Time is measured in minutes and volume of water is measured in liters. Use the equation to complete the function table.
The volume of water in the fish tank for the given time value is 0, 5, 7, 9, 11, and 13 liters.
The equation V = 3 + 2t expresses a time function, which represents the volume of fish tank as a function of time. It means that after t time, volume V is given by the equation. In the given table. t = 0,1,2,3,4,5. Hence, the volume can be determined by substituting the value of t in the equation.
When t = 0
V = 3 + 2(0) = 3 liter
When t = 1
V = 3 + 2(1) = 5 liter
When t = 2
V = 3 + 2(2) = 7 liter
When t = 3
V = 3 + 2(3) = 9 liter
When t = 4
V = 3 + 2(4) = 11 liter
When t = 5
V = 3 + 2(5) = 13 liter
Note: The question is incomplete. The complete question probably is: A 40-liter fish tank is being filled with a faucet at a constant rate of 2 liters per minute. Before the faucet is turned on, the fish tank has a volume of 3 liters. The volume of water V in the fish tank is a function of time t. Time is measured in minutes and volume of water is measured in liters. Use the equation V = 3 + 2t to complete the function table.
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Is 3 3 an additive inverse?
3 and -3 are additive inverses because 3 + (-3) = 0.
Therefore, -3 is the additive inverse of 3.
Additive Inverse:
The additive reciprocal/ Inverse of a number is its inverse. When a number is added to the additive reciprocal, both numbers sum to zero. A simple rule is to change positive numbers to negative numbers and vice versa. We know that 3+ (-3) =0. So -3 is the additive reciprocal of 3, and 3 is the additive reciprocal of -3.
If the sum of two real numbers is 0, each real number is said to be the additive reciprocal of the other real number. Therefore, R + (-R) = 0. where R is a real number. R and -R are the additive reciprocals of each other. Example: 3/4 + (-3/4) = 0. where 3/4 is the additive reciprocal of -3/4 and vice versa. This is an example of the additive reciprocal of a fraction.
We have room temperature water in a bucket. Adding 1 liter of hot water raises the temperature of the entire bucket by a certain amount. Then add another liter of cold water. Opposite temperature water in the bucket will cancel out, resulting in a bucket of room temperature water. The same rules apply when taking the additive reciprocal of a number. The additive inverse property applies to both real and complex numbers.
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Elijah has some candy bars he wants to give away. He will give each person 8 of a candy bar. If he has 3 2- 4 candy bars to give away, how many people will get candy? Show your thinking.
Answer:
He got 32 candy, he give each person , 3,50. or give only tree each person. and he live 8 candy.
What is the degree of the polynomial x4 x3 5x 3?
The degree of the polynomial x4 x3 5x 3 is 4, since it is the highest degree of the polynomial.
What is polynomial?A polynomial is an expression that consists of variables, coefficients, and operators such as addition, subtraction, multiplication, and division. It is used to represent a mathematical relationship between variables. The degree of a polynomial is the highest power that appears in the expression, and it indicates the number of terms that make up the polynomial. Polynomials are usually written in descending order of powers, and the highest power is the leading term.
The highest degree of any polynomial is considered its degree. It is also referred to as the degree of the polynomial's leading term, since it is the highest power of x. In this case, the leading term is x4.
The degree of a polynomial can be used to classify the type of polynomial it is. For example, if the degree of a polynomial is 2, it is a quadratic polynomial. Similarly, if the degree of a polynomial is 3, it is a cubic polynomial.
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The table shows a bacterial population y after x days
days, X 0,1,2,3,4
Population,8,24,72,216,648
Write an exponential function that represents the population
Y=
The exponential function that represents the population is y = a*3^x.
What is exponential function?
The formula for exponential functions is y = ab^x, where b is the constant ratio and a is the starting point. Observe that as the value of x increases by a constant amount, the value of y increases by a common ratio by looking at a table of ordered pairs. All exponential functions share this trait.
We have to find the exponential function for the given table.
Since,
Exponential function = ab^x
where,
a is the starting point
b is the common ratio.
Here,
Common ratio = 24/8 = 72/24 = 216/72 = 648/216 = 3
So, the function becomes,
Exponential function = y = a*3^x
Hence, the exponential function that represents the population is
y = a*3^x.
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6) A paint store has 240 gallons of paint to pack into boxes. Each box can hold 4 gallons of
paint. Which of the following equations can be used to find the number of boxes the paint
store can pack?
Choose ALL the correct answers.
a) 240 =
b) 4x
÷
+4
= 240
_=240 +4
= 240
= 240 x 4
Answer: 347
Step-by-step explanation:
A teacher wants to check the typing proficiency of five students. She gives all of them the same passage to type. Which student is likely to be accurate in the typing test
Solving the question asked, we can say that it is more likely that the student uses a random finger for typing.
What is probability?Probability theory is a branch of mathematics that measures the probability that an event or statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating that the event is unlikely and 1 indicating that it is certain. Probability is a numerical representation of the likelihood or probability of a particular event occurring. Another way to express probability is a percentage from 0% to 100%, or 0 to 1. Percentage of events in the complete set that are equally likely to lead to a particular event compared to the total number of outcomes.
here,
Probabilistically, we can say that the student is using random fingers for typing. Students are more observant and therefore more likely to be accurate on typing tests.
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Complete question: A teacher wants to check the typing proficiency of five students. She gives the same passage to type to all of them. Which student is likely to be accurate at the typing test?
A) students who use one hand to type
B) the student who uses random fingers to type
C) student who types by looking at the keyboard
D) student who corrects errors by looking at the keyboard
E) student who uses macros for long words
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 293 students using Method 1 produces a testing average of 82.9. A sample of 282 students using Method 2 produces a testing average of 76.5. Assume that the population standard deviation for Method 1 is 7.97, while the population standard deviation for Method 2 is 6.66. Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places. g
The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 as calculated from the given data is 5.20 and 7.60.
The confidence interval for the difference of the population mean is calculated as,
CI = ( x1 - x2 ) +- z x √SD1²/n1 + SD2²/n2
= ( 82.9 - 76.5) +- 1.96 x √7.97²/293+ 6.66²/n2.82
=6.4 ± 1.199
=(v5.201 , 7.599)
therefore , approximately 5.20 , 7.60 .
Therefore , the confidence interval between them is found to be as , ( 5.20 , 7.60 ) answer.
The confidence interval is a calculation based on the statistics of the observed data that estimates the amount of uncertainty associated with a sample.
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Help
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
The short explanation of the effects of the above operations will not affect the inequality.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9, then we have
4 x 3 x 2 x 4 x 9 < 7 x 3 x 2 x 4 x 9
864 < 1512
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
11 + 3 + (-4) > - 2 + 3 + (-4)
10 > - 3
3. -2 ≤ -2 Subtract 6 from both sides, then 8, and then 2
-2 - 6 - 8 - 2 ≤ -2 - 6 - 8 - 2
- 18 ≤ - 18
4. -4 < 8 Divide both sides by -4, then by -2
- 4 / (-4) > 8 / (-4)
1 / (-2) > - 2 / (-2)
- 1/2 < 1
The short explanation of the effects of the above operations will not affect the inequality.
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To serve 1 person at a restaurant it takes 10 minutes. To serve 5 people at a restaurant it takes 18 minutes. How many minutes will it take to serve 8 people
Help me
Please help me with both issues
Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards
What is MultiplicationMultiplication is an arithmetic operation in which a number (known as a multiplicand) is multiplied by another number (known as a multiplier) to produce a product.
In this problem, we will need to use of some mathematical operators to solve the problem
1.
He currently has 216 cards, but he needs 15 sets of cards.
1 set of card = 72 cards
Let's calculate the number of sets he currently has.
1 set of card = 72 cards
x set = 216 cards
cross multiply both sides and solve for x.
x * 72 = 216 * 1
x = 216 / 72
x = 3 sets
He currently has 3 sets of cards.
Since he wants 15 sets of cards, we will need 12 more set of cards.
The number of cards can be calculated by multiplying 12 by 72
Number of cards = 12 * 72 = 864
He needs 864 more cards.
2.
1 set of card = $27
1 set = 72 cards
But she's bringing $9 to join, we can calculate the ratio of cards she will get.
1 / 27 = x / 9
x = 9 / 27
x = 1/3
She will get 1/3 of the cards bought which will be
72 * 1/3 = 24 cards
She will get 24 cards
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Why is Avogadro's number 6.02 x10 23?
The value of Avogadro's number is 6.02214076 × 10²³. The ratio of the actual mass of an element to its atomic mass is always constant which is known as Avogadro's number.
What is one mole?
One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.
The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
It shows how many atoms or molecules make up one gram of an element's or compound's molecular weight. The value is "6.022 × 10²³" when the atomic mass of an element is divided by the actual mass of its atom.
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The histogram shows the ages of passengers riding in a tour van. How many passengers are under 45 years of age? Enter your answer as a number, like this: 42
Answer:
12
Step-by-step explanation:
3 + 4 + 5 = 12
In ΔDEF, f = 5 cm, m∠E=79° and m∠F=75°. Find the length of d, to the nearest 10th of a centimeter.
Using sine and cosine rule, the length of d in the triangle is equal to 4.5cm
What is Sine RuleThe sine rule is a mathematical formula used to calculate the lengths of the sides and angles of any triangle when given two angles and one side or two sides and one angle. It is also known as the law of sines.
To find the length of d, we have to find the length of E.
Using sine rule;
f / sin F = e / sin E
5 / sin 75 = e / sin 79
e = 5sin79 / sin 75
e = 5.7cm
To find the length of d, we have to find the angle D by using the sum of angle theorem.
m∠ E + m∠ F + m∠ D = 180°
79 + 75 + m∠ D = 180
m∠ D = 180 - 154
m∠ D = 26°
Using cosine rule
d² = e² + f² - 2efCosD
d² = 5.7² + 5² - 2(5.7)(5)cos26
d² = 20.615598
d = √20.615598
d = 4.5cm
The length of side d is 4.5cm
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what if 5464x43214x-532
Answer:
-1.256165295×10×10×10×10×10×10×10×10×10×10×10
Step-by-step explanation:
negative changes everything
A et of 3 card, pelling the word ADD, are placed face down on the table. Determine P(D, D) if two card are randomly elected with replacement. One third
two third
two ixth
four ninth
The probability of the two cards being D and D, P(D, D), is 4/9. The correct option is: 4/9.
What is probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.
Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.
Calculating probability of selecting a card:
From the question, we are to determine the probability of selecting two cards with D and D
From the formula for probability, we have that
P(D) = Number of favorable outcomes to D / Total number of possible outcomes
From the given information,
Number of favorable outcomes to D = 2
Number of possible outcomes = 3
Thus,
P(D) = 2/3
Then,
The probability of selecting two cards that have D and D with replacement is
P(D, D) = P(D) × P(D)
P(D, D) = 2/3 × 2/3
P(D, D) = 4/9
Hence, the probability is 4/9.
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What is the name of longest side of triangle?
Answer: Hypotenuse
Step-by-step explanation:
The Hypotenuse is known as the longest side of a triangle.
helppp me pleaseee i really need it
23310
Step-by-step explanation:
I actually calculated it aka 259000×9%
Carlos bought 515 Euros for his holiday to Germany. He spent £ 412 to obtain these Euros. How many Euros would Carlos have obtained if he spent £500 ?
Carlos needs a total of 400 Euros for buying 500 Euros.
The total amount available with Carlos for his holiday to Germany = 515 Euros
Amount spent to obtain these 515 Euros = £ 412
As it is clear that for buying 515 Euros he spent 412 Euros.
So, we will first find the Euros spent on buying 1 Euro.
For that, we will use Unitary Method:
So, the total Euros spent for buying 1 Euro will be = (412/515) = 0.8
So, for finding the total Euros spent for obtaining 500 Euros we will simply multiply the total Euros needed by the Euro spent for buying 1 Euro.
Thar will be equal to (0.8 * 500) = 400 Euros.
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y=-5 8x+5y=-17 substitution
[tex]8x+5y=-17[/tex] when y is -5
Substitute for y with given value:
[tex]8x+5(-5)=-17[/tex]
[tex]8x-25=-17[/tex]
Add 25 to both sides:
[tex]8x-25+25=-17+25[/tex]
[tex]8x=8[/tex]
Divide both sides by 8:
[tex]\dfrac{8x}{8} =\dfrac{8}{8}[/tex]
[tex]\fbox{x = 1}[/tex]
Is gram mole equal to mole?
No, one mole is not equal to one gram. For an object, the mole and gram numerical values differ.
1 gram, what is it?
One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.
The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.
A mole's relationship to a gram is
The product of the number of Moles of an object to its atomic weight equals one gram.
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A drawer contains 9 red socks and 11 blue socks. It is dark and you are trying to grab a matching pair. How many socks do you need to take out to be sure of a matching pair
If we pull 3 socks then there is a 100% possibility that 2 socks will be of same colour.
What is Probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportional ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The likelihood that a specific occurrence will occur. (2): the proportion of the total number of available outcomes to the number of outcomes in an exhaustive set of equally probable options that result in a certain occurrence.
There are 9 red socks and 11 blue socks
So if we find a red/blue sock in the first turn,
The second can be both blue or red so we can't be sure it will be matching or not.
At third turn any one colour of sock will match with any of the two already pulled before if they are different.
So, if we pull 3 socks then there is a 100% possibility that 2 socks will be of same colour.
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Which techniques can be used to evaluate the expression 12. 75÷1. 5? Select all that apply.
The division technique can be used to evaluate the given expression
12.75÷1. 5
The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are (÷) and (/).
“p divided by q” can be written as: (p÷q) or (p/q).
The method of verification can be expressed as:
Dividend = (Divisor × Quotient) + Remainder.
The given equation is:12.75÷1.5
We'll first write the above decimal numbers in fractional form.
12.75÷1.5
1275/100÷15/10
2. Now we'll divide it further.
⇒1275/100÷15/10
⇒1275/100×15/10
⇒1275/10×15
⇒225/10×3
⇒88/10
3. And finally, we'll write our quotient in decimal form.
⇒88/10
⇒8.8
ㅤ
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Frankie enlarged the size of a rectangle to a height of 20 cm. What is the new width if it was originally 2 cm wide and 4 cm tall
Answer: 10
Step-by-step explanation:
4 to 20 which is times by 5 so 2 times by 5 is 10
Solve for x. The triangles in each pair are similar.
Apply arithmetic operations on both sides of the equation to move the variable to one side and all other values to the opposite side.
How Do You Solve for x?Let's begin with a basic equation: x + 2 = 7.
How may x be obtained on its own?
x + 2 - 2 = 7 - 2 x = 5 after deducting 2 from both sides.
Put the solution, x = 5, back into the equation to confirm it. We get 5 + 2= 7.
Since LHS = RHS
In the triangle, find x.
Use triangle properties or the Pythagorean theorem to find the value of x, the unknown side or angle in a triangle.
Let's use an example to better understand how to solve for x in a triangle.
Using the Pythagorean theorem, we obtain AC2 = AB2 + BC2 where x2 = 72 + 242 x = 49 + 576 x = 625 x = 25 units.
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