the sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. the square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21.
Answers
a = 5 and a = 4 are the sum of both digits, of either of two two-digit numbers.
What is square number in math?
When a number is multiplied by itself, the result is a square number. For instance, 25 is a square number since it is composed of 5 lots of 5, or 5 × 5. This is also known as "five squared," or 52. Because it is 102 (10 x 10, or "ten squared"), the number 100 is likewise a square.This can also be solved algebraically. Let the 2 digits be a and b, going left to right. The number itself is then
N = 10a + b. And it's given that a + b = 9, and a2 - ab + b2 = 21. Substitute for b = 9 - a, combine all terms of a2 and a, and you get
3a2 - 27a + 60 = 0. Divide by 3
a2 - 9a + 20 = 0. Factor
(a - 5)(a - 4) = 0. So the roots are a = 5 and a = 4.
The actual numbers N are 54 and 45.
The digits can be changed since the equations including only a and b are symmetric. (If a = 5, then b must be 4; inverse)
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Related Questions
b)
Simplify each of the following as far as possible:
1) 5a-3a+2a
2) -4x²x3x²
3) (3x¹)³
4) 5-3(x+3)+6x
Answers
The simplified expression after simplification is ,
1) 4a
2) -12\(x^5\)
3) 27\(x^3\)
4) 3x-4
What is simplification of expression?
The process of solving a math problem is simply known as simplifying an expression. In essence, you aim to write an expression as simply as you can when you simplify it. By the time you're done, you shouldn't have any more addition, subtraction, multiplication, or division to do. Making anything simpler is the definition of simplify. Reducing an expression, fraction, or mathematical problem to its simplest form is known as simplification. Using calculations and solving the problem makes it simple.
Here the given expressions are,
1) 5a-3a+2a
=> (5-3+2)a
=> 4a
2)-4\(x^2\).x.3\(x^2\)
=> -4*3\(x^(2+1+2)\)
=>-12\(x^5\)
3)\((3x^1)^3\)
=> \(3^3.x^3\)
=>27\(x^3\)
4)5-3(x+3)+6x
=>5-3x-9+6x
=>3x-4
There fore the simplified expressions are
1) 4a
2) -12\(x^5\)
3) 27\(x^3\)
4) 3x-4
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Lessons > Review for Test 4What is the equation of the following graph?AOA. f(1) = 4(4)B. f(t) = 4(2-)C. f(x) = {(4)
Answers
We will have the following:
We can see that the function follows a path of exponential decay, so the expression that models it is:
\(f(x)=4(\frac{1}{2})^x\)The half price of helium-5 is 7.6 X 10 to the power of negative 22 seconds and the half-life helium -9 is 7 x 10 to the power of negative 21-second approximately how many times greater is the half life of helium and -9 then that of helium -5
Answers
Answer:
Approximately 9.211 times
Step-by-step explanation:
Given
\(x = 7.6 * 10^{-22}s\) --- half life of helium-5
\(y = 7 * 10^{-21}s\) --- half life of helium-9
Required
How many times greater is y than x
To do this, we simply divide y by x
\(\frac{y}{x} = \frac{7 * 10^{-21}s}{7.6 * 10^{-22}s}\)
\(\frac{y}{x} = \frac{7 * 10^{-21}}{7.6 * 10^{-22}}\)
Apply law of indices
\(\frac{y}{x} = \frac{7 * 10^{-21--22}}{7.6}\)
\(\frac{y}{x} = \frac{7 * 10^{-21+22}}{7.6}\)
\(\frac{y}{x} = \frac{7 * 10}{7.6}\)
\(\frac{y}{x} = \frac{70}{7.6}\)
\(\frac{y}{x} = 9.211\)
Complete the question. Show your work and answer on the page. Find the sum. Write your answer in scientific notation
Answers
The given expression is :
\((7.2\times10^{-6})+(5.44\times10^{-6})\)The multilpy are same So, we take the 10^(-6) Common
\(\begin{gathered} (7.2\times10^{-6})+(5.44\times10^{-6}) \\ (7.2\times10^{-6})+(5.44\times10^{-6})=10^{-6}(7.2+5.44) \\ (7.2\times10^{-6})+(5.44\times10^{-6})=10^{-6}(12.64) \\ (7.2\times10^{-6})+(5.44\times10^{-6})=12.64\times10^{-6} \end{gathered}\)Answer:
\((7.2\times10^{-6})+(5.44\times10^{-6})=12.64\times10^{-6}\)
If the original quantity is 8 and the new quantity
is 2, what is the percent decrease?
Answers
If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
How did we figure this out?
For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:
\(\boxed{8-2=6}\\\boxed{6/2=3}\)
We are going to take that 25% and multiply it with 3 to get are final answer.
What is the missing number of 25 and 3?\(\boxed{25*3=75}\\\boxed{So,2=75}\)
Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
Solve for x.. 3(x-8) = 29.7
Answers
Answer:
x = 17.9
Step-by-step explanation:
\(3x-24=29.7\\ Distribution Property\\\\3x=53.7\\\\Adding 24 to both sides\\\\x=17.9\\Divide by 3 to both sides\\\\Hope this helps:)\\\)
\(\text {Hello! Let's Solve this Equation!}\)
\(\text {The First Step is to Multiply 3 in the Parentheses:}\)
\(\text {3*x=3x}\\\text {3*8=24}\)
\(\text {Your new Problem is: 3x-24=29.7}\)
\(\text {The Next Step is to Add 24:}\)
\(\text {3x-24+24=29.7+24}\\\text {=53.7}\)
\(\text {Your new Problem is: 3x=53.7}\)
\(\text {The Final Step is to Divide 3:}\)
\(\text {3x/3=53.7/3}\)
\(\text {Your Answer would be:}\)
\(\fbox {x=17.9}\)
\(\text {Best of Luck!}\)
Find the x intercepts of x-4 over x2+4x+3
Answers
Answer:
B
Step-by-step explanation:
a fraction is equal to 0 when the numerator is 0
x - 4 = 0
x = 4
The correct answer is x=4.
Step-by-step explanation:
When the numerator is 0, a fraction is equal to 0.
x - 4 = 0
x = 4
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Suppose y varies inversely with x, and y=-5 when x=21. What is an equation for the inverse variation?
Answers
Answer:
y = - 105/x----------------------
General equation for inverse variation is:
y = k/x, where k- coefficient of variationFind the value of k by substituting values of x and y:
- 5 = k/21k = -5*21k = - 105Substitute the value of k to get the equation:
y = - 105/xFind the greatest common divisor for 21 and 10
Answers
Answer:
There are no common divisors
Step-by-step explanation:
Answer:
the greatest common divisor between 21 and 10 is 1
Step-by-step explanation:
factors:
10: 1, 2, 5, 10
21: 1, 3, 7, 21
hopefully this helps :)
A right rectangular prism has a surface area of 348in. . Its height is 9in., and its width is 6in. . Which equation can be used to find the prism’s length, p, in inches?
Answers
The equation that can be used to find the prism's length is 348 = 30p + 108
What is surface area of prism?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of prism is expressed as;
SA = 2B + pH
where B is the base area , p is the perimeter of the base and h is the height of the prism.
Since the prism is cuboid, then
SA = 2(lb+lh + bh)
SA = 348in²
l = p
b = 6in
h = 9 in
348 = 2( 6p+ 9p + 54)
348 = 2( 15p + 54)
348 = 30p + 108
Therefore the equation to find the length of the prism is 348 = 30p + 108
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Proving Theorems about Parallelograms: Tutorial
?
Given: Quadrilateral ABCD is a parallelogram. Prove: ZBAD ZDCB, and ZABO ZODA. Match each
statement to its corresponding reason. Scroll down to see all the choices. Click the links in the statements to view
related diagrams. Drag the items on the left to the correct location on the right.
AB CD
BO ADview diagram)
Let A, B, C, and D form a parallelogram.
Draw ACand BD. (view diagram)
AB=CD
BC=AD
AABCE ACDA
AABD ACDB
ZBAD ZDCB(view diagram)
LABC ZCDA(view diagram)
ACAC, and BD BD
given
9 of 2
Opposite sides of a
parallelogram are .
line segments have
equal measures.
drawing line segments
Reflexive Property of
Equality
SSS criterion for
Corresponding angles
of triangles are
Answers
A parallelogram is a type of quadrilateral that has opposite sides to be equal, and opposite angles to be equal.
Thus to complete the given proof in the question, the required statements and reasons are stated below:
STATEMENT REASONS
1. AB ≅ CD, Opposite sides of a
BC ≅ AD parallelogram are equal
2. A, B, C, and D form a paralelogram Given
3. Draw AC and BD Drawing line segments
4. AB = CD, Equal line segments have
BC = AD equal measures
5. ΔABC ≅ ΔCDA SSS criterion for equal
ΔABD ≅ ΔCDB triangles
6. <BAD ≅ <DCB Corresponding angles of equal
<ABC ≅ <CDA triangles are equal
7. AC = AC, and BD = BD Reflective property of equality
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Write an equation in slope-intercept form for a line that passes through the point (1, 6) and
has a slope of 2
Answers
Answer:
y=2x+4
Step-by-step explanation:
If the line has a slope of two, that means it goes up 2 on the y axis for every 1 on the x axis. So, if it goes through (1,6), then you can subtract 1 from the x axis and two from the y axis to find the y intercept, (0,4).
The distance between the points S(-5,12) and T(1,3) is equal to?
with explanation pls
Answers
(Look at the attached image)
So the answer will be approximately 11.27 units or the square root of 127.
Simplify.
−8−1+4 ⋅ 2
Answers
= −8 −1 + 8
= -9 + 8
= -1
Researchers try to gain insight into the characteristics of a ______ population by examining a of the population. Select one:
a. Description
b. Model
c. Replica
d. Sample
Answers
Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.
A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.
The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.
By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.
Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.
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i needs helps what is 7 1/3 - 3 2/3 = ????
Answers
Answer:
3 2/3
Step-by-step explanation:
7 1/3 =22/3
3 2/3= 11/3
22-11= 11
11/3= 3 2/3
Answer:
It is 3 2/3 because you can carry an one to 7 1/3 = 6 4/3 then 6 4/3 - 3 2/3 = 3 2/3
Make a stem-and-leaf plot to display the data set.
41, 41, 44, 55, 58, 59, 60, 61, 62, 63, 72, 77
Answers
The stem-and-leaf plot for the data-set in this problem is given as follows:
4|1 1 4
5|5 8 9
6|0 1 2 3
7|2 7
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
The stems for this problem are the first digits of the numbers, which are 4, 5, 6 and 7.
The leafs are the second digits, hence the plot is given as follows:
4|1 1 4
5|5 8 9
6|0 1 2 3
7|2 7
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The diameter of a cylinder is 4 m. If the height is triple the radius, which is the closest to the
?volume of the cylinder
75.40 m3 o
251.33 m3 o
100.53 m3 o
613.19 m3 o
WILL MARK BRAINLIEST OR WHATEVER NEEDED ASAP
Answers
Answer:
A. 75.40 m³
Step-by-step explanation:
Diameter of cylinder (d) = 4 m
Radius (r) = ½(d) = ½(4) = 2 m
Height (h) = 3 × r = 3 × 2 = 6 m
Volume of cylinder = πr²h
Substitute the values
Volume of cylinder = π*2²*6
Volume of cylinder = π*4*6
Volume = π*24
Volume = 75.40 m³
What is the square root rule?
Answers
The square root function involves the square root symbol √ which is mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.
We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.
If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.
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Use the standard normal distribution or theâ t-distribution to construct a 95â% confidence interval for the population mean. Justify your decision. If neither distribution can beâ used, explain why. Interpret the results.
In a recentâ season, the population standard deviation of the yards per carry for all running backs was 1.35. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 1.5
Answers
The true population mean of yards per carry for all running backs, according to our 95% confidence level, is between 3.52 and 4.592 yards per carry.
We may use the Z-distribution to create a 95% confidence interval for the population mean because the population standard deviation is known and the sample size is more than 30.
The formula for the confidence interval is:
\(CI = x + Z\alpha /2 * \alpha /\sqrt{n}\)
Where is the population standard deviation, n is the sample size, x is the sample mean, Z/2 is the Z-score corresponding to the desired degree of confidence (in this example, 95%), and is the Z-score.
From the given data, we have:
Sample mean \((x) = 4.056\)
Population standard deviation \((\alpha ) = 1.35\)
Sample size \((n) = 25\)
Using a Z-table or calculator, we can find that the Z-score for a 95% confidence level is 1.96 (rounded to two decimal places).
When the values are added to the formula, we obtain:
\(CI = 4.056 + 1.96 * 1.35/x^{25}\)
\(CI = 4.056 + 0.536\)
\(CI = (3.52, 4.592)\)
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Find the missing number so that the equation has infinitely many solutions.
– 2x+18=blank x+18
Answers
The missing term in the equation is n = -2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the missing term be represented as n
-2x + 18 = nx + 18
Subtracting 18 on both sides of the equation , we get
-2x = nx
Divide by x on both sides of the equation , we get
n = -2
Therefore , the missing term is n = -2
Hence , the equation is n = -2
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Solve 5r + 7s = 15 for s
Answers
Answer:
Here it is:
:P
Answer:
s=15/7 - 5r/7
Step-by-step explanation:
Let X be a continuous random variable rv distributed via the pdf f(x) =4e^(-4x) on the interval [0, infinity].
a) compute the cdf of X
b) compute E(X)
c) compute E(-2X)
d) compute E(X^2)
Answers
The cumulative distribution function (CDF) of X is\(F(x) = 1 - e^(-4x).\)
The cumulative distribution function (CDF) of a continuous random variable X gives the probability that X takes on a value less than or equal to a given value x. In this case, the CDF of X, denoted as F(x), is calculated as 1 minus the exponential function \(e^(-4x)\). The exponential term represents the probability density function (PDF) of X, which is given as \(f(x) = 4e^(-4x)\). By integrating the PDF from 0 to x, we can obtain the CDF.
The cumulative distribution function (CDF) is a fundamental concept in probability theory and statistics. It provides a way to characterize the probability distribution of a random variable by indicating the probability of observing a value less than or equal to a given value. In this case, the CDF of X allows us to determine the probability that X falls within a certain range. It is particularly useful in calculating probabilities and making statistical inferences based on continuous random variables.
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Help me, please
I really need
Answers
Answer:
answrr
yes ok
Step-by-step explanation:
4+4-4#_44
PLSSSSS HELPPP ITSSS MATHHH HELPPP 20 POINTSSSSS
Find the volume of the shape:
60 cm^3
90 cm^3
120 cm^3
150 cm^3
Answers
Answer:
120
Step-by-step explanation:
120120120120120120120120120
Complete the statement
Answers
Answer:
<RQS = <RSQ
Step-by-step explanation:
IRQ = RS, then QRS is an isosceles triangle and the base angles are equal
<RQS = <RSQ
what is the surface area of the wood?answer options with 5 optionsa.48 inches squaredb.68 inches squaredc.96 inches squaredd.100 inches squarede.108 inches squared
Answers
The surface area of the wood Cannot be determined.
However, even with the answer options given, it is not possible to determine the surface area of the wood without additional information. The surface area of a piece of wood depends on its dimensions and shape, and the answer options given do not provide any information about these factors.
For example, a rectangular piece of wood with dimensions 4 inches by 3 inches by 4 inches would have a surface area of 52 square inches, which is not among the answer options provided. On the other hand, a cube-shaped piece of wood with dimensions 3 inches by 3 inches by 3 inches would have a surface area of 54 square inches, which is also not among the answer options provided.
Therefore, the correct answer is still "Cannot be determined".
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In which quadrant do you find the point (-3, 4)?
A. First quadrant
B. Second quadrant
C. Third quadrant
D. Fourth quadrant
Answers
Answer:
B- Second Quadrant
Step-by-step explanation:
First Quadrant- +,+
Second Quadrant- -,+
Thrid Quadrant- -,-
Fourth Quadrant- +,-
Hi there!
»»————- ★ ————-««
I believe your answer is:
Quadrant 2
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The graph is divided by the axis into 4 parts. Quadrant II contains negative x values and positive y values. Therefore, we will see point (-3, 4) in Quadrant II.See the picture attached.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
1. A tennis ball is hit from a height of 1.1 m above the ground. The function h(d) = -0.12d² +0.22d+
1.1 models the path of the tennis ball, where d is the horizontal distance, in metres, and h(d) is the height,
in metres.
How far has the tennis ball travelled horizontally, to the nearest tenth of a metre, when it lands on the
ground? [A5]
Answers
The tennis ball has traveled a horizontal distance of 3.717 m, to the nearest tenth of a metre, when it lands on the ground. Hence, the correct option is (A) 3.7.
The given function is h(d) = -0.12d² +0.22d+1.1.
It models the path of a tennis ball hit from a height of 1.1 m above the ground.
Here, d represents the horizontal distance in meters, and h(d) represents the height in meters.
To find how far the tennis ball travelled horizontally when it lands on the ground, we need to find the value of d when h(d) = 0, because the ball will hit the ground when its height is zero.
Substituting h(d) = 0 in the given function, we get:
0 = -0.12d² +0.22d+1.1
Simplifying, we get: 0.12d² - 0.22d - 1.1 = 0
We can solve this quadratic equation using the quadratic formula, which is given by:
-b ± sqrt(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation.
Here, a = 0.12, b = -0.22, and c = -1.1.
Substituting the values, we get:
d = [0.22 ± sqrt(0.22² - 4(0.12)(-1.1))] / 2(0.12)
Simplifying,
We get:
d = [0.22 ± sqrt(0.5964 + 0.528)] / 0.24d
= [0.22 ± sqrt(1.1244)] / 0.24d
= [0.22 ± 1.0604] / 0.24
We get two values of d as follows:d = 3.717 m, -1.598 m
Since the ball cannot travel a negative distance, the only possible solution is d = 3.717 m.
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At a certain university, students who live in the dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food served there. The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question. Many students believe that the food served in the diniog tall necds improvement. Do you think that the quality of food served here needs improvement, even though that would increase the cost of the meal plant? a. In this setting, explain how bias may have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias. b. In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias.
Answers
Based on the provided information, a) bias is introduced through convenience sampling there could be specific variable associated with the first hundred students. It can be avoided by simple random sampling. b) bias is introduced through wording as it includes a negative consequence. It can be avoided by just asking for an opinion without any associated reasoning or consequences.
Bias refers to a deviation of feedback which is based on certain influences by the surveyor and respondent. Sampling bias or selection bias refers to a type of bias in which a researcher gathers a sample of respondents for a questionnaire that does not accurately represent the population. Survey bias refers to the way the question is phrased or formatted, leading people to choose a certain answer instead of another. In the given case,
a) A bias may have been introduced based on the way the convenience sample was selected as there could be specific variable associated with each of the first hundred students that walk into the dining room. The first hundred students could possibly like the food and that is the reason why they come early to the dining room. Selecting students at the dining room may also exclude the students who dislike the food and choose to eat elsewhere. A simple random sample can help avoid this bias. By randomly selecting students at the university campus would provide a more inclusive and true representation of the population.
b) A bias may have been introduced based on the way the question is worded is to maintain the current meal plan as it presents a negative consequence to introducing a new meal plan. It states that a new meal plan would result in more cost. In order to avoid bias, the survey should ask students opinion about the food without introducing any external reasoning.
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