Answer:
(a - b)² = 9Step-by-step explanation:
Givena² + b² = 15,ab = 3.FindValue of (a - b)²SolutionUse identity:
(a - b)² = a² - 2ab + b²Substitute values:
(a - b)² = a² + b² - 2ab = 15 - 2*3 = 15 - 6 = 9Answer:
(a - b)² = 9
Step-by-step explanation:
Expand (a - b)²:
[tex]\begin{aligned}\implies (a-b)^2&=a^2-2ab+b^2\\&=a^2+b^2-2ab\end{aligned}[/tex]
Given:
a² + b² = 15ab = 3Substitute the given values into the expanded equation:
[tex]\begin{aligned}\implies (a-b)^2&=a^2+b^2-2ab\\&=15-2(3)\\&=15-6\\&=9\end{aligned}[/tex]
Therefore, (a - b)² = 9.
Evaluate the expression when x =-4
Answer:
22. 2 (-4) = -8
23. (2(-4) + 11) = (-8 + 11) = 3
24. -3 (5 (-4) = -3 (-20) = 60
Answer:
22. 8
23. 3
24. -60
Step-by-step explanation:
You want the values of the given absolute value expressions when x = -4.
23. 2|x|The absolute value function changes the sign to positive, if it isn't already.
2|-4| = 2(4) = 8
24. |2x +11||2(-4) +11| = |-8 +11| = |3| = 3
25. -3|5x|-3|5(-4)| = -3|-20| = -3(20) = -60
4x7 = 2x + 15
Does the equation have one
none, or infinite solutions?
Explain why.
Answer:
There is only one solution
Step-by-step explanation:
4x - 7 = 2x + 15
+7 +7
4x = 2x + 22
-2x -2x
2x = 22
divide by 2 into both sides
x = 11
Since there is only one answer, there is only ONE solution.
Write a coordinate rule for the dilation.
Answer: 584390
Step-by-step explanation: the r4u819
let o be the point of intersection for the diagnols of quadrilateral abcd prove that abcd could be a trapezoid (that is if it has one sides parallel) is Aaod = Aboc
From the given proof below, we have been able to show that quadrilateral ABCD is a Trapezoid.
How to identify a Trapezoid?A trapezoid is also called a trapezium and it is characterized by four straight sides and one set of parallel sides. The parallel sides are referred to as the base, while the non-parallel sides are referred to as the legs.
We are told that;
O is the point of intersection for the diagonals of quadrilateral ABCD;
where;
AO/BO = CO/DO
This can also be expressed as;
AO/CO = BO/DO
Thus, if we create line OE to be parallel to DC which is OE || DC. Then it means that point E lies on BC.
Using the Basic Proportionality Theory, in ΔBDC, we can say that;
BO/OD = BE/EC ............................1
We are also given that:
AO/CO = BO/DO ..........................2
Thus, from Equations 1 and 2, we have;
AO/CO = BE/EC
Using the converse form of the Basic Proportionality Theorem, we have;
OE || AB
Therefore, AB || OE || DC.
Therefore we can conclude that ABCD is a Trapezoid.
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81 to the 5th power = 3x
x=?
The value of x according to the given equation as in the task content is; 3¹⁹.
What is the value of x according to the given expression?It follows from the task content that the value of x is to be determined from the equation given in the task content.
Therefore, since the equation given in the task content is;
(81)⁵ = 3x
(3⁴)⁵ = 3x
3²⁰ = 3x
Therefore, the value of x can be evaluated as;
x = 3²⁰/3
x = 3¹⁹.
Ultimately, the value of x from the given equation is; 3¹⁹.
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Luis has $80 in his checking account. He makes a deposit of $100, and the write a check for $40
Answer: 140 is the answer
Step-by-step explanation: Luis adds 100 to his account so which makes the account balance 180 and then writes a check so he takes 40 out of his account which means he has 140 left in his account
Last Friday, Kira and Marcy got dinner at Seaside Sushi restaurant. Kira ordered 2 pieces of tuna and 5 pieces of crab. Marcy ordered 3 pieces of tuna and 6 pieces of crab. Did Kira and Marcy order the same ratio of tuna pieces to crab pieces?
Answer:
no
Step-by-step explanation:
because Kira ordered 5 pieces of crab while Marcy has ordered 6 pieces of crab
State whether the following variables have a positive correlation, negative correlation, or no correlation.
3.)
(a.)Height of a person and how often he or she attends religious services. __________________________________
(b.)Average property tax in a school district and salary of teachers __________________________
(c.)Weight of a person and shoe size. ____________________________
The types of correlation seen between positive correlation, negative correlation, or no correlation, in the variables is:
a. Height of a person and how often he or she attends religious services. - No correlation (b.)Average property tax in a school district and salary of teachers - Positive correlation (c.)Weight of a person and shoe size. - Positive correlation What is the correlation between property taxes and teacher salaries?One of the main sources of funding for school districts is the property tax charged. This means that increased property taxes will lead to more money being available for teacher salaries which might then increase. There is therefore a positive correlation between the two.
The same is true for the weight of a person and shoe size. This is because the heavier a person is, the larger their shoe size according to research.
There is however no correlation between the height of a person and their attendance of religious services.
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Use the Product Rule of Logarithms to write the completely expanded expression equivalent to log4 (6(5 + 2x)). Make sure
to use parenthesis around your logarithm functions log(x + y).
[tex]log_{4}(2) + log_{4}(3)+ log_{4}(5+2x)[/tex] is the completely expanded logarithmic expression .
What are logarithms ?Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8.
The most common types of logarithms are the base 10 common logarithm, the base 2 binary logarithm, and the base e ≈ 2.71828 natural logarithm.
Calculationsthe product rule for logarithms is
[tex]log_{b}(MN) = log_{b}(M) + log_{b}(N)[/tex] for b > 0
now ,
[tex]log_{4}(6(5 + 2x)) \\\\log_{4}(6) + log_{4}(5 + 2x)\\ \\ log_{4}(2.3) + log_{4}(5 + 2x) \\\\ log_{4}(2) + log_{4}(3)+ log_{4}(5 +2x)[/tex]
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Which graph represents the function f(x) = –|x + 3|?
Answer:
The answer would be A. (Not sure if its A B C or D question but I will have picture below)
Step-by-step explanation:
Hope this helps you! :))
Write a quadratic function f whose zeros are 7 and -5.
Answer:
f(x) = x² -2x -35
Step-by-step explanation:
You want a quadratic function that has zeros 7 and -5.
FactorsEach zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).
f(x) = (x -7)(x +5)
f(x) = x² -2x -35
__
Additional comment
You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.
sum: 7-5 = 2
product: (7)(-5) = -35
quadratic: f(x) = x² -2x -35
1 A father is three times as old as his daughter. If the father is 31 years older than his daughter, what are their ages?
father age 46.5
daughter age 15.5
46.5 - 15.5 = 31
Find the average for the set of numbers 7, 6, 12, 5, 7, 6, 13. Average:
Answer:
Add up all the numbers and divide the product of that by the numbers there are.
7+6+12+5+7+6+13 = 56
There are 7 numbers in these set of numbers hence we divide the product (56) by 7.
56/7 = 8
The answer is 8; The average of all these numbers is 8.
Step-by-step explanation:
Joey has 80 pens and 30 of them are red. What percent are red?
Answer:
Step-by-step explanation:
Elijah has red and yellow napkins. He must set out napkins for 4 people. What are different ways to make groups of 4?
The different ways to make groups of 4 based on the napkins given is 6 ways.
What is combination?Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Thus can be illustrated by nCr
Combination formula
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
In this case, Elijah has red and yellow napkins. He must set out napkins for 4 people. This will be:
= n! / ((n – r)! r!)
= 4! / (4 - 2)! 2!
= 4! / 2!2!
= 4 × 3/2
= 6
Therefore, there are 6 ways.
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PLEASE HELP EXTRA POINTS select all true statements
Answer: C
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
To adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
a. Write an expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs.
An expression is (?) dollars.
Question 2
b. What does the coefficient of the expression in part (a) represent?
Responses
the total cost (in dollars) of adopting one dog
the total cost (in dollars) of adopting one dog
the total amount (in dollars) the veterinarian is paid when one dog is adopted
the total amount, (in dollars), the veterinarian is paid when one dog is adopted
the total cost (in dollars) of adopting x dogs
the total cost (i, n dollars), of adopting x dogs
the total amount (in dollars) the animal shelter earns when x dogs are adopted
the total amount (, in dollars) the animal shelter earns when , x, dogs are adopted
please and thank you!
Answer:$190
Step-by-step explanation:
for an expression is $80+$65+$50=190 per dog to adopt a from the animal shelter.
How does knowing the x-intercepts and the vertex of a
function help you graph a quadratic function?
A graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
With the help of the vertex and the x-intercept, the equation of the parabola can be formed which helps to graph a quadratic function because the equation of the parabola resembles the quadratic function,
Thus, a graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
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NO LINKS!! Explain the process of constructing a 95% confidence interval to test a null hypothesis and what a 95% confidence interval represents. (Use either proportions or means).
At 95% confidence, the z critical value is roughly z = 1.96
You would use a reference table or calculator to determine this value. Unfortunately it's not something that can be easily/quickly found by hand.
If we're trying to estimate the population mean (mu), then we'll use this margin of error formula
E = z*sigma/sqrt(n)
Or if we want to estimate the population proportion (p), then we use this formula
E = z*sqrt(phat*(1-phat)/n)
The confidence interval then spans from (pointEstimate)-E to (pointEstimate)+E. Where "pointEstimate" represents either xbar or phat depending on the context. Other point estimates are possible. We're focusing on these two for now.
xbar estimates mu
phat estimates p
--------------------------------
An example problem:
A manager at a soda bottling plant wants to know if the contents of the cans are 20 fluid ounces (fl oz) or not. Through past observations, the manager has noted the population standard deviation (sigma) is 1.72 fl oz.
The manager gathers a random sample of 50 cans to test their contents. They find the sample mean is 18 fl oz. Conduct a hypothesis test using a confidence interval at 95% confidence to see if the cans really do have 20 fl oz of drink in them or not.
--------------------------------
Solution:
Null Hypothesis: mu = 20
Alternate Hypothesis: mu ≠ 20
This is a two-tailed test.
E = margin of error
E = z*sigma/sqrt(n)
E = 1.96*1.72/sqrt(50)
E = 0.47676
L = lower boundary of confidence interval
L = xbar - E
L = 18 - 0.47676
L = 17.52324
L = 17.52
U = upper boundary of confidence interval
U = xbar + E
U = 18 + 0.47676
U = 18.47676
U = 18.48
The 95% confidence interval is approximately (17.52, 18.48)
This is equivalent to writing 17.52 < mu < 18.48 in which we are 95% confidence in saying mu is between those endpoints.
But wait, the hypothesized mu = 20 is not in the interval 17.52 < mu < 18.48, which indicates we must reject the null hypothesis and accept the alternate hypothesis.
The soda cans do not have 20 fl oz of drink. It appears they have slightly less than 20 fl oz.
add w and the sum of 9 and 4
The addition of w, 9 and 4 is (w+13).
According to the question,
We have the following information:
We need to add w, 9 and 4.
We already know that a variable can only be added or subtracted from the terms having the same variables. For example, 8x can only be added to 5x but not 5y.
So, in this case, w is the variable and it can not be added to any other term because the other two are whole numbers.
Now, the whole numbers can be easily added.
So, we have the following expression:
w+9+4
w+13
Hence, the addition of w, 9 and 4 is (w+13).
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Zach, Kolby, and Peyton are investing a total of $350,000 to open a coffee shop. Their investments are in the ratio
1:2:0.5, respectively.
How much has Zach invested, in dollars?
Enter your answer in the space provided.
Zach's investment is $100,000.
A ratio shows us the number of times a number contains another number.
Given that Zach, Kolby, and Peyton are investing a total of $350,000 to open a coffee shop. And their investments are in the ratio 1:2:0.5, respectively.
Therefore, Zach, Kolby, and Peyton's investment can be written as 1x, 2x, and 0.5x, respectively.
Now, the total sum of the investment of the three can be written as,
Zach's investment + Kolby's investment + Peyton's investment = $350,000
1x + 2x + 0.5x = $350,000
3.5x = $350,000
x = $350,000 / 3.5
x = 100,000
Further, Zach's investment can be written as,
Zach's investment = 1x = 1($100,000) = $100,000
Hence, Zach's investment is $100,000.
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Estimate 17.140 - 03.179 by first rounding each number to the nearest tenth.
Answer: 13.9
Step-by-step explanation:
17.140 rounded to the nearest tenth is 17.1
03.179 rounded to the nearest tenth is 3.2
17.1 - 3.2 = 13.9
Find the ordered pairs corresponding to the x- and y-intercepts of the graph of the equation.
6x + 12y = 24
Answer:
6x=24-12y
x=24-12y/6
x=4-12y
Alma ran a marathon. The graph shows the distance she ran during the marathon. Use the drop-down menus to complete the statements based on the graph.
From the proportional relationship graphed, it is found that:
The labeled point means that in 2 hours she ran 16 miles.In 1 hour, Alma ran 8 miles.Her distance changed at a unit rate of 8 miles per hour, so Alma's speed was of 8 miles per hour.If Alma ran faster, the slope of the graph would be greater.What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0, meaning that the relationship passes through the origin.
When the two variables x and y are direct proportional, the output variable y is obtained multiplying the input variable x by the constant of proportionality k, according to the rule presented follows:
y = kx.
From point (2,16) in this problem, the constant is given as follows:
k = 16/2 = 8.
Hence the equation is:
y = 8x.
Meaning that her rate is of:
8 miles per hour.
If she ran faster, the slope = constant would increase, as it represents the velocity.
Missing InformationThe problem is given by the image at the end of the answer.
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If the quotient is 0 , what is the dividend?
Answer: 0
Step-by-step explanation:
If the dividend and the divisor are the same, the quotient is always 1. If the dividend is the, then the quotient would always be 0. A division equation with 0 dividend and 0 divisor is not valid.
Answer: All real numbers
Step-by-step explanation: Anything that's being divided by 0, is always going to be 0. For example, 0/7 is always 0.
Like terms 8x-12-10x-8
a- 10 units
b-12.0 units
c-11.4 units
d-13.4 units
Using the distance formula, the distance between the point is √130.
In the given question we have to find the distance between given point in the graph.
From the graph the given points are (4,4) and (-3, -5).
The formula for the distance between point is
Distance = √{x(2)-x(1)}^2+{y(2)-y(1)}^2
From the given points; x(1)=4, y(1)=4, x(2)= -3 and y(2)= -5.
Now putting the value:
Distance = √{-3-4}^2+{-5-4}^2
Distance = √{-7}^2+{-9}^2
Distance = √49+81
Distance = √130
The distance between the point is √130.
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adult tickets
A total of 390 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times ti
number of adult tickets sold. How many adult tickets were sold?
The number of adult tickets were sold is 130 tickets.
Given,
In the question:
Total tickets were sold for the school play is 390 tickets.
The number of student tickets sold was two times number of adult tickets sold.
To find the how many adult tickets were sold?
Now, According to the question:
Based on the given conditions:
Let the number of adult tickets be x.
Formulate the condition:
x × (1 + 2) = 390
x × 3 = 390
Simplify
x = 390/3
x = 130
Hence, The number of adult tickets were sold is 130 tickets.
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It takes an older computer 3 times as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 15 minutes to send out the email. How long will it take the older computer to send out the email on its own?
60 minutes will be taken by the older computer to send out the email on its own.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
one computer takes x minutes and the other takes 3x minutes
in 1 minute, they send (1/x) and (1/3x) of the total message
together, (15/x)+(15/3x)=1, the full message
multiply by 3x to clear fractions
45+15=3x
60=3x
Divide both sides by 3
20=x
So for older computer 60 minutes it take to send out the email on its own.
Hence, 60 minutes will be taken by the older computer to send out the email on its own.
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Find the value of n(AnB) if
n(A)=5 n(B)=7 and n(AUB)= 10
what is n(AnB)=?
PLEASE HELP
By using the concept of set operation, the result obtained is
[tex]n(A \cap B) = 2[/tex]
What is a set?
Set is a well defined collection of distinct objects. The members of a set are called elements of a set. Set can be empty as well as non empty.
Set can be finite as well as infinite.
The number of elements inside a set is known as cardinal number of the set
Operations on set are union, intersection, set difference and symmetric difference
Concept of set operation has been used here
n(A)=5 n(B)=7 and n(AUB)= 10
[tex]n(A \cap B) = n(A) + n(B) - n(A \cup B)[/tex]
[tex]n (A \cap B) = 5 + 7 -10\\n(A \cap B ) =2[/tex]
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