The value of s is 45 and the value of BC is 434
How to solve for s and BC?The given parameters are:
AB = 9s + 29
DC = 10s - 16
Opposite sides of rhombus are equal.
So, we have:
9s + 29 = 10s - 16
Evaluate the like terms
s = 45
Substitute s = 45 in AB = 9s + 29
AB = 9 * 45 + 29
Evaluate
AB = 434
This means that
BC = AB = 434
Hence, the value of s is 45 and the value of BC is 434
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Find the value of x in the given figure
Step-by-step explanation:
3x° + 2x° = 180° ( supplementary angle )
5x° = 180°
x = 180° / 5
x = 36°
[tex]...[/tex]
Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.
The solution of the given exponential equation is 0.688.
Given that Mike is working on solving the exponential equation 37ˣ = 12.
An exponential equation is an exponential equation where the power (or) part of the exponent is a variable.
firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:
aˣ = y
logₐy = x
Now, we will apply this transformation to our equation and we get
log₃₇12=x
Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:
x=log12/log37
So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:
x≈1.079/1.568
x=0.688
Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.
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Oksana wrote the equation below on the whiteboard. 6 b 6 = 48 what is the value of b? 4 7 8 9
The correct answer is 7.
What is linear equation ?A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that collectively make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.
I am aware that this query's equation is,
6b + 6 = 48
subtract 6 from both side in the equation.
6b + 6 - 6 = 48- 6
6b = 42
now, divide by 6 from both side in the equation.
6b/6 = 42/6
b = 7.
Therefore, the correct answer is 7.
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I understand this is the question.
Oksana wrote the equation below on the whiteboard.
6 b + 6 = 48
What is the value of b?
(a)4
(b)7
(c)8
(d)9
f(x)=x^2-x-56=0 what are the zeros in the function?
please help!!!
Answer:
-7, 8.
Step-by-step explanation:
x^2 - x - 56 = 0
Let's see if we can factor this function:
We need 2 numbers whose product is -56 and whose sum is -1 ( which is the coefficient of x).
They are -8 and 7 , so the factors are:
(x - 8)(x + 7) = 0
x - 8 = 0 giving x = 8 and
x + 7 = 0 giving x = -7.
The zeros are -7, 8
Which explicit formula generates the infinite sequence 2, 9, 28, 65, 126,.?
O a-n²
O a-n²+1
O a-n³
O a-n³+1
Mark this and return
Save and Exit
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Answer:
n^3 + 1.
Step-by-step explanation:
Each term is 1 more than a perfect cube.
2 = 1^3 + 1
9 = 2^3 + 1
28 = 3^3 + 1
65 = 4^3 + 1
126 = 5^3 + 1
So the explicit formula is n^3 + 1.
The explicit formula that generates the given sequence is indeed aₙ = n³+1.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The nth term of the sequence can be obtained by substituting n = 1, 2, 3, ... into the expression n³+1:
a₁ = 1³+1 = 2
a₂ = 2³+1 = 9
a₃ = 3³+1 = 28
a₄ = 4³+1 = 65
a₅ = 5³+1 = 126
Hence, the explicit formula that generates the given sequence is indeed aₙ = n³+1.
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2. Two rectangular lots are adjacent to each other, as shown in the diagram below. Using a function operation, determine how many times bigger the large lot is than the small lot. Clearly identify the individual component functions and simplified final equation.
The large rectangle is 8/3 times bigger than the small rectangle.
How to explain the area?Area of large rectangle will be:
= 4x(2x - 2)
= 8x² - 8x
Area of small rectangle will be:
= (3x - 3)x
= 3x² - 3x
The ratio will be:
= 8x² - 8x/3x² - 3x
= 8(x² - x)/3(x² - x)
= 8/3
The large rectangle is 8/3 times bigger than the small rectangle.
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A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by the x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 8 feet from the base of the house and is 16 feet tall. The other tree is 11 feet from the base of the house and is 9 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth. Need answer ASAP.
The distance from the base of the tree to the tallest would be 14.21 cm
We have the following data points in this questionX1 = 8 feet
y1 = 16 feet
x2 = 11 feet
y2 = 9 feet
To proceed with the solution we have to
We have to solve for the shorter tree
[tex]\sqrt{(y2 -y1)^2 + (x2-x1)^2} \\\\= \sqrt{9-0^2 + 11-0^2}[/tex]
= 9² + 11²
= √81 +121
= 14.21
For the taller tree we would have√8² + 16²
= √64 +256
= 17.89
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help im in a rush!!!!!!!
Answer:
Your answer should be 52!!
Step-by-step explanation:
Work included on the picture below.
Which statement is true regarding the graphed functions?
I need help and can’t find the answers anywhere
Answer:
f(0)=g(0)
Step-by-step explanation:
The problem is asking for where the output (y value) of one function, f(x), matches the output of another function, g(x), otherwise called an intersection. You can see that the two lines intersect at 0 on the x axis in the graph, therefore f(0)=g(0) meaning the outputs of f(x) are the same as g(x) at x value 0.
Find the number of 4 digit numbers that contain at least 3 even digits
Answer:
2625 different numbers
Step-by-step explanation:
General outlineCombinatoricsSpecial circumstancesPartitioning the situationConclusionPart 1. CombinatoricsThis type of problem is classified as a "Combinatorics" problem: Counting up the number of ways something can happen.
Many times when attempting to count a large number of items, patterns are recognized and shortcuts to count are developed so that one doesn't need to physically count all of the items. Perhaps the trickiest part of counting with these shortcuts is to ensure that one does not over-count (counting a scenario more than once), although it is equally important that we don't under-count (fail to count a situation that applies).
Part 2. Special circumstancesIt should be noted that for a number to be a 4 digit number, it must have 4 digits, and thus the first digit must not be zero (despite that that would be an even digit, the number itself would not be a 4 digit number).
Part 3. Partitioning the situationThere are 2 main scenarios:
1. All 4 digits are even
2. Exactly 3 digits are even (meaning that exactly one digit is odd).
There are two sub-cases to Scenario 2:
2.1. The first digit is odd, and all three of the other digits are even.
2.2. The first digit is even, and exactly two of the other digits are even (meaning that exactly one of the last three digits is odd).
None of scenarios 1, 2.1, and 2.2 overlap, so we're not over-counting:
If all 4 digits are even, then there can't be exactly 3 even digits. If the first digit is odd, then not all 4 digits are even nor is the first digit even. If exactly two of the last three digits are even, then not all 4 digits are even, nor are all three of the last digits even.Further, this is all of the possibilities for a 4 digit number with least three even digits, so we're not under-counting.
Scenario 1 -- All 4 digits are even.
If all 4 digits are even, then the first digit has fours choices (2,4,6,8), and the next 3 digits each have 5 choices (2,4,6,8,0).
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.1 -- The first digit is odd, and all three of the other digits are even
If the first digit is odd, there are 5 choices for the first digit (1,3,5,7,9), and the next 3 digits each have 5 choices (2,4,6,8,0).
[tex]5*5*5*5=625\text{ choices}[/tex]
Scenario 2.2 -- The first digit is even, and exactly two of the other digits are even
If the first digit is even, there are 4 choices for the first digit (2,4,6,8), and if exactly two of the next 3 digits are even, then there are 5 choices for each of the two even digits (2,4,6,8,0), and 5 choices for the odd digit (1,3,5,7,9), and there are "3 permuted by 2" ways of ordering those three digits.
[tex]4* \left [(5*5*5) * {}_3 \! P_2 \right ]=\\\\=4*\left [5*5*5 * \dfrac{3!}{2!} \right ]\\\\=4*\left [ 5*5*5 * \dfrac{3*2*1}{2*1} \right ] \\\\=4*\left [5*5*5 * 3 \right ] \\\\=1500\text{ choices}[/tex]
Scenario 2.2 broken down (calculated without using the permutation operation) -- The first digit is even, and exactly two of the other digits are even
Then either the second digit is odd (scenario 2.2.1), the third digit is odd (scenario 2.2.2), or the fourth digit is odd (scenario 2.2.3).
Scenario 2.2.1. The second digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second digit is odd: 5 choices for the odd digit (1,3,5,7,9)
The third and fourth digits are even: 5 choices for each even digit (2,4,6,8,0).
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.2.2. The third digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second and fourth digits are even: 5 choices for each even digit (2,4,6,8,0).
The third digit is odd: 5 choices for the odd digit (1,3,5,7,9)
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenario 2.2.3. The last digit is odd.
The first digit is even: 4 choices for the first digit (2,4,6,8)
The second and third digits are even: 5 choices for each even digit (2,4,6,8,0).
The last digit is odd: 5 choices for the odd digit (1,3,5,7,9)
[tex]4*5*5*5=500\text{ choices}[/tex]
Scenarios 2.2.1, 2.2.2, and 2.2.3 comprise all of Scenario 2.2, so [tex]500+500+500=1500\text{ choices}[/tex]
Part 4. ConclusionHow many ways can a 4 digit number be formed where at least 4 of the digits are even?
This is the sum of the choices from Scenario 1, Scenario 2.1, and Scenario 2.2, so [tex]500+625+1500=2625\text{ choices}[/tex].
Which graph is the sequence defined by the function f(x) = 3(2)x-1?
On a coordinate plane, 5 points are plotted. The points are (0, 2), (1, 6), (2, 18), (3, 54), (4, 162).
On a coordinate plane, 5 points are plotted. The points are (1, 2), (2, 6), (3, 18), (4, 54), (5, 162).
On a coordinate plane, 6 points are plotted. The points are (0, 3), (1, 6), (2, 12), (3, 24), (4, 48), (5, 96).
On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Answer: On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Step-by-step explanation:
When x=1, f(x)=3. So, it passes through (1,3).
So, everything is eliminated except for option (4).
Answer:
D!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
I think of a number, subtract 5 and then multiply by 2. my answer is 80. what is my number?
Answer:
200
Step-by-step explanation:
Just do it in reverse and reverse "roles" multiplying Becomes Devidng and Devidng Becomes multiplying:
80/2=40, 40x5=200
if price of 12 eggs is rs 192 , how many eggs can be bought for rs 160
Answer:
10 eggs
Step-by-step explanation:
We need to work out the price per unit :
12 eggs = rs 192
1 egg = rs 192÷12
1 egg = rs 16
? egg = rs 160
16×? = 160
? = 160÷16
? = 10
So our final answer will be 10 eggs
Answer:
10
Step-by-step explanation:
pls HELP Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles?
5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side
5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answer:
The first choice
Step-by-step explanation:
You are setting up as you read it. The left side has 5 x and 6 units, so you would set up 5 positive x times and 6 positive unit tiles. On the the right you are setting up 4 positive x tiles and 3 negative unit tiles. It is not asking you to solve with the algebra tiles, just to set it up.
It cost jose $8.70 to send 87 text messages. How much would it cost to send 10 text messages?
Answer:
One dollar
Step-by-step explanation:
So you divide 8.70 by 87 to get 0.10. So then you multiply 0.10 by 10 to get a dollar
Sending 87 text messages cost $8.70. Sending 10 text messages would cost $1.00.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Given that,
Cost to send 87 text messages: $8.70
Number of text messages: 87
To find out how much it would cost to send 10 text messages,
Use a proportion.
If it cost Jose $8.70 to send 87 text messages,
Set up the proportion:
$8.70 / 87 messages = x / 10 messages
To solve for x,
Cross-multiply and divide:
($8.70 x 10) / 87 = $1.00
Therefore, it would cost $1.00 to send 10 text messages.
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Find the x - and y -intercepts of the graph of the linear equation 2 x plus 3 y is equal to 2x+3y=12
Answer:
x-intercept is 6 [(6, 0) is the point]
y-intercept is 4 [(0, 4) is the point]
Step-by-step explanation:
To find the x-intercept, we can set y equal to 0 and solve for x. This works because the x-intercept is the point of the graph where the line crosses the x-axis (meaning y is equal to 0 at this point. So, if we set y=0 and solve, we get this:
[tex]2x+3(0)=12\\2x=12\\x=6[/tex]
So, the x-intercept is 6; if it is written as a point, it is (6, 0) since y is 0
To find the y-intercept, we can set x equal to 0 and solve for y. This works the same way - x is equal to 0 at the point where the line crosses the y-axis. If we set x=0 and solve, we get this:
[tex]2(0)+3y=12\\3y=12\\y=4[/tex]
So, the y-intercept is 4; if it is written as a point, it is (0, 4) since x is 0
re arranging equations
please help choose answer
Answer:
D. d = √(V/5)
E. A = √(b/c).
Step-by-step explanation:
V = 5d^2
Divide both sides by 5:
V/5 = d^2
Now take the square root of both sides:
d = √(V/5)
Note - it's the square root of the whole term (V/5).
b = cA^2
A^2 = b/c
A = √(b/c).
GEOMETRY HELP ASAP PLEASE!!)
Chad had a garden that was in the shape of a rectangle Its original width was 3 feet and its original length was 8 feet.
He decided to make a new garden that was 3 feet wider and 2 feet longer than his first garden.
How much larger is the area, in square feet, of his new garden compared to his original garden?
Fill in the blank by entering only a number for your answer.
Answer:
36
Step-by-step explanation:
Chad's original garden is 3 ft x 8 ft.
original area = 3 x 8 = 24 square feet
Chad's super Chadly new garden is 3 feet wider, and 2 feet longer.
new width = 3 + 3 = 6
new length = 8 + 2 = 10
new Area = 6 x 10 = 60 square feet
To find how much larger the new area is, subtract the original area.
60 – 24 = 36 square feet
How would I do these questions?
A parabola has x- ints of -1 and 2 and passes through (4,10). Find its equation.
A parabola has x-ints of -2 and 3 and y int of -3. Find its equation.
A parabola has x-ints of 1/2 and 2 and passes through the point (1,3). Find its equation.
Any help will be greatly appreciated. I don't know the format of writing it out, so try to explain it easily so I can understand it. Thank you!
Answer:
Step-by-step explanation:
hello :
1)
the equation is : f(x)= a(x+1)(x-2) because : x- ints of -1 and 2 means :
f(-1)=0 and f(2)=0
calculate : a given f(4)=10
so : a(4+1)(4-2)=10
10a =10 so : a = 1
the equation is : f(x)= (x+1)(x-2)
2) and 3) same method but * y int of -3* meanes : f(0)= - 3
What is the PERT weighted average based on an optimistic estimate of six days, a most likely estimate of eight days, and a pessimistic time of sixteen days
the PERT weighted average is 9 days
What is PERT weighted average?
PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.
The formula for finding the PERT weighted average is given as;
PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6
We have;
Optimistic = 6 daysMost likely = 8 daysPessimistic = 16 daysSubstitute the values into the formula
PERT weighted average = [tex]\frac{6 + 4(8) + 16 }{6}[/tex]
PERT weighted average = [tex]\frac{54}{6}[/tex]
PERT weighted average = 9 days
Thus, the PERT weighted average is 9 days
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8. The heights of female students at North Shore High School are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. About how many students in a random sample of 1000 female students could we expect to have heights less than 167.5 cm
The number of students with heights less than 163 cm should be expected is 12.
According to the statement
The mean of height is 175 cm
and the standard deviation of height is 6 cm.
We use normal distribution here with formula
Z= X - μ /σ
Here X is 167.5 and μ is 175 and σ is 6 cm.
Substitute the values in it then
Z = 167.5 - 175 / 6
Z = -1.25
-1.25 have a p value 0.012
Out of 1000 students:
0.012 x 1000 = 12.
So, The number of students with heights less than 163 cm should be expected is 12.
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A rectangular swimming pool with a length of 18m and width of 8m is surrounded by a concrete patio. The patio is a uniform 3m width around the entire pool. What is the area of the patio
The area of the patio is 192 [tex]m^{2}[/tex]
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The word "area" refers to a free space. A shape's length and width are used to compute its area.
Length of swimming pool=18 m
Width of swimming pool=8 m
Area of swimming pool= 18*8 = 144[tex]m^{2}[/tex]
Width of patio=3m
Total length of swimming pool=18+2(3)=24 m
Total width of swimming pool=8+2(3)=14 m
Total area=24*14=336 [tex]m^{2}[/tex]
Area of patio= total area - Area of swimming pool
=336-144
=192 [tex]m^{2}[/tex]
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Suppose that E and F are two events and that P(E)=0.3 and P(F|E)=0.5. What is P(E and F)?
P(E and F)=
(Simplify your answer.)
E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15
Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.
P(F|E)=P(E and F)÷P(E)
It is given that P(E)=0.3,P(F|E)=0.5
Using Bayes' formula,
P(F|E)=P(E and F)÷P(E)
Rearranging the formula,
⇒P(E and F)=P(F|E)×P(E)
Substituting the given values in the formula, we get
⇒P(E and F)=0.5×0.3
⇒P(E and F)=0.15
∴The correct answer is 0.15.
If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.
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The probability of picking an ace at random out of a
deck of 52 cards is What would be the probabil-
13
ity of picking an ace at random if 2 aces were
removed from the deck?
Answer:
2/50=1/25
Step-by-step explanation:
2 aces are removed hence 2 aces are left out of 50 cards
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8x +12y = -108
Answer:
y=-(2/3)x -9
Step-by-step explanation:
shuffle the equation so that y is alone in left hand side
The coefficient of x in the right hand side is the slope of line and the other term in right hand side is constant term
The slope-intercept form of the given equation will be y = -2x/3 - 9.
What is slope-intercept form?The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given an equation, 8x +12y = -108
Converting in slope-intercept form,
12y = -108 - 8x
y = -2x/3 - 9
Hence, the slope-intercept form of the given equation will be
y = -2x/3 - 9.
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What is the slope of the line through (3,2) and (-3,4)?
Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 3, 4 )
m = [tex]\frac{4-2}{-3-3}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]
[tex]\small\mathbb\green{slope=M= \frac{y2 - y1}{x2 - x1} = \frac{4 - ( - 2)}{3 - 3} \: = \frac{6}{0} \: = ∞} [/tex]
A group of students consists of four people in all; two women and two men. They agree to take turns taking notes in lecture. One person at a time will be selected at random from the group (without replacement) until everyone has had a turn. The expected value of the number of people selected before and including the first time a woman has a turn is (Q17)______ .
The standard error of the number of people selected before and including the first time a woman has a turn is (Q18)______ .
The expected value of the number of people selected before and including the first time a woman has a turn is 1.6667 and the standard error is 0.7454.
How to illustrate the information?It should be noted that the expected value will be:
1[p(x = 1)] + 2[p(x = 2)] + 3[p(x = 3)]
= 1(0.5) + 2(0.3333) + 3(0.1667)
= 1.6667
Var(X) = E(X²) - E(X)2
= 3.3335 & (1.6667)²
= 0.555611
The standard error will be:
= ✓0.555611
= 0.7454
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PLEASE HELP IM SO STUCK PLS
Answer:
x-intercept: (-22, 0)y-intercept: (0, 6)Step-by-step explanation:
Each intercept is found by solving for the variable after the other variable is set to zero.
X-interceptSet y = 0 and solve for x:
-3x = 66
x = 66/(-3) = -22 . . . . . divide by the coefficient of x
The x-intercept is (-22, 0).
Y-interceptSet x = 0 and solve for y:
11y = 66
y = 66/11 = 6 . . . . . . . . divide by the coefficien tof y
The y-intercept is (0, 6).
__
Additional comment
The given equation is in standard form (almost). This form makes it easy to find the intercepts by dividing the constant by the variable's coefficient, as we did above.
(We say "almost" standard form because the leading coefficient is negative. It would be positive in standard form: 3x -11y = -66.)
Answer: (-22,0) and (0,6) in order
Step-by-step explanation:
x-intercept means point of graph that intersects the x-axis and y=0
y-intercept means point of graph that intersects the y-axis and x=0
So the x-intercept is -3x + 0 = 66 as y = 0
x = -22 so the coordinate is (-22,0)
The y-intercept is 0 + 11y = 66 as x = 0
y = 6 so the y-intercept is (0,6)
N=
Help me please thanks :))
The measure of n of the sector with the given area is: 100°
What is the Area of a Sector?The area of a sector of a circle = ∅/360 × πr².
We are given that:
Area of the sector = 40π
Radius (r) = 12 units
∅ = n°
Plug in the values and solve for n
40π = n/360 × π(12²)
40π = n/360 × π144
Divide both sides by 144π
40π/144π = n/360 × 144π/144π
40/144 = n/360
40(360) = n(144)
14,400/144 = n
n = 100°
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Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?
8, 10, 14
9, 12, 15
10, 14, 17
12, 15, 19
Answer:
8, 10, 14
Step-by-step explanation:
1. 8² + 10² = 164 and 14² = 196, so this works.
2. 9² + 12² = 15² = 225, so this is a right triangle.
3. 10² + 14² = 296 and 17² = 289, so this is an acute triangle.
4. 12² + 15² = 369 and 19² = 361, so this is an acute triangle.
Answer:
a
Step-by-step explanation: