Answers
Answer:
7.7 km
Explanation:
Use cosine rule as here given two sides and one angle.
Cosine rule states:
a² = b² + c² - 2bc cos(A)
While solving, treat a = 7.5 km as to that opposite angle is given of 68°
then b = missing side, c = 5.2 km, A = 68°
Applying rule:
7.5² = b² + 5.2² - 2(b)(5.2) cos(68)
56.25 = b² + 27.04 - 3.8959b
56.25 - 27.04 = b² - 3.8959b
b² - 3.8959b = 29.21
b² - 3.8959b - 29.21 = 0
apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]
[tex]\sf b = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad\:when \:\ ax^2 + bx + c = 0[/tex]
[tex]\sf b = \dfrac{ -(-3.8959) \pm \sqrt{(-3.8959)^2 - 4(1)(-29.21)}}{2(1)}[/tex]
[tex]\sf b = 7.69 291 \quad or \quad b = -3.797[/tex]
[tex]\sf b = 7.7 \quad (rounded \ to \ nearest \ tenth)[/tex]
As length cannot be negative. Hence the value of b is only 7.7 km
The answer is 7.7 km.
Let's apply the Cosine Law in this situation.
a² = b² + c² - 2bc cos(A)
Now, substitute the values based on the given diagram.
(7.5)² = b² + (5.2)² - 2(b)(5.2)(cos 68°)56.25 = b² + 27.04 - 3.896bb² - 3.896b - 29.21 = 0Here, using the Quadratic Equation, we can solve :
b = 3.896 ± √(3.896)² - 4(1)(-29.21) / 2b = 3.896 ± √15.178816 + 116.84 / 2b = 3.896 ± √132.018816 / 2b = 3.896 + 11.49 / 2b = 7.7 kmRelated Questions
What is the best interpretation of P(3) =12
Answers
The best interpretation of P(3) = 12 is that the probability of 3 is 12
What is probability?Probability is simply described as an important branch of mathematics that concerns numerical descriptions of the likelihood of the occurance of an event the proposition of how true it is.
The probability of an event is a number that must be between 0 and 1.
Given that;
0 indicates impossibility of the occurance of the event 1 represents certaintyNote that the analysis of events that is being governed by probability is known as statistics.
The types of probability are;
Theoretical ProbabilityExperimental ProbabilityAxiomatic ProbabilityHence, P(3) = 12 is the probability of 3 is 12
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eight times a number plus 6 less than twise the number is 34
turn into an equation and than find the answer
Answers
Therefore , the problem of equation comes out to be Four is the solution when transformed into an equation.
What exactly is an equation?An equilibrium is a rule that shows two expressions are equal by using the equals sign.The connotations of the measures the overall and its cognates might differ slightly among languages. For example, whereas in English an equation is really any well-formed formula made up of two expressions connected by the equals sign, an equation in French is defined as comprising one or more variables.
When attempting to solve a variable equation, the first step is to identify the variables with values that lead to equality.
The equation's solutions are the values of the unknown variables that satisfy the equality as well as the unknown variables that the equation should be solved.
Here,
8N+2N-6=34
10N-6=34
10N=40
N=4
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Yo can anyone help me I am stuck in something thanks
Answers
Answer:
23.5 it is hard to see the little dashes
Step-by-step explanation:
44.22 divided by 6.7
Answers
y’all I just need help with the vertex.
Answers
Answer:
Step-by-step explanation:
Since it is a rectangle, the vertex is easily found.
It has a width of 10, and a length of 4.
Using this, the missing vertex can be found.
Missing vertex: (6,-3)
You need 6.5 yards of fabric for a project. You already ha
2.875 yards. How many yards fabric do you need to buy to
have enough for your project?
Be sure to place your decimal point in your gridded
answer. You should use all five columns.
I
Answers
You need to buy 3.625 yards of fabric to have enough for your project.
How to find out how many yards of fabric you need to buy?To find out how many yards of fabric you need to buy, you can subtract the amount of fabric you already have from the total amount of fabric needed for the project.
Total amount of fabric needed - Fabric you already have = Fabric you need to buy
6.5 yards - 2.875 yards = 3.625 yards
so we can say that:
You need to buy 3.625 yards of fabric to have enough for your project.
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How do I know if ordered pairs are a function?
Answers
A function is a set of ordered pairs (x,y) where for each x value there is only one corresponding y value, and the relation between x and y is such that for any x value there is a unique y value.
One way to determine if a set of ordered pairs is a function is to use the vertical line test. This test involves drawing a vertical line on the coordinate plane and seeing if it intersects the graph of the ordered pairs at more than one point. If a vertical line intersects the graph of the ordered pairs at more than one point, then the set of ordered pairs is not a function. If a vertical line intersects the graph of the ordered pairs at only one point, then the set of ordered pairs is a function.
Another way to determine if a set of ordered pairs is a function is to use the rule of correspondence. If every first element of the ordered pair corresponds to one and only one second element, then the set of ordered pairs is a function, otherwise is not.
Additionally, you can also use algebraic methods like the definition of a function, where a function is a relation from a set A to a set B, such that for each element in A there is exactly one element in B.
For example, the set of ordered pairs {(1,2), (2,4), (3,6)} is a function because for each x-value (1,2,3) there is only one corresponding y-value (2,4,6) and this is unique.
In contrast, the set of ordered pairs {(1,2), (2,4), (3,6), (1,3)} is not a function because for x = 1 there are two different y values, 2 and 3.
It's important to remember that it's not enough to just check a few ordered pairs, you need to check all of them.
Is 8 a prime number?
Answers
The number 8 is not a prime number because it is divisible by the numbers other than itself such as two and four.
A prime number is that number which can only be divided either by its own or by 1.
Let us understand this by an example, assume that we are provided with the numbers 2, 4, 6 and 3.
Now let us remember the basic tables of 2 and 3 which are in an order 2, 4, 6, 8... and 3, 6, 9, 12....
Now we cannot that the number 3 and 2 are only repeated in their tables only.
But the number 4 and 6 have appeared in the table of 2 and 3 along with their own tables.
So what we can understand from here is that the numbers 2 and 3 are the prime numbers because they are not divisible by any other number then themselves but the number 4 and 6 are not prime numbers because they are divisible by the numbers other than themselves.
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The function f(x)=x√ is translated 4 units right to form function g(x).
What is the equation of g(x)?
Enter your answer in the box.
g(x) =
Answers
The equation of g(x), after the translation of [tex]f(x) = \sqrt{x}[/tex] 4 units to the right is given as follows:
[tex]g(x) = \sqrt{x - 4}[/tex]
What is a translation?Among the many transformations that a function or a figure can undergo is a translation, along with reflections, rotations and dilation.
In a translation, only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are defined as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]f(x) = \sqrt{x}[/tex]
After the translation 4 units right, the function g(x) is defined as follows:
[tex]g(x) = f(x - 4) = \sqrt{x - 4}[/tex]
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What is the y-intercept (initial value) for the function shown in the graph?
Answers
Answer:
5 is the y-intercept
Step-by-step explanation:
How do you graph a linear equation using XY tables?
Answers
we can graph a linear equation using XY tables by putting the values of X we are getting the values of y
what are equation
equation is a connection of number of variables and the constant terms attached with the variables x and y
define graph
graph can be draw in the xy plane with o as the origin and draw or find out the values of y by putting value of x in the equation
we can graph a linear equation using XY tables by putting the values of X we are getting the values of Y
and we can find out the range and domain of a given function and we can draw a graph accordingly
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How do you find horizontal dilation?
Answers
Horizontal dilation- If x is replaced by x/A in a formula and A>1, then the effect on the graph is to expand it by a factor of A in the x-direction (away from the y-axis).
If A is between 0 and 1 then the effect on the graph is to contract by a factor of 1/A (towards the y-axis).
We use the word "dilate'' to mean expand or contract.
For example, replacing x by x/0.5=x/(1/2)=2x has the effect of contracting toward the y-axis by a factor of 2.
If A is negative, we dilate by a factor of |A| and then flip about the y-axis. Thus, replacing x by −x has the effect of taking the mirror image of the graph with respect to the y-axis.
For example, the function y=√-x, which has domain {x∈R∣x≤0}, is obtained by taking the graph of √-x and flipping it around the y-axis into the second quadrant.
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In a geometric series, the sum of the first three terms is 14. 25 and the sum of the first four terms is 24. 375. Find the first term and the common ratio.
Answers
The first term and the common ratio in the geometric series are 3 and 3/2.
What is a geometric series?A geometric series is described as the sum of the sequence of numbers. The sum of the nth term of a geometric sequence is expressed as:
Sₙ = a (r^n – 1) / r – 1
In this case, if the sum of the first three terms is 14.25, it means:
n = 3
S₃ = 14.25
Now, substitute the value into the formula:
Sn = a (r^n – 1) / r – 1
S₃ = a (r^3 – 1) / r – 1
14.25 = a (r^3 – 1) / r – 1
And, if the sum of the first four terms is 24.375, it means:
n = 4
S₄ = 24.375
Substitute the value into the formula:
Sₙ = a (r^n – 1) / r – 1
S₄ = a (r^4 – 1) / r – 1
24.375 = a (r^4 – 1) / r – 1
Then, we now can divide both above equations:
14.25 / 24.375 = r^3 – 1 / r^4 – 1
14.25r^4 – 14.25 = 24.375r^3 – 24.375
14.25r^4 – 24.375r^3 = –24.375 + 14.25
14.25r^4 – 24.375r^3 = –10.125
14.25r^4 – 24.375r^3 + 10.125 = 0
After factorizing we get:
r = 3/2
This is the common ratio.
Now, substitute the value of r into the equation
14.25 = a (r^3 – 1) / r – 1
14.25 = a ((3/2)^3 – 1) / (3/2) – 1
14.25 = a (19/8) / 0.5
19a / 8 = 14.25 * 0.5
19a / 8 = 7.125
19a = 57
a = 57 / 19
a = 3
Thus, the first term is 3.
Hence, the first term in the geometric series is 3 and the common ratio is 3/2.
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helpppppp i love math :))
You are beautiful. Don't let anyone tell you different<3
Answers
There are √131 lies between the two whole numbers 11 and 12.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The square root of 131 is approximately 11.445 It lies between the two numbers 11 and 12, specifically, it is greater than 11 and less than 12.
We know that the square root of a number is the value that, when multiplied by itself, gives that number.
For example, the square root of 121 (which is 11) is 11 because 11 x 11 = 121.
In the same way, the square root of 131 is the number that, when multiplied by itself, will give 131.
Since 131 is a prime number and it is not a perfect square, the square root of 131 cannot be a whole number, it should be decimal and it lies between 11 and 12.
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what is the answer for this math question -q/7>-1 im stuck on it
Answers
All possible solutions for inequality are (-∞,-7)U(-7, ∞).
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
The inequality q/7 > -1 is a mathematical statement that compares the value of q/7 to -1.
To solve the inequality, we can start by isolating q on one side of the inequality.
To do this, we need to multiply both sides of the inequality by 7:
q/7 * 7 > -1 * 7
q > -7
Now we have the inequality q > -7, this inequality states that q is greater than -7.
To find all possible solutions for the inequality, we can use interval notation. The interval notation for the solution of this inequality is (-infinity,-7)U(-7, infinity)
It means all real numbers except -7, the solution set is an open interval.
Alternatively, we can also graph the solution set of the inequality on a number line, shading the region that represents the solution. The shaded region will be all the points to the right of -7 on the number line.
Hence, all possible solutions for inequality are (-∞,-7)U(-7, ∞).
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Sureh ha 4 coupon book, each with 6 coupon. He keep 13 of the coupon and give the ret away. Fifty percent of thoe he keep are for the movie theater
Answers
So, the final expression that represents the number of movie theater coupons Suresh has is 4.
Suresh has 4 coupon books, each containing 6 coupons, for a total of 4*6 = 24 coupons.
He wants to keep 1/3 of these coupons, so we can write an expression to represent this as: (1/3) * 24 = 8
So he keeps 8 coupons and gives away 24-8 = 16 coupons.
Out of the 8 coupons he keeps, 50% of them are for the movie theater, so we can write an expression to represent this as: 8 * 0.50 = 4
Therefore, the final expression that represents the number of movie theater coupons Suresh has is: 8 * 0.50 = 4
In this question, we have used the basic arithmetic operations like multiplication and subtraction to find the number of coupons Suresh keeps and gives away. And then we have used the percentage to find out how many movie theater coupons he has out of the total number of coupons he kept.
Complete Question: Suresh has 4 coupon books, each with 6 coupons. He keeps 1/3 of the coupons and gives the rest away. Fifty percent of those he keeps are for the movie theater. Write and evaluate an expression to show how many movie theater coupons he has.
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Is it possible to have a triangle with the sides 3cm 6cm 7cm?
Answers
Answer:
yes
Step-by-step explanation:
for the sides to form a triangle.
the sum of any 2 sides must be greater than the third.
As a check
3 + 6 = 9 > 7
3 + 7 = 10 > 6
6 + 7 = 13 >3
this meets the condition for a triangle to be made.
there are 3 times as many white tiles as there are shaded. How many tiles are white if there are 12 tiles in total?
Answers
The number of tiles that are white if there are 12 tiles in total will be 9.
How to compute the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario. It is important to note that an equation is the mathematical statement.
In this case, there are 3 times as many white tiles as there are shaded.
The number of tiles that are white if there are 12 tiles in total will be:
3x + x = 12
4x = 12
Divide
x = 3
Shaded tiles = 3
White tiles = 3x
= 3 × 3
= 9
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Katherine receives an email with a coupon code for $5 off of a pair of jeans from her favorite store. Write a function c(x) to represent the price of the jeans after the coupon code is applied to the original price of the jeans, x.
Answers
The function c(x) represents the price of the jeans after the coupon code is applied will be c(x) = 2x - 5.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
Katherine receives an email with a coupon code for $5 off of a pair of jeans from her favorite store.
Let 'x' be the cost of jeans. Then the cost of pair of jeans will be given as,
⇒ 2x
The function c(x) represents the price of the jeans after the coupon code is applied and will be given as,
c(x) = 2x - 5
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if theta is an angle in standard position and it’s terminal side passes through the point (3, -4) find the exact value of csc theta in simplest radical form
Answers
The exact value of tanθ is -4/3 that is -1.33 in the simplest radical form.
What is Tanx in terms of sinx and cosx ?
The value of Tanx can be the ratio of sinx and cosx or it can be defined by the ratio of its opposite side and adjacent side.
Given,
if theta is an angle in standard position and
it’s terminal side passes through the point (3, -4)
So, the given point is (3,-4)
By the definition we can say that ,
If the terminal side passes through the point (a,b)
than tanθ = b/a .
so, similarly
tanθ = -4/ 3
Hence, The exact value of tanθ is -4/3 that is -1.33 in the simplest radical form.
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Sample Response: The diagram should have five columns, one for each 25% and one for the total, because 25% is 1 4 of 100%. It should have 2 rows, 1 for percents and 1 for dollar amounts. What key phrases did you include in your response? 4 columns, because 25% is One-fourth of 100% 1 column for total amount 2 rows for percents and dollar amounts
Answers
The correct option regarding the number of columns representing a percentage of 25% is given as follows:
4 columns, because 25% is One-fourth of 100%.
How to obtain the number of columns of the diagram?The percentage that represents the total of the diagram is given as follows:
100%.
The ratio between the total percentage of 100% and the percentage of 25% is given as follows:
100/25 = 4.
The ratio represents the number of columns, which is of 4, and is the justification for the correct option.
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3
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
The table shows the mode of transportation to school for families with a specific number of children.
Mode of Transportation
Car
Number of
Children
0.284
1-2
63
38
3+
25
49
Total
88
87
A family from the survey is selected at random. Match the probability to each event.
0.662
Bus
0.203
0.249
101
74
175
0.624
P (3+ Children Bus)
Total
P(1-2 Children Car) - P (3+ Children Car)
Reset
P (Car 1-2 Children)
0.563
P (Bus 1-2 Children) - P (Bus 3+ Children)
▸
Next
Answers
The probability of number of 1-2 Children in car and 3 plus children in car is 0.203.
What is probability?The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.
The probability of P(1-2 children| car). P (3 plus children| car) is given by:
P = 63/88 × 25/88
P=0.203
The probability of P(Bus| 1-2 children). P (Bus | 3 plus children) is given by:
P = 38/101 × 49/74
P=0.249
The probability of P(Car |1-2 Children) is given by:
P= 63/101
P=0.624
The probability of P(3 plus children | Bus)is given by:
P=49/87
P=0.563
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Answer: The picture below
Step-by-step explanation: Correct on Edmentum, if you give me a low rating than you are mean :(
A fair quarter is flipped three times. For
each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability.
(a) Find the probability of getting exactly three heads.
(b) Find the probability of getting exactly two heads.
(c) Find the probability of getting two or more heads.
(d) Find the probability of getting exactly three tails.
Answers
Answer:
(a) P(exactly 3 heads) = P(X = 3) = (3!/3^3)(1/4)^3 = 0.21875
(b) P(exactly 2 heads) = P(X = 2) = (2!/2^2)(1/4)^2 = 0.375
(c) P(2 or more heads) = P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - (1!/1^1)(1/4) - (0!/0^0)(1/4)^0 = 0.9375
(d) P(exactly 3 tails) = P(X = 3) = (3!/3^3)(1/4)^3 = 0.21875
write an expression for x fewer than 62
Answers
The expression for x fewer than 62 can be written as 62 - x
What is a mathematical expression?An expression can be evaluated to a single value by substituting specific values for the variables and performing the operations in the correct order. Mathematical expressions can be used to model real-world phenomena, make predictions, and solve problems. Expressions are used in various branches of mathematics such as Algebra, Calculus and Geometry.
Fewer than tells us that x is less than 62, the solution is to tell us by what number that it is less than.
Hence 62 - x is the expression for x fewer than 62
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11. A cattle ranch has 1,400 acres of grazing land. The ranch has 140 cows. How many acres of grazing land does the ranch have per cow?
Answers
Step-by-step explanation:
1400-140 this is answer of this question
PLEASE HELP 2O POINTS, IMAGE BELOW
Answers
To find the m<MKL given that MK bisects <JKL proves that; m<MKL is 38^o.
What is an angle bisector?A straight line that splits a measure of an angle into two equal parts is termed as an angle bisector. So that the measure of the two parts are the same.
Given in the question that MK bisects <MKL, then;
m<JKL = m<JKM + m<MKL (definition of an angle bisector)
So that;
m<JKM = m<MKL
(3a + 20) = (2a + 26)
3a + 20 = 2a + 26
collect like terms
3a - 2a = -20 + 26
a = 6
Thus,
m<MKL = (2a + 26)
= 2(6) + 26
= 12 + 26
= 38
m<MKL = 38^o
To find the m<MKL given that MK bisects <JKL proves that; m<MKL is 38^o.
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amanda used a total of 13 gallons of gas while driving her car each hour she was driving she used 3/10 gallons of gas what was the total number of hours she was driving
Answers
The fraction 10/10 would be equal to one gallon, so just 1. So that would mean 3/10 of a gallon would equal 0.3
Divide 13 by 0.3 and you get 43.3 hours. So you’d just put 43 hours as your answer.
2) Hanif had ome toy. After elling 18 of them to the cutomer, he till ha 30 toy. How many toy did Hanif have at firt?
Answers
As per the unitary method, the number of toys ha had at first is 48.
Here we have given that Hanif had some number of toy.
Here we also know that after selling 18 of them to the customer, then he till had 30 toy in hand.
Now, we have to find how many toy did Hanif have at first.
Let us consider that x is the number of toy he had at first.
Here we know that the following value are given,
number of toys left = 30
number of toys sold = 18
Then the total number of toys at first is calculated as,
=> x = number of toys left + number of toys sold
Apply the values on the equation, then we get
=> x = 30 + 18
=> x = 48.
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what is the fractional part that make up 7/3?
Answers
Answer:
1/3
Step-by-step explanation:
7/3 = 6/3 + 1/3 = 2 + 1/3 = 2 1/3
The fractional part is 1/3.
On the second grid, create a graph of y = 3 – 4t for -2 ≤ t ≤ 7 with y on the vertical axis and t on the horizontal axis.
Answers
The graph of y = 3 - 4x is given above.
The coordinates on the graph are:
(-2, 11) and (7, -25).
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 3 - 4t
Where -2 ≤ t ≤ 7
Now,
Find the coordinates on the graph.
y = 3 - 4t
For t = -2
y = 3 - 4 x (-2) = 3 + 8 = 11
i.e
(-2, 11)
For t = 7
y = 3 - 4 x 7 = 3 - 28 = -25
i.e
(7, -25)
Thus,
The coordinates on the graph are:
(-2, 11) and (7, -25).
The graph is given below.
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