There are two(2) possible solutions for the given parameters of a triangle. Using the law of cosines, the parameters of the triangle are calculated.
What is the law of cosines?The law of cosines is used to relate the angles and side lengths of a triangle.
They are given as follows:
a² = b² + c² -2bc cos(A)
b² = a² + c² - 2ac cos(B)
c² = a² + b² - 2ab cos(C)
Calculation:The given triangle has B = 37°, a = 32 and b = 27
So, using the law b² = a² + c² - 2ac cos(B)
On substituting,
27² = 32² + c² - 2(32)c cos(37°)
⇒ c² - 50.56 c + 1024 = 729
⇒ c² - 50.56 c + 295 = 0
Since the obtained equation is quadratic, it has 2 solutions.
Using quadratic formula the solutions are calculated.
c = [50.56 ± [tex]\sqrt{50.56^2-4(1)(295)}[/tex]]/2(1)
On simplifying,
c = 43.8 and c = 6.7
Therefore, there are 2 possible solutions for the given triangle.
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A woven rattan basket can hold up 6 lbs of items. A net bag of 4 oranges weighs 12 ounces. How many bags of oranges can the basket hold ?
[tex]\huge\boxed{8\ \text{bags of oranges}}[/tex]
Let's first find how many ounces the basket can hold.
1 pound is equal to 16 ounces. Multiply that to find how many ounces the basket can hold.
[tex]6\cdot16=96[/tex]
Now, divide the weight held by the basket by the weight of each bag of oranges.
[tex]96\div12=\boxed{8}[/tex]
Select the correct answer. Write an expression to represent the sum of three times the square of a number and -7. In your expression, what is the value of the constant? (A. _7 3 B. OC. 1 D. 2 Select the correct answer .
Answer:
A. -7
Step-by-step explanation:
The student body of 115 students want to elect a president and a vice president. How many different ways can they do that
The different ways that the students can elect a president and a vice president will be 13110.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
Given data;
Total no of students = 115
The total number of ways to elect a president = 115
If one person is elected as the president the total number of ways to elect a president = 114
The different ways that the students can elect a president and a vice president are found as;
⇒ 115 ways × 114 ways
⇒ 13110 ways
Hence the different ways that the students can elect a president and a vice president will be 13110.
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HELP ASAP!!!!!!!!!!
Given: ABCD is a parallelogram, BE bisects AC and DF bisects AC.
Prove: triangle BEC is congruent to triangle DFA.
Answer:
1.) & 2.) BC and AD are congruent and parallel because in parallelogram opposite sides are equal and parallel
4.) <BCE≅<DAF because they are alternating interior angles bisected by line CA
5.) & 6.) The line BE/DF which bisects the <B/<D iS perpendicular to diagonal CA which forms the right angle
7.) Because sum of any two adjacent angles are 180
8.) This follows ASA Postulate which means that if 2 pair of angles is congruent given that they share a same side, the triangle formed will also be congruent.
Step-by-step explanation:
Take the side CA as the same side of both triangles. This side also participates on the aforementioned angles on the given. The angles <BCE≅<DAF shares the side CA which makes the angles <DFA and <BEC congruent to each other. Therefore, the two right triangles are congruent
What is a severe limitation of using the Internet for primary research? The data on the Internet are usually outdated. The educational qualifications of the respondents of surveys on the Internet cannot be identified accurately. A sample universe composed solely of Internet respondents represents a potential bias. Secondary data cannot be accessed on the Internet for conducting research. Using the Internet for primary research is the most expensive way of conducting primary research.
The severe limitation of using the internet for primary research is that a sample universe composed solely of internet respondents represents a potential bias.
Given options 1)The data on the Internet are usually outdated.
2) The educational qualifications of the respondents of surveys on the Internet cannot be identified accurately.
3) A sample universe composed solely of Internet respondents represents a potential bias.
4)Secondary data cannot be accessed on the Internet for conducting research.
5) Using the Internet for primary research is the most expensive way of conducting primary research.
We have to choose most appropriate option which shows the severe limitation of using internet for primary research.
The most appropriate option is option third which is that a sample universe composed solely of internet respondents a potential bias
There is biasness because on internet people gives their own opinion and reviews and don't think about reality. The data may have been collected for the research according to researcher's priority. The data may be outdated but it is of our choice whether we use that data or not because generally the date is given on the internet. We can also access secondary data on the internet. Using internet in research is not so expensive because some organisation provides study materials to researchers themselves.
Hence the limitation of using the internet for primary research is that a sample universe composed solely of internet respondents a potential. bias.
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a lily pad is growing in a pond and it doubles in size every day. after 30 days it covers the entire pond. on what day does it cover half the pond?
The growth of the lily pad is in geometric progression, and it covers half the pond in 29 days.
In the question, we are given that the size of the lily pad doubles itself every day.
If we assume the size of the lily pad on the first day as a, then on the second day its size will be 2a, on the third day it will be 2(2a) = 4a, and on the fourth day, it will be 2(4a) = 8a, and so on.
This makes a geometric progression, with the first term as a, and the constant ratio as 2.
We are given that on the 30th day, the size of the lily pad, covers the entire pond.
The size on the 30th day can be shown as the 30th term of this geometric progression
Therefore, size of the pond = a(2)³⁰⁻¹ = a.2²⁹. {Using the formula, aₙ = arⁿ⁻¹, where aₙ is the n-th term, a is the first term, and r is the constant ratio}.
We are asked the day on which the pond is half covered.
The size of the pond in this case = (a.2²⁹)/2 = a.2²⁸.
The day can be calculated as follows:
a.2ⁿ⁻¹ = a.2²⁸,
or, 2ⁿ/2 = 2²⁸,
or, 2ⁿ = 2²⁹,
or, n = 29.
Thus, the lily pad covers half the pond on the 29th day.
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The steps to derive the quadratic formula are shown below:
I need help pls
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4 x2 + b over a times x plus b squared over 4 times a squared equals negative c over a plus b squared over 4 times a squared
Step 5 x2 + b over a times x plus b squared over 4 times a squared equals negative 4 multiplied by a multiplied by c, all over 4 multiplied by a squared plus b squared over 4 times a squared
Step 6
Provide the next step to derive the quadratic formula. (1 point)
x plus b over 2 times a equals plus or minus b squared minus 4 times a times c all over the square root of 4 times a squared
x plus b over 2 times a equals plus or minus b minus 2 times a times c all over square root of 2 times a
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 2 times a
Answer:
(c) x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared
Step-by-step explanation:
The next step is to take the square root of both sides of the equation. It can help to show the intermediate steps.
Result so farThe last step shown in the derivation so far is ...
[tex]x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=-\dfrac{4ac}{4a^2}+\dfrac{b^2}{4a^2}[/tex]
Next stepThe left side of the above expression can be written as a square, and the right side can be written over one denominator. Then the square root is taken as the next step.
[tex]\left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2-4ac}{4a^2}\\\\\sqrt{\left(x+\dfrac{b}{2a}\right)^2}=\sqrt{\dfrac{b^2-4ac}{4a^2}}\\\\\boxed{x+\dfrac{b}{2a}=\pm\dfrac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}}\qquad\text{"next step"}[/tex]
Answer: [tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]
Step-by-step explanation:
We can rewrite the left hand side as a perfect square, more specifically
[tex]\left(x+\frac{b}{2a} \right)^2[/tex]
So, taking the square root of both sides,
[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]
HELP HELP HELP HELP
HELP HELP HELP
Answer:
[tex]\sqrt{16} = 4\\[/tex]
Step-by-step explanation:
the distance formula for graph = [tex]\sqrt{x^{2} + y^{2} }[/tex]
(simplified version)
[tex]\sqrt{0^{2} + (-4)^{2} } \\\\\\\sqrt{0 + 16} \\\\\\\sqrt{16}\\\\= 4[/tex]
I hope its right TT I just looked it up here:
https://byjus.com/maths/distance-between-two-points-formula/
you should double check here as well
write the equation of a line that is perpendicular to y=3x-2 that passes trough the point (-9,5)
[tex]\huge\boxed{y-5&=-\frac{1}{3}(x+9)}[/tex]
First, we'll find the slope of the new line. The first line has a slope of [tex]3[/tex]. Take the negative reciprocal of this (Flip the numerator and denominator, then multiply by [tex]-1[/tex]) to get [tex]-\frac{1}{3}[/tex] for the new slope.
Then, we'll use the point-slope form to make the new equation, where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-5&=-\frac{1}{3}(x-(-9))\\y-5&=-\frac{1}{3}(x+9)\end{aligned}[/tex]
the ratio of boys to girls in a chorus is 5:6. which shows an equivalent ratio. Use a proportion to solve. A 10 boys to 12 girls B 15 boys to 19 girls C 20 boys to 25 girls or D 24 boys to 28 girls
find the square by multiplying the polynomial
(4c + 4)²
Answer:
16c² + 32c + 16
Step-by-step explanation:
(4c+4)² =
(4c+4)(4c+4) =
16c² + 16c + 16c + 16 =
16c² + 32c + 16
I think this is the answer you are looking for.
Hope this helped and have a good day
-a(4a5 + 9a + 6)
Find the product and simplify the answer.
Figure AAA is a scale image of Figure BBB.
What is the value of xxx?
Quick!
f¹(-2)=[
f(-4)=
ff¹(-2)) = |
Determine two pairs of polar coordinates for (3,-3) when 0
The two pairs of polar coordinates for the given point (3, -3) with 0° ≤ θ < 360° are (3√2, 135°) and (3√2, 315°).
What is a polar coordinate?A polar coordinate is a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).
Next, we would determine the distance (r) and angle (θ) as follows:
r = √(3² + (-3)²)
r = √(9 + 9)
r = 3√2.
θ = tan⁻¹(-3/3)
θ = tan⁻¹(-1)
θ = 3π and 7π/4 (second and fourth quadrants).
Converting to degrees, we have:
θ = 135° and 315°.
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Complete Question:
Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°
SOMEONE PLEASE HELP ME ANSWER THIS I PROMISE ITS EASY
Answer:
x = 1 19/21 the one is in front of the 19/21
Step-by-step explanation:
Exact form: x = 40/21
Decimal form: x = 1.90476190
Mixed number form: x = 1 19/21.
Answer:
Let's solve your equation step-by-step.
[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]
Step 1: Simplify both sides of the equation.
[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]
[tex]\tt{ 14 = \dfrac{3}{5}(7) + \dfrac{3}{5}(10)}[/tex]
(Distribute)
[tex]\tt{ 14 = \dfrac{21}{5} x + 6 }[/tex]
Step 2: Flip the equation.
[tex]\tt{ \dfrac{21}{5} x + 6 = 14}[/tex]
Step 3: Subtract 6 from both sides.
[tex]\tt{ \dfrac{21}{5} x + 6 - \blue{6} = 14 - \blue{6}}[/tex]
[tex]\tt{ \dfrac{21}{5} = 8}[/tex]
Step 4: Multiply both sides by 5/21.
[tex]\tt{ \left( \dfrac{5}{21}\right) \times \left(\dfrac{21}{5}x \right) = \left(\dfrac{5}{21}\right) \times (8)}[/tex]
[tex]\\[/tex]
[tex]\large\tt\purple{ x = \dfrac{40}{21}}[/tex]
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I write down three different positive whole numbers that add to 96. The sum of any two is divisible by the third.
What is the largest of these three numbers?
Simple
They are 64 ,0,32Sum of all three
64+0+32=96Sum of first two
64+0=64Divide by
64/322Yes Verified
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answer:
(f + g)(x) = x - 7
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= - 3x - 5 + 4x - 2 ← collect like terms
= x - 7
Write a rational expression that satisfies the following condition: non permissible values x=y, +-2
The rational expression that satisfies x = y +-2 is 2xy/(x + y)(x² - 4).
How to illustrate the expression?It should be noted that non permissible value is the value of the variable which make the denominator of the rational expression equal to zero.
Based on the information, x + y gives x - y = 0.
x = 2 gives x - 2 = 0
x = -2 gives x + 2 = 0
Ths denominator according to the condition illustrated will be (x - y)(x - 2)(x + 2) = (x - y)(x² - 4)
Then, the rational expression can be written by taking the numerator and denominator. An example will be 2xy/(x + y)(x² - 4).
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Lou Ann needed to mail 150 invitations to her school play. The invitations came 6 to a package. Which number sentence could be used to find out how many packages Lou Ann needed?
Lou Ann needed 25 packages that contains all the 150 invitations.
Lou Ann needed to mail 150 invitations to her school play. The invitations came 6 to a package.
What is Statistic?The statistic is the study of mathematics which deal with relations between comprehensive data.
Here, 1 package contains 6 invitation
so 1 package = 6 invitations
total invitation= 150 invitations
now number of packages = Total invitation/ 6 invitation = 150/6
=25
Thus the required number of packages is 25.
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Which inequality represents all the solutions of 8(6x-7) <5(9x - 4)?
O A.
OB.
OOO
O C.
OD.
X> 12
x < 12
x> 20
x < 20
Hello,
8(6x-7) <5(9x - 4)
48x - 56 < 45x - 20
48x - 45x < -20 + 56
3x < 36
x < 36/3
x < 12
Quick algebra 1 assignment for 50 points!
Experts please help, Only answer if you know the answer! :)
See below for the demonstration of (e) graphing a line using x- and y-intercepts
The graphing method to demonstrateTo solve this question, we make demonstrate (e) graphing a line using x- and y-intercepts
The learning goalsAt the end of this exercise, you should be able to graph a line using x- and y-intercepts
A brief overviewA linear equation is represented as:
Ax + By = C
Where:
y-intercept = C/Bx-intercept = C/AThis means that we plot the points (0,C/B) and (C/A, 0) on a graph and then connect the points using a straight line.
Once this is done, the line has been graphed.
For instance, a line parallel to 3x + 8y = 16 will have a slope of -3/8
An original problem to solvePlot the graph of the following equation using the intercepts
2x + 4y = 10
We have:
2x + 4y = 10
Set x = 0 to determine the y-intercept
4y = 10
Divide by 4
y = 2.5
Set x = 0 to determine the x-intercept
2x = 10
Divide by 2
x = 5
So, we have:
(5, 0) and (0, 2.5)
Plot the above points and connect the points (see attachment for graph)
An original problem to solve by another studentPlot the graph of the following equation using the intercepts
3x + 6y = 18
We have:
3x + 6y = 18
Set x = 0 to determine the y-intercept
6y = 18
Divide by 6
y = 3
Set x = 0 to determine the x-intercept
3x = 18
Divide by 3
x = 6
So, we have:
(6, 0) and (0, 3)
Plot the above points and connect the points (see attachment for graph)
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Can someone help me please?
Answer: Circumcenter
Step-by-step explanation: The circumcenter is the point where all perpendicular bisectors of a triangle meet. The 3 perpendicular bisectors of the 3 sides of the triangle meet at the point which is labeled in this triangle as H.
Help! please answer, an explanation would be great too.
Answer:
the top one as highlighted
Step-by-step explanation:
y=Mx+c is the equation for a straight line
C is the intercept as it is at 0 it can be dropped from the expression as adding or taking away 0 makes no difference to the end value.
m is the slope
Questions in the picture
By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250
How to determine the monthly profit by the cuckoo clock sales
The profit (P) is the result of subtracting costs from sales (S). Cost (Cp) is the sum of rent (C) and production cost (C'). Now we proceed to create and solve the expression:
P = S - C - C'
P = 500 · x - 275 · x - 2500
P = 225 · x - 2500
P = 225 · 30 - 2500
P = 4250
By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250.
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Complete the number pattern
Answer:
137,131
Step-by-step explanation:
what is the answer of these two according to this piecewise function?
f(1)=?
f(5)=?
[tex]f(1)=1^2+4\cdot1+6=1+4+6=11\\f(5)=5^2+4\cdot5+6=25+20+6=51[/tex]
x =x=x, equals
^\circ
∘
x is 45° (45 degrees.)
To find this out, we first need to understand the properties of a rectangle. A rectangle has opposite sides that are equal, but more importantly, all 4 interior angles of a rectangle are right angles, meaning they are all 90 degrees. These can also be denoted by 4 square boxes in each corner.
When a rectangle is cut diagonally, the rectangle becomes two right triangles, but when joined together, of course make a rectangle. When they are cut diagonally, the triangles are congruent triangles by the Hypotenuse-Leg (HL) Congruence property.
To find the missing x in this angle, we must know that x is apart of a right angle, and if 45 is next to it, x must also be 45 degrees (90-45 = 45)
Hope this helped!
What is 2.3g as a percentage of 5.98g ? (Round the nearest whole number)
Answer:
38%
Step-by-step explanation:
2.3/5.98 x 100
= 0.38 x 100
= 38%
help me get these 10 questions u will have 100 points EZ