Mathematics High School
Answers
Answer 1
Answer:
The answer is:
[tex]\bold{c\approx 20.2\ units}[/tex]
Step-by-step explanation:
Given:
In △ABC:
m∠A=15°
a=10 and
b=11
To find:
c = ?
Solution:
We can use cosine rule here to find the value of third side c.
Formula for cosine rule:
[tex]cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
Putting all the values.
[tex]cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units[/tex]
The answer is:
[tex]\bold{c\approx 20.2\ units}[/tex]
Related Questions
When x is divided by 4, the remainder is 3. When r^2 is divided by
4, what must the remainder be?
Answers
Answer:
If x=7 that means that if 7 substitute r which is 7^2 and 7*7=49 and 49/4
=12 1/4
So the remainder is 1
Step-by-step explanation:
One of these is not an aquatic swimming A. canoeing B. shooting C. swimming D. diving
Answers
The answer is B. Shooting. Shooting is a sport on dry land, while the other three are aquatic sports, that is, they are on or in the water.
i will mark brainlist
Answers
Answer:
[tex]\boxed{x = 30}[/tex]
Step-by-step explanation:
x + 2x + 3x = 180 (Interior angles of a triangle add up to 180 degrees)
=> 6x = 180
Dividing both sides by 6
=> x = 180 / 6
=> x = 30
Answer:
x= 30
Step-by-step explanation:
3x + 2x + x = 180
6x= 180
x = 180/6
:• x = 30
What is the average rate of change for this exponential function for the
interval from x = 2 to x = 4?
O A. -6
O B. -12
O C. 12
O 0.6
Answers
Answer:6 a p e x
Step-by-step explanation:
Describe the congruence transformation that maps ΔABC onto ΔA′B′C′ in the given figure. Question 9 options:
A) Reflection along x-axis; Translation: (x, y) → (x, y – 3)
B) Reflection along y-axis; Translation: (x, y) → (x, y – 3)
C) Reflection along y-axis; Translation: (x, y) → (x, y + 3)
D) Reflection along x-axis; Translation: (x, y) → (x, y)
Answers
Answer:
B) Reflection along y-axis; Translation: (x, y) → (x, y – 3)
Step-by-step explanation:
A transformation is the movement of a point from its initial position to a new position. If an object is transformed, all its points are also transformed. Types of transformation are dilatation, rotation, reflection and translation.
The point of triangle ABC are A(-4, 4), B(-7, 1) and C(-3, -2) while for triangle A'B'Ç' is at A'(4, 1), B'(7, -2) and C'(3, -5)
If a point C(x, y) is reflected along y axis, the y coordinates is the same and the x coordinate is opposite (negated), i.e C'(-x, y). If a point C(x, y) is translated 3 units down, the new point is (x, y - 3).
ΔABC transformation to ΔA'B'C', the x coordinate is opposite and the y coordinate is 3 units downward, therefore this is a Reflection along y-axis; Translation: (x, y) → (x, y – 3)
Answer: c
Step-by-step explanation:
The answer is c bc you reflect across the y axis and then translate
Triangle D E F is shown. Lines are drawn from each point to the opposite side and intersect at point G. Line segments D C, E B, and F A are formed and cut each side into 2 equal parts. In triangle DEF, DG = 10 cm. What is CG? 5 cm 10 cm 15 cm 20 cm
Answers
Answer:
5 cm
Step-by-step explanation:
As we can see in the attached figure that G is the point at which the three medians of the triangle meet i.e we called the centroid
And, according to the property of the centroid, it divides the medians in ratio i.e 2:1
DG: CG = 2 : 1
Since the DG is 10 cm
So, the CG would be half of DG i.e 5 cm
Hence, the CG is 5 cm
Therefore the first option is correct
Answer:
the answer is 5 cm
Step-by-step explanation:
2/3 (m-1/2) +3= m/3-7 Please Explain (Will give brainliest)
Answers
Answer:
m= -29
Step-by-step explanation:
This is a bit of a complex equation, but let's work through it.
2/3 (m-1/2) +3= m/3-7
First, we need to distribute the 2/3.
(2/3)(m)+(2/3)(−1/2)+3=m/3+−7
Now we simplify that.
2/3m+−1/3+3=1/3m+−7
We can now combine like terms.
2/3m+8/3=1/3m+−7
The goal is to isolate the variable, so we should subtract 1/3m from both sides.
1/3m+8/3=−7
Lets keep going! We can subtract 8/3 from both sides.
1/3m=-29/3
Well now we know what 1/3 of m is, but we want to know what m is. So we can multiply both sides by three to finally find out what m is!
m=-29
We did it! m=-29
Find SP when CP=Rs.400 and profit%=4%
Answers
Answer:
Rs 416
Step-by-step explanation:
Given,
Cost Price ( CP ) = Rs 400
Profit % = 4 %
Selling price ( SP ) = ?
now, Let's find the value of SP:
SP = [tex] \frac{CP \: (100 + \: profit percent \: )}{100} [/tex]
Plug the values
[tex] = \frac{400(100 + 4)}{100} [/tex]
Add the numbers
[tex] = \frac{400 \times 104}{100} [/tex]
Multiply the numbers
[tex] = \frac{41600}{100} [/tex]
Divide
= Rs [tex]416[/tex]
Selling price ( SP ) = Rs 416
Hope this helps...
Best regards!!
If Camryan has 12 Tie fighters and Logan has 23 more than Camryan how many Tie fighters does Logan have.
Answers
Answer:
logan has 35 Tie fighters
Step-by-step explanation:
Camryan has 12
Logan has 23 more
23+12=35
hope i helped
-lvr
After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y). A student determined y to be –2. Evaluate the student's answer. A. The student is correct. B. The student incorrectly calculated the scale factor to be –2. C. The student incorrectly divided by the scale factor instead of multiplying by it. D. The student incorrectly added the scale factor instead of multiplying by it.
Answers
Answer:
B. The student incorrectly calculated the scale factor to be –2
Step-by-step explanation:
Given that :
After a dilation with a center of (0, 0), a point was mapped as (4, –6) → (12, y).
The student determined y to be -2
If a figure dilated with a center of (0, 0) and scale factor k, then
(x , y) → (kx , ky)
(4, -6) → (12, y)
[tex]k = \dfrac{x'}{x}[/tex]
[tex]k = \dfrac{12}{4}[/tex]
k = 3
Thus; the scale factor is 3
Now; the y-coordinate can now be calculated as;
ky = (3 × -6)
ky = -18
Therefore; the value of y = -18 and the student incorrectly calculated the scale factor to be -2.
How many feet are in a yard? How many feet are in a mile? How many yards are in a mile? Please answer this. Thank you!
Answers
Answer:
352801760
Step-by-step explanation:
1 yard = 3 feet
1 mile = 5280 feet
1 mile = 1760 yards ... (5280 ft/mi)/(3 ft/yd) = 1760 yd/mi
California, the most populous state, has approximately 4 x 107 people living in it. The population of the entire United States is approximately 3 x 108 people. How many times greater is the population of the United States than the population of California?
Answers
Answer:
7.5 times
Step-by-step explanation:
Your calculator can tell you the ratio ...
[tex]\dfrac{3\times10^8}{4\times10^7}=\dfrac{30\times10^7}{4\times10^7}=\dfrac{30}{4}=\boxed{7.5}[/tex]
The population of the US is 7.5 times as great as the population of California.
HELP
for his long distance phone service, tony pays a $5 monthly fee plus 9 cents per minute. last month, Tony's long distance bill was $17.96. for how many minutes was Tony billed?
Answers
Answer:
144 min.
Step-by-step explanation:
y=0.09x+5 ( x is the number of minutes, y is the bill amount)
17.96=0.09x+5
17.96-5=0.09x
x=12.96/0.09=144 minutes
The advertised size of a computer or television screen is actually the length of the diagonal of
the screen. A computer screen measures 30cm by 22.5cm. Determine the length of its
diagonal.
Answers
Answer:
37.5 cm
Step-by-step explanation:
See attached for reference.
let the diagonal be x,
By Pythagorean formula:
x² = (22.5)² + (30)²
x = √[(22.5)² + (30)²]
x = 37.5 cm
ASAP! PLEASE help me with this question!
Answers
Answer:
The last graph is the correct answer
Step-by-step explanation:
Here, we are interested in picking the correct graph that best answers the question.
Before we pick any of the graphs as our answer, it will be appropriate to solve the inequality.
-4h + 42 <34
-4h < 34-42
-4h < -8
Now divide both side by -4; kindly note that when dividing an inequality by a negative number, the sign will change
h > -8/-4
h > 2
So which of the graph best showcases this?
The correct answer is the last graph
Does any wonderful person want to be so kind and give your girl a hand? I am talking about the math question down below:)
Answers
Answer:
The last one, The Hypotenuse Leg Theorem, or HL Theorem,
Step-by-step explanation:
Answer:
HL theorem
Step-by-step explanation:
If any 2 right angled triangles have same length of hypotenuse then both are congruent by HL theorem
Find the mean and standard deviation. Show all work. 1. X 0 1 2 3 4 P(x) .07 .38 .22 .13
Answers
Answer:
Mean = 2.14
Standard deviation = 2.40
Step-by-step explanation:
The calculation of mean and standard deviation is shown below:-
[tex]X = .07\times0 + 0.20\times 1 + 0.38\times 2 + 0.22\times 3 + 0.13\times 4\\\\ = 0 + 0.2 + 0.76 + 0.66 + 0.52[/tex]
= 2.14
So, the mean is 2.14
Now, For computing the standard deviation first we need to find out the variance which is shown below:-
Variance is
[tex]Var(X) = P(X^2) - [P(X)]^2\\\\ P(X^2) = .07\times (0^2) + .20\times (0^1) + .38\times (0^2) + .22\times (0^3) +0.13\times (0^4)[/tex]
After solving the above equation we will get
= 5.78
Now, the standard deviation is [tex]= \sqrt{Variance}[/tex]
[tex]= \sqrt{5.78}[/tex]
= 2.404163056
or
= 2.40
Rearrange the following formula to solve for p: wa+3p=q
Answers
Answer:
wa + 3p = q
3p = q - wa -- Subtract wa
p = (q - wa) / 3 -- Divide by 3
Answer:
[tex] \boxed{\sf p = \frac{1}{3} (p - wa)} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: p: \\ \sf \implies wa + 3p = q \\ \\ \sf Subtract \: wa \: from \: both \: sides: \\ \sf 3p = q - wa \\ \\ \sf Divide \: both \: sides \: by \: 3: \\ \sf \implies p = \frac{1}{3} (q- wa)[/tex]
Please help.. ty if you do
Answers
Answer:B
Step-by-step explanation: x is less than 1 so it is a open circle on the graph and x is greater than or equal to -1 so it is a closed circle on -1, B has both of these so B is the answer
The answer is B because is B
formula of minimmum pressure
Answers
P = W/A.
Where W =weight ,A =area
According to an article by George Will (San Jose Mercury News, Feb. 28, 2002), the average U.S. consumption per person per year of French Fries is 28 pounds. Suppose that you believe that the average in Santa Clara County is not 28 pounds. You randomly survey 50 people in this county. The sample average is 24 pounds with a sample standard deviation of 10 pounds. Conduct an appropriate hypothesis test. The p-value for this test is:________.
a. 0.0068
b. 0.0034
c. 0.0136
d. 0.0047
Answers
Answer: d. 0.0047
Step-by-step explanation: The p-value is the calculated value used to compare to the significance level to determine if you reject or fail to reject the null hypothesis.
To find p-value, first find the z-score:
z = [tex]\frac{x-\mu}{SE}[/tex]
x is sample mean
μ is population mean
SE is standard error calculated by [tex]\frac{s}{\sqrt{n} }[/tex]
SE = [tex]\frac{10}{\sqrt{50} }[/tex]
SE = 1.414
z = [tex]\frac{24-28}{1.414}[/tex]
z = - 2.83
The hypotheses ([tex]H_{0}, H_{a}[/tex]) are if sample mean is equal or different from the average given, so, p-value will be the value of z from z-table multiplied by 2:
p-value = 0.00233*2
p-value = 0.0047
The p-value for this test is 0.0047
Write the equation of the line that passes through (–2, 1) and is perpendicular to the line 3x – 2y = 5.
Answers
Answer:
y = [tex]-\frac{2}{3} x[/tex] - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The line (l1) passes through (-2, 1) and is perpendicular to the line whose equation is;
3x - 2y = 5
Converting this equation to slope intercept form gives;
2y = 3x - 5
y = 1.5x - 2.5
Let the slope of the perpendicular line (l2) be m(PERP).
The product of slopes of two perpendicular lines is -1
The slope of our first line (l1) = 1.5
So 1.5 × m(PERP) = -1
m(PERP) = -1 ÷ 1.5 = [tex]-\frac{2}{3}[/tex]
Taking another point (x,y) on line (l2);
[tex]\frac{y - 1}{x + 2} = -\frac{2}{3}[/tex]
Cross multiplying this gives;
y = [tex]-\frac{2}{3} x[/tex] - [tex]\frac{1}{3}[/tex]
which is the equation of our second line (l2).
How many 5 digit numbers have five distinct digits?
Answers
Answer:3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
A pound is approximately 0.45 kilogram. A person weighs 87 kilograms. What is the person’s weight, in pounds, when rounded to the nearest whole number?
Answers
Answer:
193.33333 pounds
Step-by-step explanation:
Divide 87kg by 0.45
So, it's 87 ÷ 0.45 = 193.3333333
Answer: 190
Step-by-step explanation:
I'm marking answers as brainliest. When solving this system using elimination you should _______________. 6x - 9y = 21, 3x + y = 5 Multiply the second equation by 2. Solve the second equation for y. Set the equations equal to each other. Multiply the second equation by 9.
Answers
Answer:
Multiply the second equation by 9.
Step-by-step explanation:
To use the elimination method, you need to be able to add the equations and have one variable add to zero. That way you eliminate that variable.
The first equation has -9y. The second equation has y. If you multiply the second equation by 9, you will have 9y in the second equation. Then when you add equations, you will add -9y and 9y and will eliminate y.
Answer: Multiply the second equation by 9.
Answer:
Step-by-step explanation:
6x - 9y = 21
-6x -2y = -10
-11y = 11
y = -1
3x - 1 = 5
3x = 6
x = 2
(2, -1)
Maxim has been offered positions by two car dealers. The first company pays a salary of $10,000 plus a commission of $1,000 for each car sold. The second pays a salary of $20,000 plus a commission of $500 for each car sold. How many cars would need to be sold to make the total pay the same?
Answers
Answer:
20 cars
Step-by-step explanation:
Solve for x!
10000+1000x(the first company)=20000+500x (the second company)
-10000 -10000
1000x=10000+500x
-500x -500x
500x=10000
divide by 500 on both sides,
x=20
Check!
First company: 10000+1000(20)=10000+20000=30000
Second company: 20000+500(20)=20000+10000=30000!
30000=30000
Hope this helped!
Number of cars would need to be sold to make the total pay same is 20
What is Equation?
An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
What is Expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context
Given,
The first company pays a salary of $10,000 plus a commission of $1,000 for each car sold
therefore the expression is
10000+1000x
where x is the number of car sold
The second pays a salary of $20,000 plus a commission of $500 for each car sold
Then the expression will be
20000+500x
How many cars would need to be sold to make the total pay the same is
10000+1000x=20000+500x
1000x-500x=20000-10000
500x=10000
x=20
Hence, the number of cars would need to be sold to make the total pay the same is 20
Learn more about Equation and Expression here
https://brainly.com/question/10413253
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please help ASAP. Which statement below is NOT true for the graph of a quadratic function? a) the axis of symmetry intersects the parabola at the vertex b) when the coefficient of x^2 is positive, the vertex of the parabola is a minimum point c)The vertex of a parabola is its highest or lowest level d) the parabola is symmetrical about the y-axis
Answers
Answer:
Step-by-step explanation:
All of these statements about a vertical parabola with known vertex are true.
The statement which is not always true about the graph of a quadratic function is option d) the parabola is symmetrical about the y-axis.
What is Parabola?
A parabola is a open U shaped curve on a plane where all the points on the curve will be at an equal distance from a fixed point called focus and a fixed line called directrix.
Vertex of a parabola is the point where the parabola intersects with it's line of symmetry. So the vertex will always lie at the maximum point or the minimum point.
Axis of symmetry is the line that passes through the vertex of a parabola.
Graph of the quadratic equation will always be a parabola.
When the coefficient of x² is positive, then the vertex of the parabola will be at a minimum point and if the coefficient is negative, then the vertex will be at a maximum point.
The parabola is symmetrical to y axis only if the vertex of the parabola lies on the Y axis. So it will not be always true.
Hence the statement the parabola is symmetrical about the y-axis is not always true.
Learn more about Parabola here :
https://brainly.com/question/1440592
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HELPPP PLSSS Write the equation of the arithmetic sequence defined by a1 = 3 and a4 = 0. (Type your answer in the form an= and please do NOT use spaces.)
Answers
Answer:
[tex]a_n=4-n[/tex]
Step-by-step explanation:
Recall the definition of the general nth term of an arithmetic sequence of common difference "d":
[tex]a_n=a_1+(n-1)\,d[/tex]
we can use this formula to find the common difference knowing the first and fourth terms, and then write the general form for the sequence:
[tex]a_n=a_1+(n-1)\,d\\0=3+(4-1)\,d\\0=3+3\,d\\0-3=3\,d\\d=-1[/tex]
Then the general form for the nth term of this sequence is:
[tex]a_n=3+(n-1)\,(-1)\\a_n=4-n[/tex]
solve the equation by using substitution method X + 2 Y equal to 8 equation first 2 x minus 2 equal to 10 equation second
Answers
Answer:
(6, 1)
Step-by-step explanation:
x + 2y = 8
1. subtract 2y to get x alone -- x = -2y + 8
2. insert (-2y + 8) as x
2x - 2 = 10
2(-2y + 8) -2 = 10
3. distribute the 2
-4y + 16 - 2 = 10
4. combine like terms
-4y + 14 = 10
5. subtract 14 from both sides
-4y = -4
6. divide by -4
y = 1
7. plug y into any of the two original equations
x + 2(1) = 8
8. simplify
x + 2 = 8
x = 6
9. check answer with second equation
2(6) - 2 = 10
12 - 2 = 10
What is the solution of this system of linear equations?
A. (1, 0)
B. (0,0)
C. (0, 1)
D. X=0
Graph is attached , help quick please
Answers
Answer:
The answer is C.
Step-by-step explanation:
In order to find the solution of the linear equation, you have to find the coordinates where they intersect.
So according to the graph, both lines intersect at the coordinates of ( 0 , 1 ).
(Correct me if I am wrong)