Answer:
47°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation ...
Cos = Adjacent/Hypotenuse
The side adjacent to ∠P is the one with P in its name: RP. The hypotenuse is the side opposite the right angle, the side without the right-angle vertex in its name: PQ. So, ...
cos(∠P) = RP/PQ = 61/89
∠P = arccos(61/89) ≈ 46.733°
∠P ≈ 47°
Answer:
47 degrees
Step-by-step explanation:
A house valued at £210,000 correct to 2 significant figures. A) What is the lowest value of the house? B) What is the highest value of the house?
Answer:
Range could be 205000 to 214999. Any number in this range, when rounded to two signnificant digits will yield 210000.
The formula for converting a temperature,C, in degree Celsius ('C) to a temperature degree Fahrenheit ('F). F=(9C+160)/5 Q:) What temperature is same on both scale.
Answer:
-40
At -40, the value on both scales are the same.
-40 °C = -40 ° F
Step-by-step explanation:
Given that;
F = temperature in Fahrenheit
C = temperature in Celsius
And;
F=(9C+160)/5 .........1
For temperature to be the same on both scale;
Temperature in Fahrenheit mist be equal to the temperature in Celsius
F = C
Substituting F = C into the equation 1;
C = (9C +160)/5
Multiply both sides by 5
5C = (9C+160)
Collecting the like terms.
5C -9C = 160
-4C = 160
C = -160/4
C = -40
F = C = -40
At -40, the value on both scales are the same.
That means;
-40 °C = -40 ° F
The graph shown here is the graph of which of the following rational functions
Answer:
The answer is 100% B
Step-by-step explanation:
The graph of the polynomial rational function is f ( x ) = x / ( x + 2 ) ( x - 5 )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the polynomial function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x / ( x + 2 ) ( x - 5 )
The rational function is of the form P ( x ) / Q ( x ) , where Q ( x ) ≠ 0
So , the value of P ( x ) = x
And , the value of Q ( x ) = ( x + 2 ) ( x - 5 )
Therefore , the graph of the rational function is plotted
Hence , the graph of the polynomial is f ( x ) = x / ( x + 2 ) ( x - 5 )
To learn more about equation of graph of polynomials click :
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What is the exact value of sin(5π/12)?
(please give steps)
Answer:
0.966053748
Step-by-step explanation:
[tex] \sin \bigg( \frac{5\pi}{12} \bigg) \\ = \sin \bigg( \frac{5 \times 180 \degree}{12} \bigg) \\ = \sin ( 5 \times 15 \degree) \\ = \sin ( 75 \degree) \\ = \sin ( 45 \degree + 30 \degree) \\ = \sin 45 \degree \times \cos 30 \degree + \cos 45 \degree \times \sin 30 \degree \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ \\ = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } \\ \\ = \frac{1.732 + 1}{2 \times 1.414} \\ \\ = \frac{2.732}{2.828} \\ \\ = 0.966053748[/tex]
Find all solutions for a triangle with C = 130°, c = 17, and b = 5. Round to the nearest tenth.
a.A= 37.0°, B = 15.0°, a = 15.2
c.A = 37.0°, B = 13.0°, a = 13.4
b. A= 35.0°, B = 13.0°; a = 15.4
d no solutions
Answer:
C
Step-by-step explanation:
Use sine rule
17/sin130=5/sinB
(5×sin130)÷17=sinB
sinB=0.2253017892
B=sin^-1ans above
=13.4
A=(130+13) subtracted from 180=37°
a/sin37=17/sin130
=13.4
Find the area of the shape.
This is a [tex]90^\circ[/tex] sector of a circle of radius 8, or one-fourth of the circle, so the area is [tex]\frac{\pi(8)^2}{4}=\boxed{16\pi}.[/tex]
Answer: 50.2656
Step-by-step explanation:
Help appreciated please and thank you
Answer:
D. [tex] \frac{4 \sqrt{33} }{33} [/tex]
Step-by-step explanation:
[tex] \tan \alpha = \frac{4}{ \sqrt{33} } \\ = \frac{4}{ \sqrt{33} } \times \frac{ \sqrt{33} }{ \sqrt{33} } \\ \\ = \frac{4 \sqrt{33} }{ {( \sqrt{33)} }^{2} } \\ \\ \tan \alpha = \frac{4 \sqrt{33} }{33} [/tex]
You earn $8.50 per hour at your summer job. Write and solve an inequality that represents the number of hours you need to work in order to buy a digital camera that costs $348.50
Answer:
8.50x [tex]\geq[/tex] 348.50
41 hours
Step-by-step explanation:
x= amount of hours
Please help! Correct answer only, please! Find the following product if possible. Explain if it is not possible. A. B. C. D.
Answer:
Option (B)
Step-by-step explanation:
If A = [tex]\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}[/tex] and B = [tex]\begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}[/tex]
Multiplication of these matrices,
A.B = [tex]\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}\times \begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}(1(-2)+3(3) & 1(1)+3(4)\\ (-2)(-2)+5(3) & 1(-2)+5(4)\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}7 & 13\\ 19 & 18\end{bmatrix}[/tex]
Therefore, Option (B) will be the answer.
Cameron surveyed 200 of the students in his school about their favorite color. 60
students said their favorite color was red. What percentage of the surveyed students
said their favorite color was red?
Answer:30%
Step-by-step explanation:
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
smaller r = ( 6.5 , 0)
larger r = ( 21.5 , 0)
vertex = ( 14, -56.25)
Step-by-step explanation:
f(r) = (r -14)² -56.25 square (r-14)
f(r) = r² -28r +196 -56.25 simplify
f(r) = r² -28r + 139.75
use quadratic formula
x=−b±√(b²−4ac)/ 2a
a = 1, b =-28, c = 139.75
x=−(−28)±√(−28)2−4(1)(139.75)2(1)
x=(28±√225)/2
x=43/2 or x=13/2
or 21.5 and 6.5
This parabola is given in vertex form f (r) = a(r - h)² + k, where (h, k) is the vertex of the parabola so just write the given numbers ( 14, -56.25)
Target sells 24 bottles of water for $3.and 36 bottles of water for $4 Which is the better buy and by how much
24 bottles for $3 by 1.50 per bottle
B)
24 bottles for 53 by 700 per bottle
24 bottles for $3 by 75c per bottle
36 bottles for $4 by 1 46 per bottle
60
Answer:
The last answer choice is the correct answer
Step-by-step explanation:
im hoping this helped, if not im sorry.
Solve
1. x2 + x - 6 = 0
Answer:
x = -3 x=2
Step-by-step explanation:
x^2 + x - 6 = 0
Factor
What two numbers multiply to -6 and add to 1
3*-2 =-6
3+-2 =1
(x+3) (x-2) = 0
Using the zero product property
x+3 = 0 x-2 = 0
x = -3 x=2
This table shows the time it took a group of students to complete a quiz
A total of 937 people attended the play admission was two dollars for adults and $.75 for students the total ticket sales amounted to $1109 how many students and adults attended the school play
Answer:
325 adults
Step-by-step explanation:
x=#adults
y=#children
x+y=937
2x+0.75y=1109
2x+2y=1874
-2x-0.75y=1109
1.25y=765
y=612
x=937-612
x=325
x | f(x)
2.0 | 2.8
2.5 | 1.1
3.0 | –0.8
3.5 | –1.2
4.0 | –0.3
4.5 | 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A. between 2.0 and 2.5 and between 4.0 and 4.5
B. between 2.5 and 3.0 and between 4.0 and 4.5
C. between 2.0 and 2.5 and between 3.5 and 4.0
D. between 2.5 and 3.0 and between 3.5 and 4.0
Answer:
Option B.
Step-by-step explanation:
If the value of function is 0 at x=c, then c is a root or zero of the function. It means the graph of function intersect x-axis at its zeroes.
From the given table it is clear that the value of function are
x | f(x) | Sign
2.0 | 2.8 | Positive
2.5 | 1.1 | Positive
3.0 | –0.8 | Negative
3.5 | –1.2 | Negative
4.0 | –0.3 | Negative
4.5 | 0.7 | Positive
The sign of values of function changes in interval 2.5-3.0 and 4.0-4.5.
It means, the graph of function must intersect x-axis in interval 2.5-3.0 and 4.0-4.5. So, the zeros of the function lie between 2.5 and 3.0 and between 4.0 and 4.5.
Therefore, the correct option is B.
Answer:
between 2.5 and 3.0 and between 4.0 and 4.5
Step-by-step explanation:
B on my computer but always double check!
Shama’s age is three times the age of her son Ankit. 10 years ago Shama
was 5 times the age of Ankit. Find the present age of Shama.
Answer:
Step-by-step explanation:
Let sharma age be S and Ankit age be A
S = 3a
(s-10) = 5(a-10)
substitute 1 in 2
3a-10 = 5a -50
40 = 2a
a = 20
s = 3 * 20 = 60
Solve the given system of equations.
Answer: x= -1/2 y=3/4
Step-by-step explanation:
Answer:
x = -4y + 5/2
Step-by-step explanation:
step 1: 2x +8y + -8y = 5 + -8y
2x = -8y+ 5
step 2: divide both sides by 2
2x /2 = -8y+5/2
x= -4 + 5/2
please help will mark brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
256
Step-by-step explanation:
<1=<8 -->alt exterior angles
<4=<1 --> vertical angles
= <1=<4=<8(128)
256
A bookstore manager marks down the price of older hardcover books, which originally sell for b dollars, by 42%. Part 1 out of 4 Enter an expression for the markdown using a decimal. The markdown is ..... (Answer this question piece)
Answer:
0.42
Step-by-step explanation:
The original price of the old hardcover books was sold for b dollars. But the manager markdown the hardcover books by 42%.
The expression of the markdown using a decimal can be represented below.
Recall the markdown is 42 %. If you want to convert from percentage to a decimal, you have to move the decimal point two places to the left . The percentage sign is removed at this stage and the value is represent in decimal. Or you can just divide the percentage value by 100.
In our case the percentage value can be solved as 42/100 = 0.42 in decimal or by just simply moving the decimal points two places to the left which is 0.42.
M + 3 / 5 is equal to 7 / 5
Answer:
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A designer enlarged both the length and the width of a rectangular carpet by 60 percent. The new carpet was too large so the designer was asked to reduce its length and its width by 25 percent. By what percent was the area of the final item greater than the area of the original?
Answer:
300%
Step-by-step explanation:
Let the length of the carpet be L.
Let the width of the carpet be W.
The original area of the carpet is:
A = L * W = LW
The length and width are enlarged by 60%.
The new length is:
L + (L * 60/100) = L + 0.6L = 1.6L
The new width is:
W + (W * 60/100) = W + 0.6W = 1.6W
The length and width are then reduced by 25%.
The new length is:
1.6L + (1.6L * 25/100) = 1.6L + 0.4L = 2L
The new width is:
1.6W + (1.6W * 25/100) = 1.6W + 0.4W = 2W
The new area will be:
A = 2L * 2W = 4LW
To find the percentage increase in the area, we subtract the original area from the new area and divide by the original area:
4LW - LW = 3LW
% increase is:
[tex]\frac{3LW}{LW} * 100[/tex] = 300%
The area of the final item is 300% greater than the original item.
Answer:
44%
Step-by-step explanation:
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please help me with math
Answer:
6. composite figure
7. 60+432=492
The area of a square is 350cm². Find the length of the diagonal.
Answer: 26.46cm
Step-by-step explanation:
The formula of a diagonal of a square is square root 2 a(a is not under the square root though)
So just substitute the a (area) with 350 and solve the equation.
Answer:
26.46cm
Step-by-step explanation:
Because you are dealing with a square, take the square root of the area and then use pythagoras theorem to calculate the diagonal.
Can someone please help me I need to get this right
Answer:
Option C
Step-by-step explanation:
Option C would map (1,3) to (-1,4).
[tex](x,y)\rightarrow(x-2,y+1)[/tex]
[tex](1,3)\rightarrow(1-2,3+1)\rightarrow(-1,4)[/tex]
1 - 2 = -1
3 + 1 = 4
Option C should be the correct answer.
Answer: 3rd option (x-2, y+1)
Step-by-step explanation:
1-2 = -1
3+1 = 4
Solve the exponential equation. 4x = 0.5 -2 -1 -1/2
Answer:
[tex]x=-1/2[/tex]
Step-by-step explanation:
[tex]4^x=1/2[/tex]
Make the bases 2 on both sides of the equation.
[tex]2^{2^x}=2^{-1}[/tex]
Multiply the exponents.
[tex]2^{2x}=2^{-1}[/tex]
Cancel the bases.
[tex]2x=-1[/tex]
Divide 2 into both sides of the equation.
[tex]x=-1/2[/tex]
Square OABC is drawn on a centimetre grid. O is(0,0) A is(3,0) B is(3,3) C is(0,3). Write down how many invariant points there are on the perimeter of the square, when OABC is enlarged, scale factor 2, centre (0,0)
Answer:
1 point. O (0,0)
Step-by-step explanation:
Hi
Invariant points are those points who remain on the same location after a given transformation.
1. Plotting OABC we have it below:
2. Whenever we dilate centered, the image O'A'B'C' will be determined by the following points:
[tex]O'(0,0) \:A'(3,0) B'(6,6) \:and\:C'(0,6)[/tex]
Since the Scale factor is (2)
3. Check it out O'A'B'C' below
4. On the perimeter of O'A'B'C' (enlarged OABC) we have left 1 point invariant.
Answer:
The answer would be 2
Which of the following options have the same value as %70, percent of 80?
Answer:
A, C and E.
Step-by-step explanation:
[tex]70 \% \times 80[/tex]
[tex]70/100 \times 80[/tex]
[tex]560/10[/tex]
[tex]=56[/tex]
[tex]0.7 \times 80[/tex]
[tex]=56[/tex]
[tex]7/10 \times 80[/tex]
[tex]=56[/tex]
What is the volume of this cylinder?
Use a ~ 3.14 and round your answer to the nearest hundredth.
10 mm
7 mm
Answer:
[tex]1538.6mm^{3}[/tex]
Step-by-step explanation:
[tex]V=\pi r^{2} h[/tex]
[tex]V=3.14*7^{2} *10[/tex]
[tex]V=31.4*49=1538.6[/tex]
The probability that a foot ball team will win a game is 2/11.The probability that they will lose is 3/11.What is the probability the game will be a draw
Answer:
6/11
Step-by-step explanation:
Since there are 3 possible outcomes for the game (win,lose and draw) and the total probability for the three outcomes must be equal to 1.
Then;
The probability that the game will be a draw Pd = 1 - (probability that they will lose Pl + probability that they will win Pw)
Pd = 1 - (Pl + Pw) ........1
Given;
Pl = 3/11
Pw = 2/11
Substituting the values into equation 1;
Pd = 1 - (2/11 + 3/11)
Pd = 6/11
The probability that the game will be a draw Pd = 6/11
