Answer:
x = 36.87 degrees.
Step-by-step explanation:
4 cos x + 3 sin x = 5
Use the Auxiliary angle method:
R sin (α + x) = R sin α cos x + R cos α sin x
Comparing coefficients:
R sin α = 4 and R cos α = 3
R sin α / R cos α = 4/3
So tan α = 4/3
α = 53,13 degrees.
Now R^2(sin^2 α + cos^2 α ) = 3^2 + 4^2 = 25
R^2 = 25
R = 5.
R sin (x + 53.13) = 5
5 sin ( x + 53.13) = 5
sin (x + 53.13) = 1
x + 53.13 = 90
x = 36.87 degrees.
6.50 is 25$ of what number?
Answer:
1.625
Step-by-step explanation:
25% or 6.50 is 1.625 so multiply 25 times 6.50 then divide it by 100
find the area a polygon
Solve X^2 - 3x - 10 = 0 by using the quadratic formula
Good evening
Answer:
x = 5 or x = -2Step-by-step explanation:
Look at the photo below for the details.
:)
Answer:
x = 5 or x = -2
Step-by-step explanation:
See the attached image for the working out.
Round 67.6 to nearest whole number
Answer:Integer Part: 67
Fractional Part: 60
Step-by-step explanation: This is how to round 67.6 to the nearest whole number. In other words, this is how to round 67.6 to the nearest integer.
67.6 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:
Answer:67
Step-by-step explanation:
When you round 67.6 to the nearest whole number you take the 6 off and get 67
What is the first step to solve this equation;
11-3x=44
The first step to solve the equation 11-3x=44 is to isolate the variable x by subtracting 11 from both sides of the equation.
Explanation:To solve the equation 11-3x=44, the first step is to isolate the variable x.
To do this, we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 11 from both sides:
11 - 11 - 3x = 44 - 11-3x = 33Now we have -3x = 33 as our new equation.
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−3(y+3)=2y+3
y = ___
(type your answer as a number, "no solution" or "infinite solutions")
Answer:
y = -5/12
Step-by-step explanation:
−3(y+3)=2y+3 (multiply -3 with inside the parenthesis)
➡
-3y -9 = 2y +3
➡
-3y -2y = 3+9 add like terms
➡
-5y = 12
➡
y = -5/12
Will is 29% taller than Wanda, so Will's height is ____% of Wanda's height.
Will is 29% taller than Wanda, so Will's height is 77.5% of Wanda's height.
Solution:
Let x be Will's height, and y be Wanda's height.
Since Will is 29% taller than Wanda we have,
[tex]x=1.29y \rightarrow(y+29\% \text{ of y }\rightarrow1y+.29\rightarrow y\rightarrowy(1+.29)\Rightarrow1.29y)[/tex]
Then solving for y we get,
[tex]\Rightarrow y=\frac{x}{1.29}\rightarrow y=\frac{100x}{129}[/tex]
[tex]\Rightarrow y\approx0.7752x[/tex]
Therefore, Will is 77.5% of Wanda's height.
Will's height is 129% of Wanda's height.
Explanation:To calculate the percentage of Will's height compared to Wanda's height, we need to determine how much taller Will is than Wanda. If Will is 29% taller, it means his height is 129% of Wanda's height. This can be calculated by adding 29% to 100%: 100% + 29% = 129%. Therefore, Will's height is 129% of Wanda's height.If Will is 29% taller than Wanda, then he is 100% of Wanda's height (which is Wanda's total height) plus an additional 29% of Wanda's height. Therefore, if you combine these percentages, you will find that Will's height is 129% of Wanda's height.
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can you help me with 4 and 6 only? thank you
If I worked 208 hrs out of 409 what percentage would that be?
Step-by-step explanation:
(208/409)*100%
50.85%
There were 4 car races on saturdayand 3 on Sunday. If there were 9 cars racing in each race, how many cars raced over the two days?
Final answer:
A total of 63 cars raced over the two days: 36 cars on Saturday (4 races × 9 cars) and 27 cars on Sunday (3 races × 9 cars).
Explanation:
The student is asking to calculate the total number of cars that raced over two days. There were 4 car races on Saturday and 3 on Sunday, with 9 cars racing in each race. To find the total number of cars that raced, you would multiply the number of races each day by the number of cars in each race and then add those two products together.
For Saturday: 4 races × 9 cars per race = 36 cars
For Sunday: 3 races × 9 cars per race = 27 cars
Adding the cars from Saturday to the cars from Sunday gives us the total: 36 cars + 27 cars = 63 cars.
Therefore, over the two days, a total of 63 cars raced.
brochure that has the following problems with solutions.
Find the coordinate of point P that divides the line segment from A(-2,3) and B(1,6) in the ratio
of 1 to 3.
Answer:
P ≡ [tex](- \frac{5}{4}, \frac{15}{4})[/tex]
Step-by-step explanation:
The point P divides the line segment from A(-2,3) and B(1,6) in the ratio of 1 : 3.
So, AP : PB = 1 : 3.
Now, the coordinates of point P will be given by [tex](\frac{1 \times 1 + 3 \times (- 2)}{1 + 3}, \frac{1 \times 6 + 3 \times 3}{1 + 3})[/tex]
= [tex](- \frac{5}{4}, \frac{15}{4})[/tex] (Answer)
Note: Let there are two points with known coordinates [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] and another a point having coordinates (h,k) divides the line joining the two above points internally in the ratio m : n, then (h,k) is given by
(h,k) ≡ [tex](\frac{mx_{2} + nx_{1}}{m + n}, \frac{my_{2} + ny_{1}}{m + n})[/tex]
The section inside the border is x inches and (12-x) inches wide. How do I write a function to represent the area a of the section inside the border
Answer:
The function to represent the area a of the section inside the border is [tex]A=12x-x^2[/tex]
Step-by-step explanation:
Given section inside the border is [tex]x[/tex] inches and [tex](12-x)[/tex] inches.
We need to write the function to represent the area of the section inside the border.
We can see the length of border is [tex]x[/tex] and width of the border is [tex](12-x)[/tex].
So, the area of the rectangle will be [tex]length\times width[/tex]
The area [tex](A)[/tex] will be
[tex]A=x(12-x)\\\\A=12x-x^2[/tex]
So, the function to represent the area a of the section inside the border is [tex]A=12x-x^2[/tex]
I need this answer ASAP ROCKY??!
Answer:
OPTION C: 2x - y = -1
Step-by-step explanation:
Equations of two straight lines do not have a solution when they do not meet. Also, two parallel lines never meet.
Given the equation of the first line is: 2x - y = 1. So, the line parallel to this line should be the answer.
Note that the equations of two parallel lines only differ by a constant.
i.e, If ax + by + c = 0 is an equation of a line then the equation of the line parallel to this would be ax + by + k = 0.
Hence, the required answer is: 2x + y = -1, which is OPTION C.
I WILL GIVE BRAINLEY TO THE MOST CORRECT AND FIRST ANSWER PLUS A LOT OF POINTSS!! PLEASE HELP ME ASAPPPP!
-2 + (-6y) + 5 y - 8y y=4
4x + 5 - 5x x=12
4x + 2y - x - 8 x =1 y =5
-3 + 9 -(-4y) + 5x x =1 y =-5
-8 - 4x + y - 6x x =-9 y =9
7x + 1 - y - 3x - (-9) x =7 y =-6
5x + (-y) + 8 -6x + 9y x =4 y =-2
7 - x + 4y - 6x -3y x =-1 y =8
-x - (-y) + (-x) - y + 5 x =-3 y =-6
what is 45cm added to 1m 74cm
Answer:
45cm + 1m 74cm = 2m 19cmStep-by-step explanation:
We know:
1m = 100cm
therefore
1m 74cm = 1m + 74cm = 100cm + 74cm = 174cm
45cm + 1m 74cm = 45cm + 174cm = 219cm = 200cm + 19cm = 2m 19cm
Answer:its is 2m 19cm
Step-by-step explanation:
0.45+
1.74
______
2.19
Which is 2cm 19m. HOPE IT HELPS YOU!!!
Tyler is overdrawn at the bank by $180 He gets $70 for his birthday and deposits it what is his account balance now
Answer:
-$110
Step-by-step explanation:
An overdrawn bank account would be -$180. you would have to add $70 .
given 70 is not large enough to fully bring the balance to 0. long story short, subtract 70 from 180. since 70 is < 180 the number is therefore negative since 180 is negative in this problem
I hope this helps!!^^
Answer:
He is overdrawn by $110
Step-by-step explanation:
-180+ -70=110
Let f(x) = 2x3 – 4x.
Find f(-2).
Answer:
Step-by-step explanation:
f(x) = 2x^3 - 4x.....find f(-2).....so sub in -2 for x
f(-2) = 2(-2^3) - 4(-2)
f(-2) = 2(-8) + 8
f(-2) = -16 + 8
f(-2) = -8 <==
We have [tex]f(x)=2x^3-4x[/tex], to find [tex]f(-2)[/tex] put -2 instead of x, [tex]f(-2)=2(-2)^3-4(-2)=-16+8=\boxed{-8}[/tex].
Hope this helps.
the midpoint of AB is M(2,-2). If the coordinates of A are (-2,1), what ate the coordinates of B?
Step-by-step explanation:
To go from A to M you need to go 4 to the right and 3 down. If M is the middle you'll need to do the same to get from M to B. So (2+4,-2-3)=(6,-5)
joe divided 1.38 by .6 and what should joe's answer be?
Answer:
Step-by-step explanation:
It should be 2.3 because dividing by decimals is almost the same as dividing by normal numbers you just change the decimal point when you are done dividing.
Which system of linear inequalities has the point (3, –2) in its solution set? y less-than negative 3. y less-than-or-equal-to two-thirds x minus 4 On a coordinate plane, 2 straight lines are shown. The first dashed line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded. y greater-than negative 3. y greater-than-or-equal-to two-thirds x minus 4 On a coordinate plane, 2 straight lines are shown. The first dashed line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded. y less-than negative 3. y greater-than-or-equal-to two-thirds x minus 4 On a coordinate plane, 2 straight lines are shown. The first dashed line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded. y greater-than negative 2. y less-than-or-equal-to two-thirds x minus 4 On a coordinate plane, 2 straight lines are shown. The first dashed line is horizontal at y = negative 2. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.
Answer:
IT'S B
Step-by-step explanation:
i actually got it! i looked up this answer for 3 hours and never found it, but i got it, it's B on edge!!!
The system of linear inequalities that includes the point (3, -2) in its solution set is y less-than-or-equal-to two-thirds x minus 4.
Explanation:The system of linear inequalities that has the point (3, -2) in its solution set is y less-than-or-equal-to two-thirds x minus 4.
The first dashed line in the coordinate plane represents the inequality y = -3, where everything below the line is shaded. The second solid line, with a positive slope and passing through (0, -4) and (3, -2), represents the inequality y ≤ (2/3)x - 4, where everything below the line is shaded.
Therefore, the correct option is y less-than-or-equal-to two-thirds x minus 4.
-4 (×+7)
What is the distributive property of this problem?
Which equation represent a line that is parallel to the y-axis and passes through the point (4,3)?
Answer:
x = 4 OR 1x + 0y = 4
Step-by-step explanation:
so if it is a line parallel to the y axis, it is a vertical line. A vertical line has an undefined slope, so it cant be written in y = mx + b form.
ur equation would be : x = 4....because no matter what y is, x will always be 4.
but if u need it in standard form Ax + By = C it is :
1x + 0y = 4
The equation representing a line that is parallel to the y-axis and passes through the point (4,3) is x = 4.
Explanation:The question is asking for an equation of a line that is parallel to the y-axis and goes through the point (4,3). In a coordinate system, a line parallel to the y-axis is a vertical line. The equation for a vertical line in the coordinate plane is of the form x = c, where 'c' is the x-coordinate of any point the line passes through. In this case, since the line passes through the point (4,3), the x-coordinate is 4. Therefore, the equation of the line parallel to the y-axis that passes through (4,3) is x = 4.
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A rhombus is ____ a quadrilateral.
A) Never
B) Sometimes
C) Always
Answer:
C
Step-by-step explanation:
A rhombus always has 4 sides, making it a quadrilateral.
Feel free to ask further questions..
Find the values of the variables xy, and z in the parallelogram. The diagram is not drawn to scale
Answer:
Therefore x = 33° , y = 40° and z = 109°.
Step-by-step explanation:
i) from properties of parallel lines a pair of alternate interior angles are equal
Therefore x = 33°
ii) from properties of parallelogram that a pair of opposite angles are equal, Therefore z = 109°.
iii) from the law of triangle that the sum of all angles in a triangle is 180° and also using the property of parallel lines that a pair of alternate interior angles is equal we can say that x° + y° + z° = 180° ⇒ 31° + y° + 109° = 180°, therefore y° = 180° - 140° = 40°.
Therefore x = 33° , y = 40° and z = 109°.
The values of x, y and z in the parallelogram is 52°, 38° and 90° respectively.
What is the value of x, y and z?The angles on the same side of the transversal of a parallelogram are supplementary, that is, 180°
So,
33° + 109° + y° = 180°
142 + y = 180
y = 180 - 142
y = 38°
x° + y° = 90°
x + 38 = 90
Subtract 38 from both sides
x = 90 - 38
x = 52°
x° + y° + z° = 180°
52 + 38 + z = 180
90 + z = 180
z = 180° - 90°
z = 90°
Hence,
x = 52°
y = 38°
z = 90°
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Please help with question 1
Answer:
The volume of Solid A is 120 cm³.
Step-by-step explanation:
Given the area of the solids are in the ratio: 4 : 9
Let their actual areas be 4x² and 9x². We have assumed the common ratio as x² for easier computation.
We have area: [tex]$ A_A : A_B = $[/tex] 4x² : 9x²
This implies, the length should have been of the ratio of the square root of these numbers.
Therefore, the ratios of the lengths is: [tex]$ \sqrt{4x^2} : \sqrt{9x^2} $[/tex]
[tex]$ L_A : L_B = 2x : 3x $[/tex]
Now, volume is cube of lengths. Therefore, the ratio of volumes would be:
[tex]$ V_A : V_B = 8x^3 : 27x^3 $[/tex]
Given [tex]$ V_B = 405 cm^3 $[/tex]
[tex]$ \implies 27x^3 = 405 \hspace{1mm} cm^3 $[/tex]
[tex]$ \implies x^3 = \frac{405}{27} = 15 $[/tex]
Hence, the volume of solid A, [tex]$ V_A = 8x^3 = 8 \times 15 = \textbf{120} \hspace{1mm} cm^3 $[/tex].
Hence, the answer.
Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14?
A. 68% of the data points lie between 10 and 14.
B. 68% of the data points lie between 8 and 12.
C. 6896 of the data points lie between 10 and 18.
D. 68% of the data points lie between 10 and 16.
Answer:
Option (c) is correct.
68% of the data points lie between 10 and 18.
Step-by-step explanation:
Given : a normal distribution with a standard deviation of 4 and a mean of 14
We have to choose the sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.
Since, given 68% data.
We know mean of data lies in middle.
And standard deviation is distribute equally about the mean that is 50% of values less than the mean and 50% greater than the mean.
So, 68% of data lies
mean - standard deviation = 14 - 4 = 10
mean + standard deviation = 14 + 4 = 18
So, 68% of the data points lie between 10 and 18.
The correct sentence for a normal distribution with a standard deviation of 4 and a mean of 14, is that 68% of the data points lie between 10 and 18.
The correct answer is C.
About 68% of the data in a normal distribution lie within one standard deviation of the mean.
● 14−4=10 is one standard deviation below the mean, and
14+4=18 is one standard deviation above it.
Thus, the range of 68% of the data values is between 10 and 18. Option C, which states that "68% of the data points lie between 10 and 18," thus accurately sums up the dataset.
Simplify: -26a? + (-25a7)
Answer:
-26a - 25a^7
Step-by-step explanation:
A farm raised a total of 220
Chickens and pigs. The number of legs of the stock are 520. How many chickens and pigs are at the farm?
Answer:
180 chickens and 40 pigs
Step-by-step explanation:
We are given;
Total number of chickens and pigs as 220 Number of legs of chickens and pigs are 520We are required to determine the number of chickens and pigs in the farm;
To answer the question we need to know the following;
1 chicken has two legs 1 pig has four legsAssuming the number of chickens is x and the number of pigs is y
Then we can form two equations;
x + y = 220 ............for the total number of stock 2x + 4 y = 520 ...... for the total number of legsWe can solve the two equations simultaneously to find the number of chickens and pigs;
x + y = 220
2x + 4y = 520
Multiplying the first equation by 2, we get
2x + 2y = 440
2x + 4y = 520
Eliminating x, we get;
- 2y = -80
y = 40
Solving for x;
x = 220 - y
= 220 - 40
x = 180
Therefore, there are 180 chickens and 40 pigs at the farm
A sequence can be generated by using an=4an−1 where a1=6 (a) 6, 20, 76, 300 (b)6, 24, 96, 384 (c)6, 10, 14, 18 (d) 6, 20, 100, 500
Answer:
Option (b) 6, 24, 96, 384
Explanation:
The complete question is:
A sequence can be generated by using [tex]a_n=4a_{(n-1)}[/tex] where [tex]a_1=6[/tex] and n is a whole number greater than 1. What are the first four terms in the sequence.
The given rule [tex]a_n=4a_{(n-1)}[/tex] is a recursive formula, which means that to find any term consecutive term, from the second one, you multiply the current term by 4.
Thus:
[tex]a_1=6\\ \\ a_2=4a_1=4\times 6=24\\\\ a_3=4a_2=4\times 24=96\\ \\ a_4=4a_3=4\times 96=384[/tex]
Answer:
The option (b) is correct as the sequence is generated as 6, 24, 94, 384,...
Step-by-step explanation:
Considering the sequence
[tex]a_{n} =4a_{n-1}[/tex]
As [tex]a_{1} =6[/tex]
So,
[tex]a_{n} =4a_{n-1}[/tex]
[tex]a_{2} =4a_{2-1}[/tex]
[tex]a_{2} =4a_{1}[/tex]
[tex]a_{2} =4.6[/tex]
[tex]a_{2} =24[/tex]
[tex]a_{3} =4a_{3-1}[/tex]
[tex]a_{3} =4a_{2}[/tex]
[tex]a_{3} =4.24[/tex]
[tex]a_{3} =96[/tex]
[tex]a_{4} =4a_{4-1}[/tex]
[tex]a_{4} =4a_{3}[/tex]
[tex]a_{4} =4a_{3}[/tex]
[tex]a_{4} =4.96[/tex]
[tex]a_{4} =384[/tex]
Therefore, the option (b) is correct as the sequence is generated as 6, 24, 94, 384,...
Keywords: sequence
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In a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If
1
4
of the drink is apple juice and
3
10
is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form
Answer:
orange : cranberry : apple : orange
9 : 5 : 6
Step-by-step explanation:
Given the following ratios (fraction):
[tex]\frac{apple}{total} =\frac{1}{4}[/tex]
[tex]\frac{orange}{total} =\frac{3}{10}[/tex]
in order to add/subtract fractions, we have to ensure that the denominators are the same, we can see that for the denominators listed above, the least common multiple for 4 and 10 = 20, hence we can re-write the above as :
[tex]\frac{apple}{total} =\frac{1}{4} =\frac{5}{20}[/tex]
[tex]\frac{orange}{total} =\frac{3}{10} =\frac{6}{20} [/tex]
Hence,
Fraction of cranberry juice of the total is,
1 - [tex]\frac{5}{20}[/tex] - [tex]\frac{6}{20}[/tex]
= [tex]\frac{20}{20}[/tex] - [tex]\frac{5}{20}[/tex] - [tex]\frac{6}{20}[/tex]
= [tex]\frac{9}{20}[/tex]
Because all the denominators are the same, we can assemble the ratios of each component by taking the ratios of the numerators
cranberry : apple : orange
= ratios of their numerators
= 9 : 5 : 6