Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
When should the Empirical Rule be used?
The empirical formula should be used after calculating the standard deviation and collecting the exact data needed for a forecast.
Explanations:What is the empirical rule?The empirical rule is a term used in statistics also known as the 68–95–99.7 rule. This rule is majorly used in forecasting the final outcome of events.
The empirical rule can be used to therefore determine a rough estimate of the outcome of the impending data to be collected and analyzed. This is done after calculating the standard deviation and collecting the exact data needed.
68–95–99.7 rule,
(Combining Equation)What is the result of subtracting the second equation from the first ?-2x + y = 0 -7x + 3y = 2
We are given the following two equations
[tex]\begin{gathered} -2x+y=0\quad eq.1 \\ -7x+3y=2\quad eq.2 \end{gathered}[/tex]Let us subtract the second equation from the first equation.
Therefore, the result of subtracting the second equation from the first is
[tex]5x-2y=-2[/tex]Triangle A is rotated 90° about the origin. Which triangle shows the image?
Rotation 90° about the origin.
First, choose a point from triangle A.
For example: (-2,2)
For any point (x,y) rotated 90° =(-y,x)
So:
(-2,2) becames = (-2,-2)
Triangle D
I really need help solving this problem from my trigonometry prepbook
The terminal ray of 145° lies in II Quadrant.
The terminal ray of -83° lies in IV Quadrant.
The terminal ray of -636 lies in I Quadrant.
The terminal ray of 442 lies in I Quadrant.
the rate of change at which the water level rises is ___ centimeters per minutes. so, involving the equation ____ for y gives a y-value equal to___
We will have the following:
The rate at which the water rises is 13/4 cm per minute.
So, solvinng the equation:
[tex]\frac{13}{4}=\frac{y}{12}[/tex]For y gives a value for y equal to:
[tex]y=\frac{13\cdot12}{4}\Rightarrow y=39[/tex]What is the distance from the ball to the base of the building? Round to the nearest foot.*
Given:
[tex]\theta=37^{\circ}\text{ ; height of the building is }60\text{ ft}[/tex][tex]\begin{gathered} \tan 37^{\circ}=\frac{Height\text{ of the building}}{\text{Distance between the ball and foot of the building}} \\ 0.7536=\frac{60}{\text{Distance between the ball and foot of the building}} \\ \text{Distance between the ball and foot of the building}=\frac{60}{0.7536} \\ =80\text{ feet} \end{gathered}[/tex]80 feet is the final answer.
When the polynomial mx^3 - 3x^2 +nx +2 is divided by x+3, the remainder is -4. When it is divided by x-2, the remainder is -4. Determine the value of m and n.
Answer:
[tex]\begin{gathered} m\text{ =-2} \\ n\text{ =11} \end{gathered}[/tex]Explanation:
Here, we want to find the value of m and n
If we substituted a supposed root into the parent polynomial, the value after evaluation is the remainder. If the remainder is zero, then the value substituted is a root.
for x+ 3
x + 3 = 0
x = -3
Substitute this into the first equation as follows:
[tex]\begin{gathered} m(-3)^3-3(-3)^2-3(n)+\text{ 2 = -4} \\ -27m\text{ -27-3n+ 2 = -4} \\ -27m\text{ -3n = -4}+27-2 \\ -27m-3n\text{ = 21} \\ -9m\text{ - n = 7} \end{gathered}[/tex]We do this for the second value as follows:
x-2 = 0
x = 2
Substitute this value into the polynomial:
[tex]\begin{gathered} m(2)^3-3(2)^2+2(n)\text{ + 2 = -4} \\ 8m\text{ - 12 +2n + 2 = -4} \\ 8m\text{ + 2n = -4-2+12} \\ 8m\text{ + 2n = 6} \\ 4m\text{ + n = 3} \end{gathered}[/tex]Now, we have two equations so solve simultaneously:
[tex]\begin{gathered} -9m-n\text{ = 7} \\ 4m\text{ + n = 3} \end{gathered}[/tex]Add both equations:
[tex]\begin{gathered} -5m\text{ = 10} \\ m\text{ =-}\frac{10}{5} \\ m\text{ = -2} \end{gathered}[/tex]To get the value of n, we simply susbstitute the value of m into any of the two equations. Let us use the second one:
[tex]\begin{gathered} 4m\text{ +n = 3} \\ 4(-2)\text{ + n = 3} \\ -8\text{ + n = 3} \\ n\text{ = 8 + 3} \\ n\text{ = 11} \end{gathered}[/tex]A park has several rows of trees. Each row has 5 trees. How many trees could be in the park?
Answer: so lets say x =the exact amount of rows
so each row has 5 tree's
then a is the answer
its an equation of x·5=a
so that would be a unknown number of trees so you assume that there is more than 1 row because there is several rows so its a incomplete question
Step-by-step explanation:
Which of the following are a qualitative catecorical variables
A qualitative variable, also called a categorical variable, is a variable that isn’t numerical. It describes data that fits into categories.
From the given options below, the arrival status of a train ( early, on time, late, canceled) and a person's blood type are the only qualitative variables.
Hence, Option 3 and Option 5 are the correct answers.
I need help with a math question. Ilinked it below
EXPLANATION:
We are given a dot plot as shown which indicates the ages of members of an intermediate swim class.
The dot plot indicates a cluster to the right for the values;
[tex]11yrs-14yrs[/tex]This indicates that a reasonable amount of the members are within that age range.
For this reason, it is not likely that Mira will be able to convince her mother.
This is because Mira's age (13 years old) is within the area where the data are clustered.
Therefore;
ANSWER:
(1) The data are clustered between 11 and 14 years old
(2) It is not likely that she will be able to convince her mother
(3) Mira's age is within the area where the data are clustered.
How many times in the parabola does a line intersect?
The line can intersect the parabola at one or two points.
See the example below.
The black line intersects the parabola at (1, -1)
The blue line intersects the parabola at two points: (0, 0) and (4, 8).
What is the volume of the right triangular prism below? a 1600cm 800cm 400cm 160cm
The formula for determining the volume of a triangular prism is expressed as
Volume = area of triangular face * height of prism
The fotmula for finding the area of the triangular face is
Area = 1/2 * base * height
Looking at the diagram,
base = 8 cm
height = 10 cm
Area of triangular face = 1/2 * 8 * 10 = 40 cm^2
height of prism = 20 cm
Volume of prism = 40 * 20 = 800 cm^3
Option B is correct
10(6 + 4) ÷ (2³-7)² =
Answer:
100
Explanation:
Given the expression
[tex]10\mleft(6+4\mright)\div(2^3-7)^2[/tex]First, we evaluate the bracket and exponents.
[tex]=10\mleft(10\mright)\div(8-7)^2[/tex]This then gives us:
[tex]\begin{gathered} 100\div(1)^2 \\ =100\div1 \\ =100 \end{gathered}[/tex]Hayley's rectangular bedroom is 6 meters by 5 meters. What is the diagonal distance from one corner to the opposite corner? If necessary, round to the nearest tenth.
Hayley's rectangular bedroom is 6 meters by 5 meters. What is the diagonal distance from one corner to the opposite corner? If necessary, round to the nearest tenth.
Apply the Pythagorean Theorem
c^2=a^2+b^2
we have
a=6 m
b=5 m
c^2=6^2+5^2
c^2=36+25
c^2=61
square root c=7.8 m
answer is 7.8 metersOn a circle of radius 9 feet, what angle would subtend an arc of length 7 feet?
_____ degrees
The angle subtend an arc length of 7 feet is 44.56°
Given,
Radius of a circle = 9 feet
Arc length of a circle = 7 feet
Arc length :
The distance between two places along a segment of a curve is known as the arc length.
Formula for arc length:
AL = 2πr (C/360)
Where,
r is the radius of the circle
C is the central angle in degrees
Now,
AL = 2πr (C/360)
7 = 2 × π × 9 (C/360)
7 = 18 π (C/360)
7/18π = C/360
C = (7 × 360) / (18 × π)
C = (7 × 20) / π
C = 140 / π
C = 44.56°
That is,
The angle subtend an arc length of 7 feet is 44.56°
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what property tells us that m
Reflexive Property
1) For this assertion m∠GHK ≅ m∠GHK we have the Reflexive Property, which states that the same segment or geometric entity has the same measure.
"A quantity is congruent to itself"
m∠GHK ≅ m∠GHK
a =a
Ms. Wong sold 28 cars. She sold 8 fewer cars that 3/4 as many cass as Mr. Diaz. Which equation can be used to find the number of cars that Mr. Diaz sold,c?
The equation that we can be used to find the number of cars that Mr. Diaz sold is [tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex].
Ms Wong sold cars = 28.
She sold [tex]8[/tex] fewer cars that is 3/4 as many cars as Mr. Diaz.
Let Mr. Diaz sold [tex]x[/tex] cars.
Cars is 3/4 as many cars as Mr. Diaz so the term [tex]3/4x[/tex].
She sold 8 fewer cars.
Now from the statement the Ms Wong sold cars [tex]\frac{3}{4}x[/tex]−[tex]8[/tex].
As it is given that Ms Wong sold 28 cars.
So the equation must be
[tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex]
So equation that we can be used to find the number of cars that Mr. Diaz sold is [tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex].
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Evaluate( - 4) ^ 3/2
Answer: 8i
Using the formula C =5/9(F −32), find C when F is −58∘.? C∘
ANSWER
C = -50 degree Celcius
STEP-BY-STEP EXPLANATION:
What to find? The value of C in degree Celcius
Given Parameters
F = -58 degree Fahrenheit
The formula is given below
[tex]C=\text{ }\frac{5}{9}(F\text{ - 32)}[/tex]Substitute the value of into the equation
[tex]\begin{gathered} C\text{ = }\frac{5}{9}(-58\text{ - 32)} \\ \text{Solve the expression inside the parenthesis first} \\ C\text{ = }\frac{5}{9}(-90) \\ C\text{ = }\frac{-5\cdot\text{ 90}}{9} \\ C\text{ = }\frac{-450}{9} \\ C=-50^oC \end{gathered}[/tex]Hence, the value of C is -50 degrees
What is the probability that the spinner lands on a prime number?
Answer:
Step-by-step explanation:
50
O EQUATIONS AND INEQUALITIESSolving a decimal word problem using a linear equation with th.
Given:
[tex]PlanA=0.16\text{ for each minutes of calls}[/tex][tex]PlanB=25\text{ monthly fee plus 0.12 for each minute of calls}[/tex]To Determine: The numbers of calls for the which the two plans are equal
Solution
Let x be the number of minutes of calls for which the two plans are equal
The cost of plan A is
[tex]C_{ost\text{ of plan A}}=0.16x[/tex]The cost of plan B
[tex]C_{ost\text{ of plan B}}=25+0.12x[/tex]If the cost for the two plans are equal, then
[tex]0.16x=25+0.12x[/tex]Solve for x
[tex]\begin{gathered} 0.16x-0.12x=25 \\ 0.04x=25 \\ x=\frac{25}{0.04} \\ x=625 \end{gathered}[/tex]Hence, the number of minutes of calls for which two plans are equal is 625 minutes
2. What is an algebraic expression for each phrase?a. the product of 9 and a number tb. the difference of a number x and 1/2c. the sum of a number m and 7.1 d. the quotient of 207 and a number n
The algebraic expression for each phrase would be the following:
a. the product of 9 and a number t would be expressed as:
9*t
b. the difference of a number x and 1/2 would be expressed as:
x - 1/2
c. the sum of a number m and 7.1 would be expressed as:
m + 7.1
d. the quotient of 207 and a number n would be expressed as:
207 / n
Please help me solve this math problemRewrite in exponential form Ln3=y
1) Let's rewrite it as a logarithmic expression of the following exponential one. Let's do it step by step.
[tex]\begin{gathered} e^6=x \\ \ln e^6=\ln x \\ \ln(x)=6 \end{gathered}[/tex]Note that when we apply the natural log on both sides, we use one of those properties that tell us that we can eliminate the log since the base of a natural log is "e", as well as, "e" is the base of that power.
2) To rewrite in the exponential form we can do the following:
[tex]\ln(3)=y\Leftrightarrow e^y=3[/tex]Note that in this case, we have used the definition of logarithms.
The population of Somewhere, USA was estimated to be 658,100 in 2003, with an expected increase of 5% per year. At the percent ofincrease given, what was the expected population in 2004? Round your answer to the nearest whole number.
To solve for the expected population in 2004:
[tex]\begin{gathered} \text{Estimated population for 2003=658100} \\ \text{rate = 5 \%} \\ nu\text{mber of year = 1} \end{gathered}[/tex]Using compound interest formular to solve for the expected popupation:
Expected population = Amount
[tex]\begin{gathered} A=p(1+\frac{r}{100})^n \\ A\text{ = 658100 (1+}\frac{5}{100})^1 \\ A=658100\text{ (1+0.05)} \\ A=658100(1.05) \\ A=691005 \end{gathered}[/tex]Hence the expected population in 2004 = 691,005
The function f(x) = 6x represents the number of lightbulbs f(x) that are needed for x chandeliers. How many lightbulbs are needed for 7 chandeliers? Show your work
There are a total of 42 lightbulbs needed for 7 chandeliers
How to determine the number of lightbulbs needed?From the question, the equation of the function is given as
f(x) = 6x
Where
x represents the number of chandeliersf(x) represents the number of lightbulbs
For 7 chandeliers, we have
x = 7
Substitute x = 7 in f(x) = 6x
So, we have
f(7) = 6 x 7
Evaluate the product
f(7) = 42
Hence, the number of lightbulbs needed for 7 chandeliers is 42
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The number of lightbulbs needed for 7 chandeliers would be; 42
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the given problem, the equation of the function is;
f(x) = 6x
Where
x be the number of chandeliers and f(x) represents the number of lightbulbs.
For 7 chandeliers, x = 7
Now Substitute x = 7 in f(x) = 6x
Therefore, f(7) = 6 x 7
Evaluate the product;
f(7) = 42
Hence, the number of lightbulbs needed for 7 chandeliers would be; 42
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Fill in the blanks. (6x)^2 = _x^_
Step-by-step explanation:
[tex](6x) {}^{2} = -x { }^{?} - [/tex]I need help with this quadratic function… I thought I knew the answer, but obviously I don’t
Let us start with the following quadratic function:
[tex]f(x)=x^2-x-12[/tex]the X-intercepts are the collection of values to X which makes f(x) = 0, and it can be calculated by the Bhaskara formula:
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]where the values a, b, and c are given by:
[tex]f(x)=ax^2+bx+c[/tex]Substituting the values from the proposed equation, we have:
[tex]\begin{gathered} x_{1,2}=\frac{1\pm\sqrt{1^2-4*1*(-12)}}{2*1} \\ x_{1,2}=\frac{1\pm\sqrt{1+48}}{2}=\frac{1\pm\sqrt{49}}{2} \\ x_{1,2}=\frac{1\pm7}{2} \\ \\ x_1=\frac{1+7}{2}=\frac{8}{2}=4 \\ x_2=\frac{1-7}{2}=-\frac{6}{2}=-3 \end{gathered}[/tex]From the above-developed solution, we are able to conclude that the solution for the first box is:
(-3,0) ,(4,0)Now, the y-intercept, is just the value of y when x = 0, which can be calculated as follows:
[tex]\begin{gathered} f(0)=0^2-0-12=-12 \\ f(0)=-12 \end{gathered}[/tex]From this, we are able to conclude that the solution for the second box is:
(0, -12)Now, the vertex is the value of minimum, or maximum, in the quadratic equation, and use to be calculated as follows:
[tex]\begin{gathered} Vertex \\ x=-\frac{b}{2a} \\ y=\frac{4ac-b^2}{2a} \end{gathered}[/tex]substituting the values, we have:
[tex]\begin{gathered} x=-\frac{-1}{2*1}=\frac{1}{2} \\ y=\frac{4*1*(-12)-(-1)^2}{4*1}=\frac{-48-1}{4}=\frac{-49}{4} \end{gathered}[/tex]which means that the solution for the thirst box is:
(1/2, -49/4) (just as in the photo)Now, the line of symmetry equation of a quadratic function is a vertical line that passes through the vertex, which was calculated to be in the point: (1/2, -49,4).
Because this is a vertical line, it is represented as follows:
[tex]x=\frac{1}{2}[/tex]help meeeeeeeeee pleaseee !!!!!
The composition of functions g(x) and f(x) evaluated in x = 5 is:
(g o f)(5) = 6
How to evaluate the composition?
Here we have two functions f(x) and g(x), and we want to find the composition evaluated in x = 5, this is:
(g o f)(5) = g( f(5) )
So first we need to evaluate f(x) in x = 5, and then g(x) in f(5).
f(5) = 5² - 6*5 + 2 = 25 - 30 + 2 = -3
Then we have:
(g o f)(5) = g( f(5) ) = g(-3)
Evaluating g(x) in x = -3 gives:
g(-3) = -2*(-3) = 6
Then the composition is:
(g o f)(5) = 6
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Jenny originally bought her car for $42,000. Four years later, she sold it to a used car salesman for $14,000. What is the ratio for the amount she sold it for to the amount that it depreciated?
SOLUTION
The amout that Jenny sold the car for is $14,000
The amout that the car depriciated will be
$42,000 - $14,000 = $28,000
The ratio for the amount she sold it for to the amount that it depreciated becomes
[tex]\begin{gathered} \frac{14,000}{28,000} \\ \\ =\text{ }\frac{1}{2} \\ \\ =\text{ 1 : 2} \end{gathered}[/tex]Find all the solutions and if there is an extraneous solution, identify them and explain why they are extraneous.
ANSWER
Solution: b = 3
It is extraneous
EXPLANATION
We want to solve the equation given and to see if there are any extraneous solutions.
We have:
[tex]\begin{gathered} \frac{7}{b\text{ + 3}}\text{ + }\frac{5}{b\text{ - 3}}\text{ = }\frac{10b}{b^2\text{ - 9}} \\ \Rightarrow\text{ }\frac{7}{b\text{ + 3}}\text{ + }\frac{5}{b\text{ - 3}}\text{ = }\frac{10b}{(b\text{ + 3)(b - 3)}} \\ \text{Multiply both sides by (b + 3)(b - 3):} \\ \Rightarrow\text{ }\frac{7(b+3)(b\text{ - 3)}}{b\text{ + 3}}\text{ + }\frac{5(b\text{ + 3)(b - 3)}}{b\text{ - 3}}\text{ = }\frac{10b(b\text{ + 3)(b - 3)}}{(b\text{ + 3)(b - 3)}} \\ 7(b\text{ - 3) + 5(b + 3) = 10b} \\ 7b\text{ - 21 + 5b + 15 = 10b} \\ \text{Collect like terms:} \\ 7b\text{ + 5b - 10b = 21 - 15} \\ 2b\text{ = 6} \\ Divide\text{ both sides by 2:} \\ b\text{ = }\frac{6}{2} \\ b\text{ = 3} \end{gathered}[/tex]That is the solution to the equation.
To find if the solution is extraneous, we will insert the value of b = 3 into the original equation.
That is:
[tex]\begin{gathered} \Rightarrow\text{ }\frac{7}{3\text{ + 3}}\text{ + }\frac{5}{3\text{ - 3}}\text{ = }\frac{10(3)}{(3\text{ + 3)(3 - 3)}} \\ \frac{7}{6}\text{ + }\frac{5}{0}\text{ = }\frac{30}{(6)(0)} \\ \frac{7}{6}\text{ + }\frac{5}{0}\text{ = }\frac{30}{0} \end{gathered}[/tex]An extraneous solution is a solution that derives from solving a rational equation but does not exactly satisfy the original equation, that is, it is invalid for the equation.
By inserting b = 3 into the equation, we see that the equation is undefined.
Therefore, since b = 3 is a solution, but it does not satisfy the equation, it is an extraneous solution.