Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?
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We have to find how far is the bird from Amanda.
With the information given, we can draw:
We can start by finding the third angle.
The sum of the angles have to be equal to 180°, so we can find it as:
[tex]\begin{gathered} \alpha+55\degree+63\degree=180\degree \\ \alpha=180-55-63 \\ \alpha=62\degree \end{gathered}[/tex]Now, we can apply the Law of Sines to find the distance between Amanda (A) and the bird (B):
[tex]\frac{AB}{\sin J}=\frac{AJ}{\sin B}[/tex]where AJ is the distance between Amanda and Jamie and AB is the distance between the bird and Amanda.
We then can solve for AB as:
[tex]\begin{gathered} AB=AJ\cdot\frac{\sin J}{\sin B} \\ AB=25\cdot\frac{\sin63\degree}{\sin62\degree} \\ AB\approx25\cdot\frac{0.891}{0.883} \\ AB\approx25.23 \end{gathered}[/tex]Answer: 25.23 [Option A]
Related Questions
If 6 is subtracted from the third of three consecutive odd integers and the result is multiplied by 2, the answer is 23 less then the sun if the first and twice the second of the integers
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Graph the inequality and give interval notation for the solution. Use two o's (as in octopus) forinifinity and a U for union as needed.-- 5x + 4 >I 19 OR – 22 - 15 – 3-8 -7 -6 -5-4-3-2-] 022345678Clear All Draw:Interval notation for the above inequality and graph is
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- 5x + 4 > 19
1st step let us move 4 to the other side by subtracting both sides by 4
- 5x + 4 - 4 > 19 - 4
- 5x > 15
2nd step is move - 5 to the other side by dividing both sides by -5, BUT when we divide the sides of an inequality by a negative number we must reverse the sign of inequality
[tex]\frac{-5x}{-5}<\frac{15}{-5}[/tex]x < -3
The solution is all values smaller than -3
On the number, line draw an empty circle at -3 then draw from it an arrow pointing to the left ( - ve infinity)
The solution is {x : x < -3} or (-00, -3)
A student is trying to solve the set of two equations given below:Equation A: x + z = 6Equation B: 3x + 2z = 1Which of the following is a possible step used in eliminating the z-term
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Answer:
multiply equation A by -2
The variables x and y vary directly. Use values to write an equation that relates x and y. y=25;x=5And y=20;x=12
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A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]A lineal equation has the next form:
[tex]y=mx+b[/tex]where m is the slope and is calculated as follow:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For this case
y1=20
y2= 25
x1=12
x2= 5
so:
[tex]m=\frac{25-20}{5-12_{}}=\frac{5}{-7}=-\frac{5}{7}[/tex]then the equation will be:
[tex]y=(-\frac{1}{7})x+b[/tex]Using one of the points we calculate the b
we are going to use y=25 x=5
[tex]25=(-\frac{5}{7})5+b[/tex]Clearing the b we get:
[tex]25-\frac{25}{7}=b\Rightarrow\frac{200}{7}=b[/tex]b=200/7 or b=28.57
So the final equation is:[tex]y=-\frac{1}{7}x+\frac{200}{7}[/tex]A triangle has vertices on a coordinate grid at D(-10, -1), E(-10,6), and F(2,6). What is the length, in units, of DE?
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A triangle has vertices on a coordinate grid at D(-10, -1), E(-10,6), and F(2,6). What is the length, in units, of DE?
we know that
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]we have
D(-10, -1), E(-10,6)
substitute the given values in the formula
[tex]\begin{gathered} d=\sqrt[]{(6+1)^2+(-10+10)^2} \\ d=\sqrt[]{(7)^2+(0)^2} \\ d=\sqrt[]{49} \\ d=7\text{ units} \end{gathered}[/tex]therefore
the distance DE is 7 unitsIn an office building, 54 office are currently being rented, this represent 30% of the total units. how many offices are in the building
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given that,
54 offices are currently rented
and it represent 30% of the total unit
to get the total offices in the building
let the total offices be x
30% of x = 54
30/100 X x = 54
cross multiply
30x = 5400
dividing both sides by 30
30x/30 = 5400/30
x = 5400/30
x = 180
therefore the total offices in the building is 180
helppppppppppppppppppppppppppppppppppp
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Please step-by-step help me how much of a circle is shaded
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The given data is ratio from the the total are of circle is 1 .
let the shaded area is x then:
All area is equal to one.
[tex]\begin{gathered} \frac{1}{2}+\frac{2}{9}+x=1 \\ \frac{9+4}{18}+x=1 \\ \frac{13}{18}+x=1 \\ x=1-\frac{13}{18} \\ x=\frac{18-13}{18} \\ x=\frac{5}{18} \end{gathered}[/tex]So area of shaded region is
[tex]\frac{5}{18}[/tex]Santa worked 3.5 hours, 6.9 hours, & 4.3 hours in the last three days. If he earns $7.1 an hour, how much did he earn in the last three days?
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ANSWER:
$104.37
STEP-BY-STEP EXPLANATION:
To calculate the total profit, we must add the amount he earned each day, multiplying the salary by the number of hours, like this:
[tex]\begin{gathered} e=3.5\cdot7.1+6.9\cdot7.1+4.3\cdot7.1 \\ e=24.85+48.99+30.53 \\ e=104.37 \end{gathered}[/tex]Therefore, he earned in the last three days a total of $104.37
Which equation could be represented by the number line? A. 3 OB.-4 5=1 OC. 1+ -5)= OD. -3+4 -1
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According to the given number line, we have to go back from the second point to the first point 4 spots. In other words, the equation has to include a sum with -4.
Therefore, the answer is A since it's expressing an initial number 3, then the sum with -4.This question is from a MATH extra credit assignment, so unless I accidentally clicked on a subject other than maths... This question is also not from a test. Please help me if you can. Thank you if you do :)
Answers
Answer
$6,314
Step-by-step explanation
Compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
• A: final amount, in dollars
,• P: principal, in dollars
,• r: interest rate, as a decimal
,• n: number of times interest is applied per year
,• t: time in years
In this case, the investment is compounded annually, that is, once per year (n = 1). Substituting P = $4,625, r = 0.0352 (=3.52/100), n = 1, and t = 9 years, we get:
[tex]\begin{gathered} A=4,625(1+\frac{0.0352}{1})^{1\cdot9} \\ A=4,625(1.0352)^9 \\ A=\text{ \$}6,314 \end{gathered}[/tex]I need to find the radius and the diameter but I don't understand.
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ANSWER
Radius = 3 yd
Diameter = 6 yd
EXPLANATION
We are given the circle in the figure.
The radius of a circle is defined as the distance between the centre of a circle and its circumference.
Therefore, from the circle given, the radius is 3 yards
The diameter of a circle is defined as the total distance (through the centre) from one end of a circle to another.
It is twice the radius. Therefore, the diameter of the given circle is:
D = 3 * 2
D = 6 yards
The diameter is 6 yards.
A newsletter publisher believes that more than 31% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.01 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario. Answer
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The null hypothesis is H0: P = 0.31 and the alternative hypothesis is Ha: P > 0.31.
What is a null hypothesis?The null hypothesis is simply to predict that there is no effect of relationship between the variables.
The alternative hypothesis is to state the research prediction of a relationship or effect. In this case, the newsletter publisher believes that more than 31% of their readers own a Rolls Royce.
The null hypothesis is P = 0.31. while the alternative hypothesis will be that it's greater than 0.31.
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I need help to find the indicated operation:g(x)= -x^2 +4xh(x)= -4x-1Find (3g-h)(-3)
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We have the following functions:
[tex]\begin{gathered} g\mleft(x\mright)=-x^2+4x \\ h\mleft(x\mright)=-4x-1 \end{gathered}[/tex]And we need to find:
[tex](3g-h)(-3)[/tex]Step 1. Find 3g by multiplying g(x) by 3:
[tex]\begin{gathered} g(x)=-x^2+4x \\ 3g=3(-x^2+4x) \end{gathered}[/tex]Use the distributive property to multiply 3 by the two terms inside the parentheses:
[tex]3g=-3x^2+12x[/tex]Step 2. Once we have 3g, we subtract h(x) to it:
[tex]3g-h=-3x^2+12x-(-4x-1)[/tex]Here we have 3g and to that, we are subtracting h which in parentheses.
Simplifying the expression by again using the distributive property and multiply the - sign by the two terms inside the parentheses:
[tex]3g-h=-3x^2+12x+4x+1[/tex]Step 4. Combine like terms:
[tex]3g-h=-3x^2+16x+1[/tex]What we just found is (3g-h)(x):
[tex](3g-h)(x)=-3x^2+16x+1[/tex]Step 5. To find what we are asked for
[tex]\mleft(3g-h\mright)\mleft(-3\mright)[/tex]We need to evaluate the result from step 4, when x is equal to -3:
[tex](3g-h)(-3)=-3(-3)^2+16(-3)+1[/tex]Solving the operations:
[tex](3g-h)(-3)=-3(9)^{}-48+1[/tex][tex](3g-h)(-3)=-27^{}-48+1[/tex][tex](3g-h)(-3)=-74[/tex]Answer:
[tex](3g-h)(-3)=-74[/tex]Dr. Hughes instructs her students to solve the equation, 2x - 5y = -20, for y. What is the correct first step?Add +5y to both sides of the equation.O Add -2x to both sides of the equation.Add +2x to both sides of the equation.Divide each term in the equation by -5.
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We have the following expression given:
2x -5y = -20
For this case the correct set in order to begin is add 5y in both sides
Add +5y to both sides of the equation.
if a certain number is added to both the numerator and denominator of the fraction 8/9, the result is 6/7. Find the numer.
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Paulina bought a used car as she was entering college and planned to trade it in when she graduated four years later. She had learned in her high school financial algebra class that the average used car depreciated at an annual rate of 15%. If she had paid $13,900 for her car, how much can she expect to get when it is time for her to trade it in for a new car?
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1st year
depreciable value: $13900
annual depreciation: $13900*15% = $2085
2nd year
depreciable value: $13900 - $2085 = $11815
annual depreciation: $11815*15% = $1772.25
3rd year
depreciable value: $11815 - $1772.25 = $10042.75
annual depreciation: $10042.75*15% = $1506.41
4th year
depreciable value: $10042.75 - $1506.41 = $8536.34
annual depreciation: $8536.34*15% = $1280.45
Final value: $8536.34 - $1280.45 = $7255.89
Given f <-2, 3> and g <1, -5> find f + 2g
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Here are the steps in adding vector f and vector 2g.
1. First, multiply vector G by 2. To do this, simply multiply each component of g by 2.
[tex]<2(1),2(-5)>\Rightarrow<2,-10>[/tex]2. Add the result in step 1 to vector f.
To add, simply add each component of vector f to its corresponding component of vector g.
[tex]\begin{gathered} <-2,3>+<2,-10> \\ <-2+2,3+(-10)> \\ <0,-7> \end{gathered}[/tex]The result is <0, -7>.
Hence, f + 2g = <0, -7>. (Option 3)
Hence, f + 2g = <0, -7>. (Option 3)
Instructions: Find the value of that completes the square and creates a perfect square trinomial.
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Solution:
Given the expression;
[tex]x^2+18x+c[/tex]c is the half of square of coefficient of x. That is;
[tex]\begin{gathered} x^2+18x+c=x^2+18x+(\frac{1}{2}(18))^2 \\ \\ x^2+18x+c=x^2+18x+9^2 \\ \\ x^2+18x+c=x^2+18x+81 \\ \\ x^2+18x+81=(x+9)(x+9) \end{gathered}[/tex]Hence, the value of c is;
[tex]c=81[/tex]Which of the following ordered pairs is a solution to the equation 2x+y=2? Select all that apply.(11,0)(−4,10)(−13,4)(−11,−1)(0,2)
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You have the following equation:
2x + y = 2
In order to determine which of the given pairs is a solution, replace the values of x and y of such pairs and verify the equation, as follow:
(11,0)
2(11) + 0 = 22 ≠ 2 it's not a solution
(-4,10)
2(-4) + 10 = -8 + 10 = 2 it's a solution
(-13,4)
2(-13) + 4 = -26 + 4 ≠ 2 it's not a solution
(-11,-1)
2(-11) + (-1) = -22 - 1 ≠ 2 it's not a solution
(0,2)
2(0) + 2 = 2 it's a solution
-Quadratic Equations- Solve each by factoring, write each equation in standard form first.
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Answer
The solutions to the quadratic equations are
[tex]\begin{gathered} a^2-4a-45 \\ \text{Solution: }a=-5\text{ or }9 \\ \\ 5y^2+4y=0 \\ \text{Solution: }y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]SOLUTION
Problem Statement
The question gives us 2 quadratic equations and we are required to solve them by factoring, first writing them in their standard forms.
The quadratic equations given are:
[tex]\begin{gathered} a^2-4a-45=0 \\ 5y^2+4y=0 \end{gathered}[/tex]Method
To solve the questions, we need to follow these steps:
(We will represent the independent variable as x for this explanation. We know they are "a" and "y" in the questions given)
The steps outlined below are known as the method of Completing the Square.
Step 1: Find the square of the half of the coefficient of x.
Step 2: Add and subtract the result from step 1.
Step 3: Re-write the Equation. This will be the standard form of the equation
Step 4. Solve for x
We will apply these steps to solve both questions.
Implementation
Question 1:
[tex]\begin{gathered} a^2-4a-45=0 \\ \text{Step 1: Find the square of the half of the coefficient of }a \\ (-\frac{4}{2})^2=(-2)^2=4 \\ \\ \text{Step 2: Add and subtract 4 to the equation} \\ a^2-4a-45+4-4=0 \\ \\ \text{Step 3: Rewrite the Equation} \\ a^2-4a+4-45-4=0 \\ (a^2-4a+4)-49=0 \\ (a^2-4a+4)=(a-2)^2 \\ \therefore(a-2)^2-49=0 \\ \text{ In standard form, we have:} \\ (a-2)^2=49 \\ \\ \text{Step 4: Solve for }a \\ (a-2)^2=49 \\ \text{ Find the square root of both sides} \\ \sqrt[]{(a-2)^2}=\pm\sqrt[]{49} \\ a-2=\pm7 \\ \text{Add 2 to both sides} \\ \therefore a=2\pm7 \\ \\ \therefore a=-5\text{ or }9 \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} 5y^2+4y=0 \\ \text{ Before we begin solving, we should factorize out 5} \\ 5(y^2+\frac{4}{5}y)=0 \\ \\ \text{Step 1: Find the square of the coefficient of the half of y} \\ (\frac{4}{5}\times\frac{1}{2})^2=(\frac{2}{5})^2=\frac{4}{25} \\ \\ \text{Step 2: Add and subtract }\frac{4}{25}\text{ to the equation} \\ \\ 5(y^2+\frac{4}{5}y+\frac{4}{25}-\frac{4}{25})=0 \\ \\ \\ \text{Step 3: Rewrite the Equation} \\ 5((y^2+\frac{4}{5}y+\frac{4}{25})-\frac{4}{25})=0 \\ 5(y^2+\frac{4}{5}y+\frac{4}{25})-5(\frac{4}{25})=0 \\ 5(y^2+\frac{4}{5}y+\frac{4}{25})-\frac{4}{5}=0 \\ \\ (y^2+\frac{4}{5}y+\frac{4}{25})=(y+\frac{2}{5})^2 \\ \\ \therefore5(y+\frac{2}{5})^2-\frac{4}{5}=0 \\ \\ \text{ In standard form, the Equation becomes} \\ 5(y+\frac{2}{5})^2=\frac{4}{5} \\ \\ \\ \text{Step 4: Solve for }y \\ 5(y+\frac{2}{5})^2=\frac{4}{5} \\ \text{ Divide both sides by 5} \\ \frac{5}{5}(y+\frac{2}{5})^2=\frac{4}{5}\times\frac{1}{5} \\ (y+\frac{2}{5})^2=\frac{4}{25} \\ \\ \text{ Find the square root of both sides} \\ \sqrt[]{(y+\frac{2}{5})^2}=\pm\sqrt[]{\frac{4}{25}} \\ \\ y+\frac{2}{5}=\pm\frac{2}{5} \\ \\ \text{Subtract }\frac{2}{5}\text{ from both sides} \\ \\ y=-\frac{2}{5}\pm\frac{2}{5} \\ \\ \therefore y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]Final Answer
The solutions to the quadratic equations are
[tex]\begin{gathered} a^2-4a-45 \\ \text{Solution: }a=-5\text{ or }9 \\ \\ 5y^2+4y=0 \\ \text{Solution: }y=0\text{ or }-\frac{4}{5} \end{gathered}[/tex]9) solve using substitution method and check your answer:4x - 3y + 2z = 16- 4y - Z = 7= 146x - y
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Given the system of equations, solve the third equation for y, as shown below
[tex]\begin{gathered} 6x-y=14 \\ \Rightarrow y=6x-14 \end{gathered}[/tex]And, solve for z in the second equation,
[tex]\begin{gathered} -4y-z=7 \\ \Rightarrow z=-4y-7 \\ \Rightarrow z=-4(6x-14)-7=-24x+49 \end{gathered}[/tex]Thus, substitute the values of y and z in terms of x into the first equation, as shown below
[tex]\begin{gathered} \Rightarrow4x-3y+2z=4x-3(6x-14)+2(-24x+49)=4x-18x+42-48x+98 \\ \Rightarrow-62x+140=16 \\ \Rightarrow-62x=-124 \\ \Rightarrow x=2 \end{gathered}[/tex]Then, solving for y and z given x=2,
[tex]\begin{gathered} x=2 \\ \Rightarrow y=6*2-14=-2 \\ and \\ z=-24*2+49=-48+49=1 \end{gathered}[/tex]Therefore, the solution to the system of equations is x=2, y=-2, z=1To verify the solutions, substitute the values we found into the three equations of the system, as shown below
[tex]\begin{gathered} x=2,y=-2,z=1 \\ \Rightarrow4x-3y+2z=4*2-3*(-2)+2*1=8+6+2=16\rightarrow correct \\ \Rightarrow-4y-z=-4*(-2)-1(1)=8-1=7\rightarrow correct \\ \Rightarrow6x-y=6*2-1(-2)=12+2=14\rightarrow correct \end{gathered}[/tex]In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC? BC ≅ AD CB ≅ AB AB ≅ CD DB ≅ DC
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By CPCTC this is the only valid answer:
CB ≅ AB
Another statement should be AD≅ CD
Solve the equation for y.1/3 x + y = 4
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In order to solve the equation for y, we just need to isolate the variable y in one side of the equation. So we have:
[tex]\begin{gathered} \frac{1}{3}x+y=4 \\ y=4-\frac{1}{3}x \end{gathered}[/tex]So the answer is y = 4 - 1/3 x
Find the distance between the pair of points. (16,0) and (1, -7) The distance is. (Round to the nearest thousandth as needed.)
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Solution
For this case we can use the formula for the distance between two points:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]and replacing we got:
[tex]d=\sqrt[]{(-7-0)^2+(1-16)^2}=\sqrt[]{274}[/tex]And the correct answer after round would be:
16.553
A local real estate company has 5 real estate agents. The number of houses that each agent sold last year is shown in the bar graph below. Use this bar graph to answer the questions.
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Given:
Rachel sold 4 houses.
Heather sold 4 houses.
Kaitlin sold 12 houses.
Lena sold 11 houses.
Deshaun sold 3 houses.
Required:
a) We need to find which agent sold the most houses.
b) We need to find the number of houses Lna soldemore than Heather.
c) We need to find the number of agents who sold fewer than 4 houses.
Explanation:
a)
The greatest number of houses sold =12 houses.
Kaitlin sold 12 houses.
Answer:
The agent Kaitlin sold the most houses.
The agent sold 12 houses.
b)
Lena sold 11 houses.
Heather sold 4 houses.
The difference between 11 and 4 is 11-4 =7.
Answer:
Lena sold 7 housmore than Heather
Which is the image of vertex K after the parallelogram is rotated 180degrees about the origin?
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Answer:
The image of vertex K is (3,-2)
Step-by-step explanation:
Rotated 180 degrees about the origin means that the value of x will not change, while y will have the same distance from the origin, but in a different direction.
Vertex K:
Value of x: x = 3
Value of y: y = 2
Distance from the origin: 2 - 0 = 2
Rotated, new coordinate: 0 - 2 = -2
The image of vertex K is (3,-2)
In ABC, B = 51°, b = 35, and a = 36. What are the two possible values for angle A to the nearest tenth of a degree?Select both correct answers.
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Using the law of sines:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin (B)}[/tex]Solve for A using the data provided:
[tex]\begin{gathered} \sin (A)=\frac{\sin (B)\cdot a}{b} \\ A=\sin ^{-1}(\frac{\sin (51)36}{35}) \\ A\approx53.1 \\ or \\ A\approx126.9 \end{gathered}[/tex]In December, 64 teams qualify for a basketball tournament. After each round, half of the teams are eliminated.
Which exponential function can be used to find the number of teams left after a rounds, where is a whole number?
O f(x) = (64)
O f(x) =
(x)64
O f(x) = 64 (¹)
○ f(x) = x(¹)
Answers
The exponential function is f(x) = 64·(1/2)ˣ which can be used to find the number of teams left after a round.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
Given that 64 teams qualify for a basketball tournament. After each round, half of the teams are eliminated.
Because it is an exponential function, f(x) will reach 0 as x increases, allowing us to construct the following table of values:
x f(x)
0 64
1 32
2 16
3 8
4 4
5 2
6 1
At that point, 64 teams are in the tournament, and the total number of teams (from this point forward)
Therefore, half of the teams are eliminated after each round and the exponential function is:
f(x) = 64·(1/2)ˣ
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Please help.
A circle has a diameter of 18 inches. A central angle of 75° intercepts an arc of the circle. What is the intercepted arc length to the nearest tenth of an inch?
A.) 2.08 inches
B.) 3.8 inches
C.) 11.8 inches
D.) 23.6 inches
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Answer:
C.) 11.8 inches===========================
GivenA circle with diameter d = 18 in,Central angle θ = 75°.To findThe length of the given arcSolutionUse arc length formula:
s = πdθ/360Substitute the values and calculate:
s = 3.14 * 18 in * 75°/360° = 11.8 in (rounded)The matching answer choice is C.
