A portion of a city map is shown in the figure at the right. If you walk along Maple Street between 2nd Street and Elm Grove Lane, how far do you walk? Round your answer to the nearest tenth of a yard.
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The length is 259.4 yd.
We have to find the length of AC.
using sin rule,
we have
[tex]\frac{c }{Sin C} = \frac{b}{sinB}[/tex]
[tex]\frac{210}{sin 54} = \frac{b}{sin 88}[/tex]
[tex]b =\frac{210 sin 88}{sin 54}[/tex]
[tex]b = 259. 4161\\b = 259.4[/tex]
The length is 259.4 yd.
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Related Questions
daniel is standing 100ft from a tower and sees a bird land on top of the tower. if the angle of elevation from daniel to the top is 84.6, how tall is the tower
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make sure your calculator is in Degree mode.
Draw any two convex pentagons. For each of them measure the sum of its interior angles using a protractor. Explain the result of the measuring.
FIRST ANSWER GETS BRAINLIEST ANSWER!
Answers
Answer:
540
Step-by-step explanation:
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. if the cardboard is 17 in. long and 12 in. wide, find the dimensions of the box that will yield the maximum volume. (round your answers to two decimal places.)
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The initial measurements of the box are:
Length: 17
Width: 12
Height: 0
Right now, the volume is zero. However, if we let the height equal 0 (the amount of the cut out), we can write the following equation for the volume.
Volume = (17 - 2x)(12 - 2x)x
If you graph this, you will find a maximum value of 211.05, keeping in mind that the cut out must be less than 6.
What is the difference of the two polynomials?
(7y2 + 6xy) – (–2xy + 3)
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7y^2 + 6xy +2xy +3
7y^2 +8xy +3
8xy + 7y^2 +3
PLEASE HELP ME ON THIS....
thx
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answer
There is no solution
Describe the straight line y=9
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A car has a 12-volt battery. The engine has a resistance of 0.22 ohms. How many amps will be drawn from the battery when the key is turned? I (to the nearest hundredth)
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Answer:
54.54 amps.Step-by-step explanation:
Amps refers to the electrical current.
We have to find the electrical current when the car has a 12-volt battery and the engine has a resistance of 0.22 ohms.
The relation between these magnitudes is
[tex]V=I\times R[/tex]
Where [tex]V[/tex] is the voltage, [tex]I[/tex] is the electrical current and [tex]R[/tex] the resistance.
We know that [tex]V=12; R=0.22[/tex]. Replacing these values in the formula and solving for [tex]I[/tex]
[tex]V=I\times R\\\frac{V}{R}=I\\ I=\frac{12}{0.22}\\ I\approx 54.54 amp[/tex]
Therefore, the answer is around 54.54 amps.
The current drawn from the battery when the key is turned is approximately 54.55 amps.
To determine the current drawn from the battery, we can use Ohm's Law, which states that the current (I) is equal to the voltage (V) divided by the resistance (R):
[tex]\[ I = \frac{V}{R} \][/tex]
Given that the voltage (V) of the battery is 12 volts and the resistance (R) of the engine is 0.22 ohms, we can plug these values into the equation:
[tex]\[ I = \frac{12 \text{ volts}}{0.22 \text{ ohms}} \][/tex]
[tex]\[ I = \frac{12}{0.22} \][/tex]
[tex]\[ I \approx 54.5454 \][/tex]
Rounding to the nearest hundredth, we get:
[tex]\[ I \approx 54.55 \text{ amps} \][/tex]
Jerry lost her credit card and instead of reporting it right away, she decides to continue looking for it for a couple of days. On the second day, she makes the call and reports the card lost/stolen to the credit card company. She then logs into the account activity page of his credit card and sees a recent $500 purchase that was made by someone else. How much of this $500 charge will Jerry have to pay?
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sin 4 theta
hey, how do you simplify sin 4 theta? using double angle theory?
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You begin with double-angle formula for sine:
sin(4θ) = sin(2·2θ) = 2·sin(2θ)·cos(2θ)
Then, double-angle formula for sine again:
2·sin(2θ)·cos(2θ) = 2·2·sinθ·cosθ·cos(2θ) = 4·sinθ·cosθ·cos(2θ)
Then double-angle formula for cosine:
4·sinθ·cosθ·cos(2θ) = 4·sinθ·cosθ·(cos²θ - sin²θ)
Last, multiply:
4·sinθ·cosθ·(cos²θ - sin²θ) = 4·sinθ·cos³θ - 4·sin³θ·cosθ
Giving a test to a group of students, the grades and gender are summarized below. if one student was chosen at random, find the probability that the student was female. male total 39 female total 26
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To find the probability that a student is female, first add up both the number of males and females.
39 + 26 = 65
Now, divide the total number of females by 65 and multiply by 100.
26 / 60 = 0.4 x 100 = 40%
How do I find the holes of this function?
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We factor the function.
[tex]y= \dfrac{3x^2-7x+4}{x^2-1} = \dfrac{3x^2-3x-4x+4}{x^2-1}= \dfrac{3x(x-1)-4(x-1)}{x^2-1} \\\\\\ y = \dfrac{(3x-4)(x-1)}{(x+1)(x-1)} = \dfrac{3x-4}{x+1}, \ x \neq -1, \ x \neq 1[/tex]
We canceled (x-1) from the numerator and denominator, so when this factor is equal to zero, there is a hole on the graph, that is, at the point [tex](1, \frac{-1}{2})[/tex].
1. Simplify using only positive exponents:
(2t)⁻⁶
2. Simplify using only positive exponents:
(w⁻²j⁻⁴)⁻³(j⁷j³)
3. Simplify using only positive exponents:
a²b⁻⁷c⁴
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a⁵b³c⁻²
4. Evaluate the expression for m = 2, t = -3, and z = 0.
z⁻ᵗ(mᵗ)ᶻ
5. Use scientific notation to rewrite the number:
a. 0.0002603 in scientific notation
b. 5.38 × 102 in standard notation
Answers
[tex](2t)^{-c} = \frac{1}{(2t)^{c} } [/tex]
2. To simplify this one, we are going to use the rule for negative exponents twice, the product rule: [tex](a^{n} )(a^{m} )=a^{n+m} [/tex], and the power rule [tex](a^{n}) ^{m} =a^{(n)(m)} [/tex], so:
[tex](w^{-2} j ^{-4} ) ^{-3} (j^{7} j ^{3} )=( \frac{1}{w ^{-2}j ^{-4} } )^{3} (j ^{7+3} )[/tex]
[tex]=(w^2j^4)^3(j ^{10}) [/tex]
[tex]=(w^6j^{12})(j^{10})[/tex]
[tex]=w^6j^{22}[/tex]
3. To simplify this one we are going to use the rule for negative exponents, the product rule, and the quotient rule: [tex] \frac{a^n}{a^m} =a^{n-m}[/tex], so:
[tex] \frac{a^2b^{-7}c^4}{a^5b^3c^-2} = \frac{a^2c^4c^2}{a^5b^3b^7} = \frac{a^{-3}c^6}{b^{10}} = \frac{c^6}{a^3b^10} [/tex]
4. The first thing we need to is apply the exponents rules; in this case our rule for negative exponents:
[tex]z^{-t}(m^t)^z=( \frac{1}{z^t} )(m^{(t)(z)})= \frac{m^{tz}}{z^t} [/tex]
Now can replace our numerical values:
[tex] \frac{2^{(-3)(0)}}{0^{-3}} [/tex]
We have a negative exponent in the denominator, so lets apply oir rule for negative exponents again:
[tex]2^{(-3)(0)}0^3=2^00^3=(1)(0)=0[/tex]
5. Scientific notation is just a way of writing large an small numbers using powers of 10. The exponent of 10 will be the number of places we shift the decimal point to write the number in scientific notation. A positive exponent shows that the decimal point is shifted the right, and a negative one shows that the decimal point is shifted to the left:
a. [tex]0.0002603=2.603[/tex] x [tex]10^{-4} [/tex]
b. [tex]5.38[/tex] x [tex]10^{2} =538[/tex]
Expressions with exponents can be simplified using rules of exponents, and numbers can be converted into scientific notation by recognizing how to move the decimal point and denote magnitude with the power of ten.
To simplify expressions with exponents and convert numbers into scientific notation, we apply the rules of exponents and understand the format of scientific notation.
(2t)⁻⁶: Using the negative exponent rule, which states that a⁻⁶ = 1/a⁶, we can simplify this expression to 1/(2⁶t⁶).
(w⁻²j⁻⁴)⁻³(j⁷j³): To deal with the negative and compounded exponent, we invert and take the cube, resulting in w⁶j¹². Then, multiply the j terms together to get w⁶j¹⁵.
To simplify a²b⁻⁷c⁴ / a⁵b³c⁻², we subtract exponents when dividing like bases, resulting in a⁻³b⁻¹°c⁶.
For the expression z⁻ᵗ(mᵗ)¹, when any variables are raised to the zero power, the result is 1. Thus, the entire expression evaluates to 1 due to (mᵗ)¹ becoming 1.
Converting to scientific notation: To express 0.0002603 in scientific notation, it becomes 2.603 × 10⁻⁴. The number 5.38 × 10² in standard notation is 538.
By applying these step-by-step procedures, we can simplify expressions using positive exponents and accurately convert between standard notation and scientific notation.
The perimeters of two similar quadrilaterals are 48 cm and 60 cm, respectively. If the area of the smaller quadrilateral is 96 cm2, find the area of the larger quadrilateral.
Answers
The area of the larger quadrilateral is found by using the scale factor derived from the ratio of the perimeters of the similar quadrilaterals, which comes out to 150 cm².
The question involves finding the area of a larger quadrilateral given the perimeters of two similar quadrilaterals and the area of the smaller one. In similar figures, the ratio of their areas is the square of the ratio of their corresponding linear dimensions, such as side lengths or perimeters in this case. Since the perimeters are 48 cm and 60 cm, the ratio of the perimeters (also the scale factor) is 48/60, or 4/5. Consequently, the ratio of the areas is the square of the scale factor, which is (4/5)² or 16/25. Knowing the area of the smaller quadrilateral is 96 cm², we find the area of the larger quadrilateral by dividing the area of the smaller by the scale factor squared and then multiplying by the larger scale factor squared. This gives us (96 / (16/25)) cm² = (96 * 25/16) cm² = 150 cm².
So, the area of the larger quadrilateral is 150 cm².
help me please please
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Explanation:
Point C is the circumcenter of triangle PQR. This means that we can draw a circle centered at C that goes through points P, Q and R at the same time. This circle has a special name: circumcircle.
The segments PC, RC and QC are all radii, so they are the same length. Pick two of the given expressions and set them equal to one another. Then solve for x
I'm going to pick the expressions for PC and RC
PC = RC
3x+7 = 5x-15
5x-3x = 7+15
2x = 22
x = 22/2
x = 11
Answer:
11
Step-by-step explanation:
Gina and Lucy go to the library at 3:30 p.m. They need to be at home at 4:45 p.m. It takes them 15 minutes to walk to the library. How many minutes can they spend at the library?
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Gina and Lucy can spend 45 minutes at the library.
_____
They will get to the library at 3:45. They must start home by 4:30. From 3:45 to 4:00 is 15 minutes, and it is 30 more minutes to 4:30. The time they can spend at the library totals 45 minutes.
Carlos plots a circular planter's wall on a computer. He determines that the circle that defines the part of the planter wall that gets watered by the sprinkler is (x−10)2+(y+12)2=36.
What is the diameter, in meters, of the circular area that gets watered by the sprinkler?
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2. The standard form for the equation of a circle is:
(x-h)²+(y-k)²=r²
(h,k) is the center point.
r is the radius.
3. Keeping this on mind, you can find the value of the radius, as below:
r²=36
r=√36
r=6 m
4. Then, the diameter of the circle is:
D=2r
D=2(6m)
D=12 m
What is the diameter, in meters, of the circular area that gets watered by the sprinkler?
The answer is: 12 m
How many minutes greater is the software company's median than the bank's median?
Enter your answer in the box.
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While Playing Yahtzee and rolling 5 dice, Mei gets the result shown at right (the numbers are 2, 4, 4, 4, and 1). Mei decides to keep the three fours and reroll the other 2 dice. a. what is the probability that Mei will have 5 of a kind? b. What is the probability that she will have 4 of a kind? c. what is the probability that she will have exactly three 4's?
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B. 10/36. Ten of the options contain exactly 1 - 4.
C. The remaining 25/36 options do not include a 4.
Last winter, the ratio of days with snow to days with no snow was 1.02. Write this ratio as a fraction in simplest form.
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Final answer:
The ratio of 1.02 can be converted to a fraction by multiplying by 100 to get 102/100 and then simplifying to its simplest form, which is 51/50.
Explanation:
To write the ratio 1.02 as a fraction in its simplest form, we first recognize that 1.02 is the same as 1.02/1. If we want to express this as a fraction, we must remove the decimal point by multiplying both the numerator and the denominator by 100 (because there are two digits after the decimal point). This gives us 102/100. We can then simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Therefore, the simplified fraction is 51/50.
find the geometric mean between 18 and 2,
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Formula:
Geometric Mean = ((X₁)(X₂)(X₃)........(Xₙ))^1/ⁿ
Where,
X = Individual score
N = Sample size (Number of scores)
A sum of _________ can be factored according to the pattern (a + b)(a2 - ab + b2).
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Solution:
we are given with [tex] (a + b)(a^2 - ab + b^2) [/tex]
we have been asked to find the representation of the given factor as a Sum.
As we know that
[tex] (a^3+b^3)= (a + b)(a^2 - ab + b^2) [/tex]
Because
[tex] (a + b)(a^2 - ab + b^2)=a(a^2 - ab + b^2)+b(a^2 - ab + b^2)\\
\\
(a + b)(a^2 - ab + b^2)=a^3-a^2b+ab^2+ba^2-ab^2+b^3\\
\\
(a + b)(a^2 - ab + b^2)=a^3+b^3\\ [/tex]
Three times the number of blue marbles exceeds twice the number of red marbles by 18 also 5 times the number of blue marbles is 2 less than 6 times the number of red marbles how many of each are there?
Will give brainliest please answer quickly
Answers
The first equation would be
3B=2R+18.
The second equation would be
5B=6R-2.
To get the coefficients of R the same we will multiply the first equation by 3:
3(3B=2R+18)
which gives us
9B=6R+54
Now our system is
9B=6R+54
5B=6R-2
We will subtract the bottom equation to eliminate R:
9B=6R+54
-(5B=6R-2)
which gives us
4B=56
Divide both sides by 4:
4B/4=56/4
B=14
Substitute this into our first original equation:
3(14)=2R+18
42=2R+18
Subtract 18 from both sides:
42-18=2R+18-18
24=2R
Divide both sides by 2:
24/2=2R/2
12=R
Final answer:
By creating and solving a system of equations based on the given information, we find that there are 10 blue marbles and 8 red marbles.
Explanation:
To solve this problem, we set up two equations based on the information given:
3 times the number of blue marbles (3B) exceeds 2 times the number of red marbles (2R) by 18: 3B - 2R = 18.
5 times the number of blue marbles (5B) is 2 less than 6 times the number of red marbles (6R): 5B = 6R - 2.
Now, we can solve these equations using substitution or elimination. Using substitution, solve the second equation for B:
B = ⅜(6R - 2)
Then substitute this expression for B in the first equation:
3(⅜(6R - 2)) - 2R = 18
Solve for R:
R = 8
Now substitute R back into the equation for B:
B = ⅜(6(8) - 2) = 10
Thus, there are 10 blue marbles and 8 red marbles.
PLEASE HELP! What is the area of triangle BCD in exact form? 35 points!
Answers
The long leg is equal to sqrt(3) times the short leg
long leg = sqrt(3)*(short leg)
long leg = sqrt(3)*5
long leg = 5*sqrt(3)
The base is 5. The height is 5*sqrt(3)
b = 5
h = 5*sqrt(3)
Use this to find the area
A = b*h/2
A = 5*5*sqrt(3)/2
A = 25*sqrt(3)/2
which is the exact area in terms of a radical
You can write it out as [tex]\frac{25\sqrt{3}}{2}[/tex]
The length of a shadow of a building is 32 m . the distance from the top of the building to the tip of the shadow is 38 m . find the height of the building. if necessary, round your answer to the nearest tenth.
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Therefore, to solve the problem, you must find the third side using the
Pythagorean theorem.
We have then:
h ^ 2 + 32 ^ 2 = 38 ^ 2
We cleared h:
h = root (38 ^ 2 - 32 ^ 2)
h = 20.49390153
round to the nearest tenth
h = 20.5 m
Answer:
the height of the building is:
h = 20.5 m
A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points L(−3,10) , M(6,10) , and P(−3,−6) . Point N is the fourth vertex of the rectangle. How long is the side of the rectangle connecting points M and N?
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The answer is 16.
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Hope this helps and have a great day!
Answer:
answer 16 or 1.6
Step-by-step explanation:
Catie is trying to determine the height that a ladder reaches as it leans against a wall. She walks under the ladder and touches her forehead to it as shown. If her feet are 16 inches from the ladder's base, the ladder's base is 4.5 feet from the bottom of the wall, and Catie is 5 feet 6 inches tall, then come up with an estimate for how high the ladder reaches up the wall to the nearest tenth of a foot. Watch your units on this problem and show all work
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Catie creates a similar triangle with the ladder so we can create a proportion to solve for the height.
[tex] \frac{baseto feet}{base to wall} = \frac{catie height}{wall height} [/tex]
Convert all values to feet . 16in = 1.33 ft . 5ft 6 in = 5.5 ft
Insert values into proportions
[tex] \frac{1.33}{4.5} = \frac{5.5}{x} [/tex]
Cross multiply to get
24.75=1.33x
divide both sides by 1.33
x=18.56ft
To find the height the ladder reaches up the wall, set up a proportion using similar triangles and Catie's height as the ladder's height. The estimate for the ladder's height up the wall is 6.8 feet.
Given information:
Catie is 5 feet 6 inches tall.Her feet are 16 inches from the ladder's base.The ladder's base is 4.5 feet from the bottom of the wall.To find the height the ladder reaches up the wall, we can set up a proportion using similar triangles. Catie's height can be considered as the ladder's height, and the distance on the wall can be related to the ladder's base and height.
Using the information provided and performing the calculations, the estimate for the height the ladder reaches up the wall would be approximately **6.8 feet** to the nearest tenth of a foot.
Given the following linear function, identify the slope and y-intercept of the function: x= 1/6x+7
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hope it helps
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You receive $1,000 to put in the bank. You place it in an account that pays 4% annual interest compounded continuously. How much will you have in 15 years? Round the answer to the nearest dollar.
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A lighthouse is 15m above sea level.
The lighthouse operator sights a boat at an angle of depression of 25 degrees.
How far is the boat from the lighthouse?
Round your answer to the nearest tenth.
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tan x = opposite/adjacent
tan 25 = x/15
15 (tan 25) = x
6.9946 = x
So the boat is approximately 6.9946 m away from the lighthouse.
Answer:
41.2
Step-by-step explanation:
Find the value of a. The diagram is not to scale. a. 36 b. 144 c. 54 d. 126 **I believe the answer is B
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The value of a in the diagram is 144°.
The correct option is B.
What is a trapezoid?An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.
Given:
A trapezium has parallel bases and that one of its characteristics is that the two angles on a single side are supplementary, meaning that the total of the angles on two neighboring sides is 180°.
So,
∠a = 180 - 36
∠a = 144
∠b = 180 - 113
∠b = 67
Therefore, the value of a is 144°.
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