Answers
Part (a)
BC = opposite side (furthest leg from the reference angle)
AB = adjacent side (closest leg from the reference angle)
AC = hypotenuse (always opposite the 90 degree angle)
=============================================
Part (b)
i. False. Angle B is 90 degrees as shown by the square angle marker.
ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.
iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.
iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.
==============================================
Part (c)
cos(theta) = adjacent/hypotenuse = AB/AC
tan(theta) = opposite/adjacent = BC/AB
Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.
==============================================
Part (d)
The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.
sin(C) = opposite/hypotenuse = AB/AC
cos(C) = adjacent/hypotenuse = BC/AC
tan(C) = opposite/adjacent = AB/BC
Note the tangent ratio is the reciprocal of what we found back in part (c).
Answer & Step-by-step explanation:
(a)
The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))
The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)
The opposite is on the line CB (this is opposite the given angle)
(b)
i. false (b is a right angle)
ii. false (the side opposite C is BA)
iii. true
iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)
(c)
cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]
tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]
The cosine and tangent ratios of the given angle:
[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]
(d)
Remember SOH-CAH-TOA:
Sine=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent
Using the angle C, plug in the appropriate sides:
[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]
:Done
Related Questions
David is selling floral arrangements. Each arrangement uses 1 vase and 12 roses. Each vase costs David $2.00. Let C be the total cost of the arrangement and r be the cost of 1 rose. Which equation should David use to find the total cost of each arrangement? C = 12r + 2 12 = C + 2r C = 2r + 12 12C = r + 12
Answers
Answer:
C = 12r + 2Step-by-step explanation:
To model the equation for the cost of Each Arrangement.
We need to itemize all parameters needed.
An arrangement consists of
1. one vase
2. twelve roses
Given that 1 vase cost $2 and
The cost of one rose is r
Let the total cost of the arrangement be C
Hence C is the cost of the vase plus the cost of 12 roses combined, this is given as
[tex]C = 12r + 2[/tex]
Shawna, Dexter, and Tilana are solving the equation Negative 2.5 (5 minus n) + 2 = 15. Shawna says, "I can begin by dividing each side of the equation by –2.5 to get 5 minus n minus StartFraction 2 over 2.5 EndFraction = Negative StartFraction 15 over 2.5 EndFraction." Dexter says, "I can begin by distributing Negative 2.5 to get Negative 12.5 + 2.5 n + 2 = 15." Tilana says, "I can begin by multiplying each side of the equation by Negative StartFraction 1 over 2.5 EndFraction to get 5 minus n minus 0.8 = negative 6." Which students are correct? only Shawna and Tilana only Shawna and Dexter only Dexter and Tilana Shawna, Dexter, and Tilana
Answers
Answer:
All three students are correct
Step-by-step explanation:
Given
Equation: -2.5(5 - n) + 2 = 15
Required
Which students are correct
To determine which of the students are correct; we have to test each of their solutions
SHAWNA
Statement: Dividing each side of the equation by –2.5 to get 5 - n - 2/2.5 = -15/2.5
[tex]\frac{-2.5(5 - n) + 2}{-2.5} = \frac{15}{-2.5}[/tex]
Split fractions
[tex]\frac{-2.5(5 - n)}{-2.5} + \frac{2}{-2.5} = \frac{15}{-2.5}[/tex]
Simplify each fraction
[tex]5-n - \frac{2}{2.5} = \frac{-15}{2.5}[/tex]
Shawna is correct...
DEXTER
Statement: Distributing -2.5 to get -12.5 + 2.5 n + 2 = 15.
[tex]-2.5(5 - n) + 2 = 15[/tex]
Open brackets
[tex]-12.5 + 2.5n + 2 = 15[/tex]
Dexter is also correct...
TILANA
[tex]\frac{-1}{2.5}(-2.5(5 - n) + 2) = \frac{-1}{2.5} * 15[/tex]
Open brackets
[tex]\frac{-1}{2.5}(-2.5(5 - n)) + \frac{-1}{2.5}(2) = \frac{-1}{2.5} * 15[/tex]
Simplify each bracket
[tex](5 - n) + \frac{-2}{2.5} = \frac{-15}{2.5}[/tex]
[tex](5 - n) - \frac{2}{2.5} = \frac{-15}{2.5}[/tex]
[tex]5 - n - 0.8 = -6[/tex]
Tilana is also correct
Hence, all three students are correct
Answer:
All of them are correct
Step-by-step explanation:
The value of a collectible coin can be represented by the equation y = 2 x + 15, where x represents its age in years and y represents its total value in dollars. What is the value of the coin after 19 years? $2 $23 $38 $53
Answers
Answer:
53$
Step-by-step explanation:
They tell you the equation of how much the coin is worth after x amount of years
Step 1: Substitute x=19 into the equation y=2x+15
y = 2(19) + 15
Step 2: Solve for y
y = 2(19) + 15
y = 38 + 15
y = 53
Therefore the coin is worth 53 dollars after 19 years
Answer:
53
Step-by-step explanation:
Got it correct on Edu. 2020
Can someone please explain this to me? I don’t understand it at all.
Answers
Segment AB was added to segment BC to get segment AC
representing it as an equation,
AC = AB + BC.
Substitute the values in the equation which means you are going to find the value of x.
77 = x + 16 + 4x +11
77 = 5x + 27
(group like terms)
77 - 27 = 5x
50 = 5x
( divide both sides by 5 to make x stand alone)
50/5=5x/5
10 = x
therefore ,x = 10.
To prove that segment AB =26, place x in the statement
AB = x+16
AB=10+16
AB=26/
show that the point p(-6,2), Q(1,7) and R(6,3) are the vertices of scalene triangle
Answers
Answer:
the sides are different lengths as shown in the diagram
Step-by-step explanation:
Plotting the three points, you can see by "inspection" that the middle length side (PQ) is longer than the shortest side (QR) and shorter than the longest side (PR). You could use the distance formula to show this, or you can use a scale to measure the drawing.
A triangle with three unequal sides is a scalene triangle. ∆PQR is scalene.
Find a linear inequality with the following solution set. Each grid line represents one unit.
Pllzzzzzzz help!!!!!!!!!!
Answers
The equation of the line is y = 3x - 4, so the inequality is y <= 3x - 4.
Answer:
y <= 3x - 4
Standard form: [tex]3x-y-4\geq 0[/tex]
Copy-paste: 3x-y-4>=0
Divide a 6 and 3/4 inch line into three parts so that each part is 1/4 inch shorter than the one before it.
Answers
Answer:
Hey there!
x+x+1/4+x+2/4
3x+0.75=6.75
3x=6
x=2
The lines are 2, 2 1/4, and 2 2/4.
Let me know if this helps :)
The three numbers or parts are 2 , 2 1/4 and 2 1/2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be n = 6 3/4
Now , for the number to be divided into three parts where each number is 1/4 shorter than the one before it ,
Let the first divided number be = x
So , the second number will be 1/4 more than the first number
Second number = x + 1/4
And , the third number will be 1/4 more than the second number
Third number = x + 1/4 + 1/4
= x + 2/4
= x + 1/2
Now, the equation will be
The sum of all three numbers = 6 3/4
So ,
x + ( x + 1/4 ) + ( x + 1/2 ) = 6 3/4
3x + 3/4 = 6 3/4
Subtracting 3/4 on both sides , we get
3x = 6
x = 2
Substituting the values of x in the equation , we get
First number = 2
Second number = 2 1/4
Third number = 2 1/2
Hence , the three numbers or parts are 2 , 2 1/4 and 2 1/2
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A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 43 cables and apply weights to each of them until they break. The 43 cables have a mean breaking weight of 774.3 lb. The standard deviation of the breaking weight for the sample is 15.4 lb. Find the 90% confidence interval to estimate the mean breaking weight for this type cable.
Answers
Answer:
At 90% confidence interval, the estimate of the mean breaking weight is (770.45, 778.15)
Step-by-step explanation:
Given that:
sample size n =43
sample mean x = 774.3
standard deviation = 15.4
confidence interval = 90%
At C.I of 90% , the level of significance ∝ = 1 - C.I
the level of significance ∝ = 1 - 0.90
the level of significance ∝ = 0.10
The critical value for z at this level of significance is [tex]z_{\alpha/2} = z_{0.10/2}[/tex]
[tex]z_{0.05}[/tex] = 1.64
The margin of error can be computed as follows:
Margin of error = [tex]\mathtt{z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}}[/tex]
Margin of error = [tex]\mathtt{1.64 \times \dfrac{15.4}{\sqrt{43}}}[/tex]
Margin of error = [tex]\mathtt{1.64 \times \dfrac{15.4}{6.5574}}[/tex]
Margin of error = [tex]\mathtt{1.64 \times2.3485}[/tex]
Margin of error = 3.8515
The mean breaking weight for the 90% confidence interval is = [tex]\mathtt{\overline x \pm E < \mu }[/tex]
= [tex]\mathtt{\overline x - E < \mu < \overline x + E}[/tex]
= ( 774.3 - 3.8515 < μ < 774.3 + 3.8515 )
= (770.4485, 778.1515)
[tex]\simeq[/tex] (770.45, 778.15)
Sophie is making a copy of an angle. The original angle will be labeled G and the new angle will be labeled B. She has just finished using a compass, with the point on G, to draw an arc that intersects both rays of angle G. Which of the following should she do next
Answers
Answer:
The next step is;
Label the two intersection points
Step-by-step explanation:
To make a copy of an angle, the steps are;
1) Draw the rays of the original angle passing through the point B
2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays
3) Label the point of intersection of both rays points C and D
4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J
5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M
6) Draw a line from B passing through M to complete the second ay of the copied angle.
How would you write 7 is subtracted from the cube of a number
Answers
Answer:
n³ - 7
Step-by-step explanation:
n³ - 7
The required expression for the 7 subtracted from the cube of a number is x³- 7.
Given that,
A string of statements is given,
Here, we have to transform the statement, 7 is subtracted from the cube of a number into a mathematical inscription.
Arithmetic, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is an expression?A mathmetical expression is formulated structure of a statement using variables.
Let the number be x,
Now 7 subtracted from the cube of number x
= x³ - 7
Thus, the required expression for the 7 subtracted from the cube of a number is x³- 7.
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Answer ASAP, Will give brainliest!!
Find the length and the mid- segment
Isosceles Trapizoid
AB=48
BC=19
CD=24
DA=19
Answers
Answer:
Step-by-step explanation:
Length of mid-segment = [tex]\frac{(AB+CD)}{2}[/tex]
[tex]= \frac{48 +24}{2}\\\\\\=\frac{72}{2}\\\\[/tex]
= 36 in
A player has 15 hits in 34 times at bat and then gets
another hit. Did the batting average increase? Explain.
Answers
Answer:
yes, his batting average will increase bcz average of a batsmen is the sum of total hits per ball.
write down the missing number in the following 1,,4,9,16,25,?
Answers
Answer:
36
Step-by-step explanation:
you know the number based on the sequence
the values increase in the form of x+2
e.g. 4-1=3
9-4=5
16-9=7
25-16=9
you can see the number adds 2 for every increased number
and by following this sequence you will get the number 36
Answer:
by the square of 1, 2 ,3 the sequence has been made
Step-by-step explanation:
1 for 1²
4 for 2²
9 for 3²
16 for 4²
25 for 5²
so the later one will be 36 for 6²
so the answer is 36 thats all
you took a 20 question test and received a 65% on the test. how many question did you answer correctly
Answers
Find the product of all real values of $r$ for which $\frac{1}{2x}=\frac{r-x}{7}$ has exactly one real solution.
Answers
Answer:
-14
Step-by-step explanation:
Observe first that $x=0$ is not a solution to the equation since it makes the denominator of $\frac{1}{2x}$ equal to 0. For $x\neq 0$, we may multiply both sides by both denominators and move all the resulting terms to the left-hand side to get $2x^2-2rx+7=0$. Observe that there are two ways the original equation could have exactly one solution. Either $2x^2-2rx+7=0$ has two solutions and one of them is 0, or else $2x^2-2rx+7=0$ has exactly one nonzero solution. By trying $x=0$, we rule out the first possibility.
Considering the expression $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ for the solutions of $ax^2+bx+c=0$, we find that there is exactly one solution if and only if the discriminant $b^2-4ac$ is zero. Setting $(-2r)^2-4(2)(7)$ equal to 0 gives $4r^2-4(14) = 0$. Add 4(14) and divide by 4 to find $r^2=14$. The two solutions of this equation are $\sqrt{14}$ and $-\sqrt{14}$, and their product is $\boxed{-14}$.
The value of r from the given equation is r=(2x²+7)/2x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is [tex]\frac{1}{2x}=\frac{r-x}{7}[/tex].
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
By cross multiplication, we get
7=2x(r-x)
7=2rx-2x²
2rx=7+2x²
r=(2x²+7)/2x
Therefore, the value of r from the given equation is r=(2x²+7)/2x.
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help plz anyone :( will mark
Answers
Answer:
area of square - area of circle
s² - pie r²
3² - 3.14 x1 x1
9 - 3.14 cm²
your answer is 5.86cm²
this is area of shaded region
nearest hundered is 6cm²
plz brainlist me bro I need it plz
her answer is wrong brainlist me
Answer:
The area of the shaded region is
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the rectangle minus the area of the circle
The rectangle is a square
So.... Plz check rest in the pic!
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
Answer ASAP, will give brainliest
Answers
Answer:
A) 5.4 cm
Step-by-step explanation:
Length of mid segment = (sum of parallel sides )/2
Sum of parallel sides = PQ + SR = 9 + SR
[tex]\frac{9+SR}{2}=MN\\\\\frac{9+SR}{2}=7.2 cm\\9 +SR = 7.2*2\\\\9 + SR = 14.4\\ SR = 14.4 -9 \\SR = 5.4 cm[/tex]
Find conditions on the slope of a line through (9, 4) such that the x-intercept is negative and the slope is greater than its y-intercept. 2/5 < m < 4/9 m < 2/5 or m > 4/9 9/5 < m < 9/4 m < 9/5 or m > 9/4 Not enough information
Answers
Answer:
9/5 < m < 9/4
Step-by-step explanation:
The conditions are:
The line passes through (9,4)x-intercept is negativeThe slope (m) is greater than its y-interceptIf we take a point like (-1,0)
Slope (m) = change in y ÷ change in x = [tex]\frac{0 - 9}{-1 - 4} = \frac{-9}{-5}[/tex] = 9/5
This point satisfies the conditions above since;
The line passes through points (9,0) and (-1,0)The x-intercept is negative i.e -1The y-intercept is 0 and the slope which equals 9/5 is greater than 0From the choices given;
we can say that:
m > 9/5 and m < 9/4
And can be expressed as;
9/5 < m < 9/4
The research chemists at MegaClean created a new cleaner that keeps car and truck tires shiny and clean for one year. They believe that this product will be highly successful and will attract customers to purchase their existing line of household cleaning products.
Answers
Answer:
Complementary effect
Step-by-step explanation:
Complementary goods service is another good or item used in conjunction with the service. In general, complementary goodness does not matter when eaten alone, but when combined with another good or service, it increases the overall value of the offering. When a product shares a lucrative relationship with another product offering it is considered an affiliate, for example, an iPhone and apps used with it, so that this is good example of Complementary effectLet f(x)=logx. What is the average rate of change of f(x) from 2 to 3? Round to the nearest hundredth.
Answers
Answer:
Below
Step-by-step explanation:
Let m be the average rate of change.
● m = (f(3)-f(2)) / 3-2
● m = ( log3 - log2) / 1
● m = 0.176
Round it to the nearest tenth
● m = 0.18
Find the value of 7v-6 given that -8v-9=7 Simplify your answer as much as possible 7v-6=
Answers
Answer:
-20
Step-by-step explanation:
-8v-9=7
Add 9 to each side
-8v-9+9=7+9
-8v = 16
Divide by -8
-8v /-8 = 16/-8
v = -2
Now find
7v -6
7(-2) -6
-14 -6
-20
Answer:
negative 20?
Step-by-step explanation:
I tried to remember what I learned about a year ago...
A player has 15 hits in 34 times at bat and then gets another hit. Did the batting average increase explain
Answers
Explanation:
BA= H/AB
BA = 15/34 = 0.441
But then he gets another hit:
BA = 16/35 = 0.457
whats the factored form of 6x 2 - 8x - 8 = 0
Answers
Answer:
x = -2/3 , 2
Step-by-step explanation:
Factor 2 out of 6 x^ 2 − 8 x − 8
2 ( 3 x^ 2 − 4 x − 4 ) = 0
Factor
2 ( 3 x + 2 ) ( x − 2 ) = 0
Set 3 x + 2 equal to 0 and solve for x
x = -2/3
Set x − 2 equal to 0 and solve for x
x = 2
The final solution is all the values that make 2 ( 3 x + 2 ) ( x − 2 ) = 0
x = -2/3 , 2
Hope this can help you
A portion of a line or Ray that extends from one point to another point is called what
Answers
Answer: line segment
Step-by-step explanation:
A line segment is a ray that extends from one point to another. Hope this helps!
Answer:
line segment
Step-by-step explanation:
If a portion of a line has two endpoints (two little black dots on its end), then it is a line segment.
If it has one dot and an arrow, its a ray. This has an endpoint and goes on forever in the direction of the arrow.
1. Check the divisibility of the following numbers by 2, 3, 9 and 11 a) 76543 b) 98765436
2. Which of the following numbers are divisible by 4 or 8? a) 67894 b) 9685048
WILL MARK THEM AS BRAINLIST
Answers
Answer:
1. ( I didnt understand the question but I divided them using the calculator.)
A.) 76543
÷ 2= 38,271.5
÷ 3= 25,514.333...
÷ 9= 8,504.777...
÷ 11= 6,958.454545...
B.) 98765436
÷ 2= 49,382,718
÷ 3= 32,921,812
÷ 9= 10,973,937.333...
÷ 11= 8,978,676
2. B
A.) 67894
÷ 4= 16,973.5
÷ 8= 8,486.75
B.) 9685048
÷ 4= 2,421,262
÷ 8= 1,210,631
Explanation:
I used the calculator to divide.
I hope this helps! I'm sorry if it's wrong.
at the rate of 50 mph a car can travel 14.6 miles for each gallon of gas used. On a trip Mr. Hanson used 12.5 gallons of gas traveling at a speed of 50 mph. the number of miles covered during the trip was:
Answers
Answer:
182.5 miles in the rate of 50 mph.
Step-by-step explanation:
1 gallon = 14.6 miles in the rate of 50 mph
12.5 gallons = ?
12.5 × 14.6 = 182.5 miles in the rate of 50 mph.
The number of miles covered during the trip was 182.5 miles.
Given that, at the rate of 50 mph, a car can travel 14.6 miles for each gallon of gas used. On a trip, Mr Hanson used 12.5 gallons of gas travelling at a speed of 50 mph.
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, 1 gallon = 14.6 miles at the rate of 50 mph
12.5 × 14.6 = 182.5 miles in the rate of 50 mph.
Therefore, the number of miles covered during the trip was 182.5 miles.
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assume the initial velocity is 60 feet/second. what is the maximum horizontal distance possible and at what angle does this occur
Answers
Answer:
h = 112.5 feets
Step-by-step explanation:
The equation for horizontal distance "h" in feet of a projectile with initial velocity v₀ and initial angle theta is given by :
[tex]h=\dfrac{v_o^2}{16}\sin\theta\cos\theta[/tex]
We know that, [tex]2\sin\theta\cos\theta=\sin2\theta[/tex]
So,
[tex]h=\dfrac{v_o^2}{32}\sin2\theta[/tex]
Now we need to find the maximum horizontal distance possible and at what angle does this occur.
For maximum distance angle should be 45 degrees. Som,
[tex]h=\dfrac{60^2}{32}\sin2(45)\\\\h=112.5\ \text{feet}[/tex]
So, 112.5 feets is the maximum possible distance.
Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m = 12s, where m is the number of minutes and s is the number of sketches.
If Lori made of a sketch, she spent minutes sketching.
Answers
Answer:
A. 9
Step-by-step explanation:
Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m=12s where m is the number of minutes and s is the number of sketches if Lori made 3/4 of a sketch she spent A.9 B.12 C.16 D.20 minutes sketching
Solution
m= number of minutes
s= number of sketches
Equation is
m=12s
If Lori made 3/4 of the sketch, then the time spent is ?
s=3/4
m=?
m=12s
m= 12 × 3/4
=36/4
=9
m=9
If Lori made 3/4 of the sketch, then she spent 9 minutes sketching.
Answer:
I hope this helps
Step-by-step explanation:
heeelllpppppppppppppppp
Answers
Answer:
2/5m - 1/5
Step-by-step explanation:
2(1/5m - 2/5) + 3/5
= 2/5m - 4/5 + 3/5
= 2/5m - 1/5
Answer:
[tex]\frac{2m-1}{5}[/tex]
Step-by-step explanation:
[tex]2\left(\frac{1}{5}m-\frac{2}{5}\right)+\frac{3}{5}\\\\2\left(\frac{1}{5}m-\frac{2}{5}\right)=2\left(\frac{m}{5}-\frac{2}{5}\right)\\\\\frac{m}{5}-\frac{2}{5}=\frac{m-2}{5}\\\\=\frac{2\left(m-2\right)}{5}+\frac{3}{5}\\\\\mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{2\left(m-2\right)+3}{5}\\\\\mathrm{Expand}\:\left(m-2\right)\cdot \:2+3:\quad 2m-1\\\\=\frac{2m-1}{5}[/tex]
AB =
Round your answer to the nearest hundredth.
B
?
2
25°
С
A
Answers
Answer:
? = 4.73
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp / hyp
sin 25 = 2 / ?
? sin 25 = 2
? = 2 / sin 25
? =4.732403166
To the nearest hundredth
? = 4.73
