Answers
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Question # (1): t = 15.8 (when rounded to the nearest tenth).
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Question # (3): The length of Side EF is 7.5 (when rounded to the nearest tenth), and the length of side DF is 2.7 (when rounded to the nearest tenth).
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Here is how to solve for "Question #1" and "Question #3":
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Let us start with "Question #1":
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Remember the phrase: "SOH CAH TOA"; in which:
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Sin = opposite/hypotenuse; Cos = adjacent/ hypotenuse;
Tan = opposite/adjacent.
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We are given an triangle; one angle has a measurement of 44°. Considering this given angle, the respective hypotenuse given is "22"—along with a variable "t" for the respective "adjacent" side.
Using the above: "SOH CAH TOA" method; it would make sense to use the "CAH" {cosine = adjacent/hypotenuse} part of the mnemonic to solve for "t".
___________________________________________________________
Reason: We are given the angle measure 44°; the hypotenuse value ("22"); so the cosine of 44, or "cos 44" = adjacent/hypotenuse = "t" / 22 .
→ Write as: cos 44 = t / 22 ; Solve for "t" .
→ (cos 44)*22 = t ; → t = 22 * (cos 44);
→ t = 22 *(cos 44) = 22 * (0.719339800339) → Use a scientific calculator:
→ t = 15.825475607458 ; → Round to the nearest tenth, as indicated in the problem, to get:
________________________
→ t = 15.8 ; → which is the answer.
____________________________________
"Question #3: Find the missing lengths in the triangle. Round to the nearest tenth." [Note: There are 2 (two) missing lengths to find.].
___________________________
To get the length of side "EF"; let us use the "CAH" part of the mnemonic,
"SOH CAH TOA", (in the aforementioned previous problem given).
The "CAH" stands for the formula/property to calculate for the "cosine"—specifically, "cosine = adjacent/hypotenuse". We choose this one because we are given the measure of "angle E = 20° "; and we are given the hypotenuse, "side ED = 8"; and we want to solve for the adjacent side, which is "EF" (which we will call: "x").
→ So, cos 20 = adjacent/ hypotenuse = x /8; → Solve for "x""
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(cos 20)*8 = x ; → 8*(cos 20) = x ; →
→x = 8 * (cos 20) = 8 *(0.939692620786) → Use a scientific calculator: = 7.517540966288 ;→ Round to the nearest tenth, as indicated in the problem, to get:
__________________________
→ 7.5 ; which is the answer for the length of side EF.
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Now, we need to find the unknown length of the other side, "Side DF".
Here is one method:
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Find the measure of "Angle D". Note that for any triangle, all three sides must add up to 180°. We know that this is a right triangle, with one angle ("Angle F") having a measurement of 90°. We are also given that another angle ("Angle E") has a measurement of 20°.
→ So, the measurement of "Angle D" = 180 - (90 + 20) = 180 - 110 = 70.
→ We want to solve for the length of side "DF", which is adjacent to "Angle D" (which we know is 70°).
_____________________________________________
Let us use the "CAH" part of the mnemonic,
"SOH CAH TOA", (in the aforementioned previous problem given).
_________________________________________
The "CAH" stands for the formula/property to calculate for the "cosine"—specifically, "cosine = adjacent/hypotenuse". We choose this one because we are given the measure of angle "D"= 70°; and we are given the hypotenuse = 8. The "adjacent", or "Side DF", is the unknown value (let us make it "x").
________________________________________________
So, cos 70 = adjacent / hypotenuse = x/ 8 ; Solve for "x" :
_________________________
cos 70 = x / 8; (cos 70) * 8 = x ; 8 * (cos 70) = x;
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x = 8 * (cos 70) = 8 * (0.342020143326) → Use a scientific calculator → = 2.736161146608 ;
→Round to the nearest tenth, as indicated in the problem, to get:
________________________________________
→ 2.7 ; which is our answer, for the length of side DF.
___________________________________________
So, the answer for "Question 1" is: t = 15.8 (when rounded to the nearest tenth).
___________________________________________
For "Question #3", the length of Side EF is 7.5 (when rounded to the nearest tenth), and the length of side DF is 2.7 (when rounded to the nearest tenth).
Related Questions
The exponential expression 4^-2 is equal to what fraction value
Answers
X ^-m = 1/X^m
For example
4^-2 = 1/4^2 = 1/16. Since 4 • 4 which is the same as 4^2 is 16.
What is the mean of 4, 6, 8, 20, 12?
Answers
Answer:
The correct answer is A. 10
4+6+8+20+12=50
50/5 =10
Step-by-step explanation:
Solve for y.
7y - 6y - 10 = 13
y = -23
y = -3
y = 3
y = 23
Answers
-collect like terms
y-10=13
-move the constant to the right side and change its sign
y=13+10
add the numbers
answer is y=23
Find the perpendicular slope of the line 3X-9Y=15
Answers
So --9/3=3
(-b/a) is the equation of the slope
-9y = -3x + 15
y = (-3/-9)x + (-15/9)
y = 1/3x - 5/3....slope here is 1/3. A perpendicular line will have a negative reciprocal slope.All that means is " flip " the slope and change the sign.
So our perpendicular slope will be : -3 ( I flipped 1/3 and it became 3/1 or just 3...I then changed the sign and it became -3)
so the perpendicular slope is -3
Which pair of angles must be congruent?
A. Supplementary angles
B. Complementary angles
C. Adjacent angles
D. Vertical angles
Answers
_______________________________
If he swim 900m in a day how many kilometers he swim
Answers
on a grid, what is the distance between two points located at (2,1) and (14,6)
A.) 5
B.) 13
C.) 12
D.) 17.46
Answers
Simple Pythagorean Theorem.....
√(12)²+(5²))
√(169)
B.) 13
If two sides of a triangle are not =, the angle opposite the ___ side is the larger angle. shortest, intermediate, longest?
Answers
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
If two sides of a triangle are not equal,
According to Relationship between the angle and side , we know that the angle opposite the shortest side is the larger angle,
And,
The angle opposite the longest side is the shortest angle
So, First option is correct.
The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved for r is r = .
Find the radius of a circle that has a circumference of 16.
Answers
C = 2πr
Divide both sides by 2π:
C/2π = 2πr/2
C/2π = r
r = C/2π
C = 16
r = 16/2π
r = 8/π
Answer: 8 units
Step-by-step explanation:
Given: The formula for the circumference of a circle is [tex]C=2\pi r[/tex], where r is the radius and C is the circumference.
To solve equation for r , we divide [tex]2\pi[/tex] on both sides, we get
[tex]r=\dfrac{C}{2\pi}[/tex]
Now, the circumference of the circle = [tex]16\pi \text{units.}[/tex]
Then, [tex]r=\dfrac{16\pi}{2\pi}=8\ \text{units}[/tex]
Hence, Circumference of the circle = 8 units
Randolph has 8 ties, 6 pairs of pants, and 4 dress shirts. how many days can randolph go without wearing the same combination of these three items?
Answers
A pack of gum costs 75 cents. That is 3 cents less than three times what the pack cost 20 years ago. Which equation could be used to find the cost of the gum 20 years ago?
A)
0.3x - 0.3 = 0.75
B)
3x - 0.3 = 0.75
C)
3x - 3 = 75
D)
3 - 3x = 75
Answers
thats how we get 3x - 3 and we make it equal to 75 because we are comparing those 2 prices
So, answer is C.
Answer:
C
Step-by-step explanation:
Let the cost of a pack of gum 20 years ago = x cents
Given, present cost of a pack of gum = 75 cents
Given, present cost of a pack of gum is 3 cents less than three times what the pack costs 20 years ago.
So,
[tex]75 + 3 =3x[/tex]
[tex]75= 3x -3[/tex]
[tex]3x-3=75[/tex]
Therefore,
Equation , [tex]3x-3=75[/tex] , can be used to find the cost of the gum 20 years ago.
If the first equation is multiplied by 3 and then the equations are added, the result is _____.
3x + y = 3
x - 3y = -2
10x = 11
10x = 7
8x = 7
Answers
x=7/10, you could work backwards to find y if it asked
Answer: The correct option is (B) [tex]10x=7.[/tex]
Step-by-step explanation: The given equations are :
[tex]3x+y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-3y=-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
We are to select the correct result if the first equation is multiplied by 3 and then added to the second equation.
Now, multiplying equation (i) by 3, we get
[tex]3(3x+y)=3\times 3\\\\\Rightarrow 9x+3y=9~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
adding equation (iii) to equation (ii), we get
[tex](9x+3y)+(x-3y)=9+(-2)\\\\\Rightarrow 9x+3y+x-3y=9-2\\\\\Rightarrow 10x=7.[/tex]
Thus, the required result is [tex]10x=7.[/tex]
Option (B) is CORRECT.
Write the tangent ratios for P and Q. The figure is not drawn to scale.
Answers
Answer:
tan P = 24/7 and tan Q = 7/24
Step-by-step explanation:
tangent of any angle in a right angle triangle is always represented by
tan x = opposite side/ adjacent side = height / base
from the question we have to write tangent of P and Q.
tan P = QR/PR = 24/7
tan Q = PR / RQ = 7/24
So the answers are tangent ratios for P and Q are 24/7 and 7/24.
This is a continuous set of numbers. every real number from the starting value to the ending value is included. it is called an ___.
Answers
if y=15 when x=3/4, find x when y=25
Answers
The value of the x is 5/4 when y=25 if y=15 when x=3/4 the answer would be 5/4
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
x and y are in a proportional relationship if y=15 when x=3/4,
y ∝ x
y = kx
15 = k(3/4)
k = 20
y = 20x
Plug y = 25
25 = 20x
x = 25/20
x = 5/4
Thus, the value of the x is 5/4 when y=25 if y=15 when x=3/4 the answer would be 5/4
The complete question is:
x and y are in a proportional relationship if y=15 when x=3/4, find x when y=25.
Learn more about the proportional here:
brainly.com/question/14263719
#SPJ2
What is the number of real solutions?
–11x2 = x + 11
cannot be determined
one solution
two solutions
no real solutions
Answers
that would be -22=x+11
x=-33
so there's only one solution.
Answer:
no real solutions.
Step-by-step explanation:
-11[tex]x^{2}[/tex] = x+11. Put into standard form of a quadratic equation.
11[tex]x^{2}[/tex] + x + 11 = 0 Find a, b, and c.
a = 11, b =1, c = 11 Write and substitute into the quadratic equation[tex]\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}[/tex] .
[tex]\frac{-1 +/- \sqrt{1^{2} - 4(11)(11)} }{2(11)}[/tex] Simplify.
[tex]\frac{-1 +/- \sqrt{1-484} }{2(11)}[/tex]=
[tex]\frac{-1 +/-\sqrt{-483} }{22}[/tex] BUT because the [tex]b^{2} -4ac[/tex] part under the √ is less than 0, THERE IS NO SOLUTION!
For Earth Day, the school plans to sell the following buttons to students and the community. The school will have to pay $18 for 15 dozen buttons. How much will the school have to pay for 50 dozen buttons?
Answers
The school will have to pay $60 for 50 dozen buttons, by using a proportional calculation based on the known cost of $18 for 15 dozen buttons.
Explanation:The student's question involves calculating the cost of purchasing a larger quantity of buttons based on a known cost for a smaller quantity. To solve this, we will use proportional reasoning.
The school pays $18 for 15 dozen buttons. First, we find the cost for one dozen by dividing the total cost by the number of dozens:
$18 ÷ 15 dozen = $1.20 per dozen
Next, we calculate the cost for 50 dozen buttons by multiplying the cost per dozen by the number of dozens:
$1.20 per dozen × 50 dozen = $60
Therefore, the school will have to pay $60 for 50 dozen buttons.
Which description represents the expression 3x+4 ? A.4 less than 3 times a number B.4 divided by the product of 3 and a number C. 4 added to 3 plus a number D.the sum of 3 times a number and 4
Answers
the sum of 3 times a number and 4
Use the polynomial identity to determine which values of x and y generate the values of the sides of the following right triangle.
x = 8, y = 3
x = 3, y = 8
x = 6, y = 4
x = 4, y = 6
Answers
x^2 - y^2 = 55
substituting in to it
73 - 55 = 2y^2
18 = 2y^2
y = 3
x^2 - 73 - 9
x = 8
answer is A
Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC.
Answers
The line is 1/2 the length of the square's diagonal :
(1/2)(10√2) = 5√2.
Let CG be a distance x from the vertex of the right angle in the triangle.
Remaining distance = 5√2 - x.
(1)(x) = (2)(5√2 - x)
x = 10√2 - 2x
3x = 10√2
x = (10/3)√2.
Using Pythagorean theorem,
x^2 + y^2 = c^2
c = (10/3)√2,
and x = y,
so 2x^2 = 200/9
x = √(100/9) = 10/3 = y.
x = y = 3.333
Is the area between y = 1/x and y = 1/x^2 on the interval from x = 1 to finite or infinite?
Answers
How many real solutions does the function shown on the graph have?
Can someone explain?
One, Two, None, or can't be determined?
Answers
n is a positive integer.
Explain why n(n-1) must be an even number.
Answers
3 * (3-1). According to BIDMAS/BODMAS, we must first work out the brackets and then multiple it by the 3.
Do 3-1 = 2, 2*3 = 6 which is an even number. If we try with an even number we also get an even number:
4-1 = 3, 3*4 = 12. Even if we try this with a number like 7, 9 or 10 - we will always get an even integer, this is because, whenever we multiple an even number with an even or odd number - we always get an even number. So when we take away 1 by an even number, and multiple it with an odd number, we get even. Same applies to when we take away an odd number by 1 to get an even number and then times it by an odd number - we always get even.
Ria is an Indian student who was admitted to a US university. Her annual tuition is $42,000. She has to pay her tuition fees in US dollars. She needs to calculate how many Indian rupees she will need to buy one dollar. The dollar to rupee exchange rate is 63.76 and rupee to dollar exchange rate is 0.015. How many Indian rupees will Ria need to buy one dollar?
50.00 rupees
56.00 rupees
63.76 rupees
76.63 rupees
Answers
Answer:
C:63.76
Hope this helps
Final answer:
Ria will need 63.76 Indian rupees to buy one US dollar according to the given exchange rate.
Explanation:
The student is asking how many Indian rupees are needed to buy one US dollar based on the given exchange rates. According to the given information, the exchange rate from dollars to rupees is 63.76. This means that one US dollar is equivalent to 63.76 Indian rupees. The other exchange rate provided, which is the value of a rupee in terms of dollars (0.015), is not directly relevant to the question being asked. Therefore, Ria will need 63.76 Indian rupees to buy one US dollar.
An obtuse triangle with area 12 has two sides of lengths 4 and 10. Find the length of the third side. (There are two answers.) (Use law of cosines) ...?
Answers
Final answer:
Using the Law of Cosines, the length of the third side of the obtuse triangle is x = sqrt(52) or x = 2sqrt(13).
Explanation:
To find the length of the third side of an obtuse triangle with sides of lengths 4 and 10 and an area of 12, you can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the equation c^2 = a^2 + b^2 - 2ab * cos(C) can be used to find the length of side c.
In this case, let's assume that the third side of the triangle has length x. We can set up the equation as x^2 = 4^2 + 10^2 - 2*4*10 * cos(C), where C is the angle opposite side x.
Simplifying the equation, we get x^2 = 116 - 80*cos(C).
Since we know that the area of the triangle is 12, we can use the formula Area = 0.5 * a * b * sin(C) to find the value of sin(C). Plugging in the given values, we get 12 = 0.5 * 4 * 10 * sin(C). Solving for sin(C), we find sin(C) = 0.6.
Using this value of sin(C), we can then find the value of cos(C) by using the trigonometric identity sin^2(C) + cos^2(C) = 1. Substituting sin(C) = 0.6, we get 0.6^2 + cos^2(C) = 1. Solving for cos(C), we find cos(C) = 0.8.
Now, we can substitute the value of cos(C) into the equation x^2 = 116 - 80*cos(C), giving us x^2 = 116 - 80*0.8. Simplifying further, we get x^2 = 52, which means that the length of the third side is either x = sqrt(52) or x = -sqrt(52).
However, since we are dealing with the length of a side, it cannot be negative. Therefore, the length of the third side is x = sqrt(52), which simplifies to x = 2sqrt(13).
jamal is 167 cm tall which expression expression finds jamals height in dekametres
A.167 times 100
B.167 times 1000
C.167 divided by 100
D.167 divided by 1000
Answers
167 cm = 1.67m
1.67m = 0.167dm
D. 167/1000 = 0.167
Jamal's height can be converted to dekametres by dividing his height in centimeters (167 cm) by 1000, because there are 1000 centimeters in a dekametre.
To convert Jamal's height from centimeters to dekametres, we should recall that 1 dekametre equals 10 meters or 1000 centimeters. Since Jamal is 167 cm tall, we need to divide his height in centimeters by the number of centimeters in a dekametre to get his height in dekametres.
Therefore, the correct expression to find Jamal's height in dekametres is:
167 divided by 1000
This is option D: 167 / 1000.
Use the elimination method to solve the following system of equations.
2x - y + z = -3
2x + 2y + 3z = 2
3x - 3y - z = -4
Answers
2x - y + z = -3 (1)
2x + 2y + 3z = 2 (2)
3x - 3y - z = -4 (3)
(1) - (2) 3y +2z =5
3 .(1) - 2.(2) 3y+5z = -1
let 's solve
3y +2z =5
3y+5z = -1
z= - 2, and 3y =5+4=9, y=3, so 2x - 3 -2 = -3 implies x= 1
finally x=1, y=3 and z= -2
proof
2x - y + z = -3?? 2.1 - 3 -2 = -3 (true)
The sum of 8 and 7, doubled
Answers
What is the first step in solving a quadratic equation of the form given below?
(ax + b)2 = c
A.Divide both sides by c
B.Use the zero product rule
C.Factor out a common factor
D.Take the square root of both sides
Answers
the answer is d,,,,,,,,,,,,,,,,,
Answer:
Correct option is D.
Step-by-step explanation:
Given the quadratic equation
[tex](ax+b)^2=c[/tex]
we have to define the first step in solving a quadratic equation.
To find the value of x we have make the equation linear i.e taking the square root on both sides as c is any constant.
If c is 0 the we use the zero product rule.
Hence, our first step in solving a quadratic equation of the form
[tex](ax+b)^2=c[/tex]
is to take the square root of both sides.
Correct option is D.
what happens to the graph of a line when the slope is negative? Check all that apply. may choose more then 1.
A. As the absolute value of the negative slope gets bigger, the graph of the line gets steeper.
B. As the absolute value of the negative slope gets smaller, the graph of the line gets steeper.
C. The line goes down from left to right.
D. The line shifts down.
E. The line goes up from left to right
Answers
y=kx+n
k is coefficient which tells us about slope. The higher the k is, the faster y changes for same change of x value.
Therefore A is correct and B isnt
C is correct. because for positive changes of x you have negative change of y because of negative coeficient which when multiplied by positive value of x will give negative value.
D isnt correct. n is parameter that influences shifting.
E is oposite from C therfore it isnt correct.