Answer:
c = 45.33, C =97°, a = 40, A = 61.15° , B = 21.85°, b = 17
Step-by-step explanation:
Given that:
C = 97°, a = 40 and b = 17.
We have angle C, we need to find the side the side c opposite to the angle C. we have side a, we need to find the angle A opposite to side a. we have side b, we need to find the angle B opposite to side b.
Using cosine rule:
c² = a² + b² - 2ab × cos(C)
c² = 40² + 17² - 2(40)(17)cos(97)
c² = 2054.74
c = 45.33
Also using sine rule:
[tex]\frac{a}{sin(A)} =\frac{c}{sin(C)} \\\frac{40}{sin(A)}=\frac{45.33}{sin(97)} \\sin(A)=\frac{sin(97))40}{45.33}=0.876\\A=sin^{-1}(0.876)=61.15^0[/tex]
Also:
[tex]\frac{b}{sin(B)} =\frac{c}{sin(C)} \\\frac{17}{sin(B)}=\frac{45.33}{sin(97)} \\sin(B)=\frac{sin(97))17}{45.33}=0.3722\\B=sin^{-1}(0.3722)=21.85^0[/tex]
c = 45.33, C =97°, a = 40, A = 61.15° , B = 21.85°, b = 17
Aaron is 5 years younger than
Roy. Four years later, Roy will be
twice as old as Aaron. Find their
present ages
Answer:
Roy is 6 years old and Aaron is 1 year old.
Step-by-step explanation:
A is Aaron's age,
R is roy's age,
A = R - 5
R + 4 = 2(A+4)
We can distribute first,
R + 4 = 2A + 8
Subtract 4 from each side,
R = 2A + 4
Since A = R - 5, you can substitute in R - 5 for A in the equation,
R = 2(R-5) + 4
Distribute,
R = 2R - 10 + 4
Since - 10 + 4 = -6, we can do this,
R = 2R - 6
Subtract R from both sides,
0 = R - 6
Add 6 to both sides and you have part of your answer;
R = 6
Since A = R - 5,
A = 6 - 5
A = 1, so Aaron's age is 1.
Solve the inequality. Graph the solution. −6n>54 The solution of the inequality is .
Answer:
n =-9
Step-by-step explanation:
-6n>54
Divided by negative 6
n=we change the Sign
n=-9
Solve the triangle if B=78 degrees and a=41. Round to the nearest tenth.
Answer:
b=197.6cm
Step-by-step explanation:
Given that a = 41 and B =78°
From the diagram of the triangle,
Tan θ = opp/adj
Where θ=78°
Tan78°= b/41
b = tan78×41
b = 4.70× 41
b = 197.5944cm
To the nearest tenth
b=197.6cm
Solve the inequality d/7 > 15. Then graph the solution.
Answer:
yes answer question?
Step-by-step explanation:
Answer:dE (105,infinity)
Step-by-step explanation:
"Find a number which, when added to 3, yields 7"
may be written as:
3 + ? = 7, 3 + n = 7, 3 + x = 1
and so on, where the symbols ?, n, and x represent the number we want to find. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.
EQUIVALENT EQUATIONS
Equivalent equations are equations that have identical solutions. Thus,
3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5
are equivalent equations, because 5 is the only solution of each of them. Notice in the equation 3x + 3 = x + 13, the solution 5 is not evident by inspection but in the equation x = 5, the solution 5 is evident by inspection. In solving any equation, we transform a given equation whose solution may not be obvious to an equivalent equation whose solution is easily noted.
The following property, sometimes called the addition-subtraction property, is one way that we can generate equivalent equations.
If the same quantity is added to or subtracted from both members of an equation, the resulting equation is equivalent to the original equation.
In symbols,
a - b, a + c = b + c, and a - c = b - c
are equivalent equations.
Example 1 Write an equation equivalent to
x + 3 = 7
by subtracting 3 from each member.
Solution Subtracting 3 from each member yields
x + 3 - 3 = 7 - 3
or
x = 4
Notice that x + 3 = 7 and x = 4 are equivalent equations since the solution is the same for both, namely 4. The next example shows how we can generate equivalent equations by first simplifying one or both members of an equation.
Example 2 Write an equation equivalent to
4x- 2-3x = 4 + 6
by combining like terms and then by adding 2 to each member.
Combining like terms yields
x - 2 = 10
Adding 2 to each member yields
x-2+2 =10+2
x = 12
To solve an equation, we use the addition-subtraction property to transform a given equation to an equivalent equation of the form x = a, from which we can find the solution by inspection.
Example 3 Solve 2x + 1 = x - 2.
We want to obtain an equivalent equation in which all terms containing x are in one member and all terms not containing x are in the other. If we first add -1 to (or subtract 1 from) each member, we get
2x + 1- 1 = x - 2- 1
2x = x - 3
If we now add -x to (or subtract x from) each member, we get
2x-x = x - 3 - x
x = -3
where the solution -3 is obvious.
The solution of the original equation is the number -3; however, the answer is often displayed in the form of the equation x = -3.
Since each equation obtained in the process is equivalent to the original equation, -3 is also a solution of 2x + 1 = x - 2. In the above example, we can check the solution by substituting - 3 for x in the original equation
2(-3) + 1 = (-3) - 2
-5 = -5
The symmetric property of equality is also helpful in the solution of equations. This property states
If a = b then b = a
This enables us to interchange the members of an equation whenever we please without having to be concerned with any changes of sign. Thus,
If 4 = x + 2 then x + 2 = 4
If x + 3 = 2x - 5 then 2x - 5 = x + 3
If d = rt then rt = d
There may be several different ways to apply the addition property above. Sometimes one method is better than another, and in some cases, the symmetric property of equality is also helpful.
Example 4 Solve 2x = 3x - 9. (1)
Solution If we first add -3x to each member, we get
2x - 3x = 3x - 9 - 3x
-x = -9
where the variable has a negative coefficient. Although we can see by inspection that the solution is 9, because -(9) = -9, we can avoid the negative coefficient by adding -2x and +9 to each member of Equation (1). In this case, we get
2x-2x + 9 = 3x- 9-2x+ 9
9 = x
from which the solution 9 is obvious. If we wish, we can write the last equation as x = 9 by the symmetric property of equality.
what is one fourth + ??????? = 8?
Answer:
1/4 + 31/4 =8
Step-by-step explanation:
break 8 into a fraction as 8/1
to get it to a common denominator multiply it by 4 so you get 32/4 and subtract 1/4 from that.
Answer:
7 3/4
Step-by-step explanation:
Convert 8 from a whole number to a fraction: 8/1
Do the inverse operation 8/1 - 1/4 = 31/4
31/4 = 7 3/4
Please help it is multiple choice
Answer:
1/2
Step-by-step explanation:
which quadrilateral always has four sides of the same length
Answer:
Either a square or a rhombus.
Step-by-step explanation:
A square always has four equal sides with an additional four 90 degree angles.
A rhombus always has four equal sides, but that is it.
Choose your pick on which shape you want to be your answer.
Answer:
a square and a rhombus
Step-by-step explanation:
i have the same question
A line that includes the points (8,0) and (9,s) has a slope of 9. What is the value of s?
Answer:
s = 9
Step-by-step explanation:
We can find the slope given two points
m = (y2-y1)/(x2-x1)
9 = (s-0)/(9-8)
9 = (s)/1
S = 9
Guys I really need help I will make u BRANLIEST!!!
Answer:
h=12 in
Step-by-step explanation:
volume of cube=1/3πr²h
113.04=1/3×3.14×3²×h
h=113.04/(3.14×3)=37.68/3.14=12 in.
Answer:
12 in
Step-by-step explanation:
It's right
Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine this area.
Answer:
Using Geometry to answer the question would be the simplest:
Step-by-step explanation:
Remembering the formula for the area of a triangle which is [tex]A=\frac12bh[/tex]. One can then tackle the question by doing the following:
Step 1 Find the y-intercepts
The y-intercepts are found by substituting in [tex]x=0[/tex].
Which gives you this when you plug it into both equations:
[tex]-y=1\\y=-1\\y=8[/tex]
So the y-intercepts for the graphs are [tex](0,-1)\\[/tex], and [tex](0,8)[/tex] respectively.
Now one has to use elimination to solve the problems by adding up the equations we get:
[tex]x-y=1\\2x+y=8\\3x=9\\x=3[/tex]
Now to solve for the y component substitute:
[tex]2(3)+y=8\\y=2[/tex]
Therefore, the graphs intersect at the following:
[tex](3,2)[/tex]
Now we have our triangle which is accompanied by the graph.
now to solve it we must figure out how long the base is:
[tex]b=8-(-1)\\b=9[/tex]
The height must also be accounted for which is the following:
[tex]h=3[/tex]
Now the formula can be used:
[tex]A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2[/tex]
Answer: 13.5 units²
Step-by-step explanation:
Geometry Solution:
The base is along the y-axis from -1 to 8 = 9 units
The height is the largest x-value = 3
[tex]Area=\dfrac{base\times height}{2}\quad =\dfrac{9\times 3}{2}\quad =\dfrac{27}{2}\quad =\large\boxed{13.5}[/tex]
Calculus Solution:
[tex]\int^3_0[(-2x+8)-(x-1)]dx\\\\\\=\int^3_0(-3x+9)dx\\\\\\=\bigg(\dfrac{-3x^2}{2}+9x\bigg)\bigg|^3_0\\\\\\=\bigg(\dfrac{-3(3)^2}{2}+9(3)\bigg)-\bigg(\dfrac{-3(0)^2}{2}+9(0)\bigg)\\\\\\=\dfrac{-27}{2}+27-0-0\\\\\\=\dfrac{27}{2}\quad =\large\boxed{13.5}[/tex]
At an electric store, a heater costs } more than a food mixer.
A blender costs $27. If the total cost of the three items is $139,
what is the cost of the blender as percent of the cost of the
food-mixer?
%
Answer:
19%
Step-by-step explanation:
27/139 is equal to .194 and rounding down gives us .19 or 19%.
Which graph represents an exponential equation
Answer:
4.
Step-by-step explanation:
It is exponential equation because exponential equations have those unprece curves or increasing/decreasing curves.
PLZ MARK BRAINLIEST!!!
Generally, how long are budgets are created for?
Answer:
In the general scenario, the duration of capital expenditures spans one year, sometimes spannering two or three fiscal years. Companies utilise various approaches to measure their capital expenditures than their normal budgeting processes.
Step-by-step explanation:
The answer is above
Hope this helps.
Answer: One Year
Step-by-step explanation: A budget is a list of probable EXPENSES and expected INCOME during a given period, most often one year.
Angles A and B together create a 90° angle. ∠A = 4x −10 and ∠B = 2x − 20. Find the angle measures (what will
Answer:
see below
Step-by-step explanation:
A+ B = 90
4x-10 + 2x-10 = 90
Combine like terms
6x -20 = 90
Add 20 to each side
6x -20+20 = 90+20
6x = 110
Divide by 6
6x/6 = 110/6
x = 55/3
A = 4x-10 = 4(55/3) -10
A=63 1/3
B = 2x-10 = 2(55/3) -10
26 2/3
the difference between 9 fifty-sixes and 3 fifty-sixes.
When's the 3 digit number is rounded to the nearest hundred it round to 400.The digit in the ones place is the fourth odd number you count beginning with 1.The sum of the digits is 12.What is the number
Answer:
417
Step-by-step explanation:
count 1, 3, 5, (7) is the fourth one
it needs to be rounded to 400 so it is between 350 and 450
lets try in the 300s, 12 -(3 + 7) = 2. but 327 does not round to 400 so it does not work
lets try in the 400s, 12 - (4 + 7) = 1. put that one in the middle and you get 417 which fits the entire description
Answer:
Cannot be determined since the question is wrong.
Step-by-step explanation:
The fourth odd number is: 1, 3, 5, 7
h+t+o=12
h+t+7=12
Subtract 7 from both sides
h+t=5
If it rounds up to 400, h must be 3.
3+t=5
Subtract 3 from both sides
t=2
So our number is 327? It doesn't round up to 400 so the question is probably wrong. You probably got a typo in their like the numbers adding up to 12 or rounding to 300.
What happens when the amplitude of the grade of the sine function increases?
(Don’t pay attention to the answer chosen)
Answer:
The increase of amplitude would increase distance between the maximum and minimun point of the wave.Step-by-step explanation:
We can defined the amplitude of a wave as the height of it, because it's the distance from the maxium point to the minimum point. In other words, it's the longest vertical displacement along the wave.
Additionally, amplitude represents power, when we apply waves to real phenomenons like the sound. So, greater grade of amplitude would represent louder sounds.
Therefore, the increase of amplitude would increase distance between the maximum and minimun point of the wave.
Javier and Serah are both travelling by train. Javier's train travels 130 km in 75 minutes. Serah's train travels 377 km. It leaves at 9:35 and arrives at 12:50. Work out the difference, in km/h, between the average speed of their trains.
Answer:
The difference between the average speed is 12 kilometers per hour, where Serah's train has the greatest speed.Step-by-step explanation:
Givens
Javier's train travels 130 km in 75 minutes.Serah's train travels 377 km from 9:35 to 12:50.The average speed is defined as
[tex]s=\frac{d}{t}[/tex]
To finde Javier's speed, we need to transform 75 minutes into hours, we know that 1 hour is equivalent to 60 minutes.
[tex]h=75min \times \frac{1hr}{60min} =1.25 \ hr[/tex]
Now, we find the average speed
[tex]s_{Javier}=\frac{130km}{1.25hr}=104 \ km/hr[/tex]
Therefore, Javier's train travels 104 kilometers per hour.
On the other hand, Serah's traing travels from 9:35 to 12:50, which is equivalent to 3 hours and 15 minutes, but 15 minutes is equivalent to 0.25, so the total time is 3.25 hours, so the average speed is
[tex]s_{Serah}=\frac{377km}{3.25hr}= 116 \ km/hr[/tex]
So, the difference would be
[tex]116-104=12 \ km/hr[/tex]
Therefore, the difference between the average speed is 12 kilometers per hour, where Serah's train has the greatest speed.
Answer:
12 km/h
Step-by-step explanation:
Approximate the square root to the nearest integer.
37
Answer:
We know that 6² = 36 , which is very close to 37 . Thus square root of 37 will be very close to 6
Lucy knows about 6 Web sites that sell a designer T-shirt she loves. The mean price of the T-shirt is $14 and the range of prices is $7. Which of the following are possible prices for the T-shirt? A. $14, $14, $14, $14, $7, $7 B. $14, $14, $14, $14, $14, $21 C. $13, $13, $13, $15, $15, $15 D. $13, $12, $15, $15, $11, $18
Answer:
D
Step-by-step explanation:
When we talk of the range, that means the difference between the highest and the lowest figure in the data set
The mean refers to the sum of the values in the data set divided by the count of the value in the data set.
let’s take a look at data set option A;
mean = [4(14) + 2(7)]/6 = (56 + 14)/6 = 70/6 which is definitely not 14 which makes the option wrong
Let’s take a look at option C
mean = {13(3) + 15)3)}/6 = (39 + 45)/6 = 84/6 = 14
While the range is 15-13 = 2 which does not make it right too
Now, a look at option D
mean = (13 + 12 + 15 + 15 + 11 + 18)/6 = 84/6 = 14
range = 18-11 = 7 (highway number in the set minus lowest number)
This makes option D our answer
write each of the following numbers in words 7070 75
Answer:
7070- Seven thousand seventy/Seven thousand and seventy
75- Seventy five
Step-by-step explanation:
7070- Seven thousand seventy/Seven thousand and seventy
75- Seventy five
A tennis ball is 4 centimeters in diameter. What is the surface area of this ball?
Answer:
The answer is approximately 50.27cm²
Answer:
Here is the solution of your problem.
Please mark as brainlist!
1) Uma sala tem o formato de um trapézio, determine a área dessa sala.(a) 10,4 m² (b) 25,6 m² (c) 12,8 m² (d) 15,2 m²
Answer:
A opção correta é;
c) 12,8 m²
Step-by-step explanation:
A área de um trapézio = 1/2 × (distância perpendicular entre os lados paralelos) × (soma dos comprimentos dos lados paralelos)
No diagrama da pergunta, os comprimentos dos lados paralelos são;
3,8 me 2,6 m
A distância perpendicular entre os lados paralelos = 4 m
∴ área do trapézio = 1/2 (3,8 + 2,6) × 4 = 12,8 m²
Portanto, a área da sala = 12,8 m².
What type of triangles does the Pythagorean Theorem apply to?
Answer: right angle triangle
Step-by-step explanation:
we only use Pythagorean theorem to find the length of the missing side of a right angle triangle only.
Find the value of m, if (3/5) raise to −3 multiply 5/3 raise to 11 equals 3/5 raise to 3m+1
Answer:
[tex]m=-5[/tex]
Step-by-step explanation:
[tex]\left(\frac{3}{5}\right)^{-3}\left(\frac{5}{3}\right)^{11}=\left(\frac{3}{5}\right)^{3m+1}\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(\left(\frac{3}{5}\right)^{-3}\left(\frac{5}{3}\right)^{11}\right)=\ln \left(\left(\frac{3}{5}\right)^{3m+1}\right)\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]
[tex]\ln \left(\left(\frac{3}{5}\right)^{3m+1}\right)=\left(3m+1\right)\ln \left(\frac{3}{5}\right)\\\ln \left(\left(\frac{3}{5}\right)^{-3}\left(\frac{5}{3}\right)^{11}\right)=\left(3m+1\right)\ln \left(\frac{3}{5}\right)\\\mathrm{Solve\:}\:\ln \left(\left(\frac{3}{5}\right)^{-3}\left(\frac{5}{3}\right)^{11}\right)=\left(3m+1\right)\ln \left(\frac{3}{5}\right):\quad m=\frac{14\ln \left(5\right)-14\ln \left(3\right)-\ln \left(\frac{3}{5}\right)}{3\ln \left(\frac{3}{5}\right)}[/tex]
[tex]m=\frac{14\ln \left(5\right)-14\ln \left(3\right)-\ln \left(\frac{3}{5}\right)}{3\ln \left(\frac{3}{5}\right)}\\\mathrm{Decimal}:\quad m=-5[/tex]
During a basketball game, Jeremy scored triple the number of points as Donovan. Kolby scored double the number of points as Donovan. So, if the three boys scored 36 points, how many points did Jeremy score? And how many points did Donovan score?
Answer: Jeremy score 18 points; Donovan score 6 points.
Step-by-step explanation:
Let Jeremy's points be a
Let Donovan's point be b
Let Kolby point be c
Jeremy scored triple the number of points as Donovan. This is:
a = 3b
Kolby scored double the number of points as Donovan. This will be:
c = 2b
The the three boys scored 36 points. This will be:
a + b + c = 36
Since a = 3b and c = 2b
Plug the equations for a and c into the equation. This will be:
a + b + c = 36
3b + b + 2b = 36
6b = 36
b = 36/6
b = 6
Donovan has 6 points
Jeremy will have:
a = 3b
a = 3 × 6
a = 18
Jeremy has 18 points.
Kolby will have:
c = 2b
c = 2 × 6
c = 12
Kolby will have 12 points.
The 1st graders at City Elementary were asked whether they like dogs or cats best. The results are shown in the table. Relative Frequency Table by Row What conclusion can you draw about the relative frequency of the results?
A) A girl in this group is most likely to prefer cats.
B) A boy in this group is most likely to prefer cats.
C) A boy in this group is most likely to prefer dogs.
D) There is no association between the variables.
Answer: A girl in this group is most likely to prefer dogs
Answer:
I'm thinking the ANS is letter B
What value of t is a solution to this equation? 4t=8
t = 2
t = 3
Answer & Step-by-step explanation:
In the problem, we are given two values of t. So, all we have to do is plug in the numbers for t to see which value solves the equation.
t = 2
t = 3
4(2) = 8
4(3) = 12
So, the value of t that solves the equation is t = 2
Mila reads at a rate of 3 paragraphs per minute.
After reading for 4 minutes, she had read a total of 12 paragraphs.
This situation can be represented with a linear equation written in point-slope form,
where x represents the number of minutes and y represents the number of
paragraphs
Use this information to complete each statement about the linear equation.
CL
The slope of the linear equation is
Answer:
Y=3x because that slope is 3 and if you times it by 4 you get 12
Step-by-step explanation:
Please Help It is for my hw
Answer:
step 1: distribute -1
step 2: combine like terms
step 3: subtract 4 on both sides
step 4: divided both sides by -8, so u can isolate M alone
M=-2
Step-by-step explanation: