Answer:
Length of leg ⇒ 12
Step-by-step explanation:
Knowing this is a right angle triangle, let us apply Pythagorean Theorem to solve for the length of this other leg, which we can assign as x;
x^2 + 5^2 = 13^2 ⇒ square 5 and 13,
x^2 + 25 = 169 ⇒ subtract 25 from either side of equation,
x^2 = 144 ⇒ Take square root on either side,
Solution; Length of leg ⇒ 12
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
Someone help pleaseeee!!!!!!!!!!!
Answer:
(-1,2)
Step-by-step explanation:
The solutions to the system is where the lines intersect
The lines intersect at the point (-1,2)
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.
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]
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
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
un autobus de linea hace cuatro viajes cada dia. en cada viaje transporta 119 viajeros. ¿ cuántos pasajeros transporta al dia?
Answer:
son 119 pasajeros por vieje y hace 4 viajes ,murtiplicas la cantidad de pasajeros por la cantidad de los viajes osea 119x4 el total seria:476 pasajeros
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
Felipe dice que su calculadora no funciona. Para cambiar solo el 9 del 39.200 sumó 1.000 pero obtuvo 40.200. ¿Cómo le explicarías a Felipe por qué no cambió solo el 9?
Answer:
Felipe dio un paso incorrecto de acuerdo con el sistema de valor posicional al sumar la suma de 1,000 a 39,200. La manera correcta en que Felipe debe abordar esto se muestra en la explicación a continuación.
Step-by-step explanation:
En el sistema de valor posicional; cada número representa una entidad particular; ya sea unidad, decenas, cientos, mil, diez mil etc. En la pregunta dada, el número 39200 indica que 9 está en el valor posicional de mil, es decir, 9000.
Entonces, si Felipe desea cambiar de 8 a 9, entonces necesita restar 9000-8000 = 1000
Sin embargo; si quiere cambiar 9 a cero; entonces restará 9000 de 9000; pero ya que 9 no funciona; Primero debe restar 8000 y luego restar 1000.
Please help it is multiple choice
Answer:
1/2
Step-by-step explanation:
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.
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!
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 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
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
Rewrite the equation by completing the square.
2 x^2 -11 x +14 = 0
Answer:
x^2 - (11/2)x + 121/16 = -7
Step-by-step explanation:
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
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 area of the the regular polygon.
Answer:
Area of Regular Polygon = ( About ) 332.6 units^2; Option C
Step-by-step explanation:
~ Let us first declare consecutive notes. If we were to draw an altitude in this triangle, it would be perpendicular to the base, by definition. At the same time this shape is a regular polygon, so all sides ( and angles ) are ≅. This would mean that, by Coincidence Theorem, the altitude divides the base into the two ≅ parts. ~
1. If that is so, the altitude would split this base into parts ⇒ ( 16√3 )/2 = 8√3.
2. This would mean that the altitude can be found through Pythagorean Theorem, provided that by definition it forms a 90 degree angle at the base. Let us say x ⇒ the length of the altitude, ( 8√3 )^2 + ( x )^2 = ( 16√3 )^2 ⇒ 192 + x^2 = 768 ⇒ x^2 = 576 ⇒ length of altitude - 24 units
3. With the base 16√3 units, and the the altitude/height 24 units, we can find the area of this regular polygon to be ⇒ 1/2 * base * height ⇒ 1/2 * 16√3 * 24 ⇒ 192√3 units^2
4. That being said that area would be 192 * 1.732050808...... ⇒
Area of Regular Polygon = ( About ) 332.6 units^2
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
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
In a newspaper,it was reported that the number of yearly robberies in springfield in 2011 was 240, and then went up by 5% in 2012.How many robberies were there in springfield in 2012?
Answer:
There were 252 robberies in 2012.
Step-by-step explanation:
Number of robberies in 2011 = 240
5% Increase =
[tex]5/100*240=12[/tex]
Therefore, new number of robberies in 2012 =
[tex]240+12=252[/tex].
To confirm this figure, we use the formula,
% increase = Increase / Original number * 100
Increase= 12
Original number= 240
Therefore,
12 / 240*100 = 5
This confirms that, indeed, there was a 5% increase in 2012.
Square root of 72x^2 z^3
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]
the difference between 9 fifty-sixes and 3 fifty-sixes.
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:
Please help! Correct answers only please!
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking an even number and then picking an even number?
Simplify your answer and write it as a fraction or whole number.
Answer:
1/6
Step-by-step explanation:
Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!
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
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!!!
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.