Answer:
Step-by-step explanation:
Ratio=3:4
so,the pair of adjacent sides are 3x,4x
Pythagorean theorem,
[tex](3x)^{2}+(4x)^{2}=20^{2}\\9x^{2}+16x^{2}=400\\\\25x^{2}=400\\\\x^{2}=\frac{400}{25}\\\\ x^{2}=16\\\\x=\sqrt{16}\\\\x=4\\\\length=4x=4*4=16cm\\\\breadth=3x=3*4=12cm\\\\Perimeter=2*(l+b)\\\\=2*(16+12)=2*28\\\\=56cm[/tex]
Ethan had $8 more than Dakota. Ethan then gave 1/4 of his money to Dakota. The ratio of money Ethan had to the money Dakota had became 5:2. How much money did Ethan five to Dakota?
Final answer:
To find how much money Ethan gave to Dakota, we need to set up and solve an equation based on the given conditions, include the initial difference of $8, the 1/4 transfer of funds, and the resulting 5:2 ratio of their money.
Explanation:
Ethan had $8 more than Dakota. When he gave 1/4 of his money to Dakota, the ratio of Ethan's money to Dakota's became 5:2. To solve this, let's assume Dakota originally had D dollars and Ethan had D + 8 dollars. After giving away 1/4 of his money to Dakota, Ethan would have 3/4 of D + 8, and Dakota would have D plus 1/4 of D + 8.
The new ratio of Ethan's money to Dakota's money is 5/2, leading us to the equation 3/4(D + 8) / (D + 1/4(D + 8)) = 5/2. Solving this equation will not only give us the initial amounts of money each person had but also allow us to calculate the exact amount Ethan gave to Dakota, which is the 1/4 of Ethan's original money.
Si tomas sale de Ixtapa a las 6:00 am rumbo a Morelia a una velocidad de 70 kmxh ,a la misma hora Claudia sale de Morelia rumbo a Ixtapa a una velocidad de 40 kmxh si entre Morelia e Ixtapa hay una distancia de 660km a que distancia de Morelia se encontraran?
Answer:
El encuentro se producirá a 240 km de Morelia
Step-by-step explanation:
Velocidades Relativas
Este es un caso donde las velocidades son sumativas, pues ambos móviles van a su encuentro mútuo. La distancia total de 660 km será cubierta por ambos móviles con una velocidad relativa de 70 km/h + 40 km/h = 110 km/h
Ya que :
[tex]\displaystyle v=\frac{x}{t}[/tex]
Tenemos que
[tex]\displaystyle t=\frac{x}{v}[/tex]
[tex]\displaystyle t=\frac{660}{110}= 6 \ h[/tex]
Tomás anda a 70 km/h, así que en 6 horas recorre
[tex]x_t=6\times 70 = 420\ Km[/tex]
Claudia anda a 40 km/h, así que en las mismas 6 horas ha recorrido
[tex]x_c=6\times 40 = 240\ Km[/tex]
Se puede decir entonces, que el encuentro se producirá a 240 km de Morelia
Answer:
[tex]\large\boxed{\large\boxed{240km}}[/tex]
Explanation:
Since the question is in Spanish, I will give you the answer in Spanish.
En el punto de encuentro las distancias recorridas por Tomás y Claudia suman la distancia que existe entre Ixtapa y Morelia.
La distancia que recorre cada uno es igual al producto de su velocidad por el tiempo de recorrido.
Para Tomás esto es:[tex]distancia=velocidad\times tiempo\\ \\ d_{Tomas}=70km/h\times t[/tex]
Para Claudia la ecuación es:[tex]distancia=velocidad\times tiempo\\ \\ d_{Claudia}=40km/h\times t[/tex]
Los tiempos, [tex]t[/tex] , son los mismos al momento de encuentro, así que puedes crear una ecuación con una sola incógnita:
[tex]d_{Tomas}+d_{Claudia}=660Km=70km/h\times t+40km/h\times t[/tex]
Puedes obviar las unidades para resolver la ecuación:
[tex]660=70t+40t\\ \\ 660=110t\\ \\ 660/110=t\\ \\ 6=t\\\\ t=6[/tex]
El resultado es en horas: t = 6 horas.
Para encontrar la distancia remplaza el tiempo en la ecuación de Claudia, puesto que ella salió desde la ubicación de Morelia:[tex]d_{Claudia}=40km/h\times t=40km/h\times6h=240km[/tex]
Y esa es la respuesta. Se encontrarán a 240 km de Morelia.
Amira has two toy cars one toy car has a mass of 276 grams and the other has a mass of 180 grams
Answer:
the total mass is 456 grams.
Step-by-step explanation:
Describe in words what 250=72 + x means
Answer: x= 178. Meaning that x can only equal 178, so that statement can be true. Any other number makes this statement false.
Step-by-step explanation:
Answer:
Lemme break it down for ya. Something plus seventy- two equal two hundred fifty. And if you want or need the answer, all you got to do is subtract 250 and 72. You're welcome. And please follow me.
two numbers that multiply to -14 and add to -5
The solution is 2 and -7.
To find two numbers that multiply to -14 and add to -5, we can set up a system of equations based on the properties of multiplication and addition of numbers with different signs.
Let x and y be the two numbers we are looking for, with the following conditions:
x * y = -14 (Multiplication condition)
x + y = -5 (Addition condition)
Using the addition rules, we know that if we have two numbers with opposite signs, the sign of the larger (absolute value) number will dictate the sign of the result. Similarly, the multiplication rules tell us that two numbers with different signs will give a product with a negative sign.
Applying these principles, we can guess that one number is positive and the other negative since their product is -14. We also know that the number with the greater absolute value must be negative since their sum is -5. We can begin by listing pairs of factors of 14 (since the product is -14) keeping the sign in mind:
1 and -14
-1 and 14
2 and -7
-2 and 7
From this list, the pair that adds up to -5 is 2 and -7. Hence, the two numbers are 2 and -7.
A particle travels in a circle around a fixed point at 16 revolutions per minute. The linear velocity of the particle is 240pi inches per minute.
What is the distance, in inches, between the particle and the fixed point?
Answer:
7.5 inches.
Step-by-step explanation:
Angular velocity (ω) in radians per minute
= 16* 2π (as there are 2π radians in 1 revolution)
= 32π radians per minute.
= ω.
Linear velocity V = ω r where r = the radius of the circle.
Therefore: 240π = 32π r
r = 240 / 32
r = 7.5 inches.
The rectangular prism shown has a surface area of 488 square inches. What is the length of the prism?
Answer:
length of the prism = 244 - (width x height) / width + height)
Step-by-step explanation:
Let length be a and width be b and height be c
2 (a * b) + 2 (b* c) + 2 (a * c) = 488
2ab+ 2bc + 2ac = 488
ab + bc + ac = 244
ab + ac = 244 - ac
a (b + c) = 244-ac
a = 244-bc / b + c
Therefore the length of the prism = 244 - (width x height) / width + height)
Answer:
teh answer is 14
Step-by-step explanation:
use teh equation for surface are
A=2(lw+hl+wh)
plug in the values
488=2(6*8+6*x+x*8)
to get x=14
which is the length
THIS IS CORRECT CAUSE I HAD TO DO IT FOR CLASS AND I GOT IT RIGHT BTW. :)
Solving systems of equations y=-3x+4 and x=2y+6
Answer:
Therefore x=2 and y=-2Step-by-step explanation:
Given system of equations are
y= -3x+4
⇔3x+y=4 .........(1)
x= 2y+6
⇔x-2y=6...........(2)
Equation (1) ×2 +equation (2)
6x +2y+x-2y =8+6
⇔7x=14
[tex]\Leftrightarrow x= \frac{14}{7}[/tex]
⇔x = 2
Putting the value of x in equation (1)
3.2+y=4
⇔y+6=4
⇔y=4-6
⇔y=-2
Therefore x=2 and y=-2
Find the volume of the right circular cylinder when the circumference of it’s circular base is 44 cm and It’x height is 10 cm.
The volume of the cylinder is [tex]1539 cm^3[/tex]
Step-by-step explanation:
The volume of a cylinder is given by the equation
[tex]V=\pi r^2 h[/tex]
where
[tex]\pi r^2[/tex] is the area of the base, with r being the radius
h is the height
For the cylinder in this problem we know:
h = 10 cm (height)
c = 44 cm (circumference of the base)
The circumference is given by
[tex]c=2\pi r[/tex]
So the radius is
[tex]r=\frac{c}{2\pi}=\frac{44}{2\pi}=7 cm[/tex]
Therefore, the volume of the cylinder is:
[tex]V=\pi (7)^2 (10)=1539 cm^3[/tex]
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While shopping for clothes, Tracy spent $38 less than 3 times what Daniel spent. Write and solve an equation to find how much Daniel spent. Let x represent how much Daniel spent.
Answer:
Step-by-step explanation:
first you find that it is t=Tracy and d= Daniel
so the equation is t= d-38*3 now find the answer
Daniel spent $16.
Let's denote the amount Daniel spent as x dollars.
According to the given information, Tracy spent $38 less than 3 times what Daniel spent. Therefore, Tracy's expenditure can be represented as [tex]\( 3x - 38 \)[/tex] dollars.
Given that Tracy spent $10, we can set up the equation:
[tex]\[ 3x - 38 = 10 \][/tex]
Now, let's solve for x:
[tex]\[ 3x = 10 + 38 \][/tex]
[tex]\[ 3x = 48 \][/tex]
[tex]\[ x = \frac{48}{3} \][/tex]
[tex]\[ x = 16 \][/tex]
So, Daniel spent $16.
The complete Question is given below:
While shopping for clothes, tracy spent $38 less than 3 times what daniel spent. write and solve an equation to find out how much daniel spent. let x represent how much daniel spnet. tracy spent 10$
The manager of an amusement park recorded the number of visitors to the park. There were 800 visitors on Saturday, and 1,100 visitors on Sunday. What is the percent change from the number of park visitors on Saturday to the number of park visitors on Sunday?
Answer: [tex]Percent\ change=37.5\%[/tex] (It is an increase)
Step-by-step explanation:
You need to use the following formula to find the Percent change:
[tex]Percent\ change=\frac{V_2-V_1}{|V_1|}*100[/tex]
Where [tex]V_1[/tex] is the Initial value and [tex]V_2[/tex] is the Final value.
According to the information given in the exercise, there were 800 visitors on Saturday and 1,100 visitors on Sunday. Then, you can identify that:
[tex]V_1=800\\\\V_2=1,100[/tex]
Then, knowing these values, you must substitute them into the formula:
[tex]Percent\ change=\frac{1,100-800}{|800|}*100[/tex]
Finally, you must evaluate in order to find the Percent change from the number of park visitors on Saturday to the number of park visitors on Sunday.
You get that this is:
[tex]Percent\ change=\frac{300}{|800|}*100\\\\Percent\ change=37.5\%[/tex]
Since it is positive, it is an increase.
Answer:
37.5 percent
Step-by-step explanation:
Which parent function is represented by the graph?
107
0
A. Absolute value parent function
B. An exponential parent function
c. Quadratic parent function
D. Linear parent function
Answer:
b is right on plato
Step-by-step explanation:
Answer: Correct answer is B
Step-by-step explanation:
What is the answer to this question
Answer:
π
Step-by-step explanation:
The integral decomposes into the sum ...
[tex]\displaystyle\int_{-2}^2{\left(x^3\cos{\dfrac{x}{2}}\right)\sqrt{4-x^2}}\, dx+\dfrac{1}{2}\int_{-2}^2{\sqrt{4-x^2}}\, dx[/tex]
The first term of this sum is the integral of an odd function, so is zero. The second term of this sum is 1/2 the area under a semicircle of radius 2, so is ...
A = (1/2)(1/2)π·2² = π
The value of the integral is π.
Combine and simplify these radicals.
√8* √ 20
Answer:
4√10
Step-by-step explanation:
√(8) √(20)
= √(8 x 20)
= √(160)
= √(16 x 10)
= √(16) x √(10)
= 4 x √10
= 4√10
Answer:
4[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
[tex]\sqrt{8}[/tex] × [tex]\sqrt{20}[/tex]
= [tex]\sqrt{8(20)}[/tex]
= [tex]\sqrt{160}[/tex]
= [tex]\sqrt{16(10)}[/tex]
= [tex]\sqrt{16}[/tex] × [tex]\sqrt{10}[/tex]
= 4[tex]\sqrt{10}[/tex]
9. Lucas is in a car traveling at 15 m/s. This car starts to decelerate
steadily. It comes to a complete stop in 10 seconds. What is it's
acceleration?
Answer:
3/2 m / sec²
Step-by-step explanation:
acceleration = change in velocity / time
Here, that would be
acc'n = 15 m/s / 10 s = 3/2 m / sec²
3.14(6x)^2
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are all rhombus are squares
They are not all squares because a rhombus has all sides of equal length, but NO right angles. A square is a rhombus WITH right angles.
Hope that clears things up.
3 x + 2 (4 + 6 x ) =113
Answer:
x=7
Step-by-step explanation:
3x + 2(4 + 6x)= 113
you multiply 2 to 4 that gives you 8 and 2 to 6 that gives you 12x because the 6 has x on it
so it will be 3x + 8 + 12x= 113 then you add 3x to 12x
then you would have 15x+8=113 then subtract 8 to 113 then divide that number to 15 and you get x=7
what is formula of sec(A+B)
Answer:
(cos a cos b - sin a sin b)
Step-by-step explanation:
It's easy
Find the volume of a sphere with a radius of 4 ft.
A. 33.5 ft^3
B. 67.0 ft^3
C. 267.9 ft^3
D. 803.8 ft^3
Answer:
≈268.08 [tex]ft^{3}[/tex]
C. 267.9 [tex]ft^{3}[/tex]
Step-by-step explanation:
Equation of volume of a sphere:
V=[tex]\frac{4}{3} \pi r^{2}[/tex]Plug in radius (r) into the equation:
V=[tex]\frac{4}{3} \pi (4)^{2}[/tex]Solve using a calculator:
≈268.08 [tex]ft^{3}[/tex]
Trying to prepare a budget. Chester has done research and found that he spends an average of $120 on his phone/internet/cable service, $277 on his electric bill, and
$299 on his health insurance premium. If he earns $2800 per month, estimate the amount of money he will have after paying these bills each month.
After adding his phone/internet/cable, electric bill, and health insurance premium costs, Chester spends $696 on bills each month. With monthly earnings of $2800, he therefore should have around $2104 left over after paying these bills.
Explanation:To figure out how much money Chester will have left after paying his bills, you first have to add up all his bills. So, he pays on average $120 for his phone/internet/cable service, $277 for his electric bill, and $299 for his health insurance premium.
To add these together: 120 + 277 + 299 = $696. This is the total amount Chester pays for his bills each month.
Now, subtract this total from Chester's monthly earnings. So, Chester earns $2800 per month, and his bills total $696. So, 2800 - 696 = $2104. Therefore, Chester will have around $2104 left each month after paying these bills.
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Which is equivalent to a 270° clockwise
rotation about the origin?
O A. a 90° counterclockwise rotation
about the origin
OB. a 180° counterclockwise rotation
about the origin
O c. a 270° counterclockwise rotation.
about the origin
O D. a 360° counterclockwise rotation
about the origin
How long does it take for the Earth to go through one full day/night cycle?
Round to the nearest hour.
________hour(s)
Answer:
24 hours
Step-by-step explanation:
Express each ratio as a fraction in simplest form. A 26:169 B 36 to 78
The ratios 26:169 and 36 to 78, when expressed as fractions in simplest form, are 2/13 and 6/13, respectively, after identifying and dividing by their greatest common factors.
The task is to express each ratio as a fraction in its simplest form. Let's tackle each ratio one at a time.
A. 26:169
To convert the ratio 26:169 into a fraction in simplest form, we observe that both numbers are divisible by their greatest common factor (GCF), which is 26. Dividing both terms by 26, we get 1/6.5. However, to express this in terms of whole numbers, multiplying numerator and denominator by 2 gives us 2/13, which is the fraction in its simplest form.
B. 36 to 78
For the ratio 36 to 78, first, we convert it into fraction form, which is 36/78. The GCF of 36 and 78 is 6. Dividing both the numerator and the denominator by 6, we get 6/13. Therefore, the simplest form of the ratio 36 to 78 is 6/13.
Which expression represents the number 13,809 written in expanded form?
A 13+80+9
B 13,000+800+90
C9+1,300+80
B 3,000+10,000+9+800
Answer:
The answer is b or d, but most likely d.
Answer:
B. 13,809 = 3,000+10,000+9+800
Step-by-step explanation:
13,809 = 10,000 + 3000 + 800 + 9
Are 3 (4x-2) and 12x-2 equivalent
Final answer:
The expression 3 (4x-2) is not equivalent to 12x-2, as it simplifies to 12x-6, not 12x-2.
Explanation:
The expression 3 (4x-2) is not equivalent to 12x-2 because when we distribute the 3 across the terms inside the parenthesis of the first expression, we get 12x-6, not 12x-2.
To show this step-by-step:
Multiply 3 by 4x to get 12x.
Multiply 3 by -2 to get -6.
Combine these to get 12x-6.
As a result, 3 (4x-2) simplifies to 12x-6, and this is not equal to 12x-2 unless we are considering a special case where x equals to a value that makes -6 equal to -2, which generally isn't the case.
Evaluate the equation: x+3=18
Answer:
x=15
Step-by-step explanation:
x+3=18
x+3-3=18-3
x+0=15
x=15
sum of the 5th and 10th terms of an arithmetic sequence which are equal to the 20th term (80). find the 30th term
Yo sup??
a5=a+4d
a10=a+9d
a20=80=a+19d
a+4d+a+9d=a+19d
a=6d
80=6d+19d
80=25d
d=3.2
a=19.2
a30=a+29d
=19.2+92.8
=112
Hope this helps.
Find the numerical value of sin(a)cos(a) if sin (a)-cos (a) = 0.6
The value of sin(a)cos(a) = 0.32
Step-by-step explanation:
Step 1: Given details are sin(a) - cos(a) = 0.6
Step 2: Square the given equation on both sides.
⇒ (sin(a) - cos(a))² = (0.6)²
⇒ sin²a + cos²a - 2 sin(a)cos(a) = 0.36
⇒ 1 - 2 sin(a)cos(a) = 0.36 since sin²a + cos²a=1
⇒ - 2 sin(a)cos(a) = - 0.64
⇒ 2 sin(a)cos(a) = 0.64
⇒ sin(a)cos(a) = 0.32
Which is 5logx+6log(x + 7) written as a single logarithm?
[tex]\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 5\log(x)+6\log(x+7)\implies \log(x^5)+\log\left[ \left( x+7 \right)^6 \right] \implies \log\left[ x^5\left( x+7 \right)^6 \right][/tex]
Answer: log(x^5(x+7)^6)
Hope that helps! (: