Answer:
The age of brothers are 4 years and 2 years respectively.
Step-by-step explanation:
We are given that the ages of two brothers have a ratio of 2 to 1. When 4 years have passed, the ratio of their ages will be 8 to 6.
Let the age of the first brother be 'x years' and the age of the second brother be 'y years'.
So, according to the question;
The first condition states that the ages of two brothers have a ratio of 2 to 1, that means;[tex]\frac{x}{y} =\frac{2}{1}[/tex]
[tex]x=2y[/tex] -------------- [equation 1]
The second condition states that when 4 years have passed, the ratio of their ages will be 8 to 6, that means;[tex]\frac{x+4}{y+4}=\frac{8}{6}[/tex]
[tex]6({x+4})=8}(y+4)[/tex]
[tex]6x+24=8y+32[/tex]
[tex]6(2y)+24=8y+32[/tex]
[tex]12y-8y=32-24[/tex]
[tex]4y=8[/tex]
[tex]y=\frac{8}{4}[/tex] = 2 years
Putting the value of y in equation 1 we get;
x = 2y
x = [tex]2 \times 2[/tex] = 4 years
Hence, the age of brothers are 4 years and 2 years respectively.
Solve for b.
-b - 19 = -3b – 9
Answer:
b=5
Step-by-step explanation:
-b - 19 = -3b – 9
Add 3b to each side
-b+3b - 19 = -3b+3b – 9
2b -19 = -9
Add 19 to each side
2b-19+19 = -9+19
2b = 10
Divide by 2
2b/2 =10/2
b=5
could I have some help with this?
Answer:
1.1783
Step-by-step explanation:
The attached picture shows a cross section of the cylindrical shell that it is convenient to use as a differential of the volume. The radius from the center of revolution is (1-x), so the circumference of the shell is 2π(1-x). Of course, its height is tan(x), so the differential of volume is ...
dV = 2π(1-x)tan(x)
The indefinite integral does not have a nice closed-form solution, but it can be easily integrated numerically from x = 0 to 1 by most scientific and graphing calculators. The attached shows the volume to be about 1.1783 cubic units.
Please help ASAP!!!!
Answer:
8
Step-by-step explanation:
1/4πr² + (2x4) - 1/4πr²
r = 4
8
Sally begins hiking at an elevation of 224 ft then she descends 131 ft and climbs 67 feet higher than her current position she then descends 163 ft write an addition sentence to describe the situation then determine and interpret the sum
Answer:
Sally ends at 3 feet below zero point.
Step-by-step explanation:
Let be [tex]h[/tex] the height with respect to zero point, which is represented by the following sum:
[tex]h = \Sigma_{i=1}^{n} h_{i}[/tex]
Where:
[tex]h_{i}[/tex] - i-th travelled height, measured in feet.
In addition, positive sign means ascension, whereas negative sign means descent.
The statement can be translated into the following mathematical identity:
[tex]h = h_{1}+h_{2}+h_{3}+h_{4}[/tex]
[tex]h = 224\,ft+(-131\,ft)+67\,ft -163\,ft[/tex]
[tex]h = -3\,ft[/tex]
Sally ends at 3 feet below zero point.
Find the measure of Angle R if a = 9 square root 2 and b = 18 square root 2.
Please help!!
Answer: ∠TRa = 30°, ∠aRA = 90°, ∠TRA = 120°
Step-by-step explanation:
I'm not sure if you need the angle of the left triangle only (= 30°)
or if you need the the triangle plus the rectangle (= 120°)
Left Triangle (∠TRa)
The hypotenuse is twice the base so it is a 30° - 60° - 90° triangle
where the base corresponds to the 30° angle.
Rectangle (∠aRA)
A rectangle has four right angles --> four 90° angles.
Angle Sum Theorem
∠TRA = ∠TRa + ∠aRA
= 30° + 90°
= 120°
what expression has a negative value?
7+3(-4)(2)
-2[12/(-3)]
(15-7)-(9/3)
-5[7+(-14)]-30
Answer:
7+3(-4)(2)= -17
Step-by-step explanation:
7+3(-4)(2)
(-4)*2=-8
∴ 7+3(-8)= 7-24
= -17
2. What is an expression for the distance between the origin and a point P(x, y)?
Step-by-step explanation:
Using distance formula: { origin is (0,0)}
√(x - 0)² + (y - 0)²
√x² + y²
The distance between the origin and the point P(x,y) is √(x² + y²).
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The distance between the origin (0,0) and the point P(x,y) is calculated as below:-
Distance = √(x - 0)² + (y - 0)²
Distance = √(x² + y²)
Therefore, the distance between the origin and the point P(x,y) is √(x² + y²).
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The diameter of a car wheel is 60 cm, if the car travels at an average speed of 13.2m/s, find the number of revolutions made by the car per hour , hiving the awnser correct to nearest whole number. (take pie to be 3.142 )
The wheel has diameter 60 cm = 0.60 m, and thus circumference π(0.60 m) ≈ 5.923 m.
In one complete revolution, a point on the edge of the wheel covers this distance, so that the wheel has an angular speed of
(13.2 m/s) * (1/5.923 rev/m) ≈ 2.229 rev/s
There are 60 seconds to each minute, and 60 minutes to each hour, so converting to rev/h gives
(2.229 rev/s) * (60 s/min) * (60 min/h) ≈ 8024 rev/h
name a pair of corresponding angles
name a pair of alternate interior angles
name a pair of alternate exterior angles
name a pair of same-side interior angles
They are on the same side of the transversal cut (both to the left of the transversal) and they are both above the two black lines. It might help to make those two black lines to be parallel, though this is optional.
Other pairs of corresponding angles could be:
angle 2 and angle 6angle 3 and angle 7angle 4 and angle 8=======================================================
Alternate interior angles = angle 3 and angle 5They are between the black lines, so they are interior angles. They are on alternate sides of the blue transversal, making them alternate interior angles.
The other pair of alternate interior angles is angle 4 and angle 6.
=======================================================
Alternate exterior angles = angle 1 and angle 7Similar to alternate interior angles, but now we're outside the black lines. The other pair of alternate exterior angles is angle 2 and angle 8
=======================================================
Same-side interior angles = angle 3 and angle 6The other pair of same-side interior angles is angle 4 and angle 5. They are interior angles, and they are on the same side of the transversal.
How many ways can you distribute 4 different balls among 4 different boxes?
Use trig ratios to find the measure of the angle in this Triangle (Image)
Answer:
θ = 36.9°
Step-by-step explanation:
Trigonometric ratios in a right triangle will be,
Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{\text{AC}}{\text{AB}}[/tex]
Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex] = [tex]\frac{\text{BC}}{\text{AB}}[/tex]
Tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex] = [tex]\frac{\text{AC}}{\text{BC}}[/tex]
In the picture attached,
Given sides are,
AB = 5 and BC = 4
Therefore, to find the given angle θ only Cosine will be applicable.
Cos θ = [tex]\frac{\text{BC}}{\text{AB}}[/tex]
= [tex]\frac{4}{5}[/tex]
θ = [tex]Cos^{-1}(0.8)[/tex]
θ = 36.87°
θ ≈ 36.9°
The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2
Answer:
Perimeter is irrational
Step-by-step explanation:
The attachment is missing but the question is still answerable
Given
[tex]Area = 24200 yd^2[/tex]
Required
Determine if the Perimeter is rational or not
First, we need to determine the sides of the square;
[tex]Area = Length * Length[/tex]
Substitute [tex]Area = 24200 yd^2[/tex]
[tex]24200 = Length * Length[/tex]
[tex]24200 = Length^2[/tex]
Take Square root of both sides
[tex]\sqrt{24200} = Length[/tex]
[tex]Length = 155.563492[/tex]
The perimeter of a square is calculated as:
[tex]Perimeter = 4 * Length[/tex]
[tex]Perimeter = 4 * 155.563492[/tex]
[tex]Perimeter = 622.253968[/tex]
Because the value of perimeter can't be gotten by dividing two integers, then perimeter is irrational
Fraiser drew a model of his hometown on the coordinate plane below. Each unit of the coordinate plane represents 1 mile. A grocery store is located at (6, 4) and a school is located at (6, 8). What is the distance between the grocery store and the school?
Answer:
The distance between the grocery store and the school is 4 miles.
Step-by-step explanation:
Given that each point is represented in rectangular form. The staight-line distance ([tex]d[/tex]) between two points on a plane is given by the Pythagorean Theorem:
[tex]d =SF\cdot \sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}}[/tex]
Where:
[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Horizontal locations of points A and B, dimensionless.
[tex]y_{A}[/tex], [tex]y_{B}[/tex] - Vertical locations of points A and B, dimensionless.
[tex]SF[/tex] - Scale factor, measured in miles.
If [tex]SF = 1\,mi[/tex], [tex]A = (6, 4)[/tex] and [tex]B = (6,8)[/tex], the straight line distance is:
[tex]d = (1\,mi)\cdot \sqrt{(6-6)^{2}+(8-4)^{2}}[/tex]
[tex]d = 4\,mi[/tex]
The distance between the grocery store and the school is 4 miles.
Find the value of m. A. 32 B. 63 C. 50 D. 74
Answer:
A
Step-by-step explanation:
Tangents drawn to a circle from an external point are congruent, thus
the triangle formed by the 2 tangents is isosceles with base angles of 74°
m = 180° - (74 + 74)° = 180° - 148° = 32° ( sum of angles in Δ )
The value of the measured angle of m is 32°.
What is a Tangent of Circle?A tangent of a circle is defined as a single point where a single straight line touches or intersects the circle. A line that never touches the inside of the circle is called a tangent.
The line connecting the outer point will cut the angle between the tangents in bisect and the center are equal to each other.
According to the given figure as
A circle with center O,
Since there are two tangents to the circle drawn from an external point.
therefore the lengths of tangents drawn from an external point to a circle are equal.
So, the triangle formed by the 2 tangents is isosceles with base angles of 74°
We know that sum of angles in the triangle is 180 degrees
So ∠ m = 180° - (74 + 74)°
⇒ ∠ m = 180° - 148°
⇒ ∠ m = 32°
Hence, the value of the measured angle of m is 32°.
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Does anybody know what -3/4 = -1/8x is? And can you please show work. Thank uuu.
Answer:
x = 6
Step-by-step explanation:
3 1
- ---- = - ---- x
4 8
3 1
- ---- = - ---- x
4 2³
3 x
- ---- = - ----
4 2³
x = 6
1 point
Two benefits of having a checking account are safety and convenience.
Which of the following statements is FALSE?
a. If you have a checking account, you won't need to carry as much cash with you
b. With a checking account, you have several options for how to pay bills
c. You can cash checks for free when you cash your paycheck at your bank
d. In order to shop online, you must use a debit card
the answer is A right
Solve the equation
(If possible please show work)
Answer:
N= -3
Step-by-step explanation:
Answer:
-3=n or n=-3
Step-by-step explanation:
7+2+4n+3=n+3
9+4n+3=n+3
12+4n=n+3
-3 -3
9+4n=n
-4n -4n
9=-3n
______
-3 -3
-3=n or n=-3
In the triangle below x=? Round to the nearest tenth
Work Shown:
sin(angle) = opposite/hypotenuse
sin(35) = x/15
15*sin(35) = x
x = 15*sin(35)
x = 8.60364654526569
x = 8.6
Make sure your calculator is in degree mode
A candy store makes a 12-lb mixture of gummy bears, jelly beans, and Runts. The cost of gummy bears is $1.50 per pound, jelly beans cost $1.00 per pound, and Runts cost $1.00 per pound. The mixture calls for three times as many gummy bears as jelly beans. The total cost of the mixture is $15.00. How much of each ingredient did the store use?
Answer:
g= 6
j = 2
r= 4
Step-by-step explanation:
Gummy bears = $1.50 per pound
Jelly beans = $1.00 per pound
Runt = $1.00 per pound
Total cost of the mixture = $15.00
Let
g = quantity of gummy bears
j = quantity of jelly beans
r = quantity of runts
g + j + r=12 (1)
1.5g + 1.0j + 1.0r = 15 (2)
three times as many gummy bears as jelly beans.
g=3j
Substitute g=3j into 1
g + j + r = 12
3j + j + r =12
4j + r =12 (3)
Substitute g=3j into 2
1.5g + 1.0j + 1.0r = 15
1.5(3j) + 1.0j + 1.0r =15
4.5j + 1.0j + 1.0r = 15
5.5j + 1.0r =15 (4)
4j + r =12 (3)
5.5j + 1.0r =15 (4)
Subtract (3) from (4)
5.5j - 4j = 15-12
1.5j = 3
Divide both sides by 1.5
j = 3/1.5
= 2
j = 2
Substitute j = 2 into (3)
4j + r =12
4(2) + r =12
8 + r = 12
r= 12-8
r= 4
Substitute j=2 and r= 4 into (1)
g + j + r=12
g + 2 + 4 = 12
g + 6 = 12
g = 12-6
=6
g=6
g= 6
j = 2
r= 4
William's car used 2 gallons to travel 68 miles. How far can he travel on 9 gallons?
Answer:
306 miles
Step-by-step explanation:
68 divided by 2 is 34
34 times 9 equals
Answer:
306 miles
Step-by-step explanation:
68 divided by 2 = 34
a.k.a. 34 miles a gallon
34 times 9 miles = 306 miles
William's car can travel 306 miles with 9 gallons in its tank.
(3x2y2)3
What is the answer
Answer:
27x^6y^6
Step-by-step explanation:
We assume you want to simplify ...
[tex](3x^2y^2)^3=3^3x^{2\cdot3}y^{2\cdot3}=\boxed{27x^6y^6}[/tex]
__
The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
Using the frequency table given, find the mean, median, and mode.
You must show all of your work to receive credit.
Answer:
[tex]Mean = 69[/tex]
[tex]Mode = 66[/tex]
[tex]Median = 69[/tex]
Step-by-step explanation:
Given
The frequency table
Required
Determine the mean, median and mode
Calculating Mean
[tex]Mean = \frac{\sum fx}{\sum f}[/tex]
Where
fx = product of frequency and inches
f = frequency
So;
[tex]Mean = \frac{63 * 2 + 65 * 1 + 66 * 4 + 67 * 3 + 68 * 1 + 69 * 2 + 70 * 2 + 71 * 1 + 72 * 3 + 74 * 2 + 75 * 2}{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}[/tex]
[tex]Mean = \frac{1587}{23}[/tex]
[tex]Mean = 69[/tex]
Calculating Mode
[tex]Mode = 66[/tex]
Because it highest frequency of 4
Calculating Median
[tex]Median = \frac{\sum f}{2}th\ position[/tex]
[tex]Median = \frac{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}{2}th\ position[/tex]
[tex]Median = \frac{23}{2}th\ position[/tex]
[tex]Median = 11.5th\ position[/tex]
Approximate
[tex]Median = 12th\ position[/tex]
At this point we, need to get the cumulative frequency (CF)
Inches ---- Frequency ---- CF
63 -------------2------------------2
65 -------------1------------------3
66 -------------4------------------7
67 -------------3------------------10
68 -------------1------------------11
69 -------------2------------------13
70 -------------2------------------15
71 -------------1------------------16
72 -------------3------------------19
74 -------------2------------------21
75 -------------2------------------23
From the above table
Since the median fall in the 12th position, then we consider the following data
69 -------------2------------------13
because it has a CF greater than 12
Hence;
[tex]Median = 69[/tex]
ACTIVIDAD 1: En el Parque Nacional Selva de Florencia Un explorador
se pierde dentro de un inmenso terreno circular de diámetro 27 km.
La información que se tiene es que si camina 10 km hacia el Occidente
o 5 km hacia el Oriente, llegará al borde de la circunferencia.
Responde:
a) El punto del borde más cercano a la posición del explorador a
cuantos Km se encuentra?
b) ¿Cuánto mide el perímetro y área de este terreno sabiendo
que tiene un diámetro de 27 Km?
Answer:
a) La distancia desde el punto del borde más cercano a la posición del escáner es 5 · √5 km
b) El perímetro del área = 84,823 km
El área de la tierra = 572.555 km²
Step-by-step explanation:
a) La distancia desde el punto del borde más cercano a la posición del escáner viene dada por la fórmula de Pitágoras;
r = √a² + b²
Por lo tanto, la distancia = √ (10² + 5²) = √125 = 5 · √5 km
La distancia desde el punto del borde más cercano a la posición del escáner es 5 · √5 km
b) El perímetro está dado por la fórmula para el perímetro de un círculo que es, perímetro, s = π × D
Dónde;
D = El diámetro de la tierra = 27 km.
El perímetro = π × 27 = 84.823 km
El perímetro del área = 84.823 km
El área está dada por la fórmula del área de un círculo = π × D² / 4
El área = π × 27² / 4 = 572.555 km²
El área de la tierra = 572,555 km².
Write a function g whose graph represents a reflection in the x-axis of the graph of f(x)=1/2x-3
Answer: g(x) = -(1/2)*x + 3.
Step-by-step explanation:
First, let's define a reflection over the x-axis.
If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).
Now, when we have a function
f(x) = y, the points can be written as:
(x, y = f(x) ) = (x, f(x))
Then, after the reflection over the x-axis, we have:
(x, y = g(x)) = (x, -f(x))
So now we have g(x) = -f(x)
and we know that f(x) = (1/2)*x - 3
then our new function is g(x) = y = -f(x) = -( (1/2)*x - 3) = -(1/2)*x + 3.
g(x) = -(1/2)*x + 3.
i will give brainliest for anyone that can correctly answer my question, its in a photo
Answer:
x = 122
Step-by-step explanation:
Step 1: State what is known
In the picture we can see they marked ∠ABC with a box meaning it is a 90° angle, given that information we can now solve
Step 2: Solve
∠ABC = x - 32
90 = x - 32
90 + 32 = x
122 = x
Therefore 'x' is equal to 122
4x + 9x + 3 = WILL GIVE BRAINLY, PLUS 20 POINTS.
Answer:
13x + 3
Step-by-step explanation:
Since there is no value on the left, you just have to simplify this. You always add similar variables together, and the constant is a different value, so 4x + 9x would result in 13x. 13x + 3 would be the correct simplified answer.
Answer:
13x+3
Step-by-step explanation:
4x+9x+3
You do not add 13x to 3 because 3 does not have an x
10. A bird flies at a speed of 4 m/s. It flies for 2160 seconds from its nest to the field. How much
distance did the bird cover?
Answer:
8640 m, or 8.64 km, assuming it flew in a straight line
Step-by-step explanation:
Distance = rate (or speed) * time (d = rt)
The rate is 4 m/s and the time is 2160 s.
d = rt
d = 4 * 2160
d = 8640 m, or 8.64 km, assuming it flew in a straight line
Given the formula: d=m/V , which answer choice correctly rearranges the variables to solve for V?
Answer:
V = m/dStep-by-step explanation:
[tex]d = \frac{m}{V} \\Cross\:Multiply\\\\dV = m\\\\Divide\:both \:sides \:of\:the\:equation\:by\:d\\\\\frac{dV}{d} = \frac{m}{d} \\\\\\V = \frac{m}{d}[/tex]
The surface area S of the sphere varies directly as square of radius r and = 16 when = 2. Find when = 36 ........ with proper steps and explanation.
Answer:
r = 3
Step-by-step explanation:
Here in this question, we are told that the surface area of the sphere varies directly as square of radius;
The first thing to do here is to assign variables;
let s be the surface area and r be the radius;
Now;
Since it is a direct proportional relationship;
s = k•r^2
where k represents the constant of proportionality.
now, let’s get k at first.
From the first part of the question, s = 16 and r = 2; Substituting this, we have
16 = k•2^2
4k = 16
k = 16/4
k = 4
Now from the second part of the question, we want to find r when s = 36
Let’s rewrite our equation;
s = k•r^2
where in this case, r = ? and s = 36
36 = 4 * r^2
4r^2 = 36
r^2 = 36/4
r^2 = 9
r = √9
r = 3
Kindly note we do not pick the negative square root value as radius cannot be negative
The surface area of the sphere when the radius is 5 inches is [tex]100\pi[/tex] and this can be determined by using the given data.
Given :
The surface area of a sphere varies directly as the square of the radius. The surface area is 36 when the radius is 3 inches.The following steps can be used in order to determine the surface area S of the sphere:
Step 1 - According to the given data, the surface area S of the sphere varies directly as the square of the radius.
Step 2 - The mathematical expression of the above statement is:
[tex]\rm S= k\times r^2[/tex] --- (1)
where k is the proportionality constant.
Step 3 - Now, substitute the value of r and S in the above expression.
[tex]\rm 36\pi=k \times 3^2[/tex]
[tex]\rm k = 4\pi[/tex]
Step 4 - Now, substitute the value of [tex]\rm k = 4\pi[/tex] and r = 5 in the expression (1).
[tex]\rm S = 4\pi \times 5^2[/tex]
[tex]\rm S = 100\pi[/tex]
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Dan is a software salesman Y represent his total pay in dollars let X represent the number of copies English is fun he sells suppose that X and y are related by the equation 80x+2400=y
Answer:
1. 80
2. 2400
Step-by-step explanation:
1. what is the change in Dan's total pay for each copy of math is fun he sells?
2. what is Dan's total pay if he doesn't sell any copies of math is fun?
Given
y=80x + 2400
When x=0
y=80(0)+2400
=0+2400
=2400
When x=1
y=80x + 2400
=80(1) + 2400
=80+2400
=2480
change in Dan's total pay for each copy of math is fun he sells is
= 2480 - 2400
=80
2. Dan's total pay if he doesn't sell any copies of math is fun?
y=80x+2400
When x=0
y=80(0)+2400
=0+2400
=2400