Answer:
A. seems to be the BEST choice from the information you have provided.
Answer:
A is the most practical answer with the info you have given
Step-by-step explanation:
If there are four boys and two girls in a family what is the ratio of boys in the family to children in the family
Answer:
2:3.
Step-by-step explanation:
The number of children = 2+ 4 = 6.
So the required ratio is 4:6 which simplifies to 2:3.
Answer:
2.3
is yo sex answer
Marc is 46 years old. He is 4 years older than 3 times his sons age, find the age of his son.
Marc's son is 14 years old. We found this by creating the equation 3x + 4 = 46 based on the question, solving for x, and determining that x equals 14.
Explanation:This is a problem that requires an understanding of simultaneous linear equations. Let's denote Marc's son's age as x.
Marc is 4 years older than 3 times his son's age. Therefore, we can write this as: 3x + 4 = 46.
To find the value of x, which represents the son's age, we first subtract 4 from both sides of the equation (3x + 4 - 4 = 46 - 4). Now we have 3x = 42. To get the value of x alone, we will then divide by 3 from both sides of the equation (3x/3 = 42/3). As a result, we'll find out that x equals 14, which means Marc's son is 14 years old.
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Color-blindness is any abnormality of the color vision system that causes a person to see colors differently than most people, or to have difficulty distinguishing among certain colors (www.visionrx.com).Color-blindness is gender-based, with the majority of sufferers being males.Roughly 8% of white males have some form of colorblindness, while the incidence among white females is only 1%.A random sample of 20 white males and 40 white females was chosen.LetXbe the number of males (out of the 20) who are color-blind.LetYbe the number of females (out of the 40) who are color-blind.LetZbe the total number of color-blind individuals in the sample (males and females together).Which of the following is true about the random variables X, Y, and Z?X is binomial with n = 20 and p = .08.Y is binomial with n = 40 and p = .01.Z is not binomial.All of the above are true.Only (A) and (B) are true.What is the probability that exactly 2 of the 20 males are color-blind? (Note: Some answers are rounded.).08.2711.0143.5422.0159
Only (A) and (B) are true.
Explanation:Variable distributions:
X: Since we are sampling a specific number (20) of individuals with a known probability of color blindness (8%), X follows a binomial distribution with n = 20 and p = 0.08.
Y: Similarly, Y follows a binomial distribution with n = 40 and p = 0.01.
Z: Z is not a simple binomial because it combines two independent binomial variables (X and Y) with different parameters. Therefore, Z's distribution is not directly binomial.
Probability of 2 color-blind males:
Using the binomial probability formula for X, the probability of exactly 2 color-blind males (out of 20) is:
P(X = 2) = 20C2 * 0.08^2 * (1 - 0.08)^18 ≈ 0.2711
Therefore, only statements (A) and (B) are true:
(A) True: X is binomial with n = 20 and p = 0.08.
(B) True: Y is binomial with n = 40 and p = 0.01.
Statements (C), (D), and the answer choices for the probability of 2 color-blind males are incorrect.
A credit card company charges a customer 1.8% per month on the unpaid balance of charges on a credit card. What is the finance charge in a month in which the customer has an unpaid balance of $1,205.62?
$217.01
$21.70
$1.81
$13.72
Answer:
217.01
Step-by-step explanation:
Answer:
Roughly $21.70
Step-by-step explanation:
1,205.62 times 0.018 (1.8% converted into decimal, to do so, move the decimal over to the right two places) equals 21.7
Let t : the set of real numbers2 → the set of real numbers2 be the linear transformation satisfying t(v1) = (4, 3), t(v2) = (−1, 1), where v1 = (1, 1) and v2 = (1, −1). find t(x1, x2) for an arbitrary vector (x1, x2) in the set of real numbers2. t(x1, x2) = correct: your answer is correct. what is t(8, −2)?
First let's see if (8, -2) can be written as a linear combination of (1, 1) and (1, -1): we want to find [tex]c_1,c_2[/tex] such that
[tex]c_1(1,1)+c_2(1,-1)=(8,-2)\implies\begin{cases}c_1+c_2=8\\c_1-c_2=-2\end{cases}[/tex]
Easily done; we find [tex]c_1=3[/tex] and [tex]c_2=5[/tex].
Since [tex]T[/tex] is linear, we have
[tex]T(8,-2)=T(3(1,1)+5(1,-1))=3T(1,1)+5T(1,-1)=3(4,3)+5(-1,1)[/tex]
[tex]T(8,-2)=(7,14)[/tex]
t(x₁, x) = (1.5x₁ + 2.5x₂, 2 x₁ + x₂). And, t(8, -2) = (7, 14)
To find the linear transformation t applied to an arbitrary vector (x₁, x₂), we begin by expressing (x₁, x₂) as a linear combination of v₁ and v₂. Given t(v₁) = (4,3) and t(v₂) = (-1,1), we can use these results to construct the transformation.
Let's express any given vector (x₁, x₂):
v₂ = (1, -1)
An arbitrary vector (x₁, x₂) can be written as a linear combination of v₁ and v₂:
(x₁, x₂) = a * v₁ + b * v₂
Hence,
x₁ = a + b
[tex]b = \frac{(x_1, x_2)}{2}[/tex]
We apply the transformation t:
t(x₁, x₂) = a * t(v₁) + b * t(v₂) = [tex](\frac{((x_1 + x_2) * (4, 3)}{ 2} + \frac{((x_1 - x_2) * (-1, 1) }{ 2})[/tex]
Expanding, Combining terms we get:
t(x₁, x) = (1.5x₁ + 2.5x₂, 2 x₁ + x₂)
To find t(8, -2):
t(8, -2) = (1.5 * 8 + 2.5 * (-2), 2 * 8 + (-2))
This gives:
t(8, -2) = (12 - 5, 16 - 2) = (7, 14)
Find the product of x^2+2x-4 and 3x.
a. 3x^3+6x^2+12x
b. 3x^3+6x^2-12x
c. 3x^3+2x-4
d. -3x^3
[tex] 3x({x}^{2} + 2x - 4)[/tex]
[tex]3x \times {x}^{2} = {3x}^{3} [/tex]
[tex]3x \times 2x = 6 {x}^{2} [/tex]
[tex]3x \times - 4 = - 12x[/tex]
[tex]b. \: 3 {x}^{3} + 6 {x}^{2} - 12x[/tex]
The bus from Karen's house to school runs 26 to 75 minutes of the bus runs on Monday at 7:05am at which time could the bus run next
I’m pretty sure the answer is 8:25 a.m
PLEASE HELP! URENT!
What is the measure of ∠R ?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠R=
°
Answer:
R = 48.59 degrees
Step-by-step explanation:
We know that
sin theta = opposite / hypotenuse
sin R = 30/40
sin R = 3/4
Taking the inverse sin of each side
sin^-1 (sin R) = sin ^-1(3/4)
R = 48.59037789
To the nearest hundredth
R = 48.59 degrees
Find the measure of the arc indicated.
A) 144°
B) 150°
C) 130°
D) 131°
Answer:
Option B. [tex]150\°[/tex]
Step-by-step explanation:
we know that
In this problem
[tex](15+15x)=(17x-3)[/tex]
solve for x
[tex]17x-15x=15+3[/tex]
[tex]2x=18[/tex]
[tex]x=9[/tex]
Find the measure of arc BC
[tex]arc\ BC=17x-3=17(9)-3=150\°[/tex]
You are buying shoes online.The selling price is $29.99. Round to the nearest penny if necessary.
it's 30 dollars because it's the closest whole number
Final answer:
To calculate the total cost of an online purchase, round the sales tax to the nearest penny and add it to the item's price. When combining multiple items, sum their prices and add the rounded sales tax to find the total cost.
Explanation:
When buying shoes or any item online and encountering a selling price that includes cents, you may need to perform rounding if further calculations are required. For example, to round $6.375 to the nearest penny, we would get $6.38 because the third digit after the decimal is 5 or more, thus we increase the second digit by one. From there, we would add the rounded sales tax to the original price of the item to find the total cost.
In a different scenario where you are adding two prices together, like $8.99 and $11.99, you get the subtotal of $20.98 before tax. Then calculate the sales tax by converting the percent to a decimal and multiplying by the subtotal, rounding again to the nearest cent if necessary. Finally, add the sales tax to the subtotal to get the total cost. For instance, if the sales tax was $1.47, adding this to the subtotal of $20.98 would give you a total of $22.45.
The sum of 5/11 and 4/11 is
equal to 1
less than 1
greater than 1
Train a travels in 840 miles in 7.5 hours. Train b travels 1080 miles in 9 hours. Which train was traveling at the fastest speed, and what was that speed?
Answer:
Train B is traveling faster at a speed of 120 MPH
How to solve:
Train A is 840/7.5 = 112 which is the MPH so its 112 MPH
Train B is 1080/9 = 120 MPH
Final answer:
Train B is the faster train with an average speed of 120 miles per hour, compared to Train A which has an average speed of 112 miles per hour.
Explanation:
The question is asking to compare the average speed of two trains. To find the average speed, we divide the total distance traveled by the time taken. For Train A, it travels 840 miles in 7.5 hours, and for Train B, it travels 1080 miles in 9 hours.
Calculating the average speed of Train A: 840 miles / 7.5 hours = 112 miles per hour.
Calculating the average speed of Train B: 1080 miles / 9 hours = 120 miles per hour.
Therefore, Train B is traveling at the fastest speed with an average of 120 miles per hour.
Prove tan(x - (π / 4)) = (sin x – cos x) / (cos x + sin x) by filling in the reasons in the table below.
No way to know what reasons you're supposed to choose from...
By definition of tangent,
[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin\left(x-\frac\pi4\right)}{\cos\left(x-\frac\pi4\right)}[/tex]
The angle sum identities give
[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x\cos\frac\pi4-\cos x\sin\frac\pi4}{\cos x\cos\frac\pi4+\sin x\sin\frac\pi4}[/tex]
[tex]cos\dfrac\pi4=\sin\dfrac\pi4=\dfrac1{\sqrt2}[/tex], so we can cancel those terms to get
[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x-\cos x}{\sin x+\cos x}[/tex]
as required.
What is the value of x?
If sin (8x - 18)º = cos (5x + 4)°
Question 8 options:
1.33
27
8
90
Answer:
1.33
Step-by-step explanation:
HELP PLEASE!!! NEED FAST ANWER!!
Identify the slope of a line that described by:
down 3 and right 5
m=3/5
m=-3/5
m=5/3
m=-5/3
which one is it???
Answer: second option.
Step-by-step explanation:
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope of the line and b the y-intercept.
We know that we can calculate the slope with:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, keeping the above on mind, you have that:
- If the line moves upward from the left to right, then the slope is positive.
- If the line moves down from the left to right, then the slope is negative.
Then, if the slope described moves 3 units down and 5 units to the right, the it is negative. Therefore:
[tex]m=-\frac{3}{5}[/tex]
Answer:
[tex]-\frac{3}{5}[/tex]
Step-by-step explanation:
We are to identify the slope of a line which is described as:
'down 3 and right 5'
We know that a straight line which is sloping downwards from left to right has a negative slope.
And a straight line which goes upwards from left to right side has a positive slope.
According to the describe slope of a line, it goes 3 units down and 5 units right so it makes a negative slope which is equal to [tex]-\frac{3}{5}[/tex].
Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) f(θ) = 10 cos(θ) + 5 sin2(θ)
If
[tex]f(\theta)=10\cos\theta+5\sin^2\theta[/tex]
then the derivative is
[tex]f'(\theta)=-10\sin\theta+10\sin\theta\cos\theta[/tex]
Critical points occur where [tex]f'(\theta)=0[/tex]. This happens for
[tex]-10\sin\theta+10\sin\theta\cos\theta=0[/tex]
[tex]-10\sin\theta(1-\cos\theta)=0[/tex]
[tex]\implies-10\sin\theta=0\text{ or }1-\cos\theta=0[/tex]
In the first case, we find
[tex]-10\sin\theta=0\implies\sin\theta=0\implies\theta=n\pi[/tex]
In the second,
[tex]1-\cos\theta=0\implies\cos\theta=1\implies\theta=2n\pi[/tex]
So all the critical points occur at multiples of [tex]\pi[/tex], or [tex]n\pi[/tex]. (This includes all the even multiples of [tex]\pi[/tex].)
The critical numbers of the function will be at ([tex]\pi, n\pi[/tex])
Given the function
f(θ) = 10 cos(θ) + 5 sin2(θ)
At the turning point, [tex]\frac{df(\theta)}{d\theta} = 0[/tex]
[tex]\frac{df(\theta)}{d\theta} = -10sin \theta + 5(2sin\theta cos\theta)\\\frac{df(\theta)}{d\theta} = -10sin \theta + 10sin\theta cos\theta\\[/tex]
At the turning point,
[tex]-10sin \theta + 10sin \theta cos \theta=0\\-10sin \theta(1-cos\theta) =0\\-10sin\theta = 0 \ and \ 1-cos\theta =0\\sin\theta =0\\\theta=0 + n\pi\\\\For \ 1-cos\theta =0\\cos\theta = 1\\\theta = cos^{-1}1\\\theta = 0 + n\pi[/tex]
Hence critical numbers of the function will be at ([tex]\pi, n\pi[/tex])
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The point (4, -2) lies on a circle and the center of the circle is at the point (4, 1).
What is the equation of this circle?
A. (x - 1)2 + (y - 4)2 = 9
B. (x - 1)2 + (y - 4)2 = 3
C. (x + 4)2 + (y + 1)2 = 9
D. (x - 4)2 + (y - 1)2 = 9
Answer:
D
Step-by-step explanation:
The equation of the circle is (x-x0)^2 + (y-y0)^2 = r^2, where (x0,y0) is the center of the circle. Radius is the distance from any point to the center. Using distance formula you get r = 3.
The equation of the circle having center at point (4,1) and passing through the point (4,-2) is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
Equation of circle in parametric form -A circle having radius r and having center at (x0,y0) can be represented by the parametric equation as -
[tex](x - x0)^{2} + (y - y0)^{2} = r^{2}[/tex]
Any point say (x1,y1) which lies on the circle, must satisfy the given parametric equation of the circle.
How to frame the equation of circle from the information given in the question ?Given that the point (4,-2) lies on the circle. Also the center of circle is at (4,1). Therefore, calculating the radius of the circle which is the distance from the center to the point lying on the circle.
Using distance formula,
radius = [tex]\sqrt{(4 - 4)^{2} + (-2 - 1)^{2} }[/tex] = [tex]\sqrt{9 }[/tex] = [tex]3[/tex]
Thus forming the equation of circle from the general parametric equation,
⇒ [tex](x - 4)^{2} + (y - 1)^{2} = 3^{2}[/tex]
∴ [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
Therefore the equation of circle is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
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Brian and Carlos are sharing a large sub sandwich. Brian ate 2 / 5 of the sandwich, and Carlos ate 1 / 5 of the sandwich. How much of the sandwich is left over?
if I'm right it would be 2/5. you get your answer by adding 2/5 and 1/5 then subtract 5/5- 3/5 to get 2/5
A model is made of a car. The car is 7 feet long, and the model is 16 inches long. What is the ratio of the length of the car to the length of the model?
Answer:
112
Step-by-step explanation:
Use the x-intercept method to find all real solutions of the equation.
x^3-7x^2+4x+12=0
Answer:
the answer is c for apex
Step-by-step explanation:
Answer:
a. [tex]x=-1,2,\:or\:6[/tex]
Step-by-step explanation:
The given equation is
[tex]x^3-7x^2+4x+12=0[/tex]
To find all real solutions using the x-intercept method, we to graph the corresponding function using a graphing tool.
The corresponding function is;
[tex]f(x)=x^3-7x^2+4x+12[/tex]
The real solutions to [tex]x^3-7x^2+4x+12=0[/tex], are the x-intercepts of the graph of the corresponding function.
From the graph the x-intercepts are
(-1,0),(2,0) and (6,0).
Therefore the real solutions are
[tex]x=-1,2,\:or\:6[/tex]
Randle plans to work 8 hours every two days. At this rate how many hours will he work in 7 days
Answer:
The answer is 28
Step-by-step explanation:
The total number of work hours in 7 days will be 28 hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Randle plans to work 8 hours every two days. The total work hours in 7 days will be calculated as,
Number of hours for 6 days,
N = (6 / 2) x 8
N = 24 hours
Number of hours for 1 day,
N = 8 / 2 = 4 hours
Total hours = 24 + 4 = 28 hours
Therefore, the total number of work hours in 7 days will be 28 hours
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Carmen prepared a 2lb bag of French fries for 4 people to share equally. How many pounds of fries will each person receive?
Answer:
[tex]0.5\frac{lb}{person}[/tex]
Step-by-step explanation:
we know that
To find out how many pounds of fries each person will receive, divide the total pounds of fries by the total number of people.
so
[tex]\frac{2}{4} \frac{lb}{persons}=0.5\frac{lb}{person}[/tex]
Each person will receive 0.5lb of fries.
To solve this problem, we need to divide the total weight of the French fries by the number of people sharing them. Carmen has prepared a 2lb bag of French fries for 4 people. To find out how much each person will get, we divide the total weight of the fries by the number of people:
[tex]\[ \text{Fries per person} = \frac{\text{Total weight of fries}}{\text{Number of people}} \][/tex]
[tex]\[ \text{Fries per person} = \frac{2 \text{lb}}{4} \] \[ \text{Fries per person} = 0.5 \text{lb} \][/tex]
So, each person will receive 0.5lb of fries.
A laptop was originally sold for $975. The laptop is now on sale for $828.75. What is the percent markdown.
so the difference is 975 - 828.75 = 146.25.
if we take 975 to be the 100%, how much is 146.25 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 975&100\\ 146.25&x \end{array}\implies \cfrac{975}{146.25}=\cfrac{100}{x}\implies 975x=14625 \\\\\\ x=\cfrac{14625}{975}\implies x=15[/tex]
Answer:
146.25
Step-by-step explanation:
Which is 2logx - 6 log(x-9) written as a single logarithm.
Answer: option c
Step-by-step explanation:
To solve this problem you must keep on mind the properties of logarithms:
[tex]log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a[/tex]
Therefore, knowing the properties, you can write the expression gven in the problem as shown below:
[tex]2logx-6log(x-9)\\logx^2-log(x-9)^6\\\\log\frac{x^2}{(x-9)^6}[/tex]
Answer:
c edge
Step-by-step explanation:
Find the limit, picture provided
Answer:
C
Step-by-step explanation:
You are given that
[tex]\lim_{x \to 4} f(x)=5;[/tex][tex]\lim_{x \to 4} g(x)=0;[/tex][tex]\lim_{x \to 4} h(x)=-2.[/tex]Use the rule
[tex]\lim_{x\to x_0}(f(x)+g(x))=\lim_{x\to x_0} f(x)+\lim_{x \to x_0} g(x).[/tex]
In your case,
[tex]\lim_{x\to4}(f+g)(x)=\lim_{x\to4} (f(x)+g(x))= \lim_{x\to4} f(x)+ \lim_{x\to 4} g(x)=5+0=5.[/tex]
List these solids in order from the one with least volume to the one with the greatest volume. A. A cube with edge 5 cm B. A cylinder with radius 4 cm and height 4 cm C. A square pyramid with base edges 6 cm and height 6 cm D. A cone with radius 4 cm and height 9 cm E. A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
Answer:
The list in order from the one with least volume to the one with the greatest volume is
case C) A square pyramid with base edges 6 cm and height 6 cm
case A) A cube with edge 5 cm
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
case D) A cone with radius 4 cm and height 9 cm
case B) A cylinder with radius 4 cm and height 4 cm
Step-by-step explanation:
To solve this problem calculate the volume of each solid
case A) A cube with edge 5 cm
The volume of a cube is equal to
[tex]V=b^{3}[/tex]
where
b is the length side of the cube
substitute the value
[tex]V=5^{3}=125\ cm^{3}[/tex]
case B) A cylinder with radius 4 cm and height 4 cm
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
substitute the value
[tex]V=(3.14)(4)^{2} (4)=200.96\ cm^{3}[/tex]
case C) A square pyramid with base edges 6 cm and height 6 cm
The volume of a pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the pyramid
Find the area of the base B
[tex]B=6^{2}=36\ cm^{2}[/tex] ----> is a square
substitute the values
[tex]V=\frac{1}{3}(36)(6)=72\ cm^{3}[/tex]
case D) A cone with radius 4 cm and height 9 cm
The volume of a cone is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the cone
Find the area of the base B
[tex]B=\pi r^{2}=(3.14)(4^{2})=50.24\ cm^{2}[/tex] ----> is a circle
substitute the values
[tex]V=\frac{1}{3}(50.24)(9)=150.72\ cm^{3}[/tex]
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=(5)(5)(6)=150\ cm^{3}[/tex]
therefore
The list in order from the one with least volume to the one with the greatest volume is
case C) A square pyramid with base edges 6 cm and height 6 cm
case A) A cube with edge 5 cm
case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm
case D) A cone with radius 4 cm and height 9 cm
case B) A cylinder with radius 4 cm and height 4 cm
Find all real solutions of the equation, approximating when necessary.
x^3+4x^2=10x+15=0
Answer:
b. [tex]x\approx -2.426[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3+x^2+10x+15=0[/tex]
We solve by the x-intercept method. We need to graph the corresponding function using a graphing tool.
The corresponding function is
[tex]f(x)=x^3+x^2+10x+15[/tex]
The solution to [tex]x^3+x^2+10x+15=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercept is;
(-2.426,0)
Therefore the real solution is:
[tex]x\approx -2.426[/tex]
Answer:
b. x ≈ -2.426
Step-by-step explanation:
Given that we have possible roots we can replace these values into the equation and check if it is satisfied.
option a: 2.426^3+4*2.426^2+10*2.426+15 = 77.08 ≠ 0
option b: (-2.426)^3+4*(-2.426)^2+10*(-2.426)+15 ≈ 0
option c: 5.128^3+4*5.128^2+10*5.128+15 = 306.31 ≠ 0
option d: (-5.128)^3+4*(-5.128)^2+10*(-5.128)+15 = -65.94 ≠ 0
Using the figure, find x and y
Answer:
x = 8y = 2√3Step-by-step explanation:
The triangle is recognizable as a 30°-60°-90° right triangle, which has side length ratios ...
1 : √3 : 2
Side x is thus twice the length of short side 4, so x = 8.
Side y is √3 times the length of short side x-6 = 2, so y = 2√3.
_____
If you don't happen to recognize the triangle dimensions, you can find x and y using the Pythagorean theorem.
x = √(4² +(4√3)²) = √64 = 8
y = √(4² -2²) = √12 = 2√3
If a van traveled 210 miles in 3 hours, how far could the van travel in 5 hours
Answer:
350
Step-by-step explanation:
The rectangle shown has a perimeter of 48 cm and the given area. Its length is 6 more than twice its width. Write and solve a system of equations to find the dimensions of the rectangle.
Answer:
The length of the rectangle is 18 cm
The width of the rectangle is 6 cm
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
The perimeter of the rectangle is
[tex]P=2(x+y)[/tex]
we have
[tex]P=48\ cm[/tex]
so
[tex]48=2(x+y)[/tex] ------> equation A
[tex]x=2y+6[/tex] ------> equation B
Substitute equation B in equation A and solve for y
48=2(2y+6+y)
48=2(3y+6)
48=6y+12
6y=48-12
y=36/6=6 cm
Find the value of x
x=2(6)+6=18 cm
The area of the rectangle is
A=xy
A=18*6
A=108 cm^2
Final answer:
To solve for the dimensions of the rectangle, we set up a system of equations based on the given perimeter and the relationship between length and width and solve for both variables.
Explanation:
The student is asked to find the dimensions of a rectangle given the perimeter and a relationship between its length and width. Since the perimeter is 48 cm and the length (L) is 6 cm more than twice the width (W), two equations can be set up: 2L + 2W = 48 and L = 2W + 6. By substituting the second equation into the first, we get 2(2W + 6) + 2W = 48. Simplifying yields 4W + 12 + 2W = 48, which simplifies further to 6W + 12 = 48. Solving for W gives W = 6 cm, and substituting back gives L = 18 cm.