The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions of the rectangle.
Answers
Answer
Length = 10 ft
Width = 5 ft
Explanation
Area of the rectangle given = 50 ft²
Let the width of the rectangle be x
So this means the length of the rectangle will be 3x - 5
What to find:
The dimensions of the rectangle.
Step-by-step solution:
Area of a rectangle = length x width
i.e A = L x W
Put A = 50, L = 3x - 5, W = x into the formula.
[tex]\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}[/tex]The quadratic equation can now be solve using factorization method:
[tex]\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}[/tex]Since the dimension can not be negative, hence the value of x will be = 5.
Therefore, the dimensions of the rectangle will be:
[tex]\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\ \\ Width=x=5\text{ }ft \end{gathered}[/tex]
Related Questions
the number 6 is plotted on the number line below. Answer the following questions.
Answers
Starting point = 6
a.
To obtain a point 2 units to the right add 2.
6 + 2
b.
To obtain a point 2 units to the left, subtract 2.
6 + (-2)
6-2
Evaluate the expression when x=7 and y= -37x-6y
Answers
Answer
Answer = 67
Explanation
We are asked to evaluate
7x - 6y
when x = 7 and y = -3
So, to solve this, we just substitute for x and y.
7x - 6y
= (7 × 7) - (6 × -3)
= 49 - (-18)
= 49 + 18
= 67
Hope this Helps!!!
Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of the function for f(x)=(x-9)^2-29
Answers
Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of the function for f(x)=(x-9)^2-29
we have
f(x)=(x-9)^2-29
This is a vertical parabola, open upward
The vertex represent a minimum
The vertex of the parabola is the point (9,-29)
The domain is all real numbers
The range is the interval {-29, infinite)
[tex]y\ge-29[/tex]The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
In this problem
axis of symmetry is x=9
For the following, state the parent function. Then, tell the difference between the parent function and this child function - ir terms of the equation and in terms of the graph. Graph each function. 10. f(x) = (x + 2) - 3
Answers
Given f(x) defined as follows:
[tex]f\mleft(x\mright)=(x+2)-3[/tex]The paren: function of f(x) is:
[tex]g(x)=x[/tex]f(x) is a horizontal translation left by 2 units and vertical translation down by 3 units of g(x).
The graphs of the two functions are attached below:
• The graph of the parent function g(x) passes through the origin(0,0) while;
,• The graph of f(x) has x and y-intercepts of (1,0) and (0,-1) respectively.
Calculate the radius of this shape if the volume is 1017.876m3. Make sure your answer includes the proper units
Answers
Given:
Volume of the cone = 1017.876 cubic m
slant height = 15m
height = 12m
To find the radius of the cone, we would have to use the formula of a cone. The formula for the volume of a cone is:
[tex]\text{Volume = }\frac{1}{3}\pi r^2h[/tex]Substituting the given values:
[tex]1017.876\text{ = }\frac{1}{3}\text{ }\times\pi\text{ }\times r^2\times12[/tex]Solving for the radius r:
[tex]\begin{gathered} 12\pi\text{ }\times r^2\text{ = 3 }\times\text{ 1017.876} \\ r^2\text{ = }\frac{3\text{ }\times\text{ 1017.876}}{12\pi} \\ r^2\text{ = 80.9999} \\ r\text{ = }\sqrt[]{80.99999} \\ r\text{ = 8.9} \\ r\text{ }\approx\text{ 9 } \end{gathered}[/tex]Answer:
r = 9m
Maia flips a dime four times. What is the probability that she will get at least two heads?
Answers
Explanation:
we can only have a head or a tail when we flip
A dime flipped 4 times, the sample space of that:
HHHH, HHHT, HHTT, HTTT, TTTT, THHH, TTHH, TTTH, THTH, HTHT, HTTH, THHT,
For the total possible outcome of flipping a coin, we use the formula:
2^(number of times dimewas flipped) = 2^4
Total possible outcome = 16
To have atleast 2 heads = HHHH, HHHT, HHTT, THHH, TTHH, THTH, HTHT, HTTH, THHT, HTHH, HHTH = 11
Probability of atleast two heads:
[tex]\begin{gathered} Probability=\text{ 11/ 16} \\ \text{Probability = 0.6875} \end{gathered}[/tex]David cast a shadow 42" long at the same place and time in Emma cast a shadow 28" long. David is 66" tall. What is Emma's height?
Answers
ANSWER
Emma is 44" tall
EXPLANATION
We have that David cast a shadow 42 inches long and he is 66 inches tall.
At that same place and time, Emma cast a shadow of 28 inches.
Since they are at the same spot and time, we can conclude that the ratio of their height to shadow must be the same.
Let Emma's height be x.
The ratio of David's shadow to height is:
42 : 66 or 42 / 66
For Emma, it is:
28 : x or 28 / x
That means that:
[tex]\begin{gathered} \frac{42}{66}\text{ = }\frac{28}{x} \\ \text{Solve for x by cross-multiplying:} \\ 42\cdot\text{ x = 66 }\cdot\text{ 28} \\ x\text{ = }\frac{66\cdot\text{ 28}}{42} \\ x\text{ = 44 inches} \end{gathered}[/tex]So, Emma is 44" tall.
Need answer fast can talk about explanation later A quadrilateral can have 2 pairs of congruent a sides without being a rectangleTrue or False
Answers
EXPLANATION
The kite and dart quadrilaterals have two pairs of congruent sides without being a rectangle.
Therefore, the answer is true.
Identify the following as rational (R) or irrational (I)Which of the following are equivalent to x^4?
Answers
Start by writing the radicals as decimal numbers
[tex]\begin{gathered} \sqrt[]{9}=3 \\ \sqrt[]{10}=3.162277\ldots \\ \sqrt[]{21}=4.582575\ldots \end{gathered}[/tex]A rational number is one that can be written as a decimal number or a fraction without changing the corresponding value.
the only rational number is √9 since √10 and√21 cannot be writen as fractions in order to be called as a rational.
[tex]undefined[/tex]The medical practice you are working at has seen an average of 22.4 patients a day for the past 3 months. 3/4ths of those patients have insurance in one form or another. 1. Describe in a well-written paragraph how you will analyze this scenario and the process you will use to arrive at an answer. 2. Please express to the nearest whole number how many of the patients on average per day do not have insurance, and thus, pay cash price for their visits.
Answers
2)
Given:
The average of patients in a day, A=22.4.
The fraction of patients who have insurance, x=3/4.
It is given that 3/4 th of the patients have insurance. It measn 3/4 part of a whole(1). The rest of the patients do not have insurance. Hence, the fraction of patients who have no insurance can be calculated by subtracting 3/4 from 1,
[tex]y=1-\frac{3}{4}=\frac{4-3}{4}=\frac{1}{4}[/tex]So, 1/4 th of the patients have no insurance.
Hence, the average of the patients in a day who do not have insurance is 1/4 th of the average of patients in a day.
Thus, the number of patients on average per day do not have insurance is,
[tex]\begin{gathered} N=Ay \\ =22.4\times\frac{1}{4} \\ =5.6 \\ \cong6 \end{gathered}[/tex]Therefore, the number of patients on average per day who do not have insurance is 6.
x + y = -5(x- y=9 Solve by elimination
Answers
Answer:
(x, y) = (2, -7)
Explanation:
Given the system of equations:
[tex]\begin{cases}x+y=-5 \\ x-y=9\end{cases}[/tex]We are required to solve the system by the elimination method.
In order to do this, add the two equations.
[tex]\begin{gathered} \begin{cases}x+y=-5 \\ x-y=9\end{cases} \\ --------- \\ 2x=4 \end{gathered}[/tex]Divide both sides by 2 to solve for x.
[tex]\begin{gathered} \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}[/tex]Next, substitute x=2 into any of the equations to solve for y.
Using the first equation:
[tex]\begin{gathered} x+y=-5 \\ 2+y=-5 \\ y=-5-2 \\ y=-7 \end{gathered}[/tex]The solution to the system of linear equations is (x, y) = (2, -7).
Determine whether each relation is a function.Domain1234Range4567
Answers
A set of relations is a function if each of the Domains has its own unique pair of Range.
We are given this set of pairs,
Domain: 1 2 3 4
Range : 4 5 6 7
Since each Domain has its own unique pair of Range, we can say that this is a Function.
Question 101 ptsBrian and Marquise are saving money. Brian has saved $20 and saves $3 per week. Marquisehas saved $10 and saves $5 per week. After how many weeks will Brian and Marquise havesaved the same amount of money?55 weeks50 weeks10 weeks5 weeks
Answers
Lets call the amount of weeks till they save the same amount of money x. i.e , it will take them weeks to save the same amount.
Brian would have saved 20+3x
Marquise would have saved 10+5x
Lets equate them because they are the same amount of money, thus
20 + 3x = 10 + 5x
20 -10 = 5x -3x
10 = 2x
x = 5 weeks
Therefore it would take 5 weeks.
Option D
Select the correct answer from each drop-down menu.
А/В
D/C
9
Line r cuts parallel lines pand q as shown in the figure.
E F
H/G
р
Angles E and G are
to each other because they are
angles.
Reset
Next
Answers
Answer:
• Congruent
,• Vertical Angles
Explanation:
In the given figure:
Angles E and G form an X-Shape.
This means that they are vertical angles.
Therefore, Angles E and G are congruent to each other because they are vertical angles.
Suppose your uncle gives you money during the first 15 days of each month. He gives you $100 onthe first day, $50 the next day, then $25 on the day after that, and follows the same pattern until thefifteenth day. How much would your uncle give you in a year?
Answers
Okay, here you have a sequence problem. First, you need to find how much money your uncle gives you each month, and then you multiply that result by 12, which are the months in a year. The first term of the sequence is 100 and each day he gives you half of the previous day. The next formula is the one you need to use:
[tex]\sum ^n_{i\mathop=0}100\cdot\frac{1}{2^i}=200-100\cdot2^{-n}=200-100\cdot2^{-15}\cong199.997[/tex][tex]199.997\cdot12=2399.96[/tex]I need help with this. In the question there are 3 more options. 1 and 2 and 4. 3 only. And then 1 only.
Answers
We will have that the alternative way to write the number are:
[tex]\begin{gathered} \sqrt[3]{64} \\ \\ (\sqrt[3]{8})^2 \\ \\ 4 \end{gathered}[/tex]So, the alternative ways to write them are 1, 2 and 4.
Determine the number of non-negative integers M that satisfy exactly three of the four statements below.(1) M is prime(2) M + 3 is prime(3) 1 < √ < 8(4) M + 5 has an odd number of factors
Answers
SOLUTION
A non-negative integer is either positive or zero. It's the union of the natural numbers and the number zero.
A prime number is a number with only two factors, which are 1 and the number itself
Let consider the number
[tex]2[/tex]1) It satisfies the first statement
M is prime
2 is prime
2) M+3 is prime
since
[tex]\begin{gathered} m=2 \\ 2+3=5\text{ } \\ 5\text{ is prime } \end{gathered}[/tex]Hence
The second statement is satisfied
The third statement says
[tex]\begin{gathered} 1<\sqrt[]{m}<8 \\ \text{which is } \\ 1<\sqrt[]{2}<8 \end{gathered}[/tex][tex]\begin{gathered} \text{ since } \\ \sqrt[]{2}=1.414\ldots \\ \text{the third statement is satisfied } \end{gathered}[/tex]Hence the third statement is satisfied
M=2
Since exactly 3 of the 4 statements is satisfied
From the second condition,
[tex]M+3\text{ is prime }[/tex]All prime numbers except 2 are odd numbers
Also,
The sum of two odds is even
[tex]\text{let n be the prime numbers satisfying all the given conditions above }[/tex]from the second condition,
M+3 is prime
[tex]\begin{gathered} n+3\text{ is even } \\ \text{which contradicts the second conditions } \end{gathered}[/tex]Hence
There is no other prime number that satisfies exactly three of the four conditions above
Therefore,
The number of non-negative integers that satisfy exactly three of the four conditions is 1
There is only one non-negative integer M which is 2 that satisfy the condition 1,2,3 above
A mouse is trapped in amaze to find his way out he walks 15 miles is makes a 90° left turnwalks 8 miles makes another 90° left turn and walks 10 miles what is the magnitude of the resultant vector?
Answers
ANSWER
The magnitude of the resultant vector is 11.18 miles
EXPLANATION
To find the magnitude of the resultant vector, we will first need to sketch the diagram
From the diagram above, you will see that the resultant vector is R and this can be calculated by using Pythagora's theorem
[tex]\begin{gathered} \text{ Pythagora's theorem; c}^2\text{ = a}^2\text{ + b}^2 \\ \text{ R}^2\text{ = 10}^2\text{ + 5}^2 \\ \text{ R}^2\text{ = 100 + 25} \\ \text{ R}^2\text{ = 125} \\ \text{ Take the square roots of both sides} \\ \text{ R = }\sqrt{125} \\ \text{ R = 11.18 miles} \end{gathered}[/tex]Hence, the magnitude of the resultant vector is 11.18 miles
Recommendations Skill plans Math 13 Language arts Eighth grade > T.14 Volume of spheres om What is the volume of this sphere? Use a 3.14 and round your answer to the nearest hundredth. 20 m cubic meters
Answers
From the picture, the diameter of the sphere is 20 m, then its radius is 20/2 = 10 m.
The volume of a sphere is computed as follows:
[tex]V=\frac{4}{3}\pi r^3[/tex]Substituting with r = 10 m, we get:
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot10^3 \\ V=\frac{4}{3}\cdot3.14\cdot1000 \\ V=4186.67m^3 \end{gathered}[/tex]What do you know to be true about the values of p and g?pºgº6030°4545O A. p>gO B. p
Answers
Solution:
Given the triangles as shown below:
The sum of interior angles in a triangle equals 180°.
Thus, in ΔABC,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180 \\ \text{where} \\ \angle A=60,\text{ }\angle B=p,\text{ }\angle C=30 \\ 60+p+30=180 \\ \Rightarrow p+90=180 \\ p=180-90 \\ \Rightarrow p=90\degree \end{gathered}[/tex]Similarly, in ΔXYZ,
[tex]\begin{gathered} \angle X+\angle Y+\angle Z=180 \\ \text{where} \\ \angle X=45,\text{ }\angle Y=q,\text{ }\angle Z=45 \\ 45+q+45=180 \\ \Rightarrow90+q=180 \\ q=180-90 \\ \therefore q=90\degree \end{gathered}[/tex]Since the p and q are similarly evaluated to be 90°, we can conclude that the values of p and q are equal.
Hence,
[tex]p=q[/tex]The correct option is C.
(These "x/x" are fractions).2/3x+6=1/2x+1/4xA) 6B)72C)14 2/5D) 2
Answers
We have to find the value of x in the expression:
[tex]undefined[/tex]Hi, i am doing a graded practice test for algerbra 2 and I need some help with a few of the questions, thanks so much.
Answers
Given the equation:
[tex]\log _2(7x)+\log _22=1[/tex]As we know: log a + log b = log (ab)
So,
[tex]\begin{gathered} \log _2(7x\cdot2)=1 \\ \log _2(14x)=\log _22 \\ \\ 14x=2 \\ x=\frac{2}{14} \\ \\ x=\frac{1}{7} \end{gathered}[/tex]So, the answer will be x = 1/7
Answer:
x = 1/7
Step-by-step explanation:
pls mark brainliest
juan bought 2units and 3/8 pounds of deli ham that cost 5.99 per pound. what was the cost, to the nearest cent, of ham that juan bought
Answers
We have that he bought 2 units and 3/8 of a unit of ham, we determine its cost as follows:
*We find the simple fraction that represents what he bought:
[tex]2\frac{3}{8}=(\frac{16}{8}+\frac{3}{8})=\frac{19}{8}[/tex]Now, we determine it's cost:
[tex]c=\frac{2.99\cdot\frac{19}{8}}{1}\Rightarrow c\approx14.23[/tex]These values are the cost of one unit times the quantity we want to know the cost of, divided by the unit.
From this, we have that the cost of the ham Juan bought he had to pay approximately $14.23.
A store is having a 40% off sale! If an item is originally priced at $20, what will be the sale price?
Answers
Original Price = $20
Discount = 40%
First Calculate the discount amount by multiplying the original price (20) by the percentage discount in decimal form ( divided by 100)
20 x (40/100) = 20 x 0.4 = 8
Then subtract the discount amount to the original price:
20-8 = 12
Sale price : $12
Karen invested her savings in two investment funds. The amount she invested in fund A. was $2000 less than the amount she invested in fund B. Fund A returned a 8% profit and fund B returned a 6% profit. How much did she invest in fund B, if the total profit from the two funds together was $1940
Answers
Step 1:
Let the invested on B = m
Amount invested on A = m - 2000
Step 2
Profit is in percentage of the cost of investment
A profit is 8%
[tex]\begin{gathered} A\text{ profit = 8\% of m - 200}0 \\ =\text{ }\frac{8}{100}\text{ }\times\text{ (m - 2000)} \\ =\text{ 0.08m - 16}0 \end{gathered}[/tex][tex]\begin{gathered} B\text{ profit = 6\% of m} \\ =\text{ 0.06m} \end{gathered}[/tex]Step 3
Total profit = $1940
[tex]\begin{gathered} 0.08m\text{ - 160 + 0.06m = 1940} \\ 0.14m\text{ = 1940 + 16}0 \\ 0.14m\text{ = 2}100 \\ m\text{ = }\frac{2100}{0.14} \\ \text{m = \$15000} \end{gathered}[/tex]Final answer
She invested $15,000 in fund B
To manufacture an automobile requires painting, drying, and polishing. Epsilon Motor Compary produces three types of cars, the Deita, the Beta, and the Sigma. EachDelta requires 9 hours for painting, 2 hours for drying, and 5 hours for polishing. A Beta requires 33 hours for painting, & hours for drying, and 6 hours for polishing, anda Sigma requires 4 hours for painting, 3 hours for drying, and 2 hours for polishing. If the company has 190 hours for painting, 66 hours for drying, and 54 hours forpolishing per month, how many of each type of car are produced?GThe Epsilon Motor Company produces:__ Deltas__ Betas__ Sigmas in a month
Answers
Let d represent the number of Deltas produced
Let b represent the number of Betas produced
Let s represent the number of Sigmas produced
Each Delta requires 9 hours of painting. Each Beta requires 33 hours of painting and each Sigma requires 4 hours of painting. If the company has 190 hours of painting, then the equation representing this situation is
9d + 33b + 4s = 190
Each Delta requires 2 hours of drying. Each Beta requires 8 hours of drying and each Sigma requires 3 hours of drying. If the company has 66 hours of drying, then the equation representing this situation is
2d + 8b + 3s = 66
Each Delta requires 5 hours of polishing. Each Beta requires 6 hours of polishing and each Sigma requires 2 hours of polishing. If the company has 54 hours of polishing, then the equation representing this situation is
5d + 6b + 2s = 54
From the third equation, if we divide both sides by 2, we have
2.5d + 3b + s = 27
s = 27 - 2.5d - 3b
We would substitute s = 27 - 2.5d - 3b into the first and second equations. By substituting s = 27 - 2.5d - 3b into the first equation, we have
9d + 33b + 4(27 - 2.5d - 3b) = 190
9d + 33b + 108 - 10d - 12b = 190
33b - 12b + 9d - 10d = 190 - 108
21b - d = 82 equation 4
By substituting s = 27 - 2.5d - 3b into the second equation, we have
2d + 8b + 3(27 - 2.5d - 3b) = 66
2d + 8b + 81 - 7.5d - 9b = 66
2d - 7.5d + 8b - 9b = 66 - 81
- 5.5d - b = - 15
b = - 5.5d + 15
We would substitute b = - 5.5d + 15 into equation 4. We have
21(- 5.5d + 15) - d = 82
- 115.5d + 315 - d = 82
- 115.5d - d = 82 - 315
- 116.5d = - 233
d = - 233/- 116.5
d = 2
We would substitute d = 2 into b = - 5.5d + 15. We have
b = - 5.5 * 2 + 15 = - 11 + 15
b = 4
We would substitute b = 4 and d = 2 into s = 27 - 2.5d - 3b. We have
s = 27 - 2.5 * 2 - 3 * 4 = 27 - 5 - 12
s = 10
Therefore, the Epsilon motors produce 2 Deltas, 4 Betas and 10 Sigmas in a month
Two trains leave towns 471 miles apart at the same time and travel toward each other. One train travels 21 miles per hour slower than the other. If they meet in 3 hours, what is the rate of each train?.
Answers
Let the slower train's velocity be x-21
Let the faster train's velocity be x
We know that the approach speed is the sum of both speeds, so x+x -21= 2x-21.
The approach rate is given by Distance/time = 471/3 = 157mpH
x+x-21=157
2x=157+21
2x=178
x=89mph
The slower train is travelling 89-21 = 68mph
The faster train is travelling 89mph.
Q The value of n is a distance of 1.5 units from -2 on a number line. Click on the number line to show the possible values of n. -5 -4 -3 -2 -1 they 0 1 2 3 4 LO
Answers
Input data
n is a distance of 1.5 units from -2
Procedure
n - 1.5 = -2
n = -2 + 1.5
n = -0.5
Also
n + 1.5 = -2
n = -2 - 1.5
n = -3.5
kid has 7 apple he give 1 to
Answers
The angles 2x and 36 are vertical angles, which means that they are angles opposite to the same vertex and thus they are equal:
[tex]2x=36[/tex]Now we have to solve this equation to find the value of x.
To solve for x, divide both sides of the equation by 2:
[tex]\frac{2x}{2}=\frac{36}{2}[/tex]On the left-hand side, the 2 on the numerator and the 2 on the denominator cancel each other and we are left only with x:
[tex]x=\frac{36}{2}[/tex]And on the right-hand side 36/2 is equal to 18:
[tex]x=18[/tex]Answer: x=18
Candidate A makes 48 speeches. Candidate B makes 16 speeches. a. Write the ratio of speeches by candidate A to candidate B
Answers
The ratio of speeches by candidate A to candidate B can be made as:
[tex]48\colon16[/tex]If we divide both numbers by 16, we get:
[tex]\begin{gathered} \frac{48}{16}\colon\frac{16}{16} \\ 3\colon1 \end{gathered}[/tex]Answer: the ratio of speeches by candidate A to candidate B is 3:1