Answers
Answer:
6468 mm²
Step-by-step explanation:
Given:
21 mm = length of the shortest of the small rectangleLet y = length of the longest of the small rectangleTherefore, the area of the small rectangle is:
= width × length
= 21 × y
= 21y mm²
From inspection of the larger rectangle
longest side length = 4 × 21 = 84 mmshortest side length = (2y + 21) mmTherefore, the area of the larger rectangle is:
= width × length
= 84(2y + 21)
= 168y + 1764 mm²
We know that the area of the larger rectangle is 11 times the area of the smaller rectangle. Therefore,
⇒ 11 small rectangles = larger rectangle
⇒ 11(21y) = 168y + 1764
⇒ 231y = 168y + 1764
⇒ 63y = 1764
⇒ y = 28
Therefore, the missing side length of the smaller rectangle is 28 mm.
Finally, to find the area of the larger rectangle, substitute the found value of y into the found expression for its area:
⇒ area = 168y + 1764
⇒ area = 168(28) + 1764
⇒ area = 4704 + 1764
⇒ area = 6468 mm²
Related Questions
i am stuck on this question please help me
Answers
Answer:
h = 8 units, b = 20 units
Step-by-step explanation:
h = 2 units
2 x 4 = 8
b = 5 units
5 x 4 = 20 units
Therefore, h = 8 units and b = 20 units
Hope this helps :)
please help
i added a picture
Answers
All digits in a dropdown number are different and one of the digits is the average of all the digits. it has at least two digits. for example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number.
Answers
The dropdown numbers is an illustration of combination
The smallest dropdown number is 1025
How to determine the smallest dropdown number?From the question, we have the following parameters:
The dropdown number is 4-digitThe digits are different.We start counting from 1023, 1024, 1025, 1026...........
The sum of digits in 1023 is 6, and the average is 1.5The sum of digits in 1024 is 7, and the average is 1.75The sum of digits in 1025 is 8, and the average is 2The number 1025 satisfies the given conditions
Hence, the smallest dropdown number is 1025
Read more about combination at:
https://brainly.com/question/11732255
line d has a slope of 7/3. line e is perpendicular to line d. what is the slope of line e?
Answers
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
Here we have the number:-
[tex]\boxed{\frac{7}{3}}[/tex]
Flop it over:-
[tex]\boxed{\frac{3}{7} }\longleftarrow\sf{the~numerator~and~denominator~switch~places}[/tex]
Change its sign:-
[tex]\boxed{-\frac{3}{7}}[/tex]
Hence, the slope of line e is:-
[tex]\bigstar{\boxed{\pmb{Slope=-\frac{3}{7}}}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
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Question 1: 11 pts
Find the vertex of the parabola y = x2 - 10x + 16.
A. (-5,91)
B. (-9,5)
C. (5,-9)
D. (8,0) and (2,0)
Answers
[tex]\\ \rm\rightarrowtail y=x^2-10x+16[/tex]
[tex]\\ \rm\rightarrowtail y=x^2-10x+16+9-9[/tex]
[tex]\\ \rm\rightarrowtail y=x^2-10x+25-9[/tex]
[tex]\\ \rm\rightarrowtail y=(x-5)^2-9[/tex]
Vertex form
y=a(x-h)^2+kSo
vertex:-
(h,k)=(5,-9)what is 12x + 11y - 4x -5y
Answers
Answer:
8x+6y
Step-by-step explanation:
Combine like terms:
12x-4x=8x
+11y-5y=6y (because 11 is the bigger number and 5 is smaller, the answer is positive [+])
Answer:
8x + 6y
Step-by-step explanation:
1) Rearrange terms and combine like terms:
12x + 11y - 4x - 5y —> 12x - 4x +11y - 5y
2.Simplify (aka add/subtract like terms)
12x - 4x +11y - 5y
- 12x - 4x = 8x
- 11y - 5y = 6y
= 8x + 6y
Hence, 8x + 6y is your answer :)
Need help! Here's the question...
John invests £8000 for n years in a savings account.
To find the value, V ,of her investment after n years he uses the formula:
V=8000*(1.025)^n
a)Write down the annual rate of interest John earns
Answers
Answer:
the answer is 2.5%
Step-by-step explanation:
im good at math
Hope this helps!
Helppppp!!!!!!!!!
I need this before midnight
Answers
Answer:
a) 9am
b) 10am
c) 50 miles
d) 30 minutes
e) 11:30
f) 90 miles
if you could just tell me what I should say in the presentation, that would be great :) thx
Answers
Answer:
we're u asking for this
What is ur statistical question
What is the measure of arc XZ if the angle equals 135 and the radius is 17 km
Answers
now, let's make the assumption that the arcXZ has a central angle of 135° and a radius of 17.
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=17\\ \theta =135 \end{cases}\implies s=\cfrac{(135)\pi (17)}{180}\implies s=\cfrac{51\pi }{4}\implies s\approx 40.06[/tex]
1) Find the slope of the line
2) find the slope between the two points
help please, thank you
Answers
Answer:
1 = 3/2
2 = -1/14
Step-by-step explanation:
The equation for the slope of a line is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] (difference in Y divided by the difference in X) or simply just Rise/Run.
For the first one, we have to pinpoint two points on the graph. There's one point placed on the x-axis 2 units away from the origin (2,0) and one four units to the right and 3 units up from the origin (4,3). Since it's on a graph, the easiest way to calculate it is by counting the units up and then right from (2,0) to (4,3). You can count that (4,3) is 3 units up and 2 units right from (2,0). Since slope is Rise/Run, the slope is 3/2.
For the second one, you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. The Y of the second point is 2, and the Y of the first point is 1. The X of the second point is -17, and the X of the first point is -3.
You can plug all 4 numbers in to get (2-1)/(-17- -3)
2-1 = 1 and -17 - -3 = -14. So your slope is 1/-14 or -1/14.
A board-game club meets each week at the local library. People bring different board games to play, like checkers and chess. Out of the 50 people that meet each week, 67% prefer to play checkers over chess. Construct an 83% confidence interval for the population mean of people that prefer to play checkers over chess.
Answers
Using the z-distribution, as we are working with a proportion, it is found that the 83% confidence interval is (0.5789, 0.7611).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have an 83% confidence level, hence[tex]\alpha = 0.93[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.83}{2} = 0.915[/tex], so the critical value is z = 1.37.
The other parameters are [tex]n = 50, \pi = 0.67[/tex].
Then, the bounds of the interval are given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 - 1.37\sqrt{\frac{0.67(0.33)}{50}} = 0.5789[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 + 1.37\sqrt{\frac{0.67(0.33)}{50}} = 0.7611[/tex]
The 83% confidence interval is (0.5789, 0.7611).
More can be learned about the z-distribution at https://brainly.com/question/25890103
Answer:
CI = (57.89%, 76.14%)
Step-by-step explanation:
First, solve for the 83% critical z-value (za/2). Second, solve for the margin of error. Third, solve for the confidence interval by subtracting and adding the margin of error with the sample probability of success.
Mr. Wilson bought a bag of birdseed and put half of it in his bird feeder. He split the other half equally among his 4 pet birds. How much of the bag did each pet bird get?
Answers
Answer:
each pet bird got 1/8 of the bag of birdseed
Step-by-step explanation:
the easiest way to do this is to divide the bag into eighths. if you divide the bag into eighths, 4/8 of the bag, being half, goes into the bird feeder. the other 4/8 of the bag is divided among Mr. Wilson's four pet birds, leaving each bird to get 1/4 of the bag when split evenly.
hope this helps
Amy earns £10.00 per hour. She gets a raise, and her new hourly rate is £11.50 What is the percentage change in her hourly rate?
Answers
Percentage Change = (new rate - old rate) / (old rate)
New Rate = 11.5
Old Rate = 10
(11.5 - 10) / 10
1.5 / 10 = 15 / 100 = 0.15 = 15%
The percentage change in her hourly rate is 15%.
Hope this helps!
( new-old / old ) x 100
(11.50-10)/10 = 0.15
0.15 x 100 = 15%
A population of bacteria is increasing by 10% cach hour. Find the percentage increase in the population every 3 hours.
Answers
What is the rule and how do you find n? 100 points and brainliest to answer!
Answers
Answer:
n = 6
Step-by-step explanation:
Let's convert the x and y values into (x,y) form.
(x, y) ⇒ (3, 5), (4, 7), (n, 11), (8, 15)
Now, let's find the rule in slope intercept form. To find the equation in slope intercept form, pick any two points. Then find the slope of the line.
⇒ (3, 5) and (4, 7)
Now, find the slope using the slope formula.
[tex]\dfrac{y_{2} - y_1}{x_2 - x_1} = \text{Slope}[/tex]
[tex]\rightarrow \dfrac{7 - 5}{4 - 3} = \text{Slope}[/tex]
[tex]\rightarrow \dfrac{2}{1} = 2 =\text{Slope}[/tex]
Now, let's use point slope form to find the equation in slope intercept form.
[tex]y - 5 = 2(x - 3)[/tex]
[tex]\rightarrow y - 5 = 2x - 6[/tex]
[tex]\rightarrow y = 2x - 1 \ \ \ \ \ (\text{Rule})[/tex]
Now, substitute the value of y into the equation.
[tex]11 = 2x - 1[/tex]
[tex]\rightarrow 12 = 2x[/tex]
[tex]\rightarrow \boxed{x = n = 6}[/tex]
Take two points find equation
(3,5)(4,7)Slope:-
m=7-5/4-3=2Equation in point slope form
y-5=2(x-3)y=2x-6+5y=2x-1Now put n
11=2n-12n=12n=6Find the distance between the two points in simplest radical form.
Answers
Answer:
13 units
Step-by-step explanation:
A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is ...
d² = 12² +5² = 144 +25 = 169
d = √169 = 13
The distance between the two points is 13 units.
_____
Additional comment
This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.
A lake is 85 feet across using scale 1 inch :4 feet how many inches
Answers
Answer:
85÷4=21.25 is the anwer
if i was asked to think of a number and multiply it by 2, I could write this algebraically as 2x Write the following using x as your unknown. "I think of a number, take away 1 and multiply the result by 3.
Answers
Step-by-step explanation:
(x - 1)×3
a random number minus 1, and the result is multiplied by 3.
bingo !
Answer:
3(x - 1).
Step-by-step explanation:
Taken away 1 is x - 1
Multiply this by 3 is 3(x - 1).
There are 777 students in a class: 222 boys and 555 girls. If the teacher picks a group of 333 at random, what is the probability that everyone in the group is a girl?
Answers
The probability is 0.1429.
The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:
5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.
The probability that everyone in the group is a girl is 2/7.
What is probability?Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.
Total number of students in a class = 7
Number of boys students = 2
Number of girls students = 5
The probability that everyone in the group is a girl is;
[tex]\rm Probability =\dfrac{Total \ number \ of \ girls}{Total \ number \ of \ boys}\\\\Probability=\dfrac{2}{7}[/tex]
Hence, the probability that everyone in the group is a girl is 2/7.
Learn more about probability here;
https://brainly.com/question/14461856
#SPJ4
Select the equivalent expression.
-3
24)
(9) 9
=?
62
Answers
Answer:
Step-by-step explanation:
???? Could you verify the question please?
200 dabloon bitcoins
Answers
Answer:
3b. [tex]\displaystyle 10; Mental\:Mathematics[/tex]
3a. [tex]\displaystyle \frac{5}{8} \times 16[/tex]
Explanation:
Dividing a mixed number\fraction is in similarity to multiplying its multiplicative inverce, which is what you see in the above answer. However, I did not figure it out this way. I did this:
[tex]\displaystyle \boxed{10} = \frac{5}{\frac{1}{2}} \Rightarrow \boxed{10} = \frac{5}{8} \div \frac{1}{16}[/tex]
Either way is fine, as long as you know what you are doing.
I am joyous to assist you at any time.
Which statement about the asymptotes is true with respect to the graph of this function f(x)= 3x^2-3/x^2-4
Answers
Answer:
D. The graph has two vertical asymptotes and one horizontal asymptote.
Step-by-step explanation:
Please Help me Its A Math Problem !!! I will AWARD BRAINLIST...
Answers
Answer:
no, the vertex of Function A is 6 units lower
Step-by-step explanation:
The vertex of Function A can be found several ways:
putting the equation in vertex formevaluating the function on the axis of symmetrygraphing the function__
Vertex FormTo put the equation in vertex form, we can consider separately the variabel terms and the constant. Once we have the variable terms separated, we can "complete the square" and then simplify the result to vertex form. The vertex form of a quadratic is ...
y = a(x -h)² +k . . . . for vertical scale factor 'a' and vertex (h, k)
We have ...
y = 2x² +12x +10
y = 2(x² +6x) +10
We complete the square by adding the square of half the x-coefficient inside parentheses. We subtract the same quantity outside parentheses, so we don't change the equation any.
y = 2(x² +6x +9) +10 -2(9)
y = 2(x +3)² -8 . . . . . . simplify to vertex form
The vertex of Function A is (-3, -8), which is (-2 -(-8)) = 6 units lower than the vertex of Function B in the graph. Bob is incorrect.
__
Axis of SymmetryThe axis of symmetry of quadratic expression ax² +bx +c is x=-b/(2a). For the given Function A, the axis of symmetry is ...
x = -12/(2(2)) = -3
The height of the vertex is the y-value for that x-value:
y = 2(-3)² +12(-3) +10 = 18 -36 +10 = -8
This is lower than the vertex of the graphed function, which is at y=-2. Bob is incorrect.
__
GraphingThe graph of Function A is the solid red curve in the attached. The graph of Function B is added as the dashed blue curve for reference. The graph clearly shows the vertex of Function A is lower than that of Function B. Bob is incorrect.
_____
Additional comment
Modern graphing calculators make the graphing option the quickest and easiest way to find the vertex of the function. The only "work" is to type the equation into the calculator.
Paul is running Tennis shop. He sells balls and rackets. Rackets (R) cost $1.20 each and Balls (B) cost $2:0 each. At the end of a month, Paul made a total of $70 and sold a total of 90 Rackets and Balls combined. Which system of equations represents this situation?
A. 2R + 1.20B = 90, B - R = 160.
B. 1.20R + 2B = 90, R - B = 90
C. 1.20R + 2B = 70, and R + B = 90
D. 1.20B + 2R = 90 and 2B + R = 70
Answers
The system of equations that represent the situation are 1.20R + 2B = 70, and R + B = 90.
What are the system of equations?
The system of equations are sets of equations that have to be solved simultaneously in order to determine their required values. They are often referred to as simultaneous equations.
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
7k^2=21,952
Volume of cylinders, cones, and spheres
What is the answer please
Answers
Answer:56Step-by-step explanation:7k²=21952
k²=21952/7
k²=3136
k=√3136
k=56
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ILL MARK BRAINILEST !! 80 POINTS
Question 1: 11 pts
Find the vertex of the parabola y = x2 - 10x + 16.
A. (-5,91)
B. (-9,5)
C. (5,-9)
D. (8,0) and (2,0)
Answers
Hope it helps!!!
Given g(x)=5x-3g(x)=5x−3, find g(-4)g(−4).
g(x)=5x-3
g(x)=5x−3
g(\color{green}{-4})=5(\color{green}{-4})-3
g(−4)=5(−4)−3
Plug input into x
-20-3
−20−3
Multiply
-23
−23
Answers
Answer:
the answer is 529
Step-by-step explanation:
see the explanation photo
the coordinating grid shows points L, M, N, and O. all the coordinates for these points are integers. what is the value of the x-coordinates of point M
Answers
Answer:
-6
Step-by-step explanation:
Hope this helps!!!
A triangular bandana has an area of 38 square inches. The height of the triangle is 9
inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base.
Answers
Answer:
Base=8.4 inches
Step-by-step explanation:
Area of triangular bandana is 38sq inches
Height of triangle is 9 inches
Area of ∆ =½×b×h
38=½×b×9
38×2=b×9
76/9=b
b=8.4 inches