Answer:
Width: 1694 cm or 16.94 m
Length: 1706 cm or 17.06 m
Step-by-step explanation:
1. Write out the known equations:
First, the equation for the perimeter of a rectangle:
[tex]Perimeter = 2(Width) + 2(Length)[/tex]
We also know that the rectangle is 12 cm longer than it is wide. This leads to the second equation:
[tex]Length=Width+12[/tex]
2. Solve the system of equations for width:
Since we know the length in terms of width, and we know the perimeter, we can plug these values into the equation for the perimeter. First, let's rearrange the equation for perimeter to solve for width:
[tex]Perimeter = 2(Width) + 2(Length)\\Perimeter-2(Length)=2(Width)\\2(Width)=Perimeter-2(Length)\\Width=\frac{Perimeter-2(Length)}{2}[/tex]
Now, plug in the known values (since there are 100 cm in one metre, I'm multiplying the perimeter of 68 m by 100 to convert to centimetres--the perimeter of 68 m is equal to 6800 cm):
[tex]Width=\frac{6800-2(Width+12)}{2}[/tex]
Now, solve the equation for width:
[tex]Width=\frac{6800-2(Width+12)}{2}\\2(Width)=6800-2(Width+12)\\2(Width)=6800-2(Width)-24\\2(Width)+2(Width)=6800-24\\4(Width)=6800-24\\4(Width)=6776\\Width=1694cm[/tex]
3. Solve for length using width:
Now that we know the width, we can easily solve for the length using our previously established equation for length, [tex]Length=Width+12[/tex], as shown:
[tex]Length=Width+12\\Length=1694+12\\Length=1706cm[/tex]
4. Convert to metres.
If you want to know the answer in metres, you can convert from centimetres by dividing by 100:
1694/100 = 16.94 m
1706/100 = 17.06 m
Need asap! Please!
Answer:
∠ 5 is the angle of depression
Step-by-step explanation:
angle of depression is the angle from the horizontal, downwards
from the diagram this is ∠ 5
Mrs. Morales wrote a test with 14 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. The maximum number of points possible on the test is 100.
Answer:
There are 10 spelling questions and 5 vocab questions
Step-by-step explanation:
5 questions total
Total number of points: 100
Spelling questions are worth 5 and represented by x
Vocab questions are worth 10 and represented by y
Therefore:x+y=15
5x + 10y= 100
So: x+y=15
x = 15-y
5x +10y =100
5(15 -y) +10y =100
75 -5y +10y =100
75 +5y = 100
5y=25
y=5
x +y=15
x+5=15
x=10
Did I do this equation correctly?
Answer:
yes you are, good job !
Step-by-step explanation:
(04.05 MC)
The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Emerson is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 1,264(1.09)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years.
r (number of years) 1,2,3,4.
g(r) (amount in dollars) 1,375, 1,512.50,1,663.75,1,830.13
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer.
Answer:
A) increasing by 9% each year
B) Account B
Step-by-step explanation:
[tex]f(x)=1264(1.09)^x[/tex]
Part A
The amount of money in account A is increasing by 9% each year.
General form of an exponential function: [tex]f(x)=ab^x[/tex]
[tex]a[/tex] is the initial value, [tex]b[/tex] is the growth factor and [tex]x[/tex] is time.
If b < 1 then the function is decreasingIf b > 1 then the function is increasingAs b = 1.09 > 1 then the function is increasing
[tex]b[/tex] is the decimal form of percentage change.
Therefore, for b > 1, percentage increase = b - 1
for b < 1, percentage decrease = 1 - b
So as b = 1.09 > 1, percentage increase = 1.09 - 1 = 0.09 = 9%
Part B
From inspection, the amount in account B is increasing exponentially.
Therefore, we can use [tex]y=ab^x[/tex]
To determine the growth factor [tex]b[/tex], divide one value of g(r) by its previous value:
[tex]\implies b=\dfrac{1512.50}{1375}=\dfrac{11}{10}=1.1[/tex]
[tex]\implies g(r)=a(1.1)^r[/tex]
To determine [tex]a[/tex], input a pair of values (r, g(r)) into the equation and solve:
[tex]\implies 1375=a(1.1)^1[/tex]
[tex]\implies a=\dfrac{1375}{1.1}=1250[/tex]
Therefore, the equation for account B: [tex]g(r)=1250(1.1)^r[/tex]
Comparing the growth factor [tex]b[/tex] of both equations, account B recorded a greater percentage change in amount of money over the previous year since 1.1 > 1.09
PleAse help number 14 please
Step-by-step explanation:
14.
G must be congruent to B (the vertexes with the right angle).
and then
GH = GF = CB = AB (they are both isoceles triangles meaning both legs have the same length, and then these legs must be congruent bergen the triangles, so, in fact, all 4 sides must have equal length).
therefore,
5y mm = 25 mm
y = 5
(2x + 5) mm = 25 mm
2x + 5 = 25
2x = 20
x = 10
(3z + 14) mm = 35 mm
3z + 14 = 35
3z = 21
z = 7
1)
Write as an algebraic inequality:
Twenty subtracted from the product of seven and a number exceeds one hundred.
What is an word expression for 2d + 7…. PLEASE I NEED AN ANSWER
Answer:
two and D plus seven
Thats what i believe it is.
OOPS I SENT IT IN BY MISTAKE I MEANT:
two and a number plus seven
I was breaking it down my bad
Answer: Frank went to the store and purchased $7 of merch. He later went to the supermarket and bought 2 packages of blueberries. How much money did he spend in total?= 2d+7
Step-by-step explanation:
Hope you understand!
work out the value of x
Answer:
[tex] x = 67.5 \degree[/tex]
Step-by-step explanation:
[tex]x + 3x + 90 \degree = 360 \degree \\ \\ \implies \: 4x = 360 \degree - 90 \degree \\ \\ \implies \: 4x = 270 \degree\\ \\ \implies \: x = \frac{270 \degree}{4} \\ \\ \implies \: x = 67.5 \degree[/tex]
Solve 8=2^(x+4)
A. X=-4
B. x= -1
C. X= 0
D. X=7
Answer:
[tex]\boxed{\underline{\tt B.\:x=-1}}[/tex]
Step-by-step explanation:
[tex]\tt 8=2^{(x+4)}[/tex]
(First, convert both sides to the same base):-
[tex]\tt 2^3=2^{x+4}[/tex]
(Now, cancel the base of 2 on both sides):-
[tex]\tt 3=x+4[/tex]
(Subtract 4 from both sides):-
[tex]x+4-4=3-4[/tex]
[tex]\tt x=-1[/tex]
~
The following shape has 1 pair of parallel sides.
10
10
7
What is the area of the shape?
units
Answer:
56 units squared
Step-by-step explanation:
First, we want to find the area of the triangle taken out of the top. We can tell that the rectangle area that it's in is 28 units because it's 7 across and 10-6=4. To find the area of a triangle you just divide that 28 by 2 to get 14. 70-14 is 56. Ik I'm not the best at explaining things so if you have any questions feel free to ask bc I explained this weirdly.
8. Evaluate:
-5•-√25=
Show work
Answer:
25
Step-by-step explanation:
" • " means multiply.
The value of √25 = 5
-5•-√25
= -5 x -5
= 25
plssssssssssssssssssssss helpppp
Answer:
1. (12+24+20+28)÷4=21
2. 6× 9^2= 486 cm^2
3. a. Length^2
b. Length× breadth
c. (1/2)× base × perpendicular height
area= (1/2)× 12cm × 13cm= 78 cm^2
perimeter = 14+14+12= 40cm
Step-by-step explanation:
In a class of 29 students, there are
15 boys.
Write a ratio of the
number of boys to girls.
Answer:
Number of students in 6th grade = 29
Number of boys = 15
Number of girls = 29-15 = 14
Ratio of boys to girls = 15 : 14
Step-by-step explanation:
smchmack me with dat brainliest
Answer:
15:14
Step-by-step explanation:
15 boys
total 29
29-15=14 because the rest of the class would have to be girls
I am composed of only rectangular faces. I have 8 vertices. I am a solid figure.
what am I?
Answer:
the answer for your question is "It's a cuboid"
Answer: Rectangular Prism
Step-by-step explanation:
Rectangular faces ✔️
8 vertices (4 on each side) ✔️
Solid figure ✔️
Giving brainliest !
3-1 4/6?
Answer:
[tex]\frac{4}{3}[/tex] or [tex]1\frac{1}{3}[/tex] (don't worry, they are the same thing)
Step-by-step explanation:
[tex]3-1\frac{4}{6}[/tex]
[tex]3-\frac{10}{6}[/tex]
[tex]\frac{18}{6} -\frac{10}{6}[/tex] (18/6 is equivalent to 3, and 10/6 is equivalent to 1 4/6)
[tex]\frac{8}{6}=\frac{4}{3}[/tex] (8/6 is equivalent to 4/3)
Hope this helps!
3 divided by 1107
SHOW WORK PLEASE WITH PICTURE
Answer: 1107 ÷ 3 = 369
Ok done. Thank to me :>
Write a recursive formula for An, the nth term of the sequence 8, 40, 200, ....
Answer:
I don't know the answer but have a amazing day!<3
Step-by-step explanation:
Be happy.
please show work, urgent thank you!
If the highest power of the numerator is less than the highest power of the denominator, then the limit as it approaches infinity is zero
Hope that helps!
10. The y-intercept uses which letter?
M
Z
B
Y
Answer:
if it were an equation it would be y = mx + b and B would be the y intercept and mx is slope.
Step-by-step explanation:
Hey there!
The y-intercept is
b
Remember Slope-Intercept form, where
m is the slope
b is the y-intercept
I hope you find my answer helpful.
Good luck!
Have a great day!
~Stars~
In basketball, Shaquille makes 40% of his free throw attempts. He goes to the free throw line to shoot one-and-one (if he makes the first shot, he gets to shoot one more). He scores 1 point per free throw. What is the expected value of the number of points he will score? 0. 064 0. 24 0. 56 0. 80.
Shaqquille's expected value is 0.56 points.
Step-by-step explanation:
Situations:
1) he makes 1st shot + he makes 2nd shot
P(A) = 0.4 · 0.4 = 0.16 ( 16 % )
2) he makes 1 st shot + he misses 2nd shot
P(B) = 0.4 · 0.6 = 0.24 ( 24 % )
3) he misses 1st shot and he has no more attempts
P (C) = 0.6 ( 60 %)
0.16 · 2 + 0.24 · 1 + 0.6 · 0 = 0.32 + 0.34 = 0.56
The expected value is 0.56 points.
) A comet travels at an average speed of 264,000 km/h. It takes 8 days for the comet to reach Earth. Find the distance, in km, the comet travelled.
Answer:
Distance the comet travelled: x
1 day = 24 hours
24 * 8 = 192 hours
x = 264,000 * 192 = 50,688,000 (because speed = distance/time, so distance = speed * time)
Awnser all please I am struggling on it *BRAINLIEST* reward
Answer:
a- she needss to buy 4 packs
b- he needs to buy 5 boxes
Step-by-step explanation:
hehe , give her brainliest
Directions: Find each of the following percentile points under the normal curve. Complete your procedures.
1. P90
2. P60
3. P30
A circle is cut in eighths. What is the angle measure of each piece?
Answer:
45°
Step-by-step explanation:
A circle is worth 360°. If you were to cut it into eights, you would be dividing 360 by 8, too.
360 ÷ 845Thus, the answer is 45°.
what is the value of the experession 1/8 dived by 3
Step-by-step explanation:
it will be 1/8x3
1/24
pls mark me brainlist
#6
In 2014, the average cost of a new car in the United States was 3.2 x 104 dollars.
About 1.6 x 10' new cars were sold in the U.S. during 2014. Which is the
approximate total cost of the cars sold in the U.S. during 2014?
How do i draw the pie chart, like where do i put the lines?
[tex]Answer:[/tex]
Here's a picture example!
What is the mode, median, maximum, and range in math?.
Answer:
In explanation
Step-by-step explanation
Ok for me to tell you I'm going to give an example.
Data set=
40,50,60,30,105,19,40
For this data set our mode would be 40 because mode is the number that appears most in a data set and as you can see 40 appears twice while every other number only appears once.
For median=would also be 40.
Because median is the number that is in the middle when you sort them least to greatest so 40 is in the middle when you put them in least to greatest.
The maximum is 105
Because the maximum is the highest number in the data set so 105 is the biggest number.
Range is 86.
For range is the highest number subtracting the lowest number and highest number is 105 and lowest number is 19 so 105 - 19=86
Hope this helps have a great day:)
Find the value of x.
PLEASE HELP ME!!!!!!!!!!
Solution:
Step-1: Find the missing side length using Pythagoras theorem:
115² = 69² + x²=> 13225 = 4761 + x²=> 13225 - 4761 = x²=> 8464 = x²=> x = √8464 = 92Step-2: Find the area of the rectangle:
Area of rectangle = LB=> 69 x (92 + 100)=> 69 x 192=> 13248 units²Apply Pythagorean theorem
[tex]\\ \rm\bull\rightarrowtail b^2=115^2-69^2[/tex]
[tex]\\ \rm\bull\rightarrowtail b^2=13225-4761[/tex]
[tex]\\ \rm\bull\rightarrowtail b^2=8464[/tex]
[tex]\\ \rm\bull\rightarrowtail b=92[/tex]
Now length=192Breadth=69Area=Length×Breadth
[tex]\\ \rm\bull\rightarrowtail Area=192(69)=13248units^2[/tex]
The wheel of a shopping cart that must be replaced is 3.5 inches in diameter. However, the only wheel you have is 2.75 inches in diameter. To keep the cart level, you must brace it out with a piece of metal. How much should you extend the new wheel out?
Answer:
you should extend the new wheel out by .75 cm
Step-by-step explanation:
2.75 + .75 = 3.5
