A 100 m2hay shed is to be extended to give 475 m2of oor space in total, as shown. All angles are right angles. Find the value of x.
Answers
Answer:
[tex]x = 15.[/tex]
Step-by-step explanation:
Given
See attachment for floor space
Required
Find x
The floor can be partitioned into three space.
The dimension and the area of each space is:
Dimension: 10 by 10
[tex]A_1 = 10* 10 = 100[/tex]
Dimension: 10 by x
[tex]A_2 = 10* x = 10x[/tex]
Dimension: x by x
[tex]A_3 = x* x=x^2[/tex]
So, the total area is:
[tex]Area =100 +10x + x^2[/tex]
Given that:
[tex]Area = 475[/tex]
So, we have:
[tex]100+10x+x^2 =475[/tex]
Rewrite as:
[tex]x^2 +10x+100-475=0[/tex]
[tex]x^2 +10x-375=0[/tex]
Expand
[tex]x^2 + 25x -15x -375 = 0[/tex]
Factorize
[tex]x(x + 25) -15(x +25) = 0[/tex]
Factor out x + 25
[tex](x+25)(x-15)=0[/tex]
Solve:
[tex]x = -25\ or\ x = 15[/tex]
x cannot be negative; So:
[tex]x = 15.[/tex]
Related Questions
Here are some cards with angles written on them.
45°
165°
5°
90°
102°
31°
53°
Moira picks one of the cards at random.
What is the probability that the angle on the card is greater than 100°?
Answers
the answer is 165 I think because I didn't understand the question
Explanation: There are only two numbers that are greater than 100 (102,165). Divide the number of cards that are greater than 100° by the amount of cards that are given.
(2/7) = about 0.29
The average time it takes to travel from home to school is 22 ½ minutes. Depending upon weather and morning traffic, the actual time on a given day can vary up to 5 ½ minutes.
Answers
Answer:
[tex]17 \le t \le 28[/tex]
Step-by-step explanation:
Given
[tex]t = 22\frac{1}{2}[/tex] --- average time
[tex]\triangle t = 5\frac{1}{2}[/tex] --- the variation
Required
The inequality to represent the scenario
To do this, we simply add and subtract the variation from the average time.
i.e.
[tex]t \± \triangle t[/tex]
So, the inequality is:
[tex]22\frac{1}{2} - 5\frac{1}{2} \le t \le 22\frac{1}{2} + 5\frac{1}{2}[/tex]
Solve:
[tex]17 \le t \le 28[/tex]
Please help me solve my problem!!!
Answers
Answer:
180(n-2) or B
Step-by-step explanation:
Which expressions are equivalent to One-half + 3 c + StartFraction 4 Over 5 EndFractionCheck all that apply.
Answers
Answer:
(13+30c)/10
Step-by-step explanation:
Given the expression;
1/2 + 3c + 4/5
Find the LCM
= 5(1)+10(3c)+2(4)/10
= (5+30c+8)/10
= (13+30c)/10
Hence the required sum is (13+30c)/10
65 70 75 80 85
Brand A
HIH
15
50
60
70
85
Brand B
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Price ($)
Which statement is the most appropriate comparison of the spreads?
O A. The interquartile range (IQR) for brand A, $20, is less than the IQR
for brand B. $70.
O B. The median for brand A, $75, is greater than the median for brand
B, $60.
O C. The interquartile range (IQR) for brand A, $10, is less than the IQR
brand B. $20.
O D. The interquartile ranges (IQRs) for brands A and B are both $20.
Answers
Given:
Two box plots for Brand A and Brand B.
To find:
The correct statement for the given box plots.
Solution:
In a box plot, the left end of the box represents the first quartile [tex](Q_1)[/tex], right end of the box represents the third quartile [tex]Q_3[/tex] and the line inside the box represents the median.
The interquartile range of a data set is:
[tex]IQR=Q_3-Q_1[/tex]
From the box plot of Brand A, it is clear that
[tex]Q_1=70[/tex]
[tex]Median=75[/tex]
[tex]Q_3=80[/tex]
So, the interquartile range (IQR) for brand A is:
[tex]IQR=80-70[/tex]
[tex]IQR=10[/tex]
From the box plot of Brand B, it is clear that
[tex]Q_1=50[/tex]
[tex]Median=60[/tex]
[tex]Q_3=70[/tex]
So, the interquartile range (IQR) for brand B is:
[tex]IQR=70-50[/tex]
[tex]IQR=20[/tex]
The median for brand A, $75, is greater than the median for brand B, $60.
The interquartile range (IQR) for brand A, $10, is less than the IQR
brand B. $20.
Therefore, the correct options are B and C.
PLEASE HELPPPPP I NEED TO PASS SUMMER SCHOOL
Answers
Answer:
c
Step-by-step explanation:
used socratic
work out the m and c for the line: y=x-7
Answers
Answer:
Step-by-step explanation:
Compare the given y = x - 7 to the general slope-intercept formula
y = mx + b
Here the slope is 1 and the y-intercept, b, is -7.
Answer:
Step-by-step explanation:
Slope - y intercept form : y = mx +c
y = x - 7
m = 1
c = -7
There were 60 7th grade students last year in CHAMPS. This year, there are 48 7th grade students. What is the percent decrease from last year to this year?
Answers
20%
Hope this helps! :)
______________
What is the domain of the relation
graphed below?
Answers
Answer:
Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Step-by-step explanation:
wala muna akung ma explantion hahah sore
Which expression has the largest value? Each has as a factor. A 92 × 38\ \ \frac{9}{2}\ \times\ \frac{3}{8} 2 9 × 8 3 B 1089 × 38\frac{10}{89}\ \times\ \frac{3}{8} 89 10 × 8 3 C 123 × 381\frac{2}{3}\ \times\ \frac{3}{8}1 3 2 × 8 3 D 278 × 382\frac{7}{8}\ \times\ \frac{3}{8}2 8 7 × 8 3
Answers
Answer:
if your in high school why you need the answer
Step-by-step explanation:
t f
hi i am a boy that does math at school
help w this questionn ^^
Answers
Answer:
BC = 8 cm
Step-by-step explanation:
tan(x) = sin(x)/cos(x)
sin(x) is the opposite side of the angle x.
cos(x) is the side with a right angle to sin(x).
2 = 12/EC
EC = 12/2 = 6 cm
=>
CD = ED - EC = 10 - 6 = 4 cm
now, the same tan(x) relation had to be true for BCD.
tan(x) = BC/CD
2 = BC/4
BC = 8 cm
X
ſocm
Jicm
A) 2V5 cm
B) V13 cm
D) V19 cm
C) 1 cm
ASAP
Answers
Answer:
using pythagoras theorem
hyp 2=opp 2+adj 2
=( √6)(√6)+(√7)(√7)
hyp 2=13
hyp=√13
Given:
A right angle triangle with legs [tex]\sqrt{6}[/tex] cm and [tex]\sqrt{7}[/tex] cm. The length of the hypotenuse is x.
To find:
The value of x.
Solution:
Pythagoras theorem: In a right angle triangle,
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
Using the Pythagoras theorem, we get
[tex]x^2=(\sqrt{7})^2+(\sqrt{6})^2[/tex]
[tex]x^2=7+6[/tex]
[tex]x^2=13[/tex]
Taking square root on both sides, we get
[tex]x=\sqrt{13}[/tex] [Because side length is always positive]
The measure of hypotenuse is [tex]\sqrt{13}[/tex] cm.
Therefore, the correct option is B.
determinants and inverses
Answers
Answer:
qustion number 1 the last one .
qustion number 2 the first one .
8. Ethan has $63 in his bank account at the
end of June. During the month of June, he
deposited $285 and wrote cheques for $85,
$41, and $9. As well, he withdrew $75
from a bank machine.
a) Write an integer to represent the
value of Ethan's bank account at
the beginning of June.
Answers
Answer:
-$12
Step-by-step explanation:
Working backwards from the $63, you need to add back what was withdrawn and subtract what was deposited.
63+75+9+41+85-285= -$12
Please helpppp i have a test tomorrow the problem is in the picture below
Answers
Answer:
yes
Step-by-step explanation:
will give brainliest to correct answer
Answers
Answer:
A = 5
B = -13
C = 7
Step-by-step explanation:
The general formula of quadratic equation is ax^2+bx+c.
find the slope! i have more to come so please help:(
Answers
=================================
Work Shown:
Rise = -3
Run = 2
Slope = rise/run = -3/2 = -1.5
----------------
Notes:
The rise and run correspond to the vertical and horizontal portions of the triangle shownThe rise is negative because we're going downhill when moving from left to right, so that also means the slope is negative. The run is always positive.Answer:
m = - 3 / 2
Rise : -3
Run : 2
Step-by-step explanation:
According to the picture,
first coordinate : ( 2 , 1 )
second coordinate : ( 4 , - 2 )
Formulae : m=(y2-y1)/(x2-x1)
Substituting,
m = ( - 2 - 1 ) / ( 4 - 2 )
m = - 3 / 2
If this helps you, please mark brainliest!
Please help thank you! Brainliest
Answers
Answer:
D
Step-by-step explanation:
(-32÷4)^2 -9 + (-7)
=(8)^2 -9 + (-7)
Help me please. NO LINKS
Answers
Answer:
A. 7986.45
[tex] \frac{4}{3} \pir3[/tex]
Samantha places a mirror on the ground between herself and an apartment building and
stands so that when she looks into the mirror, she sees the top of the building. The center of
the mirror is 1.22 meters from her feet and 7.32 meters from the base of the building.
Samantha's eye is 1.82 meters above the ground. How tall is the building?
Answers
Answer:
The correct solution is "10.92 meters".
Step-by-step explanation:
The given values are:
Center of the mirror,
= 1.22 meters
Base,
= 7.32 meters
Samantha's eye,
= 1.82 meters
Let the height of the building will be "x".
Now,
The height of the building will be:
⇒ [tex]\frac{1.82}{x} =\frac{1.22}{7.32}[/tex]
By applying cross-multiplication, we get
⇒ [tex]x=\frac{1.82\times 7.32}{1.22}[/tex]
⇒ [tex]=\frac{13.322}{1.22}[/tex]
⇒ [tex]=10.92 \ meters[/tex]
Twenty planes are at an airport. Eight planes take off, then five planes land, then 7
more take off, then 9 land. How many planes are left at the airport? PLS HELPP
Answers
Answer:
19
Step-by-step explanation:
20 - 8 = 12
12 + 5 = 17
17 - 7 = 10
10 + 9 = 19
please help this is for my finalllll
Answers
Answer:
K= J-5
Step-by-step explanation:
Answer:
K=J-5
Step-by-step explanation:
First we have K+5=J, but we need to find K.
Move K to the other side of the equation, change the sign to subtraction, the opposite of addition, and there you have it!
K=J-5
Hope this helps!
--Applepi101
A bicycle tire has a radius of 26 inches. How many revolutions will this tire make if the bicycle is pedaled 1 mile? (Use 3.14 for π and 1 mile = 5280 feet).
Answers
Determine the domain of the following graph:
Answers
Answer:
-10<x<6
Step-by-step explanation:
Find where x starts and where x ends
What is the length of /AB?
Answers
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
Nigel has 2 dogs. One eats 2 1/2 pounds of food each week. The other eats 1 3/8 pounds each week. Together how much food do the dogs eat in a week
Answers
whole part = 3
fractional part = 7/8
===========================================================
Explanation:
1/2 = 4/8
So the mixed number 2 & 1/2 is the same as 2 & 4/8
Adding on 1 & 3/8 will mean the fractional portions add to 4/8+3/8 = 7/8 and the whole number portions add to 2+1 = 3
Overall, the total amount eaten is 3 & 7/8 pounds
Answer:
27 1/8 pounds
Step-by-step explanation:
2.5 multiplied by 7 would be 17.5 and 1 and 3/8's by 7 would be 7 multiplied by 3 = 21/8 which would be 9 and 5/8's added up with the first 7 pounds
Looking into the sky one night, Tori wondered how far into outer space she would get if she drove a car for 3.21 × 103 hours at a rate of 70mph. She calculated and determined that a car travelling at 70 mph covers approximately 1.13 × 105 meters per hour.
Tori wrote this expression to determine the distance she would travel into outer space.
(3.21 × 103)(1.13 × 105)
Estimate the distance travelled.
Almost-equals30 × 1015 meters
Almost-equals3 × 108 meters
Almost-equals30 × 108 meters
Almost-equals3 × 1015 meters
Answers
Answer:
the answer is B
Step-by-step explanation:
smort :)
Answer:
bbbbbbb
Step-by-step explanation:
I really need help with this problem
Answers
Answer:
Measure of angle K is 52.5 degrees
Step-by-step explanation:
Here, we have a case of two sides being congruent
mathematically when two sides are congruent, then we have an isosceles triangle
For an isosceles triangle, the base angles are equal
LM faces K , while M faces KL
What this mean is that L faces KM
From above, we can see that K = M = ?
Let us call this x
Mathematically, the sum of angles in a triangle is 180 degrees
75 + x + x = 180
2x = 180-75
2x = 105
x = 105/2
x = 52.5
!!!!!!!!!PLEASE HELP!!!!!!!!
Answers
Answer: D
Step-by-step explanation:
We're given a point (a,b) that happens to be on the unit circle, a²+b²=1, so a is the cosine of the angle θ and b is its sine.
Answer:
option 4
Step-by-step explanation:
what is the correct answer
Answers
Step-by-step explanation:
you tu tubless
ar vi ing
..............