Answer:
i) Her claim is incorrect
ii) see below
iii) 44 cm
Step-by-step explanation:
Given:
width of picture = x cmlength of picture = (x + 4) cmIf the picture is enlarged by a scale factor of 3 to form a poster, then the dimensions of the poster will be:
width of poster = 3x cmlength of poster = 3(x + 4) cmArea of rectangle = width × length
⇒ Area of poster = (3x) × 3(x + 4)
= 9x(x + 4)
= 9x² + 36x cm²
Part (i)Inputting x = 31 into the area of poster formula found above:
⇒ 9(31)² + 36(31)
= 8649 + 1116
= 9765 cm²
Therefore, as 9765 ≠ 1053 her claim in incorrect.
Part (ii)Using the formula for the area of poster found in part (i).
Area of poster = 1053 cm²
⇒ 9x² + 36x = 1053
⇒ 9x² + 36x - 1053 = 0
⇒ 9(x² + 4x - 117) = 0
⇒ x² + 4x - 117 = 0
Part (iii)First find x by solving the equation from part (ii):
⇒ x² + 4x - 117 = 0
⇒ x² + 13x - 9x - 117 = 0
⇒ x(x + 13) - 9(x + 13) = 0
⇒ (x - 9)(x + 13) = 0
⇒ x = 9, x = -13
As width cannot be negative, x = 9 only
Perimeter of picture = 2(width + length)
= 2(x + x + 4)
= 2(2x + 4)
= 4x + 8
Input found value of x into the expression for the perimeter:
⇒ Perimeter of picture = 4(9) + 8
= 36 + 8
= 44 cm
A square notepad has sides that are 10 centimeters long. What is the notepad's area?
Answer:
100cm²
Step-by-step explanation:
The notepad is square.
The area of a square = length X width.
All the sides of a square are the same length.
Therefore, the area of the notepad = 10 X 10 which equals 100.
Don't forget the units!
The units for area is cm².
The units for volume is cm³.
This is area so your answer is 100cm².
Hope this helped, have a nice day!
HELP ME AND ANSWER BOTH PARTS PLEASE!
Anyone know the answer?
James is using cement to make a new sidewalk and new steps.
He will make a new rectangular sidewalk that is 8 feet long, 4 feet wide, and 0.25 foot thick.
What is the volume, in cubic feet, of the cement used to make the sidewalk? Show or explain all of the steps you used to determine your answer.
Enter answer, including explanation, here
The volume, in cubic feet, of the cement used to make the sidewalk is 8 cu.ft.
What is a Cuboid ?A cuboid is a three dimensional figure with six rectangular faces .
The volume of the cuboid is given by
V = length * breadth * height
It is given in the question that
a new rectangular sidewalk that is 8 feet long, 4 feet wide, and 0.25 foot thick , this will be in the shape of a cuboid
The volume of cement required = 8 * 4 * 0.25
= 8 cu.ft
The volume, in cubic feet, of the cement used to make the sidewalk is 8 cu.ft.
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Ninety members of a gym were asked whether or not they use a treadmill when they exercise and whether or not they lift weights when they exercise.
The results of the poll are as follows:
14 members do not use a treadmill or lift weights
31 members use a treadmill but do not lift weights
28 members lift weights but do not use a treadmill
17 members use a treadmill and lift weights
Which two-way table represents the information found in the poll?
The answer is Y
Step-by-step explanation:
You have to compare the numbers with conditions both in Rows and Columns.
1. if axb = 0 then either a or b or both must equal....
Pleaseeee!
I need help evaluating this:
Tan 2 theta-(1-tan^ 2 )=?
Answer:
[tex]\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]
Key:
• [tex]-\left(a-b\right)=-a+b[/tex]
Step-by-step explanation:
[tex]\tan \left(2\theta\right)-\left(1-\tan ^2\left(\theta\right)\right)[/tex]
[tex]-\left(1-\tan ^2\left(\theta\right)\right)=-1+\tan ^2\left(\theta\right)[/tex]
[tex]=\tan \left(2\theta\right)-1+\tan ^2\left(\theta\right)[/tex]
Convert 5.6 times 10 to power of 4 to ordinary form
The points E(- 4, 6), F(- 6, - 2), G(2, - 4) , and H(4, 4) form quadrilateral EFGH. Plot the points then click the "Graph Quadrilateral " button.
The slope of EF, FG, GH, and HE is 4, -1/4, 4, and -1/4 respectively. And the length of sides EF, FG, GH, and HE will be √68, √68, √68, and √68 units respectively.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The points E(-4, 6), F(-6, -2), G(2, -4) , and H(4, 4) form quadrilateral EFGH.
Then the slopes are calculated below.
Slope of EF = (6 + 2)/(-4 + 6)
Slope of EF = 8/2
Slope of EF = 4
Slope of FG = (-4 + 2)/(2 + 6)
Slope of FG = -2/8
Slope of FG = -1/4
Slope of GH = (4 + 4)/(4 - 2)
Slope of GH = 8/2
Slope of GH = 4
Slope of HE = (6 - 4)/(-4 - 4)
Slope of HE = -2/8
Slope of HE = -1/4
Then the distance between the point will be
EF² = (-6 + 4)² + (-2 - 6)²
EF² = (-2)² + (-8)²
EF² = 4 + 64
EF = √68
FG² = (2 + 6)² + (-4 + 2)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
GH² = (4 - 2)² + (4 + 4)²
GH² = (2)² + (8)²
GH² = 4 + 64
GH = √68
FG² = (4 + 4)² + (4 - 6)²
FG² = (8)² + (-2)²
FG² = 64 + 4
FG = √68
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a water tap fills a tank within 4 hours, at the bottom of the tank
there is a hole for empty. the tank takes one hour to be empty. If the tap and the hole
are turning on together, the tank is fully filled. how long will the tank take to be completely
empty?
(70 min, 80 min, 90 min, 100 min)
Let V be the volume of the tank. The tap fills the tank at a rate of V/(4 hours), or V/4 per hour. The hole empties the tank at a rate of V per hour. If both the tap and hole work together, the net rate of water flow is V/4 - V or -3V/4 per hour.
Starting with a full tank, the volume v of water at time t is given by the function
v(t) = V + (-3V/4) t
Solve v(t) = 0 to find the time it takes to empty:
V - 3V/4 t = 0
V = 3V/4 t
t = V / (3V/4) = 4/3
So it takes 4/3 hours = 80 minutes to empty a full tank.
A physical therapist claims that 75% of people lose their balance if they close their eyes while standing on one foot. A gymnast feels that the rate is less than 75%. To test this, she randomly selects 100 people and finds that 80 of them lose their balance while standing on one foot. To determine if these data provide convincing evidence that the proportion of people who lose their balance while standing on one foot and closing their eyes is less than 75%, 150 trials of a simulation are conducted. The gymnast is testing the hypotheses: H0: p = 75% and Ha: p < 75%, where p = the true proportion of people who will lose their balance while standing on one foot and closing their eyes. Based on the results of the simulation, what is the estimate of the P-value of the test? A dotplot. A number line labeled simulated sample percentage of people who lose balance goes from 64 to 88 percent. 64, 3; 66, 3; 67, 4; 68, 8; 69, 5; 70, 7; 71, 8; 72, 11; 73, 15; 74, 12; 75, 11; 76, 8; 77, 18; 78, 10; 79, 10; 80, 5; 81, 4; 82, 2; 83, 2; 84, 1; 85, 2; 87, 1. 0.1133 0.17 0.887 0.92
Answer:
75
Step-by-step explanation:
becAUSE IF YOU TEST IT THATS UR ANSWER
Find each square (x+4)^2
Answer:
[tex]x^{2} +8x+16[/tex]
Step-by-step explanation:
There are 2 ways to find the square of a binomial. You can use FOIL or use a formula. Just remember that the square of a binomial will always be a trinomial.
FOIL
Since we are squaring a binomial we can rewrite the expression as (x+4) * (x+4). FOIL stands for First, Outside, Inside, Last. This explains how to multiply out 2 binomials. This method will give you 4 different terms that can then be combined to find the answer.
First - multiply the first terms of each binomial
x * x = [tex]x^{2}[/tex]Outside - multiply the terms on the outside of both binomials
x * 4 = 4xInside - multiply the terms on the inside of both binomials
4 * x = 4xLast - multiply the last terms of each binomial
4 * 4 = 16Now we can combine these terms to create the new polynomial [tex]x^{2} +4x+4x+16[/tex]. Then, combine like terms for the final answer: [tex]x^{2} +8x+16[/tex].
Shortcut
Another way to square binomials is to use the formula [tex]a^{2} +2ab+b^{2}[/tex], where a is the first term and b is the second term. So, for this formula, the binomial would look like (a+b).
So, we can apply this formula by plugging in x for a and 4 for b.
[tex]x^2+2*4*x+4^2[/tex]Then, multiply the middle term
[tex]x^{2} +8x+4^2[/tex]Finally, square 4
[tex]x^2+8x+16[/tex]This gives us the same final answer as the method above.
Step-by-step explanation:
(x+4)^2
you can also expand it
(x+4)(x+4)
x^2+4x+4x+16
x^2+8x+16
The graphs of f(x) = -2x and g(x)=()* are shown.
What are the solutions to the equation -2x = ()*?
Select each correct answer.
0-2
0 -1
02
04
-10-8-6-4
10
8
6-
72
-4
6
in
8
10+
2 4 6 8 10
The solutions to the equation -2x = 2^x are (1,2) and (2,4)
How to determine the solutions?The attached graph represents the missing part of the question
The equations are given as:
f(x) = -2x
g(x) = 2^x
The solution to -2x = 2^x is the points where the graphs of f(x) and g(x) intersect
From the attached graph, the points of intersection are:
(1,2) and (2,4)
Hence, the solutions to the equation -2x = 2^x are (1,2) and (2,4)
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please answer the question below, will give brainliest to first answer :)
Answer:
None of these answers are correct
Step-by-step explanation:
neither of them are rays.
a ray goes from the center to the edge of a circle.
What is 6x-6x56 =?
Show all work.
Answer:
6x-6x56 =-2016
Step-by-step explanation:
You have to subtract, then multiply by 56 to get -2016, as it shows a negative.
answer please image is below 35 points btw
The charge for renting a hedge trimmer is $10 plus $5 per day the total for renting a trimmer was $85. Which equation can you use to find the number of days the trimmer was rented? Please help !!!!
Answer:
15days.
Step-by-step explanation:
total amount=$85
renting amount=$10
amount per day=$5
to find the number of days the trimmer was rented it will be;
total amount-renting amount ÷$5
$85-$10÷$5
$75÷$5
=15days
Keith is working two jobs this summer as a lifeguard and a tutor. he earns $16 an hour as a lifeguard and $18 an hour as a tutor. he wants to earn at least $250 to put towards his car. what is one possible combination of hours he can work at each job to earn at least $250?
Answer:
He could work 10 hours as a lifeguard, and 5 hours as a tutor
Step-by-step explanation:
If he makes $16 an hour as a lifeguard
and $18 an hour as a tutor,
He could work 10 times $16, to make $160 for 10 hours.
Now we subtract this from $250, this makes $90.
We know need to find out how many times 18 goes into 90, 5 times.
So we know that he could work 10 hours as a lifeguard and 5 hours as a tutor.
I hope this is right.
I hope this helps too, have a nice day!
Mr. Fishie bought a tank for $15 and 10 fish which cost $f each. If he gave the cashier two 20-dollar bills, what was his change in terms of f?
Answer:
$25 - $10f
Step-by-step explanation:
Fishie's name is fishy.
We know Mr. Fishie spent $15 on a tank. His 10 fish cost 10*$f. His total is:
Total =15 + 10*f
His change after 2 $20 would be:
$40 - ($15 - $10f), or
$25 - $10f
Mike purchased a vehicle for Rs 59425 and spent Rs 8652 on repairs. How much did the vehicle cost him?
Answer:
68077
Step-by-step explanation:
he had spent 68077 because by 59425+8652 makes 68077
the amount (a) that principal (p) will be worth after t years at interest rate (r) compounded annually is
a = p(1 + r)^t
suppose $6,000 is invested at 5.5% and yields a total of $7,255. how many was it invested
The number of years the money was invested with annual compounding is 3.45 years.
How many years was it invested?When an amount earn interest compounded annually, it means that both the amount invested and the interest earned increases in value once a year.
Number of years = (In FV / PV) / r
Where:
FV = future valuePV = present valuer = interest rate(In 7255 / 6000) 0.055 = 3.45 years
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Drag the tiles to the correct boxes to complete the pairs.
Match the subtraction expressions with their answers.
From simplification of the given algebra, the correct answers are as shown below.
How to solve algebra problems?1) (a² - b)/(a³b²)
This reduces to;
(a²/(a³b²)) - b/(a³b²)
⇒ a/(ab²) - 1/(a³b)
2) The algebraic expression is;
(b - a)/a³b³
⇒ b/a³b³ - a/a³b³
⇒ 1/a³b² - 1/a²b³
3) The algebraic expression is;
(2 - ab²)/(a²b³)
⇒ (2/(a²b³)) - (ab²)/(a²b³)
⇒ 2/(a²b³)) - 1/(ab)
4) The algebraic expression is;
(2 - ab²)/(a²b³)
⇒ 2/(a²b³) - 1/ab
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
c. diameter
because when a line intersects the center and even touches the centre is called a diameter
hope it helps.
Answer:
C
Step-by-step explanation:
Diameter
Factor completely AND solve for the solutions of the quadratic.
The mean of a set of 10 number is 56,
If the mean of the first nine is 55 find the 10th number
Answer:
65
Step-by-step explanation:
10*56=5609*55=495560-495=65=65A car travelled a distance of 50km in an hour.what distance did it travel in 30min at the same speed?
Answer:
The car would have traveled 25 km.
Step-by-step explanation:
Set up the Proportion [tex]\frac{50}{60} = \frac{x}{30}[/tex]. Solving that proportion gets you an answer of 25, getting you the answer 25 km in 30 minutes. I hope this helps! :)
Paula walks 1/12 mile in 5/3 minutes. What rate is equivalent to the rate she walked?
The rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute
Calculating RateFrom the question, we are to determine the rate which is equivalent to the rate Paula walked
Using the formula,
[tex]Rate = \frac{Distance}{Time}[/tex]
From the given information,
Distance = 1/12 mile
Time = 5/3 minutes
Putting the parameters into the formula, we get
[tex]Rate =\frac{\frac{1}{12} }{\frac{5}{3} }[/tex]
[tex]Rate = \frac{1}{12} \div \frac{5}{3}[/tex]
[tex]Rate = \frac{1}{12} \times \frac{3}{5}[/tex]
[tex]Rate = \frac{3}{60}[/tex]
[tex]Rate = \frac{1}{20}[/tex] mile/minute
Hence, the rate that is equivalent to the rate Paula walked is 1/20 mile/minute OR 0.05 mile/minute
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solve these algebraic fractions please with step by step explanation would be great
Answer:
first ans =x-7
second ans= x+y/x-y
Step-by-step explanation:
I think you would get it and it doesn't need explanation.
!!20 POINTS AND BRAINLIEST!!! HELP ASAP!!!
How much ribbon would be needed to go around a package that had a length 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3 centimeters?
(show work)
Answer:
23cm
Step-by-step explanation:
If you multiply like terms you will get the answers. Then you add last to get 23cm
The required length ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).
Given that,
Package that had a length of 2x^2+3x-5/x^2+x-3 centimeters and width x^2-x-5/x^2+x-3.
How much ribbon would be needed to go around the package in centimeters is to be determined.
Perimeter is the measure of the figure on its circumference.
The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
Quantity of ribbon = perimeter of the rectangular package
= 2 * length + 2* width
= 2 * (2x^2+3x-5/x^2+x-3) + 2(x^2-x-5/x^2+x-3)
= 2 (3x^2 + 2x -10) / (x^2 + x - 3)
Thus, the required length of ribbon needed to go around the package is 2(3x^2 + 2x -10) / (x^2 + x - 3).
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Factor: 5x2 – 15x – 20.
(a) 5(x-4)(x+1),
(b) -2(x-4)(x+5),
(c) -5(x+4)(x-1),
(d) 5(x+4)(x+1).
Answer:
[tex]a)~5(x-4)(x+1)[/tex]
Step-by-step explanation:
[tex]~~~5x^2 -15x -20\\\\=5(x^2 -3x -4)\\\\=5(x^2 -4x +x -4)\\\\=5\textbf{[}x(x-4) +(x-4)\textbf{]}\\\\=5(x-4)(x+1)[/tex]
3.3.1. Calculate the new cost per night of the standard and family standard chalets. Round of (4) your answer to the nearest hundred. 3.3.2. Calculate the percentage increase that Pule proposes for the Luxe suite. Use the following formula: Percentage Difference Original 1 x 100% (3) 3.4. Pule decides to run a special on the Family standard chalet. He will charge: R4 000 per night but will decrease the amount by R100 per person occupying the chalet. 3.4.1. Use the information above to complete the table below: Number of 1 2 3 4 5 8 9 10 people(c) 4 000 3 900 Cost per night (R) (n) (3) 3.4.2. Write an equation that shows the relationship between the cost per night C and the number of people staying in the chalet n. (3) 3.4.3. The graph below shows the cost of renting the family standard chalet at the usual rat On the same set of axes, draw the graph that represents renting the chalet at the spe rate. (Remember to include all missing graph elements). (4)
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in math when you do not know the exact number in a calculation.
Given that:
Pules Rs 4000 per night but will decrease the amount by R100 per person occupying the chalet.
Number of People Cost per night
1 4000
2 3900
3 3800
4 3700
5 3600
6 3500
7 3400
8 3300
9 3200
10 3100
let C be cost per night and n be the number of people of staying in chalet.
equation: C= 4000-100(n-1)
for n=1: C= 4000- 0=4000
n=2, C= 4000-100(1)= 3900
The graph is attached below:
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