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Related Questions
A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x^2−6x+9 yd^2.
Area of the flagpole plot: x^2−6x+9
Find the length of the base of the flagpole by factoring. (Hint: Because the area of the flagpole is an expression that involves the variable x, the length of the base will also involve the variable x.)
The length of the base of the flagpole is
Answers
Answer:
[tex]x-3[/tex]
Step-by-step explanation:
The area of the flagpole base is [tex]x^2-6x+9\ \text{yd}[/tex]
where the factor of the equation is the length of the base.
In order to find the length we need to factorize the equation
[tex]x^2-6x+9[/tex]
[tex]=x^2-3x-3x+9[/tex]
[tex]=x(x-3)-3(x-3)[/tex]
[tex]=(x-3)(x-3)[/tex]
The length of the base of the flagpole is [tex](x-3)\ \text{yd}[/tex].
The area of a square base is the product of the side lengths.
The length of the base is x - 3
The area is given as:
[tex]\mathbf{Area =x^2 - 6x + 9}[/tex]
Expand
[tex]\mathbf{Area =x^2 - 3x - 3x + 9}[/tex]
Factorize
[tex]\mathbf{Area =x( x- 3) - 3(x - 3)}[/tex]
Factor out x - 3
[tex]\mathbf{Area =( x- 3) (x - 3)}[/tex]
Express as squares
[tex]\mathbf{Area =( x- 3)^2}[/tex]
Rewrite the area as:
[tex]\mathbf{Length^2 =( x- 3)^2}[/tex]
Take square roots of both sides
[tex]\mathbf{Length =x- 3}[/tex]
Hence, the length of the base is x - 3
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The parallelogram shown bellow has an area of 15 units over 2
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Answer:
The value of h is [tex]\frac{5}{2}[/tex] units
Step-by-step explanation:
In any parallelogram, there are two different pair of bases b1, b2 and their corresponding heights h1, h2, where h1 ⊥ b1 and h2 ⊥ b2The area of parallelogram = b1 × h1 OR b2 × h2In the given figure
∵ Every two opposite sides of the parallelogram are equal
∴ The length of the base of the height h is 3 units
∵ The area of the parallelogram = [tex]\frac{15}{2}[/tex] units
∵ Area of parallelogram = b × h
→ Substitute the values of the area and the base in the rule above
∴ [tex]\frac{15}{2}[/tex] = 3 × h
∴ [tex]\frac{15}{2}[/tex] = 3h
→ Divide both sides by 3 to find h
∵ [tex]\frac{15}{2}[/tex] ÷ 3 = 3h ÷ 3
∴ [tex]\frac{15}{6}[/tex] = h
→ Simplify the fraction by divide up and down by 3 and switch the 2 sides
∴ h = [tex]\frac{5}{2}[/tex] units
A photographer charges a sitting fee of $15 plus $3 for each pose. Write a function to describe the situation. Find a reasonable domain and range for up to 5 poses.
Please help i really don't understand how to find the domain and range.
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Answer:y=3x+15
Step-by-step explanation: (1,18), (2,21), (3,24), (4,27), (5,30) domain is your x values 1,2,3,4,5. Range is your y values. I’d assume someone wouldn’t pay $15 for 0 poses.
The function for the given situation is f(x)=15+3x and a reasonable domain and range for up to 5 poses is 5 and 30 respectively.
Given that, a photographer charges a sitting fee of $15 plus $3 for each pose.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Let the number of poses be x and the total cost be y.
The function for the given situation is y=15+3x
Thus, f(x)=15+3x
For 5 poses:
Put x=5 in the obtained function, we get
f(5)=15+3(5)
= 15+15
= 30
So, the ordered pair is (5, 30)
Hence, the function for the given situation is f(x)=15+3x and a reasonable domain and range for up to 5 poses is 5 and 30 respectively.
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Which fraction and decimal forms match the long division problem?
Answers
Answer:
0.44444444
Step-by-step explanation:
Answer: 4/9 and 0.4 repeating
Step-by-step explanation:
Given: AB ∩ CD = O, m∠NOD = x,m∠AON = 44º, m∠BOC = 102º.
Find: x.
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Answer:
x= 58
Step-by-step explanation:
minus 44 from 102
• The packages of henna powder cost $12 each and the squeeze
bottles cost $3 each. What is Sushmila's total cost for the supplies?
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Answer:
Step-by-step explanation:
If she is just buying one henna package and one squeeze bottles the total is 12 + 3 which is 15
Answer:
27
Step-by-step explanation:
I got it right
Write the equation of the line that is parallel to y = -2x + 4 and passes through (3, 1) in slope-intercept form.
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Answer:
y = -2x + 7
Step-by-step explanation:
y = -2x + 4
Slope in above equation is -2. Parallel lines share the same slope so the new equation will also have a slope of -2.
y-intercept through point (3, 1):
y = mx + b
1 = -2(3) + b
1 = -6 + b
b = 7
Equation of line that is parallel to original:
y = mx + b
y = -2x + 7
The difference of 9 and three times a number is that number increased by 5. Find the number. just give me the equation
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Answer:
9-3n=n+5
Step-by-step explanation:
n= the number
3
3. Write an expression that is equivalent to
5
(3y + 15). (4 points)
O 3
-y + 9
5
03
-y + 15
5
09
5
Y + 9
09
- y + 15
5
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Answer:
9/5y+15
Step-by-step explanation:
A tourist can bicycle 26 miles in the same time as he can walk 6 miles. If he can ride 10 mph faster than he can walk, how much time should he allow to walk a 25-mile trail
Answers
Answer:
It would take him 3 miles to talk a 25-mile trail
Step-by-step explanation:
The employees at a bank ordered 2 turkey sandwiches and 4 salads from a local deli. The total cost for the order was $23. If a salad costs $1 less than a turkey sandwich, what is the cost of a turkey sandwich and the cost of a salad?
Answers
Answer:
Cost of turkey sandwich is $4.50 and cost of salad is $3.50
Step-by-step explanation:
Let cost of 1 turkey sandwich be $t and cost of 1 salad be $s.
2t + 4s = 23 --(1)
s + 1 = t
s = t - 1 --(2)
Sub (2) into (1):
2t + 4(t - 1) = 23
6t - 4 = 23
6t = 27
t = 4.5
sub t = 4.5 into (2):
s = 4.5 - 1
s = 3.5
therefore, cost of turkey sandwich is $4.50 and cost of salad is $3.50
The odds against an event are 19 to 12 find the probability that The event will occur
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Answer:
the event is odds against an event of the 19 to 12 is probability is the 19
The probability of occurring the event is 12/31.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
We know if the odds against an event is a : b then the probability of occurring the event is b/(a + b).
Given, The odds against an event are 19 to 12.
∴ The probability of occurring the event is 12/(19 + 12) = 12/31.
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The area of a rectangle is 72 square metres. The length of the rectangle is twice the width. Find the width of the rectangle.
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Working:
Find common factors of 72:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Work out which ones multiply together to make 72 and as the question states that the length is twice the width, we need to find two numbers that multiply to make 72 and one of the numbers is double the other number.
These numbers would be 6 and 12. (6 x 12 = 72)
Therefore:
Area = 72m²
Width = 6m
Length = 12m
6. Melanie put $1500 into an account 2 years later the account was worth $1700.
What was the interest rate of the investment?
(8 Points)
6.67%
8.089
17. 196
44.796
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please help answer
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Answer: C.
Step-by-step explanation: The side opposite the smallest angle in a triangle is the shortest side, and vice versa. Thus, we can say that WY is the shortest, XY is the medium, and WX is the longest. Thus, the answer is C.
Answer:
I honestly dont knoooooow
What value should go in the empty boxes to complete the calculation for finding the product of 0.61 x 0.45? Both numbers are the same, however, only input the number one time in your answer.
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Answer:
the empty boxes would both be 4
but it says only put the number one time in answer
so it would be 4
Step-by-step explanation:
The original price of a shirt was 20$. It decreased to 15$. what is the percent decrease of thee price of this shirt ?
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Six comics are to perform on a single evening. Find the probability
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Answer:
1 in 6
Step-by-step explanation:
Find the x-intercept of each line defined below and compare their values.
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x intercept of line b is (1,0)
The x intercept of line A is (-6, 0) and x intercept of line B is (3, 0)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Equation of line A
y=-2/3x-4
When y=0
0=-2/3x-4
4=-2/3x
-6=x
So the x intercept for line A is -6.
Let us find equation of line B by using table
Slope = -1
Now let us find y intercept
2=-1(-1)+b
b=3
So equation is y=-x+3
Now let us find the x intercept
Put y=0
0=-x+3
x=3
(3, 0) is x intercept of line B
Hence, the x intercept of line A is (-6, 0) and x intercept of line B is (3, 0)
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Can you guys please with me out with the question please
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Answer:
Team score in first game < 19
Step-by-step explanation:
Point Scored in Third Game =X
Points Scored in First Game = X+6 (6 more than third game)
Points Scored in Second Game = 23
Total Points ={( First Game) +( Second Game) + (Third Game)} < 55
{ ( X+6) + (23) + (X)} < 55
X+29+X < 55
2X+29 < 55
2X< 55-29
2X < 26
X <26/2
X<13
So the point scored in First game is: (X+6)
Where X < 13
So the point in First game is < 19
3. Lisa's checking account charges her a $35 overdraft fee plus the purchase amount
for each purchase that cause her account balance to go below or stay below $0.
On Monday, her account balance was only $40. She made the following purchases
in order:
$25 on a gift for her friend
$10 on fast food
$37 on groceries
$15 on gas
She then deposited a $650 check into her account.
What is her new account balance? IS
(8 Points)
5498
$533
$568
$603
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In what year did WW1 begin
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Answer:
28 July 1914 – 11 November 1918
please mark me brilliant
Answer:
It started on: July 28, 1914
Step-by-step explanation:
It ended on – November 11, 1918
Evan's favourite hobby is origami. He plans to make 100 paper cranes to hang from the ceiling of his bedroom. Yesterday, he made 28 paper cranes in 4 hours. Today, he made 21 paper cranes at the same rate.
How long did Evan spend making paper cranes today?
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Answer:
it took him 3 hours
Step-by-step explanation:
28 divideed by 4= 7
21divided by 7=3
A checking account is overdrawn if it has a
negative balance. Marc's account is overdrawn by
$45. What will the balance be after he deposits
$170 and writes a check for $59?
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Answer:
64.
Step-by-step explanation:
170 - 59 = 109
109 - 45 = 64
or do
59 + 45 = 104
104 - 170 = 64
Answer: it’s 66
Step-by-step explanation:
ljfehhgsdddzcSDJCHjgsDdlhfcgadscbsdhcSDMlnSBDZx
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Answer:
?
Step-by-step explanation:
Can anyone help me find the value of x of this mid segment triangle?
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Answer:
Step-by-step explanation:
You have the correct answer. The sides are cut in half. 16 and x are in the same ratio 2:1
16 / 8 = 2:1
at 6:00 PM it’s 24°F at midnight the temperature was 636°F lower than Apple what will the temperature at midnight
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Answer:
A)12 F.
Step-by-step explanation:
PICTURE PLEASEEEEEEEEEEE
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Answer: C
Step-by-step explanation: Because none of the triangles are the same.
A Salesman earns 8% commission on all the merchendise that he sells. Last month he sold $4000 worth of merchandise. How much commission ( in dollars) did he earn last month?
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Answer:
$320
Step-by-step explanation:
For this question, you just need to find 8% of $4000.
1. Convert 8% to a decimal. 8% = 0.08
2. Multiply. 0.08 ($4000) = $320
Myra is cooking meat the double number line shows that he needs 12 hours too cook 5 kilograms of meat how long does myron need to cook 3 kilograms of meat
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Step by Step Explanation: 12 divided by five equals 2.4
2.4 times 3 equals 7.2