Answer:
width=x
length=5x
area= 300ft2
area=lxb
300=5x(x)
300=5x^2
x^2=60
x=7.74
7.74(5)=38.7
dimensions are 38.7ft by 7.74 ft
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Step-by-step explanation:
the area of a rectangle is
length × width = 300 ft²
length = width + 5
(width + 5) × width = 300
width² + 5×width = 300
width² + 5×width - 300 = 0
the general solution to such a quadratic equation is
width = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 5
c = -300
width = (-5 ± sqrt(5² - 4×1×-300))/(2×1) =
= (-5 ± sqrt(25 + 1200))/2 =
= (-5 ± sqrt(1225))/2 = (-5 ± 35)/2
width1 = (-5 + 35)/2 = 30/2 = 15 ft
width2 = (-5 - 35)/2 = -40/2 = -20 ft
negative lengths for an actual object don't make sense, so width = 15 ft is our solution.
length = width + 5 = 15 + 5 = 20 ft
how to ask a girl out on a date
Answer:
1. you can ask directly or indirectly
For the figure shown on the right, find the value of the variable and the measures of the angles.
***
R
(3x+15)°
(x-20)
Answer:
x = 37 , ∠ P = 17° , ∠ Q = 126° , ∠ R = 37°
Step-by-step explanation:
the sum of the 3 angles in Δ PQR = 180°
sum the 3 angles and equate to 180
x + x - 20 + 3x + 15 = 180
5x - 5 = 180 ( add 5 to both sides )
5x = 185 ( divide both sides by 5 )
x = 37
Then
∠ P = x - 20 = 37 - 20 = 17°
∠ Q = 3x + 15 = 3(37) + 15 = 111 + 15 = 126°
∠ R = x = 37°
Question 1
What is a counterexample for the conjecture?
If the perimeter of a rectangle is 40 units, the area must be at least 1 square unit.
OA) A square with a side length of 10 units has a perimeter of 40 units and an
area of 100 square units.
OB) A rectangle with length 19.99 units and width 0.01 unit has a perimeter of
40 units and an area of 0.1999 square unit.
OC) A rectangle with length 15 units and width 5 units has a perimeter of 40
units and an area of 75 square units.
OD) A rectangle with length 40 units and width 0.0125 unit has a perimeter of
80.025 units and an area of 0.5 square unit.
The counterexample for the conjecture If the perimeter of a rectangle is 40 units, the area must be at least 1 square unit is: A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.
What is counterexample?The term counterexample refers to an instance or example that makes the statement false. This is used in logic to check if a statement is true or not. Counter example tend to counter the statement being discussed with valid points.
The question wants to show the relationship that may exist between perimeter and area of a rectangle.
The counterexample provided the dimensions that gave the perimeter which is 40 but failed to give area of 1 square unit
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Draw and label center D at (-4,-2)
PLEASE HELP!!
SEE PICTURES!
Answer: G=62, I = 62, H =54
Step-by-step explanation:
3x+26=4x+14
x=12
G=36+26 = 62
180-62-62=54
Mike says the opposite of 5 is –5 and the absolute value of 5 is –5. Is he correct?
Use the drop-down menus to explain your answer.
I don't know what the dropdown menus are, but Mike is half-correct. The opposite of a number is the number with the opposite sign, so the opposite of 5 is -5. But the absolute value of a number is its distance from zero on a number line, and distances can't be negative, so the absolute value of 5 is 5, not -5.
find c for this equation!
ab + c = d
Answer:
c=d-ab
Step-by-step explanation:
ab+c=d
move over to the other side
change sides change signs
c=d-ab
Answer:
c=d−ab
Subtract ab from both sides of the equation
the sum of simple interest and compound interest of a certain interest on a sum of money for 2 years at the rate of 7% p.a is Rs 85470. by how much percent the compound interest is more than the simple interest?
Answer: 3.3%
Step-by-step explanation:
Principal not given.
SI = PRT/100
CI = P(1+R/100)^T -
SI + CI = 85470
[P×7×2]//100 + P [1+ (7/100)]^2 = 85470
on solving: P = 3,00,000
P = 300000 SI for 2 years = 42000
CI = Rs 43470
The difference= Rs 1470
as percentage to CI = [1470/ 43470] ×100
= 3.38%
A triangle has three sides: AB, BC, CA. We know that angle A is greater than angle C. Find the range for side AC.
A) AB< CA< BC
B) BC- AB < CA < AB + BC
C) BC< CA< AB
D) AB + BC < CA < BC- AB
Answer:
BC- AB < CA < AB + BC
Step-by-step explanation:
The sides opposite the larger angles are longer than the sides opposite smaller angles.
So, BC (opposite < A) is longer than AB (opposite < C) so,
BC > AB
The other side AC cannot be greater than AB + BC, otherwise the triangle would not exist, so,
AC < AB + BC
Also, CA > BC - AB
The range for AC is
BC- AB < CA < AB + BC
I dont even need help with the question.
[tex]32^{\frac{1}{25}}\cdot 2^x ~~ = ~~8^{\frac{1}{4}}\implies (2^5)^{\frac{1}{25}}\cdot 2^x~~ = ~~(2^3)^{\frac{1}{4}}\implies 2^{\frac{5}{25}}\cdot 2^x~~ = ~~2^{\frac{3}{4}} \\\\\\ \stackrel{same~exponent}{\underset{same~base}{2^{\frac{5}{25}+x}~~ = ~~2^{\frac{3}{4}}}}\implies \cfrac{5}{25}+x~~ = ~~\cfrac{3}{4}\implies \cfrac{1}{5}+x~~ = ~~\cfrac{3}{4}[/tex]
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{1}{5}+x \right)~~ = ~~20\left( \cfrac{3}{4} \right)}\implies 4+20x~~ = ~~15 \\\\\\ 20x=11\implies {\Large \begin{array}{llll} x=\cfrac{11}{20} \end{array}}[/tex]
how do you solve i?
9 = i +7
show your work
Answer: i is just a variable I believe so _ + 7 = 9
So i (<- the variable) would = 2
Step by step
Please help
Answer:
its 3 because 4^-n=1/256
We move all terms to the left:
4^-n-(1/256)=0
We add all the numbers together, and all the variables
-n+4^-(+1/256)=0
We add all the numbers together, and all the variables
-1n-(+1/256)=0
We get rid of parentheses
-1n-1/256=0
We multiply all the terms by the denominator
-1n*256-1=0
We multiply elements
-256n-1=0
We move all terms containing n to the left, all other terms to the right
-256n=1
n=1/-256
n=-1/256
Find a term that results in 66x^9 when multiplied by 22x^-3
Answer: 3x^12
Step-by-step explanation:
66 / 22 = 3
We can add exponents when multiplying them.
-3 + 12 = 9
Marco needs to buy some cat food. At the nearest store, 3 bags of
cat food cost $17.25. How much would Marco spend on 6 bags of
cat food?
Marco would spend $ on 6 bags of cat food.
Answer: 34.50
Step-by-step explanation: Since 3 bags cost 17.25 and Marco would buy 6, 3 times 2 is 6 so 17.25 times 2 is 34.50
find the sum by using a number line -9+8=
Hello! So...
We are given the following to solve:
[tex]-9+8=?[/tex]
In order to solve this, we simply need to add.
[tex]-9+8=-1[/tex]
Hence, our solution is -1, and would be marked -1 on a number line. Graph is displayed below.
____________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Show that quadrilateral ABCD is a parallelogram.
Slope of AB = 2; Slope of DC = 2
Slope of AD = -1/2; Slope of BC = -1/2
Both pairs of opposite sides are parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.
What is a Parallelogram?A parallelogram is a quadrilateral that has two pairs of opposite sides that have the same lengths and are parallel to each other.
Since the opposite sides of a parallelogram are parallel, therefore, they have the same slope value.
Slope = change in y / change in x.
Find the slope of AB and DC. then AD and BC:
Slope of AB = (-2 - 2)/(-3 -(-1)) = -4/-2
Slope of AB = 2
Slope of DC = (-3 - 1)/(-1 - 1) = -4/-2
Slope of DC = 2
Slope of AD = (-3 -(-2))/(-1 -(-3)) = -1/2
Slope of AD = -1/2
Slope of BC = (2 - 1)/(-1 - 1) = 1/-2
Slope of BC = -1/2
Therefore, since AB and DC have the same slope, they are parallel, so also is AD and BC parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.
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WHAT IS 483 AS A DECIMAL
Answer: 0.483
Step-by-step explanation: add a zero and a point to the right f it
super genius people. here question mark
[tex]3 \sqrt{5} - 2 \sqrt{7} + \sqrt{9 \times 5} - \sqrt{4 \times 7} \\ = 3 \sqrt{5} - 2 \sqrt{7} + ( \sqrt{9} \times \sqrt{5} ) - ( \sqrt{4} \times \sqrt{7} ) \\ = 3 \sqrt{5} - 2 \sqrt{7} + 3 \sqrt{5} - 2 \sqrt{7} \\ = 3 \sqrt{5} + 3 \sqrt{5} - 2 \sqrt{7} - 2 \sqrt{7} \\ = 6 \sqrt{5} - 4 \sqrt{7} [/tex]
OPTION C IS THE ANSWER.
Answer:
6√5 - 4√7
Step-by-step explanation:
hope it helps!!
jeremy and his dad are sharing the responsibilities for their new plumbing company. combined, jeremy and his dad worked at least 85 combined hours last week. they collected a total of more than $1000 by charging $20 per hour. let x
The system of inequalities that models the situation is given as follows:
x + y ≥ 85.20(x + y) ≥ 1000.x ≥ 0.y ≥ 0.Which system of inequalities models the situation?Before we build the inequalities, we have to consider that the variables of the system are given as follows:
Variable x: Number of hours worked by Jeremy.Variable y: Number of hours worked by his dad.Jeremy and his dad worked at least 85 combined hours last week, hence the first inequality is:
x + y ≥ 85.
They collected a total of more than $1000 by charging $20 per hour, hence the second inequality is:
20x + 20y ≥ 1000.
20(x + y) ≥ 1000.
The minimum number of hours that each can work is of 0, that is, they cannot work a negative number of hours, hence the constraints are:
x ≥ 0.y ≥ 0.What is the missing information?The problem is incomplete, and it asks for the system of inequalities that models the situation.
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Simplify.
6‾√+36‾√
Responses
182‾√
18 2
436‾‾‾√
4 36
18
18
46‾√
Based on the information illustrated, it should be noted that 6 × ✓3 .will be 36.
How to calculate the value?It should be noted that the information that's illustrated has to do with the square root of numbers. It should be noted that a square root simply means a number that when multiplied by itself will be able to give the original number that's given in the question.
Based on the information, the numbers will be illustrated thus:
6 × ✓36
It should be noted that ✓36 = 6
Therefore, 6 × ✓36
= 6 × 6
= 36
Therefore, the correct option is 36.
Note that the options aren't well written.
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Which of the following is an arithmetic sequence?
A) 3, -3, 4, -4, 5, -5
B)1, 2, 4, 7, 10
C) 4, 7, 10, 13, 16
D)2, 4, 8, 16, 32
Answer:
The answer is C
Step-by-step explanation:
The increase between the numbers in a arithmetic sequence is always the same, in this case the number always increased by 3.
Here is a another example
3, 5, 7, 9
The difference between the consecutive terms is always 2
I will give brainliest
The algebraic equation and the original price is:
original price - discount = sales price
x - 27 = 89
x = 116
What is the original price?An algebraic equation is made up of two expressions that are made up of variables or numbers that are connected by an arithmetic operation.
A discount reduces the price of a good or service. In order to determine the price of a good after the discount has been applied, subtract the amount of the discount from the original price of the item.
original price - discount = sales price
x - 27 = 89
Combine similar terms: x = 89 + 27
Add similar terms together: x = 116
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Select three names for the angle.
Answer:
Step-by-step explanation:
Here, what they're really saying is to find 3 different ways to rearrange the letters A, B, and C. Then, put them together to give the angle a combination of "names"
(1 ABC
(2 BAC
(3 CAB
Hope this helps! :D
Kevin has x dollars in an account that pays 2.2% interest, compounds quarterly. Express his balance after one quarter algebraically
Balance of Kevin after 1 quarter will be 1.0055(x)
What is quarterly compounded compound interest?Compound interest is interest that is calculated using both the starting amount and the interest that has accrued over time.
Interest is considered to be compounded quarterly if it is compounded four times each year.
If interest is compounded four times or quarterly each year, the formula for the amount at time t is as follows.
A = P( ( 1 + (r/4))⁴ⁿ
A = Accumulated amount
P= Principal amount
r = interest rate
n = time
Given that Kevin has x dollars in an account that pays 2.2% interest, compounds quarterly
∴ P = x
r = 2.2% = 2.2/100
To find balance after one quarter , i.e. time n = 1/4 year
⇒ Balance = accumulated amount =$ x(1 + 2.2/400)¹ = $ 1.0055(x)
Therefore, Balance of Kevin after 1 quarter will be 1.0055(x)
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find the value x in the triangle
Answer:
x = 5
Step-by-step explanation:
Comment
The three sides need to add up to 23 (the perimeter is given as 23)
Givens
The sides are
x (x + 3)2xThe perimeter is 23Solution
x + x + 3 + 2x = 23 Combine
4x + 3 = 23 Subtract 3 from both sides
4x + 3-3 = 23-3 Combine
4x = 20 Divide by 4
4x/4 = 20/4
x = 5
The three sides of a triangle is x, x+3 and 2x. If the perimeter is 23 feet. Find the value of x.
Explanation -:In this question we are given
the perimeter of a triangle is 23 feet.sides of the triangle xx+3 2x.We are asked to calculate the value of x.
To solve this problem first we have to form an equation.
Let us solve this question.
We know that the perimeter of a triangle is the sum of all three sides.
According To Question
x + x + 3 + 2x = 23
→ 2x + 3 + 2x = 23
→ 4x + 3 = 23
→ 4x = 23 - 3
→ 4x = 20
→ x = 20/4 = 5
x = 5
The value of x is 5.
[tex] \rule{70mm}{2pt}[/tex]
Read the screenshot, please.
Answer:
You need at least 101 cans of food in order to meet or surpass the goal.
Step-by-step explanation:
a.
135+89=224
224+c>=325
b.
224-224+x>=325-224
x>=101
You need at least 101 cans of food in order to meet or surpass the goal.
40 point question!! Functions. (ignore pencil marks)
Answer:
[tex]\textsf{D)} \quad P(n)=0.024n^2-0.3n+4.3[/tex]
Step-by-step explanation:
From inspection of the graph, when the number of coils is 10, the length of the spring is between 0 cm and 20 cm.
Substitute n = 10 into the equation of each given answer option:
[tex]\begin{aligned}\textsf{Option A}: \quad P(10)&=10^2+4.3\\ & =100+4.3\\&=104.3\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Option B}: \quad P(10)&=10^2-0.3(10)+4.3\\ & = 100-3+4.3\\&=97+4.3\\&=101.3\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Option C}: \quad P(10)&=0.24(10^2)+4.3\\&=0.24(100)+4.3\\&=24+4.3\\&=28.3\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Option D}: \quad P(10)&=0.024(10^2)-0.3(10)+4.3\\ & = 0.024(100)-3+4.3\\&=2.4-3+4.3\\&=-0.6+4.3\\&=3.7\end{aligned}[/tex]
Therefore, as 0 < P(10) < 20, the only suitable equation is Option D:
[tex]\boxed{P(n)=0.024n^2-0.3n+4.3}[/tex]
Write a complete two-column proof for following information.
B
C
Given: AB = 3y - 1, BC = 7y, AC = 29
Prove: AB = 8
Hence proved that triangle AB = 3(3) - 1 = 9 - 1 = 8.
What is triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.
Given that,
AB + AC = AC
3y - 1 + 7y = 29
10y = 29 + 1 = 30
y = 30/10 = 3
Therefore, AB = 3(3) - 1 = 9 - 1 = 8.
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-4(-6-b)=1/3(B+16) solve for B ANSWER NOW PELASE.
The simplified solution for B in the equation -4 ( - 6 - b) = 1/3 (B + 16) is B = 56 + 12b
Given,
The equation: - 4 (- 6 - b) = 1/3 (B + 16)
We have to simplify the equation and find B.
Lets simplify:
-4 ( - 6 - b) = 1/3 (B + 16)
Here,
(- 4 × - 6) - 4 × - b = 1/3 × B + 1/3 × 16
24 + 4b = B/3 + 16/3
24 + 4b = (16 + B) / 3
Multiply 3 to both sides:
(24 + 4b) × 3 = (16 + B) × 3 / 3
72 + 12b = 16 + B
Add -16 to both sides:
72 + 12b - 16 = 16 + B - 16
Then,
B = 72 + 12b - 16
B = 56 + 12b
That is, the simplified solution for B in the equation -4 ( - 6 - b) = 1/3 (B + 16) is B = 56 + 12b
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Find the 10th term of the geometric sequence 8,-16,32,…
Answer: -4096
Step-by-step explanation: Use the geometric sequence formula to find the 10th term (image attached). So, the 10th term = 8(-2)^9
Note: the common ratio can be found by 2ndterm/1stterm
Answer:
a₁₀ = -4096
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence:
[tex]\boxed{a_n=ar^{n-1}}[/tex]
where:
aₙ is the nth term.a is the first term.r is the common ratio.n is the position of the term.Given terms of the geometric sequence:
a₁ = 8a₂ = -16a₃ = 32To find the common ratio (r), divide consecutive terms:
[tex]\implies \dfrac{a_3}{a_2}=\dfrac{32}{-16}=-2[/tex]
Substitute the values of a and r into the formula to create an equation for the nth term of the sequence:
[tex]\implies a_n=8(-2)^{n-1}[/tex]
To find the 10th term of the sequence, substitute n = 10 into the equation:
[tex]\begin{aligned}\implies a_{10}&=8(-2)^{10-1}\\&=8(-2)^{9}\\&=8(-512)\\&=-4096\end{aligned}[/tex]
Therefore, the 10th term of the given geometric sequence is -4096.
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