Answer:
The dimensions of the rectangle are length = 22 meters and width = 13 meters.
Step-by-step explanation:
It is given that the length of a rectangle is 4 meters less than twice the width and if the area of the rectangle is 286 square meters we need to calculate the dimensions.
Firstly, let us look at the dimensions of the rectangle;
=> Let 'l' be the length and 'b' be the width of the rectangle.
Now, let us look at the area of a rectangle;
=> l × b
So, we get an equation from the above condition;
=> l = 2b - 4
Now, the area of the rectangle is given that is 286 square meters;
=> A = 286 sq. m.
Using the above-mentioned formula for the area of the rectangle we get;
=> A = l × b
=> 286 = (2b - 4) × b
=> 286 = 2b² - 4b
=> 2b² - 4b - 286 = 0
After solving it further we get;
=> 2b² - 4b - 286 = 0
=> b² - 2b - 143 = 0
=> b² - 13b + 11b - 143 = 0
=> (b - 13) + (b + 11) = 0
Now, after equating both the sides we get;
=> (b - 13) = 0
=> b = 13
and
=> (b + 11) = 0
=> b = -11
But, b = -11 is not possible so, the width of the rectangle is 13 meters.
And the length of the rectangle would be,
=> l = 2b - 4
=> l = 2 × 13 - 4
=> l = 22
Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters.
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If a recipe serve six people and requires one 1/2 cups of flour, how much flour do you need if you are serving 15 people? Write your answer as a decimal rounded to the nearest hundredth.
Answer:
Step-by-step explanation:
1 1/2 cups = 1.05
Nicole and Kiri are evaluating the conditional If 15 is a prime number, then 20 is divisible by 4. Both think that the conditional is true, but their reasoning differs. Is either of them correct? Explain.
Neither of Nicole and Kiri are correct that evaluating the conditional If 15 is a prime number, then 20 is divisible by 4.
Nicole reasoning is incorrect because despite the fact that 20 is divisible by 4, it does not mean the conditional is true. The conditional states that “15 is a prime number”- this is incorrect. Because this is incorrect the validity of the conclusion does not justify the validity of the hypothesis. Kiri’s reasoning is inaccurate despite the fact that his explanation of the hypothesis is correct, the hypothesis has no direct implication on the conclusion.
Hence, their belief that the conditional is true are both wrong. A conditional is only true if the premise for that conditional is first true in itself and also directly affects the conclusion.
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Find the distance from point A(−14, 5) to the line −x+2y = 14. Round your answer to the nearest tenth.
Approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.
The perpendicular line to a point is the path that travels the shortest distance between them.
The equation for the indicated line is -x + 2y = 14, which can be expressed as the following in slope and intercept form:
-x + 2·y = 142·y = 14 + xy = 14/2 + x/2 = x/2 + 7y = x/2 + 7The y-intercept is 7, and the slope, m1, is 1/2.
As a result, the slope, m2, of the line perpendicular to the line y = x/2 + 7 (y = -x + 2y = 14) is m2 = -1/m1 = -1/(1/2) = -2.As a result, we know that the line from A(-1/4, 5) to the line -x + 2y = 14 has a slope of -2.Consequently, the line's equation is:
y - 5 = -2(x - (-1/4))y - 5 = -2·x - 1/2y = -2·x - 1/2 + 5 = -2·x + 9/2y = -2·x + 9/2Therefore, the coordinates of the point on line A(-1/4, 5) that coincides with the perpendicular from the line -x + 2y = 14 (y = x/2 + 7) are as follows:
-2·x + 9/2 = x/2 + 79/2 - 7= x/2 + 2·x-2.5 = 2.5·xx = -2.5/2.5 = -1x = -1y = x/2 + 7 = -1/2 + 7 = 6.5y = 6.5The location on the line -x + 2y = 14 (y = x/2 + 7) that is perpendicular to the point A(-1/4, 5) has the coordinates: (-1, 6.5)
The following formula is used to calculate the distance between points A and B:
[tex]l=\sqrt{\left(y_2-y_1\right)^2+\left(x_2-x_1\right)^2}[/tex]Where: (x₁, y₁) = (-1/4, 5), and (x₂, y₂) = B(-1, 6.5)
Using the values as plug-ins, we have;
[tex]\begin{aligned}&I_{A B}=\sqrt{(6.5-5)^2+((-1)-(-1 / 4))^2}=\sqrt{(-0.75)^2+(1.5)^2}=\sqrt{\frac{45}{16}}=\frac{3}{4} \cdot \sqrt{5} \\&l_{A B}=\frac{3}{4} \cdot \sqrt{5} \approx 1.677\end{aligned}[/tex]
Therefore, approximately 1.7 units separate A(-1/4, 5) from the line -x + 2y = 14.
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Simplify each expression.
ln e⁸³
ln e⁸³ = 83, by definition and properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
As seen by the definition of logarithms, [tex]log_b(a)=x[/tex]In case of natural logarithm, b = e, i.e., [tex]log_e(a)=x[/tex] = ln (a) = xIn the question, ln (e)⁸³, a = e
By property of logarithms, [tex]log_b(a)^{m}=m(log_b(a))[/tex],
=> 83 (ln (e)) = 83 [tex]log_e(e)[/tex]
Since, [tex]log_e(e)[/tex] = 1, ln (e)⁸³ = 83 (1) = 83.
Hence, ln e⁸³ = 83, by definition and properties of logarithm.
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Can someone please describe the domain and range in these sets?
Answer:
a.
D=[-6,4)
R=(-3,4]
b.
D=[-6,7)
R=[-1,6)
Step-by-step explanation:
[,] <-- used for when the point is included in the answer (closed circle or greater than/less than or equal to sign)
(,) <-- used for when the answer does not include point (open circle or greater than/less than sign not equal to)
Plug in the points where shown on each line.
Hey again! Just answered your last domain and range question so I hope I helped again!
Twelve boxes each containing 8 packets of sweets is redistributed into 4 larger boxes. How many packets are there in each of the larger boxes if the sweets were evenly distributed?
Answer:
24
Step-by-step explanation:
8 * 12 = 96
96 / 4 = 24
Have a great night! :D
Hope this helps.
Maddie is buying flour to make cookies for a bake sale. At the store a 3 pound bag costs $3.69. She needs 25 pounds of flour to make enough cookies for a bake sale. How much will it cost for the flour?
Cost of 25 pound flour is $30.75.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Price of 3 pound flour = $3.69
She needs 25 pounds of flour to make enough cookies for a bake sale.
Now, Price of 3 pound flour = $3.69
Hence, Cost of 1 pound flour = $3.69 ÷ 3 = $1.23
So, Cost of 25 pound flour = 25 x $1.23
= $30.75
Therefore, Cost of 25 pound flour is $30.75.
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. The perimeter of a rectangular pool is 74 feet. The width
is 9 feet shorter than the length. What is the length and
width of the pool?
Answer: the length is 23 feet the width is 14 feet
Step-by-step explanation:
Let the length is x feet
Hence, the width is (x-9) feet
The perimeter of a rectangular pool is:
P=(2)(x+(x-9))
74=(2)*(2x-9)
74=(2)(2x)-(2)(9)
74=4x-18
74+18=4x-18+18
92=4x
(4)(23)=(4)(x)
Divide both parts of the equation by 4:
23 feet=x
23-9=x-9
14 feet=x-9
Find the new given amount given the original amount and the percent of change
$7; 20% increase
The new amount is $ __
Answer:
8.4
Step-by-step explanation:
7 x .2 is the increase 1.4
Add 1.4 to 7 to get 8.4
A periodic function goes through 5 complete cycles in 4 min . What is the period of the function?
(A) (1/5) min (B) (1/4) min (C) 48 s (D) 75 s
The period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
A periodic function goes through 5 complete cycles in 4 min
From the question:
f = 5/4 cycles per minutes
f = 5/240 cycles per seconds [1 minutes = 60 seconds]
f = 1/48
Period = 1/f
Period = 48 minutes
Thus, the period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.
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The period of the given periodic function is 48 sec.
What is periodic function?
A periodic function is a function which returns same values at regular intervals. Let f be a periodic function then
f( x +P ) = f(x) , for every x in the domain of f and P is some non zero constant
P is the regular interval or period after which a periodic function returns same values.
P=[tex]\frac{1}{f}[/tex]
where [tex]f[/tex] is the frequency of the periodic function
or [tex]f[/tex] = no of cycles per unit time
Given that a periodic function goes through 5 cycles in 4 min
therefore frequency for this periodic function , f is given by
[tex]f=\frac{5}{4}[/tex] cycles per min
or
[tex]f=\frac{5}{4*60} \\f=\frac{5}{240} \\[/tex]
[tex]f=\frac{1}{48}[/tex] cycles per sec
Thus,
Period of the given periodic function , P =[tex]\frac{1}{f}=1/\frac{1}{48}=48[/tex] sec
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If C=24, what values of A and B complete Ax+By=C for each graph? Write the standard form for each equation.If C24, what values of A and B complete for each graph? Write the standard form for each equation.
The standard form for the equation of this line is equal to 3A - 4B = 12.
What is a linear equation?A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
In Mathematics, the standard form of a linear equation is given by the following:
Ax + By = C.
When C = 24, the line passes through point (4, 0) and we have;
Ax + By = C.
4A + B(0) = 24.
4A = 24
A = 24/4
A = 6
When C = 24, the line passes through point (0, -3) and we have;
A(0) + B(-3) = 24
-3B = 24
B = -24/3
B = -8
Therefore, the standard form for the equation of this line is given by:
6A - 8B = 24
Dividing all through by 2, we have:
3A - 4B = 12
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Solve each equation. Check your answers.
log 2 x=-1
log (2x) = -1 => x = 0.05, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: log (2x) = -1
Raising both sides to 10, in order to remove the logarithm:
=> [tex]10^{log_{10}(2x)} = 10^{-1}[/tex]
=> 2x = [tex]\frac{1}{10}[/tex] ( as [tex]a^{log_a(x)} = x[/tex])
=> x = [tex]\frac{1}{20} =[/tex] 0.05
Hence, log (2x) = -1 => x = 0.05, by properties of logarithm.
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PLEASE HELP ASAP!!!
Answer: y = x + 4.
Reason: -2 + 4 = 2 and -1 + 4 = 3 so, any equation added with 4 would be y or x + 4 = y.
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Simplify each expression.
3¹/₄+27¹/₄
The expression has to be written in it's prime factor form. 27 = 3x3x3 = 3^3 in index form. 3=3^1 . By power rule (a^m)^n = a^mn.
(3^1)^1/4+(3^3)^1/4
3^1/4 + (3^2x3^1)^1/4
3^1/4+3^2/4x3^1/4
3^1/4(1+3^1/2)
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3x{12-[2x(12-3-2x3)]+4
Answer:
30
Step-by-step explanation:
Quadratic Formula
Multiply and simplify. √5 x³ . √40 x y⁷
On simplifying the expression √5 x³ . √40 x y⁷ we get 10√2 x⁴y⁷
How do we multiply numbers?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.
Given,
√5 x³ . √40 x y⁷
⇒ √5 × √40 × x⁴ × y⁷
⇒ √200 × x⁴y⁷
⇒ 10√2 x⁴y⁷
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Use a table to solve each equation. Round to the nearest hundredth.
6²x=10
[tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: [tex]6^{2x} = 10[/tex]
Taking logarithm on both sides:
=> log ([tex]6^{2x}[/tex]) = log 10
=> 2x (log 6) = log 10 ( as [tex]log_b(a)^m = m (log_b(a))[/tex])
=> 2x = [tex]\frac{log10}{log6}[/tex]
=> 2x = [tex]\frac{1}{0.778}[/tex]
=> 2x = 1.285
=> x = 0.642
Hence, [tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.
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Which of the following could represent the cost of 5 t-shirts and a $7 tax?
Answer:
y = 5x + 7
Step-by-step explanation:
I am guessing, but you are leaving something out.
y = the total cost.
x = the number of shirts.
Answer:
The total cost for the 7 shirts including tax is 7n + 6
Step-by-step explanation:
We want to find the Cost of 7 t-shirts and $6 tax.
Now, the let the cost of the 7 shirts be n. Thus, we can now say that cost of 7 shirts is 7n.
Now, since there is an additional cost of $6 for tax, we can now say that the total cost for the 7 shirts including tax is expressed as;
7n + 6
Thus, we conclude that the total cost for the 7 shirts including tax is 7n + 6
btw Zarahs office is 2cm wide and 4 cm long
The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office
Given data
Zarah's office is 2 cm wide and 4 cm long
Another office is 8 cm long and 4 cm wide
How to solve for the size of the officesArea of an office = length * width = long * wide
Area of Zarah's office = 4 cm * 2 cm = 8 cm2
Area of another office = 8 cm * 4 cm = 32 cm2
comparing the two areas
say by how much is 32 cm2 greater than 8 cm2
32 cm2 / 8 cm2 = 4
The statement the office is twice as large as Zarah's office is inappropriate, from the calculation it was solved to be that the office is 4 x Zarah's office.
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What is the arithmetic mean between 5 and 19
Answer:
the arithmatic mean of 5 and 19 is: 5,7,9,11,13,15,17,19.
Step-by-step explanation:
hope this helps
Mr. Smith's water bill for this month is $5988, how many units does he use if the cost per unit is $41? (show working)
Please help!!!! w+ 5w + 4 = 3 (2w - 1) Show your work!!!!
Answer:
No solution
Step-by-step explanation:
Given equation:
[tex]w+5w+4=3(2w-1)[/tex]
Distribute the parentheses:
[tex]\implies w+5w+4=3 \cdot 2w- 3 \cdot 1[/tex]
[tex]\implies w+5w+4=6w- 3[/tex]
Combine like terms:
[tex]\implies 6w+4=6w-3[/tex]
Add 3 to both sides:
[tex]\implies 6w+4+3=6w-3+3[/tex]
[tex]\implies 6w+7=6w[/tex]
Subtract 6w from both sides:
[tex]\implies 6w+7-6w=6w-6w[/tex]
[tex]\implies 7=0[/tex]
As 7 ≠ 0 there is no solution.
If point A is located at (5,-7), and there are 8 points between A and B , what could be the possible coordinates for points B ?
Possible coordinates for points B (-3, 13)
Given that
point A (5 , -7)
and there are 8 points between A and B.
The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.
The equation of a circle centerd in the point (x0, y0) is:
(x - x0)² + (y - y0)² = r²
where r = radius of the circle
So we can draw a circle of 8 units around A, and get:
(X - 5)² + (Y - (-7))² = 8²
So from this equation we can find all the possible values of B.
Y = √(8² - (X- 5)²) - 7
So for a given value of X, you can find the value of Y. where (8² - (X-5)²) can not be a negative number, so
8² ≥ (X - 5)²
So X = -3 (because (-3 - 5)² = 8²)
to X = 13 (because (13 - 5)² = 8²)
So X is in the range (-3, 13)
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Suppose that x and y vary inversely. Write a function that models each inverse variation and find y when x=-5 . x=12 when y=4
Using inverse variation, the function model will be y = 48. 1/x and the value of y at x = -5 will be -48/5
What precisely is the inverse of a function?Those with inverse properties cancel each other out. In other words, f(g(x)) = g(f(x)) = x if g(x) is f's inverse (x). We have a great approach we can use to achieve this given an equation for which we desire the inverse.
Not every action has an equivalent. It is obvious that f(x) will never again have the same value if it has an inverse. We designate a unique name for this resource.
Inverse variation is y = k. 1/x
given y = 4
x = 12
So, 4 = k. 1/12
So, the value of k = 48
We can conclude that the value of constant variation is 48
when x = -5, the value of y will be -
y = k.1/x
y = 48 . 1/-5
y = -48/5
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What is the difference between −125 and 18?
At a sale, dresses were sold for $56 each. If the dresses originally cost $200 each, what percentage of its original price was a dress sold for?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The percentage at which the dress was sold from its original price is 28%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The selling price of the dress = $56
The original price of the dress = $200
The percentage at which the dress was sold from its original price.
= 56/200 x 100
= 56/2
= 28 %
Thus,
The percentage at which the dress was sold from its original price is 28%.
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In figures, ____ matching marks show that line segments have the same length. (Fill in the blank)
Answer:
hatch
Step-by-step explanation:
the hatch marks on the triangle represent the same length
if a side has one hatch mark it has the same length as the other side with one hatch mask
the same goes for the one with two hatch marks
Solve the equation −128 = 4x for x.
The solution for x in the equation -128 = 4x is -32
The collection of values used to replace the unknowns in an equation to make it true is known as the solution. Two fundamental algebraic laws, the additive property and the multiplicative property, are utilized to find the solutions to equations with a single unknown raised to a single power.
Given that,
The equation: -128 = 4x
We have to find x:
That is:
-128 = 4x
x = ( -128 / 4 )
x = -32.
Therefore, the solution for the given equation -128 = 4x is -32.
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The velocity v of an object dropped from a tall building is given by the formula v=√64d , where d is the distance the object has dropped. Solve the formula for d .
The distance, d = v²/64.
Let 'v' denote the velocity of an object dropped from a tall building.
Let 'd' be the distance the object has dropped.
Given that the relation between v and d is, v =√(64d)
This equation gives 'v' in terms of 'd'.
We need to solve this formula for d.
For this, consider v =√(64d)
We square on both sides to get rid of the square root.
⇒ v² = 64d
Now isolating d to one side of the equation,
⇒ d = v²/64 is the formula for d
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I keep getting the answer of 28.89° but that’s wrong and I don’t know how to get to the right answer.
Answer:
for (a) i got 15
Step-by-step explanation:
AE=17, AB=16 which makes AM=8
so from there u do pythagorean theorem
17^2 - 8^2 = 225
√255= 15
Answer:
26.565⁰
Step-by-step explanation:
Triangles AEM and BEM are congruent since
AE = BE
m∠AME = m∠BME=90°
and EM is the common side
So AM = BM = AB/2 = 16/2 = 8
Triangle EAM is a right triangle with hypotenuse AE = 17 and AM = 8
So EM² = (17² - 8²) by the Pythagorean theorem
EM² = 289 - 64 = 225
EM = √225 = 15 cm
To find m∠ECM, note that triangle ECM is a right triangle with m∠EMC = 90° and the side opposite ∠EMC = EC, the side opposite ∠ECM is EM
By the law of sines
EC/sin90 = EM/sin(∠ECM)
So,
sin(∠ECM) = EM/EC since sin 90 = 1
So we have to compute EC
Again note that the triangle MCB with sides BM, MC and BC is a right triangle with m∠CBM = 90°
The hypotenuse is MC
So MC ² = MB² + BC² = 15² + 30² = 1125
MC = √1125 = 33.54 cm
Therefore
sin(∠ECM) = EM/MC = 15/33.54 = 0.4472
m∠ECM = sin⁻¹ (0.4472)
= 26.565⁰
To be honest I am not 100% sure of this answer, please check and see if this works. Thanks