[Mathematical Solutions]
1.) [tex]\frac{2}{7} + \frac{1}{4} = \frac{15}{28}[/tex]
2.) [tex]\frac{5}{9} +\frac{3}{8} = \frac{67}{72}[/tex]
3.) [tex]3\frac{5}{6} - 2\frac{7}{15} =\frac{41}{30}[/tex] as the Exact Form, or [tex]1\frac{11}{30}[/tex] as the Mixed Number Form.
Hope this helps!
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
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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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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What’s APY? can someone please simplify the definition.
APR, or effective annual rate, can also be called an effective annual rate or EAR when "r" is the annual interest rate and "n" is the number of compounding periods to be completed each year. :D
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
(help quick please) Solve
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
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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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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36x² - 65x + 25 = 0
Work out the value of x.
Let’s solve this step-by-step
First factor the equation,
(9x - 5) (4x - 5) = 0
Then set each factor equal to zero,
9x - 5 = 0 and 4x - 5 = 0
Both x = 5 / 9 or x = 5 / 4 are correct
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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. 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
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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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!
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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Simplify
6-√√25
4
DONE
11
Answer:
1/4, alternate forms are .25 and 2^-2
Step-by-step explanation:
Square Root of 25 is 5
6-5 =1
1/4
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.
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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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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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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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
Paula walked on the treadmill for 11 minutes. The machine told her she had a total of 759 strides. What was her rate in strides per minute?
A.
69 strides per minute
B.
70 strides per minute
C.
67 strides per minute
D.
68 strides per minute
Answer:
A. 69 strides per minute
Step-by-step explanation:
In order to find the strides per minute divide 759 by 11
➟ 759/11
➟ 69
∴ Her rate was 69 strides per minute
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.
HALP I NEED HALP AND I DONT GOT A LOT POINTS LEFT PLS I NEED THIS.
Its just vector sums pls help
thunder from a bold of lightning travels 1/10 mile 1/2 second. At this rate how many miles can it travel
in one second
Thunder from a bolt of lightning can travel 1/5 miles in one second.
Given, distance = 1/10 mile and
time = 1/2 second .
we need to find distance travelled in one second.
The distance travelled by thunder bolt from lightning in one second can be calculated using unitary method. So, to calculate we will relate the known distance with given time. Further, we will compare it at with desired time.
So, distance travelled in 1/2 second = 1/10 mile
Hence, distance travelled in 1 second = 1/10 ₊ 1/10
Shifting 2 to the numerator and 10 to the denominator. The new fraction will be -
Distance travelled in 1 second = 2/10 = 1/5
Distance travelled in 1 second = 1/5 mile
Hence, thunder from a bolt of lightning can travel 1/5 miles in one second.
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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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3x{12-[2x(12-3-2x3)]+4
Answer:
30
Step-by-step explanation:
Quadratic Formula
What is the difference between −125 and 18?
someone help me with thisss
The equation of the line that is perpendicular to the given line and that passes through the given points is x + 3y = 6
From the question, we are to determine the equation of the described line.
First,
We will determine the slope of the line that the equation was given.
The equation of the line is
y = 3x - 9
Comparing the equation to the general form of the equation of a straight line
y = mx + b
Where m is the slope
and b is the y-intercept
Thus,
By comparison,
m = 3
That is, the slope of the given line is 3
NOTE: Two lines are perpendicular if the product of their slope is -1.
That is,
m₁ × m₂ = -1
3 × m₂ = -1
m₂ = -1/3
The slope of the line that is perpendicular to the given line is -1/3.
We have that the line passes through the point (3, 1).
Then,
Using the point-slope form of the equation of a line
y - y₁ = m(x - x₁)
m = -1/3
x₁ = 3
y₁ = 1
Then,
y - 1 = -1/3(x - 3)
Multiply through by 3
3(y -1) = -1(x - 3)
3y - 3 = -x + 3
3y + x = 3 + 3
x + 3y = 6
Hence, the equation of the line that is perpendicular to the given line and that passes through the given point is x + 3y = 6
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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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