Final answer:
Erica will have 1 1/6 yards of fabric left after using 2/3 of the 3 1/2 yards she purchased to make a curtain.
Explanation:
The student's question is about how much fabric Erica will have left after using 2/3 of the 3 1/2 yards she bought to make a curtain. To solve this problem, we first need to convert the mixed number of yards of fabric to an improper fraction. We start by multiplying the whole number, 3, by the denominator of the fraction, 2, and then adding the numerator, 1. This gives us (3 × 2) + 1 equals 7, so Erica has 7/2 yards of fabric.
Next, we determine how much fabric she uses by multiplying 7/2 yards by 2/3. Doing the multiplication, (7/2) × (2/3), we can cancel out the common factor of 2 to simplify the calculation. The result is 7/3 yards of fabric used for the curtain.
To find out how much fabric is left, we subtract the used fabric from the total amount Erica originally had, which is 7/2 yards. So, we calculate 7/2 - 7/3 yards. To subtract these fractions, they need to have a common denominator. Multiplying 7/2 by 3/3 and 7/3 by 2/2 gives us equivalent fractions with a common denominator of 6. We now have (21/6) - (14/6) yards, and subtracting these gives us 7/6 yards of fabric remaining. This can also be represented as 1 1/6 yards, which is how much Erica will have left after making the curtain.
Solve using the quadratic formula.
3x^2+6x+7=0
The quadratic equation 3x^2+6x+7=0 has two complex solutions which is x=-1±√(48)i/6.
To solve the quadratic equation 3x^2+6x+7=0 using the quadratic formula, we first need to identify the coefficients a, b, and c from its standard form, which is ax^2+bx+c=0. In this case, a=3, b=6, and c=7.
The quadratic formula is given by x=(-b±√(b^2-4ac))/(2a).
Now, we will calculate the discriminant which is b^2-4ac. In this case, it is 6^2 - 4*3*7, which equals 36 - 84, or -48. Since the discriminant is negative, this means that there are no real solutions to the equation, but two complex solutions.
Applying the quadratic formula, we get the solutions:
x=(-6 ± √(-48))/(2*3)
This simplifies to:
x=(-6 ± √(48)i)/6
Therefore, the solutions are x=-1±√(48)i/6. The quadratic formula helped us to find the complex roots of the quadratic equation.
What angle represents 3.5 rotations counterclockwise?
The angle represents by 3.5 rotations in counterclockwise is 1260 degree or [tex]\frac{7}{2}\pi[/tex] radian.
In one complete rotation, the angle made is = 360 degree or [tex]\pi[/tex] radian
So, In 3.5 rotation, angle made is, = [tex]360*3.5=1260[/tex] degree
Or, = [tex]3.5*\pi=\frac{7}{2}\pi[/tex] radian
Therefore, The angle represents by 3.5 rotations in counterclockwise is 1260 degree or [tex]\frac{7}{2}\pi[/tex] radian.
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The ratio if the base edges of two similar pyramids is 3:4 the volume of the larger pyramid is 320 in^3. What is the volume of the smaller pyramid???
ratio of voljumes = 3^3 : 4^3 or 27:64 small/large = 27 / 64 vol of smaller = 27 * 320 / 64 =135
Answer:
135 cubic inches.
Step-by-step explanation:
Given : The ratio of the base edges of two similar pyramids is 3:4
The volume of the larger pyramid is 320 cubic inches.
To Find: What is the volume of the smaller pyramid?
Solution:
The ratio of the base edges of two similar pyramids is 3:4
The volume of the larger pyramid is 320 cubic inches.
The ratio of the volume of pyramids is equal to the ratio of the cubes of the sides of pyramids .
So, [tex]\frac{3^3}{4^3} =\frac{\text{Volume of smaller pyramid}}{320}[/tex]
[tex]\frac{27}{64} =\frac{\text{Volume of smaller pyramid}}{320}[/tex]
[tex]\frac{27}{64} \times 320 =\text{Volume of smaller pyramid}[/tex]
[tex]135 =\text{Volume of smaller pyramid}[/tex]
Thus the volume of smaller pyramid is 135 cubic inches.
73 divided by 8 with remainder
The final result is 73 divided by 8 equals 9, with a remainder of 9.
When you divide 73 by 8, use long division to find the quotient and remainder.
1. Write the dividend (73) and the divisor (8) as shown:
8 | 73
2. Start dividing: Since 8 is larger than 7, we move to the next digit.
3. Bring down the next digit (3) to the right of the remainder:
8 | 73 | 8
- 64
_____
9
4. The remainder is 9.
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Assume a 30-month cd purchased for $3000 pays simple interest at an annual rate of 5.5%. how much total interest does it earn? what is the balance at maturity?
The total simple interest earned on a $3000 CD over 30 months with an annual interest rate of 5.5% is $412.50 and the balance at maturity is $3412.50.
Explanation:To calculate the total amount of simple interest earned on a certificate of deposit (CD) we use the formula I = Prt, where I is interest, P is the principal amount (initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years. For the given 30-month CD purchased for $3000 with an annual simple interest rate of 5.5%, we first convert 30 months to years by dividing by 12 (30 / 12 = 2.5 years).
Using the formula: I = $3000 × 0.055 × 2.5 = $412.50. Therefore, the total interest earned is $412.50.
To calculate the balance at maturity, we add the total interest to the principal: Balance = Principal + Interest = $3000 + $412.50 = $3412.50.
Beck used a compass and straightedge to accurately construct line segment OS as shown in the figure.
Which could be the measures of angle POS and angle POQ?
A) m∠POS = 60° , m∠POQ = 120°
B) m∠POS = 50° , m∠POQ = 110°
C) m∠POS = 50° , m∠POQ = 120°
Observe the figure below.
The given figure shows that the construction of line segment OS. We can observe clearly that OS is bisector of angle POS.
The bisector divides the angle into two equal angles.
So, [tex]\angle POS = \frac{1}{2} \angle POQ[/tex]
Let us observe the given options.
In first option, [tex]60^\circ = \frac{1}{2} \times 120^\circ[/tex]
Therefore, [tex]m \angle POS = 60^\circ, m \angle POQ=120^\circ[/tex]
So, Option A is the correct answer.
Given:
AB = BC
ADB =
Answer:
[tex]m{\angle}D=60^{\circ}[/tex]
Step-by-step explanation:
From the given figure, it can be seen that [tex]m{\angle}A=60^{\circ}[/tex], [tex]m{\angle}B=60^{\circ}[/tex], thus
From ΔABD, using the angle sum property, we have
[tex]m{\angle}A+m{\angle}B+m{\angle}D=180^{\circ}[/tex]
⇒[tex]60^{\circ}+60^{\circ}+m{\angle}D=180^{\circ}[/tex]
⇒[tex]120^{\circ}+m{\angle}D=180^{\circ}[/tex]
⇒[tex]m{\angle}D=180^{\circ}-120^{circ}[/tex]
⇒[tex]m{\angle}D=60^{\circ}[/tex]
therefore, the measure of [tex]{\angle}ADB[/tex] is [tex]60^{\circ}[/tex].
Hence, ΔABD is an equilateral triangle.
7.25 cm plus 7.2 cm plus 8cm equals what
how can i factor this?
x^(2n)-2x^(n)+1
I need help with this question
Convert to proper fraction or mixed number (do not reduce to lowest terms)
5.27 ...?
5.27 can be converted to a mixed number 5 27/100, where 5 is the whole number and 27/100 is the decimal part expressed as a fraction, without reducing to lowest terms.
Explanation:To convert the decimal number 5.27 to a proper fraction or a mixed number, we first recognize that .27 is the decimal part of 5.27. We can write .27 as a fraction by considering it as 27 hundredths, which is 27/100. Therefore, we have the whole number 5 and the fraction 27/100. Combining these, we get the mixed number 5 27/100. Since we are instructed not to reduce to lowest terms, the mixed number remains as is.
What is the estimate quotient for 555÷ 8
The estimated quotient for 555 ÷ 8 would be 70.
To estimate the quotient for 555 ÷ 8, we can follow these steps:
We know that Quotients are number that is obtained by dividing one number by another number.
Dividend ÷ Divisor = Quotients
Round the dividend, 555, to the nearest ten:
555 rounds to 560.
Divide the rounded dividend, 560, by the divisor, 8:
560 ÷ 8 = 70.
Therefore, the estimated quotient for 555 ÷ 8 is 70.
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What is the measure of angle ABD on trapezoid ABCD?
24
40
64
92
Let
m∠ABD--------> x degrees
we know that
The sum os the internal angles of a trapezoid is equal to [tex] 360 degrees [/tex]
So
[tex] 2*116+2*(24+x)=360\\ 232+48+2x=360\\ 2x=360-280\\ x=40degrees [/tex]
therefore
the answer is
The measure of the angle m∠ABD is [tex] 40 degrees [/tex]
Is -√127 rational or irrational?
Answer:
Irrational
Step-by-step explanation:
A rational number can be expressed as a ratio of two integers , p and q of the form \[\frac{p}{q}\]
So following are examples of rational numbers:
\[\frac{1}{2}\] is a rational number\[\frac{3}{4}\] is a rational number2 is a rational number as it can be expressed as \[\frac{2}{1}\]On the other hand , any number which cannot be expressed in this form is called an irrational number. For example:
\[\sqrt{2}\]\[\sqrt{3}\]\[-\sqrt{127}\]What is the work to 256.50 divided y 8 equal?
6.8-4.2b=5.6b-3 is this equation identify or has no solution
Answer:
1 = b
Step-by-step explanation:
6.8 - 4.2b = 5.6b - 3
First you must add 4.2b to both sides.
Then you will get 6.8 = 9.8b - 3.
Next you must add 3 to both sides.
You will then get 9.8 = 9.8b
Finally divide both sides by 9.8.
You will be left with 1 = b
Find the x-intercept of the tangent line to the graph of f at the point P(0,f(0)) when f(x)= e^-x(5cosx+2sinx)
Unit 2 | Lesson 10
Lesson Assessment:
Core Focus: Problem Solving with Equations Quiz
Question Navigator
Choose the answer.
1.
Marco and Drew stacked boxes on a shelf. Marco lifted 9 boxes and Drew lifted 14 boxes. The boxes that Drew lifted each weighed 8 lb less than the boxes Marco lifted.
Which expression represents the total number of pounds Drew lifted?
Let m represent the weight of the boxes that Marco lifted.
A.
m − 8
B.
14(m − 8)
C.
9(m + 8)
D.
112m
Question Resources
What is the area of a circle with endpoints (-2, 0), (0, 2), (0, -2), and (2, 0).
Will be rewarded 50 points for CORRECT and WELL EXPLAINED answer.
A goat is tethered by a 6 metre rope to the outside corner of a shed measuring 4 metres by 5 metres in a grassy field. What area of grass can the goat graze? ...?
Final answer:
The area of grass that the goat can graze is calculated as a quarter-circle with a radius equal to the length of the rope, which is 6 metres, resulting in an area of approximately 28.27 square metres.
Explanation:
The area of grass a goat can graze when tethered by a 6 metre rope to the outside corner of a shed is a segment of the grassy field. To calculate this area, one must consider two scenarios based on the dimensions of the shed:
If the shed's dimensions of 4 metres by 5 metres do not allow the goat to reach the opposite corner, then the area grazed is a quarter-circle with the rope as the radius.
If the shed's dimensions allow the goat to reach around the corner, then additional area calculations are necessary for the extended grazing area beyond the corner.
In the stated problem, the rope's length does not allow the goat to graze beyond the opposite corner of the shed. Therefore, we calculate the area as a quarter-circle, which is a fraction (1/4) of the area of a full circle with radius 6 metres. The formula for the area of a circle is πr², where r is the radius.
To find the grazeable area, we use:
Area = (1/4) × π × radius² = (1/4) × π × 6² = (1/4) × π × 36
Area = 9π square metres (approximately 28.27 square metres)
The effective grazing area is 22.26 square meters.
The goat can graze in a quarter-circle sweep around the corner where the shed does not block its path.
Step-by-Step Calculation
The goat can graze around the corner up to a 6 metre radius, but the shed blocks its grazing in certain directions.
Calculate the total quarter-circle area the goat can cover:
Area = (1/4) * π * radius² = (1/4) * π * 6² = (1/4) * π * 36 = 9π square metres.
Subtract the area where the shed blocks grazing:
From one corner, the shed blocks a rectangular area measuring 4 meters by 6 meters.
Total area blocked by the shed: 6m * 4m = 24 square meters
Adjust for quarter-circle section, dividing the blockage by 4: 24 / 4 = 6 square meters
The area of grass the goat can graze = Total area - Blocked area
9π - 6 ≈ 28.26 - 6 ≈ 22.26 square metres
Thus, the total area grazed by the goat is 22.26 square meters.
What is the value of x?
x+58=6x+58=6
Enter your answer in the box in simplest form.
x =
Answer: The required value of x is -52.
Step-by-step explanation: We are given to find the value of x from the following equation :
[tex]x+58=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the value of x, we need to solve the equation (i).
The solution of equation (i) is as follows :
[tex]x+58=6\\\\\Rightarrow x=6-58\\\\\Rightarrow x=-52.[/tex]
Thus, the required value of x is -52.
There were 500 people at a play. the admission price was $6 for general public and $3 for students. the admission receipts were $2640. solve a system of equations to find how many students attended.
Find the integral of sqrt(4x-x^2)dx.
The value of integral is 2 * arc sin((x - 2) / 2) + (x - 2) * √(4 - (x - 2)²) / 2 + C.
To solve the integral ∫ √(4x - x²) dx, follow these steps:
Complete the Square: Rewrite the quadratic expression under the square root. Start with: 4x - x²
Rearrange it to the standard quadratic form: -x² + 4x. To complete the square, factor out the negative sign: (x² - 4x)
Next, complete the square inside the parentheses:
x² - 4x = (x - 2)² - 4
So, we get:
(x² - 4x) = - [(x - 2)² - 4] = 4 - (x - 2)²
Therefore:
√(4x - x²) = √(4 - (x - 2)²)
Substitute Variables: Let u = x - 2. Then, du = dx, and the integral becomes:
∫ √(4 - u²) du
Apply the Trigonometric Substitution: Use the trigonometric substitution u = 2 sin θ. Then du = 2 cos θ dθ. Substitute these into the integral:
∫ √(4 - (2 sin θ)²) * 2 cos θ dθ
= ∫ √(4 - 4 sin² θ) * 2 cos θ dθ
= ∫ √(4 (1 - sin² θ)) * 2 cos θ dθ
= ∫ 2 cos θ * 2 cos θ dθ
= ∫ 4 cos² θ dθ
Use Trigonometric Identity: Apply the double-angle identity cos² θ = (1 + cos 2θ) / 2:
∫ 4 cos² θ dθ
= ∫ 4 * (1 + cos 2θ) / 2 dθ
= ∫ (4 + 4 cos 2θ) / 2 dθ
= ∫ (2 + 2 cos 2θ) dθ
Integrate each term:
∫ 2 dθ + ∫ 2 cos 2θ dθ = 2θ + sin 2θ + C
Back-substitute: Replace θ with the original variable x. Recall u = 2 sin θ, so θ = arcsin(u / 2). Since u = x - 2, substitute back:
θ = arcsin((x - 2) / 2)
Therefore:
2 * arcsin((x - 2) / 2) + sin(2 * arcsin((x - 2) / 2)) + C
Using the identity sin(2θ) = 2 sin θ cos θ:
sin(2 * arcsin((x - 2) / 2))
= 2 * (x - 2) / 2 * √(1 - ((x - 2) / 2)²)
= (x - 2) * √(4 - (x - 2)²) / 2
integrate t sec^2 (2t) dt
Answer:
[tex]\int {t\times \sec^2(2t)} \, dt \\\\ \text{Integrating by parts}\\\\=\frac{t\times \tan 2t}{2}-\int{(\frac{d}{dt}(t) \times \int{{\ sec^{2}(2t)}}) dt}\\\\=\frac{t\times \tan 2t}{2}-\int{\frac{\tan 2t}{2}} dt\\\\=\frac{t\times \tan 2t}{2}-\frac{\log sec 2t}{4}+C[/tex]
Where C is Constant of Proportionality.
Given that f(x) = x² + 4x, evaluate f(-2).
Answer:
The evaluation is [tex]f(-2)=-4[/tex]
Step-by-step explanation:
We were given an explicit function of x, wich has the form
[tex]f(x)=x^2+4x[/tex]
The problem ask to evaluate f(-2), this means to put the value x=-2 into the function, so
[tex]f(-2)=(-2)^2+4(-2)=4-8=-4[/tex]
Therefore, the answer is
[tex]f(-2)=-4[/tex]
The initial number of views for a certain website was 15. The number of views is growing exponentially at a rate of 22% per week. What is the number of views expected to be four weeks from now? Round to the nearest whole number. Enter your answer in the box. ( please answer my questions never get answered...)
Answer:
i took the test
Step-by-step explanation:
which of the following is not a perfect square?
A. 36
B. 45
C. 64
D. 81 ...?
Among the options given, B. 45 is not a perfect square because no integer squared equals 45.
Explanation:The question is asking us to identify which number among the given options is not a perfect square. A perfect square is a number that can be expressed as the product of an integer with itself. Here are the given options with explanations:
A. 36 - This is a perfect square because 6 x 6 equals 36.B. 45 - This is not a perfect square because there is no integer which, when multiplied by itself, equals 45.C. 64 - This is a perfect square because 8 x 8 equals 64.D. 81 - This is a perfect square because 9 x 9 equals 81.Therefore, the number that is not a perfect square in the options provided is B. 45.
You are expecting a call from a friend anytime between 3:00 P.M. and 5:00 P.M. At 3:20 P.M, you discover that someone accidentally left the phone off the hook. What is the probability that you missed your friend’s call?
The probability that you missed your friend’s call is 1/6
How to determine the probability?The range is given as:
Range = 3:00 P.M. and 5:00 P.M.
The number of minutes in the range is:
Total = 120 minutes
At 3:20 that you notice the phone is off the hook, the number of minutes missed is:
Time missed = 20 minutes
The probability is then calculated as:
P = 20/120
Evaluate
P = 1/6
Hence, the probability that you missed your friend’s call is 1/6
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What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
y+6=5(x+2)y+6=5(x+2)
y−6=5(x−2)y−6=5(x−2)
y+2=5(x+6)y+2=5(x+6)
y−2=5(x−6)
The sum of two consecutive integers is at most 223.
What is the larger of the two integers?
Answer:
112
Step-by-step explanation: