42.54 is the same as 42 _____' 24".
Answer:
[tex]42.54\°=42\°+32'+24''[/tex]
Step-by-step explanation:
we have
[tex]42.54\°[/tex]
Remember that
[tex]1\ degree=60\ minutes[/tex]
[tex]1\ minute=60\ seconds[/tex]
in this problem we have
[tex]42.54\°=42\°+0.54\°[/tex]
Convert [tex]0.54\°[/tex] to minutes
[tex]0.54\°=0.54*60=32.4'[/tex]
so
[tex]42\°+0.54\°=42\°+32.4'=42\°+32'+0.4'[/tex]
Convert [tex]0.4'[/tex] to seconds
[tex]0.4'=0.4*60=24''[/tex]
therefore
[tex]42.54\°=42\°+32'+24''[/tex]
A frame of width a surrounds a 5 by 7 inch photograph. Find the expression that represents the area of the frame in terms of a. HELP ASAP
A. a 2 − 35
B.a 2 + 12a + 35
C. None of these
D. 4a 2 + 24a
E. a 2 + 12a
The area of the frame is found by subtracting the area of the photograph from the total area of the framed photograph. After simplification, the expression for the frame's area is 24a + 4a². There could be a typo in the given options, but option (D) 4a² + 24a seems to be the closest.
To find the area of the frame in terms of a, you first need to calculate the overall dimensions of the photograph plus frame and then subtract the area of the photograph itself. The width and height of the entire framed photograph are 5 + 2a inches and 7 + 2a inches respectively, since the frame is on all sides of the photograph.
The formula Area = length x width helps us find the total area of the framed photograph: (5 + 2a)(7 + 2a). Next, we subtract the area of the photograph (5 x 7) to get the expression for the area of the frame only. Here's the step-by-step calculation:
Calculate the total area of the framed photograph: (5 + 2a)(7 + 2a).This expands to: 5 x 7 + 10a + 14a + 4a².Combine like terms: 35 + 24a + 4a².Subtract the area of the photograph: 35 + 24a + 4a² - 35.The area of the frame simplifies to: 24a + 4a².Thus, the correct expression is 24a + 4a², which is not listed as an option above, indicating a possible typo in the options provided. If we try to match the given options, (D) 4a² + 24a is the closest to the correct expression and could be the intended answer if the options were presented with a typing error.
The graph of quadratic function f(x) has a minimum at (-2,-3) and passes through the point (2,13). The function g(x) is represented by the equation g(x)=-(x+2)(x-3)
How much greater is the y-intercept of g(x) than f(x)?
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The y-intercept of function g(x) is 9 greater than the y-intercept of function f(x).
Explanation:The question is asking for the difference in the y-intercepts of two quadratic functions f(x) and g(x). The minimum point of a function gives us both the x-value of the vertex and the y-intercept. Here, for f(x), the minimum point is given as (-2,-3) which means the y-intercept is -3. Similarly, for the function g(x)=-(x+2)(x-3), expanding this equation gives us g(x) = -x^2 + x + 6. Here, we see that the constant term, 6, is the y-intercept. Therefore, the difference in the y-intercepts of g(x) and f(x) is 6 - (-3) = 9.
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The front side of a playhouse is shown in this scale drawing. The height of the door in the drawing 1.8 inches. The scale that maps the drawing to the actual playhouse is 1 inch to 2.5 feet.
Final answer:
To find the actual height of a door in a playhouse from a scale drawing with a scale of 1 inch to 2.5 feet, simply multiply the drawing measurement (1.8 inches) by the scale factor, which gives an actual height of 4.5 feet.
Explanation:
To determine the actual height of the door on the playhouse from the scale drawing, you need to use the provided scale ratio, which is 1 inch to 2.5 feet.
Since the height of the door in the drawing is 1.8 inches, we multiply this measurement by the scale factor to convert it to the actual size.
Calculation: 1.8 inches × 2.5 feet/inch results in an actual door height of 4.5 feet on the actual playhouse.
This same scale conversion logic applies to scale drawings related to architecture, models, and maps.
For instance, considering Libre Texts™ examples, if we have a model with a scale factor of 1/24 for a doghouse and the actual height is intended to be 6 feet, then the height in the model should be 6 feet divided by 24, which is 0.25 feet or 3 inches. Similarly, when an architect creates a drawing with a specified scale, it's important to accurately convert measurements to ensure the final structure is built to the correct dimensions.
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The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring. What is the constant of the quadratic function in this equation?
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Based on the ideal gas law, what is the volume, in liters, of a sample that contains 1,200 moles?
A. 6,000
B. 24,000
C. 36,000
D. 60,000
54 points
BC is parallel to DE. What is the length of CE? A) 2 1/3 B) 2 2/3 C) 3 1/3 D) 3
Answer:
2 2/3
Step-by-step explanation:
AB
BD
=
AC
CE
3 /2 = 4 /CE → CE = 8 /3 = 2 2 /3
Which of the ollowing statements best describes he relationship between a line and a point in a plane
Janet has three times as many dimes as nickels and twice as many quarters as nickels. If she has $3.40 in all, how many nickels, dimes, and quarters does she have?
If n represents the number of nickels Janet has, which of the following equations could be used to solve the problem?
5n + 10n + 25n = 340
n + 3n + 2n = 340
5n + 30n + 50n = 340
Answer:
[tex]5n+30n+50n= 340[/tex]
Step-by-step explanation:
Janet has three times as many dimes as nickels and twice as many quarters as nickels.she has $3.40 in a.
Let n be the number of nickels
d be the number of dimes and q be the number of quarts
1 nickel = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
Convert the dollars into cents by multiplying by 100
3.40 dollars = 3.40 times 100 is 340 cents
Janet has three times as many dimes as nickels and twice as many quarters as nickels
dimes is 3 times of nickels
[tex]d=3n[/tex]
quarts is twice as many as nickels
[tex]q=2n[/tex]
Now we frame equation
5 nickels plus 10 dimes plus 25 quarts is total 340 cents
[tex]5n+10d+25q= 340[/tex]
Replace d and q
[tex]5n+10(3n)+25(2n)= 340[/tex]
[tex]5n+30n+50n= 340[/tex]
Which expression is equivalent to square root of 2x^5/18? Assume
Answer with explanation:
The Meaning of equivalent expression is those expressions, in which when you replace the variables by some constant values , in the original expression and the reduced expression,the both expression produce the same numerical value.
The expression which is equivalent to:
[tex]\rightarrow\sqrt {\frac{2x^5}{18}}\\\\=\sqrt{\frac{x^5}{9}}\\\\=\frac{x^2}{3}\times\sqrt{x}[/tex]
This can be illustrated by
Original Expression
[tex]A=\sqrt {\frac{2x^5}{18}}\\\\ \text{put, x=1}\\\\A=\sqrt{\frac{2 \times 1^5}{18}}\\\\A=\sqrt{\frac{1}{9}}\\\\A=\frac{1}{3}\\\\\text{Equivalent Expression B}\rightarrow \frac{x^2}{3}\times \sqrt{x}\\\\\text{put,x=1}\\\\B=\frac{1^2}{3}\times \sqrt{1}\\\\B=\frac{1}{3}[/tex]
Which is a solution of x2 – x – = 0?
[tex]x^2-x=0\\\\x(x-1)=0\iff x=0\ \vee\ x-1=0\\\\\boxed{x=0\ \vee\ x=1}[/tex]
if dy/dx= sin x/ cos y and y(0) = 3pi/2, find an equation for y in terms of x
Final answer:
The problem requires finding an equation for y in terms of x given a differential equation and an initial condition. Solving for y, we get:[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
Explanation:
To solve this ordinary differential equation (ODE), we can separate variables and then integrate both sides. Given:
[tex]\[\frac{dy}{dx} = \frac{\sin(x)}{\cos(y)}\][/tex]
We separate variables by multiplying both sides by \(dx\) and dividing by Cos(y) to isolate y terms:
[tex]\[\cos(y) \, dy = \sin(x) \, dx\][/tex]
Now, we integrate both sides. For the left side, we integrate with respect to y, and for the right side, we integrate with respect to x:
[tex]\[\int \cos(y) \, dy = \int \sin(x) \, dx\][/tex]
Integrating each side gives us:
[tex]\[ \sin(y) = -\cos(x) + C\][/tex]
Where C is the constant of integration.
Given the initial condition [tex]\(y(0) = \frac{3\pi}{2}\)[/tex], we can plug this into the equation to find [tex]\(C\):[/tex]
[tex]\[ \sin\left(\frac{3\pi}{2}\right) = -\cos(0) + C \][/tex]
[tex]\[ -1 = -1 + C \][/tex]
[tex]\[ C = 0 \][/tex]
So the equation becomes:
[tex]\[ \sin(y) = -\cos(x) \][/tex]
Therefore, solving for y, we get:
[tex]\[ y = \arcsin(-\cos(x)) \][/tex]
This is the equation for y in terms of x.
How do you know a radical expression is in simplest form?
19. A carpenter is putting a skylight in the roof. If the roof measures (10x + 9) by (7x + 7) and the skylight measures (x + 5) by (3x + 3), what is the area of the remaining roof after the skylight is built?
(A). 67x^2 + 115x + 48
(B). 73x^2 + 151x + 78
(C). 70x^2 + 133x + 63
(D). 3x^2 + 18x + 15
20. What is the factored form of the expression?
w^2 + 16w + 64
(A). (w + 8)(w - 8)
(B). (w + 64)(w - 1)
(C). (w + 8)^2
(D). (w - 8)^2
21. What is the factored form of the expression?
d^2 + 22d + 121
(A). (d + 11)^2
(B). (d - 11)^2
(C). (d - 11)(d + 11)
(D). (d - 121)(d - 1)
22. What is the factored form of the expression?
r^2 - 49
(A). (r - 7)(r + 7)
(B). (r + 7)(r + 7)
(C). (r - 7)(r - 7)
(D). (r - 7)(r + 9)
Hence, option (A) is correct.
Hence, option (C) is correct.
Hence, option (A) is correct.
Hence, option (A) is correct.
What is a factor?
A factor is a number that divides another number, leaving no remainder.
In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
There are two methods of finding factors: multiplication and division.
Here given that,
19)
The area of the ceiling is given by [tex](10x+9)(7x+7)[/tex].
[tex]10x(7x)+7(10x)+9(7x)+9(7)\\=70x^2+70x+63x+63\\=70x^2+133x+63\\[/tex]
The area of the skylight is of the form [tex](x+5)(3x+3)[/tex].
[tex]x(3x)+3(x)+5(3x)+5(3)\\=3x^2+3x+15x+15\\=3x^2+18x+15\\[/tex]
We subtract to find out the remaining ceiling:
[tex](70x^2+133x+63)-(3x^2+18x+15)\\=70x^2+133x+63-3x^2-18x-15\\=67x^2+115x+48[/tex]
Hence, option (A) is correct.
20)
For the factor, we find factors of
[tex]8(8)=64\\8+8=16[/tex]
Therefore we have:
[tex](w+8)(w+8)[/tex]
Hence, this is the same binomial twice, we write it as [tex](w+8)^2[/tex]
Hence, option (C) is correct.
21)
Again we look for the factors
[tex]11(11)=121\\11+11=22[/tex]
so it is of the form [tex](d+11)(d+11)[/tex].
Hence this is the same binomial twice, we have [tex](d+11)^2[/tex].
Hence, option (A) is correct.
22)
Factors [tex]-49[/tex] that sum to [tex]0[/tex]
As
[tex]-7(-7)=49\\-7-7=-14[/tex]
So:
[tex](r-7)(r+7)[/tex]
Hence, option (A) is correct.
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What is the slope of the line that passes through the points E(3, 0) and F (6, -3)?
Hello!
Step-by-step explanation:
Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]
[tex]\frac{(-3)-0=-3}{6-3=3}=\frac{-3}{3}=-1[/tex]
Therefore, the slope is -1.
Answer is -1.
Hope this helps!
Thanks!
-Charlie
Have a great day!
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You have 1500 and want to invest it for the future. Bank of westminster has a saving account with an interest rate of 3% compounded yearly, but a local credit union is offering 2% compounded continuously. Which account would give you more money if you leave the money in the account for 10 years? How much more? Show all calculation and label everything
A rental car costs a one time fee of $150 and then an additional $80 for each day it is rented. If the Nawa family's total bill was $470, how many days did they rent the car?
Nawa family rented the car for 2 days.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
A rental automobile costs $150 for the first day and an extra $80 for each consecutive day booked. If the entire bill for the Nawas family was $470.
The total cost of the rental car per day is :
⇒ one-time fee + additional fee
⇒ $150 + $80
Apply the addition operation,
⇒ $230 per day.
The Nawas paid $470 for the rental car, so they rented the car for $470 / $230 per day = 2 days.
Therefore, his family rented the car for 2 days.
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The school store started selling music CDs five years ago. They sold $22,600 worth in the first year. But, since MP3 players became so popular, the total yearly sales of CDs have dropped 14% per year since then. What is the total money collected for music CDs sold in the school store over the last five years? Use the geometric series formula to calculate your answer.
The total money collected for music CDs sold in the school store over the last five year is $85,557
Geometric Series Formula:
To calculate the total money collected for music CDs sold in the school store over the last five years, we can use the formula for the sum of a geometric series: Sum = a * (1 - r^n) / (1 - r), where a is the initial value, r is the common ratio, and n is the number of terms.
Given Data:
Initial sales in the first year = $22,600
Annual decrease rate = 14%
Duration = 5 years
Calculation Steps:
Calculate the common ratio: r = 1 - 0.14 = 0.86
Plug the values into the formula: Sum = $22,600 * (1 - 0.86^5) / (1 - 0.86) = $85,557
Arnold borrowed $7890 at 11.5 percent for five years. How much did Arnold Pay in interest?
A.$2,199
B.$2,300
C.$1,150
D.$2.520
Answer:
Option D. $2520 is correct
Step-by-step explanation:
Principal value = $7890
Rate of interest = 11.5 annually
[tex]\text{Monthly Rate of Interest = }\frac{11.5}{12}=0.96\%=0.0096[/tex]
Time = 5 years
⇒ n = 60 months
[tex]\text{Monthly Payment = }\frac{rate\times \text{Principal value}}{1-(1+r)^{-n}}\\\\\text{Monthly payment = }\frac{0.0096\times 7890}{1-(1+0.0096)^{-60}} \\\\\implies\text{Monthly Payment = }\$173.50[/tex]
Total payment made by Arnold = No. of months × Monthly Payment
⇒ Total Payment = 60 × 173.50
⇒ Total Payment = $10410
Money borrowed = $7890
Hence, Amount of interest = Total payment - Amount borrowed
⇒ Interest = 10410 - 7890
⇒ Interest = $2520
Therefore, Option D. $2520 is correct
What is the quotient of 8,688 ÷ 24?
362
434
450
8,664
Two examples of items the weigh less than an ounce
Factor completely. x2−12x+35 Enter your answer in the box.
The complete factor of x² − 12x + 35 is (x - 7(x - 5).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would factor completely the quadratic function x² −12x+35 by using the factorization method as follows;
x² − 12x + 35 = 0
x² − 7x - 5x + 35 = 0
x(x - 7) - 5(x - 7) = 0
(x - 7(x - 5) = 0.
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Complete Question:
Factor completely. x² −12x+35 Enter your answer in the box.
Which is an equation of the line graphed below?
A. y=2x-3
B. y=1/2x-3
C. y= -1/2x-3
D. y= -2x-3
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How do u do question 27 and 29. Find the measure of angle x?
The area of a rug, which is shaped like a rectangle,is 4x²+4x square feet. Factor this polynomial to find expressions for the dimensions of the rug
Final answer:
The expressions for the dimensions of a rectangular rug with an area of 4x²+4x square feet are 4x feet and (x + 1) feet after factoring the polynomial.
Explanation:
To find the expressions for the dimensions of the rug with an area of 4x²+4x square feet, we need to factor the polynomial. Factoring out the greatest common factor (GCF), we get:
4x² + 4x = 4x(x + 1).
This indicates that one dimension of the rug is 4x feet and the other dimension is (x + 1) feet. The rug can be visualized as a rectangle where one side is 4 times a certain length x, and the other side is that length plus one.
The center of a circle is at (−3, 1) and its radius is 9.
What is the equation of the circle?
(x+3)2+(y−1)2=18
(x−3)2+(y+1)2=18
(x−3)2+(y+1)2=81
(x+3)2+(y−1)2=81
The standard form of the circle equation is in the form [tex] (x-h)^{2}+(y-k)^{2}=r^{2} [/tex] with the center being at the point [tex] (h,k) [/tex] and the radius being "r".
We have to find the equation of circle with center (-3,1) and radius as 9.
So, h= -3, k=1 and r=9
Equation of circle is:
[tex] (x-(-3))^{2}+(y-1)^{2}=(9)^{2} [/tex]
[tex] (x+3)^{2}+(y-1)^{2}=81 [/tex] is the required equation of the circle.
Therefore, Option 4 is the correct answer.
if you were to solve the following system by substitution what would be the best variable to solve and from what equation? 2x+8y=12 3x-8y=11
Answer:
X in 1st
Step-by-step explanation:
You are buying a $14.95 item that has 4.5% sales tax. You give the cashier a $20 bill. How much change do you get back?
Answer:
4.38 is the aount you get back
Step-by-step explanation:
14.95*.045=.67
14.95+.67=15.62
20-15.62=4.38
Brainleist plz
You give the cashier a $20 bill. $4.38 you get back.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
You are buying a $14.95 item that has 4.5% sales tax.
That means,
the total price = 14.95 + 4.5% of 14.95.
= 14.95 + 0.67
= 15.62
You give the cashier a $20 bill.
You get in return,
= 20 - 15.62
= $4.38
Therefore, you get back $4.38.
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