there are 36 quarters.
Let the number of nickels be x
Let the number of quarters be y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
nickels x $0.05 $0.05x
quarters y $0.25 $0.25y
-------------------------------------------
TOTALS 52 ----- $3.60
The first equation comes from the second column.
x + y = 11
The second equation comes from the last column.
0.05x + 0.25y = 3.60
Get rid of decimals by multiplying every term by 100:
5x + 25y = 360
So we have the system of equations:
x+y=52
5x+25y=360
We solve by substitution. Solve the first equation for y:
x + y = 52
y = 52 - x
Substitute (52 - x) for y in 5x + 25y = 360
5x + 25(52 - x) = 360
5x + 1300 - 25x = 360
-20x + 1300 = 360
-20x = -940
x = = 5 the number of nickels.
Substitute in y = 52 - x
y = 52 - (5
y = 47 quarters.
The number of quarters is 52-x or 52-5 or 47 quarters.
The law of cosines is a2 +62 - 2abcosC = (2. Find the value of 2abcosC.
2
4
B
A
5
Answer:
[tex]2abcosC = 37[/tex]
Step-by-step explanation:
Given
[tex]a^2 + b^2 - 2abcosC = c^2[/tex]
Required
[tex]2abcosC[/tex]
[tex]a^2 + b^2 - 2abcosC = c^2[/tex]
Add [tex]2abcosC[/tex] to both sides
[tex]a^2 + b^2 - 2abcosC+2abcosC = c^2+2abcosC[/tex]
[tex]a^2 + b^2 = c^2+2abcosC[/tex]
Subtract [tex]c^2[/tex] from both sides
[tex]a^2 + b^2 -c^2= c^2 -c^2+2abcosC[/tex]
[tex]a^2 + b^2 -c^2= 2abcosC[/tex]
From the attachment:
[tex]a = 4[/tex] [tex]b = 5[/tex] and [tex]c = 2[/tex]
So, we have:
[tex]4^2 + 5^2 -2^2= 2abcosC[/tex]
[tex]16 + 25 -4= 2abcosC[/tex]
[tex]37= 2abcosC[/tex]
i.e.
[tex]2abcosC = 37[/tex]
Answer:
A. 37
Step-by-step explanation:
Angela works 18 hours a week for 12 weeks in the summer at the local swimming pool as a life guard. She earns $13 per hour. Her employer takes 15 percent out of her check for federal income tax withholding and 6.2 percent for Social Security and 1.45 percent for Medicare. She will receive 12 paychecks, one for each week she works. Calculate Angela’s weekly gross pay
Answer:
We know that per week, she works 18 hours.
For each of these hours, she earns $13.
Then in one week, she earns a total of:
18*$13 = $234
This is her gross pay (the pay before the taxes apply)
Now we know that her employer takes:
15% for federal income tax withholding.
6.2% for Social Security
1.45% for Medicare.
If we add all of these, we get:
15% + 6.2% + 1.45% = 22.65%
This means that 22.65% of $234, is taken by her employer to pay taxes and such.
Then the amount left is:
M = $234 - ( 22.65%/100%)*$234 = $234 - 0.2265*$234 = $180.999
And we can round the last digit to $181 (because we can not have a 0.009 of a cent)
This means that her weekly net pay is $181
And she works for 12 weeks, this means that in total, she will earn:
12*$181 = $2,172
3 There are 8 teams in the
recreational soccer league. Each
team is comprised of 9 fourth-
grade students and 5 fifth-grade
students. Which expression could
be used to find the total number of
students in the soccer league?
A. (8 + 9) * 5 =
B. (8 x 9) + 5 =
C. 8 + (9x5) =
D. 8 (9 + 5) =
Answer:
On each team there is the same number of teammates, the answer is D. 8 (9 + 5).
Step-by-step explanation:
If you add up the amount of teammates then multiply that by the number of teams.
Therefore, D. 8 (9 + 5) is the answer.
1 2 3 4 5 6 7 8 9 10
10 + 10= ?
Answer:
I'm confused what you are asking... if you are looking for the answer to 10 + 10 it's 20 ♡♡
Plz help I’ll appreciate it plz help
Answer:
x = 36
Step-by-step explanation:
Here, we want to get the value of x
As we can see on the markings, the base angle are equal
Thus, the other base angle is x too
mathematically, the sum of all the interior angles of a triangle = 180
thus;
3x + x + x = 180
5x = 180
x = 180/5
x = 36
The drama club spent $450 on tickets and buses for a field trip to the theater. 15 members of the drama club attended the field trip. The total cost for the buses was $60. What was the cost of each theater ticket? Pick the correct equation and then solve for the cost of each theater ticket.
Answer: 525
Step-by-step explanation:
450+15+60=525
Answer:
The cost of each ticket is $30.
Step-by-step explanation:
$450 is the total cost, so to get individual ticket prices you need to divide by the total number of drama club members.
450 ÷ 15 = 30
(a) The perimeter of a rectangular garden is 314 m.
If the length of the garden is 85 m, what is its width?
(b) The area of a rectangular window is 4800 cm
2
If the width of the window is 64 cm, what is its length?
Answer:72 for the garden and 75 for the window
Step-by-step explanation:
Please answer correctly !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answer: c
Step-by-step explanation: a parrelagram has each side parrel
Answer:
B. - it has four right angles
Find the value of x
A.55
B.60
C.85
D.120
Answer:
A
[tex]x + 125° = 180° \: \: (angles \: on \: straight \: line) \\ x = (180 - 125)° \\ x = 55°[/tex]
What is the value of Angle 'a'?
a
47°
Answer:
133
Step-by-step explanation:
180-47=133
Answer: if the shape is a triangle, 180-47=133
if it is any other shape, 360-47=313
Step-by-step explanation:
6 cm
8 cm
what’s the hypotenuse
Answer:
10 cm
Step-by-step explanation:
This is the Pythagorean triple 3, 4, 5, in which the two legs are multiples of 3 and 4, while the hypotenuse is a multiple of 5. Observing the given numbers it can be deduced that the second multiple of 5 is what is needed to complete this triple, therefor the hypotenuse must be 10 cm.
Name
4.
Banl
two
Line m is the perpendicular bisector of AB and
intersects the segment at point P. Which
statement is true?
(A)
© AP = 2 AB
PA & BP
(В)
AB = AP
BP = 2 AB
Answer:
a)
Step-by-step explanation:
PA ≅ BP
Perpendicular bisector means it divides the line into two equal part at 90°
What is the solution set for the inequality.
t - 10 ≥ 7
A
{18, 19, 20, 21}
B
{17, 3, 14, 25}
C
{17, 20, 30, 44}
D
{8, 11, 15, 17}
Hope you get the right answer
Step-by-step explanation:
PLEASE HELP, 30 points AND brainliest if I get an explanation :)
Find the values of the ratios (red to blue) of the perimeters and areas of the similar figures. Write the ratios as fractions in simplest form.
Answer:
Please check the explanation.
Step-by-step explanation:
BLUE PENTAGON
The blue shape represents the Pentagon
The length of the side a = 7
As there are 5 sides.
Thus,
The Perimeter of the Blue Pentagon = P = 5a = 5(7) = 35
Using the formula to determine the area of the Pentagon
[tex]A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}a^2\:\:\:\:\:\:\:\:\:\:\:\:\:[/tex]
[tex]A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}\left(7\right)^2\:\:\:\:\:\:[/tex]
[tex]A\approx 84.3\:\:\:[/tex]
Thus,
The Area of the Blue Pentagon = [tex]A\approx 84.3\:\:\:[/tex]
RED PENTAGON
The red shape represents the Pentagon
The length of the side a = 4
As there are 5 sides.
Thus,
The Perimeter of the Red Pentagon = P = 5a = 5(4) = 20
Using the formula to determine the area of the Pentagon
[tex]A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}a^2\:\:\:\:\:\:\:\:\:\:\:\:\:[/tex]
[tex]A=\frac{1}{4}\sqrt{5\left(5+2\sqrt{5}\right)}\left(4\right)^2\:\:\:\:\:\:[/tex]
[tex]\:A\approx 27.5[/tex]
The Area of the Red Pentagon = [tex]\:A\approx 27.5[/tex]
Conclusion:
The Perimeter of the Blue Pentagon = 35
The Perimeter of the Red Pentagon = 20
Thus, the ratio of the perimeter is: 35/20 = 7/4
The Area of the Blue Pentagon = 84.3 = 843/10
The Area of the Red Pentagon = 27.5 = 275/10
Thus, the ratio of the Area is:
[tex]\frac{\frac{843}{10}}{\frac{275}{10}}=\frac{843}{275}[/tex]
What is the actual length of the microchip?
Answer:
12 millimeters is the actual length of a microchip
Explore: Solving Two-Step Equations Solve the two-step equation. -9x + 0.4 = 4 Which operation must be performed to move all the constants to the right side of the equation? Then, which operation must be performed to isolate the variable? The solution to the equation is x = .
Answer:
x = -0.4
Step-by-step explanation:
Given:
-9x + 0.4 = 4
To move all constant to the right side of the equation, perform subtraction operation
That is, subtract 0.4 from both sides of the equation
-9x + 0.4 - 0.4 = 4 - 0.4
-9x = 4 - 0.4
-9x = 3.6
Perform division operation to isolate the variable
That is, divide both sides by -9
-9x / -9 = 3.6 / -9
x = -0.4
Answer:
1 Subtract 0.4
2 Divide by -9 on both sides
3 -0.4
Step-by-step explanation:
May I please have brainliest
Can someone pretty please help me... it’s only 2 questions! :(
Answer:
9. C 10. C
Step-by-step explanation:
Please gimme brainliest
Answer: c for both
Step-by-step explanation:
Promote means support, and the “general welfare” is the general good of the people.
The Preambles of the constitution at the beginning of it, so it couldn’t be a a conclusion, and there were no indexes in the Constitution. It had to be a summary or an introduction, Ndola it’s an introduction, it did not explain everything in the document like a a bunch, but it did state that it was a constitution.
Also, the question end should with an, so it had to be an answer starting with a vowel, so one of the last two, since the last one I saw wrong, it had to be c.
How do you know square root c is a right angle?
Answer:
angle c is right angle because,
it is proved by Pythagoras theorem....
now,we check that
[tex] {10 }^{2} = {8}^{2} + {6}^{2} \\ 100 = 6 + 36 \\ 100 = 100 \\ lhs = rhs \\ hence \: \: proved \: angle \: c \: is \: right \: angle[/tex]
60% of what number is 55?
Answer:
33
Step-by-step explanation:
Answer:
[tex]let \: that \: number \: be \: x \\ 60\% \times x = 55 \\ \frac{60x}{100} = 55 \\ 60x = (55 \times 100) \\ 60x = 5500 \\ x = \frac{5500}{60} \\ x = \frac{275}{3} \\ the \: number \: is \: \frac{275}{3} [/tex]
Answer the viable point to please! But Answer Both!!
What is the value of h(-2) if h(x)=4x^2-x+9?
Answer:
16x² + 2x + 9
Step-by-step explanation:
To evaluate h(- 2x) , substitute x = - 2x into h(x), that is
h(- 2x)
= 4(- 2x)² - (- 2x) + 9
= 4(4x²) + 2x + 9
= 16x² + 2x + 9
Evaluate 7b-b when b=4
Thank you!!
Answer:
The correct answer is 24.
Step-by-step explanation:
True or False.
If
F(x) = ∫ -23x sin(t) dt
then the second fundamental theorem of calculus can be used to evaluate F '(x) as follows
F '(x) = sin (3x)
Answer:
False.
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Integration
IntegralsDefinite IntegralsIntegration Constant CIntegration Rule [Fundamental Theorem of Calculus 2]: [tex]\displaystyle \frac{d}{dx}[\int\limits^x_a {f(t)} \, dt] = f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle F(x) = \int\limits^{3x}_{-2} {sin(t)} \, dt[/tex]
Step 2: Differentiate
Chain Rule: [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot \frac{d}{dx}[3x][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot 3\frac{d}{dx}[x][/tex]Basic Power Rule: [tex]\displaystyle F'(x) = \frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt] \cdot 3x^{1 - 1}[/tex]Simplify: [tex]\displaystyle F'(x) = 3\frac{d}{dx}[\int\limits^{3x}_{-2} {sin(t)} \, dt][/tex]Integration Rule [Fundamental Theorem of Calculus 2]: [tex]\displaystyle F'(x) = 3sin(3x)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
2 consecutive numbers that add up to 719
Answer:
359+360
Step-by-step explanation:
Answer:
359+360
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 719. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 719. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 719
Priya and Han both factored the number 80. Priya says they should both get the same answer even if they started with different factor pairs. Han disagrees. Who is correct
Answer:
Priya is right.
Step-by-step explanation:
The factors of 80 is 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factor pairs of 80 are
1 x 80, 2 x 40, 4 x 20, 5 x 16 and 8 x 10
If Priya picks 2 x 40, then it's prime factorisation will be, 2 x 2 x 2 x 2 x 5 = 2⁴ x 5.
If Han picks, 5 x 16 = 5 x 2 x 2 x 2 x 2 = 5 x 2⁴ = 2⁴ x 5. This is the same.
Therefore, Priya is correct, because the factors of 80 are always the same, therefore which ever you start with, you'd always get the same answer.
I want to know how to expand x(4 - 3.4y)
Answer:
X(4-3.4y)
= 4x - 3.4xy
Step-by-step explanation:
Heather works 40 hours a week and she earns $11.50 per hour. When Heather works over 40 hours, her pay is 1.5 times her hourly pay. How much does Heather earn if she works 46 hours in one week?
Answer:
563.5
Step-by-step explanation:
it's pretty easy ngl
Answer:
563.5
Step-by-step explanation:
Carl earns $3.25 per hour walking his neighbor’s dogs. He walks them 1/3 of an hour in the morning and 1/2 of an hour in the afternoon.
a. How much time does Carl spend dog walking every day?
b. How much time does Carl spend dog walking in a week?
c. Ten minutes is equal to 1/6 of an hour. How many minutes does Carl work dog walking each week?
d. How much money does Carl earn each week?
what percent of 18 is 24
SIDE NOTE:its not 75%
what is 283.192 rounded to the nearest hundredth
Answer:
283.19
Step-by-step explanation:
Find the number in the hundredth place 9 and look one place to the right for the rounding digit 2 . Round up if this number is greater than or equal to 5
and round down if it is less than 5 .
Answer:
283.19
Step-by-step explanation:
So as you should already know, the 2 is the hundreds, 8 is the tenths, and 3 is the ones, but you may not know the ones after it. The number after the little dot (decimal) is a 1 and is called the tenths and the one after is the hundredths and then thousandths and so on. You want to know the hundredths so just keep all of the numbers until you get to the number that is 2 places after the decimal and look at the last number and if its below 5, keep the hundredths the same but if its 5 or over make the hundredths 1 higher. for example 3 stays the same because the next number is below 5. This is how you do rounding with decimals! Please give Brainliest if this helps!