Anatoliy has a combination of 104 nickels and quarters totaling $22. Which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, anatoliy has? n = q = 22 0. 05n + 0. 25q = 104 n + q = 104 5n + 25q = 22 n + q = 104 0. 05n + 0. 25q = 22 n + q = 22 5n + 25q = 104.
The equation which is correct is :
n + q = 104
Since we have given that:
Number of nickels and quarters = 104
Total amount from them = $22
Let the number of nickels be 'n'
Let the quarters be 'q'
So, the equation will be
n + q = 104 -------------------------------------------- (1)
Since we know that
value of nickels = 0.05 dollars
Value of quarters = 0.25 dollars
So, the equation will be
0.05n + 0.25q = $22 ------------------------------------ (2)
So, there are two system of linear equation can be used to find the number of nickels and the number of quarters. i.e.
n + q = 104
0.05n + 0.25q = $22
Using elimination we can find the value of n and q :
0.05( n + q =104 )
⇒0.05n+0.05q=5.2-----------(3)
Now, from equation (2) and (3), we get,
0.05 n + 0.05q = 5.2
0.05 n + 0.25q = 22
(-) (-) (-)
------------------------------------
0 + 0.2q = 16.8
q = 16.8 ÷ 0.2
q = 84
Putting the value of q = 84 in equation (1),
n + q = 104
⇒ n + 84 = 104
⇒ n = 104 - 84
⇒ n = 20
Hence, n +q =104 equation is correct.
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Arnulfo deposited $55 into a savings account. According to the rule of 72, what interest rate will cause his money to double in approximately 23 years?.
Interest rate will cause his money to double in approximately 23 years is 3.13%.
Given:
Arnulfo deposited $55 into a savings account and interest is in semi annually.
For 23 years the interest payments will be = 23*2
= 46
Interest rate = 2*72 / 46
= 144/46
= 72/23
= 3.13%
Therefore Interest rate will cause his money to double in approximately 23 years is 3.13%.
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a store put dress shirts on sale for 2 for $27.00. How much will
someone pay if they buy 5 shirts?
Answer:
$67.50
Step-by-step explanation:
27(2) = 54
27/2 = 13.5
54+13.5 = 67.5
Answer:
67.5
explanation:
27/2= 13.5
5*13.5= 67.5
I will mark brainliest!! help much needed >_<
Find the missing value so that the line passing through the 2 points has the given slope.
(-20, y) and (-11, 15); slope: 0
a. 15
b. -13
c. 11
The missing value of that makes the line that passes the given points have a slope of 0 is determined as: a. 15.
What is the Slope of a Line?The slope (m) is defined as the rise of a line over its run. The formula for finding the slope (m) of a line is given as:
Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Given the points (-20, y) and (-11, 15) has a slope (m) of 0. Therefore, let:
(-20, y) = [tex](x_1, y_1)[/tex]
(-11, 15) = [tex](x_2, y_2)[/tex]
m = 0
Substitute the values into the slope formula:
0 = (15 - y) / (-11 -(-20))
0 = (15 - y) / 9
Multiply both sides by 9
0 = 15 - y
0 + y = 15 - y + y
y = 15
The answer is: a. 15.
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In the figure below, m1 equals (x-9) degrees, and m2 equals 8x degrees. Find the angle measures.
Answer: m1=2 and m2=88
Step-by-step explanation:
90=x-9+8x
99=9x
x=11
Sarah mailed her computer to Store B for repairs. Her bill was:
Initial Repair Cost = $1,350
Sales Tax of 7 percent = $94.50
Total Cost of Computer Repair = $1,444.50
Shipping = 2 percent of Total Cost
What is the cost to ship this computer from Store B?
$
Answer: $28.89
Step-by-step explanation: 2% of 1,444.50 is $28.89
What is the slope of the line that passes through the points(7,-4) and (11, –4)? Write your answer in the simplest form.
Answer the questions of the function below.
What is the slope of the line?
What is the y-intercept?
What is the x-intercept?
Answer:
slope and x-intercept is -1/2
y-intercept is 5
Find the area of the floor of a square room in square metres of which each side is 800 cm
Answer:
A = 64 m²
Step-by-step explanation:
Step 1: What is the question asking
A = ? m²Step 2: What is known
sides = 800 cmStep 3: Conversion
convert 800 cm to metersKilo, Hecto, Deca, Base, Deci, Centi, Milli800 cm = 8 mStep 4: Answer the question/solve for the area
Area of a square = s²A = s² = 8² = 64 m²differentiative
2x-3
2x+1
The differential equation is 8x-4 when the equation is (2x-3)(2x+1).
Given that,
The equation is (2x-3)(2x+1)
We have to find the differentiative equation.
Calculus differentiates the process of locating a function's derivatives. A derivative is the pace at which one function changes in relation to another. Sir Isaac Newton set the foundations for the laws of differential calculus. Numerous scientific disciplines make use of the limits and derivatives ideas. The essential ideas of calculus are differentiation and integration.
Differentiation is the rate at which one quantity changes in relation to another.
Take the equation
(2x-3)(2x+1)
We can do in two ways
1st way
Multiply
4x²+2x-6x-3
Subtraction
4x²-4x-3
Differentiation
8x-4
The equation is 8x-4.
2nd way
We have a formula in differentiation that is
u.v=uv'+vu'
Take u as 2x-3 and v as 2x+1
(2x-3)(2)+(2x+1)(2)
4x-6+4x+2
8x-4
Therefore, The differential equation is 8x-4 when the equation is (2x-3)(2x+1).
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Anyone ?. Need help
Step-by-step explanation:
it is a parallelogram.
that means both pairs of opposite sides are parallel and the sides of each pair are equally long.
the sum of all internal angles is 360°.
the opposing angles are equal.
and therefore neighboring angles are complementary angles (or a linear pair) : together they have 180°.
so,
76 = 4x - 8
84 = 4x
x = 21
-3z + 8 + 76 = 180
-3z + 84 = 180
-3z = 96
z = -32
-3z + 8 = -6y - 10
-3×-32 + 8 = -6y - 10
96 + 8 = -6y - 10
104 = -6y - 10
114 = -6y
y = -19
Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons. Select the equation that represents the given situation and find the number of hours of Sophia's lesson.
The equation to represent the situation is y = 15 + 30x.
The number of hours Sophia used for the guitar training after paying 75 dollars is 2 hours.
How to use equation to represent situations?Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons.
The equation that can be used to represent the given situation is as follows:
let
x = number of hours used for the training
y = total cost
Therefore,
y = 15 + 30x
Now, Sophia's mother spent 75 dollars for her daughters training. Let's find the hours Sophia used.
Therefore,
75 = 15 + 30x
75 - 15 = 30x
60 = 30x
divide both sides by 30
x = 60 / 30
x = 2
Therefore, she used 2 hours for the training.
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Someone please help me with this problem, thank uuu
Answer:
B
Step-by-step explanation:
HELP! ASAP!! 50 points if you help!
Heidi earned $30 in commission.
The amount of money that the store made from Heidi's sales is equal to $720.
How to calculate commission.In this exercise, you're required to determine the amount of money earned by the salesperson as commission based on the price at which she sold a jewelry.
Mathematically, the amount of commission earned on the sales of a product can be calculated by using this mathematical expression:
Commission = Percent commission × Sales price
Given the following data:
Percent commission = 4%
Sales price = $750.
Substituting the given parameters into the formula, we have;
Commission = 4/100 × 750
Commission = 0.04 × 750
Commission = $30.
Next, we would determine the amount of money that the store made from her sales:
Sales = $750 - $30.
Sales = $720.
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Gordon is 5 years older than Krutika. David is 6 years younger than Krutika. If the total of their ages is 86, how old is the eldest of them?
Answer:
Step-by-step explanation:
Well let Krutica’s age = x
K = x, G = x+5, D = x-6
K+G+D = 86
x + x+5 + x-6 = 86
3x = 87
x = 29
Gordon is the eldest of the few:
29 or x+5=
34 years old
Answer: Gordon is 34 years old
Given: <1 and <2 are complementary. <1 and <3 are complementary
Prove: 22 = 23
Complete the proof.
Answers:
1st box: [tex]\boldsymbol{90}[/tex]
2nd box: [tex]\boldsymbol{90}[/tex]
3rd box: [tex]\boldsymbol{\text{m}\angle 2 = \text{m}\angle 3}[/tex]
===============================================
Explanation:
Complementary angles form a corner. Note that "complementary" and "corner" both start with "C" to help remember the rule.
By "corner", I refer to a 90 degree angle.
Since [tex]\angle 1\text{ and } \angle 2[/tex] are complementary, we know that [tex]\text{m}\angle 1+\text{m}\angle 2 = 90[/tex] simply by the definition of what it means to be complementary.
---------------
Through similar logic, [tex]\angle 1\text{ and } \angle 3[/tex] are complementary which means [tex]\text{m}\angle 1+\text{m}\angle3 = 90[/tex]
We can then equate the left hand sides (LHS) of both equations since both LHS expressions equal 90. This is an example of the substitution property in action.
That's how we end up with [tex]\text{m}\angle 1+\text{m}\angle 2 = \text{m}\angle 1+\text{m}\angle 3[/tex]
After this point, subtract [tex]\text{m}\angle1[/tex] from both sides to cancel them out. We'll be left with [tex]\text{m}\angle 2 = \text{m}\angle 3[/tex], which concludes with [tex]\angle 2 \cong \angle 3[/tex] to show the two angles are congruent.
Question 1 (1 point)
The scatter plot shows the number of days since several people filled their cars with
gas and the gallons of gas in their tank. Which is the most reasonable estimate of the
gallons of gas in a tank if it has been 3 days since filling up?
GALLONS OF GAS
8875294
DAYS SINCE FILLING UP
10 gallons
13 gallons
23 gallons
17 gallons
Answer:
D) 17 gallonsStep-by-step explanation:
Estimated line of best fit added to the graph (see attached).
The most reasonable value of y corresponding to x = 3 is approximately 18 gallons.
The matching answer choice is D.
Answer:
(D) 17 gallons
Step-by-step explanation:
What is the solution to the equation 6x−5=15, given the replacement set {56, 53, 103} ?.
The solution of the given equation is x = 10/3
The replacement value is 10/3.
This is incorrect question
Correct question is :
What is the solution to the equation 6x−5=15, given the replacement set {5/6, 5/3, 10/3}
Given,
In the question:
The equation is given as:
6x - 5 = 15
To find the solution of the given equation.
Now, According to the question:
The equation is:
6x - 5 =15
Combine the like terms:
6x = 15 + 5
6x = 20
x = 20 /6
x = 10/3
Hence, The solution of the given equation is x = 10/3
The replacement value is 10/3.
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b) Simplify 18x³y³ + 2x³y
The GCF: 2x³y
answer: 2x³y2x³y(9y³+1)
Nathaniel invested $2,900 in an account paying an interest rate of 5.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?
Answer:
$5252.53============================
GivenInvested amount P = $2900,Annual interest rate r = 5.4% = 0.054,Time t = 11 years,Compound number = continuous.Find the balance after 11 yearsUse equation for continuous compound:
[tex]P(t) = P_0e^{tr}[/tex],where P(t) - final amount, P₀ - initial amount, t - time, r - interest ratePlug in the values and calculate:
[tex]P(11) = 2900e^{11*0.054}=5252.53 \ rounded[/tex]Answer:
$5,252.53 (nearest cent)
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amount.P = Principal amount.e = Euler's number (constant).r = Annual interest rate (in decimal form).t = Time (in years).Given values:
P = $2,900r = 5.4% = 0.054t = 11 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]
[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]
[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]
[tex]\implies \sf A=5252.53457...[/tex]
Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).
A, B, C, D, E, F, G and H form a cuboid. AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm. Find ED rounded to 1DP.
According to the Pythagoras theorem, the value of ED is 8.4 cm
Pythagoras theorem:
Pythagoras theorem defines that the right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given,
A, B, C, D, E, F, G and H form a cuboid.
AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm.
Now, we need to find the value of Ed and round off it into 1 decimal place.
Here we have the cuboid with the edges named as A, B, C, D, E, F, G and H.
Now, we have to use the value of BC and CG to find the value of hypotenuse of BG.
Because, BG and ED are opposite to each other.
Which means both have the same hypotenuse value.
So, according to the Pythagoras theorem,
=> BG² = BC² + CG²
=> BG² = (2.3)² + (8.1)²
=> BG² = 5.29 + 65.61
=> BG² = 70.9
So, the value of BG is 8.42.
Therefore, the value of ED is 8.4 When we round off this into one decimal place.
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19) For which value of s is the value of the expression s + 6 ÷s greatest?
A. 1
B. 2
C. 3
D. 4
The correct option A. 1, is the value of the variable 's' for which the solution of the expression is greatest .
Define the meaning of the greatest value?whenever one value exceeds another. We employ the "greater than" symbol. as in: 9 > 6.For the given question,
The expression is-
(s + 6) ÷ s
Use the options;
A : s = 1
= (s + 6) ÷ s
= (1 + 6) ÷ 1
= 7
B : s = 2
= (s + 6) ÷ s
= (2 + 6) ÷ 2
= 4
C : s = 3
= (s + 6) ÷ s
= (3 + 6) ÷ 3
= 3
D : s = 4
= (s + 6) ÷ 4
= (4 + 6) ÷ 4
= 2.5
Thus, the value of the variable 's' for which the solution of the expression is greatest is 1.
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Isaac works at a deli. He made a 30-cup batch of potato salad, and now he is filling 2.5-cup
to-go containers to sell to customers.
Write an equation that shows how the number of cups of potato salad remaining,y, depends
on the number of to-go containers Isaac has filled, x.
y =
Help
The equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.
Isaac made a 30-cup batch of potato salad, and now he is filling 2.5-cup
to-go containers to sell to customers.
Let y represent the number of cups of potato salad remaining,
And x represents the number of to-go containers Isaac has filled,
As per the given situation, we can write the equation as:
y = 30 - x ....(i)
Substitute the value of x = 2.5 in the above equation,
y = 30 - 2.5
y = 27.5
Thus, the equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.
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Draw a square and it diagonals. Guess the measures of these angles.
All angles of a square are 90° regardless of the length of its sides. However, all sides must be the same length.
What is a square?A square is a term to refer to a geometric figure that is characterized by the following characteristics:
Has four sidesIt has four 90° anglesAll its sides have the same lengthOne key to identifying a square and the value of its angles is to add them together. The sum of the angles of any geometric figure must result in 360°.
90° + 90° + 90° + 90° = 360°Additionally, if we mark the diagonals of a square we must take into account that these angles will have a different value. To find this value we must divide the angle in half, because these diagonals divide the figure into two parts.
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For each situation below, find the unit rate
Drag each situation on the left to the unit rate on the right
Questions: Choices:
Ricky spent $15.00 on 4 pizzas $8.00
William paid $20.00 for 2 1/2 pounds of blackberries $13.50
$3.75
The unit rate of Ricky purchase is $3.75 per pizza.
The unit rate of William purchase is $8 per pounds of blackberries.
What is unit rate?Unit rate is the ratio of two different units, with denominator as 1.
In other words, a unit rate is a rate where the second quantity is one unit , such as $10 per pound, 30 miles per hour, 22 Indian Rupees per Nigerian naira, etc.
Let's find the unit rate of the situations.
Ricky spent $15.00 on 4 pizzas
unit rate = 15 / 4
unit rate = 3.75 dollars per pizza
William paid $20.00 for 2 1/2 pounds = 5 / 2 pounds of blackberries.
Therefore,
unit rate = 20 ÷ 5 / 2
unit rate = 20 × 2 / 5
unit rate = 40 / 5
unit rate = 8 dollars per pounds of blackberries
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please help with the geometry homework
The triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.
First, let us understand the SAS congruency theorem:
This one denotes Side - Angle - Side and it means that if 2 sides and one angle of a triangle are equal to the corresponding 2 sides and one angle of another triangle, then they are both congruent.
We are given:
SR and ST are straight lines.
side SX ≅ side SY
side XR ≅ side YT
So,
side SR ≅ side ST
In triangle RSY and triangle TSX;
side SR ≅ side ST (above proved)
∠RSY ≅ ∠TSX (Common)
side SY ≅ side SX (Given)
So, triangle RSY ≅ triangle TSX by SAS congruency theorem.
Thus, the triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.
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Which is the equation in slope-intercept form
for the graph of the line shown?
F. y=-3x - 2
G. y=-3x + 2
H. y = 3x - 2
I. y = 3x + 2
Please help me!
a major credit card company has determined that customers charge between $300 and $1500 per month. the monthly amount charged is uniformly distributed. find the standard deviation of the monthly amount charged. (round to four decimal places if needed)
The standard deviation of the monthly amount charged is 346.41
Step 1: Identify the values of a and b, where [a , b] is the interval over which the continuous uniform distribution is defined.
Since it takes between 300 and 1500 minutes to be seated at the restaurant, we have:
a = 300
b = 1500
Step 2: Calculate the variance using the formula Var(x) = [tex]\frac{(b-a)^{2} }{12}[/tex]
Using the formula for the variance and the values identified in step 1
(a = 300 , b = 1500), we have:
Var(x) = [tex]\frac{(b-a)^{2} }{12}[/tex]
= [tex]\frac{(1500 - 300)^{2} }{12}[/tex]
= 1440000/12
= 120,000
the variance is 120,000
Step 3: Calculate the standard deviation by taking the square root of the variance. σ = [tex]\sqrt{Var(x)}[/tex]
The standard deviation is the square root of the result from step 2 (variance = 120,000)
σ = [tex]\sqrt{Var(x)}[/tex]
σ = [tex]\sqrt{120000}[/tex]
= 346.41
The standard deviation of the monthly amount charged is 346.41
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can someone please help asap !!!
Answer:
a = -1
b = -9
Step-by-step explanation:
when x = -2 put -2 for x in the equation:
a(3- (-2)) = -2*(-2) + b and then solve
a(3+2) = 4+b
5a = 4+b
then look at the numbers in the box and try for which number this equation will work. when you put a = -1 and b = -9 you will see it is equal on both sides because each side is -5
Do You Understand?
1.8
? Essential Question How can you use
the properties of operations to multiply linear
expressions?
It is possible to multiply or divide an equation by the same number on each side of the equation without changing the answer, according to the "multiplication property" of the equation.
How can you use the properties of operations to multiply linear expressions?
According to the equation's "multiplication property," it is possible to multiply or divide an equation by the same number on each side of the equation without changing the equation's outcome. The result of multiplying two terms with two different signs will be negative, while the product of two factors with the same sign will be positive. If a and b are positive integers and x is a variable, then (xa * xb) = x(m + n). The identity, commutative, associative, and distributive properties of multiplications are four properties that can facilitate the process. They offer guidelines for solving multiplication problems quickly using properties that always hold true for particular equations.
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