Mel paid $15.75 for 6 greeting
cards. Some of the cards cost
$2.50 each, and some cost $3.25
each. Let x represent the number
of cards that cost $2.50 each,
and y represent the number of
cards that cost $3.25 each. This
situation can be represented by
the system x + y = 6 and
2.5x + 3.25y = 15.75. How many
of each type of card did Mei
purchase?
Answers
Answer:
Step-by-step explanation:
x + y = 6 -------------(I)
y = 6 -x
2.5x + 3.25y = 15.75 -------------(II)
substitute y = 6 - x in equation (II)
2.5x + 3.25*(6 - x) = 15.75 {Distributive property: a(b +c) =a*b + b*c}
2.5x + 3.25*6 - x * 3.25 = 15.75
2.5x + 19.5 - 3.25x = 15.75
2.5x - 3.25x + 19.5 = 15.75 {Combine like terms}
-0.75x + 19.5 = 15.75
-0.75x=15.75 - 19.5
-0.75x = -3.75
x = -3.75/-0.75
x = 5
Plugin x = 5 in (I)
5 + y = 6
y = 6 - 5
y = 1
Related Questions
A rectangular garden is to be twice as long as it is wide. If 360 yards of fencing, including the gate, will enclose the garden, what will be the length of the garden, in yards?
Answers
Step-by-step explanation:
length = 2 × width
the perimeter of a rectangle is
2×length + 2×width
and it is 360 yards in our case
2×length + 2×width = 360
and then we use the first equation (2×width = length) in this second equation :
2×length + length = 360
3×length = 360
length = 360/3 = 120 yards
The cost to rent a moving yan for a day is an initial cost of $29 plus $0.35 per mile driven, Find a function to model the cast of the moving van rental
based on the initial cost and miles driven
Answers
Hello!
miles driven = x
the initial cost = 29
f(x) = 29 + 0.35x
Find the length of the missing side of the trapezoid below. [asy] size( 100 ) ; real top = 5 ; real bottom = 8 ; real height = sqrt(40) ; real slant = 7 ; pair ll = (-bottom,0) ; pair lr = (0,0) ; pair ur = lr+(0,height) ; pair ul = ur-(top,0) ; draw( ll--lr--ur--ul--cycle ) ; draw(rightanglemark( ur , lr , ll , 20 )) ; draw(rightanglemark( ul , ur , lr , 20 )) ; label( "$"+string(bottom)+"$" , ll--lr , S ) ; label( "$"+string(top)+"$" , ul--ur , N ) ; label( "$"+string(slant)+"$" , ul--ll , W ) ; [/asy] Give your answer in simplified form.
Answers
As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.
what is pythagoras theorem ?A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to Pythagoras' Theorem, is equal to the sum of the squares of the lengths of the other two sides (the legs). Formally, Pythagoras' theorem asserts that if a right triangle has legs of lengths a, b, and c, and a hypotenuse of length c, then:
\(a^2 + b^2 = c^2\)
Pythagoras, an ancient Greek mathematician, is credited with discovering and proving this theorem, therefore it bears his name.
given
The Pythagorean theorem can be used to determine the length of the omitted side. Let x be the length of the side that is missing. The right triangle that results has a hypotenuse that is top-bottom in length and legs that are x and slant in length. This can be expressed as:
x2 + slant2 = (top - bottom)2
$$
To put it simply, we have:
\begin{align*} \s(top - bottom) (top - bottom)
2 &= x 2 + slant 2, top 2 - 2top "cdot bottom + bottom 2 - slant 2," x 2 &= "sqrt" top 2 - 2top "cdot bottom + bottom 2 - slant 2," and "end align"
begin-aligning* x = sqrt((5),2,5,8,and(8),2,-7,2). sqrt = 25 - 80 + 64 - 49; sqrt = 40; sqrt = boxed 2i sqrt 10; end align;
As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.
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teri wants to buy as many pencils and pens as possible. she wants three pencils for every pen. each pencil costs $0.15 and each pen costs $0.20. she cannot spend more than $6.50
Answers
The maximum number of pens and pencils she can purchase is 10 pens and 30 pencils. The result is obtained by using substitution method on inequality problem.
How to find the maximum value in inequality?The most important thing in inequality problem is the inequality symbol. The symbols are:
">" = greater than"<" = less than"≤" = at least/no more than"≥" = greater than or equal toTeri wants to buy as many pencils and pens as possible by spending no more than $6.50. She wants three pencils for every pen. Each pencil costs $0.15 and each pen costs $0.20.
Find the maximum number of pens and pencils she can purchase?
Let's say:
x = number of pencilsy = number of pensThe money spent is no more than $6.50. It means the maximum money spent is $6.50. We got the inequality.
0.15x + 0.20y ≤ 6.50
She wants 3 pencils for 1 pen. We have x = 3y.
Substitute x with 3y!
0.15(3y) + 0.20y ≤ 6.50
0.45y + 0.20y ≤ 6.50
0.65y ≤ 6.50
y ≤ 10
x = 3y = 3(10) = 30
Hence, Teri can purchase 10 pens and 30 pencils with the money she can spend.
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One of your friends is testing the effect of drinking coffee on the duration of cold symptoms. The common cold lasts, on average, 6 days. Your friend starts with no expectations as to whether drinking coffee will have any effect on cold duration. After seeing the results of the experiment, in which the average cold duration was less than 6 days, your friend tests a one-sided alternative about the population mean cold duration when drinking coffee,H0: μcoffee = 6Ha: μcoffee < 6She finds z = â1.68 with one-sided P-value P = 0.0465.What is the correct two-sided P-value for z = â1.68? Round your answer to 4 decimal places.
Answers
Answer:
Null hypothesis:\(\mu \geq 6\)
Alternative hypothesis: \( \mu <6\)
For this case after conduct the one lower tail test we got the following p value:
\( p_v = P(t <-1.68) = 0.0465\)
And for this case if we want to conduct a bilateral test or two sided the sytem of hypothesis are:
Null hypothesis:\(\mu = 6\)
Alternative hypothesis: \( \mu \neq 6\)
And for this case the p value can be calculated like this:
\( p_v = 2* P(t <-1.68) =2* 0.0465= 0.0930\)
Step-by-step explanation:
For this case we are trying to proof the following system of hypothesis:
Null hypothesis:\(\mu \geq 6\)
Alternative hypothesis: \( \mu <6\)
For this case after conduct the one lower tail test we got the following p value:
\( p_v = P(t <-1.68) = 0.0465\)
And for this case if we want to conduct a bilateral test or two sided the sytem of hypothesis are:
Null hypothesis:\(\mu = 6\)
Alternative hypothesis: \( \mu \neq 6\)
And for this case the p value can be calculated like this:
\( p_v = 2* P(t <-1.68) =2* 0.0465= 0.0930\)
(3x^4+10×^3-2×^2+28×+27)÷(×+4)
Answers
Answer:
Step-by-step explanation: 21
f(x) = x + 2
g(x) = 3x² - 5
Find (f.g)(x).
OA. (f g)(x) = 3x³ - 10
OB. (f g)(x) = 3x³ + 6x² - 5x - 10
OC. (f. g)(x) = 3x³ + 10
OD. (f g)(x) = 3x³ + 6x² + 5x + 10
SUBMIT
Answers
Answer:
It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10
Step-by-step explanation:
In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.
• Take the products of both functions.
f(x)g(x) = 3x²+5 • x-2
• Next, expand the functions. We expand by combining like terms.
= 3x^3 - 6x^2 + 5x - 10
Since the function cannot be simplified further, this leads to option B being our answer.
Hope this helps!
WILL GIVE BRAINLYEST 100 POINTS !!!! A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−6, 2), (−6, −7), (6, 2), and (6, −7). What is the area, in square inches, of the painted face of the brick?
144 in2
108 in2
72 in2
42 in2
Answers
The area, in square inches, of the painted face of the brick is; 144 in²
How to find the area of a square with coordinates?The area of a square is given by;
A = L²
where;
L is the length of the side of the square
The sides of a square all have the same length, and as such we just need to find the length of one side.
The length of the side of the square here is the distance between two vertices, which can be calculated as
L = √[(x₂ - x₁)² + (y₂ - y₁)²]
However, to avoid long process, since it is a square, we can use subtraction of coordinates to get the side length which is gotten by using the first 3 coordinates;
Horizontal length = (6 + 6) = 12
Thus;
Area = L² = 12² = 144 in²
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PLEASEEE HELP WITH MARK BRAINLIEST!!!
What is the value of k?
Answers
Answer:
190 degrees or 1 degree
Step-by-step explanation:
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V = 3r2h
Write the formula to calculate the height, h.
Answers
Answer:
V/3r²
Step-by-step explanation:
We are to make h the subject of the formula as shown;
V = 3r²h
Divide both sides by 3r²
V/3r² = 3r²h/3r²
V/3r² = h
Rearrange
h = V/3r²
Hence the formula to calculate the height h is V/3r²
Answer:
h = V/3r²
Step-by-step explanation:
just did the test
3²-(-3²)=? what's the answer please
Answers
Answer:
0
Step-by-step explanation:
3^2 is 9, and (-3)^2 is 9.
so, 9-9=0
Pls click on me I need help( I’m trying to show my mom I’m smart
Answers
Answer:
30
Step-by-step explanation:
30 because 15/20=30/40
Find the difference of functions at x= - 3, (g - f)(-3), given f(x) and g(x): g(x) = x^2−15, and f(x) =2x
Answers
Answer:
0
Step-by-step explanation:
Solution:-
We are given two functions as follows:
\(f ( x ) = x^2 - 15\\\\g ( x ) = 2x\)
We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.
The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )
We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:
\([ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\\)
Now evaluate the above determined function at x = -3 as follows:
\(( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0\)
Listed below is a table showing the number of employees. 20 years or older by gender in the United states
Answers
The total number of workers that were studied can be found to be 139,340,000.
The percent of workers unemployed would be 5. 4 %.
Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.
How to find the employment figures ?Number of employed workers :
= 74,624,000 + 64, 716, 000
= 139,340,000
Percentage unemployed :
= ( 4, 209,000 + 3,314,000 ) / 139,340,000
= 5. 4 %
Percentage of unemployed men :
= 4,209,000 / 74,624,000
= 5.6 %
Percentage of unemployed women:
= 3,314,000 / 64, 716, 000
= 5. 1 %
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The full question is:
a. How many workers were studied?
b. What percent of the workers were unemployed?
c. Compare the percent unemployed for the men and the women.
A shampoo company conducted a survey and found that 3 out of 8 people use their brand of shampoo. Which proportion could be used to
find the expected number of users n in a city of 75,000 people?
75.000
Answers
Answer:yes
Step-by-step explanation:yes
Answer:
3/8 = x/75,000
Step-by-step explanation:
We are looking for x, the number of people in a city of 75,000 that use the shampoo.
3 is to 8 as x is to 75,000
3/8 = x/75,000
please help me with this math question with solutions please
2×+4=4!
Answers
Answer: x= 10
Step-by-step explanation:
2x+4=24
2x=24-4
2x=20
x=10
Answer:
Step-by-step explanation:
2x+4=4
subtract 4 from both sides
2x=0
divide by 2 on both sides
x=0
Select the correct answer from the drop-down menu. The missing term in the denominator is
Answers
Answer: where is the answer choices
Step-by-step explanation:
A goal is to get at least 10% of daily calories from polyunsaturated fats as are found in various nuts, oils, and fish. One serving of walnuts (about 15 pieces) has about 20 g of polyunsaturated fat. Each fat gram had 9 calories. About what percent of daily calories does one serving of walnuts provide, assuming a 2,000 calorie diet?
Answers
Answer:
9%
Step-by-step explanation:
(20*9)/2000=0.9
Find the present value of an annuity which pays ` 200 at the end of each 3 months for 10 years assuming
money to be worth 5% converted quarterly?
(a) ` 3473.86
(b) ` 3108.60
(c) ` 6265.38
(d) None of thes
Answers
The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.
To find the present value of an annuity, we can use the formula:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.
Plugging in these values into the formula, we get:
PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05
Simplifying the equation, we find:
PV ≈ 200 * (1 - 0.12198) / 0.05
PV ≈ 200 * 0.87802 / 0.05
PV ≈ 35160.4 / 0.05
PV ≈ 7032.08
Therefore, the present value of the annuity is approximately `7032.08.
None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.
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The two top concert tours in 2016 were concert A and concert B. Based on average ticket prices, it cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B. Three tickets for concert B cost a total of $687. How much did an average ticket cost for each tour?
Answers
The average ticket cost for each concert is given as follows:
Concert A: $188.83.Concert B: $95.67.How to obtain the ticket costs?The ticket costs are obtained by a system of equations, for which the variables are given as follows:
Variable a: cost for Concert A.Variable b: cost for Concert B.It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:
6a + 6b = 1707
a + b = 284.5.
Three tickets for concert B cost a total of $687, hence the cost for concert B is of:
3b = 687
b = 287/3
b = $95.67.
Replacing into the first equation, the cost for concert A is given as follows;
a = 284.5 - 95.67
a = $188.83.
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In circle O, secants ADB and AEC are drawn from external point A
such that points D, B, E, and C are on circle O. If AD = 8, AE = 6,
and EC is 12 more than BD, the length of BD is
(1) 6
(2) 22
(3) 36
(4) 48
Answers
The length of BD is 22.
In the given scenario, let's consider the following information.
AD = 8
AE = 6
EC is 12 more than BD.
To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.
From the given information, we know that AD = 8 and AE = 6.
Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.
First, let's find the intercepted arc corresponding to AD:
Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16
Similarly, we can find the intercepted arc corresponding to AE:
Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12
Now, we know that EC is 12 more than BD.
Let's assume the length of BD as x.
BD + 12 = EC
Now, let's consider the intercepted arcs theorem:
Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C
16 - 12 = Angle B - Angle C
4 = Angle B - Angle C.
Since Angle B and Angle C are vertical angles, they are congruent:
Angle B = Angle C.
Therefore, we can say:
4 = Angle B - Angle B
4 = 0
However, we have reached an inconsistency here.
The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.
As a result, we cannot determine the length of BD based on the given information.
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x divided by 12; x =2/3
Answers
Step-by-step explanation:
x÷12
2/3/12
2×12/3
24/3
8
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Isabella sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
105 visitors purchased no costume.
41 visitors purchased exactly one costume.
8 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth.
Answers
The probability that the next person will purchase one or more costumes can be found by dividing the number of visitors who purchased one or more costumes by the total number of visitors.
The total number of visitors is 105 + 41 + 8 = 154.
The number of visitors who purchased one or more costumes is 41 + 8 = 49.
So the probability that the next person will purchase one or more costumes is 49/154, which is approximately 0.32 to the nearest hundredth.
Kay loves to save coins. She has a piggy bank that she has been filling for a long time with only dimes and nickels. Recently, her piggy bank was filled to the brim so Kay counted her coins and she discovered that she had $10. She also noticed that she has 11 less dimes than nickels. How many coins were in Kay's bank?
Answers
The total number of coins that were in Kay's bank are 137 coins.
How to determine the number of coins?In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let d represent the number of dimes.Let n represent number of nickels.Since she has 11 less dimes than nickels, an equation which models this situation is given by;
n = d + 11 ....equation 1.
Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.
Additionally, the coins are worth 10 dollars;
0.1d + 0.05n = 10 ....equation 2.
By solving both equations simultaneously, we have:
0.1d + 0.05(d + 11) = 10
0.1d + 0.05d + 0.55 = 10
0.15d = 9.45
d = 63 dimes.
For nickels, we have:
n = d + 11
n = 63 + 11
n = 74
Now, we can determine the total number of coins;
Total number of coins = n + d
Total number of coins = 74 + 63
Total number of coins = 137 coins.
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Triangle JKL has vertices at the points J(2.5,3), K(3.2,-4.7), and L(-6.9,3). Find the slope of side JL.
A. undefined
B. -11
C. -0.76
D. 0
Answers
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope of side JK first, using the coordinates of points J(2.5, 3) and K(3.2, -4.7):
slope_JK = (-4.7 - 3) / (3.2 - 2.5)
slope_JK = (-7.7) / (0.7)
slope_JK ≈ -11
Now, let's calculate the slope of side KL, using the coordinates of points K(3.2, -4.7) and L(-6.9, 3):
slope_KL = (3 - (-4.7)) / (-6.9 - 3.2)
slope_KL = (7.7) / (-10.1)
slope_KL ≈ -0.76
Therefore, the slope of side JK is approximately -11, and the slope of side KL is approximately -0.76.
The options provided are:
A. undefined
B. -11
C. -0.76
D. 0
Based on the calculations, the correct answer would be:
B. -11
which of the following is an expression for”doubling a number n and dividing by 3”?
Answers
Answer:
2n/3
Step-by-step explanation:
hope this helps!! moo
Can someone help me out figure what the answers are. Was only able to get 4.
Answers
The completed table of the functions and inverses can be presented as follows;
1. t(x) → a(x)
2. Q(x) → B(x)
3. G(x) → c(x)
4. f(x) → D(x)
5. y(x) → w(x)
6. e(x) → R(x)
7. U(x) → H(x)
8. P(x) → J(x)
9. m(x) → k(x)
10. S(x) → n(x)
Which method can be used to complete the table?Making x the subject of the given functions to find the inverse gives;
1. a(x) = 2•(x - 6)
Therefore;
x = (a(x)/2) + 6
t(x) = (x/2) + 6
Therefore;
t(x) → a(x)2. G(x) = (1/4)•x²
4•G(x) = x²
x = 2•√(G(x))
3. B(x) = √(x)/4
4•B(x) = √(x)
x = 16•(B(x))²
Q(x) = 16•x²
Therefore;
G(x) → c(x)4. D(x) = (x + 6)/2
x = 2•D(x) - 6
f(x) = 2•x - 6
Therefore;
f(x) → D(x)5. y(x) = (4•x + 2)²
(√(y(x)) - 2)/4 = 4•x
w(x) = (√(x) - 2)/4
Therefore;
y(x) → w(x)6. R(x) = (1/4)•(4•x)²
x = √(4•R(x))/4 = √(R(x))/2
e(x) = √(x)/2
Therefore;
e(x) → R(x)7. H(x) = 2•x + 6
(H(x) - 6)/2 = H(x)/2 - 3
x = H(x)/2 - 3
U(x) = x/2 - 3
Therefore;
U(x) → H(x)8. J(x) = (√(x + 2))/4
x = (4•J(x))² - 2
P(x) = (4•x)² - 2
Therefore;
P(x) → J(x)9. k(x) = x/4 + 3
x = 4•(k(x) - 3) = 4•k(x) - 12
m(x) = 4•x - 12
Therefore;
m(x) → k(x)10. n(x) = 4•(x + 3)
x = n(x)/4 - 3
S(x) = x/4 - 3
Therefore;
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Simplify. 3√-50 Enter your answer, in simplest radical form, in the box.
they are looking for an imaginary number. will give brainliest. 30 POINTS GIVEN
Answers
An imaginary number is a number that, when squared, has a negative result. The imaginary number is given by √-1. It is denoted by i.
The simplest radical form of 3√-50 is 3√50i.
What is an imaginary number?An imaginary number is a number that, when squared, has a negative result. The imaginary number is given by √-1. It is denoted by i.
We have,
3√-50
We can separate √-50 = √-1 x √50
We can write as:
= 3 x √-1 x √50
= 3√50 i
This is the simplest radical form of 3√-50.
Thus the simplest radical form of 3√-50 is 3√50i.
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A tennis racket is normally priced at 90.00 is on for 30% off. What is an expression for the sale price of the racket,
Answers
Answer:
90×0.7
Step-by-step explanation:
I think this is the correct answer.
100-30=70
70=0.7
Given the function f(x) = 0.5|x - 41-3, for what values of x is f(x) = 7?
x = -24, x = 16
x= -16, x = 24
x=-1, x = 9
x = 1, x = -9
Answers
The values of x for which f(x) = 7 are x = 61 and x = 21.
To find the values of x for which f(x) = 7, we can set up the equation and solve for x.
The given function is f(x) = 0.5|x - 41| - 3.
Setting f(x) equal to 7, we have:
0.5|x - 41| - 3 = 7.
First, let's isolate the absolute value term:
0.5|x - 41| = 7 + 3.
0.5|x - 41| = 10.
To remove the absolute value, we can consider two cases:
Case: (x - 41) is positive or zero:
0.5(x - 41) = 10.
Multiplying both sides by 2 to get rid of the fraction:
x - 41 = 20.
Adding 41 to both sides:
x = 61.
So x = 61 is a solution for this case.
Case: (x - 41) is negative:
0.5(-x + 41) = 10.
Multiplying both sides by 2:
-x + 41 = 20.
Subtracting 41 from both sides:
-x = -21.
Multiplying both sides by -1 to solve for x:
x = 21.
So x = 21 is a solution for this case.
Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.
for such more question on values
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