Answer:
Based on the number of cookies each girl made and if Kristina and Liz made the same number of cookies, then Heather made 4.2 dozen cookies.
Step-by-step explanation:
In order to find the number of cookies that Heather made, you need to set up two equations that represent the number of cookies that Kristina and Liz each made. Since Kristina made 2.4 dozen less than 6 times as many dozen as Heather, we can represent that with the equation 6c - 2.4. Since Liz made 1.8 dozen more than 5 times as many dozen as Heather, we can represent that with the equation 5c + 1.8. We can set both equations equal to each other since Liz and Kristina made the same number, so 6c - 2.4 = 5c + 1.8. Solving for 'c', which represents how many dozen cookies Heather made, we get 4.2
Let's assign a variable to represent the number of dozens of cookies Heather made. We'll call this variable \( H \).
According to the problem:
- Kristina made \( 6 \times H - 2.4 \) dozen cookies.
- Liz made \( 5 \times H + 1.8 \) dozen cookies.
We are also given that Kristina and Liz made the same number of cookies, so we can set these two expressions equal to each other to find the value of \( H \):
\[ 6H - 2.4 = 5H + 1.8 \]
Now, we'll solve this equation for \( H \).
Step 1: Isolate the variable \( H \) on one side.
To do this, we'll first subtract \( 5H \) from both sides of the equation:
\[ 6H - 5H - 2.4 = 5H - 5H + 1.8 \]
\[ H - 2.4 = 1.8 \]
Step 2: Now we need to get \( H \) alone, so we'll add \( 2.4 \) to both sides:
\[ H - 2.4 + 2.4 = 1.8 + 2.4 \]
\[ H = 4.2 \]
So, Heather made \( 4.2 \) dozen cookies.
To ensure this is the correct number of dozens Heather made, we can plug this value back into the original expressions for Kristina and Liz's cookies to verify that they made the same amount:
Kristina: \( 6 \times 4.2 - 2.4 = 25.2 - 2.4 = 22.8 \) dozen cookies
Liz: \( 5 \times 4.2 + 1.8 = 21 + 1.8 = 22.8 \) dozen cookies
Both Kristina and Liz made 22.8 dozen cookies, confirming our solution that Heather made 4.2 dozen cookies.
Write an algebraic expression for each word expression. Then evaluate the expression for these values of the variable : 1/2,4,and 6.5
1.) The quotient of p and 4
2.) 4 less than the sum of x and five
Answer:
1)p/4,2,1,1.625 2)x+1,3/2,5,7.5
Step-by-step explanation:
1) p/4
1/2 divided by 4=2
4/4=1
6.5/4=1.625
2) x+1
1/2+1=3/2
4+1=5
6.5+1=7.5
Sarah feeds her fish every 2 days and her snake every 6 days. In 30 days, how many times will Sarah feed her fish and snake on the same day?
Answer:
So if sarah feeds her fish every two days, youd divide each number by 30. So the fish would be fed 15 times and the snake 5 times. Hope you get it correct! Good Luck!
Answer: hello mate!
Sara feeds her fish every 2 days: this means that if we took the 0 in a day that she feed both animals; then the fish gets food on the day 2, on the day 4, on the day 6, etc
And the snake gets food on days 6, 12, 18, etc.
now we want to count the number of days where both animals get food on the same day. Because 6 is a multiple of 2, we can see that every day that the snake is feed, the fish also feed, this is because the minimal common multiple between 2 and 6 is 6.
then we can see that each 6 days Sarah feeds her fish and snake on the same day. Now we need to see the number of times that this event happens in 30 days; we can see this dividing 30 days by 6 days:
30/6 = 5
Then in the span of 30 days, there are 5 times where both animals get food on the same day.
If f(x) = 4x2 – 6 and g(x) = x2 – 4x – 8, find (f – g)(x).
Answer: Use the given functions to set up and simplify (f - g)(x). You should get 3x^2 +4x+2
1) What is the solution of the given system?
5x-y=-7
3x-y=-2
A: (-2.5,-5.5)
B: (-2.5,11)
C: (5,2.5)
D: (2.5,5.5)
2) what is the solution of the given system?
5x+7y=32
8x+6y=46
A: (8, 5)
B: (1, 5)
C: (7, 0)
D: (5, 1)
Answer:
1 x=-2.5 y = -5.5
2. x=5 y=1
Step-by-step explanation:
1) What is the solution of the given system?
5x-y=-7
3x-y=-2
Multiply the second equation by -1
-1*(3x-y)=-1(-2)
-3x +y = 2
Now add the first equation to the modified second equation
5x-y=-7
-3x +y = 2
------------------
2x = -5
Divide each side by 2
2x/2 = -5/2
x = -2.5
Now we need to find y
-3x+y =2
-3(-2.5) +y =2
7.5 +y =2
Subtract 7.5 from each side
7.5 -7.5 +y =2-7.5
y = -5.5
2) what is the solution of the given system?
5x+7y=32
8x+6y=46
Divide the second equation by 2
8x/2+6y/2=46/2
4x+3y =23
Multiply the first equation by 4
4 (5x+7y)=32*4
20x+28y = 128
Now multiply the modified 2nd equation by -5
-5(4x+3y )=-5(23 )
-20x -15y = -115
Lets add the new equations together to eliminate x
20x+28y = 128
-20x -15y = -115
---------------------
13y = 13
Divide each side by 13
13y/13 =13/13
y=1
Now substitute back in to find x
5x+7y=32
5x +7(1) =32
5x +7 =32
Subtract 7 from each side
5x+7-7 =32-7
5x =25
Divide by 5
5x/5 =25/5
x=5
evaluate the exponent
(-12) EE2
Answer:
Hence final answer is 144.
Step-by-step explanation:
Expression is not typed in proper format but as per given instruction "evaluate the exponent", I think it is:
[tex]\left(-12\right)^2[/tex]
So let's simplify that:
[tex]\left(-12\right)^2[/tex]
[tex]=\left(-12\right)\left(-12\right)[/tex]
[tex]=+144[/tex] {Since product of two negative numbers is always positive.
[tex]=144[/tex]
Hence final answer is 144.
Three hens can lay 3 eggs in 3 days.
How many hens would lay 3 eggs in 9 days?
What is the value of the expression? 3(68−12)+0.25 Enter your answer, in simplest form, in the box
Answer:168.25
Step-by-step explanation:
3(68−12)+0.25
=(3)(56)+0.25
=168+0.25
=168.25
Answer: 168.25 is the correct answer! :)
Step-by-step explanation: I took the test because of the first person!
Hope it helps for you too! Good luck
Donata bought 4 lemons and 4 plums at the local supermarket for a total of $ 21.60. Dan bought 11 lemons and 6 plums at the same store for a total of $40.90 how much does one lemon cost. .... helppppp. How Much does 1 plum cost?
Answer:
Each lemon costs $1.70. Each plum costs $3.70.
Step-by-step explanation:
You have two unknowns and two statements about costs. First, define a variable for each unknown. Then, translate the statements about the costs into two equations. Then, solve the system of equations.
Let L = price of 1 lemon
Let P = price of 1 plum
Donata:
4 lemons and 4 plums for $21.60
4L + 4P = 21.6 Equation 1
Dan:
11 lemons and 6 plums for $40.90
11L + 6P = 40.9 Equation 2
Here is the system of equations.
4L + 4P = 21.6 Equation 1
11L + 6P = 40.9 Equation 2
Divide both sides of Eq. 1 by 4.
L + P = 5.4
Multiply both sides by -6.
-6L - 6P = -32.4
Add the equation above to the Eq. 2.
5L = 8.5
L = 8.5/5
L = 1.7 <------- price of a lemon
L + P = 5.4
1.7 + P = 5.4
P = 3.7 <------ price of a plum
Each lemon costs $1.70. Each plum costs $3.70.
An initial population of 1,500 increases at an annual rate of 15%. Write an exponential function to model the population increase. Use the function to find the population after 15 years.
To model the population increase, use the formula P = P0 * (1 + r)^t, where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the number of years. The population after 15 years can be found by substituting t = 15 into the function.
Explanation:To model the population increase, we can use the formula for exponential growth.
The formula is P = P0 * (1 + r)^t, where P is the final population, P0 is the initial population, r is the annual growth rate (as a decimal), and t is the number of years.
In this case, the initial population is 1,500 and the annual growth rate is 15%. So the exponential function to model the population increase is P = 1500 * (1 + 0.15)^t.
To find the population after 15 years, we can substitute t = 15 into the function. P = 1500 * (1 + 0.15)^15
Given the equations f(x)= 4x+3 and g(x)=2x-1 find f-g
Answer: 2x+4
Subtract the equations like so
f - g = (4x+3) - (2x-1)
f - g = 4x+3 - 2x + 1 ... distribute the negative to all terms inside parenthesis
f - g = (4x-2x) + (3+1)
f - g= 2x + 4
how do you evaluate the function f(x)=x+6 when x = -2,0 & 5? (step by step please!)
Answer:
f(-2) = 4
f(0) = 6
f(5) = 11
Step-by-step explanation:
f(x)=x+6 when x = -2
Substitute x=-2
f(-2) = -2+6
f(-2) = 4
f(x)=x+6 when x = 0
Substitute x=0
f(0) = 0+6
f(0) = 6
f(x)=x+6 when x = 5
Substitute x=5
f(5) = 5+6
f(5) = 11
a man's speed with the current is 15km/hr and the speed of the current is 2.5km/hr.the man's speed against the current is
Answer:
10 km/h
Step-by-step explanation:
Let s = man's speed and c = speed of current
s + c = 15
c = 2.5 Insert value of c
s + 2.5 = 15 Subtract 2.5 from each side
s = 12.5 km/h
=====
Speed against current
= 12.5 – 2.5
= 10 km/h
Sue sold 26 more newspapers than bill, and bill sold three times as many as Harry. If Harry sold p newspapers, how many did Sue sell?
Answer:
Let p =Harry's papers
Then 3p =Bill's papers (3 times the number Harry has)
Then 3p + 26 = Sue's papers (26 more than Bill)
melissa pays a car insurance premium of $160 each month. she starts to carpool to work. she informs her car insurance conpany. the company takes 5% off. how much is her monthly car insurance premium
Answer:
152$
Step-by-step explanation:
160-5%=152
Answer:
$152
Step-by-step explanation:
160 × 5% = 8
160 - 8 = $152
You are in charge of decorating your gym for a home coming dance. You bought 6 bags of balloons and 5 bags of sparkling balloons for 19.20$. But you realize this is not enough. Than you buy 8 bags of balloons and 2 bags of sparkling stars for 15.80$. What was the price for each item
.
Answer:
I believe your answer would be 8 dollars and 75 cents. I don't know for sure.
Step-by-step explanation:
Using the provided systems of linear equations method, one bag of regular balloons costs $1.45, and one bag of sparkling balloons costs $2.10.
Explanation:The subject of this question is a typical example of a system of linear equations. Here, we are given two different purchases which give us two equations. We have:
1) 6B + 5S = 19.20 ---> Eq (1) (where B stands for one bag of balloons and S stands for one bag of sparkling balloons)
2) 8B + 2S = 15.80 ---> Eq (2)
Now, to find the prices of B and S (the number of bags of balloons and bags of sparkling balloons, respectively), we can solve this system of equations in two steps: multiplying Eq (2) by 2.5 and then subtracting Eq (1) from the result. This gives:
20B + 5S = 39.5
Then subtract Eq (1) from this new equation, which yields 14B = 20.3. So, one bag of balloons (B) costs $1.45. Substituting B = 1.45 into Eq (1), we get 6(1.45) + 5S = 19.2, which simplifies to 5S = 10.5. Thus, one bag of sparkling balloons (S) costs $2.10. So, the cost per bag of regular balloons is $1.45, and the cost per bag of sparkling balloons is $2.10, and this is how you go about decorating your gym on a budget.
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Can someone please help me with these problems I don't know how to do them. Thank you
[tex] \bold{FOR \: 1st \: image }[/tex]
By straight line angles property,
▶60 + 4x +20 =180
▶80 +4x =180
▶4x = 180 -80
▶4x = 100
x = 25
So, Second angle
▶4 ×25 +20
▶100 + 20
▶120
[tex] \bold{FOR \: 2nd \: image }[/tex]
3x + x =116
4x=116
x = 29
other angle = 3 ×29
=87
[tex] \bold{FOR \: 3rd \: image }[/tex]
ANGLE CAB + ANGLE ACB = 90
2x + x + 30 =90
3x + 30 =90
3x = 90 - 30
3x= 60
x=20
So, angle CAB = 2 ×20 = 40
please help solve 6x < 42
6x<42
Divide 6 by both sides
x<7
I need help with #2
Answer:
28 < x < 114
Step-by-step explanation:
x cannot be larger than or even equal to 71 + 43 = 114. So it must be less than 114.But there are limits on the other end as well. 43 +x > 71, otherwise you won't have a triangle. so you have to solve that inequality as well43 + x > 71 Subtract 43 from both sides.43-43 + x > 71 - 43x > 28To put this in the form of the answer you need it looks like this.28 < x < 11412z-5+3z combine like terms help plz hurry
Answer:
15z-5
Step-by-step explanation:
12z+3z=15z
-5=-5
Answer:
-3(-4y + 3) + 7y
distribute the -3 through the parenthesis
12y - 9 + 7y
19y - 9
Lettter A
Step-by-step explanation:
75.9 divided by 22 with remainders
Answer:
3.45
Step-by-step explanation:
When you divide them you will get 3. And reminders are basically decimals. So basically .45 is the reminder
Plzzz give brainlest im almost expert just need one more and plzz thank me
what is the distance between the points -3, 5 and -3,-9?
Answer:
the distance is 14
Step-by-step explanation:
To find the distance between 2 points, we can use the distance formula
d = sqrt( (x2-x1)^2 + (y2-y1) ^2 )
d = sqrt( (-3--3)^2 +(-9-5) ^2 )
= sqrt( (-3+3)^2 + (-14)^ 2)
= sqrt(0^2 +14^2)
= sqrt( 14^2)
= 14
Hi there! :)
Answer:
14
*The answer must have a positive sign.*
Step-by-step explanation:
[tex]x=\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}[/tex]
[tex]x=\sqrt{(-3--3)^2+(-9-5)^2}[/tex]
[tex]x=\sqrt{(-3+3)^2+(-14)^2}[/tex]
[tex]x=\sqrt{(0^2+14^2)}[/tex]
[tex]x=\sqrt{14^2=14}[/tex]
Final answer is 14.
Hope this helps!
Thanks!
-Charlie
Have a nice day! :)
:D
Which value is the product of (-14/19)(-1 5/14) in simplified form?
[tex]\left(-\dfrac{14}{19}\right)\left(-1\dfrac{5}{14}\right)\\\\\text{the product of two negative numbers is positive}\\\\\text{convert the mixed number to the improper fraction}\\\\\left(\dfrac{14}{19}\right)\left(\dfrac{14+5}{14}\right)=\dfrac{14\!\!\!\!\!\diagup^1}{19\!\!\!\!\!\diagup_1}\cdot\dfrac{19\!\!\!\!\!\diagup^1}{14\!\!\!\!\!\diagup_1}=1[/tex]
Answer:
1
Step-by-step explanation:
(-14/19)(-1 5/14)
We need to convert -1 5 /14 to an improper fraction so we can multiply
-1 5/14 = - (14*1 +5) /14 = -19/14
(-14/19) * (-19/14)
=1
does this graph represent a function? why or why not?
A rescue helicopter is used to help victims who fell in a ditch. The helicopter begins at sea level, which is an elevation of 0 feet. It then travels down for 100 seconds at a speed of 10.5 feet per second. It then travels directly up for 150 seconds at a speed of 5.2 feet per second. After this 250 second period, how much time, in seconds, will it take for the rescue helicopter to travel back to sea level at the helicopter's maximum speed of 15.8 feet per second?
Answer:
The helicopter still needs to fly up sec 17.0886 at maximum speed.
Step-by-step explanation:
solve for c if the product of c and 7 is less than 49
Answer:
c< 7
Step-by-step explanation:
the product of c and 7 is less than 49
Product means multiply
7c< 49
Divide each side by 7
7c/7 < 49/7
c< 7
Answer:
C = 7
Step-by-step explanation:
Equation:
C * 7 = 49
The opposite of multiplication is division, so we can find the solution through division:
49 / 7
= 7
C equals 7
We can check our work through multiplication:
7 * 7 = 49
Good Luck,
- I.A. -
What is the sale of the original price?
The percent of discount is 25 percent.
The sale price is 40 dollars.
Please help I’ll give Brainliest!!
Answer:
50 dollars
Step-by-step explanation:
40*25%=10
40+10= 50 dollars
Add it to find the original sales price which would end up being 50 dollars! Hope this helps, have a good day. c;
which monomials are divisible by 9
Answer:
Numbers are divisible by 9 if the sum of all the individual digits is evenly divisible by 9
Step-by-step explanation:
5+3+6+4 = 18
18 is divisible by 9 so therefore, those numbers are monomials of the number 9.
Monomials that are divisible by 9 are those whose numeric coefficient is divisible by 9. For example, the monomial 27x or 81y^2 are both divisible by 9 because their numeric coefficients (27 and 81, respectively) are divisible by 9.
Explanation:In mathematics, a monomial is an algebraic expression consisting of one term. Monomials that are divisible by 9 are those whose numeric coefficient is divisible by 9. For example, if you have a monomial like 27x, you can check if it's divisible by 9 by dividing the numeric coefficient (27) by 9. Since 27 divided by 9 is equal to 3, you can conclude that 27x is divisible by 9. Another example would be 81y^2 where the numeric coefficient is 81. Because 81 divided by 9 equal to 9, 81y^2 is also divisible by 9. So any monomial with a numeric coefficient that is a multiple of 9 is divisible by 9.
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Brad make 3 cups of pancake batter. If he needs 3/4 cup of batter to make 4 pancakes, how many pancakes can Brad make
Answer:
(3/4) cup/4 pancakes = 3 cups/x pancakes
(3/4)x = 12
x = 16
Brad can make 16 pancakes.
Brad can make 16 pancakes with 3 cups of batter, based on the ratio of 3/4 cup batter for every 4 pancakes.
To determine how many pancakes Brad can make with 3 cups of batter, when 4 pancakes require 3/4 cup of batter, we can set up a straightforward ratio and proportion calculation.
First, we divide the total batter amount by the batter requirement for a single group of pancakes: 3 cups / (3/4 cups) = 3 / 0.75 = 4 groups of pancakes.Because each group consists of 4 pancakes, we then multiply the number of groups by the number of pancakes in each group: 4 groups \\times 4 pancakes/group = 16 pancakes.Therefore, Brad can make 16 pancakes with 3 cups of batter.
A survey about phone service has a margin of error of 5%. Out of 150 people surveyed, 103 said that they were pleased with their service. The phone company has 72,000 customers. What is the range of the number of people that are satisfied?
A. 46,968 to 51,912 customers
B. 46,986 to 51,192 customers
C. 46,698 to 51,291 customers
D. 48,696 to 52,191 customers
Answer:
The range of the number of people that are satisfied is option A. 46,968 to 51,912 customers.
Step-by-step explanation:
Hi, to solve this problem you need to calculate the total number of customers that are pleased with the service, based on the 150 people sample.
so:
(72,000 x 103 )÷150 = 49,440
The next step is to calculate the 5% margin of error of that result.
49,440 x 0.05= 2,472
Finally, to obtain the range you need to add and subtract the margin to the total number of customers that are pleased with the service.
49,440-2,472= 46,968
49,440 + 2,472=51,912
So, the range of the number of people that are satisfied is option A. 46,968 to 51,912 customers.
Which function has the greatest rate of change? A. x y 3 3 4 6 5 9 B. y = 4 + 6x C. 12x + 6y = 18 D. A linear function that goes through point 1, negative 1 and point 0, 4
Answer:
B. y = 4 + 6x
Step-by-step explanation:
We know that the rate of change of a straight line is equal to the slope of the line.
Now, the general form of a straight line is y = mx + b, where m is the slope and b is the y-intercept.
Also, the slope of a line joined by [tex]( x_{1},y_{1} )[/tex] and [tex]( x_{2},y_{2} )[/tex] is given by [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
So, using these, we will find the slopes of the lines given in the options.
A. Here, we are given two points (3,3) and (4,6). Then, the slope is given by,
[tex]m_{1}=\frac{6-3}{4-3}[/tex] i.e. [tex]m_{1}=3[/tex].
B. We have the equation of line y = 4 + 6x. On comparing it with the general form, we get that the slope is 6 i.e. [tex]m_{2}=6[/tex].
C. We are given the standard form of a line. First, we convert it into the slope-intercept form ( or the general form ).
i.e. 12x + 6y = 18 → 2x + y = 3 → y = -2x + 3
Now, on comparing this equation with the general form of a line, we get that the slope is -2. i.e. [tex]m_{3}=-2[/tex].
D. Here, we are given a linear function passing through (1,-1) and (0,4). Then the slope is given by,
[tex]m_{1}=\frac{4+1}{0-1}[/tex] i.e. [tex]m_{4}=-5[/tex].
Hence, we obtain that the function y=4+6x has the greatest slope or the greatest rate of change i.e. [tex]m_{2}=6[/tex].