y2 = m(x2-x1) + y1
Hope this helps :)
At a summertime poolside snack bar, 200 ice cream scoops were sold in one day. Double scoops were sold for $1.25 each and single scoops were sold for $1 each. If the proceeds from the sale of the cones were $221.75, how many of each kinds of cone were sold? In all, how many scoops of ice cream were sold?
Answer:
a) 87 double scoops and 113 single scoops.
b) 287 scoops of ice cream.
Step-by-step explanation:
1. You need to make a system of equations, where double scoops are represented by [tex]x[/tex] and the single scoops are represented by [tex]y[/tex]:
[tex]\left \{ {{x+y=200} \atop {1.25x+y=221.75}} \right.[/tex]
2. You can apply the Elimination Method:
- Multiply the first equation by -1 to cancel the variable [tex]y[/tex] from the system. Add both equations:
[tex]0.25x=21.75[/tex]
- Solve for [tex]x[/tex]:
[tex]x=\frac{21.75}{0.25}\\x=87[/tex]
- Substitute the value of [tex]x[/tex] into one of the original equations and solve for [tex]y[/tex]:
[tex]87+y=200\\y=113[/tex]
3. You can calculate the total number of scoops of ice cream that where sold as below:
[tex]2x+y[/tex]
4. Substitute values:
[tex]2(87)+113=287[/tex] scoops of ice cream
Answer: The number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.
Step-by-step explanation: Given that at a a summertime poolside snack bar, 200 ice cream scoops were sold in one day.
Double scoops were sold for $1.25 each and single scoops were sold for $1 each. The proceeds from the sale of the cones were $221.75.
We are to find the number of single scoop cones, double scoop cones and the number of scoops of ice cream that sold.
We Let x and y represents the number of cones of single scoop and double scoop ice cream that sold.
Then, according to the given information, we have
[tex]x+y=200\\\\\Rightarrow x=200-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]1\times x+1.25y=221.75\\\\\Rightarrow x=221.75-1.25y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Comparing equations (i) and (ii), we get
[tex]200-y=221.75-1.25y\\\\\Rightarrow 1.25y-y=221.75-200\\\\\Rightarrow 0.25y=21.75\\\\\Rightarrow y=\dfrac{21.75}{0.25}\\\\\Rightarrow y=87.[/tex]
From equation (i), we get
[tex]x=200-87=113.[/tex]
Therefore, total number of scoops that were sold is
[tex]113+2\times87=113+174=287.[/tex]
Thus, the number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.
Which picture shows the correct graph of |x|=5?
|x| = 5
x = 5 or x = -5
You need a graph that has a closed dot on -5 and a closed dot on 5.
Answer: B. Picture B
Please help me with this
The perimeter of the rectangle:
[tex]P_R=2(4x+2+2x)=2(6x+2)=(2)(6x)+(2)(2)=12x+4[/tex]
The perimeter of the square:
[tex]P_S=2(5x-3+3x+1)=2(8x-2)=(2)(8x)+(2)(-2)=16x-4[/tex]
The perimeter of the rectangle is equal to the perimeter of the square. We have the equation:
[tex]12x+4=16x-4\qquad|\text{subtract 4 from both sides}\\\\12x=16x-8\qquad|\text{subtract 16x from both sides}\\\\-4x=-8\qquad|\text{divide both sides by (-4)}\\\\x=2[/tex]
The side lengths of the square:
[tex]5x-3\to5(2)-3=10-3=7[/tex]
The side lenghts of the rectangle:
[tex]4x+2\to4(2)+2=8+2=10\\2x\to2(2)=4[/tex]
Other method.
If the first figure is a square, then the length of the sides are equal.
Therefore
[tex]5x-3=3x+1\qquad|\text{add 3 to both sides}\\\\5x=3x+4\qquad|\text{subtract 3x from both sides}\\\\2x=4\qquad|\text{divide both sides by 2}\\\\x=2[/tex]
Further part of the solution as above.
the recipe for an omelet says 5 eggs make 2 serving. how many eggs are required to make 8 serving?
Evaluate 3⋅(1−21/0−^3)+12
A.−3,012
B. −2,988
C.2,600
D.3,066
identify the initial amount,a,and the growth factor,b,in each exponential function.Break b into (1+r)where r is the rate of growth. Give r as a percentage. y=1.05(1.46)^x
Given function : [tex]y=1.05(1.46)^x[/tex]
We need to identify a " initial amount", b "growth factor", r " rate of growth".
We know, exponential growth formula
[tex]y=a(b)^x[/tex], where a is initial amount, b is growth factor. On comparing with given function let us find values of a and b.
[tex]y=1.05(1.46)^x[/tex] ⇔ [tex]y=a(b)^x[/tex].
We can see a= 1.05 and b = 1.46.
Now, b=1+r.
Therefore, 1+r =1.46.
Subtracting 1 from both sides, we get
1+r-1 =1.46-1
r = 0.46.
On converting 0.46 into percentage, we get
0.46 × 100 = 46.
Therefore, intial amount a = a= 1.05 , growth factor b = 1.46, and the rate of growth r= 46%.
Final answer:
The initial amount, a, is 1.05, and the growth factor, b, is 1.46 in the exponential function y=1.05(1.46)ˣ. The growth rate, r, when expressed as (1+r), is 46%.
Explanation:
To identify the initial amount a and the growth factor b in the exponential function y=1.05(1.46)ˣ, we look at the standard form of an exponential function, which is y=a×bˣ. Comparing this with the given function, we can see that the initial amount a is 1.05 and the growth factor b is 1.46.
To express the growth factor in the form of (1+r), where r is the rate of growth, we can set b = 1 + r. This means that r would be b - 1, which is 1.46 - 1 = 0.46. To express r as a percentage, we multiply by 100, resulting in a growth rate of 46%.
oint) Solve the following inequality. Enter the answer in interval notation. 10x - 5 < -10(8x - 2)+3 Answer: Note: If the answer includes more than one interval, write the intervals separated by the "union" symbol, U. If needed, enter \infty as infinity and -\infty as -infinity.
Which point is on the graph of f(x)=3x5^x?
By substituting x=1 into the function f(x)=3x5^x, we find that the point (1,15) is on the graph.
To find a point that lies on this graph, we can select a value for x, substitute it into the function, and calculate the corresponding y value. Let's try x=1:
f(1) = 3(1)51 = 3(5) = 15.
Therefore, the point (1,15) is on the graph of f(x)=3x5^x.
What is the answer???♀️♀️♀️
5-(-8) = 5 + 8 =13
As multiplication of two negatives is positive
Tom saves $5 each month, how many months will he need to save $20?
4 months because:
1 month = 5 dollars
so you add 5 until you get to 20 dollars. And as many times as you added 5 is how
many months. So:
5= 5
5 + 5 = 10
5+5+5= 15
5+5+5+5= 20
^ ^ ^ ^
1 2 3 4
your answer is 4 months ^^
Which ordered pair is a solution of the equation?
x+7y=17
Choose 1 answer:
(Choice A)
A
Only (10,1)
(Choice B)
B
Only (-4,3)
(Choice C)
C
Both (10,1) and (-4,3)
(Choice D)
D
Neither
The ordered pair is a solution of the equation is option C) Both (10, 1) and (-4, 3)
Which ordered pair is a solution of the equation?To know which ordered pair is a solution of the equation x + 7y = 17, we can substitute the values of x and y from each option into the equation and see if it holds true:
A) (10, 1)
Substitute x = 10 and y = 1 into the equation:
10 + 7(1) = 10 + 7 = 17
So, (10, 1) is a solution.
B) (-4, 3)
Substitute x = -4 and y = 3 into the equation:
-4 + 7(3) = -4 + 21 = 17
So, (-4, 3) is also a solution.
So, both (10, 1) and (-4, 3) satisfy the equation x + 7y = 17, the correct answer is: option C) Both (10, 1) and (-4, 3)
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20x^2-30=4x solve for x
Answer:
x=1.3288 or -1.1288
Step-by-step explanation:
Given [tex]20x^{2}-30=4x[/tex]
Subtract 4x from both sides
[tex]20x^{2}-4x-30=0[/tex]
Since we can factor out 2 from whole equation, let's factor out 2.
[tex]2(10x^{2}-2x-15)=0[/tex]
Divide with 2 on both sides
[tex]10x^{2}-2x-15=0[/tex]
We got the quadratic equation, we can solve for x using quadratic formula.
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac} } {2a}[/tex]
[tex]x=\frac{2\pm\sqrt{2^{2}-4X10X(-15)} } {2X10}[/tex]
[tex]x=\frac{2\pm\sqrt{604} }{20}[/tex]
[tex]x=\frac{2\pm2\sqrt{151}}{20}[/tex]
[tex]x=1.3288or-1.1288[/tex]
Find the distance CD rounded to the nearest tenth.
C=(5,6) and D (2,2)
CD=
Use the distance formula to find the distance between points C (5,6) and D (2,2).
d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
Plug the corresponding values in to the equation.
d=[tex]\sqrt{(2-5)^2+(2-6)^2}[/tex]
Then simplify the rest of the equation.
d=[tex]\sqrt{(-3)^2+(-4)^2}[/tex]
d=[tex]\sqrt{9+16}[/tex]
d=[tex]\sqrt{25}[/tex]
d=[tex]5[/tex]
The distance of the two points CD is 5.
To find the distance between point C=(5,6) and point D=(2,2), we use the distance formula which results in d=5.0 units rounded to the nearest tenth.
To calculate the distance between point C and point D, we use the distance formula derived from the Pythagorean theorem. The coordinates given are C=(5,6) and D=(2,2). The distance formula is:
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
Substituting the coordinates of points C and D into the formula gives us:
d = √{(2 - 5)² + (2 - 6)²}
This simplifies to:
d = √{(-3)² + (-4)²}
Further simplifying:
d = √{9 + 16}
d = √{25}
Finally, taking the square root of 25:
d = 5
Therefore, the distance between point C and point D, rounded to the nearest tenth, is 5.0 units.
Which equations show how to find 16-9?
A. 9+1=10 , 10 +5 =15
B. 9+1=10 , 10+6=16
C. 9+2=11 , 11+6=17
D. 9+1=10 , 10+9=19
The option B, [tex]\(9 + 1 = 10\)[/tex] and [tex]\(10 + 6 = 16\)[/tex], correctly shows how to find [tex]\(16 - 9\)[/tex], as it demonstrates that starting with 9 and adding 1 to it and then adding 6 more yield the result of 16. Option b is the correct answer.
The equation to find [tex]\(16 - 9\)[/tex] should involve subtracting 9 from a number and getting a result of 16. Among the provided options:
A. 9+1=10 , 10 +5 =15: This equation does not result in 16.
B. 9+1=10 , 10+6=16 : This equation satisfies the condition [tex]\(16 - 9 = 16\)[/tex], so it's the correct answer.
C. 9+2=11 , 11+6=17 : This equation does not result in 16.
D. 9+1=10 , 10+9=19 : This equation results in 19, not 16.
So, option B, [tex]\(9 + 1 = 10\)[/tex] and [tex]\(10 + 6 = 16\)[/tex], correctly shows how to find [tex]\(16 - 9\)[/tex], as it demonstrates that starting with 9 and adding 1 to it and then adding 6 more yields the result of 16.
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As line becomes the value of its slope get bigger
What is your question exactly??
Five-hundred twenty-one million, three hundred four thousand, six hundred two and three tenths. In standard form
Comb someone help me
C is the correct statement
∠CBE and ∠DEB are same side interior angles
The length of a rectangle is 12 units longer than the width. The perimeter is 7 times the width. Find the length and the width of the rectangle?
Log explanation below; answer is at bottom.
If the length, l, is 12 units longer than the width, w, then w = l - 12. If the perimeter, p,
p = 2l +2w,
is 7 x w, then
w = p/7
When two things are set equal to the same variable, they are equal to each other, so,
l - 12 = p/7
Now you need to get rid of the p so you are only working with one variable. To do this you plug in whatever p is equal to for p, so,
l - 12 = (2l + 2w)/7 now to get rid of the w do the same thing we did with p just for w. So,
l - 12 = (2l + 2(l - 12))/7
To solve this you want to multiply both sides by 7 first to get rid of the fraction.
7l - 84 = 2l + 2(l - 12)
Next you want to distribute the 2 over the l and the 12.
7l - 84 = 2l + 2l - 24
Next you want to combine like terms on each side.
7l - 84 = 4l - 24
Next add 84 and subtract 4l from sides to isolate the variable.
3l = 60
Now divide each side by 11 to get your answer.
l = 20.
To find the width,
w = l - 12
Just plug in and solve.
w = 20 - 12
w = 8
So your length and width are 20 and 8.
l = 20
w = 8
The width of the given rectangle is 8 units and the length is 20 units.
To find the length and the width of a rectangle when given that the length is 12 units longer than the width and the perimeter is 7 times the width, we can set up two equations. Let's denote the width as w and the length as l. According to the problem, l = w + 12 and the perimeter P = 2l + 2w is equal to 7w.
Set up the equations
l = w + 12
P = 2l + 2w
P = 7w
Substitute the value of l into the perimeter equation
7w = 2(w + 12) + 2w
Solve for w
7w = 2w + 24 + 2w
7w = 4w + 24
3w = 24
w = 8
Find the length using the width
l = w + 12
l = 8 + 12
l = 20
Javier has 4 boxes of comic books. The mean number of books in each box is 25 . Which number line shows what could happen to the mean if he fills two more boxes, one with 26 comic books and one with 30 comic books?
The mean could increase from 25 to 27.
Explanation:The mean number of books in each box is 25. If Javier fills two more boxes, one with 26 comic books and one with 30 comic books, the mean could increase or stay the same. Let's calculate the mean with and without the additional boxes:
Mean without additional boxes: (4 boxes * 25 books per box) / 4 = 25
Mean with additional boxes: (6 boxes * 25 books per box + 26 books + 30 books) / 8 = (150 + 26 + 30) / 8 = 27
Therefore, the mean could increase from 25 to 27 if Javier fills two more boxes with 26 and 30 comic books.
Find the number that makes the ratio equivalent to 2:8.
A ratio is used to describe how two or more quantities are related. For example, we might say that a fruit drink calls for sugar crystals to be mixed with water in a ratio of 2:8. This means that for every 2 scoops sugar crystals, there will need to be 8 ounces of water. If there were 200 scoops of sugar crystals, there would need to be 800 ounces of water.
Sure, we'll start off by simplifying the ratio 2:8. Simplifying it gives us 1:4.
Our aim is to find a number, let's denote it by x, such that the ratio 2:x will be the same as 1:4.
To find such an x, we need to set up an equation using the principle of equivalence of ratios. This gives us 2/x = 1/4.
Now we proceed to solve this equation for x. We do this by cross-multiplying the fractions in the equation.
Cross-multiplication gives us 2*4 = x*1. Simplifying this yields 8 = x.
Hence, we can conclude that the number x that makes the ratio 2:x equivalent to 2:8 is 8.
What is the GCF of two prime numbers
It must be 1.
Factors of prime numbers are 1 or themselves, the only factor common to all prime numbers is 1.
Echy~
The Greatest Common Factor (GCF) of two prime numbers is always 1.
The Greatest Common Factor (GCF) of two prime numbers is always 1 because prime numbers are numbers with only two factors: 1 and themselves.
For example, the GCF of 3 and 5, both prime numbers, is 1 because they do not have any common factors other than 1.
Therefore, when dealing with two prime numbers, the GCF will always be 1.
What is 15-5(4x-7)=50
Simplifying
15 + -5(4x + -7) = 50
Reorder the terms:
15 + -5(-7 + 4x) = 50
15 + (-7 * -5 + 4x * -5) = 50
15 + (35 + -20x) = 50
Combine like terms: 15 + 35 = 50
50 + -20x = 50
Add '-50' to each side of the equation.
50 + -50 + -20x = 50 + -50
Combine like terms: 50 + -50 = 0
0 + -20x = 50 + -50
-20x = 50 + -50
Combine like terms: 50 + -50 = 0
-20x = 0
Solving
-20x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '-20'.
x = 0.0
Simplifying
x = 0.0
emily earns $75 per day plus a commission. her commission is 15%. she sells $600 worth of furniture. how much does she earn for the day
It would be $165. If she earns $75 a day, plus what she make from selling the furniture. That 15% of $600 is $90. Simply add $90+$75 and your answer is $165.
the parent function of a quadratic equation is vertically stretched by a factor of 2, then translated 5 units to the right and 1 unit down. write the equation of the new function in vertex form
A vertical stretch appears as a multiplier for the function value. Translation right appears as a value subtracted from the independent variable. Translation up appears as a value added to the function value.
For function f(x), stretching by a factor of 2, then translation 5 right and -1 up will give the function
... g(x) = 2f(x-5) -1
When f(x) = x², this becomes ...
... g(x) = 2(x -5)² -1
... g(x) = 2x² -20x +49
The equation of the new function in vertex form after the parent function of a quadratic equation is vertically stretched by 2, translated 5 units to the right and 1 unit down is y = 2(x - 5)^2 - 1.
Explanation:The parent function of a quadratic equation is given by f(x) = x^2. When it is vertically stretched by a factor of 2, it becomes 2f(x) = 2x^2. 5 units translation to the right will give f(x - 5) = 2(x - 5)^2 and a 1 unit downward shift gives f(x) = 2(x - 5)^2 - 1. Therefore, the equation of the new function in vertex form is y = 2(x - 5)^2 - 1.
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Zoe has 1500 beads. She wants to make 6 friendship bracelets. She needs 215 beads for each bracelet. How many beads will Zoe have left after making all six of the bracelets? explain
Zoe will have 210 beads left after making all six of the friendship bracelets.
Explanation:Zoe has 1500 beads and wants to make 6 friendship bracelets, with 215 beads needed for each bracelet. To find the total number of beads needed for all the bracelets, multiply the beads required for one bracelet (215) by the number of bracelets (6). This equals 1290 beads. To find the number of beads Zoe will have left after making all the bracelets, subtract the total number of beads needed (1290) from the initial number of beads (1500). Therefore, Zoe will have 210 beads left.
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The speed limit on the highway is 55 mph which equality best describes this me assuming the variable S represents be help ASAP
The answer is the speed is less than or equal to 55 mph.
S≤55
Simplify
9 – 5(–7x + 5)
9-5(-7x+5)
------------------
9+35x-25
35x+9-25
35x-16
Hello!
[tex]9 - 5(-7x + 5)[/tex]
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓↓
First you had to expand.
[tex]-5(-7x+5):35x-25[/tex]
[tex]9+35x-25[/tex]
Then simplify it should be the correct answer.
[tex]9+35x-25:35x-16[/tex]
[tex]=35x-16[/tex]
Answer⇒⇒⇒⇒35x-16
Hope this helps!
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Have a great day!
-Charlie
A report prepared by a credit bureau which shows details of an individual’s credit history is a _____.
The answer is Credit Report
Answer:
Credit Report fellas!
Step-by-step explanation:
If length of one side of cube is 20 cm, then volume of cube must be...
A: 4000 cm 3
B: 6000 cm 3
C: 800 cm 3
D: 8000 cm 3
D
the volume (V ) of a cube = s³ ( where s is the length of the side )
here s = 20, hence
V = 20³ = 8000 cm³
find the product 0.9×079=
Answer is 71.1 because 0.9 x 079 in a calculator is 71.1