Mark ordered gummy bears and caramels for his candy shop. He ordered a total of twenty five pounds of there ingredients. Gummy bears cost $5 per pound, and caramels cost $8 per pound. He spent a total of $140.
A. Write a system of equations that describes the situation. Define each variable you use.
B. Solve the system of equations from part A using the substitution or elimination method. Write your solution using a complete sentence. Is the solution reasonable? Why or why not?
Answer:
20 pounds of Gummyballs and 5 pounds of caramel was ordered
Step-by-step explanation:
Let :
Gummyball = a
Caramel = b
a + b = 25 - - - (1)
5a + 8b = 140 - - - (2)
From (1)
a = 25 - b
Put into (2)
5(25 - b) + 8b = 140
125 - 5b + 8b = 140
125 + 3b = 140
3b = 15
b = 5
From a = 25 - b
a = 25 - 5
a = 20
Hence,
20 pounds of Gummyballs and 5 pounds of caramel was ordered
Which pair of numbers has a sum of 100?
( A) 39,61
(B) 49,61
(C) 59, 51
(D) 39,51
Answer:
a
Step-by-step explanation:
39+61 is the only pair that make 100.
Plz help me with this question
Answer:
C
Step-by-step explanation:
Remark
There are probably a couple of ways that you could do this. I'm going to pick the most obvious way.
Givens.
KN = 2.5
NO = 10
LM = 3
MP = x
Equation
NO/KN = PM / LM
Solution
10 / 2.5 = x / 3 Cross multiply
2.5x = 10 * 3 Combine
2.5x = 30 Divide by 2.5
x = 30/2.5
x = 12
That looks like it should be the answer, and it almost is, but you are asked for LP.
LP = LM + MP
LP = 3 + 12
LP = 15
The answer is 15
in a 5th grade class, 9/10nof the students like going to the movies. Of those students 4/5 like popcorn. Of the students that like popcorn, 2/3 of them also like candy. what fraction of the students class like popcorn at the movies? What faction lf the students in class like popcorn and candy at the movies?
Answer:
48%
Step-by-step explanation:
9/10 of the students like going to the movies.
4/5 of 9/10 is 72/100 or 72%.
2/3 of 72 is 48.
So, 48% of the students like popcorn, candy, and going to the movies.
HELP I NEED HELP ASAP
The function f(t)=1,500,000(0.885)^t models the population of a small country after t years. Which statement is true?
A. The population is growing at a rate of 88.5%
B. The population is declining at a rate of 11.5%
C. The population is declining at a rate of 88.5%
D. The population is growing at a rate of 11.5%
Answer:
B. The population is declining at a rate of 11.5%
Step-by-step explanation:
if your graph the equation you will clearly see that it is declining and if you don't know how to graph the equation then go to the demos calculator, its an app & website, super easy to use. most people would assume the answer would be one of the 88.5% just because it's in the original equation but the .885 in the equation doesn't represent the rate of change there for the answer is 11.5%.
5xy4 25x2y 5x2y2 What is the greatest common factor (GCF) of the monomials shown above?
Answer:
5xy
Step-by-step explanation:
I'm going out on a limb and assuming exponents.
[tex]5xy^{2} \\25x^{2}y \\5x^{2} y^{2}[/tex]
We can note that 5 is a common factor for the coefficients. All the terms share at least one x. All the terms share all least one y. So the GCF of these monomials is 5xy.
PLS HELP ASAP I MEAN ASAP PLS
Answer:
(B). - 3 ≤ x < 1
Step-by-step explanation:
[tex]\frac{\sqrt{x+3} }{\sqrt{1-x} }[/tex]
Given expression is defined for
1). x + 3 ≥ 0 ⇒ x ≥ - 3
and
2). 1 - x > 0 ⇒ x < 1
- 3 ≤ x < 1
PLEASE HELP ME WITH THIS I WILL MARK BRAINLIEST
Answer:
a=60
Step-by-step explanation:
all you do is add 90+135+75 which is 300
then subtract 300 from 360, which is 60
360-(90+135+75)=60
Use the Distributive Property to simplify the expression. 8(s−1) =
Answer:
the answer would be 8s -8
Step-by-step explanation:
I learned this a long time ago
Answer:
anong grade Yan tol??g7 g7 g8 g9 g10 g11 g12?
Given that 3 apples and 4 pears cost $1.95, 4 pears and 1 orange cost $1.60, and 1 orange and 3 apples cost $1.15, what is the cost of 1 apple?
Answer:
Step-by-step explanation:
Given that 3 apples and 4 pears cost $1.95, 4 pears and 1 orange cost $1.60, and 1 orange and 3 apples cost $1.15, what is the cost of 1 apple?
Let us represent
Number of apples = x
Number of pears = y
Number of oranges = z
Given that
3 apples and 4 pears cost $1.95
3x + 4y = 1.95
4 pears and 1 orange cost $1.60
4y + z = 1.60
z = 1.60 - 4y
1 orange and 3 apples cost $1.15
z + 3x = 1.15
z = 1.15 - 3x
what is the cost of 1 apple?
Ten people put 63 boxes on a red truck and 38 boxes on a blue track About how many boxes did they load in all
Answer:
63+38=101
Step-by-step explanation:
Jessica is bringing cupcakes to school for her birthday. She is placing them in a rectangular box that can fit 4 more cupcakes long that it can wide. They will not all fit in the box, so she is also bringing a bag that can hold 12 cupcakes. The amount of cupcakes she is bringing can be represented as x(x + 4) + 12. Solve for the number of cupcakes wide and long the box will hold. Part A) What does x represent?
Answer:
the amount of cupcakes
Step-by-step explanation:
you said the amount of cupcakes can be represented by
Salesman Scott received $2,792.79 for selling a property. If the gross commission was 6.5 % of the sale price, the listing salesman received 12% of the gross commission and Scott received 45% of the balance, how much did the property sell for?
Answer: The property sold for $5,870.41.
Step-by-step explanation:
Let x be the selling price of the property.
Then, gross commission = 6.5% of x = 0.065x
listing salesman received = 12% of ( 0.065x) = 0.12 (0.065x) = 0.0078 x
Balance = x - ( 0.065x) - (0.0078 x)
= (1+0.065-0.0078)x
= 1.0572x
Scott received = 45% of (1.0572x)
=0.45 (1.0572x)
= 0.47574x
Now, [tex]0.47574x=2,792.79[/tex]
[tex]\Rightarrow\ x=\dfrac{2792.79}{0.47574}\\\\\Rightarrow\ x=5870.41[/tex]
Hence, the property sold for $5,870.41.
School A has graduated 1,700 students and graduates
50 students every year. School B has graduated 600
students, but graduates 150 every year. How many years (Y)
will it be before School B has as many graduates as School A?
Answer:
the answer is 11 years
Step-by-step explanation:
if school A is graduated 50/years,
the graduated in 11 years is 550
added of graduated 1,700 in 550 is 2,250
if school B is graduated 150/years,
the graduated in 11 years is 1650
added of graduated 600 in 1650 is 2,250
so School A and B is to be equal in 11 years
if anyone is able to help please do :)
Answer:
49.12?
Step-by-step explanation:
half circle= 4 squared *3.14/2=25.12
triangle=pythagorean theorem to find h=8. 8*6/2= 24
25.12+24=49.12
triangle ABD~ triangle DBC the perimeter of triangle ABD=36, fond the perimeter of triangle DBC.
Answer:
Perimeter of ΔDBC = 48 units
Step-by-step explanation:
It's given in he question,
ΔABD ~ ΔDBC
Therefore, by the definition of similar triangles,
Corresponding sides of both the triangle will be proportional.
[tex]\frac{AB}{DB}= \frac{BD}{BC}= \frac{AD}{DC}[/tex]
[tex]\frac{9}{12}= \frac{12}{16}= \frac{AD}{DC}[/tex]
[tex]\frac{3}{4}=\frac{AD}{DC}[/tex]
AD = [tex]\frac{3}{4}DC[/tex] ----------(1)
Since, perimeter of ΔABD = 36,
AB + BD + AD = 36
9 + 12 + AD = 36
AD = 36 - 21
AD = 15
From equation (1),
15 = [tex]\frac{3}{4}(DC)[/tex]
DC = 20
Perimeter of ΔDBC = DB + BC + DC
= 12 + 16 + 20
= 48
Therefore, perimeter of ΔDBC = 48 units is the answer.
1. Write a rule for the transformation performed if Q(3 , 5) translates to Q’( 3, 18).
2. Consider the point Q(4,-3) which is translated to (3,2). What would the pre-image of P(1, 2) be under the same translation?
Function Notation.
Find the range values (y-values) for function f(x)=2x^2-4 when the domain (x-value) is (-2,0,1)
f(-2)=2(-2)^2-4= ?
f(0)=2(0)^2-4= ?
f(1)=2(1)^2-4= ?
Answer:
1. vertical translation (the point goes straight up)
2. P'(0,7) (the translation was up five units and over 1 unit)
3. f(-2)=2(-2)^2-4= (all y values are 4) (0,4)
f(0)=2(0)^2-4= (all y values are -4) (0,-4)
f(1)=2(1)^2-4= (all y values are -2) (0,-2)
PLS HELP!!
Solve for a side in right triangles
BC = ???
round your answer to the nearest hundredth
Answer:
39 centimeters
Step-by-step explanation:
I am very sorry if I'm wrong! ✿✿✿
hola cual es la raiz cuadrada de √639+(393)
Answer:
393 + 39√6
Step-by-step explanation:
√639 + (393)
Simplify
393 + 39√6 (Answer)
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Hey It's Chloe again, sorry.
But what is the perimeter of a rectangle?
Answer:A perimeter is the sides of a shape added together.
Step-by-step explanation:
Answer:
The perimeter of a rectangle is the total length of all the sides of the rectangle.
Step-by-step explanation:
The perimeter of a rectangle is the total length of all the sides of the rectangle. We can find the perimeter by adding all four sides of a rectangle. Since opposite sides of a rectangle are always equal, we need to find the dimensions of only two sides to find the perimeter of a rectangle.
If you have a 2 inches by 4 inches rectangle, you would have 2 inches + 4 inches + 2 inches + 4 inches = 12 inches
Here is a polygon. Use the scale factor of 1/2 determine the new side length for A *
Answer:
i need to see the polygon my guy
Step-by-step explanation:
Find the scale factor of the small triangle to the large triangle.
Answer:
scale factor is: 2.25
Step-by-step explanation:
What is m/3= -1.5 what is m???
Answer:
-4.5
Step-by-step explanation:
M would be -4.5 because if you multiply -1.5 by 3 you get -4.5. Therefore the equation would be -4.5/3= -1.5 .
Hope this helps :))
The compound interest on a sum of money in
2 years and 4 years are Rs 5,460 and Rs 12,066.60
respectively. Find the difference between principal
and compound interest of 3 years.
Answer:
The difference between the principal and the compound interest in three years is Rs 17,994
Step-by-step explanation:
The compound interest is given according to the following formula;
[tex]C.I. = P \cdot \left ( 1 + \dfrac{r}{n} \right ) ^{n\cdot t} - P[/tex]
The given amount of the compound after 2 years = Rs 5,460
The given amount of the compound after 4 years = Rs 12,066.60
Therefore, we have;
[tex]5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P[/tex]...(1)
[tex]12,066.60 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{4} - P[/tex] ...(2)
Dividing equation (2) by (1), we have;
[tex]\dfrac{12,066.60}{5,460} = \dfrac{P \cdot \left ( \left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1\right )}{P \cdot \left (\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 \right ) } =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 }[/tex]
[tex]Let \ \left ( 1 + \dfrac{r}{100} \right ) ^{2} = x, we \ get;[/tex]
[tex]\dfrac{12,066.60}{5,460} =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 } = \dfrac{x^2 - 1}{x - 1}[/tex]
∴ 12,066.60 × (x - 1) = 5,460 × (x² - 1) = 5,460 × (x - 1) ×(x + 1)
∴ 12,066.60 × (x - 1)/(x - 1) = 5,460 × (x + 1)
12,066.60/5,460 = x + 1
x = 12,066.60/5,460 - 1 = 1.21 = 121/100
x = 121/100
[tex]\left ( 1 + \dfrac{r}{100} \right ) ^{2} = x = \dfrac{121}{100}[/tex]
[tex]1 + \dfrac{r}{100} =\sqrt{ \dfrac{121}{100}} = \dfrac{11}{10}[/tex]
We get
[tex]\dfrac{12,066.60}{5,460} =\dfrac{221}{100}[/tex]
[tex]\therefore \dfrac{12,066.60}{5,460} =\dfrac{221}{100} = \left ( 1 + \dfrac{r}{100} \right ) ^{2}[/tex]
[tex]1 + \dfrac{r}{100} = \sqrt{ \dfrac{221}{100} } = \dfrac{\sqrt{221} }{10}[/tex]
[tex]\dfrac{r}{100} = \dfrac{\sqrt{221} }{10} - 1[/tex]
[tex]\dfrac{r}{100} = \dfrac{11}{10} - 1 = \dfrac{1}{10} = 0.1[/tex]
r = 100 × 0.1 = 10%
r = 10%
Therefore, we have;
[tex]5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P = P \times \left ( 1 + 0.1\right ) ^{2} - P[/tex]
[tex]5,460 = P \times \left ( 1 + 0.1\right ) ^{2} - P = P \times \left (\left ( 1 + 0.1\right ) ^{2} - 1\right) = P \times \dfrac{21}{100}[/tex]
[tex]P = \dfrac{100}{21} \times 5,460 = 26,000[/tex]
The principal = Rs. 26,000
The compound interest in 3 years is therefore;
[tex]CI_3 = 26,000 \times \left ( 1 + \dfrac{10}{100} \right ) ^{3} - 26,000= 8606[/tex]
The difference, 'd', between the principal and the compound interest in three years, is given as follows;
d = P - CI₃
d = 26,600 - 8606 = 17994
The difference between the principal and the compound interest in three years, d = Rs 17,994.
YALL WHAT IS THE ANGLE OF C
65
65
Answer:
A,G
Step-by-step explanation:
Answer:
50 degrees
Step-by-step explanation:
Chloe earned a grade of 87% on her multiple choice math final that had a total of 200
problems. How many problems on the final exam did Chloe answer correctly?
200 x 0.87 = 174
She answered 174 questions correctly.
Answer:
Chloe answered 174 problems correctly.
Explanation:
To find percentage, you would multiply the percentages decimal to the total.
0.87x200=174
What is the value of the expression 11 - (34.48?
1) 3
O2) 5
O 3) 8
4) 9
Answer:
-23.48
Step-by-step explanation:
Hoped this helped!!
Math Teacher is giving extra credit to who ever can come up with the best theme for his kids birthday party!!!
I will give a Branliest!
Has To Be A Movie!!!!
You can choose
A. Hunger Games
B. Men in Black
C. Classic Horror Movies
D. Jurassic Park
OR!!
Awnser With your own suggestion!!!!!!!
Step-by-step explanation:
i think it is sponge Bob square pants
Mrs. Hanson has a potato salad recipe that calls for 238 pounds of potatoes, but she wants to make 112 times as much as the recipe calls for.
The diagram represents the number of pounds of potatoes that Mrs. Hanson needs.
How many pounds of potatoes does Mrs. Hanson need?
Enter your answer as a mixed number in simplest form by filling in the boxes. please hurry dont say what to add or mutply say the answer i am on k12
Answer:
3 9/16 lbs
Step-by-step explanation:
took quiz
simplify -8-(12)+(-2)
Answer:
-22
Step-by-step explanation:
-8-(12)+(-2)
-8-12-2
-20-2
-22
HOPE THIS HELPS!