Answer: Each blueberry pie costs $14 and each blackberry pie costs $18.
Step-by-step explanation:
If X is the price of a blueberry pie and Y is the price of a blackberry pie we have that:
3*X + 12*Y = $258
4*X + 3*Y = $110
We have a system of equations, to solve it first we can isolate one of the variables in one of the equations, let's isolate X in the first equation.
3*X = $258 - 12*Y
X = $258/3 - (12*Y)/3 = 86 - 4*Y
now we can replace it in the second equation and get:
4*(86 - 4*Y) + 3*Y = 110
344 - 16Y + 3Y = 110
344 - 13Y = 110
13Y = 344 - 110 = 234
Y = 234/13 = 18
So each blackberry pie costs $18.
And we can replace it in the equation for X and get the value of X.
X = 86 - 4*Y = 86 - 4*18 = 14
So the price of a blueberry pie is $14.
Answer:
the cost each of one blueberry pie is $14
and one blackberry pie is $18
Step by step explanation:
Given that;
Beth sold 3 blueberry pies and 12 blackberry pies for a total of $258.
Ming sold 4 blueberry pies and 3 blackberry pies for a total of $110.
Let x represent the cost of blueberry pies and y the cost of blackberry pie.
3x + 12y = 258 ........1
4x + 3y = 110 ..........2
To solve the simultaneous equations;
Multiply equation 2 by 4, equation 2 becomes;
16x +12y = 440 .......3
Subtract equation 1 from 3;
16x-3x + 12y-12y = 440-258
13x = 182
x = 182/13 = 14
Substituting x=14 to equation 2
4(14) + 3y = 110
3y = 110 - 4(14)
3y = 54
y = 54/3
y = 18
the cost each of one blueberry pie is $14
and one blackberry pie is $18
You are working as a car salesperson at a motor shop. You earn a 2% commission on every car sale, in addition to your wage of $20 an hour. After a 8 hour day, your car sales totaled to $25,000. What are your total earning for that day? (Show Work.)
A: 500
B: 160
C: 660
Answer:
660
Step-by-step explanation:
20 * 8 = 160
25,000 * 2% = 500
500 + 160 = 660
Therefore your answer is 660
The temperature at 4pm was 65 degrees Fahrenheit. The temperature dropped 5 degrees every hour from 4pm to 10pm. What is the temperature at 10pm? What are you doing dividing or multiplying? Can you write an equation to represent the problem and explain your process?
Answer: 35
Step-by-step explanation: It's an arith metic sequence that can be represented throigh the equation y= 65-5x where 5 is the amount of hous since 4pm and if you insert 6 for x you get 35
The mathematics problem involves subtraction, where the temperature drops 5 degrees per hour from 4pm to 10pm. The equation to represent this would be 65 - 5*6 = T. After performing the calculation, we find the temperature at 10pm is 35 degrees Fahrenheit.
Explanation:In this problem, you are dealing with a decline in temperature over time, which is considered as a subtraction problem. Since the temperature drops by 5 degrees every hour from 4pm to 10pm, that's a total of six hours (10pm - 4pm = 6 hours), so you'll subtract 5 degrees 6 times from the initial temperature of 65 degrees.
The equation to represent this problem is:
65 - 5*6 = T
This means you are subtracting 5 degrees six times from the initial temperature of 65 Fahrenheit to get the temperature (T) at 10pm. So, the calculation would be:
65 - (5*6) = 65 - 30 = 35
So, the temperature at 10pm is 35 degrees Fahrenheit.
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a set of symbols that expresses a mathematical rule is called a
A set of symbols that expresses a mathematical rule is called a formula.
What are mathematical symbols?A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
Given is a definition as -
"A set of symbols that expresses a mathematical rule is called a ?".
A set of symbols that expresses a mathematical rule is called a formula.In mathematics, a formula is a fact, rule, or principle that is expressed in terms of mathematical symbols. Examples of formulas include equations, equalities, identities, inequalities, and asymptotic expressions.Therefore, a set of symbols that expresses a mathematical rule is called a formula.
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Final answer:
A set of symbols expressing a mathematical rule is called a mathematical model or equation, using variables and relationships to define concepts such as a set or a group in group theory.
Explanation:
A set of symbols that expresses a mathematical rule is often referred to as a mathematical model or equation. These models are essential for describing phenomena in a precise and universal language that transcends natural language, allowing for consistent replication and understanding across various fields of study. In mathematics, we use variables like x, y, or n and symbols to create equations which express relationships or rules. For example, to define a set of all even numbers, we could write the rule as the set of all real numbers x such that x/2 is an integer. This uses the structure of the equation to convey the membership rule for the set, which in this context would be described by the notation '{x : x/2 is an integer}' where the colon represents 'such that'.
Furthermore, when these symbols and rules are organized into a specific system with defined properties, such as closure, identity, inverses, and associativity, they can form a group, which is a fundamental concept in group theory.
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer:
28.46
Step-by-step explanation:
Use a^2+b^2=c^2 to find height
Then use the area formula bh/2 to find area :))
Answer: 44.1
Step-by-step explanation:
Translate this phrase into an algebraic expression:
500 increased by twice Matt's saving
Use the variable m to represent Malt s savings.
I need to find the the answer to this question thank you
Answer:
The answer is 116 degrees.
Step-by-step explanation:
will give first person who answers this correctly Brainiest!!!!
Can someone help me please? It’s like my 3rd time trying to get some answers for this question. Thanks. :)
Answer:
both rates of change equal the slope of the line (3/4)
Step-by-step explanation:
Part a)
We calculate the rate of change using the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
for the first interval [0,6], we calculate the y-values at x=0 and x=6;
at x=0 : [tex]y=\frac{3}{2} (0)+2=2[/tex]
at x=6 : [tex]y=\frac{3}{2} (6)+2=11[/tex]
therefore, the rate of change in this interval is: [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{11-2}{6-0}=\frac{9}{6} =\frac{3}{2}[/tex]
For the second interval [-4,4], we calculate the y-values at x=-4 and x=4;
at x=-4 : [tex]y=\frac{3}{2} (-4)+2=-4[/tex]
at x=4 : [tex]y=\frac{3}{2} (4)+2=8[/tex]
therefore, the rate of change in this interval is: [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{8-(-4)}{4-(-4)}=\frac{12}{8} =\frac{3}{2}[/tex]
Part b):
Notice that both rates of change equal the value of the slope of the linear function (3/2)
Which is the answer
Answer:
D
Step-by-step explanation:
Because when you half answer D it will give you Matrix A.
If cot O= 12/5, find tan O
Answer: Tan O= 5/12
Step-by-step explanation:
Cot O=12/5
Looking at the pythagoras theory
Cot= 1/tan
So
Cot O=1/tango
Cross multiply
CotO tan O=1
Make tan the subject of formula
TanO= 1/Cot O
Cot O=12/5
Substitute for cot O
Tan O= 1/12/5
Tan O= 5/12
When b > 1, as x grows in the negative direction, y______ . When 0 < b < 1, as x grows in the negative direction, y_____ .
Answer:
decrease, increase.
Step-by-step explanation:
Assume that y varies inversely with x. If y = 4 when x = 4, find y = when x = 2.
y = [?]
Answer: Y=8
Step-by-step explanation:
Final answer:
To find the new value of y when x = 2 and knowing that y varies inversely with x, we first calculate the constant of variation k with the given values and then apply it to find the new y value, resulting in y = 8.
Explanation:
To solve the problem where y varies inversely with x, we use the inverse variation formula, which is y = k/x, where k is the constant of variation. First, we will find the value of k using the given values of y and x when y = 4 and x = 4.
Using the formula and substituting the known values:
k = xy = 4 × 4 = 16
Now, using k and solving for y when x = 2:
y = k/x = 16/2 = 8
Therefore, when x = 2, y = 8.
A rain barrel holds 47 gal. 1 qt of water. Mr. Jiko uses 12 gal. 2 qt to water his flower garden and 7 gal. 1 qt. to water his
trees. How much water is left in the rain barrel?
care sa nu mai
o proces po 2 e o water he tower an den ana 7 n. a over his
Answer:
27 gallons, 2 quarts
Step-by-step explanation:
The measurements are given in gallons and quarts. Lets convert everything to quarts.
We know:
4 quarts = 1 gallons
So,
Rain Barrel Capacity = 47*4 + 1 = 189 quarts
Jiko uses 12 gallon 2 quart to water flower garden = 12*4 + 2 = 50 quarts
Jiko uses 7 gallons 1 quarts to water trees = 7*4 + 1 = 29 quarts
He used up = 50 + 29 = 79 quarts
Remaining Water in Rain Barrel = 189 - 79 = 110 quarts
In gallons and quarts:
27 * 4 = 108 quarts
So, water left = 27 gallons, 2 quarts
Rewrite the product (3x2)(2x5) as a equivalent expression in simplest exponential form?
Answer:
[tex]3 {x}^{2} (2 {x}^{5} ) = 6 {x}^{7} [/tex]
By visual inspection determine the best fitting repression model for the scatterplot
A. Quadratic
B. No pattern
C. Linear
D. Exponential
Answer:
exponential
Step-by-step explanation:
For snack mrs Taylor distributes 10 pounds of grapes evenly amongst her 25 students how many pounds does each student receive
Answer:
0.4
Step-by-step explanation:
10 divided by 25
Alice will be serving punch at an event she is hosting next month. The graph below shows the number of servings based on the amount of punch available. What is the rate of change of the graph?
Answer:
There is no graph
Step-by-step explanation:
Answer: ben
Step-by-step explanation:b
e
n
ben
Find the length of X.
Answer:
x=12
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
15/9=x/6
15/9 simplified by 3 equal 5/3
5/3=10/6 (multiplied by2 )
10/6=x/6
so x=10
The y-value for the midline is equal to?
Answer:
answer is b (max y + min y)/2
Step-by-step explanation:
Answer:
(max y + min y)/2
Step-by-step explanation:
k=4
A cylindrical tank is half-full of oil.
The cylinder has a base radius of 100cm. The height of the cylinder is 250cm.
1 litre= 1000cm^3
How many litres of oil are in a tank?
Round your answer to the nearest litre.
Answer:
3927 litres of oil to the nearest litre.
Step-by-step explanation:
The volume of the cylinder = π r^2 h
= π * 100^2 * 250.
When half full the volume is
1/2 * π * 100^2 * 250
= 3926991 cm^3 Dividing this by 1000:
= 3927 litres.
A cylindrical tank is half-full of oil.
There are 3928 liters of oil in the tank
Volume of CylinderVolume of cylinder is teh amount of material the cylinder holds. Volume is the density of the cylinder.
Volume Formula :
[tex]volume = \pi r^2h[/tex]
Given the radius of the cylinder is 100cm
Height of the cylinder is 250 cm
Substitute all the values inside the formula
[tex]V=\pi (100)^2(250)\\V=2500000\pi[/tex]
Cylinder tank is half full of oil . To find half of the volume , we divide the volume by 2
[tex]V=2500000\pi\\Half - full = \frac{2500000}{2}\pi \\Half-full =3926990.817 cm^3[/tex]
Given that 1 litre= 1000cm^3
convert cubic centimeter to litres
[tex]1000cm^3= 1litre \\3926990.817 cm^3=\frac{3926990.817 }{1000} \\1250000 cm^3=3927.99 liters[/tex]
There are 3928 liters of oil in the tank
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what's the least common denominator of 1/3 5/8 and 1/2?
The least common denominator of 1/3 5/8 and 1/2 will be 24.
What is Least common multiple?
The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Given that;
The numbers are,
⇒ 1/3, 5/8 and 1/2
Now,
To find the least common denominator of 1/3 5/8 and 1/2,
We need to find the least common multiple of 3, 8 and 2 as
The LCM of {3, 8, 2} = 24
Thus, The least common denominator of 1/3 5/8 and 1/2 will be 24.
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The least common denominator of 1/3, 5/8, and 1/2 is 24. It's the smallest number that all the denominators (3, 8, and 2) can divide into evenly, and it helps in adding or comparing fractions with different denominators.
Explanation:The least common denominator (LCD) of the fractions 1/3, 5/8, and 1/2 is the smallest number that all of the denominators can divide into evenly. When looking for the least common denominator, we can use the method of listing multiples or the method of prime factorization.
For the fractions given, we list the multiples of each denominator:
3's multiples: 3, 6, 9, 12, 15, 18, 21, 24, ...8's multiples: 8, 16, 24, 32, 40, ...2's multiples: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ...The smallest multiple that they all have in common is 24, which is the least common denominator. It's important to note that by finding the LCD, we can easily add or compare fractions with different denominators.
A rectangle has a perimeter of 18cm. It’s length is 5cm greater than its width. Find the dimension
Answer:
The width is 2 cm and the length is 7 cm.
Step-by-step explanation:
Hope this helps!
The function f is defined by f(x)=5x+k, where k is a constant. Find k, if the value of f at x=2 is equal to 14.
WILL MARK BRAINLIEST!
Answer:
k = 4
Step-by-step explanation:
f(x)=5x+k
Let x =2
f(2) = 5*2 +k
f(2) = 10+k
We know f(2) = 14
14 = 10+k
Subtract 10 from each side
14-10 = 10+k-10
4 =k
We are given the function f(x) = 5x + k when k is a constant, x equals 2, and f(x) equals 14
Steps to solve:
14 = 5x + k; x = 2
~Substitute
14 = 5(2) + k
~Simplify
14 = 10 + k
~Subtract 10 to both sides
14 - 10 = 10 - 10 + k
~Simplfy
4 = k
Best of Luck!
Sally will earn $30 for every 5 hours that she babysits. Which of the following equations can be used to represent the proportional relationship?
Answer:
30 times one for every 5 hours she baby sits
Answer:
B. [tex]y = 6x[/tex]
Step-by-step explanation:
Step 1: Divide 30 by 5
[tex]\frac{30}{5}\\\\=30 \div 5\\\\= 6[/tex]
Therefore, the answer closest to that is B. y = 6x.
A see-saw is 25 feet long with a fulcrum in the middle of the board. If a 60 lb. child sits three feet from the fulcrum, what is the lowest weight that will lift the child?
Answer:
14.4 lb
Step-by-step explanation:
In a see-saw in equilibrium, the torque generated by one side needs to be the same generated in the other side. The torque is calculated by the product between the mass and the distance to the center of the see-saw.
The torque generated by the child is:
T1 = 60 * 3 = 180 lb*feet
So, the torque generated by the weight needs to be higher than T1 in order to lift the child.
The lowest mass is calculated when the mass is in the maximum distance, that is, 12.5 feet from the center.
So, we have that:
T2 = 180 = mass * 12.5
mass = 180/12.5 = 14.4 lb
So the lowest weight is 14.4 lb
The concept of leverage acting through a see-saw requires a balancing of forces on either side of the fulcrum. By calculating the torque from the child's weight and distance from the fulcrum, we can estimate the minimal weight needed on the other side to lift the child. The answer is approximately 14.4 lbs when placed 12.5 feet from the fulcrum.
Explanation:The concept being explored here is leverage, specifically in the context of a see-saw. The see-saw operates on the principle of a basic lever where the two sides are balanced around a pivot point known as the fulcrum.
The input force, or effort, is defined by the weight of the child and the distance from the fulcrum they are sitting, while the output force, or resistance, is the weight needed on the other side to lift the child off the ground.
Here's how you calculate it: the child's weight of 60 lbs is 3ft from the fulcrum. So, the torque, or turning force, created by the child is 60lbs x 3ft = 180 lb-ft. Since we're looking for balance, the weight needed to lift the child would produce the same amount of torque. Technically, that could be achieved with a number of combinations of weight and distance, but given that the question asks for the smallest weight, the weight needs to be placed at the furthest available distance from the fulcrum, which would be half the length of the see-saw (12.5 feet). So, the weight would be 180 lb-ft / 12.5 ft = 14.4 lbs.
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What is the length of arc S shown below? Enter an exact expression in units. The angle in the figure is a central angle in radians.
Step-by-step explanation:
The radius of the circle = 10
The central angle of the arc = 3[tex]\frac{\pi }{2}[/tex]
By formula, S = rΘ
where S is the lenth of the arc
r is the radius of the circle
Θ is the central angle of the arc
substituting the values in the formula, we get
S = rΘ = 10 (3[tex]\frac{\pi }{2}[/tex]) = 15[tex]\pi[/tex] = 47.1
Line segment AB is perpendicular to CB Ray BD disects /ABC .What is m /DBC
Answer:
The measure of angle DBC is 45°.Step-by-step explanation:
You can observe a representation of the problem in the image attached.
Notice that angle ABD and DBC are congruent.
Also, those angles are complementary, which means
[tex]\angle ABD + \angle DBC = 90\°[/tex]
And we know that [tex]\angle ABD = \angle DBC = x[/tex]
So,
[tex]x+x=90\°\\2x=90\°\\x=\frac{90\°}{2}\\ x=45\°[/tex]
Which means that [tex]\angle DBC = 45\°[/tex]
Therefore, the measure of angle DBC is 45°.
Answer:
< DBC is [tex]45^{0}[/tex]
Step-by-step explanation:
The line segment AB perpendicular to CB implies that a right angle is formed at point B. So that, AB and CB meets at B at [tex]90^{0}[/tex] to each other. Since the ray BD bisects <ABC, i.e it divides <ABC into two equal parts.
Thus,
[tex]\frac{90^{0} }{2}[/tex] = [tex]45^{0}[/tex]
Therefore, < DBC = [tex]45^{0}[/tex]
and < DBC = < ABD = [tex]45^{0}[/tex]
These two angles are said to be complementary angles. Complementary angles are set of two or more angles that add up to [tex]90^{0}[/tex].
Justine and Meagan played a trivia game. Justine answered a question incorrectly and lost 7 points. Then Meagan answered correctly and got the opposite score. Which is the correct way to represent that “the opposite of Justine’s score was equal to Meagan’s score”? a.–7 = 7
b.–(–7) = –7
C.–(7) = –7
D.–(–7) = 7
Answer:
-(-7)=7
Step-by-step explanation:
the opposite of the Justine score (-7) = Meghan score (7)
-(-7)=7
Final answer:
The correct representation of Meagan's score as the opposite of Justine's is -(-7) = 7, which is option D, where the double negative results in a positive score.
Explanation:
The trivia game scenario presents a situation where Justine and Meagan end up with opposite scores, with Justine losing 7 points and Meagan gaining the opposite. To express this numerically, if Justine's score change is represented as -7, then Meagan's score, being the opposite, is the negation of Justine's score, which is -(-7). This negation flips the sign of Justine's score change, resulting in a positive 7 for Meagan. Therefore, the correct way to represent that “the opposite of Justine’s score was equal to Meagan’s score” is -(-7) = 7.
A commuter airline files a new route between two cities that are 400
kilometers apart. One of the two cities is 200 kilometers from a third
city. The other one of the two cities is 300 kilometers from the third
city. Do the paths between the three cities form a right triangle?
Using the Pythagorean theorem, it is determined that the paths between the three cities, given their distances of 200 km, 300 km, and 400 km, do not form a right triangle because the sum of the squares of the shorter distances does not equal the square of the longest distance.
Explanation:To determine if the paths between the three cities form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The equation is a² + b² = c².
According to the provided distances, one city is 200 kilometers (a) from a third city, and the other city is 300 kilometers (b) from the third city.
The two original cities are 400 kilometers (c) apart.
Plugging these numbers into the Pythagorean theorem:
Since a² + b² does not equal c² (130000 ≠ 160000), the paths do not form a right triangle.
How do you subract integers?
Answer:
you could just add a negative if that makes since to you
Step-by-step explanation:
Adjust the sign on the integer to be subtracted to subtract integers. When all signs are positive, then the answer is positive. If both signs are negative, then the answer is negative. When the signs vary, deduct the lesser absolute value from the greater absolute value.