Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.
Given: The total amount Jerome earned this weekend is $252.50.
He earned every weekend = $80.
He earned 15% of the cost of meals as tips by serving them.
To find: The cost of meals served by Jerome in this weekend.
The total amount, $252.50, is the sum of the tips amount Jerome earned from serving meals and sum of the amount Jerome earned every weekend. To solve this, we must first translate the conditions of the problem, into an algebraic expression with a variable referring to the unknown quantity. This expression is then converted to an equation to find the value of the unknown quantity.
Let x be the cost of meals that Jerome served this weekend.
The equation for the problem statement becomes
[tex]\$80 + \frac{15}{100} x = \$252.50\\\\[/tex]
Keeping only the x term on the left side of the equation and constant terms on the right side we get
[tex]\frac{15}{100} x = \$252.50 - \$80\\\\\frac{15}{100} x = \$172.50\\\\\\[/tex]
Multiply both the sides of the equation by 100
[tex]\frac{15}{100} x \times 100 = \$172.50 \times 100\\\\15x = \$17250[/tex]
Divide both sides of the equation by 15
[tex]\frac{15x}{15} = \frac{\$17250}{15}\\\\x = \$1150[/tex]
What is algebra?Algebra is a field of mathematics in which letters are substituted for numbers, and an algebraic equation depicts a scale in which what is done on one side of the scale is likewise done on the other side of the scale, with the numbers acting as constants.
What is an equation?An equation is a mathematical statement that two expressions are equal. If it is an algebraic equation, two algebraic expressions has to have the same value on either side of the equal sign.
What is an algebraic expression?A meaningful collection of numbers, variables, and signs (positive or negative) of operations that must make mathematical and logical sense is referred to as an algebraic expression.
Expressions contain any number of algebraic terms. They use signs of operation like addition, subtraction, multiplication, and division and also do not contain an equality sign (=).
Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.
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what is the hypotenuse???
To find the answer to this problem, you will need to use the Pythagorean Theorem.
What is the Pythagorean Theorem?
The Pythagorean Theorem is an equation that represents the summation of the sides of a right triangle.
a² + b² = c², where a is the shortest leg of the triangle, b is the longest leg and c is the hypothenuse.
You have been given a (12) and b (16)
First, plug your given information into the equation: 12² + 16² = c²
Next, simplify your equation by squaring both terms:
12² = 144
16² = 256
Then, add these two answers together: 144+ 256= 400
This leaves you with the equation: 400 = c²
To isolate the c as an individual term, take the square root of both sides:
[tex]\sqrt{400} = \sqrt{c^{2} }[/tex]
The above equation leaves you with the answer 20 = c, which is the hypothenuse
someone help asap please
The gradient of this straight line through the points is 0.16.
The gradient of this lines simply means that it would require one (1) unit to use £0.16 worth of electricity.
How to calculate the gradient of a line?Mathematically, the gradient of a straight line can be calculated by using this formula;
Gradient, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Gradient, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided through this graph, we have the following data points:
Points on x-axis = (30, 100).
Points on y-axis = (4, 15).
Substituting the given points into the formula, we have the following;
Gradient, m = (15 - 4)/(100 - 30)
Gradient, m = 11/70
Gradient, m = 0.16
This ultimately implies that, £0.16 worth of electricity would require one (1) units to be used by David.
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The graph below is a polynomial function in the form f(x)=(x-a)(x-b). What are a and b?
A=
B=
The value of a and b for the given polynomial function f(x)=(x-a)(x-b) are a= -1, 2 and b=2, -1.
What is meant by polynomial function?A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. For instance, the polynomial 2x+5 has an exponent of 1. The zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function are the four most common types of polynomials in precalculus and algebra.
Given,
f(x)=(x-a)(x-b)
From the above graph, f(x) passes through points (2, 0), (-1, 0), (0, -2)
Let us take (2, 0)
(2-a)(2-b)=0
4-2b-2a+ab=0
(-1, 0)⇒(-1-a)(-1-b)=0
1+b+a+ab=0
(0, -2)⇒-2=(-a)(-b)
ab= -2
a= -2/b
4-2b-2a-2=0
-2a-2b+2=0
a+b-1=0
b²-2b+b-2=0
b(b-2)+1(b-2)=0
b= 2 or b= -1
a+2-1=0
a= -1
a-1-1=0
a=2
The value of a and b for the given polynomial function f(x)=(x-a)(x-b) are a= -1, 2 and b=2, -1.
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HELP PLS
Graph -8x - y = 8.
Answer:
Step-by-step explanation:
The graph of y = 8 is a horizontal line through 8, on the y-axis
Please help I'm stuck!
Answer:
For this question, you would have to subtract
1.679-1.439 = 0.24 Melvin pays 0.24 cents less. (not that much honestly lol!!)
Gage bought 5 pairs of running shoes for $49 each.
He raised the price and sold the shoes for $65 each.
How much total profit did he make by selling all
five pairs of running shoes?
Answer:
$80
Step-by-step explanation:
His buying cost for 1 pair of shoes: $49
His selling price for 1 pair of shoes: $65
His profit on selling 1 pair of shoes: $65 - $49 = $16
His profit on selling 5 pairs of shoes: 5 × $16 = $80
simplify: cube root of m 1/2 × n -1/3 / m -5/2 × n 8/3
Answer:
[tex]\frac{3m^{2}n-2-40nm }{6m}[/tex]
Step-by-step explanation:
Help me with is ixl please
Answer:
∠EGC
Step-by-step explanation:
Just like for the other problem, you're looking for an angle that's opposite the one you're given and is the same size as the one you're given (meaning they're congruent). If you use you hands to cover the parts of the line AD, you can see how ∠FGB and ∠EGC are opposite of each other and are congruent..
..........i need help past due
Answer: second and third from the top right
Step-by-step explanation: 1:2 and 1 to 2 are the same thing, and are ratios. The rest of the answers have nothing to do with ratios.
The number of point a baketball team cored ha 3,4, and 5 a factor. What i the leat number of point the team could have cored
The least number of point the team could have scored is the LCM of the factors given = 60.
Factor 1 = 3
Factor 2 = 4
Factor 3 = 5
therefore, LCM
= 4 * 5 * 3 [because they don't have any factors in common]
= 60
The positive integers that can divide a number evenly are referred to as factors. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied.
Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.
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log: (x) + log3(2x - 1) = log3 (6)
The solution of the logarithmic expression is 2x² - x - 6 = 0.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is log(x) + log3(2x - 1) = log3 (6). The expression will be solved as below,
log(x) + log3(2x - 1) = log3 (6)
log ( 3x (2x-1) = log18
3x ( 2x - 1 ) = 18
x ( 2x - 1 ) = 6
2x² - x = 6
2x² - x - 6 = 0
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Apply the Multiplication Property of Equality to write an equation equivalent to 7n = 28
due today lol
The equivalent equation is when n is equal to 4.
What is Multiplication Property of Equality?According to the multiplication property of equality, when we multiply both sides of an equation with the same number, the two sides remain equal.When we multiply either sides of an equation by the same number, the two sides remain equal, according to the multiplication property of equality. That is, if a, b, and c are all real numbers and a = b, thenaxc = bxc.
The four equality properties of addition, subtraction, multiplication, and division can be used to solve an equation. We simply add, subtract, multiply, or divide both sides of an equation to find the value of an unknown variable.Here given equation,
7n = 28
Multiply both sides of equation by 1/7
7n x 1/7 = 28 x 1/7
7n / 7 = 28 / 7
n = 28 / 7
n = 4
So the equation equivalent to 7n = 28 is n = 4.
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mrs. smith told her students that anyone who scores over 90% on the test will get an extra 30 minutes of recess. which group contingency is this?
Mrs. smith told her students that anyone who scores over 90% on the test will get an extra 30 minutes of recess: Among the group contingency this is an independent group,
What is group contingency?A particular kind of contingency known as a group contingency (GC) takes use of peer influence by using group reinforcement.
The instructor may use a group contingency to praise an entire class or a smaller subset of pupils for finishing assignments, exhibiting good classroom behavior, or engaging in other desired behavior. Multiple kids' problematic behaviors can be addressed at once using group contingencies.
Dependent, independent, and interdependent group contingencies are the three different types.
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The complete question is as follows:
Mrs. Smith implemented a procedure where she exclaimed that if any student scored over 90% on the test, they would get an extra 30 minutes of recess. Which group contingency is this?
a. Token economy
b. Dependent group contingency
c. Interdependent group contingency
d. Independent group
Factor 2x^2 - 4x - 30 completely.
Answer: 2(x-5)(x+3)
Step-by-step explanation:
(x+3)(2x-10)
2(x-5)(x+3)
I need help on this equation i know the answer is (4,6) i dont know were to put the points in the graph i also need help explaing hw i got the answer because i am not sure how
Answer:
Step-by-step explanation:
The sequences below are either arithmetic sequences or geometric sequences. For each sequence, determine whether it is arithmetic or geometric, and write the
formula for the
The
n’th term of that sequence.
8,16,32,…
4,11,17,….
Answer:
The sequences below is geometric sequences. 8,16,32
Step-by-step explanation:
It is geometric as far as it goes.
Notice that the ratio between each successive pair of terms is constant:
4/2=2
8/4=2
16/8=2
That these ratios are all the same is sufficient for the given terms to form a geometric sequence with general term:
an=[tex]2^{n}[/tex]
The sequence then continues:
2
,
4
,
8
,
16
,
32
,
64
,
128
,
256
,
512
,
1024
,
2048
,
...
The question is in the "...". Any finite number of terms does not determine an infinite sequence.
For example we can match the sequence
2
,
4
,
8
,
16
with a cubic polynomial:
[tex]a_{n}[/tex]=1/3([tex]n^{3}[/tex] -3[tex]n^{2}[/tex] +8n)
Then we would find that the next terms would be
30
,
52
,
84
,
.
the second 4 11 ,17 is wrong
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The equation and the table show the cost,y, for different sports programs as functions of the number of classes, x.
Based on the table and equation given:Gymnastics is less expensive when the classes is 1.Ice-skating is less expensive when the classes is 3 or 4.
How to Apply Equations and Tables?Given that y represents the cost, and x represents the number of classes, to complete the statements, the table is given for Gymnastics while the equation, y = 18x + 20 is given for Ice-skating program.Since the table already shows the cost for each specific number of classes for Gymnastics, find that of Ice-skating program for 1, 2, 3, and 4 classes.For 1 class, substitute x = 1 into y = 18x + 20:
y = 18(1) + 20
y = $38
For 2 class, substitute x = 2 into y = 18x + 20:
y = 18(2) + 20
y = $56
For 3 class, substitute x = 3 into y = 18x + 20:
y = 18(3) + 20
y = $74
For 4 class, substitute x = 4 into the equation y = 18x + 20:
y = 18(4) + 20
y = $92
From the above, we can conclude that, Gymnastics is less expensive when the classes is 1.
Ice-skating is less expensive when the classes is 3 or 4.
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in a probability experiment, eric flipped a coin 36 times. the coin landed on heads 24 times. what is the ratio of heads to tails in this experiment?
The ratio of heads to tails in the probability test is 2:1 or (D) 2/1.
What is the ratio?A ratio is a relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other.
For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.
So, we know that the coin is flipped 36 times in the probability test:
Head = 24
Tails = 36 - 24 = 12
The ratio of heads to Tails:
Heads:Tails
24:12
24/12
2/1
2:1
Therefore, the ratio of heads to tails in the probability test is 2:1 or (D) 2/1.
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Complete question:
In a probability, experiment Eric flip a coin 36 times. The coin landed on the head 24 times. What is the ratio of heads to tails in this experiment?
A.3/2
B.1/2
C.2/3
D.2/1
write the following algebraically using x as unknown
"i think of a number , take away 1 and multiply the result by 3
Answer: 3(x-1)
Step-by-step explanation:
3 (x-1)
Find the slope of the line that passes through (10, 10) and (3, 2).
Answer: m=8/7
Step-by-step explanation:
use this formula m=y2-y1/x2-x1
Please help with this question. Giving brainliest
Answer:
m∠1 = (180 - 110)° = 70°
m∠2 = (180 - 115)° = 65°
m∠3 = 115°
m∠4 = m∠2 = 65°
m∠5 = (180 - (65 + m∠1))° = 45°
m∠6 = m∠5 = 45°
m∠7 = m∠6 = 45°
A jar of coins contains six times as many quarters as dimes if the totalamount of money is 28.80 how many quarters and dimes are in the jar
There are total amount of 108 quarters and 18 dimes in a jar.
What is total?Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.
There are six times more quarters than dimes in a jar of coins.
If x represents the dimes, then the number of quarters will be 6*x if there are 28.80 in total.
A dime is worth 10 cents. In terms of money, we have 10 times as many dime.
A quarter is equal to 25 cents. We have 6 times as many quarters, which is 150 times (6 x 25).
10x +150x = 28.80
160x = 28.80
x = 0.18 that is for coins it will be 10x
10*0.18
18 dimes
similarly
6 times dimes is equal to quarters that is 6*18
108 quarters are there.
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Find the total cost: Alexandra bought a television set for $1105 in New York, where the sales tax rate was
8.75% of the purchase price.
The total cost of the Television is $ 1201.68.
What is Sales tax:The governments collect a consumption tax known as a sales tax on purchasing goods and services. It is always expressed as a percentage of the Purchase cost of goods and services. Here
Total cost = Purchase price + sales tax.Here we have
Alexandra bought a television set for $ 1105 in Newyork
The rate of sales tax = 8.75%
Therefore,
The total cost of Television = Cost of Television + sales tax
As we know sales tax = 8.75%
=> tax on Television = 8.75% of 1105
= [tex]\frac{8.75}{100} \times 1105[/tex]
= 0.0875 × 1105
= 96.68
The total cost of Television = 1105 + 96.68
= 1201.68
Therefore,
The total cost of the Television is $ 1201.68.
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pls help
law of sines and cosines
Answer:
1. 29 2. 35
Step-by-step explanation:
check the attached file
451 dived by 51
HELP!
I need to subtract!!!
After dividing 451 by 51, we get a quotient of 008 and a remainder of 43.
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.
On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.
It's not necessary for this number to be an integer.
For instance, if 20 apples are distributed equally among 4 persons, each person will get 5 of them.
So, we have 451/51.
Now calculate as follows:
451/51
Quotient = 008
Remainder = 43
(Refer to the image attached below)
Therefore, after dividing 451 by 51, we get a quotient of 008 and a remainder of 43.
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PLEASE HELP!! if QN bisects
Answer:7
Step-by-step explanation:
Find the slope of the line.
Answer: -2
Step-by-step explanation:
Slope is rise/ run or y2 - y1 / x2 - x1
We see that y goes down by 6, and x go over by 3
So slope is -6/3 = -2
Clare vwas solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can't find it. Where is Clare's mistake and what is the solution to the equation? 12(5 + 2y) = 4y- (5-9y) 72 + 24y = 4y -5-9y 72 + 24y = -5y -5 24y = -5y - 77 29y = -77 -77 y29
Clare's mistake is at the second step and the solution to the equation is -65/11.
What is the distributive property of multiplication?In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.
Based on the information provided above, we can logically deduce that Clare's mistake is at the second step because the product of 12 and 5 is equal to 60, rather than 72. Additionally, Clare did not distribute the negative sign to all the terms of the equation.
By applying the distributive property of multiplication to the given mathematical expression, we have the following:
12(5 + 2y) = 4y - (5 - 9y)
60 + 24y = 4y - 5 + 9y
60 + 24y = 13y - 5
24y - 13y = -5 - 60
11y = -65
y = -65/11
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What is the difference between a formal and informal proof? (Please give explanations)
A) A formal proof uses a table or a list of steps, whereas an informal proof uses paragraphs.
B) A formal proof provides the reasons for steps, whereas an informal proof does not.
C) A formal proof is much shorter, whereas an informal proof is longer.
D) A formal proof uses equations, whereas an informal proof only uses text.
The difference between a formal and informal proof in arithmetics is that a formal proof uses equations, whereas an informal proof only uses text. That is option D.
What is formal and informal proof?A formal proof is defined as the concept used in arithmetics to show that the final answer to an expression obeys a particular rule of an equation or formula.
An informal proof is defined as the concept that shows the answer to a mathematical expression without the use of formula or derived equation.
Therefore, the difference between the formal and informal proof is that a formal proof uses equations, whereas an informal proof only uses text.
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what is the equation of the line that passes through the point(-6,-7) and has a slope of 1/3
Answer:
The equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:
x - 3y + 15 = 0
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
To find the equation of the line that passes through the point (-6, -7) and has a slope of 1/3, we can use the point-slope form of a line:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line and m is the slope of the line.
Plugging in the given values, we have:
y - (-7) = (1/3)(x - (-6))
Which simplifies to:
y + 7 = (1/3)x + 2
Multiplying both sides by 3, we have:
3y + 21 = x + 6
Subtracting 21 and 6 from both sides, we have:
3y - x - 15 = 0
Therefore, the equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:
x - 3y + 15 = 0