Answer: $50
Step-by-step explanation:
Let's denote the amount of money Gabriella had before buying the cake as "a". Then we can write an equation to find "a":
a - $25.52 = $24.48
Adding $25.52 to both sides:
a = $25.52 + $24.48
So,
a = $50
Therefore, Gabriella had $50 before buying the cake.
Does each relation represent a function
(1,3), (2,5), (2,7), (4,9)
(1,3), (2,5), (3,7), (4,9)
(1,3), (1,5), (1,7), (1,9)
(1,3), (2,3), (3.3), (4.3)
the first one yes
the 2nd one yes
the 3rd one no 4th also no
Step-by-step explanation:
A line has a slope of –9 and includes the points (–7,u) and (9,9). What is the value of u?
A line has a slope of –9 and includes the points (–7,u) and (9,9).
The value of u is 153.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
A line has a slope of –9 and includes the points (–7,u) and (9,9).
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
-9 = (9 - u)/(9 + 7)
-9 = (9- u)/16
9 - u = -144
u = 153.
Therefore, the value of u is 153.
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Drag the tiles in the correct box. Consider the graph of the function f (x) =2x. Match each transformation of function f to a feature of the transformed function.
Answer:drag 1st 2 3rd box 2nd to 1st box 3rd to 1st box 4th to 4th
Step-by-step explanation:
so easy
Points X and Y lie in both plane P and plane Q. What object defines the intersection of the two planes
A straight line defines the intersection of the two planes.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Points {X} and {Y} lie in both plane P and plane Q.
Two common points can only lie on a straight line. So, a straight line defines the intersection of the two planes.
Therefore, a straight line defines the intersection of the two planes.
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What is the slope of a line that is parallel to the line y = 3/4x+2?
O -4/3
O -3/4
O 3/4
O 4/3
As a result, the given line, y = 3/4x+2, and any line having a slope of 3/4 are parallel.
what is slope ?The slope of a line establishes its steepness. "Texture overflow" is the name of a gradient-related math problem (the change in y divided by the change in x). The sloping is the ratio of either the longitudinal (rise) to the horizontal (run) change in elevation between any two places. The gradient form of an equation is used to represent a linear relationship when its expression is expressed as y = mx + b. The y-intercept is situated where the slope of the line is m, b is c, and (0, b). For instance, either y-intercept and curve of something like the calculation y = 3x - 7 (0, 7). The line has a slope of m, a b value at the y-intercept, and (0, b). As
given
Given line equation, y = 3/4x + 2.
The slope of a line parallel to the supplied line must be determined.
Since every line parallel to the provided line will have the same slope as the supplied line since y = 3/4x+2,
Where, y = mx + c is the general equation of the line. m denotes the line's slope, and c the y-intercept.
Therefore, for the given line equation, y = 3/4x+2 Slope is m= 3/4 when we compare and.
As a result, the given line, y = 3/4x+2, and any line having a slope of 3/4 are parallel.
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Write an equation of the line in point-slope form that passes through the given points (-2,3) and (-4,-4)
Answer:
tu x ella = ERROR
Step-by-step explanation:
Explain why the statement "It will always rain on my birthday" uses inductive reasoning.
Create your own quadratic function ,f(x), and then evaluate the function at f(x-3). Find the domain of your function.
Domain of the function is all real numbers
What is a function?A relation is a function if it has only One y-value for each x-value.
Let us consider a function f(x)= x² + 2x - 3
Now let us find the value of f(x-3)
Plug in the value x as x-3
f(x-3)= (x-3)² + 2(x-3) - 3
= x² +9-6x+ 2x-6 - 3
= x² -4x
The domain of this function is all real numbers. This means that any real value can be plugged into the function and produce a real output.
Hence, domain of this function is all real numbers
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a
[Ω]
+
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You want to buy a $237,000 home. You plan to pay 20% as a down payment, and take out a 30 year
loan for the rest.
a) How much is the loan amount going to be?
b) What will your monthly payments be if the interest rate is 6%?
c) What will your monthly payments be if the interest rate is 7%?
Enter an integer or decimal number [more]
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The values will be Loan amount=$186900, When simple interest is 6% then monthly payment=$1453.66 per month, When simple interest is 7% monthly payment=$1609.4 per month
What is simple interest?Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount.
Simple interest formula is given as:
SI=P*R*T/100
Where SI = simple interest
P = principal
R = interest rate (in percentage)
T = time duration (in years)
In order to calculate the total amount, the following formula is used:
Amount (A) = Principal (P) + Simple Interest (SI)
Now,
Initial amount=$237000
Down-payment=20%=20/100*237000=$47400
Amount left=237000-47400=$186900
So, Loan amount=$186900
For interest rate=6%
Total amount=186900+186900*6*30/100
=186900+336420
Total amount=$523320
Therefore, monthly payment=523320/360
monthly payment=$1453.66 per month
For interest rate=7%
Total amount=186900+186900*7*30/100
=186900+392490
Total amount=$579390
Therefore, monthly payment=579390/360
monthly payment=$1609.4 per month
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Resolva as expressões a seguir e registre os resultados na forma fracionária e na forma decimal
two-fifths of the students in central middle school are boys. One third of the girls have blonde hair and one quarter of the boys have blonde hair.
(A) what fraction of the students in central middlev school have blonde hair.
(B) if 36 of the students of central middle school have blond hair, then how many total does central middle school have.
PLEASE HELP
I did number one but i think its wrong
Answer: A: 3/10 of the school has blonde hair. B: there are 120 students
Step-by-step explanation: I might have done this wrong but anyway, I multiplied 2/5 by 1/4 and got 1/10, meaning 1/10 of the boys have blonde hair. I multiplied 3/5 (because 5/5 - 2/5 = 3/5) by 1/3 and got that 2/10 of the girls are blonde. I added these, and got that 3/10 of the school are blondes. That's A. Then, I set up the equation 3/10 = 36/x (x equals the total number of students in the school). When I solved it I got x = 120, meaning there are 120 students in the school.
m∠3=82 Find m∠4 I-Ready
The angle 4 is equal to 98degree.
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
Given;
m∠3=82
Now
m∠3+m∠4=180 (since the angles are supplementary)
82+m∠4=180
m∠4=180-82
m∠4=98degree
Therefore, the angle 4 will be 98degrees.
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Answer:
98 degrees
Step-by-step explanation:
A road descends a vertical distance of 2000 feet over a distance of 3.5 miles as shown in the diagram.
Find the approximate measure of , the angle shown in the diagram. Give your answer to the nearest thousandth of a degree. Show or explain how you found your answer. (Use 1 mile = 5280 feet.)
The value of θ from the triangle ABC is θ = 6.213°
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ABC
Now , the opposite side of the triangle AB = 2,000 feet
The hypotenuse of the triangle AC = 3.5 miles
The hypotenuse of the triangle AC = 3.5 x 5,280
The hypotenuse of the triangle AC = 18,480 feet
Now , from the trigonometric relations ,
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin θ = 2000 / 18480
On simplifying the equation , we get
sin θ = 0.108225
Taking inverse on both sides of the equation , we get
θ = sin⁻¹ ( 0.108225 )
θ = 6.213°
Hence , the value of θ is 6.213°
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What is the Hcf for 18 and 36
Answer:
18
Step-by-step explanation:
GCF - The highest number that divides into two or more numbers, we are given the number 18 and 36.
Out of all the numbers divisible by 18 and 36, 18 is the greatest number out of all, making it the GCF.
Answer:
6
Step-by-step explanation:
The HCF (highest common factor) is the product of all the primes of both numbers!
1) List the prime factors of 18...
18 = 2 × 3 × 3
2) List the prime factors of 36...
2 × 2 × 3 × 3
3) Now see what numbers are in both!
We can see that the numbers 2 & 3 are in both prime factors so all we need to do is multiply them...
2 × 3 = 6Have a lovely day :)
Solve for x. 8x-8+3(2x+2) = -4(x+3)
Answer:
x = - 5/9
Step-by-step explanatiion:
8x-8+3(2x+2) = -4(x+3) is the original equation
Consider each term and simplify
3(2x+2) = 6x + 6
-4(x + 3) = -4x - 12
Therefore the original expression becomes:
8x - 8 + 6x + 6 = -4x - 12
Move -4x to the left side; becomes + 4x
4x + 8x - 8 + 6x = -12
Group like terms on left side and simplify
(4x + 8x + 6x) (-8 +6) = -12
18x - 2 = - 12
Move -2 to right side -> becomes +2
18x = 2 - 12 = - 10
x = -10/18 = - 5/9
Jacob has 17 yards of fabric. He uses 1 third of it to make a cape. How many yards of fabric does Jacob use for the cape.
Answer:
49/3 or 16 1/3
Step-by-step explanation:
Answer:
Jacob uses 5.67 yards of fabric for the cape.
Step-by-step explanation:
(pre calc) HELP ASAP
The solution is Option D.
The limit of the infinite series diverges and the limit goes off to infinity
What is convergent and divergent series?If a series is convergent then it has bounded partial sums. Equivalently, if a series fails to have bounded partial sums then it is divergent.
When the series' limits reach its finite range of values, the series is said to be convergent. It is important that, partial sum of series, there should be a limit existed and that is finite in nature then only series converges
An infinite series is one that doesn't converge at any point , had a series of incomplete sums that went on forever and had no end. A series diverges when each sum does not approach zero.
Given data ,
Let the infinite series be represented as A
Now , the value of A is
A = ∑n=1 to ∝ ( 3n⁴ / ( 15n⁴ + 5 )
On simplifying the equation , we get
A = 3 ∑n=1 to ∝ ( n⁴ / ( 15n⁴ + 5 )
In the equation , where the limit goes to infinity, there will finally be no exact solution because the sum of the series will be infinity and the infinite series diverges
Hence , the limit of the equation is infinity
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32 players show up to practice one day, and the coach realizes she can't
make equal teams of 6. With 32 players, how many players can the coach
put on each team so that each player is on a team and every team has the
same number of players?
Answer:
8 teams of 4 players or 4 teams of 8 players
Step-by-step explanation:
8 x 4 = 32
Nilsa borrows $2,000 for 90 days at 18% exact interest.
On solving the provided question, we can say that so, the Interest Rate to be paid will be as = 5.08%
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.
Interest Rate =($ Paid in Interest / $ Amount borrowed) X (360 / borrowed period)
= ($33 / $2600) X (360 /90)
=0.050769231
=5.08%
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what is 18x+26.6 need asap
18x+26.6
18x+133/5
1/5(90x+133)
What is the difference between the area of Figure A and the
area of Figure B? Each grid square represents 1 square foot
The difference between the area of Figure A and the areas of Figure B is 2 ft².
What is the difference between the area of the two figures, Figure A and Figure B?The difference between the area of the two figures, Figure A and Figure B is determined by finding the area of the two figures.
The area of Figure A is found as follows:
The triangle on the right of figure A is cut out and moved to the left in order to form a rectangle.The area of figure A is then calculated.The area of A = 3 × 4
The area of A = 12 ft²
The area of B = ½ × 4 × 3 + ½ × 4 × 2
The area of B = 10 ft²
Difference between the area of A and B = 12 - 10 ft²
Difference between the area of A and B = 2 ft²
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What is m∠LKH? - View the image attached.
Answer:
∠ LKH = 25°
Step-by-step explanation:
LK is the midsegment of Δ FGH
LK joins the midpoints of the sides FH and GH and is parallel to the third side FG.
Then
∠ LKH = ∠ FGH = 25° ( corresponding angles )
(4a*2c)+(8a*2c)-(10a*2c)
Answer: 4ac
Step-by-step explanation: Combine like terms and follow PEMDAS
THEORY
1a. In a class of 58 students, 35 offer Biology, 28 offer Economics and 15 offer Physics. Each
students offers at least one of the three subjects. If 12 students offer both Biology and
Economics, 7 students offer both Biology and Physics and 5 students offer both Economics and
Physics, how many students offer all three subjects?
b. A regular polygon with (2m+1) sides has each interior angle equal to 1440. Find the value of
m.
A. 9 students offer all three subjects.
B. The only possible value of m is 8.
Solution
A. We can use the Principle of Inclusion-Exclusion (PIE) to find the number of students who offer all three subjects.
Let's call the number of students who offer all three subjects "x".
The total number of students who offer Biology is 35, but we have to subtract the number of students who offer only Biology and Economics (12) and only Biology and Physics (7) to avoid counting them twice.
So, the number of students who offer Biology only is 35 - 12 - 7 + x = 16 + x.
Similarly, the number of students who offer Economics only is 28 - 12 - 5 + x = 11 + x.
And the number of students who offer Physics only is 15 - 7 - 5 + x = 3 + x.
The total number of students who offer at least one of the three subjects is 58, so:
16 + x + 11 + x + 3 + x = 58
30 + 3x = 58
3x = 28
x = 9
So, 9 students offer all three subjects.
B. In a regular polygon with (2m + 1) sides, each interior angle is equal to (2m + 1 - 2) * 180 / (2m + 1) = (2m - 1) * 180 / (2m + 1).
We know that this value is equal to 1440, so:
(2m - 1) * 180 / (2m + 1) = 1440
Expanding the right side:
2m - 1 = 1440 * (2m + 1) / 180
Dividing both sides by (2m + 1) and rearranging:
2m = 1440 * 2 / 180 + 1
2m = 16 + 1
m = 8.5
Since m must be a positive integer, the only possible value of m is 8.
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-2x + 9y=-41 and -2x -5y =1
3x - 4y= 22
-3x + 2y = -2
X =
y =
answer
y = -10
x = 10
eplanation
A standard die is rolled. Find the probability that the number rolled is even
The probability of rolling an even number is P = 0.5
How to find the probability?We know that the possible outcomes of a standard die are {1, 2, 3, 4, 5, 6}
The outcomes that are even are {2, 4, 6}
If all the outcomes have the same probability, then the probability of rolling an even number is equal to the quotient between the nmber of even outcomes (3) and the total number of outcomes (6).
Then the probability is:
P = 3/6 = 1/2
That is the probability of rolling an even number,
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Mitchell travels from the US to Canada, where he exchanges 150 US dollars for Canadian dollars. He then spends 20 Canadian dollars, returns to the US, and exchanges the remaining money back to US dollars. How many US dollars does Mitchell have remaining? O 129.46 O 130.00 O 130.66 O 134.59
Going by current exchange rates, Mitchell has $134.13 dollars remaining.
What is unit conversion?Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.
The current exchange rate of Canadian dollars to US dollars is:
CAD $ 1.26 : 1 USD
When Mitchell first exchanged the USD to CAD$, it became:
= 150 x 1.26
= CAD$ 189
He then spends CAD$ 20 which leaves him with:
= 189 - 20
= CAD$ 169
He then exchanges this back to US$:
= 169 / 1.26
= US$ 134.13
Mitchell has US$ 134.13 remaining.
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Kaya babysits to add money to her savings. She draws a graph to show how much she can earn by babysitting. What is the equation of Kaya’s line in slope-intercept form? What do the slope and y-intercept represent in the situation? Show your work.
The equation of the line of Kaya’s line in slope-intercept form is y = 15x + 25.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given this, Kaya babysits to add money to her savings. She draws a graph to show how much she can earn by babysitting.
To calculate the equation of the line we at least need Two points on the line.
Two points on the graph (0, 25) and (5, 100) and also the y-intercept of the given line is 25(where x is 0)
From the general formula of the slope-intercept form of an equation:
y=mx+b,
where m is the slope
b is the y-intercept,
Since. m = (y - y')/ (x -x')
In our case m = (100 - 25)/5-0)
m = 75 /5
m = 15
and b = 25
Thus, the equation of a line:
y = 15x + 25
Therefore, The equation of the line of Kaya’s line in slope-intercept form is y = 15x + 25.
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2 2/3 +2 1/6 as a fraction
Answer:
You can either write it as a whole number: 4 5/6
Or as 29/6
Step-by-step explanation:
Step-by-step explanation:
first step : convert both terms into real fractions (not mixed numbers).
second step : bring both fractions to the same denominator (bottom part).
third step : perform the addition.
1.
2 2/3 = (2×3 + 2)/3 = 8/3
2 1/6 = (2×6 + 1)/6 = 13/6
2.
we bring both fractions to .../6.
remember, we need to do the same multiplication for the numerator and the denominator to keep the overall value of the fraction unchanged.
to get from 3 to 6 we need to multiply by 2.
so,
8/3 = 8/3 × 2/2 = 16/6
3.
16/6 + 13/6 = 29/6
if you want to convert this to mixed numbers, this would be
29/6 = (4×6 + 5)/6 = 4 5/6