1. If f(x) = log2 (x) and g(x) is the image of f(x) after a
translation five units to the left, which equation
represents g(x)?
1. g(x) = log 3 (x + 5)
2. g(x) = log 3 (x) + 5
3. g(x) = log 3 (x - 5)
4. g(x) = log 3 (x) - 5
Answers
Hi! The correct answer is 2. g(x) = log3 (x) + 5. Message me if you need further help.
The transformation of a function may involve any change. The correct option is 2. The value will be g(x) = log₂(x+5).
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k \times f(x)
Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)
As we know to shift a function towards the left horizontally, we need to add the number of units to the value of x. Therefore, the function of g(x) will be written as,
g(x) = log₂(x+5)
Hence, the correct option is 2. The value will be g(x) = log₂(x+5).
Learn more about Transforming functions:
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Related Questions
Write a two column proof
Answers
Answer:
see the explanation
Step-by-step explanation:
The correct question is
Prove ∠H≅∠J
we know that
The Angle-Side-Angle postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent,
we have
∠HIG≅∠JKI ----> given problem
∠HGI≅∠JIK ----> by corresponding angles (HG and JI are parallel lines)
GI≅IK ----> given problem
so
two angles and the included side of triangle HIG are congruent to two angles and the included side of triangle JKI
therefore
triangle HIG ≅ triangle JKI ---> by ASA postulate
Remember that
If two figures are congruent, then its corresponding sides and corresponding angles are congruent
Hence
∠H≅∠J ----> by definition of congruence (corresponding angles are congruent)
Can somebody help
Select the correct solution in the table.
Consider the equation below.
3^(-x) - 3 = 4^x - 1
Select the approximate solution to the equation.
x 3^(-x) -3 4^x - 1
-1.75 3.83 -0.91
-1.5 2.19 -0.88
-1.25 0.95 -0.82
-1 0 -0.75
-0.75 -0.72 -0.65
-0.5 -1.27 -0.50
-0.25 -1.68 -0.29
Answers
Answer:
-0.75
Step-by-step explanation:
The table values listed for the left side expression and the right side expression are closest together when the value of x is -0.75.
__
A graphing calculator shows the expressions both have a value near -0.658 when x ≈ - 0.775. The closest table value to x = -0.775 is x = -0.75.
Answer: x = -0.75
-0.72 -0.65
Step-by-step explanation:
Consider the equation below.
3^(-x) - 3 = 4^x - 1
consider the values of x = 1.75, -1.5, -1.25, -1, -0.75,-0.5,-0.25
x 3^(-x) -3 4^x - 1
-1.75 3.83 -0.91
-1.5 2.19 -0.88
-1.25 0.95 -0.82
-1 0 -0.75
-0.75 -0.72 -0.65
-0.5 -1.27 -0.50
-0.25 -1.68 -0.29
The bold values when x = -0.75 gives -0.72 and -0.65 is the approximate solution to the equation
by approximation -0.72 when rounded off = -0.7
and -0.65 when rounded off = -0.7
if there are 170 students in 12th grade what percentage of 12th grade students have more then one college in mind? round to the nearest percent
Answers
Answer:
nearest percent is about 56%
Answer:
56
Step-by-step explanation:
For all values of x, which expression is equivalent to 2x + 5 − x + 3x + x − 2?
Answers
Answer:
5x + 3
Step-by-step explanation:
1) Collect like terms.
(2x − x + 3x + x) + (5 − 2)
2) Simplify
5 x + 3
Answer:
D.) hope this help if i don´t then o well
Step-by-step explanation:
3.1 in standard form
Answers
3.1 is already in standard form.
Matthew has 2 dozen eggs. He uses 3/4 of the first dozen and 5/6 of the second dozen for baking.
How many eggs were left over?
Answers
Answer:
5 eggs.
Step-by-step explanation:
Well, 3/4 of 12 is 9 and 5/6 of 12 is 10. So, 12 - 9 = 3 and 12 - 10 = 2
Therefore, Matthew has 5 eggs left over.
I hope I helped ^^
Answer:
5/12 dozen eggs
Step-by-step explanation:
confirmed!
please what is the derivative of y=cos(^7)base x
Answers
The derivative of y=cos(^7)base x is
Dydx = (cos(7x))x⋅(ln(cos(7x))−7x(tan(7x)))
Step-by-step explanation:
step 1 :
y= (cos(7x))x
Take the natural logarithm of either side, bringing the t x down to be the coefficient of the right hand side we get the answer:
step 2 :
⇒ln y = xln (cos (7x))
Differentiate each side with respect to x. The rule of implicit differentiation: ddx (f(y)) = f'(y) ⋅ dydx
step 3 :
∴1y ⋅ dydx = ddx (x) ⋅ln (cos(7x)) + ddx (ln (cos(7x)))⋅x
Use the chain rule for natural logarithm functions – ddx ( ln (f(x)) )= f'(x)f(x) - we can differentiate the ln (cos (7x))
step 4 :
Ddx (ln (cos(7x))) = −7xsin (7x) cos( 7x 7tan (7x)
Returning to the original equation:
1y ⋅dydx = ln (cos(7x))−7xtan(7x)
Substitute the original y as a function of x value from the start back in.
Dydx = (cos(7x))x⋅(ln(cos(7x))−7x(tan(7x)))
May someone please help me?
Answers
Answer:
grapes cost $1.25 per pound
blueberries cost $4 per pound
Step-by-step explanation:
We have two unknowns, the cost of grapes and the cost of blueberries.
I'll call grape g and blueberries b.
since 21lb grapes and 44lb of blueberry cost $202.25, we can set up our first equation.
21g + 44b = 202.25
and the question also said 30lb grape and 22lb blueberries cost $125.50, we can set up our second equation.
30g + 22b = 125.5
now that we have two equations, you can use any methods you want to solve for the variable. I'm gonna use elimination.
21g + 44b = 202.25
-2(30g + 22b = 125.50)
━━━━━━━━━━
-39g = -48.75
g = 48.75/39
g = 1.25, grapes cost $1.25 per pound
now use substitution to find the cost of blueberries. you know the value of g now so plug it back in to one of the equation.
21g + 44b = 202.25
21(1.25) + 44b = 202.25
26.25 + 44b = 202.25
44b = 176
b = 4 , blueberries cost $4 per pound
What is the perimeter of △LMN?
8 units
9 units
6 + StartRoot 10 EndRoot units
8 + StartRoot 10 EndRoot units
Answers
Answer:
The perimeter of △LMN is 8 + [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Step 1: Finding the length of LM
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= 2
[tex]x_2[/tex]= -2
[tex]y_1[/tex]= 4
[tex]y_2[/tex]=1
LM = [tex]\sqrt{(-2-2)^2 +(1-4)^2}[/tex]
LM = [tex]\sqrt{(-4)^2 +(-3)^2}[/tex]
LM = [tex]\sqrt{16 +9)}[/tex]
LM = [tex]\sqrt{25}[/tex]
LM = 5
Step 2: Finding the length of MN
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= -2
[tex]x_2[/tex]= -1
[tex]y_1[/tex]= 1
[tex]y_2[/tex]= 4
LM = [tex]\sqrt{(-1-(-2))^2 +(4 - 1)^2}[/tex]
LM = [tex]\sqrt{(11+2)^2 +(3)^2}[/tex]
LM = [tex]\sqrt{1 +9)}[/tex]
LM = [tex]\sqrt{10}[/tex]
Step 3 : Finding the length of NL
Distance formula = [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
here
[tex]x_1[/tex]= -1
[tex]x_2[/tex]= 2
[tex]y_1[/tex]= 4
[tex]y_2[/tex]= 4
NL = [tex]\sqrt{(2-(-1))^2 +(4 - 4)^2}[/tex]
NL = [tex]\sqrt{(3)^2 +0}[/tex]
NL = [tex]\sqrt{9 +0}[/tex]
B = [tex]\sqrt{9 }[/tex]
NL = 3
Step 4: Finding the perimeter of the triangle
Perimeter = length of LM + length of MN + length of NL
Perimeter = 5 + [tex]\sqrt{10}[/tex] + 3
Perimeter = 8 + [tex]\sqrt{10}[/tex]
Answer:
its D on edg
Step-by-step explanation:
Solve for h.
3(h +1) = 18
Answers
Answer: h =5
Step-by-step explanation:
3(h+1) = 18
Expand the L.H.S to give
3h + 3 = 18
subtract 3 from both sides
3h = 15
divide through by 3
h = 15/3
h = 5
Step-by-step explanation:
Divide both sides by 3
H+1=6
Move the constant to the right
H=6-1
Subtract the numbers
Steve made a sign for his room that is shaped like a triangle. It is 4.5 feet long and 3 feet high. He wants to make another sign that is shaped like a triangle and similar to the first sign. The new sign will be 4 feet high.
Part A
Write a proportion that Steve can use to find the length, x, of the new sign.
Part B
What is the length, in feet, of the new sign? Make sure to show your work and explain your reasoning.
Answers
Answer: PART A : [tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]
PART B : 5.9 FEET
Step-by-step explanation:
Length of the first sign = 4.4 feet
height of the first sign = 3 feet
Length of the second sign = x feet
height of the second sign = 4 feet
If two shapes are similar , then the ratio of their sides are equal,
That is ;
[tex]\frac{h_{1}}{h_{2} }[/tex] = [tex]\frac{L_{1}}{L_{2} }[/tex]
PART A
[tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]
PART B
[tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]
cross multiplying , we have
3x = 4.4 x 4
3x = 17.6
Divide through by 3
x = 17.6/3
x = 5.86666666666667
x≈ 5.9 feet
Therefore , the length of the new sign is 5.9 feet
simplify the expression-
3k+ -9k+ -6+10k
Answers
Answer:
4k-6
Step-by-step explanation:
[tex]3k+ -9k+ -6+10k=3k-9k-6+10k=4k-6[/tex]
Answer:
4k-6
Step-by-step explanation:
3k+-9k=-6k ; -6k + 10k = 4k ; 4k+ -6 = 4k-6
solve the system of equations below.
2 x 4 y = 10
2 x 4y = -10
A. X=3, Y=1
B. X=6, Y= -4
C. No solution
D. Infinitely many solutions
Answers
Let’s solve this. First we need to put the first equation into y=mx+b form. Let’s do this now.
First equation-
2•4y=10
*subtract 2*
4y=8
*divide 4*
y=2
Now that we know the value of y, let’s substitute that into the second equation.
2•4y= -10
2•4(2)= -10
2•8= -10
16= -10
When solved, these equations produce a result where both sides do not equal each other. 16 does not equal -10, making this have no solution.
This is your answer! Hope this helps comment below for more questions :)
If the domain of the square root function f(x) is x <_7, which statement must be true?
A) 7 is subtracted from the x-term inside the radical.
B) the radical is multiplied by a negative number.
C) 7 is added to the radical term. D) the x-term inside the radical has a negative coefficient.
PLZ HURRY TIMED QUIZ
Answers
The correct statement must be D) the x-term inside the radical has a negative coefficient, as this would ensure the value inside the square root is nonnegative for the domain x \<= 7.
Explanation:The statement 'If the domain of the square root function f(x) is x \<=7, which statement must be true?' implies a restriction on the input values (domain) of the square root function. This restriction ensures that the value inside the square root is nonnegative, as the square root of a negative number is not a real number. When looking at the options provided, the correct answer can be deduced.
A) Since the domain is 'x \<=7', it does not necessarily mean that 7 is subtracted from the x-term inside the radical.
B) Multiplying the radical by a negative number isn't related to the domain restriction and would not ensure nonnegative values inside the radical.
C) 7 is added to the radical term does not guarantee nonnegative values either, since if x is negative, adding 7 might not be enough to make the inside of the radical nonnegative. Moreover, the domain 'x \<=7' suggests we are limiting x itself, not the expression inside the radical.
D) The x-term inside the radical having a negative coefficient could ensure that for all x \<= 7, the value inside the square root is nonnegative. This is because as x decreases (to values less than or equal to 7), this operation would actually make the term inside the square root larger (or at least nonnegative).
Therefore, the best choice that must be true is option D) the x-term inside the radical has a negative coefficient.
Final answer:
The statement that must be true for the square root function with domain x \<= 7 is that 7 is subtracted from the x-term inside the radical to ensure all values under the radical are non-negative within the domain.
Explanation:
If the domain of the square root function f(x) is x \<= 7, this refers to the set of all x values that the function can accept without resulting in an undefined or imaginary result. Specifically, the function must avoid producing a negative number under the square root, since the square root of a negative number is not a real number. The correct answer to this question must satisfy the condition that the expression under the square root is greater than or equal to zero for all x in the domain.
The correct statement that must be true is A) 7 is subtracted from the x-term inside the radical. This is because if we consider [tex]\sqrt{x - 7}[/tex], for all values x \<= 7, x - 7 will always be a non-negative number, satisfying the condition. Therefore, the expression under the square root will be zero or positive within the domain, making the square root real and defined.
geometry please help!
Answers
Answer:
i think it's D
Step-by-step explanation:
A relation just represents if the numbers have anything to do with each other. A function is where each number has just one output, which it does in this case since you would say 1 year is however many hours and you wouldn't say the same number of hours for another year gone by.
PLZ help super really super fast
Answers
Answer:
The one in the top left corner and bottom middle
The expression 4x gives the perimeter of a square with a side length of x units.
What is the perimeter of a square with a side length of 5/7?
Answers
Answer:
Perimeter of square is [tex]\frac{20}{7} \ units \approx2.86\ units.[/tex]
Step-by-step explanation:
Given:
Perimeter of square = [tex]4x[/tex]
where side length = 'x' units.
We need to find the Perimeter of square with side length[tex]\frac{5}{7}[/tex]
Now We know that;
[tex]x= \frac{5}{7}[/tex]
Substituting the value of x in perimeter of square formula we get;
Perimeter of square = [tex]4\times\frac{5}{7} = \frac{20}{7} \ units \approx2.86\ units.[/tex]
Hence Perimeter of square is [tex]\frac{20}{7} \ units \approx2.86\ units.[/tex]
please help !!
prove abp = dcp
Answers
Answer:
∠1≅∠2-------------------------(Given)m∠1=m∠2-------------------(Definition of congruent angles)∠ABP, ∠1 and ∠DCP,∠2 form linear pair---------------Linear pairm∠ABP+m∠1=180° and m∠DCP+m∠2=180°--------definition of linear pair∠ABP≅∠DCP--------------------If equals are subtracted from equals, the remainders are equalAP≅DP----------------------------GivenΔABP≅ΔDCP-------------------AASStep-by-step explanation:
Given, ∠1≅∠2, ∠3≅∠4 and AP≅DP,
We know that,∠1≅∠2(given)
⇒m∠1=m∠2(definition of congruent angles)
∠[tex]ABP+[/tex]m∠1=180° and ∠[tex]DCP[/tex]+m∠2=180° (Linear Pair)180°=180°(Reflexive)
⇒m∠[tex]ABP+[/tex]m∠1=m∠[tex]DCP[/tex]+m∠2
But m∠1 =m∠2 (definition of congruent angles)
⇒m∠[tex]ABP+[/tex]m∠1=m∠[tex]DCP[/tex]+m∠1
m∠[tex]ABP+[/tex]=m∠[tex]DCP[/tex] ( If equals are subtracted from equals, the remainders are equal)
[tex]AP[/tex]=[tex]DP[/tex](GIven)Therefore, Δ[tex]ABP=[/tex]Δ[tex]DCP[/tex] (by AAS criteria)
condition are:
m∠1=m∠2 (Angle)m∠[tex]ABP[/tex]=m∠[tex]DCP[/tex] (Angle)AP=DP (Side)15 POINTS!!!!!!! A music store has 500 guitar picks. They order 15 boxes with 9 picks each. They sell 19 boxes that have 10 picks each. The store manager says they now have about 450 guitar picks.
Is the manager's estimate reasonable?∵∴
Answers
Answer:
B. The manager estimate is reasonable. They ordered about 150 picks and sold about 200 picks, so they should have about 50 fewer than they started with.
Step-by-step explanation:
Given:-
Previous guitar In-stock before ordering and selling(P) = 500 picks. -----(equation 1)
Now, ordered guitar is 15 boxes of 9 picks each.
Ordered guitar=15 [tex]\times[/tex] 9
Hence, Ordered guitar(O)=135 picks ------------(equation 2)
Now, selled guitar is 19 boxes of 10 picks each.
So, Selled guitar = 19[tex]\times[/tex] 10
Hence, Selled guitar(S) =190 picks ------------(equation 3)
Now to calculate current in-stock of guitar we can write as,
Current guitar in-stock(C) = Previous in-stock(P) + Ordered guitar(O) - Selled guitar(S)
[tex]C=P+O-S[/tex]
[tex]C=500+135-190[/tex]
[tex]C=635-190[/tex]
[tex]C=445[/tex]
[tex]\therefore[/tex] Current guitar in-stock(C) = 445 picks ------(equation 4)
So, difference in-stock (D) = Previous guitar in-stock(P)- Current guitar in stock(C)
[tex]D=P-C[/tex]
[tex]D=500-445[/tex]
[tex]D=55[/tex]
Therefore Difference in Previous and current stock of guitar(D) = 55 = 50 pick approx.
Hence, the manager estimate is reasonable. They ordered about 150 picks and sold about 200 picks, so they should have about 50 fewer than they started with.
Answer:
we have the same test lol dont give me brainlist its just a statment
Step-by-step explanation:
A laptop case has an original price of $45. Ellen has a
coupon for 35% off the original price. Find how much
Ellen paid for the laptop case.
Answers
Answer:
29.25
Step-by-step explanation:
you need to take 35 and turn it into a decimal making it .35 then multiply 45 by .35 and you get 15.75 then subtract that from 45
Which expressions are equivalent to (7^-2)*(7^6)
A. 7^2/7^-2
B. 7^6/7^-2
C. 7^-12
D. (7^2)^2
Answers
Answer:
D
Step-by-step explanation:
(7^-2)*(7^6)=7^-2+6
......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2.
A country has 32 parks that allow camping and 43 parks that have playgrounds. Of those, 10 parks both allow camping and have playgrounds. The country has a total of 110 parks. What is the probability of randomly selecting a park that neither allows camping nor has a playground? Write your answer as a decimal rounded to the nearest hundredth.
Answers
Answer:
25
Step-by-step explanation:
Given:
32 parks allow camping
43 parks allow playgrounds
10 parks both allow camping and playgrounds
110 total parks
First, we need to add 32, 43, and 10
32 + 43 + 10 = 85
Then, we find the difference of 110 and 85
110 - 85 = 25
Since it isn't a decimal, there is no point in rounding.
barbra went for a walk in the city park. To cut across the rectangular park, she chose the path shown by the dotted line in the drawing below. At what angle, x, did Barbra cut across the park?
Answers
Note: As you have missed to add the attach drawing. After a little research I found the correct drawing of your question. Hence, I am answering your question based on that drawing I have attached.
Answer:
Barbra cut across the park at an angle x = 51.5° as shown in attached figure. Please check the attached figure as complete solution, along with complete question, is given there.
Step-by-step explanation:
All the angles of a rectangle have same size and measure. So, each of the angles in a rectangle is a right angle. Let suppose a, b, c and d are the angles of a rectangle as shown in attached figure.
All the angles combine to make 360 degree. In other words, ever angle in a rectangle is 90 degree.
Please check the attached figure below as it would visualize and make you understand how the below calculation is done.
As a, b, c and d are the angles of a rectangle. As the length of the rectangle is 370 feet and width of rectangle is 294 feet.
So,
tan (a) = opp / adj
tan (a) = 294 / 370
tan (a) = 0.79459
[tex]a = tan^{-1}(0.79459)[/tex]
a = 38.47 °
As every angle of a rectangle makes 90°.
so,
<a + <x = 90°
<x = 51.50° ∵ <a = 38.47°
Therefore, angle x = 51.50° is the angle Babra cut across the park.
Keywords: angle,
Learn more about using rectangle measure from brainly.com/question/12135418
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Three oblique pyramids have the same regular square base. Which one has a volume of 15 cubic units if the area of the bases are all 15 square units?
Answers
Answer:
The one which has a height of 3 units. H=3
Step-by-step explanation:
Well, the volume of pyramid is equal to the area of base multiply by the height of pyramid and divide by 3. Writing as a formula it can be expressed as V=(A*H)/3 where V is volume of pyramid, A is area of base and H is the height of pyramid. If V=15 cubic units and A=15 square units, H should be equal to 3 (to be cancelled out by 3. Please look at formula above) in order to make V=15.
Answer:
b
Step-by-step explanation:
If the vertices of a right triangle are located at (2,6), (2,3), and (6,3), what is the length of the hypotenuse?
A. 2.5 units
B. 5 units
C. 10 units
D. 25 units
Answers
Answer:
5 units
Step-by-step explanation:
ez pz lemon squeezy. hippity hoppity your math is now my property. splish splash your opionion is trash
plz help me quick!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Exact Form: 5/2
Decimal Form: 2.5
Mixed Number Form: 2 1/2
Step-by-step explanation:
HELP ASAP PLEASE
Which types of dilation are the given scale factors?
Select Expansion or Contraction to correctly describe the type of dilation for each given scale factor.
Answers
-4= Contraction
2.5=Expansion
2/3= Contraction
-3/4= Contraction
Best way to solve this, if the scale factor is less than one, is a contraction. If it is greater than one, than it is an expansion.
If one lens increases the size of an image by 80% and another increases the size by 50% by what percent will the image be increased if the two lenses are used together?
Answers
Answer:
130%
Good luck!
Answer:
170%
Try it, I tried it, and it worked
A charity organization is having a fundraiser.
PPP represents the fundraiser's profit (in dollars) if nnn tickets are sold. A negative profit means the expenses exceeded the income from tickets.
P=70n-1500P=70n−1500
Answers
Answer:
Hence, the price of single ticket is $70.
Step-by-step explanation:
Consider the provided equation.
[tex]P(n) = 70n - 1500[/tex]
As we know that: Profit = Income – Cost
Here, P(n) represents the fundraiser's profit (in dollars) and n represents the number of tickets sold and cost is 1500
Since, n is multiplied by 70 that represents the price of per ticket is $70.
Hence, the price of single ticket is $70.
The expenses of the fundraiser are $40.
Step 1:
To find the expenses of the fundraiser, we can use the given equation:
[tex]\[ P = 70n - 1500 \][/tex]
Here, P represents the profit and n represents the number of tickets sold.
Step 2:
Since profit is the difference between income and expenses, and a negative profit means expenses exceeded income, we can set the profit P to zero and solve for the number of tickets n. Then, we can use the value of n to find the expenses.
When [tex]\( P = 0 \)[/tex]:
[tex]\[ 0 = 70n - 1500 \][/tex]
Solving for n:
[tex]\[ 70n = 1500 \][/tex]
[tex]\[ n = \frac{1500}{70} \][/tex]
[tex]\[ n \approx 21.43 \][/tex]
Since you can't sell a fraction of a ticket, we take the next whole number, which is 22.
Step 3:
Now, we can find the expenses using the value of [tex]\( n \)[/tex]:
[tex]\[ P = 70 \times 22 - 1500 \][/tex]
[tex]\[ P = 1540 - 1500 \][/tex]
[tex]\[ P = 40 \][/tex]
Therefore, the expenses of the fundraiser are $40.
Complete Correct Question:
A charity organisation is having a fundraiser. P represents the fundraiser's profit in dollars if 7 tickets are sold. A negative profit means the expenses exceeded the income from tickets. P=70n-1500 What are the expenses of the fundraiser?
Abby bought two slices of pizza and three bottles of water for $7.25 Cameron bought four slices of pizza and one bottle of water for $8.25 what is the solution
Answers
The solution is price of 1 slice of pizza is $ 1.75 and price of 1 bottle of water is $ 1.25
Solution:
Let "p" be the price of 1 slice of pizza
Let "b" be the price of 1 bottle of water
Given that Abby bought two slices of pizza and three bottles of water for $7.25
So we can frame a equation as:
two slices of pizza x price of 1 slice of pizza + three bottles of water x price of 1 bottle of water = $ 7.25
[tex]2 \times p + 3 \times b = 7.25[/tex]
2p + 3b = 7.25 ------- eqn 1
Cameron bought four slices of pizza and one bottle of water for $8.25
So we can frame a equation as:
four slices of pizza x price of 1 slice of pizza + one bottles of water x price of 1 bottle of water = $ 8.25
[tex]4 \times p + 1 \times b = 8.25[/tex]
4p + 1b = 8.25 ----- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "p" and "b"
Multiply eqn 1 by 2
4p + 6b = 14.5 ----- eqn 3
Subtract eqn 2 from eqn 3
4p + 6b = 14.5
4p + 1b = 8.25
( - ) ------------------
5b = 6.25
b = 1.25
Substitute b = 1.25 in eqn 1
2p + 3b = 7.25
2p + 3(1.25) = 7.25
2p + 3.75 = 7.25
2p = 3.5
p = 1.75
Summarizing the results:
price of 1 slice of pizza = $ 1.75
price of 1 bottle of water = $ 1.25