Here we are given a geometrical shape with the following inner and an arc angle as follows:
[tex]The property to note here is from geometric properties of a circle.Property: The inner angle is always the mean of corresponding verticaly opposite arc angles.
We can express the above property in lieu to the geometry question at hand. We see that the two arc angles:
[tex]\text{Arc CD = 55 degrees , Arc BG = ?}[/tex]Ther inner vertically opposite angle are:
[tex]<\text{ DFC < }BFG\text{= 40 degrees }[/tex]The property can be expressed mathematically as follows:
[tex]<\text{ DFC = }\frac{1}{2}\cdot\text{ ( Arc CD + Arc BG )}[/tex]Next plug in the respective values of angles and evaluate for the arc angle BG as follows:
[tex]\begin{gathered} 40\text{ = }\frac{1}{2}\cdot\text{ ( 55 + Arc BG )} \\ 80\text{ = 55 + Arc BG } \\ \text{\textcolor{#FF7968}{Arc BG = 25 degrees}} \end{gathered}[/tex]Therefore the correct option is:
[tex]\textcolor{#FF7968}{25}\text{\textcolor{#FF7968}{ degrees}}[/tex]2. A common formula in physics is shown below. my2 FE a) Solve for m in terms of F, v, and r. b) Solve for v in terms of F, m, and r.
1)
a) Solving for m, is isolating the m variable on the left side like this
[tex]\begin{gathered} F=\frac{mv^2}{r}\text{ } \\ mv^2=Fr\text{ } \\ m=\frac{Fr}{v^2} \\ \end{gathered}[/tex]We need to Cross multiply like a ratio, and then divide both sides by v²
Now we can solve for m.
b) Similarly, let's now solve for v, in terms of F, m and r
[tex]undefined[/tex]40% of x is 35.Write an equation that shows the relationship between 40%, x, and 35.My equation is: ___Use your equation to find x.x = ___
Answer:
E
87.5
Explanation:
40% of x is 35 can be expressed as an equation as shown below;
[tex]\begin{gathered} \frac{40}{100}\times x=35 \\ \end{gathered}[/tex]Let's go ahead and solve for x;
[tex]\begin{gathered} \frac{40}{100}\times x=35 \\ \frac{4}{10}x=35 \\ 4x=350 \\ x=\frac{350}{4} \\ x=87.5 \end{gathered}[/tex]Function f(x) = |x| is transformed to create function g(x) = |x - 7| + 2.What transformations are performed to function f to get function g?Select each correct answer.Function f is translated 7 units to the left.Function f is translated 7 units down.Function f is translated 2 units up.Function f is translated 7 units to the right.Function f is translated 7 units upFunction f is translated 2 units to the right.Function f is translated 2 units to the left.Function f is translated 2 units down.
We will have the following:
*Function f is translated 7 units rigth.
*Function f is translated 2 units up.
Hi there! I have a probability quiz this week and I grabbed some problems from my worksheet. This one in particular has me stumped:At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remainder are lorries. If every vehicle is equally likely to leave, find the probability of:a) a van leaving first.b) a lorry leaving first.c) a car leaving second if either a lorry or van had left first.Can you help??
Explanation
In the question, we are given that;
[tex]\begin{gathered} \text{Number of vehicles = 100} \\ \text{Number of cars =60} \\ Number\text{ of vans =30} \\ \text{Number of lorries =10} \end{gathered}[/tex]Since each of the vehicles is equally likely to leave;
Part A
[tex]Pr(van)=\frac{\text{number of vans}}{Total\text{ number of vehicles}}=\frac{30}{100}=0.3[/tex]Answer: 0.3
Part B
[tex]Pr(\text{lorry)}=\frac{number\text{ of lorries}}{\text{Total number of vehicles}}=\frac{10}{100}=0.1[/tex]Answer: 0.1
Part C
First we find the probability of a lorry or van leaving
[tex]Pr(\text{Lorry or van) = }pr(lorry)+pr(Van)=0.1+0.3=0.4\text{ or }\frac{4}{10}[/tex]Next, we find the probability of a car; but remember that one of either a lorry or van has left the car park already, so the total number of vehicles will reduce by 1
[tex]Pr(car)=\frac{60}{99}=\frac{20}{33}[/tex]Therefore, the probability of a car leaving second if either a lorry or van had left first is
[tex]Pr((\text{lorry or van) and car)) }=\frac{4}{10}\times\frac{20}{33}=\frac{8}{33}[/tex]Answer:
[tex]\frac{8}{33}[/tex]Below is the graph of =y3x.Translate it to become the graph of =y+3−x41.
The Solution:
Given:
[tex]y=3^x[/tex]Required:
To translate it to become:
[tex]y=3^{x-4}+1[/tex]The Transformations:
A horizontal shift of 4 units to the right.
A vertical shift of 1 unit up.
Below is th graph:
please help I don't understand how to find the volume of the cylinder(please add an explanation).
Explanation
From the image, we can see that the radius of the cylinder is given as
[tex]\frac{d}{2}=\frac{20}{2}=10ft[/tex]The height of the cylinder is 40ft. Therefore, the volume of the cylinder is
[tex]volume=\pi r^2h=3.14\times10^2\times40=12560[/tex]Answer: 12560 cubic feet
Which equation can be used to find 40 percent of 25? 199 25 40 40-1 100x4 400 4044 16 40x4 160 25x4 100 40:4 100=4 10 25
To find percentage is find a quantity smaller than a given number. In this case number is 25, and is required to find 40% of 25.
Should Jenna buy the smart phone at top quality or big value? support your answer with a mathematical evidence. Assume that getting the lowest price is Jenna's only consideration.?
Let the price of the item be t as stated in the question.
This means if Top quality is selling them at 15% off the list price, then the new price can be represented as;
(A)
[tex]\begin{gathered} Price=t-discount \\ \text{Price}=t-(t\times0.15) \\ \text{Price}=t-0.15t---(1) \\ \text{The second expression that can be used to }represent\text{ the discounted price is;} \\ \text{Price}=(t-0.15t) \\ \text{Price}=0.85t---(2) \end{gathered}[/tex](B)
Equation 1 shows the original list price less the discounted amount (which is 15 percent times the list price, t). The result is the price now paid eventually
Equation 2 shows the percentage of the list price that would be paid by Jenna after deducting the discount, which means she would be paying 85 percent of the list price (that is 0.85)
(C)
A smartphone on sale at 1/4 off its list price, would also mean its being sold at a discount of 25%. One-quarters of 100 percent would be 25, hence the smartphone is at 25% off the list price.
However, where the phone is being sold at 75% of its list price means, the list price now has 25% taken off. That is, the price at Big Value is
[tex]\begin{gathered} \text{Price}=0.75t \\ \text{Discount=t-0.75t} \\ \text{Discount}=0.25 \end{gathered}[/tex]That means the discount at Big value is 25% (or 0.25)
The discount at Top Quality is 25% (0.25 or 1/4)
Jenna can buy at either of the store. Since she is already at Top Quality, she can just go ahead and buy it right there
What is the sale price of a $63 sweater if the discount rate is 15%?Round to the nearest cent. Do not put a $ in your answer.
Answer:
Concept:
The formula to calculate the selling price of the sweat will be
[tex]\text{Selling price=original price - discount}[/tex]Step 1:
Calculate the discount price
The discount rate given is
[tex]=15\%[/tex]The discounted price will be
[tex]\begin{gathered} =\frac{15}{100}\times\text{ \$63} \\ =\frac{945}{100} \\ =\text{ \$9.45} \end{gathered}[/tex]Step 2:
Calculate the selling price, we will have
[tex]\begin{gathered} \text{Selling price=original price - discount} \\ \text{Selling price}=63-9.45 \\ \text{Selling price}=53.55 \end{gathered}[/tex]Hence,
The sale price of the sweater will be = $ 53.55
In this figure, AB and CD are parallel.unitsAB is perpendicular to line segmentIf the length of EF is a units, then the length of GH is
AB is perpendicular to EF or GH because make a right angle
EF and GH have the samaevalue because they are between two paralells lines and make an right angle
Suppose that the dollar value v () of a certain house that is t years old is given by the following exponential function.v (t) = 637,000 (1.02)^tFind the initial value of the house.s1Does the function represent growth or decay?O growth O decayBy what percent does the value of the house change each year?
Given the function:
[tex]v(t)=637000(1.02)^t[/tex]Where:
v(t) represents the value of the house after t years.
Let's find the following:
• (a). Find the initial value of the house.
Apply the exponential function:
[tex]f(x)=a(b)^x[/tex]Where:
a is the initial value
b is the growth of decay factor.
Here, we have:
a = 637000
b = 1.02
Therefore, the initial value of the house is 637,000 dollars.
• (b). Does the function represent growth or decay?
If b is greater than 1 the function represents a growth function.
If b is less than 1, the function represents a decay function.
Here, we have:
b = 1.02
Therefore, the function represents a growth function.
• (c). By what percent does the value of the house change each year?
Apply the formula:
[tex]f(x)=a(1+r)^x[/tex]Where r is the growth rate.
Thus, to find r, we have:
1 + r = 1.02
r = 1.02 - 1
r = 0.02
The growth rate is 0.02
To convert the rate to percent multiply by 100:
Growth percent = 0.02 x 100 = 2%
Therefore, the value of the house increases by 2% each year.
ANSWER:
• (a). 637000 dollars
,• (b). Growth
,• (c). 2%
ANSWER:
• (a). 637000 dollars
,
• (b). Growth
,
• (c). 2%
Function F, shown below, assigns to a temperature given in degrees Celsius it's equivalent in degrees Fahrenheit. Function C, also shown below, assigns to a temperature given in degrees Kelvin its equivalent in degrees Celsius. Choose the response below that shows the correct expression for F(C(x)) and then choose the response below that correctly interprets the meaning of F(C(x)).F(x)=(9/5)x+32 C(x)=x−273
Given:
The expressions are given as,
[tex]\begin{gathered} F(x_)\text{ = \lparen}\frac{9}{5})x\text{ + 32} \\ C(x)\text{ = x - 273} \end{gathered}[/tex]Required:
The value of F(C(x)) and its response.
Explanation:
The required function is calculated as,
[tex]\begin{gathered} F(C(x))\text{ = }\frac{9}{5}\text{ \lparen x - 273\rparen + 32} \\ F(C(x))\text{ = }\frac{9x}{5}\text{ - }\frac{2457}{5}\text{ + 32} \\ F(C(x))\text{ = }\frac{9x}{5}\text{ + 32 - }\frac{2457}{5} \\ F(C(x))\text{ = }\frac{9x}{5}\text{ + }\frac{160}{5}\text{ - }\frac{2457}{5} \\ F(C(x))\text{ = }\frac{9x}{5}\text{ - }\frac{2297}{5} \\ F(C(x))\text{ = }\frac{9x}{5}\text{ - 459}\frac{2}{5} \\ \end{gathered}[/tex]Use the table below to answer the questions. a. Is this a proportional relationship? b. What is the constant of proportionality. X Y-2 6 1 -32 -6
hello
the relationship on the question is a direct proportion. i.e, when x in
assume you pay 300 per month into a retirement account for 12 years and they count has an APR of 3.05 compounded monthly question what is the account balance at the end of the 12 years round to the nearest cent
Given:
$300 per month in 12 years.
1 year = 12 months = 300 x 12 = $3600
For 12 years = $3600 x 12 = $43 200
Principal (P) = $43 200
rate(r) = 3.05% = 0.0305
Time (t) =12
n = 12
Using the formula below:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute into the formula and evaluate
[tex]A=43200(1+\frac{0.0305}{12})^{12\times12}[/tex][tex]=43200(1+0.00254166667)^{144}[/tex][tex]=43200(1.00254166667)^{144}[/tex][tex]\approx62263.55[/tex]Therefore, the account balance at the end of the 12 years is $62263.55
is the prime factorization of what composite number? 91 point
Answer: The question isn't clarified, what are you looking for?
Step-by-step explanation:
Answer:
The Prime Factors of 91 are 1, 7, 13, 91
Step-by-step explanation:
Pat is walking to a restaurant 9 blocks away. Pat has walked 3 blocks in 7minutes. How many more minutes to reach the restaurant?
We can solve this question in the following way:
We have that Pat has walked 3 blocks in 7 minutes, and now, we can post the following: how long will it take to walk 9 blocks?
Then, we have:
Then, we can solve for x as follows:
We need to multiply 9 blocks by 7 minutes, and then we divide the result by 3 blocks (see the red lines).
[tex]x=\frac{9bl\cdot7\min}{3bl}\Rightarrow x=\frac{63\min}{3}\Rightarrow x=21\min [/tex]This answer comes from having into account the following proportion:
[tex]\frac{9bl}{3bl}=\frac{x}{7\min}\Rightarrow x=\frac{9bl\cdot7\min}{3bl}=21\min [/tex](We have here proportional quantities.)
It will take 21 min to walk the 9 blocks. However, Pat has walked for 7 minutes. Therefore, Pat needs to walk for (21 min - 7 min) = 14 minutes.
Therefore, Pat will need to walk for 14 minutes more to reach the restaurant.
Answer:
15 minutes
Step-by-step explanation:
15 minutes
The blocks remaining is 7 - 2 = 5. The rate is (2 blocks)/(6 min).
So (2 blocks)/(6 min) = (5 blocks)/(x min).
2/6 = 5/x (units omitted for simplicity)
(2/6) × x = (5/x) × x (Multiplying both sides by x so x is not at the bottom).
(2/6) × x = 5
6 × (2/6) × x = 6 × 5
2x = 30
x = 15
Pat will take 15 minutes to walk the remaining 5 blocks.
Match each function with its graph 1. f (x) =x³+3x²2. f (x) = -x (x-1) (x+2)3. f (x) = -x³+3x²4. f (x) = x (x+1) (x-2)
to understand this graphs you must find the roots on each of the functions.
start by funtion 1.
[tex]\begin{gathered} x^3+3x^2=0 \\ x\cdot(x^2+3x)=0 \\ x=0 \\ (x^2+3x)=0 \\ x(x+3)=0 \\ x=0 \\ x+3=0 \\ x=-3 \end{gathered}[/tex]for function 1 you will need to find a graph that only intercept the x-axis on 0 an -3. In this case it will be the graph A.
Do the same for each function
[tex]\begin{gathered} -x\cdot(x-1)\cdot(x+2) \\ x=0 \\ x-1=0 \\ x=1 \\ x+2=0 \\ x=-2 \end{gathered}[/tex]function 2, the interceptions are 0,1 and -2. Graph C will be the correct one for this function
function 3
[tex]\begin{gathered} -x^3+3x^2=0 \\ x\cdot(-x^2+3x)=0 \\ x=0 \\ (-x^2+3x)=0 \\ x(-x+3)=0 \\ x=0 \\ -x+3=0 \\ x=3 \end{gathered}[/tex]for fuction 3, roots will be 0 and 3, the associated graph will be D
and lastly the roots for function 4.
[tex]\begin{gathered} -x\cdot(x+1)\cdot(x-2) \\ x=0 \\ x+1=0 \\ x=-1 \\ x-2=0 \\ x=2 \end{gathered}[/tex]The associated graph is B.
can you help me please
If the value of x increases and the value of y also increases then we can say that the slope is Increases,
If the value of x increases but the value of y decreases then we can say that the slope is decreases.
In the given coordinates of tempreature and icecreams sold is
as the value of Tempreature increases from 60 to 80, the number of icecreams (value of y) is also increases,
but at tempreature =90 the number of icecreams is 20,
thus, the value of y is decreases at x=90
Hence slope changes sign
first it gets positive from tempreature (0 to 80) and then decreases to 90
Answer : C) Slope changes sign
Top side length is 23.4ft. You can use the Pythagorean Theorem or the Cosine ratio or the Sine ration to solve for the remaining side. What is the remaining side (hypotenuse)? Round the answer to one decimal place.
The Hypotenuse = 38.1 feet
Explanations:From the diagram shown:
The adjacent side, A = 30 ft
Let
Let the side facing <38° be represented by B
Let the hypotenuse side be C
The right angle is facing the hypotenuse.
Sum of angles in a triangle = 180°
To calculate the hypotenuse side C, use the sine rule formula below:
[tex]\begin{gathered} \frac{\sin c}{C}=\text{ }\frac{\sin a}{A} \\ \frac{\sin 90}{C}=\text{ }\frac{\sin 52}{30} \\ \frac{1}{C}=\text{ }\frac{0.788}{30} \\ 0.788C\text{ = 30} \\ C\text{ = }\frac{30}{0.788} \\ C=38.1^{} \end{gathered}[/tex]The Hypotenuse = 38.1 feet
Which of the following choices are equivalent to the expression below? Check all that applyx^(3/8)
Given:
[tex]x^{\frac{3}{8}}[/tex]To find:
the equivalence of the given expression
[tex]\begin{gathered} We\text{ will apply exponent rule:} \\ x^{\frac{1}{b}}\text{ = }\sqrt[b]{x} \\ x^{\frac{a}{b}}\text{ = \lparen}\sqrt[b]{x})\placeholder{⬚}^a \\ \\ Applying\text{ same rule to the given expression:} \\ x^{\frac{3}{8}}\text{ = \lparen}\sqrt[8]{x})\placeholder{⬚}^3 \end{gathered}[/tex][tex]\begin{gathered} (\sqrt[8]{x})\placeholder{⬚}^3\text{ can also be written as \lparen}\sqrt[8]{x^3}) \\ x^{\frac{3}{8}}=\text{ \lparen}\sqrt[8]{x^3}\text{ \rparen} \end{gathered}[/tex][tex]\begin{gathered} from\text{ \lparen}\sqrt[8]{x})\placeholder{⬚}^3,\text{ }\sqrt[8]{x}\text{ = x}^{\frac{1}{8}} \\ \\ (\sqrt[8]{x})\placeholder{⬚}^3\text{ = \lparen x}^{\frac{1}{8}})\placeholder{⬚}^3 \\ =(\text{x}^3)\placeholder{⬚}^{\frac{1}{8}} \end{gathered}[/tex]Which equation is the inverse of y = 16x2 + 1?O y=+T6x-1O y =16+Oy AVTOINX-1Оy=
We need to find the inverse function of:
[tex]undefined[/tex]n applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year.
Part A.
The inital salary is $58,000, then we have:
[tex]a_1=58000_{}[/tex]Since we have an increase of 3% each year we know that the second year the salary would be:
[tex]\begin{gathered} a_2=1.03a_1 \\ a_2=1.03\cdot58000 \end{gathered}[/tex]The third year the salary would be:
[tex]\begin{gathered} a_3=1.03a_2 \\ a_3=1.03(1.03)58000 \\ a_3=(1.03)^258000 \end{gathered}[/tex]and so on for year 4 and 5.
Since the increase in salary is only the first five years we conclude that this can't be represented by a geometric series.
For the first five year we can calculate the salary using a geometric sequence with common ratio 1.03, then for the first five years the salary is given by
[tex]a_n=(1.03)^{n-1}_{}\cdot58000\text{ for }1\leq n\leq5[/tex]The salary for the any subsequent year is given by:
[tex]a_n=(1.03)^4\cdot58000\text{ for }n>5[/tex]Part B.
Since we are adding a certain quantity each year we conclude that this offer can be represetend by an algebraic series given by:
[tex]\begin{gathered} b_n=56000+(n-1)3000 \\ b_n=56000+3000n-3000 \\ b_n=3000n+53000 \end{gathered}[/tex]Part C.
After five years the income for offer A is:
[tex]a_5=(1.03)^4\cdot58000=65279.51[/tex]For offer B is:
[tex]b_5=3000(5)+53000=68000_{}[/tex]Therefore after 5 years job offer B has a greater total income.
If the area of square 2 is 225 units?, andthe perimeter of square 1 is 100 units, what isthe area of square 3?
Step 1. Find the length of the side of square 2.
Since square 2 has an area of:
[tex]\text{area}=225units^2[/tex]We can calculate the length of its sides (all sides in a square are equal) with the following formula that relates the area of a square "a", which the length of its side "l":
[tex]a=l^2[/tex]Solving this equation for the length "l" by taking the square root of both sides:
[tex]\sqrt[]{a}=l[/tex]Substituting the area of square 2 to find the length of the side of square 2:
[tex]\begin{gathered} \sqrt[]{225}=l \\ 15=l \end{gathered}[/tex]The length of square 2 is 15 units:
Step 2. Find the length of the side of square 1.
We are told that the perimeter of square 1 is 100 units:
[tex]p=100\text{units}[/tex]Here, "p" represents the perimeter.
Now we use the formula that relates the perimeter "p" to the length of the side of the square "l":
[tex]p=4l[/tex]And since we need to find "l" we solve that equation for "l" by dividing both sides by 4:
[tex]\frac{p}{4}=l[/tex]Substituting the value of the perimeter to find l:
[tex]\begin{gathered} \frac{100}{4}=l \\ \\ 25=l \end{gathered}[/tex]The length of the side of square 1 is 25 units:
Step 3. Find the length of the side of square 3.
Since we are asked for the area of square 3, first we need to calculate the length of its side, and we find it by using the Pythagorean Theorem in the triangle that is in the middle of the squares.
I will label the values as follows for reference:
25 is the hypotenuse of the triangle which is represented by "c"
15 is one of the legs of the triangle which is represented by "b"
and the missing length of the side of square 3 will be the second leg of the triangle "a". The following image shows this better:
The Pythagorean theorem is as follows:
[tex]a^2+b^2=c^2[/tex]Since the letter we need is a, we solve for it:
[tex]\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]Now, substitute the values c and b that we previously defined:
[tex]a=\sqrt[]{(25)^2-(15)^2}[/tex]Solving the operations:
[tex]a=\sqrt[]{625-225}[/tex][tex]\begin{gathered} a=\sqrt[]{400} \\ a=20 \end{gathered}[/tex]We have found the length of the side of square 3: 20 units.
Step 4. Calculate the are of square 3 using the area formula for a square:
[tex]a=l^2[/tex]Where "l" is the length of the side of the square, in this case, 20 units:
[tex]a=(20units)^2[/tex][tex]a=400units^2[/tex]Answer:
[tex]400units^2[/tex]Plot the points (-3,4) and (4,4) on the coordinate plane below.What is the distance between these two points?
To find the distance between two points A and B you can use the formula
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Where A and B have the coordinates} \\ A(x_1,y_1) \\ B(x_2,y_2) \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} A(-3,4) \\ B(4,4) \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{(4_{}-(-3))^2+(4-4)^2} \\ d=\sqrt[]{(4_{}+3)^2+(0)^2} \\ d=\sqrt[]{(7)^2} \\ d=7 \end{gathered}[/tex]Therefore, the distance between these points is 7 units.
Graphically,
Complete the ratio table of the median price of renting a two-bedroom apartment by finding the value of x and y. Round answers to two decimal places. Norfolk $951 Richmond $1,042 1 X Х 100 у To solve the values set up and solve a a. Bar Chart b. Ratio c. Proportion d. Weighted Average x = y =
2+4=6 is true
7*8=56 is true
So the statement 2+4=6 AND 7*8=56 is also true
So the answer for question #36 is a) the statement is true because both proporsitions are true
a garden table and a bench cost $613 combined. the garden table cost $87 less then the bench. what is the cost of the bench ?
the cost of the bench is 350
Explanation
Step 1
let
x represents the cost of the garden table
y represents the cost of the bench
so
a)a garden table and a bench cost $613 combined.
[tex]x+y=613\rightarrow equation\text{ (1)}[/tex]b)the garden table cost $87 less then the bench,( in other words, you have to add 87 to the price of the garden table to obtain the cost of the bech)
[tex]\begin{gathered} x+87=y\rightarrow Equation(2) \\ \end{gathered}[/tex]Step 2
solve the equations
a)isolate x in equaiton (1) and replace in equation (2)
[tex]\begin{gathered} x+y=613\rightarrow equation\text{ (1)} \\ \text{subtrac y in both sides} \\ x+y-y=613-y \\ x=613-y \end{gathered}[/tex]now, replace in equation (2)
[tex]\begin{gathered} x+87=y\rightarrow Equation(2) \\ (613-y)+87=y\rightarrow Equation(2) \\ 700-y=y \\ \text{add y in both sides} \\ 700-y+y=y+y \\ 700=2y \\ \text{divide both sides by 2} \\ \frac{700}{2}=\frac{2y}{2} \\ 350=y \end{gathered}[/tex]it means, the cost of the bench is 350
Write the standard form of the quadratic function f(x) whose graph has vertex (1,2) and passes through (2,4)
Step 1. We are given the vertex of the quadratic function:
[tex](1,2)[/tex]And a point:
[tex](2,4)[/tex]Required: Find the standard form of the quadratic equation.
Step 2. Since we know the vertex of the quadratic function we will start by using the vertex form of the quadratic function:
[tex]y=a(x-h)^2+k[/tex]Where (h, k) is the vertex, in this case:
[tex]\begin{gathered} h=1 \\ k=2 \end{gathered}[/tex]Step 3. To use the previous equation
[tex]y=a(x-h)^{2}+k[/tex]We will need to find the value of a. For that, we substitute the h and k values:
[tex]y=a(x-1)^2+2[/tex]And as the values of x and y, we substitute the values of the given point (2,4) where x=2 and y=4
[tex]4=a(2-1)^2+2[/tex]Solving for a:
[tex]\begin{gathered} 4-2=a(1)^2 \\ 2=a(1) \\ 2=a \end{gathered}[/tex]Step 4. Now that we know that the value of a is 2, we go back to our general equation:
[tex]y=a(x-h)^{2}+k[/tex]Substitute the value of a, h, and k:
[tex]y=2(x-1)^2+2[/tex]This is the equation in the vertex form, but we need it in standard form.
Step 5. The standard form of the quadratic function is:
[tex]f(x)=ax^2+bx+c[/tex]To convert our equation into the standard form, first, we change y by f(x):
[tex]\begin{gathered} y=2(x-1)^{2}+2 \\ \downarrow \\ f(x)=2(x-1)^2+2 \end{gathered}[/tex]Then, we use this formula for the binomial squared:
[tex](a-b)^2=a^2-2ab+b^2[/tex]The result is:
[tex]f(x)=2(x^2-2x+1)+2[/tex]Simplifying:
[tex]\begin{gathered} f(x)=2x^2-4x+2+2 \\ \downarrow \\ \boxed{f\mleft(x\mright)=2x^2-4x+4} \end{gathered}[/tex]That is the standard form of the quadratic function.
Answer:
[tex]\boxed{f(x)=2x^{2}-4x+4}[/tex]determine the fractional value of each division problem 5 divide 95 divide 22 divide 10
Given:
5 divide 9
5 divide 2
2 divide 10
Required:
Find the fractional value of each division problem.
Explanation:
Fractional numbers are numbers that are written in the form of a numerator and denominator.
5 divide 9
[tex]5\div9=\frac{5}{9}[/tex]5 divide 2
[tex]5\div2=\frac{5}{2}[/tex]2 divide 10
[tex]\begin{gathered} 2\div10=\frac{2}{10} \\ =\frac{1}{5} \end{gathered}[/tex]Final Answer:
The fractional value of each division problem is
5 divide 9
[tex]=\frac{5}{9}[/tex]5 divide 2
[tex]=\frac{5}{2}[/tex]2 divide 10
[tex]\begin{gathered} =\frac{2}{10} \\ =\frac{1}{5} \end{gathered}[/tex]Marc sold 457 tickets for the school play. Studen tickets cost $2 and adult tickets cost $3. Marc's sales totaled $1161. How many adult tickets and how many student tickets did Marc sell? 210 adult, 247 student b. 247 adult, 210 student 215 adult, 242 student d. 242 adult, 215 student
The given situation can be written as a system of equations. Based on the given information you have:
x + y = 457
2x + 3y = 1161
where x is the number of student tickets and y is the number of y tickets.
In order to determine the values of x and y, proceed as follow:
- multiply the first equation by -2:
(x + y = 457)(-2)
-2x - 2y = -914
- then, add the previous equation to the second equation of the system:
-2x - 2y = -914
2x + 3y = 1161
y = 247
- next, replace the previous value of y into the first equationof the system, and solve for x:
x + y = 457
x + 247 = 457
x = 457 - 247
x = 210
Hence, the number of student tickest sold was 210, and adult tickets sold was 247
A construction crew is lengthening a road that originally measured 43 miles.The crew is adding 1 mile to the road each day. Let L be the length in brackets in miles after the days over construction right in equation relating L to D then use this equation to find the length of the road after 15 days
The original measurement is 43 miles.
The rate is 1 mile each day.
Use this information, we can express the following
[tex]L=1\cdot D+43[/tex]So, for 15 days, we have
[tex]L=1\cdot15+43=15+43=58[/tex]Hence, after 58 days, the length of the road will be 58 miles.