The given function is
[tex]f(x)=-x^2+2[/tex]The parent function refers to the simplest function possible.
Hence, the parent function is[tex]f(x)=x^2[/tex]Which graph represents 7x+2y<8? four different graphs to chose from.
we have the inequality
7x+2y < 8
the solution for this inequality is the shaded area below the dashed line 7x+2y=8
so
the slope of the dashed line is negative
the intercepts of the dashed line are
y-intercept is (0,4)
the x-intercept is (8/7,0)
therefore
the answer is option BIf x varies directly with y and x=6 when y=8, find x when y=18.Options:13.5122412.5
Given:
x varies directly with y, and x=6 when y=8
Required:
We need to find the value of x when y =18.
Explanation:
if x varies directly as y the equation of variation is expressed as follows.
[tex]y=kx[/tex]Substitute x =6 and y =8 in the equation to find teh value of k.
[tex]8=k(6)[/tex]Divide both sides by 6.
[tex]\frac{8}{6}=\frac{k(6)}{6}[/tex][tex]\frac{4}{3}=k[/tex]We get k =4/3.
The equation is
[tex]y=\frac{4}{3}x[/tex]Substitute y =18 in the equation to find the value of x.
[tex]18=\frac{4}{3}x[/tex]Divide both sides by 3/4.
[tex]18\times\frac{3}{4}=\frac{4}{3}x\times\frac{3}{4}[/tex][tex]13.5=x[/tex]We get x =13.5
Final answer:
[tex]x=13.5\text{ when y =18.}[/tex]
The total revenue from the sale of a poplar book is approximately by the rational function Where x us the number of years since publication and r(x) is the total revenue in millions of dollars. Use this function to complete parts a through dFind the total revenue at the of the first year ?
f(x) = -3x² + 6x + 1
find f(6)
Step-by-step explanation:
this is a college question ? and you don't know how to do this ?
come on, remember ! I don't know how you ever made it into college, if you don't understand this.
with f(6) we say x = 6, and now we simply have to put 6 into all the places of x and calculate.
f(6) = -3×6² + 6×6 + 1 = -3×36 + 36 + 1 = -2×36 + 1 =
= -72 + 1 = -71
Let f(x) = x2 - 9a and g(a) = 3 - x?.(f+g)(7) =- (f - 9)(7) =.· (f9)(7) =• (4) (7) -
Given the functions:
[tex]f(x)=x^2-9x[/tex][tex]g(x)=3-x^2[/tex]1) (f+g)(x) You have to calculate the sum between f(x) and g(x) for x=7
First, calculate the sum between both functions:
[tex]\begin{gathered} (f+g)=(x^2-9x)+(3-x^2) \\ (f+g)=x^2-9x+3-x^2 \end{gathered}[/tex]Order the like terms together and simplify:
[tex]\begin{gathered} (f+g)=x^2-x^2-9x+3 \\ (f+g)=-9x+3 \end{gathered}[/tex]Substitute the expression with x=7 and solve:
[tex]\begin{gathered} (f+g)(7)=-9x+3 \\ (f+g)(7)=-9\cdot7+3 \\ (f+g)(7)=-60 \end{gathered}[/tex]The result is (f+g)(7)= -60
2) (f-g)(7) You have to calculate the difference between f(x) and g(x) for x=7
First, calculate the difference between both functions:
[tex](f-g)=(x^2-9x)-(3-x^2)[/tex]First, erase the parentheses, the minus sign before (3-x²) indicates that you have to change the sign of both terms inside the parentheses, as if they were multiplied by -1, then:
[tex](f-g)=x^2-9x-3+x^2[/tex]Order the like terms and simplify:
[tex]\begin{gathered} (f-g)=x^2+x^2-9x-3 \\ (f-g)=2x^2-9x-3 \end{gathered}[/tex]Substitute the expression with x=7 and solve:
[tex]\begin{gathered} (f-g)(7)=2x^2-9x+3 \\ (f-g)(7)=2(7)^2-9\cdot7+3 \\ (f-g)(7)=2\cdot49-63-3 \\ (f-g)(7)=98-66 \\ (f-g)(7)=32 \end{gathered}[/tex]The result is (f-g)(7)= 32
3) (fg)(7) In this item you have to calculate the product of f(x) and g(x) for x=7
First, determine the product between both functions:
[tex](fg)=(x^2-9x)(3-x^2)[/tex]Multiply each term of the first parentheses with each term of the second parentheses:
[tex]\begin{gathered} (fg)=x^2\cdot3+x^2\cdot(-x^2)-9x\cdot3-9x\cdot(-x^2) \\ (fg)=3x^2-x^4-27x+9x^3 \\ (fg)=-x^4+9x^3+3x^2-27x \end{gathered}[/tex]Substitute with x=7 and solve:
[tex]\begin{gathered} (fg)(7)=-(7^4)+9\cdot(7^3)+3\cdot(7^2)-27\cdot7 \\ (fg)(7)=-2401+9\cdot343+3\cdot49-189 \\ (fg)(7)=-2401+3087+147-189 \\ (fg)(7)=644 \end{gathered}[/tex]The result is (fg)(7)=644
4) (f/g)(7) First, divide both functions:
[tex](\frac{f}{g})=\frac{x^2-9}{3-x^2}[/tex][tex]\begin{gathered} (\frac{f}{g})=\frac{(x-9)x}{3-x^2} \\ (\frac{f}{g})=\frac{(-1)(x-9)x}{(-1)(3-x^2)} \\ (\frac{f}{g})=\frac{(-x+9)x}{(-3+x^2)} \\ (\frac{f}{g})=\frac{(9-x)x}{(x^2-3)} \\ (\frac{f}{g})=\frac{9x-x^2}{x^2-3} \end{gathered}[/tex]Substitute with x=7 and solve:
[tex]\begin{gathered} (\frac{f}{g})(7)=\frac{9\cdot7-7^2}{7^2-3} \\ (\frac{f}{g})(7)=\frac{63-49}{49-3} \\ (\frac{f}{g})(7)=\frac{14}{46} \\ (\frac{f}{g})(7)=\frac{7}{23} \end{gathered}[/tex]The result is (f/g)(7)= 7/23
Can you please help me and I have more questions
As given that P as profit and m as amount of money and h as hours:
[tex]P=m-(250+4h)[/tex]The equation to calculate the amount of money m when profit is $415:
Put the the value of P as 415 in given equation:
[tex]\begin{gathered} 415=m-(250+4h) \\ 415=m-250-4h \\ 415+250+4h=m \\ m=665+4h \end{gathered}[/tex]So the desired equation for calculate amount of money m is:
[tex]m=665+4h[/tex]Please help I don’t know which to multiply or decide
a)
Answer:
Explanation:
From the information given, it costs $23 to rent a bike for 4 hours. Let x represent the number of hours that a customer gets per dollar. We have the following equations
4 = 23
x = 1
By cross multiplying,
x * 23 = 4 * 1
23x = 4
x = 4/23 = 0.17
A customer gets 0.17 hour per dollar
Simplify 4.3 1/2 x 2 1/2
Start by making the mixed numbers as fractions
[tex]\begin{gathered} 3\frac{1}{2}=\frac{3\cdot2+1}{2}=\frac{7}{2} \\ 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2} \end{gathered}[/tex]then, find the product between them
[tex]\frac{7}{2}\times\frac{5}{2}=\frac{35}{4}[/tex]write the fraction as a mixed number
[tex]\frac{35}{4}=8\frac{3}{4}[/tex]find the circumference to the nearest whole number the whole number is 14
Answer:
The circumference is 88 in
Explanation:
The circumference of a circle can be determined, using the formula:
[tex]C=2\pi r[/tex]Where r is the radius of the circle.
Given a radius of 14 in, then
[tex]\begin{gathered} C=2(14)\pi \\ =28\pi \\ =28\times3.14 \\ =87.92 \\ \approx88in \end{gathered}[/tex]A.Find the equation of the line of best fit round one decimal place, if needed choose the correct answer
B.the correlation coefficient is
C. The predicted number of cars sold in year 10 is
An equation for the line of best fit is equal to: D. y = 4.8x + 10.
The correlation coefficient, R² is equal to 0.988.
The predicted number of cars sold in year 10 is equal to 490 cars.
How to find an equation of the line of best fit for the data?In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the number of years would be plotted on the x-axis of the scatter plot while the number of cars sold would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the number of years and cars sold in the table, a linear equation for the line of best fit is given by:
y = 4.8x + 10
Next, we would determine the predicted number of cars sold in year 10:
y = 4.8x + 10
y = 4.8(10) + 10
y = 480 + 10
y = 490 cars.
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
Find each measure measurement indicated. Round your answers to the nearest tenth. Please show work. Answer number 1.
Let's redraw the given figure, to easily understood the problem:
The figure appears to be a triangle with the following given,
c = AB = 17 cm
a = BC = unknown
b = CA = 44 cm
θ = 125°
m∠B means it is the angle at vertex B of the triangle, it is also the only angle given in the figure.
Therefore, the measure of m∠B is 125°.
1. BC = 16 ft2. PQ = 22 cm139RS1с3. JK = 3 mm4. GH = 13 ydGK126845. YZ = 9 in6. EF = 28 mEF11542ZCG
Let's begin by listing out the given information:
The area of a sector is calculated using the formula:
1.
[tex]\begin{gathered} Area=\frac{\theta}{360^{\circ}}\times\pi r^2 \\ \theta=51^{\circ} \\ r=BC=16ft \\ \pi=3.14 \\ Area=\frac{51^{\circ}}{360^{\circ}}\times3.14\times16^2 \\ Area=113.88\approx114 \\ Area=114ft^2 \end{gathered}[/tex]The circumference of a circle is 37.68 meters, what is the radius?
how much money should be deposited today in the account that are 7%, compounded and semi-annually so they will accumulate to 11,000 in 3 years
The rule of the compound interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the new amount
P is the initial amount
r is the rate in decimal
n is the number of the periods per year
t is the number of years
Since the rate is 7% compounded semi-annual, then
r = 7/100 = 0.07
n = 2
Since the amount after 3 years will be $11 000, then
A = 11 000
t = 3
Substitute them in the rule above to find P
[tex]\begin{gathered} 11000=p(1+\frac{0.07}{2})^{2(3)} \\ 11000=p(1.035)^6 \end{gathered}[/tex]Divide both sides by (1.035)^6 to find P
[tex]\begin{gathered} \frac{11000}{(1.035)^6}=P \\ 8948.507087=P \end{gathered}[/tex]Round it to the nearest cent (2 decimal places)
P = $8948.51
The amount invested was $8948.51
help ! brainliest !!!
Graph the function and then determine the asymptote of the function.
We need to graph the following function:
[tex]y=\log _{1/2}(x)-4[/tex]We know that the domain of a logarithmic function can't be negative, then our domain is
[tex]x\in(0,\infty)[/tex]We need to analyze this function at its extremes to find the asymptotes.
Let's calculate the limit of this function at x = 0 and at infinity.
[tex]\begin{gathered} \lim _{x\to0}\log _{1/2}(x)-4=\infty \\ \lim _{x\to\infty}\log _{1/2}(x)-4=-\infty \end{gathered}[/tex]By definition, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. From our limits, we have an vertical asymptote at x =0 and no horizontal asymptotes.
This logarithmic function, comes from infinity at x = 0, an decays to minus infinity as x grows. We have the following graph:
Use the quadratic formula to solve for X.3x2 + 4x = 9Round your answer(s) to the nearest hundredth.Select all that apply.O x= 2.52x = 1.19x = -2.52x= -1.18O x = -20.00x = 20.00
a = 3, b = 4, c = -9
[tex]x\text{ = }\frac{4\pm\text{ }\sqrt[]{4^2-4(3\times-9)}}{2\times3}[/tex][tex]x_1=2.52[/tex][tex]x_2\text{ = -1.1}8[/tex]micah runs a lemonade stand.He sells large cups of lemonade for$0.50 and small cups of lemonade for$0.35.Create an expression represents how much money he could earn
Answer:
The expression for the amount of money in dollars he could earn is;
[tex]0.50x+0.35y[/tex]Explanation:
Let x represent the number of cups of large cups of lemonade he sell and
y represent the number of cups of the small cups of lemonade he sell.
Given that;
He sells large cups of lemonade for $0.50
and small cups of lemonade for $0.35.
The amount he will male by selling x cups of large cups of lemonade and y cups of small cups of lemonade is;
[tex]0.50x+0.35y[/tex]The expression for the amount of money in dollars he could earn is;
[tex]0.50x+0.35y[/tex]Answer:
the dude above me is wrong this is the right answer 0.85(l + s)
Step-by-step explanation:
You have $28 to buy 7 goldfish for your new fish tank. Write and solve an inequality that represents the prices you can pay per fish.
If the price per each goldfish is p
The total cost of 7 goldfishes is 7p and it has to be less or equal to 28
The the inequality is:
7p <= 28
Solving for p:
7p <= 28
p <= 28/7 = 4
p <= 4
Answer:
You can pay up to $4 per each goldfish
Inequality: 7p <= 28
Jessica currently has $180 dollars in her bank account and will add an additional $15 each week. Nate has $120dollars in his account and will add $20 each week.A. After how many weeks will they have the same amount of money in their accounts?B. What is the amount, in dollars, that each person will have after this many weeks?
Answer:
(a)12 weeks
(b)$360
Explanation:
Part A
Let the number of weeks when they have the same amount of money in their accounts be x.
[tex]\begin{gathered} \text{Jessica's amount after x weeks }=180+15x \\ \text{Nate's amount after x weeks }=120+20x \end{gathered}[/tex]If the amount of money is equal:
[tex]180+15x=120+20x[/tex]Solve for x:
[tex]\begin{gathered} 180-120=20x-15x \\ 60=5x \\ \frac{60}{5}=\frac{5x}{5} \\ x=12 \end{gathered}[/tex]Therefore, they will have the same amount of money after 12 weeks.
Part B
The amount that each person will have, (Using Jessica's Equation)
[tex]\begin{gathered} \text{Amount}=180+15x \\ =180+15(12) \\ =180+180 \\ =\$360 \end{gathered}[/tex]The amount, in dollars, that each person will have after 12 weeks is $360.
Use add or sub formula to write as trig fun tho on
The formula to write this function is going to be:
[tex]tan(a-b)=\frac{tan(a)-tan(b)}{1+tan(a)*tan(b)}[/tex]Substituing:
[tex]\frac{tan(43)-tan(18)}{1+tan(43)tan(18)}=tan(43-18)[/tex]In this case a= 43 and b=18:
[tex]tan(43-18)=tan(25)=0.466\approx0.5[/tex]The answer is: tan(25).
Below is the graph of a trigonometric function. It intersects its midline at (-1.7, -10) and again at(5.1, -10). What is the period
you can get the Period graphically if you see the points A and B are the upper points of the graph. if you subtract them you get the period
in this case, let me see
Here they give you the points where the graph cross the midline, if you see, that is half of the period, so
Period= 2* (5,1-(-1,7))= 13,6
You have to subtract the points to know the distance between that points, and the graph is
when you subtract the points, you are getting the distance between (for example) the green point on my draw
And the period is the time it takes for one complete oscillation, after this, it repeats over and over
So between 3 of these green points we have a period
to know the value, we need to know the distance between them (in this case (5,1-(-1,7))= 6,8
each square have 1 period on it, and the value is 2 times the distance between the green points
Answer:
Period= 2* (5,1-(-1,7))= 13,6
Which function has the following domain and range? Domain: {-7,-3,0,4,12}Range: {-5,1,2}
The domain of a function is the values that x can assume, while the range is the values that the function assume.
So, we are looking for the function with points that have x equal to -7, -3, 0, 4 and 12 and y values equal to -5, 1 and 2.
"A" only has x equal to -7 and and -5, and y equal to 12 and 2.
"B" has an x value of -4, which can't exist if the domain is the wanted one.
"D" has x value of -5, which eliminates the alternative for the same reason.
"C" is the correct answer because have all the x and y values and no other than x = {-7, -3, 0, 4, 12} and y = {-5, 1, 2}.
So "C" is the corect answer.
This is a 1st-grade math problem 12 + _____ = 13 + 7
I'll say that the unknown number is "x", then our expression is
[tex]12+x=13+7[/tex]And we want to find out the value of "x"
To solve it, we will first do the sum on the right side:
[tex]12+x=20[/tex]Now, we want to have "x" alone on the left side, then, let's subtract 12 on both sides
[tex]\begin{gathered} 12-12+x=20-12 \\ \\ x=20-12 \\ \\ x=8 \end{gathered}[/tex]Then the value of x is 8, let's test it:
[tex]\begin{gathered} 12+8=13+7 \\ \\ 20=20 \end{gathered}[/tex]Correct! 12 + 8 is 20. Then, the unknown number is 8
Answer:
Step-by-step explanation:
12 + 1 = 13 + 7=20
Here are the numbers of times 13 people ate out last month 7, 3, 4, 3, 6, 4, 7, 6, 5, 7, 3, 6,5Find the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, tap on "No mode."Explanation
In statistics, the mode is the value that occurs most frequently in a data set. This goes in the form of a column when we find two modes, that is, two data that have the same maximum absolute frequency.
First, we are going to count how many times each number is repeated in the data set.
[tex]\begin{gathered} 7\to3\text{ times} \\ 3\to3\text{ times} \\ 4\to2\text{ times} \\ 6\to3\text{ times} \\ 5\to2\text{ times} \end{gathered}[/tex]The highest frequency in the data set as we can see is 3. That is, the mode will be all the numbers that have that frequency in this case 7, 3 and 6
Michael says that 5 = 5 Is his answer correct? Explain. (1 O A. 00:00 Yes. Both expressions are equal to 625 СВ. 00:00 Yes Both expressions are equal to O C. 00:00 No. The first expression is equal to and the second expression is equal to 625 00:00 No. The first expression is equal to 625 and the second expression is equal to
Michael says that
[tex]5\cdot(\frac{1}{5^3})=5(5^3)[/tex]We are asked whether he is correct or not?
Let us simplify the equa
wich of the following is the correct value of 0.22 0.4?
Answer:
The decimal place will be placed to the left by the total number of digits after the two numbers.
Explanation:
The multiplication we are asked to perform is
[tex]1.35\times4.2[/tex]which has a total of 3 digits after the decimal point.
Now we know that
[tex]135\times42=5670[/tex]therefore, to find 1.35 x 4.2 we just shift the decimal place in the above to the left by 3 units
therefore
[tex]1.35\times4.2=5.67[/tex]which is our answer!
The ratio of the cat's weight to the rabbit's weight is 7 to 4. Together, they weigh 22 pounds. How much does the rabbit weigh?
cat's weight: rabbit's weight
7:4
[tex]undefined[/tex]numbers. у xt Y y page ted. 8 7+ 6- 5 above in every Good; Fair; 3 2+ 1+ + x -9-8-7-6-5-4-3-2 1 2 3 4 5 6 7 8 9 -2 -3 -5 -6 -77 -87 -9-
step 1
Find the slope
we need two points
we take
(-6,0) and (0,4)
m=(4-0)/(0+6)
m=4/6
m=2/3
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=2/3
b=4
substitute
y=(2/3)x+4triangle A B C is translated 6 units to the left and 1 unit up to create A'B'C'.
The correct answer is 6.1 square units.
The translation of triangle ABC to triangle A'B'C' will not change the dimensions of the original triangle.
Hence, the area of triangle ABC will not be affected by the translation.
[tex]\begin{gathered} \text{Area of }\Delta ABC=\frac{1}{2}bh \\ \text{where b=2, h=6.1} \\ \text{Area of}\Delta ABC=\frac{1}{2}\times2\times6.1 \\ \text{ = 6.1 square units} \end{gathered}[/tex]Hence, the correct answer is 6.1 square units