Angela can arrange pictures in 6 different ways; (1 x 32), (2 x 16), (4 x 8), (8 x 4), (16 x 2), (32 x 1).
Given,
Angela have 32 pictures with her.
She wants to arrange it in an album with equal number of pictures in each row.
We have to find the possible arrangements.
Here,
32 pictures.
Lets see the possibilities.
1 row = 32 pictures in a row2 rows = 32/2 = 16 pictures in each row4 rows = 32/4 = 8 pictures in each row8 rows = 32/8 = 4 pictures in each row16 rows = 32/16 = 2 pictures in each row32 rows = 1 picture in each row.That is,
Angela can arrange pictures in 6 different ways; (1 x 32), (2 x 16), (4 x 8), (8 x 4), (16 x 2), (32 x 1).
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Write an equation in the form r(x) = p(x) / q(x) for each function shown below.Pls see pic for details
c.
The line equation is of the form
[tex]y=mx+c\ldots(1)[/tex]From the graph, we observe and find these points
(1,5) and (0,4) lie on the given line.
Substituting x=1, y=5 in equation (1), we get
[tex]5=m(1)+c[/tex][tex]m+c=5\ldots\text{.}(2)[/tex]Substituting x=0, y=4 in equation (1), we get
[tex]4=m(0)+c[/tex][tex]c=4[/tex]Substituting c=4 in equation (2), we get
[tex]m+4=5[/tex][tex]m=5-4[/tex][tex]m=1[/tex]Substituting c=4,m=1 in equation (1), we get
[tex]y=x+5[/tex]We need to write this equation in the form of r(x) = p(x) / q(x).
[tex]r(x)=\frac{p(x)}{q(x)}\ldots(3)[/tex]Let r(x)=x+5, q(x)=x, and subsitute in the equation , we get
[tex]x+5=\frac{p(x)}{x}[/tex]Using the cross-product method, we get
[tex]x(x+5)=p(x)[/tex][tex]x\times x+x\times5=p(x)[/tex][tex]x^2+5x=p(x)[/tex]Substitute values in equation (3), we get
[tex]x+5=\frac{x^2+5x}{x}[/tex]Hence the required equation is
[tex]x+5=\frac{x^2+5x}{x}[/tex]Can anybody help me out with this? I would really appreciate it! I don't need a huge explanation just the answer and a BRIEF explanation on how you got it.
The range of the following function is
[tex]\mleft\lbrace y>1\mright\rbrace[/tex]We can also call the range of a function an image, the range or image of a function is a set, we can see this set looking at the graph and see which values of y the function have, remember that we can have the same y value for different x value, looking at our graph we can see that this function comes from high y values, have a vertex on (3,1), in other words, it stops at y = 1 and then start growing again, and go on repeated values of y, then we can say that the image (values of y that the function assumes) is all values bigger than 1, therefore {y > 1}.
The post office offers flat-rate mailing of packages: $1.50 for a package weighing less than 4 oz, $2.50 for a package weighing 4 oz to less than 8 oz, and $3.50 for a package weighing 8 oz to 12 oz. write an equation that would represent the situation.
To solve the problem, we will define a function that given the weight of the package, will determine the cost of the mailing. Let x be the weigth of the package in oz and let f(x) be the cost of mailing the package. We are told that if the weight is less than 4, then the rate is 1.50. So, in math notation that would be f(x) = 1.50 if x<4. Now, we are told that if the package weights between 4 and less than 8, then the rate is 2.50. So, that is f(x) = 2.50 if 4<=x<8. Finally, we are told that if the package weights between 8 and 12, the cost is 3.50. So f(x) = 3.50 if 8<=x<=12. So the final math expression for f(x) is
1.50 if x<4
f(x) = 2.50 if 4<=x<8
3.50 if 8<=x<=12.
2. What is an algebraic expression for each phrase?a. the product of 9 and a number tb. the difference of a number x and 1/2c. the sum of a number m and 7.1 d. the quotient of 207 and a number n
The algebraic expression for each phrase would be the following:
a. the product of 9 and a number t would be expressed as:
9*t
b. the difference of a number x and 1/2 would be expressed as:
x - 1/2
c. the sum of a number m and 7.1 would be expressed as:
m + 7.1
d. the quotient of 207 and a number n would be expressed as:
207 / n
Write an explicit rule for the following arithmetic sequence: 28, 38, 48, 58,
When you have an arithmetic sequence you can use the next general formula to get the explicit formula:
[tex]a(n)=a(1)+d(n-1)[/tex]Where a(1) is the first term in the sequence, d is the difference between each term in the sequence, and n is the nth term
You have the sequence: 28,38,48,58
The difference in this sequence is d=10
The first term is: a(1)=28
Then:
[tex]a(n)=28+10(n-1)[/tex][tex]a(n)=28+10n-10[/tex][tex]a(n)=18+10n[/tex]Then, the explicit rule for the given arithmetic sequence is: a(n)=18+10nWriting and evaluating a function modeling continuous exponential growth or decay given two outputs
Explanation
The model has the form
[tex]y=ae^{-kt}[/tex]Where a=initial amount
y= final amount
K= growth rate constant
t= time
When 140 kg of substance is left after 7 hours, the formula can be remodeled to be.
[tex]\begin{gathered} 140=400e^{-7k} \\ e^{-7k}=\frac{140}{400} \\ e^{-7k}=\frac{7}{20} \\ \ln (e^{-7k})=\ln (\frac{7}{20}) \\ -7k=\ln (\frac{7}{20}) \\ k=\frac{\ln(\frac{7}{20})}{-7} \\ \therefore k=\frac{\ln (\frac{20}{7})}{7} \end{gathered}[/tex]Therefore, the first solution is
[tex]y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}[/tex]For part b we have 16 hours.
[tex]\begin{gathered} y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}=400e^{-\ln (\frac{20}{7})\frac{16}{7}} \\ y=36.302\approx36\operatorname{kg}\text{ (To the nearest whole number)} \end{gathered}[/tex]Thus, the answer is 36kg
I need help with this question can you please help me
Given the following question:
[tex]\begin{gathered} x^2+3x-5=0 \\ \text{ Convert using the quadratic formula:} \\ x^2+3x-5=0=x_{1,\:2}=\frac{-3\pm\sqrt{3^2-4\cdot\:1\cdot\left(-5\right)}}{2\cdot\:1} \\ x_{1,\:2}=\frac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1} \\ \text{ Solve} \\ 3^{2}-4\times1(-5) \\ 1\times-5=-5 \\ 3^2-4\times-5 \\ 3^2=3\times3=9 \\ =29 \\ =\sqrt{29} \\ x_{1,\:2}=\frac{-3\pm \sqrt{29}}{2\cdot \:1} \\ \text{ Seperate the solutions:} \\ x_1=\frac{-3+\sqrt{29}}{2\cdot \:1} \\ x_2=\frac{-3-\sqrt{29}}{2\cdot\:1} \\ \text{ Simplify} \\ 2\times1=2 \\ x=\frac{-3+\sqrt{29}}{2} \\ x=\frac{-3-\sqrt{29}}{2} \end{gathered}[/tex]Your answers are the first and second options.
how many millielters are in 1/5 liters
We know,
1 liter=1000 milliter.
So, millilters in 1/5 liters is,
[tex]\frac{1}{5}liter\times\frac{1000\text{ milliter}}{1\text{ liter}}=200\text{ milliter}[/tex]Therefore, there are 200 milliters in 1/5 liters.
i need help with my homework PLEASEMCHECK WORK WHEN FINISHED
Given:
The population of a town increases by 9 % annually.
The current population is 4,500.
Required:
We need to find the equation that gives the population of the town.
Explanation:
The population can be found by the following equation.
[tex]Th\text{e population =4500+9 \% of 4500}[/tex]Let now be the current population of the town =4500.
Let Next be the population of the town.
The population can be found by the following equation.
[tex]Next\text{ =Now+9\% of Now.}[/tex][tex]Next\text{ =Now+}\frac{9}{100}\times\text{Now.}[/tex]Take the common term now out.
[tex]Next\text{ =Now\lparen1+}\frac{9}{100})[/tex][tex]Use\text{ }\frac{9}{100}=0.09.[/tex][tex]Next\text{ =Now\lparen1+0.09})[/tex][tex]Next\text{ =Now\lparen1.09})[/tex][tex]Next\text{ =Now}\times\text{1.09}[/tex]Final answer:
[tex]Next\text{ =Now}\times\text{1.09}[/tex]11-3x75-1 what is the answer?
Answer:
Step-by-step explanation:
-215
Answer:
-215
Step-by-step explanation:
the answer to 11-3x75-1 is -215
Can you please help with 44For the following exercise, sketch a graph of the hyperbola, labeling vertices and foci
We have the following equation of a hyperbola:
[tex]4x^2+16x-4y^2+16y+16=0[/tex]Let's divide all the equations by 4, just to simplify it
[tex]x^2+4x-y^2+4y+4=0[/tex]Just to make it easier, let's put the term if "x" isolated
[tex]x^2+4x=y^2-4y-4[/tex]Now we can complete squares on both sides, just remember that
[tex]\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ \\ (a-b)^2=a^2-2ab+b^2 \end{gathered}[/tex]Now let's complete it!
[tex]\begin{gathered} x^2+4x=y^2-4y-4\text{ complete adding 4 on both sides} \\ \\ x^2+4x+4=y^2-4y-4+4 \\ \\ (x+2)^2=y^2-4y \\ \end{gathered}[/tex]We already completed one side, now let's complete the side with y^2, see that we will add 4 again, then
[tex]\begin{gathered} (x+2)^2=y^2-4y \\ \\ (x+2)^2+4=y^2-4y+4 \\ \\ (x+2)^2+4=(y-2)^2 \end{gathered}[/tex]And now we can write it using the standard equation!
[tex]\begin{gathered} (y-2)^2-(x+2)^2=4 \\ \\ (y-2)^2-(x+2)^2=4 \\ \\ \frac{(y-2)^2}{4}-\frac{(x+2)^2}{4}=1 \end{gathered}[/tex]And now we can graph it like all other hyperbolas, the vertices will be:
[tex](-2,4)\text{ and }(-2,0)[/tex]And the foci
[tex]\begin{gathered} c^2=a^2+b^2 \\ \\ c^2=2^2+2^2 \\ \\ c^2=2\cdot2^2 \\ \\ c^{}=2\, \sqrt[]{2} \end{gathered}[/tex]Then the foci are
[tex](-2,2+2\, \sqrt[]{2})\text{ and }(-2,2-2\, \sqrt[]{2})[/tex]Now we can plot the hyperbola!
What is the smallest degree of rotation that will map a regular 96-gon onto itself? ___ degrees
The smallest degree of rotation is achieved through the division of the full circumference over the total number of sides
[tex]\frac{360\text{ \degree}}{96}=3.75\text{ \degree}[/tex]The answer would be 3.75°
b. Write
√x
as a single radical in simplest form.
5√x
Answer:
(tenth root of x to the third power)
see image
Step-by-step explanation:
To do this problem you need to know how to convert radicals to an expression with a fraction exponent(and back to radicals again), ALSO exponent rules for division ALSO subtracting fractions.
Square root x can be written as x^ 1/2
fifth root x can be written as x^ 1/5
When you are dividing expressions with the same base, exponent rules say to SUBTRACT the exponents.
1/2 - 1/5 change to common denominator
5/10 - 2/10
= 3/10
x^1/2 / x^1/5 =
x^ (1/2 - 1/5) =
x^ (5/10-2/10) =
x^ 3/10
Then change back to a radical. Remember "down and out" or "roots are down" and "up, up, up" or "exponents are up"
the number down below goes out (outside) the radical. And the number up top is up and exponents are up, up, up
see image.
x^3/10 =
tenth root (x^3)
see image.
Do the data in the table you made support the notion the arch is not a parabola? Explain why.
The parabola that has the height and width similar to the Gateway arc, gives;
(a) The quadratic equation of the parabola is presented as follows;
[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]
(b) The completed table is presented as follows;
Width. Height
567. 63.12
478. 225.67
308. 459.2
What is the shape of the graph of a quadratic function?The shape of a quadratic function is a parabola, which is either upward facing or downward facing
(a) The given dimensions of the arc are;
Height = 625
Width at the base = 598
The points on the parabola are therefore;
(0, 0), (598÷2, 625) = (299, 625), (598, 0)
The equation of the parabola is of the form;
f(x) = a•x² + b•x + c, which gives;
f(0) = 0 = a×0² + b×0 + c = c
c = 0
f(299) = 625 = a×299² + b×299 + 0...(1)
f(598) = 0 = a×598² + b×598...(2
(a×598² + b×598) - 2×(a×299² + b×299) = 0 - 2×625
a•178802 = -2×625
a = -2×625 ÷ 178802
a ≈ -6.991 × 10^(-3)
b ≈ 4.181.
The equation is therefore;
[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]
(b)
The table of values is completed as follows;
When the width is 567 feet, x = 299 - 567÷2 = 15.5
[tex] \displaystyle{f(15.5) = -6.991 × 10^{-3} \times 15.5² + 4.181 \times 15.5 approx 63.12} [/tex]
When the width is 478 feet, x = 299 - 478÷2 = 60
[tex] \displaystyle{f(60) = -6.991 × 10^{-3} \times 60² + 4.181 \times 60 approx 225.67} [/tex]
When the width is 308 feet, x = 299 - 308÷2 = 145
[tex] \displaystyle{f(145) = -6.991 × 10^{-3} \times 145² + 4.181 \times 145 approx 459.2} [/tex]
The table is therefore presented as follows;
Width. Height
567. 63.12
478. 225.67
308. 459.2
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Angles of Polygons The figure below is a pentagon whose interior angles have the same measure.What is the sum of the measures of these 5 angles?
Given the number of sides of a pentagon:
Number of sides = 5
Let's find the sum of the measures of the 5 equal angles.
To find the sum of the measures of interior angles of a polygon, apply the formula:
[tex]S=(n-2)*180[/tex]Where:
n is the number of sides = 5
Thus, we have:
[tex]\begin{gathered} S=(5-2)*180 \\ \\ S=(3)*180 \\ \\ S=540^o \end{gathered}[/tex]Therefore, the sum of the interior angles of the pentagon is 540 degrees.
ANSWER:
540°
I don’t understand how to get the second x intercept
In this problem
the vertex is given ------> (40/2,12)-------> (20,12)
The first intercept is (0,0)
therefore
second intercept is
x-intercept=20+20=40
(40,0) is the coordinates of the second x-intercept
(the vertex is the midpoint between the first and second x-intercept)
see the attached figure
what would be the value if m in a angle on 50 degrees and 10m
50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.
10m = 90 - 50
10m = 40
m = 40/10
m = 4
hailey is going to rent an apartment for $864 a month in addition to the first month's rent when moving in a security deposit of $216 is required what will be the total payments required when moving in
We are given that a total amount is $864, if a deposit of $216 is given, then the total amount to pay is the following:
[tex]864-216=648[/tex]Therefore, there is $648 to pay.
If you are given odds of 5 to 6 in favor of winning a bet, what is the probability of winning the bet?
5 to 6 odds means that, out of 11 possible outcomes, odds are that there will be 5 of one kind of outcome and 6 of another kind of outcome.
In this case, you are given 5 to 6 odds, which means that out of 11 possible outcomes you will win a bet 5 times, and lose it 6.
In fraction, it will look like this:
[tex]\frac{11}{11}\text{ \lparen these are all the possible outcomes, which equals 1\rparen = }\frac{5}{11}(the\text{ outcomes in which you win, which equals .4545, so 45.45\%\rparen + }\frac{6}{11}\text{ \lparen the outcomes in which you lose, which equals 0.5454, so 54.54\% \rparen}[/tex]Because of that, the probability of winning the bet is 45.45%, and in a fraction, it is 5/11, which means you will win in 5 out of 11 scenarios.
One function has an equation in slope-intercept form: y = x + 5. Another function has an equation in standard form: y + x = 5. Explain what must be different about the properties of the functions. See if you can determine the differences without converting the equation to the same form.
Without converting the equations to the same form, the property that must be different in the functions is the slope
How to determine the difference in the properties of the functions?From the question, the equations are given as
y = x + 5
y + x = 5
From the question, we understand that:
The equations must not be converted to the same form before the question is solved
The equation of a linear function is represented as
y = mx + c
Where m represents the slope and c represents the y-intercept
When the equation y = mx + c is compared to y = x + 5, we have
Slope, m = 1
y-intercept, c = 5
The equation y = mx + c can be rewritten as
y - mx = c
When the equation y - mx = c is compared to y + x = 5, we have
Slope, m = -1
y-intercept, c = 5
By comparing the properties of the functions, we have
The functions have the same y-intercept of 5The functions have the different slopes of 1 and -1Hence, the different properties of the functions are their slopes
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3 * 10 ^ - 6 = 4.86 * 10 ^ - 4 in scientific way
Answer:
3*10=30
10^-6=1^-6. (10 raised to the power of-6)
therefore 3*1^-6=3
is equal to
4.86*10=48.6
10^-4=1^-4
therefore 48.6*1^-4=48.6
A car's cooling system has a capacity of 20 quarts. Initially, the system contains a mixture of 7 quarts of antifreeze and 13 quarts of water. Water runs into the system at the rate of 1 gal min , then the homogeneous mixture runs out at the same rate. In quarts, how much antifreeze is in the system at the end of 5 minutes? (Round your answer to two decimal places.)
After 5 minutes there will be 2.29376 quarts of antifreeze in the system.
Given,
The capacity of the cooling system of a car = 20 quarts
The mixture in the system is 7 quarts of antifreeze and 13 quarts of water.
The running rate of water = 1 gal/min
Homogenous mixture also runs 1 gal/min
We have to find the antifreeze in the system at the end of 5 minutes;
Here,
1 quart = 0.25 gallons
7 x 0.25 = 1.75 gallons of antifreeze
13 x 0.25 = 3.25 gallons of water
1 = 0.2 of 5
Minute 1 = 1.75 x 0.8 = 1.4Minute 2 = 1.4 x 0.8 = 1.12Minute 3 = 1.12 x 0.8 = 0.896Minute 4 = 0.896 x 0.8 = 0.7168Minute 5 = 0.7168 x 0.8 = 0.573440.57344 gallons = 2.29376 quarts
After 5 minutes there will be 2.29376 quarts of antifreeze in the system.
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in the diagram the figures are simular, what is x?triangle with 30cm and 13cmtriangle with 24cm and x
If the figures are similar, the proportion between the corresponding sides is the same.
The side of 30 cm corresponds to the side of 24 cm, and the side of 13 cm corresponds to the side of x cm.
So if the proportion is the same, we have that:
[tex]\begin{gathered} \frac{30}{24}=\frac{13}{x} \\ 30\cdot x=24\cdot13 \\ x=\frac{24\cdot13}{30}=\frac{4\cdot13}{5}=\frac{52}{5}=10.4 \end{gathered}[/tex]So the value of x is 10.4 cm, therefore the answer is b.
Leila runs at 12 mph find the number of miles she can travel if she runs for 2 hours
20 POINTS ANSWER I WILL MARK BRAINLIEST!!!!!!!!!!
Answer: 24 mph
Step-by-step explanation:
If she can run 12 mph/ 12 miles per hour
She runs for 2 hours
12 · 2 = 24
A car travels 273 miles in 6 hours. How muchtime will it take traveling 378 miles
hello
the car travels 273 miles in 6 hours, how many hours will it take to travel 378 miles.
let the number of unknown hours be represented by x
[tex]\begin{gathered} 273mi=6\text{hrs} \\ 378mi=\text{xhr} \\ \text{cross multiply bith sides} \\ 273\times x=6\times378 \\ 273x=2268 \\ \text{divide both sides by 273} \\ \frac{273x}{273}=\frac{2268}{273} \\ x=8.3076\text{hrs} \end{gathered}[/tex]the car spent approximately 8.31 hours to travel a distance of 378 miles
You go to a candy store and want to buy a chocolate
To find the amount of servings, we just need to divide the entire bar weight by the serving weight. Solving this calculation, we have
[tex]\frac{14.8}{2.4}=\frac{37}{6}=6.166666666..\text{.}[/tex]HELP PLEASE!
Dave has a piggy bank which consists of dimes, nickels, and pennies. Dave has seven
more dimes than nickels and ten more pennies than nickels. If Dave has $3.52 in his piggy bank, how many of each coin does he have?
Dave has 17 nickels, 24 dimes and 27 pennies in his piggy bank.
According to the question,
We have the following information:
Dave has 7 more dimes than nickels and 10 more pennies than nickels.
Now, let's take the number of nickels to be x.
So,
Dimes = (x+7)
Pennies = (x+10)
Now, Dave has $3.52 in his piggy bank.
We will convert nickels, dimes and pennies into dollars.
We know that 1 nickel = 0.05 dollars, 1 dime = 0.1 dollars and 1 pennies = 0.01 dollars.
Now, we will convert the given numbers of nickel, dime and pennies into dollars.
x Nickels in dollars = $0.05x
(x+7) dimes in dollars = $0.1(x+7)
(x+10) pennies in dollars = $0.01(x+10)
Now, we will them.
0.05x + 0.1(x+7) + 0.01(x+10) = 3.52
0.05x + 0.1x + 0.7 + 0.01x + 0.1 = 3.52
0.16x + 0.8 = 3.52
0.16x = 3.52-0.8
0.16x = 2.72
x = 2.72/0.16
x = 17
Now, we have:
Number of nickels = 17
Number of dimes = (17+7)
Number of dimes = 24
Number of pennies = (17+10)
Number of pennies = 27
Hence, the number of nickels, dimes and pennies are 17, 24 and 27 respectively.
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Find the Z-score for which 5% of the distributions area lies between-z and z
The equation that will represent this situation will be:
[tex]\begin{gathered} P(-z\le x\le z)=P(x\le z)-(1-P(x\le z))=0.05 \\ \end{gathered}[/tex]Thus:
[tex]\begin{gathered} P(x\le z)-1+P(x\le z)=0.05 \\ 2\cdot P(x\le z)-1=0.05 \\ 2\cdot P(x\le z)=0.05+1 \\ 2\cdot P(x\le z)=1.05 \\ P(x\le z)=\frac{1.05}{2} \\ P(x\le z)=0.525 \end{gathered}[/tex]If we check in a standard normal table. the z-score that corresponds to a probability of 0.525 is 0.063.
Answer: z-score is 0.063.
Plot the ordered pair (-4,-1) state which quadrant or on which axis the point lies
Answer:
Th
Explanation:
Given the ordered pair (-4, -1), we have that x = -4 and y = -1. Plotting this point, we'll have;
Quadrants are labeled in an anti-clockwise direction with the top right portion of the graph being the 1st quadrant. Looking at the plotted point, we can see that the point is in the 3rd quadrant.
Please look at the image below. By the way this is my homework.Use the definition of congruence to decide whether the two figures are congruent. Explain your answer. Give coordinate notation for the transformations you use.
Congruent Shapes
Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),
All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.
The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.
Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is
xm = (-6+4)/2 = -1
Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:
xm = (-8+6)/2 = -1
For the points R(-4,-6) and D(2,-6):
xm = (-4+2)/2 = -1
For the points Q(-9,-4) and D(8,-4):
xm = (-9+8)/2 = -0.5
Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent
For both shapes to be congruent, the coordinates of Q should have been (-10,-4)
