Determine whether the pair of fractions below are equivalent by writing each fraction in lowest terms.262822143
Answers
To determine if they are equivalent, we will find each of them in lowest term:
To write in lowest term, we will find numbers common to both numerator and denominator. Then cancel them out
[tex]\begin{gathered} \frac{26}{28}\colon\text{ 2 is common to numerator and denominator} \\ \\ \frac{2\times13}{2\times14}\text{ = }\frac{13}{14} \\ \\ No\text{ other number is common , so lwest term is }\frac{13}{14} \end{gathered}[/tex][tex]undefined[/tex]Related Questions
What are 6 different expressions that have the same value as 10 to the 8 power?(show using exponents,multiplication, and division)
Answers
Answer
(10²)⁴
(1/10⁻⁸)
10⁴ × 10⁴
10¹² ÷ 10⁴
1,000 × 100,000
10,000,000,000 ÷ 100
All of them are equal to 10⁸
Explanation
The laws of indices will help us solve this
- When a variable carries a power and is raised to an extra power, the answer is the variable carrying the product of these two powers.
- When a variable is raised to the power of a negative number, this is the same as 1 over that variable raised to the positive value of that power
- When the same variable, carrying different powers are multiplied with each other, then, the result is that same variable raised to the power of the sum of the two powers from before multiplication.
So, some of the ways to write expressions that will give 10 raised to the power of 8 include
First one
(10²)⁴ = 10⁸
Second one
(1/10⁻⁸) = 10⁻⁽⁻⁸⁾ = 10⁸
Third one
10⁴ × 10⁴ = 10⁴⁺⁴ = 10⁸
Fourth one
10¹² ÷ 10⁴ = 10¹²⁻⁴ = 10⁸
Fifth one
1,000 × 100,000 = 100,000,000 = 10⁸
Sixth one
10,000,000,000 ÷ 100 = 100,000,000 = 10⁸
Hope this Helps!!!
goodmorning, i just need an answer for 1A & 1B , 1c is already answered
Answers
Given:
[tex]g(x)=\frac{1}{4}\sqrt[3]{x-3}+2[/tex]The function represents the number of users in millions who logged into a website since midnight.
1a. How many users have logged in by 9 am?
at 9am x = 9
Substitute x = 9 into g(x)
This gives
[tex]g(9)=\frac{1}{4}\sqrt[3]{9-3}+2[/tex]Simplify the expression
[tex]\begin{gathered} g(9)=\frac{1}{4}\sqrt[3]{3}+2_{} \\ g(9)=\frac{1}{4}\times1.44+2 \\ g(9)=2.36\text{ million} \end{gathered}[/tex]Therefore, 2360000 users have logged into the website by 9 am.
1b Domain and range of the function.
The domain of the function is the set of all input values for which the function is real and defined.
The values of x in g(x) starts from midnight
Hence at midnight x = 0, there are 24 hours in a day
Hence the domain of g(x) is
[tex]\lbrack0,24)[/tex]Range
The range of the function is the set of values of the dependent variables for which a function is defined
Since the function g(x) is defined for all dependent variables x
Then the range of the function is
[tex]\lbrack1.639,2.69)[/tex]The range is in millions
One pump can empty a pool in 3 days, whereas a second pump can empty the pool in 9 days. How long will it take the two pumps, working together, to empty the pool?It will take the two pumps ___days to empty the pool together.If needed, round answer to 3 decimal places.Enter DNE for Does Not Exist, oo for Infinity
Answers
The first pump has a rate of 1/3 a day.
The second pumo has a rate of 1/9 a day.
If both pumps are working together then the total rate is:
[tex]\frac{1}{3}+\frac{1}{9}=\frac{9+3}{27}=\frac{12}{27}[/tex]each day.
Then it will take a total of:
[tex]\frac{27}{12}=2.25[/tex]Therefore it will take the two pumps 2.25 days to emprty the pool together.
Tickets of a program at college cost $3 for general admission or $2 with a student ID.If 182 people paid to see a performance and $440 was collected, how many ofeach type of ticket were sold?In a program at college ____ tickets were sold for general admission and ____ tickets were sold with a student ID.
Answers
Solution
Given that
This is a system of equations problem.
Let G = the number of general admission tickets and S = the number of student ID tickets.
G + S = 182 Total tickets.
3G + 2S = 440 Total price paid for tickets.
G + S = 182
S = 182 - G
3G + 2S = 440
3G + 2 * (182 - G)= 440
3G + 364 -2G = 440
G = 440 - 364 = 76 General admission tickets
Substitute this into either equation and solve for S.
We already solved one for S symbolically, so we'll use that.
S = 182 - G
S = 182 - 76 = 106 Student ID tickets
In a program at college __76__ tickets were sold for general admission and _106___ tickets were sold with a student ID.
Triangle A has points/coordinates of C(-2, 4), D(-3, 2), E(-1, 1). List the coordinates of the new image after Triangle A is reflected across the Y-axis.
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The coordinate points of the triangle are:
[tex]\begin{gathered} C\mleft(-2,4\mright) \\ D\mleft(-3,2\mright) \\ E\mleft(-1,1\mright) \end{gathered}[/tex]The graph of this original points is as follows:
Now, to make the reflection across the Y-axis, we follow this rule of transformation:
[tex](x,y)\longrightarrow(-x,y)[/tex]so the points become the following:
[tex]\begin{gathered} C^{\prime}(2,4) \\ D^{\prime}(3,2) \\ E^{\prime}(1,1) \end{gathered}[/tex]Which, if we graph them, we get :
Answer:
[tex]\begin{gathered} C^{\prime}(2,4) \\ D^{\prime}(3,2) \\ E^{\prime}(1,1) \end{gathered}[/tex]Find the y-intercept of the parabola y = x2 - 7x + 10. Simplify your answer and write it as a proper fraction, improper fraction, or integer.
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NO* 5GThe movement of the progress bar may be uneven because questions can be worth more or less(including zero) depending on your answer.The two triangles below are similar because IZA = MZEand mzB = mZF.EBADLOUISE L. HAYWhich option lists the other corresponding sideling
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For two similar triangles, the corresponding angles are always congruent.
We know two pairs of corresponding angles:
m∠A=m∠E
m∠B=m∠F
As mentioned above, all corresponding angles are congruent, so the remaining pair must be equal:
m∠C=m∠D
Having established the corresponding pairs we can name both triangles. When you name the triangles, the letters of the corresponding vertices must be in the same position, starting with the first corresponding pair ∠A and ∠E the name of the triangles can be:
Following the order of the letters, you can determine the corresponding sides:
[tex]\begin{gathered} \bar{AB}\cong\bar{EF} \\ \bar{BC}\cong\bar{FD} \\ \bar{CA}\cong\bar{DE} \end{gathered}[/tex]The correct option is the second:
[tex]undefined[/tex]What I’d the sum of the numbers 1 up to 200
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SOLUTION
The given sum of numbers are
[tex]1+2+3+4+5+\cdots+200[/tex]Notice that this represents an arithmetic series with
First term a=1
Last term l=200
Number of terms n = 200
Using the arithmetic sum formula
[tex]S_n=\frac{n}{2}\lbrace a+l\rbrace[/tex]Substituting values gives
[tex]\begin{gathered} S_n=\frac{200}{2}(1+200) \\ S_n=100(201) \\ S_n=201,100 \end{gathered}[/tex]Therefore the total sum is 201,100
Use the table to evaluate the given composite function (G o f)(-5)=
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We were given that:
[tex]\begin{gathered} g(5)=2 \\ f(5)=-1 \end{gathered}[/tex]We will proceed to calculate (G o f)(-5), we have:
[tex]undefined[/tex](b) The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1500 after 1 day, what is thesize of the colony after 3 days?Approximately mosquitoes(Do not round until the final answer. Then round to the nearest whole number as needed.)}.vix
Answers
Given:
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1500 after 1 day,
Required:
what is the size of the colony after 3 days?
Explanation:
We know
[tex]A=A_0e^{kt}[/tex][tex]\begin{gathered} Where, \\ A_0=\text{ Starting amount} \\ e=\text{ Euler's constant} \\ k=\text{ Amount of increase} \\ t=\text{ time} \end{gathered}[/tex]Now,
[tex]\begin{gathered} 1500=1000e^k \\ \frac{1500}{1000}=e^k \\ 1.5=e^k \\ ln1.5=klne \\ k=0.405 \end{gathered}[/tex]After 3 days
[tex]\begin{gathered} A=1000\times e^{(0.405\times3)} \\ A=1000\times e^{1.215} \\ A=1000\times3.370 \\ A=3370 \end{gathered}[/tex]Answer:
After 3 days there will be 3370 mosquitoes.
5) Point G is rotated counter-clockwise about H and by an angle of 45°. If it's image is G Prime and segments GH, G prime H, G prime G prime are drawn which of the following is true ? A)GH is congruent to G prime HB) Gh is perpendicular to G prime HC) Gh is parallel to G prime H D) H is the midpoint of segment G prime G
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We are given that a point is rotated counterclockwise about an angle of 45 degrees. A diagram of this is the following:
Now, since the rotation of point G to point G' won't affect the distance of segment GH, this means that
[tex]GH=G^{\prime}H[/tex]Rotation is a type of transformation called isometries, that is, transformations that do not change the distance.
Describe the transformation of f(x)= x2 represented by g. Then graph each function.
Answers
There are two tranformations goinf from f(x) to g(x)
Frist, there is a reflection with respect to the x-axis, which is done by changing the sign of the whole function:
[tex]f_1(x)=-f(x)=-x^2[/tex]Next, to get to g(x), ther is a vertical compression of 2, which is done by dividing the whole function by 2:
[tex]g(x)=\frac{f_1\mleft(x\mright)}{2}=-\frac{1}{2}x^2[/tex]So, to graph it, we can start from f(x):
[tex]f(x)=x^2[/tex]Then reflect and compress like we have done.
We get the function og g(x):
[tex]g(x)=-\frac{1}{2}x^2[/tex]fill in the values of the table for the function shown
Answers
To find the value of y, we need to replace each of the values of x in the equation of the function.
For example for the first value of x, -8, replace x for -8, this way:
[tex]\begin{gathered} y=\sqrt[3]{x} \\ y=\sqrt[3]{-8} \\ y=-2 \end{gathered}[/tex]The first value of y is -2.
Follow the same procedure for the resting values of x:
[tex]\begin{gathered} y=\sqrt[3]{-1} \\ y=-1 \end{gathered}[/tex][tex]\begin{gathered} y=\sqrt[3]{0} \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} y=\sqrt[3]{1} \\ y=1 \end{gathered}[/tex][tex]\begin{gathered} y=\sqrt[3]{8} \\ y=2 \end{gathered}[/tex]Now, fill in the table using the obtained values of y:
The letters COCONUT are written on 8 cards. A card is chosen, what is the probability that it will be a letter in the word CHOCOLATE?
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We have the Word COCONUT and the word CHOCOLATE as we can see the common letter in the word are C, O, T
The probability to obtain a letter that in the word Chocolate is
[tex]P(\text{letter in the word chocolate)=P(C)+P(O)+P(T)}[/tex]where
[tex]\begin{gathered} P(C)=\frac{2}{7} \\ P(O)=\frac{2}{7} \\ P(T)=\frac{1}{7} \end{gathered}[/tex]then we substitute this information
[tex]P(\text{letter in the word chocolate)=}\frac{2}{7}+\frac{2}{7}+\frac{1}{7}=\frac{5}{7}[/tex]The probability to chose a card that it will be a letter in the word CHOCOLATE is 5/7
2. Identify each measurement as the diameter, radius, or circumference of the circular
object. Then, estimate the other two measurements for the circle.
a. The length of the minute hand on a clock is 5 in.
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ANSWER:
Diameter: 10 in
Radius: 5 in
Circumference of the circular: 31.4 in
STEP-BY-STEP EXPLANATION:
The minute hand represents the radius of the clock, therefore the radius is 5 inches. The diameter is twice the radius, so they would equal 10 inches.
And we calculate the circumference like this:
[tex]\begin{gathered} c=2\cdot\pi\cdot r \\ c=2\cdot3.14\cdot5 \\ c=31.4\text{ in} \end{gathered}[/tex]How do I write the equation of the line passing through (-3, 5) and parallel to the line y = 2x + 6.
Answers
parallel
y=2x+11
Explanation
Step 1
find the equation of the line:
two lines are parellel if the slope is the same for both,so
let
[tex]y_1=2x+6[/tex]this function is written in slope-intercept form y=mx+b, where m is the slope
[tex]\begin{gathered} y=2x+6\rightarrow y=mx+b \\ \text{hence} \\ slope_1=m_1=2 \\ so \\ slope_1=slope_2=m_2=2 \end{gathered}[/tex]it means the slope of the line we are looking for is 2
Step 2
now,let's find the equation of the line
to do that, we can use this formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope} \\ \text{and (x}_1,y_1)\text{ is a point from the line} \end{gathered}[/tex]then,let
[tex]\begin{gathered} \text{slope}=2 \\ \text{passing point=(-3,5)} \end{gathered}[/tex]Now,replace in the formula and solve for y
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=2(x-(-3)) \\ y-5=2(x+3) \\ y-5=2x+6 \\ \text{add 5 in both sides} \\ y-5+5=2x+6+5 \\ y=2x+11 \end{gathered}[/tex]so, the answer is
[tex]y=2x+11[/tex]I hope this helps you
1. The graphs show the distance, d, traveled by two cars, A and B, over time, T Distance is measured in miles and time is measured in hours. Which car traveled slower? Explain how you know.
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A slower car will travel less distance in the same time.
To know which car traveled slower, we have to compare the distance travelled for the same time, for example t = 3 hours. We can select any time because the speeds are constant (that is why the distance is a proportional function of time).
We can compare them in the graph as:
In the graph we can see that, in 3 hours, car B traveled a longer distance than car A.
Then car A is slower.
Answer: the slower car is car A.
Which of the following reasons would justify Statement 4?A AAAB. AASC. ASAD SAS
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You can notice in the given image, that both triangles have one equal side.
Furthermore, you can notice that there are two congruent angles.
Then, you hva two congruent angles and one congruent side.
The statement that explains step 4 is then, ASA, which means congruence in angle-side-angle.
A hot air balloon can gold 90,00 cubic feet of air.A hot airballoon can hold 90,000 cubic feet of air. It is being inflated at a rate of 6,000 cubic feet per minute. The total cubic feet of air a(t) is a function of the time in the minutes t.
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the Given:
The hot air balloon is inflated at a rate of 6000 cubic feet.
Let f(t) be the function representing total amount of air for time t.
The function is given as,
[tex]undefined[/tex]Solve the equation for x, and enter your answer in the box below. x + 15 = 36
Answers
SOLUTION
x + 15 = 36
You collect like terms by taking 15 to meet 36. When 15 crosses the = sign it becomes -15.
x = 36 - 15
x = 21
all you need is in the photo which of the following mapping diagram represents the relation?
Answers
ANSWER
A. It is not a function
B. The second one
EXPLANATION
A. We want to determine if the relation is a function.
To do this, we have to examine the relation closely.
For a relation to be classified as a function, each value in the domain (the input values) must yield only one value in the range (the output).
From the relation given, we have that two numbers in the domain each give two numbes in the range.
That is:
4 -> 7 and 1
3 -> 8 and 9
Therefore, it is not a function
B. The correct option is the second one.
SInce, 3 and 4 each map out to two values, there is no need for repeating them.
Find the sale price when the original price is $58 and the discount rate is 9%
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When the discount rate is 9%, this means the sale price of the product will be 100% - 9% =91% the original price.
91% of $58 is
[tex]\frac{91}{100}\times58=52.78[/tex]The sale price after a discount rate of 9% is $52.78
Write an equation for a rational function with:
Vertical asymptotes at x = 2 and x = -4
x-intercepts at x = 1 and x = 4
y-intercept at 9
y=
Answers
The equation for a rational function with: Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is
[tex]y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}[/tex]
How to determine the equation for a rational functioninformation gotten from the question
From the question given above, the following data were obtained:
Vertical asymptotes at x = 2 and x = -4x-intercepts at x = 1 and x = 4y-intercept at 9y =?Rational function means that the equation will be a fraction
The rational function that models the Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is written as follows
The numerator
x-intercepts at x = 1 and x = 4
x = 1 ⇒ (x - 1)
x = 4 ⇒ (x - 4)
This means the equation will have (x - 1) (x - 4) as the numerator
The denominator
Vertical asymptotes at x = 2 and x = -4
x = 2 ⇒ (x - 2)
x = -4 ⇒ (x + 4)
This means the equation will have (x - 2) (x + 4) as the denominator
y-intercept at 9
expressing the functions derived already gives
[tex]y=a\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}[/tex]
substituting x = 0 and y = 9 and solving gives a
[tex]9=a\frac{(0 - 1) (0 - 4)}{(0 - 2) (0 +4)}[/tex]
[tex]9=a\frac{(4)}{(-8)}[/tex]
4a = 9 * -8
a = -36
The equation of the rational function is [tex]y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}[/tex]
Learn more on equation for a rational function at :
https://brainly.com/question/28032338
#SPJ1
May I please get help with graphing it. I also need help with finding out weather it is a square, rectangle, triangle, or If it is none of them.
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We have to graph the vertices of the polygon: (7,2), (7,-2), (-1,-2) and (-1,2).
The first number of the ordered pair correspond to the x-coordinate while the second one correspond to the y-coordinate.
We can graph this as:
We can see that the polygon is a rectangle, as it has 2 pair of equal sides and 4 right angles at its vertices.
how can I use deductive reasoning to show that
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Therefore,
[tex]\Delta PQS\cong\Delta RQS\text{ (SAS congruence rule.)}[/tex]So,
[tex]\angle P\cong\angle R[/tex]Is the value of makayla’s scooter growing or decaying A growingB decaying
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given exponential function
[tex]f\mleft(x\mright)=13500\cdot0.89^x[/tex]STEP 2: Explain the standard exponential function
Exponential function is given as
[tex]y=a\cdot b^x[/tex]where:
a is the initial or starting value of the function,
b is the growth factor or growth multiplier. b determines the rate at which the graph grows or decays.
STEP 3: Compare the given function with the standard exponential function
[tex]\begin{gathered} \text{By comparison,} \\ a=13500 \\ b=0.89 \end{gathered}[/tex]STEP 4: Mention the condition for determining a growth or decay in an exponential function.
If a is positive and b is greater than 1, then it is an exponential growth
If a is positive and b is less than 1 buth greater than 0, then it is an exponential decay.
STEP 5: Reach a conclusion
It can be seen from Step 3 that a is positive(13500) and b(0.89) is greater than zero but less than 1, therefore this implies according to the condition in step 4 that the value of the scooter is decaying.
Question 5Ginny has $10,000 in a savings account earning 4% simple interest annually. Ginny plans on savingthis money for a long time. Let's calculate Ginny's Total account balance in 20 years.a $18
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ANSWER
$18,000
EXPLANATION
Ginny has $10,000 in a savings account.
The interest is 4% simple interest.
We want to calculate Ginny's total account balance after 20 years.
To do this, we will first caluclate the interest and then we will add it to the initial balance.
To calculate Simple Interest, we use:
[tex]\text{Simple Interest = }\frac{P\cdot\text{ R }\cdot\text{ T}}{100}[/tex]P = principal = $10000
R = rate = 4%
T = time = 20 years
Therefore:
[tex]SI\text{ = }\frac{10000\cdot\text{ 4 }\cdot\text{ 20}}{100}\text{ = \$8000}[/tex]Therefore, her account balance after 20 years is:
Amount = $10000 + $8000 = $18,000
A board is 20 inches long. It must be cut into four pieces of equal length, and each of the three cuts will cause a waste of 1/2 inches. How long will each piece be after the Cuts are made
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Let the length of each cut be x.
Therefore, the following equation holds true:
[tex]4x+3(\frac{1}{2})=20[/tex]Therefore,
[tex]\begin{gathered} 4x=20-\frac{3}{2}=18.5 \\ x=4.625\text{ inches} \end{gathered}[/tex]Therefore, the required length is 4.625
if jaden drove 40 miles how many gallons of gas would be left in the tank
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The x axis of the graph show the distance driven and y axis represnt Gas remains
at 40 miles of distance i.e x =40
Then value of y at x = 40 is 3.5 i.e. y = 3.5
the triangle will be rotated 270 degrees counter clockwise about the origin click in each vertex of the rotated triangle starting and ending of the same vertex
Answers
Coordinates
(0,0)
(0,6)
(-6,5)