Here are the graphs of three equations:y = 50(1.5) ^xy = 50(2)^xY = 50(2. 5)^xWhich equation matches each graph? Explain how you know
Answers
The graphs below are exponential function graphs, the general formular takes the form
[tex]y=ab^x[/tex]The graph of
[tex]y=50(1.5)^x[/tex]Is shown below
The graph of
[tex]y=50(2^x)[/tex]Is shown below
The graph of
[tex]y=50(2.5^x)[/tex]Is shown below
Hence,
[tex]\begin{gathered} y=50(1.5)^x\rightarrow C \\ y=50(2)^x\rightarrow B \\ y=50(2.5)^x\rightarrow A \end{gathered}[/tex]The equation of the exponential function is
[tex]\begin{gathered} y=ab^x \\ a=50\rightarrow the\text{ initial value} \\ b\rightarrow growht\text{ factor} \end{gathered}[/tex]Thus the higher the growth factor the greater the rate of attaining a higher value within a short period.
That is why you see that the function with growth factor of 2.5 grows faster than that of 2 and also 1.5.
So the at x value of 3, the function with the greatest growth factor will have the highest y-value.
This implies , growth factor of 2.5 will have the highest, that corresponds to graph with colour green. Function with growth factor 2 will be the next to that of 2.5, that is red colored graph, and the last will be blue.
Related Questions
Which of the following is the median of the data set? 15 20 20 25 30 35 40 40 45 50 55(1) 28(2) 30(3) 32(4) 34
Answers
Median: The media is the middle number in a list of values. If there is an even number of values (so there is no middle number) then average the middle two values together.
so:
[tex]set\colon\mleft\lbrace15,20,20,25,30,35,40,40,45,50,55\mright\rbrace[/tex]From the data set, we can conclude that the middle number (median) is:
[tex]35[/tex]Jen L cut out the following figures on the solid lines and folded them on the third lines which figure formed a rectangle prism
Answers
A rectangular prism is a figure that has the following shape:
When the figure is unfolded the shape it has is the following:
Therefore, the right answer is the bottom right shape.
The systolic blood pressure of women is normally distributed with a mean of 150 mmHg. and a standard deviation of 10 mmHg. What percentage of a 50-year-old women have a systolic blood pressure between 130 mmHg. and 170 mmHg.?
Answers
The required percentage of a 50-year-old woman have a systolic blood pressure between 130 mmHg. and 170 mmHg is 95.44%.
Given that,
The systolic blood pressure of women is normally distributed with a mean of 150 mmHg. and a standard deviation of 10 mmHg.
What is probability?
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
z = [ x - μ]/σ
Accoding to the question,
= p[z < (170-150)/10] - p[z < 130-150/10]
= p [z <2] - p [z < -2]
= 0.9772 - 0.0228
= 95.44%
Thus, the required percentage of a 50-year-old woman have a systolic blood pressure between 130 mmHg. and 170 mmHg is 95.44%.
Learn more about probability here:
brainly.com/question/14290572
#SPJ1
If using the method of completing the square to solve the quadratic equationX2 + 15x + 7 = 0, which number would have to be added to "complete thesquare"?
Answers
ANSWER
225/4
EXPLANATION
To complete the square we want to write a part of the equation in the form:
[tex](a+b)^2=a^2+2ab+b^2[/tex]The second term squared is the one we have to add to the equation in order to complete the square.
In this case, the coefficient of x is 15, so b is:
[tex]b=\frac{15}{2}[/tex]And b²:
[tex]b^2=\frac{225}{4}[/tex]If we add 225/4 to both sides of the equation:
[tex]x^2+15x+\frac{225}{4}+7=\frac{225}{4}[/tex]We complete the square:
[tex](x+\frac{15}{2})^2+7=\frac{225}{4}[/tex]write the following comparison as a ratio in simplest form using a fraction, a colon and the word to. _ 198 cents to 234 cents is?
Answers
Given data:
The expression for the kratio of 198 cents to 234 cents is,
[tex]\begin{gathered} \frac{198}{234}=\frac{18\times11}{18\times13} \\ =\frac{11}{13} \\ =11\colon13 \end{gathered}[/tex]Thus, the correct option is (d).
write an explicit formula for an nth term of the sequence 7, 35, 175,....
Answers
hello
to write an explicit formula, we have to determine what type of sequence is it
7, 35, 17
this is clearly a geometric progression with values of
first term = 7
common ratio = 5
the explicit formula of a geometric progression is given as
[tex]\begin{gathered} a_n=a\cdot r^{(n-1)}^{} \\ n=\text{nth term} \\ a=\text{first term} \\ r=\text{common ratio} \end{gathered}[/tex]now let's substitute the variables into the equation
[tex]\begin{gathered} a_n=a\cdot r^{(n-1)} \\ a_n=7\cdot5^{(n-1)} \\ a_n=35^{(n-1)} \end{gathered}[/tex]the equation above is the explicit formula for the sequence
Match each measurement on the left with an equal measurement on the right. Some answer options on the right will not be used.31/2 yards66 inches2 miles21/2 miles51/2 feet10,560 feet101/2 feet91/2 feet12,300 feet13,200 feet
Answers
Solution
Recall
1 yard is 3feet
1 foot is 12inches
1 mile is 5,280 feet
[tex]3\frac{1}{2}\text{yards =10}\frac{1}{2}\text{ ft}[/tex][tex]66\text{inches =5}\frac{1}{2}ft[/tex][tex]\begin{gathered} 1\text{ miles = 5280 ft} \\ 2\text{miles = 10,560ft} \end{gathered}[/tex][tex]\begin{gathered} 1\text{mile = 5280 ft} \\ 2\frac{1}{2}\text{miles =}13,200ft \end{gathered}[/tex]4.The value of x isis order these expressions from least to greatest:χ1- xx-1-1 = x
Answers
To answer this question we have to evaluate each expression at the given value of x.
Recall that to evaluate an expression we substitute the variable by the given value.
Evaluating each expression at
[tex]x=-\frac{1}{4}[/tex]we get:
[tex]\begin{gathered} x=-\frac{1}{4}, \\ 1-x=1-(-\frac{1}{4})=1+\frac{1}{4}, \\ x-1=-\frac{1}{4}-1=-(1+\frac{1}{4}), \\ -\frac{1}{-\frac{1}{4}}=\frac{1}{\frac{1}{4}}=4. \end{gathered}[/tex]Therefore, the numbers ordered from least to greatest are:
[tex]x-1,\text{ x, 1-x, -1/x.}[/tex]Answer:
[tex]x-1,\text{ x, 1-x, -1/x.}[/tex]write the following division expression using a division symbol and as a fraction 7 divided by x
Answers
We are asked to write the following division expression using a division symbol and as a fraction.
7 divided by x
Using a division symbol:
Here you need to write the dividend (7) then the division sign and finally the divisor (x)
[tex]\begin{gathered} dividend\: \div\: divisor \\ 7\: \div\: x \end{gathered}[/tex]As a fraction:
Here you need to write the dividend (7) in the numerator (top) and the divisor (x) in the denominator (bottom)
[tex]\begin{gathered} \frac{dividend}{divisor} \\ \frac{7}{x} \end{gathered}[/tex]Therefore, the division expression using a division symbol is
[tex]7\: \div\: x[/tex]Therefore, the division expression as a fraction is
[tex]\frac{7}{x}[/tex]identify two different types of optional deductions that an employer may subtract from a paycheck
Answers
Two possible deductibles can be the social care or the medical care
5] Great America has a season pass that costs $45 plus $7 each time you attend thepark, or you can pay $12 each time you go. How many times do you have to go beforeyou pay the exact same amount?
Answers
Let the number of time he attend the park be represented with n.
So that,
C = 45 + 7n ....eqn(1)
C = 12n ..........eqn(2)
Equating both equations, we have,
[tex]\begin{gathered} 12n=45+7n \\ \text{Collecting like terms, we get} \\ 12n-7n=45 \\ 5n=45 \\ \text{Dividing both sides by 5, we get} \\ n=\frac{45}{5}=9 \end{gathered}[/tex]He has to attend the park 9 times before he can pay exactly the same amount.
So, the correct answer is 9.
Is the system of equations consistent and independent, consistent and dependent, or inconsistent? Y=-3x+1 y=-6x+2
Answers
Reason:
The equations are y = -3x+1 and y = -6x+2
The slopes of each equation are -3 and -6. Compare the equations to the form y = mx+b to determine the slope m.
Since the slopes are different, it means the lines aren't parallel and intersect at exactly one location. This immediately tells the reader the system is consistent and independent.
-----------------------------
Extra info:
parallel lines have equal slopes, but different y intercepts.consistent = system has at least one solution. When written with "independent" it leads to "exactly one solution".independent = neither equation is a scaled version of one another, i.e. they produce different lines. In contrast a dependent system is where two lines perfectly overlap to produce infinitely many solutions all along that line.inconsistent = the lines are parallel and never intersect; leading to no solutions.The graph shows the profit, y, of a community fundraiser, with respect to the number of tickets sold, x.Use the graph to complete each statement.Drag and drop the answers into the boxes. The y-intercept is Response area.The y-intercept represents Response area.
Answers
Answer:
The y-intercept is -700
The y-intercept represents the initial amount of expenses.
Explanation:
The y-intercept of the graph is the point where the graph crosses the vertical axis. In this case, it is also the value of the profit when the number of tickets sold is 0.
Therefore, the answers are:
The y-intercept is -700
The y-intercept represents the initial amount of expenses.
Find the area of the shaded region. Use 3.14 for π as necessary.The circle centered on point A, and has a radius of 5 cm, is shaded. BC is a diameter of the circle. Point D is on the cicle, such that line AD is perpendicular to line BC. Triangle BCD is not shaded.A. 132 cm²B. 53.5 cm²C. 26.8 cm²D. 17.1 cm²
Answers
Given
radius = 5 cm
To get the area of the shaded region, get the difference between the area of the circle, and the area of the triangle
We have the following
[tex]\begin{gathered} A_{\text{circle}}=\pi r^2 \\ A_{\text{circle}}=(3.14)(5\text{ cm})^2 \\ A_{\text{circle}}=(3.14)(25\text{ cm}^2) \\ A_{\text{circle}}=78.5\text{ cm}^2 \\ \\ A_{\text{triangle}}=\frac{1}{2}bh \\ A_{\text{triangle}}=\frac{1}{2}(10\text{ cm})(5\text{ cm})\text{ *the base is twice the radius} \\ A_{\text{triangle}}=25\text{ cm}^2 \\ \\ A_{\text{shaded area}}=A_{\text{circle}}-A_{\text{triangle}} \\ A_{\text{shaded area}}=78.5\text{ cm}^2-25\text{ cm}^2 \\ A_{\text{shaded area}}=53.5\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the shaded region is 53.5 cm².
Use the compound interest formula to determine the final value of the following amount. $1900 at 10.4% compounded monthly for 4.5 years . What is the final value of the amount?
Answers
Answer:
$3027.80
Explanation:
The compound interest formula is the following.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A = final amount
P = principle amount
r = interest rate / 100
n = number of compounds per interval
t = time interval
Now in our case,
A = unknown
P = $1900
r = 10.4/100
n = 12 months / year ( because the interest is compounded monthly)
t = 4.5 yrs
Therefore, the compound interest formula gives
[tex]A=1900(1+\frac{10.4/100}{12})^{12*4.5}[/tex]Using a calculator, we evaluate the above to get
[tex]\boxed{A=\$3027.80}[/tex]which is our answer!
Suppose you invest $2200 at an annual interest rate of 5.3% compounded continuously. How much will you have after 7 years?
Answers
Answer:
$3188.20
Explanation:
From the information given:
• Principal, P = $2200
,• Interest Rate, r=5.3% = 0.053
,• Time, t=7 years
For a principal compounded continuously, we use the formula to determine the amount in the account:
[tex]A(t)=Pe^{rt}[/tex]Substituting the given values, we have:
[tex]\begin{gathered} A(t)=2200\times e^{0.053\times7} \\ =\$3188.20 \end{gathered}[/tex]You will have $3188.20 after 7 years.
If angle AOB and angle BOC are complementary angles, and m angle AOB = x°, what is the measure of the supplement of angle BOC?
Answers
Complementary angles are angles whose sum is 90 degrees.
If angle AOB and angle BOC are complementary and angle AOB is x degrees, it means that angle BOC is (90 - x) degrees
Supplementary angles are angles whose sum is 180 degrees. If angle BOC is (90 - x) degrees, then the measure of its supplement would be
180 - (90 - x)
= 180 - 90 + x
= 90 + x
the measure of the supplement of angle BOC is (90 + x) degrees
Write an equation in point-slope form for the line through the given point with the given slope (9,-1); m =4/3 A . Y-1=4/3(x-9)B. Y-9=4/3(x+1) C. Y+1=4/3(x-9)D. Y-1=4/3(x+9
Answers
Step 1: List the given data
[tex]\begin{gathered} m\text{ = }\frac{4}{3} \\ \text{Coordinates (x}_{1\text{ , }}y_1)\text{ = ( 9, -1 )} \end{gathered}[/tex]Step 2: Write the equation of a line formula in a point-slope form
[tex]y-y_1=m(x-x_1\text{ )}[/tex]Step 3: Substitute all values in the point-slope form equation.
[tex]\begin{gathered} y\text{ - (-1) = }\frac{4}{3}(x\text{ - 9)} \\ y\text{ + 1 = }\frac{4}{3}(x\text{ - 9)} \end{gathered}[/tex]Step 4: Final answer
[tex]y\text{ + 1 = }\frac{4}{3}(\text{ x - 9) Option C}[/tex]The function f(t) = -5t to the 2nd power+20t +60 models the approximate height of an object t seconds after it is launched. how many seconds does it take the object to hit the ground?
Answers
We know that if we replace t by some number in the equation:
f(t) = -5t² + 20t + 60
the result will be the height of a launched object.
When the object hits the ground its height is 0.
Then
-5t² + 20t + 60 = 0
We want to solve the highlighted equation fot t, the values of t that make it result in 0 will be the seconds when the object is in the ground.
Solving the equation for tIn order to solve the equation
-5t² + 20t + 60 = 0
we want to factor the left side:
Step 1- Common factor
The common factor of -5t², 20t and 60 is -5:
(-5) · 1 = -5
(-5) · (-4) = 20
(-5) · (-12) = 60
Then
-5t² + 20t + 60 = -5(t² -4t - 12)
Then, replacing the equation
-5t² + 20t + 60 = 0
↓
-5(t² -4t - 12) = 0
↓ taking -5 to the right side
(t² -4t - 12) = 0/(-5) = 0
t² - 4t - 12 = 0
Step 2- Factoring a trinomial
We continue the factoring.
We want to factor t² - 4t - 12.
It should look something like:
t² - 4t - 12 = (t + _ )(t + _ )
To complete it we will use two numbers whose:
- product is -12 (third term t² - 4t - 12)
- sum is -4 (second term t² - 4t - 12)
The pair of numbers whose product is -12 are:
(-1) · 12 = -12
1 · (-12) = -12
(-2) · 6 = -12
2 · (-6) = -12
(-3) · 4 = -12
3 · (-4) = -12
We add them, the pairs whose result is -4 is the pair we will use:
-1 + 12 = 11
1 - 12= -11
-2 + 6 = 4
2 - 6 = -4
-3 + 4 = 1
3 - 4 = -1
Then, we will use 2 and -6 (their product is the third term and their sum is the second term):
t² - 4t - 12 = (t + _ )(t + _ )
↓
t² - 4t - 12 = (t + 2)(t - 6)
Then, using the equation we had:
t² - 4t - 12 = 0
↓
(t + 2)(t - 6) = 0
Step 3- finding the possible t values
When a product of two numbers is 0, it means that one of them is 0:
In this case
We have that
(t + 2)(t - 6) = 0
then
t + 2 = 0 or t - 6 = 0
This means that t could have two possible values:
t + 2 = 0 → t = -2
or
t - 6 = 0 → t = 6
Since t means the seconds the object takes to hit the ground, it cannot have a negative value, because it would mean that it happened in the past. so t cannot be -2
Answer: It takes to the object 6 seconds to hit the ground t = 6how many terms the expression x^3+4x^2+2x^-9
Answers
How many terms the expression
x^3+4x^2+2x^-9? 3 TERMS
6 Ms. Carson drove 96 miles in 15 hoursWhat was her speed in miles per hour!48 miles per hourB.54 miles per hourС64 miles per hourD. 144 miles per hour
Answers
Hi can you help me with this problem?Formulate a system of equations for the situation below and solve.The total number of passengers riding a certain city bus during the morning shift is 1300. If the child's fare is $0.50, the adult fare is $1.50, and the total revenue from the fares in the morning shift is $1550, how many children and how many adults rode the bus during the morning shift?children=adults=
Answers
Let "A" represent the number of adults that ride the bus and "C" represents the number of children that ride the bus.
On a certain morning shift 1300 people rode the bus, this means that the number of adults and the number of children add up to 1300. You can express the total number of passengers on that shift as follows:
[tex]A+C=1300[/tex]The child's fare is $0.50, so if C children ride the bus a total of 0.50C will be paid.
The adult's fee is $1.50, so if A adult rides the bus, the total earned will be 1.50A.
If you add both fares, you will determine the total fares for the shift, which was $1550
[tex]1.50A+\text{0}.50C=1550[/tex]Using both equations you have determined the number of adults and children that rode the bus:
-First, write the first expression for one of the variables, for example, write it for A:
[tex]\begin{gathered} A+C=1300 \\ A=1300-C \end{gathered}[/tex]-Second, replace the expression obtained in the second equation
[tex]\begin{gathered} 1.50A+0.50C=1550 \\ 1.50(1300-C)+0.50C=1550 \end{gathered}[/tex]Now you have to solve for C
→ Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 1.50\cdot1300-1.50\cdot C+0.50C=1550 \\ 1950-1.50C+0.50C=1550 \end{gathered}[/tex]→Simplify the like terms
[tex]\begin{gathered} 1950+(-1.50C+0.50C)=1550 \\ 1950+-C=1550 \\ 1950-C=1550 \end{gathered}[/tex]→Subtract 1950
[tex]\begin{gathered} 1950-1950-C=1550-1950 \\ -C=-400 \end{gathered}[/tex]→ Multiply both sides by -1 to invert the sign:
[tex]\begin{gathered} (-1)(-C)=(-1)(-400) \\ C=400 \end{gathered}[/tex]Finally, once you have determined the value of C, you can calculate the value of A as follows:
[tex]\begin{gathered} A=1300-C \\ A=1300-400 \\ A=900 \end{gathered}[/tex]So, 400 children and 900 adults rode the bus.
please find the slopes and lengths then fill in the words that best describes the type of quadrilateral.
Answers
We can find the slopes using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]And the lengths using the following formulas:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Therefore:
[tex]m_{QR}=\frac{5-2}{-1-(-9)}=\frac{3}{8}[/tex][tex]m_{RS}=\frac{9-5}{1-(-1)}=\frac{4}{2}=2[/tex][tex]m_{ST}=\frac{6-3}{-7-1}=\frac{3}{8}[/tex][tex]m_{TQ}=\frac{6-2}{-7-(-9)}=\frac{4}{2}=2[/tex][tex]\begin{gathered} L_{QR}=\sqrt[]{(-1-(-9))^2+(5-2)^2} \\ L_{QR}=\sqrt[]{73} \end{gathered}[/tex][tex]\begin{gathered} L_{RS}=\sqrt[]{(1-(-1))^2+(9-5)^2} \\ L_{RS}=2\sqrt[]{5} \end{gathered}[/tex][tex]\begin{gathered} L_{ST}=\sqrt[]{(6-9)^2+(-7-1)^2} \\ L_{ST}=\sqrt[]{73} \end{gathered}[/tex][tex]\begin{gathered} L_{TQ}=\sqrt[]{(6-2)^2+(-7-(-9))^2}_{} \\ L_{TQ}=2\sqrt[]{5} \end{gathered}[/tex]Since:
[tex]\begin{gathered} m_{RS}=m_{TQ}\to m_{RS}\parallel m_{TQ} \\ m_{QR}=m_{ST}\to m_{QR}\parallel m_{ST} \end{gathered}[/tex]And:
[tex]\begin{gathered} L_{QR}=L_{ST} \\ L_{RS}=L_{QT} \end{gathered}[/tex]According to this, we can conclude it is a parallelogram
12-foot-long wooden beam is supported on both ends. When a weight load is placed in the center of the beam,it causes the beam to sag. The sag is called deflection. The graph shows the deflection of the beam,in inches, as a function of the weight load, in pounds, placed in the center of the beam. for every 50-pound increase in the weight load, what will be the change in the deflection?
Answers
the change in the deflection with every 100 pounds is,
[tex]=\frac{0.5-0}{100-0}[/tex][tex]=\frac{0.5}{100}[/tex]so for every 50 pounds will be,
[tex]\begin{gathered} =(\frac{\frac{0.5}{100}}{2}) \\ =\frac{0.5}{200} \\ =0.0025 \end{gathered}[/tex]so for every 50 pound increase in the weight, the change in the deflection is 0.25
I don’t know if my answer is correct I got 28
Answers
1) Consider that in 2 days she took 7 bottles each one with 16oz of water:
So we can write out the following:
[tex]undefined[/tex]10 + 8x + 2 = 4x + 36
Answers
we have
10 + 8x + 2 = 4x + 36
solve for x
step 1
Combine like terms left side
12+8x=4x+36
step 2
subtract 12 both sides
8x=4x+36-12
8x=4x+24
step 3
subtract 4x both sides
4x=24
step 4
Divide by 4 both sides
x=6
the answer is x=6Mariana receives a $20 gift card for downloading music and wants to determine how many songs she can purchase.Each downloaded song costs $1.29. If m represents the number of songs downloaded, which inequality represents thegiven situation?20m 2 1.2920m 1.2901.29ms 2001.29m 2 20Mark this and retumSave and ExitNextSubmit
Answers
Mariana has a $20 gift card for downloading music → this means that she can spend at most $20 on music, you can symbolize this situation as ≤20
If each song costs $1.29 and she buys "m" number of songs, the total cost of the songs can be expressed as 1.29m
Then the inequality that represents the number of songs she can download is
[tex]1.29m\leq20[/tex]Pat is 20 years older than his son Patrick. In 2 years, the sum of their ages will be 90. How old are they now?Patrick is years old, and Pat is ?years old.
Answers
Let "x" be the age of Patrick.
Pat is 20 years older than his son Patrick so we can represent this as "x+20".
In two years, the age of patrick will be x+2 and the age of Pat will be x+22.
Since in 2 years, the sum of their ages will be 90, we can write:
[tex]\begin{gathered} x+2+x+22=90 \\ 2x+24=90 \\ 2x=66 \\ x=33 \end{gathered}[/tex]And, the age of Pat is x+20 which is 53.
Therefore, Patrick is 33 years old, and Pat is 53 years old.
Let log, 4= 3; log, C = 2; log, D= 5 Ac? Do log What is the value of O A. -11 O B.-15,378 O c. 49 D. 2
Answers
Given:
[tex](x+2)^2+(y-3)^2=9[/tex]Circle equation is
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) be the center of the circle and r be the radius.
[tex]\text{Center(-}2,3)\text{ and radius 3}[/tex]Option C is the correct answer.
x/4 (this part is division)
x/4 + 3 = 3
What does x equal?
Answers
To isolate the x, you need to first subtract 3 on both sides.
x/4 + 3 - 3 = 3 - 3
=
x/4 = 0
Then you need to multiply (4) on both sides to because it is the bottom of the fraction x/4.
x/4 (4) = 0 (4)
x = 0
Answer:x=0
Step-by-step explanation: