Answer : The linear function of the graph when move down 3 units is y = x - 3
The graph shift vertically because it is down 3 units
The standard equation of a linear function is
y = mx + b
Where b = intercept and m = slope
Move 3 unit down means b = -3
Hence, y = x-3
Answer is y = x - 3
x/4 (this part is division)
x/4 + 3 = 3
What does x equal?
Answer:x=0
Step-by-step explanation:
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
write an explicit formula for an nth term of the sequence 7, 35, 175,....
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
4.The value of x isis order these expressions from least to greatest:χ1- xx-1-1 = x
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]the sales tax for the city of Los Angeles is 9.75% how much will you pay for an item that costs $200?
Answer:
$219.5
Explanation
Given
Original cost of an item = $200
Sales tax = 9.75%
Tax = 9.75/100 * 200\
Tax = 9.75 * 2
Tax = $19.5
Amount you will pay = $200 + $19.5
Amount you will pay = $219.5
Is the system of equations consistent and independent, consistent and dependent, or inconsistent? Y=-3x+1 y=-6x+2
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.Mariana 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
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]Suppose you invest $2200 at an annual interest rate of 5.3% compounded continuously. How much will you have after 7 years?
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.
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.?
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
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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"?
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 division expression using a division symbol and as a fraction 7 divided by x
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]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
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]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?
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 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
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]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
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]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
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.
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.
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.
how many terms the expression x^3+4x^2+2x^-9
How many terms the expression
x^3+4x^2+2x^-9? 3 TERMS
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?
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
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]Find sum of the pairs of complex numbers.2,8
Given:
Complex numbers are 2 and 8.
Required:
We need to find the sum of the complex numbers.
Explanation:
The given complex can bw\e written as follows.
[tex]2+i(0)\text{ and }8+i(0).[/tex][tex]Add\text{ }2+i(0)\text{ and }8+i(0)[/tex][tex](2+i(0))\text{ + \lparen}8+i(0))=(2+8)+i(0+0)[/tex][tex](2+i(0))\text{ + \lparen}8+i(0))=10+i(0)[/tex]Final answer:
[tex]10[/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?
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 = 6The 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.
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 sector of a circle that has a central angle of \Pi radians and a radius of 0.7 in.Round your answer to the nearest hundredth.The area is ___ in^2
In order to find the area of the sector, let's consider the formula for the area of a circle:
[tex]A=\pi r^2[/tex]The complete circle is equivalent to a sector with central angle 2pi. Knowing this, we can write the following rule of three:
[tex]\begin{gathered} central\text{ }angle\rightarrow area \\ 2\pi\rightarrow\pi r^2 \\ \pi\rightarrow x \end{gathered}[/tex]Now, we can write the following proportion and solve it for x:
[tex]\begin{gathered} \frac{2\pi}{\pi}=\frac{\pi r^2}{x}\\ \\ 2x=\pi r^2\\ \\ x=\frac{\pi r^2}{2}=\frac{\pi\cdot0.7^2}{2}=0.77\text{ in^^b2} \end{gathered}[/tex]Therefore the area is 0.77 in².
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?
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!
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?
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.
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
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.
Hi can anybody help me with this?(there is a part two)
ANSWER:
Part A.
D. 6(p - 0.5) = 5.10
Indenting the zeros and state their multiplicities describe the effect on the graph
Answer:
6) The given equation is,
[tex]f(x)=(x+7)^2(2x+1)(x-4)^3[/tex]we know that,
The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity.
we get,
Zero Multiplicity Effect
-7 2 Touches the x axis at x=-7
-1/2 1 Passese through the x axis at x=-1/2
4 3 Passes through the point and the curve bend at x=4
9. Find the equation(s) of the line(s) through (2,-2) if the sum of the intercer 10. Find the angle that line l, makes with line l. (a) hirty 10, 4:3x - 2y=5 (b) 1,: 2x + 3y = 6,1 -11. Find the coordinates of the point. (a) equidistant from (4.-) and the origin; as well as on the line 2 (b) equidistant from (3, 8) and (-2,5) on the y-axis (c) J x + 3y = 7 5.1 - 6 = -28 12. Find the equation of the line passing through the point (4.-1) and
Let:
[tex]\begin{gathered} x+3y=7_{\text{ }}(1) \\ 5x-6y=-28_{\text{ }}(2) \end{gathered}[/tex]From (1):
[tex]x=7-3y_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 5(7-3y)-6y=-28 \\ 35-15y-6y=-28 \\ 35-21y=-28 \\ -21y=-63 \\ y=\frac{-63}{-21} \\ y=3 \end{gathered}[/tex]Replace the value of y into (3):
[tex]x=7-3(3)=7-9=-2[/tex]Therefore:
x = -2
y = 3
or
(x,y) = (-2,3)