We need two ordered pairs of the table
(12,6)=(x1,y1)
(14,8)=(x2,y2)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-6}{14-12}=\frac{2}{2}=1[/tex]the equation is
[tex]\begin{gathered} y-6=1(x-12) \\ y=x-12+6 \\ y=x-6 \end{gathered}[/tex]the equation is
y=x-6
Question 11
11 of 12
Which choice shows 13*07*4) correctly rewritten using the associative property and
then correctly simplified?
O (1347)*4=91*4=364
O 13*(4*7)=13*28=364
o 13*4*7=52*7=364
O (13*74)=962
Question ID: 116141
Submit
The associative property states that the way the factors are grouped in a multiplication does not change the result.
Grouping 7 and 4
13 * (4*7) = 13 *(28 ) = 364
13 and 7
(13*7)*4 = 91*4= 364
13 and 4
(13*4)*7 = 52*7 = 364
So, the correct options are a and b ( the first 2 options)
3.2= -4w+9.6 Solve for w
The given expression is,
[tex]3.2=-4w+9.6[/tex]On solving we have,
[tex]\begin{gathered} 4w=9.6-3.2=6.4 \\ w=\frac{6.4}{4}=1.6 \end{gathered}[/tex]Thus, the value of w
Find the value of c using the given chord and secant lengths in the diagram shown to right . c= (Round to the nearest tenth as needed .)
ANSWER
c = 6.4
EXPLANATION
The intersecting chords theorem says that the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.
One secant segment is (9+19) and its external segment is 9. The other is (13+c) and its external segment is 13:
[tex]9\cdot(9+19)=13\cdot(13+c)[/tex]Solving for c:
[tex]\begin{gathered} 9\cdot28=13^2+13c \\ 252=169+13c \\ 252-169=13c \\ 83=13c \\ c=\frac{83}{13} \\ c=6.3846\ldots \\ c\approx6.4 \end{gathered}[/tex]if f(x) = 3x⁴ + x² + 3 then what is the remainder when f(x) is divided by x + 1
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).
suppose you want to subtract: -4-(-2)
SOLUTION
To answer this question, let us first understand some rules that guide operations as this:
[tex]\begin{gathered} -\times-=+ \\ -\times+=- \\ +\times+=+ \\ +\times-=- \end{gathered}[/tex]So going back to treat this question:
[tex]-4-(-2)[/tex]Re-writing this subtraction as an ADDITION of signed numbers, we will have:
[tex]\begin{gathered} -4-(-2) \\ =-4+2 \end{gathered}[/tex]Now to complete this problem the final solution will result in:
[tex]\begin{gathered} =-4+2 \\ =-2 \end{gathered}[/tex]The final answer is -2
Solve for a 76=4/5a+16
Answer:
a=75
Step-by-step explanation:
76=4/5a+16
first get the a term by itself on one side
76-16=4/5a
simplify
60=4/5a
now divide both sides by 4/5 or multiply by 5/4(its the same thing)
60*5/4=4/5a*5/4
now simplify
75=a
Suppose f(x)= 2+4x^2.Simplify as much as possible: f(1)/f(2)= ______
Given,
The expression is,
[tex]f(x)=4x^2+2[/tex]Taking x =1,
Subsituting the value of x in the given function then,
[tex]\begin{gathered} f(1)=4(1)^2+2 \\ =4\times1+2 \\ =4+2 \\ =6 \end{gathered}[/tex]Taking x =2,
Subsituting the value of x in the given function then,
[tex]\begin{gathered} f(2)=4(2)^2+2 \\ =4\times4+2 \\ =16+2 \\ =18 \end{gathered}[/tex]Divide f(1) by f(2) then,
[tex]\frac{f(1)}{f(2)}=\frac{6}{18}=\frac{1}{3}[/tex]Hence, the simplified value is 1/3.
I get 15 percent discount at a store if I find a I like for 40 how much will I have to pay for it
price: $40
Given that you get a 15% discount, you get a discount of $40*15% = $6.
Then, you have to pay $40 - $6 = $34
One number is five more than three times another. If their sum is increased by one, the result is twenty-six. Find the numbers.The smaller of the numbers is ? and the larger is ? .
Let:
x = The smaller number
y = The larger number
[tex]y=3x+5_{\text{ }}(1)[/tex][tex]x+y+1=26_{\text{ }}(2)[/tex]Replace (1) into (2):
[tex]x+3x+5+1=26[/tex]Add like terms:
[tex]4x+6=26[/tex]Solve for x:
[tex]\begin{gathered} 4x=26-6 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Replace x into (1):
[tex]\begin{gathered} y=3(5)+5 \\ y=20 \end{gathered}[/tex]Answer:
The smaller number is 5
The larger number is 20
You invested $5000 between two accounts paying 7% and 8% annual interest. If the total interest earned for the year was $380, how much was invested at each rate?
Let x be the amount invested in the account paying 7% and y the amount invested in the account paying 8%, then we can set the following system of equations:
[tex]\begin{gathered} x+y=5000 \\ 0.07x+0.08y=380 \end{gathered}[/tex]Solving the first equation for x and substituting it in the second equation we get:
[tex]0.07(5000-y)+0.08y=380[/tex]Solving for y we get:
[tex]\begin{gathered} 350-0.07y+0.08y=380 \\ 0.01y=30 \\ y=3000 \end{gathered}[/tex]Substituting y=3000 in the first equation and solving for x we get:
[tex]\begin{gathered} x+3000=5000 \\ x=2000 \end{gathered}[/tex]Therefore, $2000 was invested in the account paying 7%, and $3000 was invested in the account paying 8%.
Mrs. Peck is making school supply baskets. She purchased 27 composition booksand 9 packs of map pencils. Which shows the ratio of packs of map pencils tocomposition books.
Number of composition books: 27
Number of packs of map pencils: 9
The ratio of packs of maps pencils to composition books: 9 to 27
9/27 = 1/3
1:3
Consider the functions f(x)=4-X^2 and g(x)=3x+5.Find the value of f(g)g-2))).
Solution
First find the g(x)
g(-2)= 3(-2) +5
g(-2)= -6+5
g(-2)= -1
substitute for x in f(x) when x is -1
[tex]\begin{gathered} F(-1)=4-(-1)^2 \\ F(-1)\text{ = 4-1} \\ F(-1)\text{ =3} \end{gathered}[/tex]The correct option is the last option
If the probability of an event is what is the probability of the event not happening?20/69Write your answer as a simplified fraction.
If an event has a probability P of happening, then there is a probability of (1-P) of the event not happening.
In this case the probability of the event is p=20/69.
Then, the probability of the event not happening is:
[tex]P(\text{not happening})=1-p=1-\frac{20}{69}=\frac{69-20}{69}=\frac{49}{69}[/tex]Answer: the probability of the event not happening is 49/69.
 A scuba diver is swimming at a depth of 70 feet .He descended at a rate of 5 feet every 12 seconds.At this rate ,how many seconds did it take for the diver to reach the depth of 70 feet?
Which expression fits this description? • The expression is the quotient of two quantities. • The numerator of the expression is the product of 5 and the sum of x and y. • The denominator is the product of negative 8 and x. 5x + y 5(x + y) - (8 + x) 5x + y –8+x 5(x + y) -82 - 8x Done -
Given the word problem:
The numerator of the expression is the product of 5 and the sum of x and y and The denominator is the product of negative 8 and x.
The numerator will be the value on top in a fraction.
Here, the numerator is the product of 5 and the sum of x and y ==> 5(x + y)
The denominator is the value below in a fraction.
Here, the denominator is the product of negative 8 and x ==> -8x
Therefore, the expression that fits this description is:
[tex]\frac{5(x+y)}{-8x}[/tex]c-884= -853solve for c
c-884= -853
solve for c
that means Isolate the variable c
so
step 1
Adds 884 both sides
c-884+884=-853+884
simplify
c=31A. Find the domain of f(x). Write your answer in interval notation.B. Find the range of f(x). Write your answer in interval notation.C. Find the following:i. f(0)ii. f(-2)iii. f(8)iv. f(3)V. fl-1)D. Find all x's (approximately) such that f(x)=1.
A) D = [-8, 5) U [-4, -1) U (-1, 3] U (3, 5) U [6,8]
B) R =(-7,-5) U (-4,5] U [6, 7]
C)
i. f(0) = 1
ii. f(-2) = 1
iii. f(8) = 7
iv. f(3) = 4
D.
x= 1,
x= -2
x= -4
x = -7.7 (approximately)
A) Examining the graph, we can write the Domain (the set of entries) as:
D = [-8, 5) U [-4, -1) U (-1, 3] U (3, 5) U [6,8]
Note that as we're dealing with the Real Set there are infinite values within each interval. And the Domain is the union of all intervals.
B) Examining that, for the Range (Outputs) y-axis, we can write the following:
R =(-7,-5) U (-4,5] U [6, 7]
Note that as there are some discontinuities we can't write them as a unique interval.
C) For this item, let's find out each value by locating the y-coordinate on the graph when the value of x is within the parentheses:
i. f(0) = 1 When x = 0, y = 1
ii. f(-2) = 1
iii. f(8) = 7
iv. f(3) = 4
Note that for this value, we have an open dot for -5 so it does not include it
v. f(-1) = Undefined
Both open dots
D. When f(x) = 1, i.e. y= 1 we have the following x-coordinates:
x= 1,
x= -2
x= -4
x = -7.7 (approximately)
4. Look at the figures below.How was each point of Polygon ABCDE shifted to get Polygon BCDE?A right I unit and down 4 unitsBright I unit and down 1 unitC. left 1 unit and up 4 unitsD. left I unit and up 1 unitTi
Given a polygon ABCDE with the coordinates
[tex]A(-7,2),B(-8,4),C(-6,5),D(-5,6),E(-5,3)[/tex]The image of the polygon has vertices A'B'C'D'E' with coordinates
[tex]A^{\prime}(-6,-2),B^{\prime}(-7,0),C^{\prime}(-5,1),D^{\prime}(-4,2),E^{\prime}(-4,-1)[/tex]The transformation rule as observed from the image is
[tex](x,y)\Rightarrow(x+1,y-4)[/tex]Hence, the polygon has been shifted to the right by 1 unit and down by 4 units
Option A is the right answer
The dollar value v(s) of a certain car model that is t years old is given by» (t) = 25.900(0,92)Find the initial value of the car and the value after 12 years.Round your answers to the nearest dollar as necessary.Initial value:Value after 12 years.sx 5 ?
we have the following:
[tex]\begin{gathered} v(t)=25900\cdot(0.92)^t \\ v(0)=25900\cdot(0.92)^0=25900\cdot1=25900 \\ v(12)=25900\cdot(0.92)^{12}=25900\cdot0.3676=9522.56 \end{gathered}[/tex]therefore, tue intial value is 25900 and value after 12 yeras is 9523
If we use RH as the base of this triangle, the height is ___ units.
ANSWER
[tex]6\text{ units}[/tex]EXPLANATION
To find the height of the triangle, using RH as the base, we simply have to find the vertical distance between the base and the top of the triangle.
To do that, find the difference between the y-coordinates of the top and the bottom of the triangle.
That is:
[tex]\begin{gathered} 8-2 \\ 6\text{ units} \end{gathered}[/tex]The height of the triangle is 6 units.
Can you please help me out with a question
ANSWER:
[tex]\text{center}=(\frac{3}{2},-\frac{1}{2})[/tex]STEP-BY-STEP EXPLANATION:
The center of the circle would be the mean value between the end points, and we can calculate it like this:
[tex]\begin{gathered} (M_1,M_2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{replacing} \\ (M_1,M_2)=(\frac{-2+5_{}}{2},\frac{-4+3_{}}{2}) \\ (M_1,M_2)=(\frac{3_{}}{2},-\frac{1_{}}{2}) \end{gathered}[/tex]30.4. The figure below is going to be enlarged so that the area of the new, similar shape will be 400 cm?. What will the perimeter of the new, enlarged shape be?5 cm24. Perimeter of enlarged shape=cmicm10 cmArea = 100 cm2
Q. 4:
We are asked to find the perimeter of the enlarged shape.
The perimeter of the enlarged shape can be found by multiplying the scale factor with the perimeter of the original shape.
The scale factor is the ratio of the area of the enlarged shape to the area of the original shape.
[tex]SF=\frac{400\;cm^2}{100\;cm^2}=4[/tex]So, the scale factor is 4.
The perimeter of the original shape can be found by adding all the side lengths.
[tex]P=5+4+10+6+3+2=25\;cm[/tex]So, the perimeter of the original shape is 25 cm
Finally, the perimeter of the enlarged shape is
[tex]P=4\times25=100\;cm[/tex]Therefore, the perimeter of the enlarged shape is 100 cm
What is the 6th term in the geometric sequence described by this explicitformula?an = 500. (0.5)(n-1) choose one A. 1250B. 7.8125C. 15.625OD. 12,500
a6=?
[tex]a_6=500\times0.5\times(6-1)[/tex][tex]a_6=250\times5=1250[/tex]option A
select the point(s) of the x intercept of the function shown below
ANSWER:
(-1, 0) and (3, 0)
STEP-BY-STEP EXPLANATION:
The x-intercept is the points where the graph crosses the x-axis, we can calculate it graphically like this:
Identify which of the following graphs is the graph of two equivalent vectors.
By definition, two vector are equivalent when they have the same length, and they point in the same direction. Any two or more vectors will be equal if they are collinear, codirected, and have the same magnitude.
Two Step problem:STEP 1: 7x^2 = -4using the standard form ax^2 +bx + c =0 of the given quadratic equation, factor the left hand side of the equation into two linear factors. STEP 2: 7x^2 = -4xsolve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary. PICTURE OF ANSWER BOX ATTACHED: is for step #2
Step 1
x(7x+4)
Step2
x_1=0, x_2 =-4/7
Step 1)
1) Let's factor that incomplete quadratic equation (since c=0):
7x² = -4x Add 4x to both sides
7x² + 4x = 0 Place outside the parenthese the common factor: x
x(7x+4) = 0
Step 2)
Now we can solve that:
x(7x+4)=0 Which number multiplied by x yields 0?
Then we can state that x_1 = 0
Solving that Linear Factor:
(7x +4) = 0 Removing the Parentheses
7x +4 = 0 Subtract 4 from both sides
7x = -4 Divide both sides by 7
x = -4/7
3) Hence, the answers are:
Step 1
x(7x+4)
Step2
x_1=0, x_2 =-4/7
4. The pair of events that is non-mutually exclusive is A. Turning over an odd number and turning over an even number B. Turning over a prime number and turning over a perfect square C. Turning over a one-digit number and turning over a two-digit number D. Turning over a multiple of 2 and turning over a multiple of 7 5. A student draws one card at random from a standard deck of 52 playing cards. The probability that the card is a diamond or a face card is A. 0.058 B. 0.077 C. 0.423 D. 0.481 Use the following information to answer the next question. On any particular Saturday evening, the probability that Hannah will go 1 to the movies and go for a coffee is The probability that she will go
In one deck we have Spades, Clubs, Hearts, and Diamonds. Each one has 13 cards and 3 face cards. So the let's do this step by step. The probability to get a diamond card is:
[tex]P(diamond)\text{ = }\frac{13}{52}[/tex](13 diamond cards in a total of 52). Then the probability to get a face card is:
[tex]P(facecard)\text{ = }\frac{12}{52}[/tex](12 face cards in a total of 52). We have to sum these probabilities but also we have to subtract the possibilities that include a card that is a face card and diamond (because if we don't do that we are going to count these cards two times). This probability is:
[tex]P(DiamondandFaceCard)\text{ = }\frac{3}{52}[/tex](We have only 3 cards in the deck that are diamond and face cards). Therefore, the probability will be:
[tex]\text{Probability = P(diamond) + P(facecard) - P(Diamond and Face Card)}[/tex][tex]\text{Probability = }\frac{13}{52}\text{ + }\frac{12}{52}\text{ - }\frac{3}{52}[/tex][tex]\text{Probability = }0.423[/tex]solve Equation: 4(x-6)=76
We have the next equation
[tex]4(x-6)=76[/tex][tex]\begin{gathered} x-6=\frac{76}{4} \\ x-6=19 \\ x=19+6 \\ x=25 \end{gathered}[/tex]Joanna is wrapping a present in the box shown.find the amount of wrapping paper in square inches that Joanna needs
First we need to convert 1 ft to inches
1ft= 12 in
We will use the formula of surface area
[tex]SA=2lw+2lh+2wh[/tex]where l is the length, w is the width and h is the height
In our case
l=12 in
w=8in
h=6 in
we substitute
[tex]SA=2(12)(8)+2(12)(6)+2(8)(6)[/tex]we simplify
[tex]SA=432\text{ in}^2[/tex]She needs 432 square inches
Nanny using using an app that shows him how many kilometers he has to run to prepare for a Marathon. The app says here an 8.0 45 kilometer who wants to Post online how many miles away Danny ran blank miles.(one mile = 1.609 km)
The conversion for distance in kilometer to miles is as,
[tex]\begin{gathered} 1\text{ mile=1.609 km} \\ 1\text{ km=}\frac{1}{1.609}\text{ miles} \end{gathered}[/tex]Determine the number of miles in 8.045 km.
[tex]\begin{gathered} 8.045\text{ km=8.045}\cdot\frac{1}{1.609}\text{ miles} \\ =5\text{ miles} \end{gathered}[/tex]So Nanny ran 5 miles.