Given points (1,-3) and (5,-1).
Since the slope of the line passing through two points
[tex](x_1,y_1)(x_2,y_2)[/tex]The slope of the equation is
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-(-3)}{5-1} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]Therefore, the slope of the line is 1/2.
Now, use the slope and the point (1,-3) to find the y-intercept.
[tex]\begin{gathered} y=mx+c \\ -3=\frac{1}{2}\times1+c \\ c=-3-\frac{1}{2} \\ c=-\frac{-7}{2} \end{gathered}[/tex]Write the equation in slope-intercept form as
[tex]\begin{gathered} y=mx+c \\ y=\frac{1}{2}x-\frac{7}{2} \end{gathered}[/tex]2. Consider drawing a card at random from a standard deck of cards,Part A: Determine the probability that the card is a spade, given that it is black,Part B: Determine the probability that the card is red, given that it is a heart,Part C: Determine the probability that the card is an ace, given that it is black.Part D: Determine the probability that the card is a queen given that it is a face card,
Consider drawing a card at random from a standard deck of cards,
Part A: Determine the probability that the card is a spade, given that it is black,
Part B: Determine the probability that the card is red, given that it is a heart,
Part C: Determine the probability that the card is an ace, given that it is black.
Part D: Determine the probability that the card is a queen given that it is a face card,
we have 52 cards
A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)
so
Part A: Determine the probability that the card is a spade, given that it is black,
If the card is black, that means the possible outcomes are 26 cards
so
P=13/26
P=0.5Part B: Determine the probability that the card is red, given that it is a heart,
if the card is a heart, that means, the possible outcomes are 13
so
P=13/13
P=1because all the cards that are heart are red
Part C: Determine the probability that the card is an ace, given that it is black.
if the card is black the possible outcomes are 26
therefore
P=2/26
P=1/13Part D: Determine the probability that the card is a queen given that it is a face card
what is the equation of the line passing through (-4,0) and (01)
The perimeter of a parallelogram is 76 meters. The width of the parallelogram is 2 meters less that it’s length. Find the length and the width of the parallelogram.
Answer:
The length of the parallelogram is 20 meters.
The width of the parallelogram is 18 meters.
Explanation:
The perimter of a parallelogram is calculated by addition of the lengths of all the enclosed sides.
⇒ x + (x - 2) + x + (x -2) = 76
Remove the brackets
x + x - 2 + x + x - 2 = 76
Collecting the like terms, we have
4x - 4 = 76
4x = 80
x = 80/4
x = 20 meters, which is the length of the parallelogram.
For width, we have,
20 - 2 = 18 meters.
Answer:
The length of the parallelogram is 20 meters.
The width of the parallelogram is 18 meters.
Explanation:
The perimter of a parallelogram is calculated by addition of the lengths of all the enclosed sides.
⇒ x + (x - 2) + x + (x -2) = 76
Remove the brackets
x + x - 2 + x + x - 2 = 76
Collecting the like terms, we have
4x - 4 = 76
4x = 80
x = 80/4
x = 20 meters, which is the length of the parallelogram.
For width, we have,
20 - 2 = 18 meters.
Frank will choose 7 colors to use for an art project. If there are 10 colors to choose from, how many different color combinations are possible?
120
Explanation:
total colours = 10
number of colours to be chosen = 7
We apply combination
The different color combinations possible:
[tex]^{10}C_7=\frac{10!}{(10-7)!7!}[/tex][tex]\begin{gathered} =\frac{10!}{3!7!}=\frac{10\times9\times8\times7!}{3\times2\times1\times7!} \\ =\frac{720}{6} \\ \text{= 120} \end{gathered}[/tex]The different color combinations possible is 120
match the function rule with the graph of the function (number 24)
It is given that the function is:
[tex]y=\frac{3}{4}\times4^x[/tex]Therefore y=0 then the value of x will be:
[tex]\begin{gathered} 0=4^x \\ x=-\infty \end{gathered}[/tex]Now at x=0, y will be:
[tex]y=\frac{3}{4}[/tex]at x=1, y will be:
[tex]y=\frac{3}{4}\times4=3[/tex]These 3 points that is (-inf,0),(0,3/4),(1,3) are on graph D.
Hence option D is coreect.
Ms. Kirk has at most $75 to spend on workout supplements. She boughtthree containers of protein powder for $47. She wants to buy protein barsthat cost $4 each. How many protein bars can she buy?
total money is 75$
protein cost = 47$
so the remaining money is
75 - 47 = 28 $
now she bought the protein bars of 28$
cost of one protein bar is 4$
so the number of protein bars that she bought is
[tex]=\frac{28}{4}=7[/tex]so she bought 7 protein bars.
At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner radius is 7 yd and its outer radius is 9 yd.We are going to give a new layer of coating to the path. If one gallon of coating can cover 5v * d ^ 2 how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for pi.)
Question 37?Find the indicated function and state its domain in interval notation?
Given the functions:
[tex]\begin{gathered} f(x)=-\sqrt[]{x-3} \\ g(x)=3x \end{gathered}[/tex]You need to multiply them, in order to find:
[tex](f\cdot g)(x)[/tex]Then, you get:
[tex]\begin{gathered} (f\cdot g)(x)=(-\sqrt[]{x-3})(3x) \\ (f\cdot g)(x)=-3x\sqrt[]{x-3} \end{gathered}[/tex]In order to find the Domain, you need to remember that the Domain of a Radical Function are those input values (x-values) for which the Radicand is positive. Then, in this case, you need to set up that:
[tex]x-3\ge0[/tex]Now you have to solve for "x":
[tex]x\ge3[/tex]Therefore:
[tex]Domain\colon\lbrack3,\infty)[/tex]Hence, the answer is:
[tex]\begin{gathered} (f\cdot g)(x)=-3x\sqrt[]{x-3} \\ \\ Domain\colon\lbrack3,\infty) \end{gathered}[/tex]To achieve mastery of this lesson, make sure you develop responses to the following questions: How are exponential functions graphed? How do you compare exponential functions? How do you transform exponential functions? help
For exponential functions, it is found that:
They are graphed looking at the asymptote, the intercept, the rate of change and the end behavior.They are compared by the rate of change.They are transformed with translations and stretching/compression.What is an exponential function?An exponential function is modeled according to the rule presented as follows:
[tex]y = ab^x + c[/tex]
In which the coefficients of the rule are given as follows:
a is the intercept of the function, the value of y when it crosses the y-axis.b is the rate of change of the function.c is the asymptote of the function.To graph the function, along with the coefficients of the function, the end behavior of the function is needed, as follows:
Limit of y when x goes to negative infinity: gives the behavior at the left end of the graph.Limit of y when x goes to positive infinity: gives the behavior at the right end of the graph.They are compared by their rate of changes, if they are increasing/decreasing, and which one increases faster.
The transformations are as follows:
Translation: a constant is added to either x or y(changing the asymptote if y), meaning that the function can be moved down, up, left or right.Stretching: a constant multiplies x or y, meaning that the graph can be either compressed or stretched vertically or horizontally.More can be learned about exponential functions at https://brainly.com/question/25537936
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O GRAPHS AND FUNCTIONSWriting an equation for a function after a vertical and horizo
Given:
The point (0,0) lies on the graph f(x) and (4,-3) lies on the graph h(x).
To find:
We need to find the equation for the function h(x).
Explanation:
Consider the translation point which is translated horizontally a unit and vertically as b units.
[tex](x^{\prime},y^{\prime})\rightarrow(x+a,y+b)[/tex]The point (4,-3) can be written as follows.
[tex](4,-3)\rightarrow(0+4,0-3)[/tex]We get the function h(x) after f(x) translated horizontally 4 units right and vertically 3 units down.
The function can be written as follows.
[tex]h(x)=f(x-4)-3[/tex][tex]\text{Replace x=x-4 in f(x)=}\sqrt[]{x\text{ }}\text{ and substitute in the equation.}[/tex][tex]h(x)=\sqrt[]{x-4}-3[/tex]Final answer:
[tex]h(x)=\sqrt[]{x-4}-3[/tex]Determine the value of b for which x = 1 is a solution of the equation shown.
2x + 14 = 10x + b
b=
Answer
Step-by-step explanation:
solve for b.
2x+14=10x+b
Step 1: Flip the equation.
b+10x=2x+14
Step 2: subtract 10x from both sides.
b+10x+−10x=2x+14+−10x
b=−8x+14
Answer:
b=−8x+14
Use the slope formula to find the slope of the line that passes through the points (5,2) and (13,3)A)m=7B)m=-2/11C)m=1/8D)m=3/11
Given the word problem, we can deduce the following information:
1. The line that passes through the points (5,2) and (13,3).
We can get the slope of the line using the slope formula:
Based on the given points, we let:
We plug in what we know:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{3-2}{13-5} \\ \text{Simplify} \\ m=\frac{1}{8} \end{gathered}[/tex]Therefore, the answer is c. m=1/8.
need help please 16x=-44-4y
-8x=28+4y
Answer: (x,y)= (-2/5,-43/5)
Step-by-step explanation:
The formula for the perimeter of a
rectangle is P = 2l + 2w. Solve the formula for
w.
Select the graph for the solution of the open sentence. Click until the correct graph appears. Ix| + 3 > 3
Given the sentence;
[tex]\mleft|x\mright|+3>3[/tex]Subtracting 3 from both sides;
[tex]\begin{gathered} \mleft|x\mright|+3>3 \\ |x|+3-3>3-3 \\ \mleft|x\mright|>0 \end{gathered}[/tex]Given the absolute value of x to be greater than zero, the range of value of x is;
[tex]\begin{gathered} x>0 \\ or \\ x<0 \end{gathered}[/tex]Therefore, the correct graph of the solution is;
The following circle passes through the origin. Find the equation.
Answer
(x - 2)² + (y - 2)² = 8
Step-by-step explanation
The equation of the circle centered at (h, k) with radius r is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this case, the center of the circle is the point (2, 2), then h = 2 and k = 2, that is,
[tex](x-2)^2+(y-2)^2=r^2[/tex]Given that the circle passes through the center, then the point (0, 0) satisfies the above equation. Substituting x = 0 and y = 0 into the equation and solving for r²:
[tex]\begin{gathered} (0-2)^2+(0-2)^2=r^2 \\ 4+4=r^2 \\ 8=r^2 \end{gathered}[/tex]Substituting r² = 8 into the equations, we get:
[tex](x-2)^2+(y-2)^2=8[/tex]Solve the following system of equations graphically on the set of axes below. Plot two or more dotes on the graphy = 2x - 8 y = -x + 4
Given:-
[tex]y=2x-8,y=-x+4[/tex]To find the graphical representation.
So the graph of y=2x-8 is,
Also the graph of y=-x+4 is,
Combining we get the graph
So the point is (4,0).
Use the rectangle at the right to answer the following questions. a. Find the area of the entire rectangle. Show your work. b. Calculate the perimeter of the figure. Show your work.
Length of the entire rectangle = 12 + 5 = 17
Width of the entire rectangle = 6+4 = 10
Part a
Area of rectangle = Length x width
Area of the entire rectangle = 17 x 10 = 170 square units
Part b
Perimeter of rectangle = 2( length + width )
Perimeter of the entire rectangle = 2(17 + 10 )
=2 (27) = 54
Perimeter of the entire rectangle = 54 units
Length of the entire rectangle = 12 + 5 = 17
Width of the entire rectangle = 6+4 = 10
Part a
Area of rectangle = Length x width
Area of the entire rectangle = 17 x 10 = 170 square units
Part b
Perimeter of rectangle = 2( length + width )
Perimeter of the entire rectangle = 2(17 + 10 )
=2 (27) = 54
Perimeter of the entire rectangle = 54 units
Hannah is saving money to buy some lirns. She invests $290 in a savings account that earns 7.6% interest, compounded annually. How much money will she have in her account after 2 years? Answer in dollars and round to the nearest cent.
Principal amount, P= $290.
Rate, r = 0.076
Time, t = 2
Therefore, the total amount in her account after 2 years is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Hence,
[tex]\begin{gathered} A=290(1+0.076)^2 \\ =335.755 \end{gathered}[/tex]Therefore, the amount is 335.80 dollars.
That is, 335 dollars and 80 cents.
Model x2 + 3x + 5 in the Gizmo by dragging or clicking blue x?-tiles, green x-tiles, and yellow 1-tilesinto the top bin. How many of each type of tile did you use?
A.
x^2 and 2x^2 means:
3 x^2 tiles
3x - 4x = -x
ONE -x tiles
5 - 1 is "4"
B.
2x^2 - 4x - 1
This is just an expression
so there are 2 x^2 tiles, 4 -x tiles and one 1-tiles
Use the distance formula to calculate the length of the leg CD
To calculate the distance between two points on the coordinate system you have to use the following formula:
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Where
d represents the distance between both points.
(x₁,y₁) are the coordinates of one of the points.
(x₂,y₂) are the coordinates of the second point.
To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph
C(2,-1)
D(-1,-2)
Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)
[tex]\begin{gathered} d_{CD}=\sqrt[]{(2-(-1))^2+((-1)-(-2))}^2 \\ d_{CD}=\sqrt[]{(2+1)^2+(-1+2)^2} \\ d_{CD}=\sqrt[]{3^2+1^2} \\ d_{CD}=\sqrt[]{9+1} \\ d_{CD}=\sqrt[]{10} \end{gathered}[/tex]The length of CD is √10 units ≈ 3.16 units
13. slove for x so the [tex]f(x) = 5[/tex]
Solution
We have the following function given:
f(x) = -3x+5
And we need to do the following:
5= -3x+5
And if we subtract 5 in both sides we got:
0 =-3x
Dividing both sides by -3 we got:
[tex]\frac{0}{-3}=\frac{-3x}{-3}[/tex]And finally we got:
x= 0
Problem 17
17) f(-2)= 3
18) f(0)= 3
19) f(1)= 0
20) f(-1)= 5.2
Solve any quality express your answer in interval notation you decimal forms for numerical values
Solution
[tex]\begin{gathered} 5z-11<-6.6+3z \\ Subtract\text{ 3z from both side} \\ 5z-3z-11<-6.6+3z-3z \\ 2z-11<-6.6 \\ Add\text{ 11 to both sides } \\ 2z-11+11<-6.6+11 \\ 2z<4.4 \\ \end{gathered}[/tex][tex]\begin{gathered} Divide\text{ both sides by 2} \\ \frac{2z}{2}<\frac{4.4}{2} \\ z<2.2 \\ z<2.2 \end{gathered}[/tex]In interval notation, we have
[tex]\left(-\infty \:,\:2.2\right)[/tex]The answer is
[tex]\left(-\infty \:,\:2.2\right)[/tex]The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 433 ft long and 4 mm in diameter has a resistance of 1.22 ohms, find the length of a wire of the same material whose resistance is 1.43 ohms and whose diameter is 5 mm.
Given:
The resistance
in the inequality 6a+4b>10, what could be the possible value of a if b=2?
We are given the following inequality:
[tex]6a+4b>10[/tex]If we replace b = 2, we get:
[tex]\begin{gathered} 6a+4(2)>10 \\ 6a+8>10 \end{gathered}[/tex]Now we solve for "a" first by subtracting 8 on both sides:
[tex]\begin{gathered} 6a+8-8>10-8 \\ 6a>2 \end{gathered}[/tex]Now we divide both sides by 6
[tex]\frac{6a}{6}>\frac{2}{6}[/tex]Simplifying:
[tex]a>\frac{1}{3}[/tex]Therefore, for b = 2, the possible values of "a" are those that are greater than 1/3
5. Noah is solving an equation and one of his moves is unacceptable. Hereare the moves he made. Which answer best explains why the "divide eachside by x step is unacceptable? *2(3+6) - 4= 8 + 6321 + 12 - 4= 8 + 612.1 + 8 = 8 + 6.120 = 602 = 6original equationapply the distributive propertycombine like termssubtract 8 from both sidesdivide each side by IO When you divide both sides of 2x = 6x by x you get 2x^2 = 6x^2.When you divide both sides of 2x = 6x by x it could lead us to think that there is nosolution while in fact the solution is x = 0..aWhen you divide both sides of 2x = 6x by x you get 2 = 6x.aOWhen you divide both sides of 2x = 6x by x it could lead us to think that there is nosolution while in fact the solution is x = 3..
SOLUTION
Write out the original equation
[tex]2(x+6)-4=8+6x[/tex]Then, Apply the distributive property on the left hand side of the equation
[tex]\begin{gathered} 2x+12-4=8+6x \\ 2x+8=8+6x \end{gathered}[/tex]Then combine trhe like terms subtracting 6x from both side
[tex]\begin{gathered} 2x+8-6x=8+6x-6x \\ 2x-6x+8=8 \end{gathered}[/tex]Subtract 8 from both sides of the last equation
[tex]\begin{gathered} 2x-6x+8-8=8-8 \\ 2x-6x=0 \\ -4x=0 \\ \end{gathered}[/tex]hence
Divide both sides by -4, we have
[tex]\begin{gathered} -\frac{4x}{-4}=\frac{0}{-4} \\ \text{Then} \\ x=0 \end{gathered}[/tex]Therefore, the solution is x=0
Hence
When we divide both sides of the equation by x, we have
[tex]\begin{gathered} \frac{2x}{x}=\frac{6x}{x} \\ 2=6 \\ \text{which implies thier is no solution} \end{gathered}[/tex]While the solution is x=0
Therefore
When we divide the equation by 2x=6x by x it could lead us to think that there is no solution while the solution is x=0
Answer; The second option is right
the figure below has a point marked with a large. First translate to figure 4 units up then give the coordinates of the mark point in the original figure in the final figure.:
Large point coordinates (original)= (1,-4)
To obtain the coordinates of the new point, add 4 to the y coordinate.
(1,-4+4) = (1,0)
the math club has 18 members and 50% are sixth graders.The science club has 25 members and 40% are sixth graders. The principal wants to know which club has more sixth graders.
The science club had more sixth graders.
How to calculate the value?The math club has 18 members and 50% are sixth graders. The number of sixth graders will be:
= Percentage × Number of members
= 50% × 18
= 0.5 × 18
= 9
The science club has 25 members and 40% are sixth graders. The number of sixth graders will be:
= Percentage × Number of members
= 40% × 25
= 0.4 × 25
= 10
Since 10 is more than 5, the science class has higher number.
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Hi, i tried to solve this problem, but I can't manage to do it, can you help me ?
Length of y is 25.2.
Given:
The angle is given as 35 degree and a side is 36.
The objective is to find the length of the side y.
In a right angled traingle, the side opposite to the given angle is called oppotise side, the other smaller side is called adjacent side and the longer side is called hypotenuse.
Here, opposite side is y and adjacent side is 36.
Then, the relationship between oppsote and adjacent can be calculated using the trigonometric ratio of tan theta.
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 35^0=\frac{y}{36} \\ y=36\cdot\tan 35^0 \\ y=36(0.7) \\ y=25.2 \end{gathered}[/tex]Hence, the length of y is 25.2.
Marco states that 7.696696669...... is a rational numberbecause it is a repeating decimal. Is he correct? Justifyyour answer.Yes he is correct because it keeps going and going and it will go on forever and ever so that is my guess
The answer is NO, Marco is wrong.
The number 7.696696669.... has not a repeating decimal there is no a number that is repeating, like 0.6969696969... in the last number the 69 is repeating, in the Marco's number the decimal number change every time.