Answer:
2x+19
Step-by-step explanation:
Let x be the number
2x+19
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
Find the equation of the line containing the following: (0,10) and (-5,0)
A linear equation in the slope-intercep form is y = mx + b.
To find the equation, follow the steps below.
Step 01: Substitute the point (0, 10) in the equation.
[tex]\begin{gathered} y=mx+b \\ 10=m\cdot0+b \\ 10=b \end{gathered}[/tex]Then,
[tex]y=mx+10[/tex]Step 02: Substitute the point (-5, 0).
[tex]0=-5m+10[/tex]Subtract 10 from both sides:
[tex]\begin{gathered} 0-10=-5m+10-10 \\ -10=-5m \end{gathered}[/tex]And divide both sides by -5:
[tex]\begin{gathered} \frac{-10}{-5}=\frac{-5}{-5}m \\ 2=m \end{gathered}[/tex]Step 03: Write the linear equation.
[tex]y=2x+10[/tex]Answer:
[tex]y=2x+10[/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
Question 9 of 10 What is the measure of 7 shown in the diagram below? 110- O A. 71• O B. 35.5° X C 32° 39- Z D. 74.50
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Diagram
arc vw = 110 °
angle = 39°
arc xy = ?
Step 02:
We must analyze the diagram to find the solution.
39 = 1/2 ( 110 - arc xy)
39*2 = 110 - arc xy
78 - 110 = - arc xy
- 32 = - arc xy
arc xy = -32 / - 1 = 32
The answer is:
arc xy = 32°
Answer:
Step-by-step explanation:
Answer is C
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
#SPJ1
what is the equation of the line passing through (-4,0) and (01)
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.
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
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.
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 formula for the perimeter of a
rectangle is P = 2l + 2w. Solve the formula for
w.
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
What is the max/min of the quadratic equation in factored form: f(x) = 0.5(x +3)(x-7)
F(x) = 1/2(x+3)(X-7)
Step 1 ; expand the function
F(x)= 1/2(x²-7x+3x-21)
F(x) = 1/2(x² - 4x-21)
F(x) = 1/2x² - 2x-21/2
Step 2 : Take the second derivative of F(x)
This means you are to differentiate F(X) twice
[tex]\begin{gathered} F(x)=\frac{1}{2}x^2-2x-\frac{21}{2} \\ \text{First derivative is} \\ F^!(x)\text{=x-2} \\ F^{!!}(x)=1 \\ \text{the second derivative =1} \end{gathered}[/tex]The second derivative is greater than 0, so it is a minimum point
Put x=1 in F(x) to find the value
[tex]\begin{gathered} f(x)=\frac{1}{2}(1)^2_{}-\text{ 2(1)-}\frac{21}{2} \\ f(x)=\frac{1}{2}-2-\frac{21}{2} \\ f(x)=-2-\frac{20}{2} \\ f(x)\text{ =-12} \end{gathered}[/tex]The minimum of the quadratic equation is -12
How do you know if something is one solution,no solution, or infinite solutions?
A linear equation can have solutions in three forms: one solution, no solution, and infinite solutions.
ONE SOLUTION EQUATION:
These are equations that will give only one solution when solved, such that the variable is equal to a single answer.
If the graph is drawn, the linear equations all cross or intersect at one point in space.
An example of a one-solution equation is shown below:
[tex]3x+5=2x-7[/tex]Solving this equation, we have:
[tex]\begin{gathered} 3x-2x=-7-5 \\ x=-12 \end{gathered}[/tex]We can therefore see that it has only one solution, one value for x which is -12.
NO SOLUTION EQUATION:
In this case, the coefficients of the variables on both sides of the equation are the same. Simplifying the equation will give an expression that is not true.
Graphically, the system is inconsistent and the linear equations do not all cross or intersect.
Consider the equation below:
[tex]2x+5=2x-7[/tex]If we attempt to solve the equation by subtracting 2x from both sides, we have the solution below:
[tex]\begin{gathered} 2x+5-2x=2x-7-2x \\ 5=-7 \end{gathered}[/tex]We can see that what we have left is not a valid statement, since 5 is not equal to -7:
[tex]5\neq-7[/tex]Thus, we can say that the equation has no solutions.
INFINITE SOLUTION EQUATION:
This follows the same format as the no solution equations. However, the final statement gotten from the simplification of the equation will give us a true statement instead.
Graphically, the linear equations are the same line in space and some variables are unconstrained.
Consider the equation below:
[tex]2x+5=2x+5[/tex]If we subtract 2x from both sides, we have:
[tex]\begin{gathered} 2x+5-2x=2x+5-2x \\ 5=5 \end{gathered}[/tex]Since the statement left is true, as 5 is equal to 5, then the equation has an infinite number of solutions.
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]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.
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]What percent of 120 is 30?
To find what percent of 120 is 30.
We will use the relationship
[tex]\frac{is}{of}\times100\text{ \%}[/tex]In our case
[tex]\begin{gathered} is=30 \\ of=120 \end{gathered}[/tex][tex]\frac{30}{120}\times100\text{ \%=25\%}[/tex]Thus, the answer is 25%
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
Writing and evaluating a function modeling continuous exponential growth or decay given doubling time or half-life
We were given the following details:
Half-life = 11 minutes
Initial amount = 598.8 grams
[tex]\begin{gathered} y=a_0e^{kt} \\ where\colon \\ y=amount \\ a_0=Initial\text{ }Amount \\ e=euler^{\prime}s\text{ }constant \\ k=decay\text{ }constant \\ t=time \end{gathered}[/tex]a)
We have the exact formula to be:
[tex]undefined[/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
solve the system by addition method x + 4y = 34x + 5y = - 10
y = 2
so,
x + 4 * 2 = 3
x = 3 - 4 * 2 = 3 - 8 = -5
so,
x = -5 and y = 2
A country with 16 states and a population of 615529 contains 128 seats in a House of Representatives.What is the average number of seats assigned per state?
Since there are 128 seats available and these 128 seats will be filled in by people from 16 states, we will divide 128 by 16 to get the average number of seats assigned per state.
[tex]128\div16=8[/tex]Therefore, the average number of seats assigned per state is 8.
Is the following relation a function? Justify your answer.
No, because there is an input value with more than one output value
No, because there is an output value with more than one input value
Yes, because each input value has only one output value
Yes, because each output value has only one input value
Answer:
A
Step-by-step explanation:
There are two inputs for one output, which means the relation is not a function.
Answer:
A
Step-by-step explanation:
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.
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
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.
Some fireworks are fired vertically into the air from the ground at an initial velocity of 80 feet per second. This motion can be modeled by the quadratic equation s(t) = -16t^2 + 80t. If a problem asks you to find how high the firework can go (this is the point where it explodes), what are they asking you for? (a) x coordinate of the vertex (b) y coordinate of the vertex (C) x coordinate of the roots (d) y coordinate of the roots
We are to know the highest point of the fireworks.
If we graph the quadratic, we will have a parabola with a maximum.
We basically want the maximum point. This occurs at the vertex.
• The x-coordinate of the vertex is at what time the maximum point occurs.
,• The y-coordinate of the vertex is the exact height (max).
Thus, when we are asked to find how high the firework can go, we will find the y-coordinate of the vertex.
Answer(b) y coordinate of the vertexFrank 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
3|x -1| > 9Group of answer choicesx> 4 or x < -2x > 4x < 4 or x > -2x > 7 or x < -5
Answer:
[tex]x\text{ > 4 or x < -2}[/tex]Explanation:
Here, we want to get the correct x values
We have this as follows:
[tex]\begin{gathered} 3|x-1|\text{ > 9} \\ =\text{ 3(x-1) > 9} \\ 3x-3\text{ > 9} \\ 3x\text{ > 9 + 3} \\ 3x\text{ > 12} \\ x\text{ > 12/3} \\ x\text{ > 4} \\ \\ OR \\ \\ -3(x-1)\text{ > 9} \\ -3x\text{ + 3 > 9} \\ -3x\text{ > 9-3} \\ -3x\text{ > 6} \\ x\text{ < 6/-3} \\ x\text{ < -2} \end{gathered}[/tex]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