To apply the zero product property we first need to write all the terms of the equation on side:
[tex]\begin{gathered} m^2=27-6m \\ m^2+6m-27=0 \end{gathered}[/tex]Now we need to factorise the expression on the right:
[tex]\begin{gathered} m^2+6m-27=0 \\ (m+9)(m-3)=0 \end{gathered}[/tex]The last line indicates that the product of two numbers is equal to zero this means that one of them has to be zero (this is the zero product property), then we have:
[tex]\begin{gathered} m+9=0 \\ m=-9 \\ or \\ m-3=0 \\ m=3 \end{gathered}[/tex]Therefore, the solutions of the equation are m=-9 and m=3
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.
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.
One function has an equation in slope-intercept form: y = x + 5. Another function has an equation in standard form: y + x = 5. Explain what must be different about the properties of the functions. See if you can determine the differences without converting the equation to the same form.
Without converting the equations to the same form, the property that must be different in the functions is the slope
How to determine the difference in the properties of the functions?From the question, the equations are given as
y = x + 5
y + x = 5
From the question, we understand that:
The equations must not be converted to the same form before the question is solved
The equation of a linear function is represented as
y = mx + c
Where m represents the slope and c represents the y-intercept
When the equation y = mx + c is compared to y = x + 5, we have
Slope, m = 1
y-intercept, c = 5
The equation y = mx + c can be rewritten as
y - mx = c
When the equation y - mx = c is compared to y + x = 5, we have
Slope, m = -1
y-intercept, c = 5
By comparing the properties of the functions, we have
The functions have the same y-intercept of 5The functions have the different slopes of 1 and -1Hence, the different properties of the functions are their slopes
Read more about linear functions at
https://brainly.com/question/15602982
#SPJ1
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.
Describe the transformation of f(x) that produce g(x). f(x)= 2x; g(x)= 2x/3+7Choose the correct answer below.
The vertical translation involves shifting the graph either up or down on the y axis. For example.
[tex]\begin{gathered} y=f(x) \\ \text{translated upward }it\text{ will be } \\ y=f(x)+k \end{gathered}[/tex]When a graph is vertically compressed by a scale factor of 1/3, the graph is also compressed by that scale factor. This implies vertical compression occurs when the function is multiplied by the scale factor. Therefore,
[tex]\begin{gathered} f(x)=2x \\ \text{The vertical compression by a scale of }\frac{1}{3}\text{ will be} \\ g(x)=\frac{1}{3}(2x)=\frac{2}{3}x \end{gathered}[/tex]Finally, the vertical translation up 7 units will be as follows
[tex]g(x)=\frac{2}{3}x+7[/tex]The answer is a. There is a vertical compression by a factor of 1/3 . Then there is a vertical translation up 7 units.
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.
2) Katie and Jacob are enlarging pictures in a school yearbook on the copy machine. The ratio of the width to the length of the enlarged photo will be the same as the ratio of the width to the length of the original photo. 25 points One of the photographs that they want to enlarge is a 3" x 4"photo. katie says that she can enlarge the photo to a 9" x 12", but Jacob disagrees. He says it will be 11" x 12". Who is correct? Explain your reasoning in words. * Enlarged Photo Original Photo 3 inches 4 inches
The original picture Katie and Jacob want to enlarge is 3 by 4 photographs
This means that the initial length of the photograph is 3 and the intial width of the photographs is 4
If both of them want to enlarge the photograph, then the scaling factor must be the same for both the width and length
Katie enlarge the photo to a 9 x 12
The ratio of the original photograph is 3 to 4
That is, 3 : 4
Katie enlarge the photo to a 9 x 12
Ratio of the enlarged photo by katie is 9 to 12
That is, 9 : 12
Equate the two ratio together
3/4 = 9/12
Introduce cross multiplication
We have,
3 x 12 = 4 x 9
36 = 36
Therefore, the ratio which katie enlarged the photo results to a proportion
For Jacob
Jacob enlarged the photo to 11 x 12
Equating the two ratios
3/4 = 11/12
3 x 12 = 4 x 11
36 = 44
This does not give us a proportion
Therefore, Katie is correct while Jacob is wrong
Simplify each expression.26. -2 · 11ly27. -5s(-4t)28. 3(-p)(-2q)29. -j(11k)30. 7x(-2y)
We need to multiply each term in the expression and take into account the rules for signs.
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
Do the following lengths form an acute, right, or obtuse triangle? 99 90 39 O Acute, 7921 < 7921 Right, 7921 = 7921 Obtuse, 7921 > 7921
As we can see the interior angles of this triangle are less than 90° , therefore this triangle is an ACUTE TRIANGLE
Hello! I need some help with this homework question, please? The question is posted in the image below. Q7
SOLUTION
Since -3 is a zero of the function then x=-3
This implies
x+3 is a factor of the polynomial
Following the same procedure, since 2 and 5 are zeros then
x-2 and x-5 are factors
Hence the polynomial can be written as
[tex]y=a(x+3)(x-2)(x-5)[/tex]Since the graph passes through the point (7,300)
Substitute x=7 and y=300 into the equation
This gives
[tex]300=a(7+3)(7-2)(7-5)[/tex]Solve the equation for a
[tex]\begin{gathered} 300=a(10)(5)(2) \\ 300=100a \\ a=\frac{300}{100} \\ a=3 \end{gathered}[/tex]Substitute a into the equation of the polynomial
[tex]y=3(x+3)(x-2)(x-5)[/tex]Therefore the answer is
[tex]y=3(x+3)(x-2)(x-5)[/tex]Does the formula represent a linear or nonlinear function? Explain
A linear function is an equation in which each term is either a constant or the product of a constant and the first power of a single variable. In other word, a linear function represents a straight line.
In our case, we have 2 variables: the volume (V) and the radius (r). However, the relationship is not linear because the radius is raised to the third power (not the first power). Therefore, the volume formula is a nonlinear function.
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:
An airplane travels at 550 mph. How far does the airplane travel in 5 1/2 hours
Answer:
At a speed of 550mph, the airplane covers 3,025 miles in 5 1/2 hours.
Explanation:
Given:
• The speed of the airplane = 550 miles per hour
,• Time taken = 5 1/2 hours
We want to find out how far the airplane travels.
The distance covered is calculated using the formula:
[tex]Distance=Speed\times Time[/tex]Substitute the given values:
[tex]Distance=550\times5\frac{1}{2}[/tex]Simplify:
[tex]\begin{gathered} Distance=550\times\frac{11}{2} \\ =275\times2\times\frac{11}{2} \\ =275\times11 \\ =3025\text{ miles} \end{gathered}[/tex]The airplane covers 3,025 miles in 5 1/2 hours.
Find P (A and B) for the following. P(A) = .65 and P(B) =.69 and P(A and B) =.48P(A and B)
We know that
[tex]\begin{gathered} P(A)=0.65 \\ P(B)=0.69 \end{gathered}[/tex]The probability of the intersection of the two events is:
[tex]P(AandB)=0.48[/tex]Answer:
GIven , P(A) = 0.65 P(B) = 0.69
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
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%
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)
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
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]I have 5 digits in my number. I do not have any tens. My digits add upto the product of 2 and 6. My biggest place has a value of 30,000. Myhundreds and thousands place adds up to three. The value of mythousands place is bigger than my hundreds. I only have one 0 in mynumber. The sum of my ten thousands, thousands, and hundredsequals the value of my ones place.
Let's begin by listing out the information given to us:
I have 5 digits in my number means the number is XXXXX (10,000 - 99,999)
No tens: the place value of 'tens' is zero
My digits add up to the product of 2 and 6: 2 * 6 = 12
[tex]\begin{gathered} \Sigma X=2\cdot6=12 \\ \Sigma X=12 \end{gathered}[/tex]My biggest place has a value of 30,000: this restricts the number to lie between 10,000 - 30,000
My hundreds and thousands place adds up to three: this can either be 2 + 1 or 1 + 2 or 0 + 3 or 3 + 0
The value of my thousands place is bigger than my hundreds: this implies that it is 2 + 1 or 3 + 0
I only have one 0 in my number: this cannot be in the 'ten thousands' place, it is the 'tens' place value (I do not have any tens)
The sum of my ten thousands, thousands, and hundreds equals the value of my ones place: the value of the 'ones' place is 6, the value of the 'ten thousands' is 2, the value of the 'thousands' is 3, the value of the 'hundreds' is 1
Hence, the number is 23,106 (remember that "My biggest place has a value of 30,000")
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]Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.A.) - 2B.) -1/2C.) 1/2D.) 2
In order to solve this problem we have to remember that the equation of any line takes the form
[tex]y(x)=mx+b[/tex]Therefore,
[tex]y(kx)=\text{mkx}+b[/tex]In other words, multiplying k by x is just multiplying the slope m by a factor of k.
The slope of g(x) is
[tex]m=2[/tex]and the slope of f(x) is
[tex]m=1[/tex]We see than the slope of g(x) is 2 times the slope of f(x); therefore, k = 2 which is choice D.
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.
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]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 vertex5. 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
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
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
I NEED HELP WITH THIS ASAP ILL MARK YOU BRAINLIEST Put each set of numbers from greatest to least
Every number is equivalent to:
[tex]\begin{gathered} 7.18\times10^{-3}=0.00718 \\ \sqrt{\frac{25}{49}}=\frac{5}{7}=0.7143 \\ \frac{7}{10}=0.7 \\ 0.\bar{8}=0.8888 \\ \frac{3}{4}=0.75 \\ 80\text{ \% = 0.8} \end{gathered}[/tex]So, each number from greatest to least is:
[tex]0.\bar{8},80\text{ \%, }\frac{3}{4},\sqrt{\frac{25}{49}},\frac{7}{10},7.18\times10^{-3}[/tex]