step 1
Find the slope m
we need two points
so
(200,100) and (80,220)
m=(220-100)/(80-200)
m=120/-20
m=-6
step 2
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=-6
(x1,y1)=(200,100)
substitute
y-100=-6(x-200)
Convert to slope intercept form
y-100=-6x+1200
y=-6x+1300step 3
Find the equation in standard form
Ax+By=C
where
A is a positive integer
B and C are integers
so
y=-6x+1300
6x+y=1300Question 3(Multiple Choice Worth 2 points)
(01.06 MC)
Simplify √√-72-
--6√√2
6√-2
6√√2i
061√2
Answer:
[tex]6i\sqrt{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{-72}[/tex]
Rewrite -72 as the product of 6 · -1 · 2:
[tex]\implies \sqrt{36 \cdot -1 \cdot 2}[/tex]
Apply the radical rule [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sqrt{36} \sqrt{-1} \sqrt{2}[/tex]
Carry out the square root of 36:
[tex]\implies 6\sqrt{-1}\sqrt{2}[/tex]
Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex] :
[tex]\implies 6i\sqrt{2}[/tex]
4(px+1)=64The value of x when p is -5 is ?
Answer:
x = -3
Explanation:
Given the equation:
[tex]4\left(px+1\right)=64[/tex]We are required to find the value of x when p is -5.
[tex]\begin{gathered} 4\left(px+1\right)=64\colon p=-5 \\ 4\left(-5x+1\right)=64 \\ -20x+4=64 \\ -20x=64-4 \\ -20x=60 \\ \text{Divide both sides by -20} \\ x=\frac{60}{-20} \\ x=-3 \end{gathered}[/tex]how many ones equal 4 tens
We have to find the number of ones in 4 tens.
As we know that, there are 10 ones in a 10.
Therefore, in 4 tens, the total number of ones would be 1 x 4 x 10 = 40
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.
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
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]A bakery makes and sells hot cocoa bombs during the holidays. The first 12 hot cocoa bombs of an order cost is $4.00 each. Each of the next 6 hot cocoa bombs cost $3.50 each. For orders exceeding 18, the cost drops to $3 each. The function C(x) represents the bakery's pricing.
Solution
Step 1
Given data for C(x), the bakery's pricing
[tex]\begin{gathered} F\text{or this range 0}\leq x\leq12ofhotcocoabombs\text{ we use C(x) =4x} \\ \text{For this range }1218,ofhotcocoabombs\text{ we useC(x) = }3x+15 \end{gathered}[/tex]Required
Step 1
To find the cost of 8 hot cocoa bombs
[tex]\begin{gathered} C(8)\text{ lies in the range 0}\leq x\leq12 \\ \text{Hence we use 4x where x = 8} \\ \text{The cost of 8 hot cocoa bombs = 4(8) = \$32} \end{gathered}[/tex]Step 2
To find the cost of 18 hot cocoa bombs
[tex]\begin{gathered} C(18)\text{ lies in the range 12}Step 3To find the C(30)
[tex]\begin{gathered} C(30)\text{ lies in the range x}\ge18 \\ \text{Hence we use 3x +15, where x = 30} \\ C(30)\text{ = 3(30) + 15 = 90 + 15 = \$105} \\ \end{gathered}[/tex]Step 4
What C(30) represents.
C(30) represents the cost of ordering 30 hot cocoa bombs which is $105
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]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.
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
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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.
Dilate trianglesDraw the image of AABC under a dilation whose center is A and scale factor is
Since the dilation is centered at vertex A, the coordinates of A' are the same of A.
Then, to find the coordinates of B, let's multiply the distance AB by the scale factor:
[tex]\begin{gathered} AB=12.6\\ \\ A^{\prime}B^{\prime}=12.6\cdot\frac{1}{4}=3.15 \end{gathered}[/tex]Doing the same for AC, we have:
[tex]A^{\prime}C^{\prime}=AC\cdot\frac{1}{4}=11.3\cdot\frac{1}{4}=2.825[/tex]The points B' and C' are on the sides AB and AC, respectively.
Knowing this, let's draw the image A'B'C':
Since AB = BC, we also have A'B' = B'C' = 3.15.
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.
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 have the area of the circle but having trouble find the area of the triangle
To calculate the area of the triangle we need the length of the base and the height, being the height perpendicular to the base.
The base of the triangle has a length that is equal to the diameter of the circle. It can also be expressed as 2 times the radius r. So the base is:
[tex]b=2\cdot r=2\cdot4=8\operatorname{cm}[/tex]The height is the segment perpendicular to the base that goes up to the vertex at the top. as it goes from the center of the circle to the border of the circle, it has a length that is equal to the radius r:
[tex]h=r=4\operatorname{cm}[/tex]Then, we can calculate the area of the triangle as:
[tex]A=\frac{b\cdot h}{2}=\frac{8\cdot4}{2}=\frac{32}{2}=16\operatorname{cm}^2[/tex]We can calculate the area of the circle as:
[tex]A_c=\pi r^2\approx3.14\cdot4^2=3.14\cdot16=50.24[/tex]The probability that a randomly selected point within the circle falls in the white area is equal to the ratio of white area to the area of the circle.
The white area is equal to the area of the circle minus the area of the triangle.
Then, we can calculate the probability as:
[tex]p=\frac{A_w}{A_c}=\frac{A_c-A_t}{A_c}=\frac{50.24-16}{50.24}=\frac{34.24}{50.24}\approx0.68=68\%[/tex]Answer: The probability is p=0.68.
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
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]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
A student worked 51 hr during a week one summer. The student earned $5. 10 per hour for the first 40 hr and $7.65 per hour for overtime. How much did the student earn during the week?
We will determine the earnings for the week as follows:
[tex]W=40(5.10)+11(7.65)\Rightarrow W=288.15[/tex]So, the student earned $288.15 that week.
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 the volume of a pyramid with a square base, where the side length of the base is
11 in and the height of the pyramid is 15.1 in. Round your answer to the nearest
tenth
Answer:
53.7 cubic inches
Step-by-step explanation:
Use the volume formula for a square pyramid:
[tex]V = \dfrac{1}{3} (A_{\mathrm{base}} \cdot h)\\\\\mathrm{or} \\\\A = \dfrac{l^2h}{3}[/tex]
where l is the side length of the base and h is the height of the pyramid.
Now substitute in the given values:
[tex]V = \dfrac{1}{3}((11 \, \mathrm{in})^2 \cdot 15.1 \, \mathrm{in})[/tex]
[tex]V = \dfrac{1}{3}(121 \, \mathrm{in}^2 \cdot 15.1 \, \mathrm{in})[/tex]
[tex]V = \dfrac{1}{3}(1,821 \, \mathrm{in}^3)[/tex]
[tex]V = 53.7 \, \mathrm{in}^3[/tex]
So, the volume of the pyramid is 53.7 cubic inches.
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
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.
You randomly draw a marble from a bag of marbles that contains 7 blue marbles 2 green marbles and 1 red marbles
Given the following:
7 blue marbles
2 green marbles
1 red marbles
We to find the probability of not drawing a blue marble.
We will be solving it in two ways.
First let's get the total marbles
Total Marble = 7 + 2 + 1 = 10
recall that probablity is number of favourable outcome divide by number of total outcome.
So,
probablity of Drawing a Blue Marble is = 7/10
probability of not Drawing Blue Marbles = 1 - Probability of Drawing Blue Marbles
= 1 - 7/10
= 10 - 7
10
= 3/10
OR
Probability of not Drawing Blue Marbles = Probablity of drawing Green or Red Marbles.
= 2/10 + 1/10
= 3/10
Therefore, the probability of not Drawing Blue Marbles is 3/10.
In ΔVWX, m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2. Find m∠W.
The measure of angle W in the triangle is 29 degrees
How to determine the measure of angle W?The definition of the angles are given as
m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2)
Where the triangle is given as
Triangle VWX
The sum of angles in a triangle is 180 degrees
This means that
V + W + X = 180
Substitute the known values in the above equation
So, we have
6x - 4 + x + 12 + 3x + 2 = 180
Evaluate the like terms
10x = 170
Divide by 10
x = 17
Substitute x = 17 in m∠W=(x+12)
So, we have
m∠W=(17+12)
Evaluate
m∠W = 29
Hence, the angle W is 29 degrees
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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%
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]Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8
Step 1. Graphing the first inequality.
The first inequality is:
[tex]y>3x+7[/tex]to graph this, we need to graph the line 3x+7, which compared with the slope-intercept equation
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept, the line
[tex]y=3x+7[/tex]is a line with a slope of 3 and a y-intercept at 7:
SInce the inequality is:
[tex]y>3x+7[/tex]The solution just for this inequality are the values greater than the red line, but not including the red line so we represent is a dotted line and a shaded part above:
Step 2. Graph the second inequality.
The second inequality is:
[tex]y\le-3x-8[/tex]As we did with the first inequality, we graph the line -3x-8 first.
comparing -3x-8 with the slope-intercept equation:
[tex]y=mx+b[/tex][tex]y=-3x-8[/tex]we can see that the slope m is -3 and the y-intercept b is -8. This line is shown in blue in the following diagram along with our results for the previous inequality:
Since the inequality form is:
[tex]y\le-3x-8[/tex]We shade the values below this blue line:
The final solution will be the intersection between the red part and the blue part:
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