To determine the equation of the line you need to determine its slope first.
You know that the line 6y=x-12 is perpendicular to the line you have to determine, two lines that are perpendicular, their slopes are opposite reciprocals. For example, let "m" represent the slope of one of the lines and "n" represent the slope of the perpendicular line, you can express their relationship as follows:
[tex]m=-\frac{1}{n}[/tex]To determine the slope of the given line, you have to write it in slope-intercept form:
[tex]y=mx+b[/tex]Where
m represents the slope
b represents the y-intercept
Given the line:
[tex]6y=x-12[/tex]-Divide both sides by 6
[tex]\begin{gathered} \frac{6y}{6}=-\frac{x}{6}=-\frac{12}{6} \\ y=-\frac{1}{6}x-2 \end{gathered}[/tex]The slope of this line is the coefficient of the x-term, n=-1/6
Its opposite reciprocal is:
[tex]\begin{gathered} m=-\frac{1}{n} \\ m=-(-\frac{1}{\frac{1}{6}}) \\ m=-(-1\cdot6) \\ m=-(-6) \\ m=6 \end{gathered}[/tex]The slope of the line you have to determine is m=6
Now that you have the slope of the line, using the point-slope form, you can determine the equation of the line:
[tex]y-y_1=m(x-x_1)[/tex]Where
m represents the slope of the line
(x₁,y₁) represent the coordinates of one point of the line
Replace the formula with m=6 and (x₁,y₁)=(4,-7)
[tex]\begin{gathered} y-(-7)=6(x-4) \\ y+7=6(x-4) \end{gathered}[/tex]The next step is to write the equation in slope-intercept form:
-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+7=6\cdot x-6\cdot4 \\ y+7=6x-24 \end{gathered}[/tex]-Pass "+7" to the right side of the equation by applying the opposite operation "-7" to both sides of it:
[tex]\begin{gathered} y+7-7=6x-24-7 \\ y=6x-31 \end{gathered}[/tex]Finally, write the equation of the line using function notation:
[tex]f(x)=6x-31[/tex]Emilia and Liam are purchasing a home. They wish to save money for 12 years and purchase a house that has a value of $200,000 which cash. If they deposit money into an account paying 4% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase?
Answer:
Explanation:
Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4519 patients treated with the drug. 133 developed the adverse reaction of nausea Construct a 90% confidence interval for the proportion of adverse reactions. a) Find the best point estimate of the population proportion p.
We will have the following:
*First: We determine the standard deviation of the statistic, this is:
[tex]\sigma=\sqrt[]{\frac{\sum ^{133}_1(x_i-\mu)^2}{N}}[/tex]So, we will have:
[tex]\mu=\frac{\sum^{133}_1x_i}{N}\Rightarrow\mu=\frac{8911}{133}\Rightarrow\mu=67[/tex]Then:
[tex]\sigma=\sqrt[]{\frac{\sum^{133}_1(x_i-67)^2}{133}}\Rightarrow\sigma=\sqrt[]{\frac{196042}{133}}\Rightarrow\sigma=\sqrt[]{1474}\Rightarrow\sigma=38.39270764\ldots[/tex]And so, we obtain the standar deviation.
*Second: We determine the margin of error:
[tex]me=cv\cdot\sigma[/tex]Here me represents the margin of error, cv represents the critical value and this is multiplied by the standard deviation. We know that the critica value for a 90% confidence interval is of 1.645, so:
[tex]me=1.645\cdot38.39270764\ldots\Rightarrow me=63.15600407\ldots\Rightarrow me\approx63.156[/tex]*Third: We determine the confidence interval as follows:
[tex]ci=ss\pm me[/tex]Here ci is the confidence interval, ss is the saple statistic and me is the margin of error:
[tex]ci\approx133\pm63.156\Rightarrow ci\approx(69.844,196.256)[/tex]And that is the confidence interval,
Hello! I'm hitting a bit of a snag on this. I think I'm reading it too many times
The solution:
Given:
[tex]\begin{gathered} \text{ A sphere of radius 4m.} \\ \\ A\text{ cube of side 6.45m} \end{gathered}[/tex]Required:
To compare the volume and area of bot shapes.
The Sphere:
[tex]\begin{gathered} Area=4\pi r^2=4(4)^2\pi=64\pi=201.062m^2 \\ \\ Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\times\pi\times4^3=268.083m^3 \end{gathered}[/tex]The Cube:
[tex]\begin{gathered} Area=6s^2=6\times6.45^2=249.615m^2 \\ \\ Volume=s^3=6.45^3=268.336m^3 \end{gathered}[/tex]Clearly, we can see that:
Both shapes have approximately the same volume.
But the cube has a greater volume than that of the sphere.
Therefore, the correct answer is [option 4]
Mario ordered a pizza for dinner. WHEN IT Came Mario quickly ate 1/8 of the pizza. While Mario was getting napkins, his pet poodle ate 1/3 of the pizza.
Mario ordered a pizza for dinner. when pizza came, Mario quickly ate 1/8 of the pizza and his pet ate 1/3 of the pizza, then the remaining fraction of pizza left is 13/24
The fraction of pizza that Mario eat = 1/8
The fraction of pizza that his pet eat = 1/3
Total fraction = (1/8) + (1/3)
= 11/24
The remaining fraction of pizza = 1 - 11/24
= 13/24
Hence, Mario ordered a pizza for dinner. when it came, Mario quickly ate 1/8 of the pizza and his pet ate 1/3 of the pizza, then the remaining fraction of pizza left is 13/24.
The complete question is :
Mario ordered a pizza for dinner. When it Came Mario quickly ate 1/8 of the pizza. While Mario was getting napkins, his pet poodle ate 1/3 of the pizza. What is the fraction of pizza that left?
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What is 120 percent of 118?
120 percent of 118 is expressed mathematically as;
120% of 118
120/100 * 118
= 12/10 * 118
= 6/5 * 118
= 708/5
= 141.6%
Hence 120 percent of 118 is 141.6%
The function f(x) = 40(0.9)^x represents the deer population in a forest x years after it was first studied. What was the deer population when it was first studied?a. 44b.40c. 36d.49
We are given the function that models a deer population:
[tex]f(x)=40(0.9)^x[/tex]Where x is the years since the study started. If we want to know the initial population, we want to find the population at x = 0 years.
Thus:
[tex]f(0)=40(0.9)^0=40\cdot1=40[/tex]The correct answer is option b. 40
Write the equation of a line in point slope form that goes through the points (7,-5) and (3,8)
Write the equation of a line in point slope form that goes through the points (7,-5) and (3,8)
step 1
Find the slope
m=(8+5)/(3-7)
m=13/-4
m=-13/4
step 2
write the equation in point slope form
so
y-y1=m(x-x1)
we take the point (7,-5)
substitute
y+5=-(13/4)(x-7)If you take the point (3,8)
we have
y-8=-(13/4)(x-3)If you roll a die 96 times, approximately how many times could you expect it to land on 3 or 4?
Given:
It is given that you roll a die 96 times.
Required:
We have to find the expectation of landing on 3 or 4.
Explanation:
If you roll a die then there are 6 possibilities (1-6) and the possibility of landing on 3 or 4 is 2.
Then the probability of landing on 3 or 4 is
[tex]\frac{2}{6}=\frac{1}{3}[/tex]If you roll the die 96 times then the probability of landing 3 or 4 is
[tex]\frac{1}{3}\times96=32[/tex]Final answer:
Hence the final answer is:
You could expect it to land on 3 or 4 is
[tex]32[/tex]1. As part of a summer internship, five people -- Cindy, Damaris, Eugenio, Fareed, and Guzal -- are to be assigned to floors 1-5 in a dormitory. Each person will occupy his or her own entire floor and no other people will be in the dormitory. The assignment of people to floors must follow the following rules:Eugenio lives immediately above Damaris.Cindy is not on the first floor.Fareed does not live immediately below Damaris.Guzal lives either on the first floor or the fifth floor.Which one of the five people could be assigned to live on any of the five floors in the dormitory? A. Cindy B. Damaris C. Eugenio D. Fareed E. Guzal2. If Fareed lives neither directly above nor directly below Cindy in the dormitory, which one of the following people must live on the fourth floor? A. Cindy B. Damaris C. Eugenio D. Fareed E. Guzal
SOLUTION
(1) From the question, if Eugene lives immediately above Damaris, then Eugene can only live between floors 1 to 4.
And Damaris can only live between floors 2 to 5.
Guzal can only live on floors 1 or 5
Siince Cindy cannot live on the first floor, she can only live between floors 2 to 5, Since Fareed does not live immediately below Damaris. Fareed can live between floors 1 to 5.
Hence the answer is Fareed, option D
3. For the polynomial: ()=−2(+19)3(−14)(+3)2, do the following:A. Create a table of values that have the x-intercepts of p(x) in the first column and their multiplicities in the second column.B. State the degree and end behavior for p(x). C. Hand sketch a rough graph of p(x). You should have the x-int labeled, but you do not need tick marks for all numbers in between.
Part A. We are given the following polynomial:
[tex]\mleft(\mright)=-2\mleft(+19\mright)^3\mleft(-14\mright)\mleft(+3\mright)^2[/tex]This is a polynomial of the form:
[tex]p=k(x-a)^b(x-c)^d\ldots(x-e)^f[/tex]The x-intercepts are the numbers that make the polynomial zero, that is:
[tex]\begin{gathered} p=0 \\ (x-a)^b(x-c)^d\ldots(x-e)^f=0 \end{gathered}[/tex]The values of x are then found by setting each factor to zero:
[tex]\begin{gathered} (x-a)=0 \\ (x-c)=0 \\ \text{.} \\ \text{.} \\ (x-e)=0 \end{gathered}[/tex]Therefore, this values are:
[tex]\begin{gathered} x=a \\ x=c \\ \text{.} \\ \text{.} \\ x=e \end{gathered}[/tex]In this case, the x-intercepts are:
[tex]\begin{gathered} x=-19 \\ x=14 \\ x=-3 \end{gathered}[/tex]The multiplicity are the exponents of the factor where we got the x-intercept, therefore, the multiplicities are:
Part B. The degree of a polynomial is the sum of its multiplicities, therefore, the degree in this case is:
[tex]\begin{gathered} n=3+1+2 \\ n=6 \end{gathered}[/tex]To determine the end behavior of the polynomial we need to know the sign of the leading coefficient that is, the sign of the coefficient of the term with the highest power. In this case, the leading coefficient is -2, since the degree of the polynomial is an even number this means that both ends are down. If the leading coefficient were a positive number then both ends would go up. In the case that the leading coefficient was positive and the degree and odd number then the left end would be down and the right end would be up, and if the leading coefficient were a negative number and the degree an odd number then the left end would be up and the right end would be down.
Part C. A sketch of the graph is the following:
If the multiplicity is an odd number the graph will cross the x-axis at that x-intercept and if the multiplicity is an even number it will tangent to the x-axis at that x-intercept.
Create a table of values to represent the equation y = x - 9
Answer:
Explanation:
Here, we want to create a table of values to represent the given equation
To do this, we need to select a range of values for x
This can be a range of any set of numbers
With respect to this question, we shall be choosing -2 to +2 with an increment of 1
The values of x are thus: -2,-1 , 0, +1 and +2
So, now let us get the corresponding y-values using the equation rule
Now, let us get the y-values
when x = -2
y = -2-9 = -11
when x = -1
y = -1-9 = -10
when x = 0
y = 0-9 = -9
when x = 1
y = 1-9 = -8
when x = 2
y = 2-9 = -7
Thus,we have the table of values as follows:
Which of the following equations represents a line that passes through thepoints (6,-5) and (-6, -7)?
Problem
Which of the following equations represents a line that passes through the
points (6,-5) and (-6, -7)?
Solution
For this case the equation for a line is given by:
y= mx +b
And we can find the slope m with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And replacing we got:
[tex]m=\frac{-7+5}{-6-6}=\frac{-2}{-12}=\frac{1}{6}[/tex]Then we can find the intercept with this formula:
-5 = 1/6 (6)+b
And solving for b we got:
b= -5-1 =-6
And our equation would be:
y= 1/6 x -6
And the best option would be:
I.
On the Richter Scale, the magnitude R of an earthquake of intensity I is given by the equation in the image, where I0 = 1 is the minimum intensity used for comparison. (The intensity of an earthquake is a measure of its wave energy). Find the intensity per unit of area I for the Anchorage Earthquake of 1989, R = 9.2.
we have the formula
[tex]R=\log _{10}\frac{I}{I_0}[/tex]we have
R=9.2
I0=1
substitute in the given equation
[tex]\begin{gathered} 9.2=\log _{10}\frac{I}{1} \\ 9.2=\log _{10}I \\ I=10^{(9.2)} \\ \end{gathered}[/tex]I=1,584,893,192.46
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The
quadratic function h(t) = − 16t² + 84t+ 72 models the ball's height about the ground, h(t), in feet, t
seconds after it was thrown. Please help me identify the height of the ball in feet and how many seconds it takes to hit the ground
The height of the ball was 182.25 feet and it took 6 seconds for the ball to hot the ground.
Given that:-
Quadratic equation:-
[tex]h(t)=-16t^2+84t+72[/tex]
We have to find the ball's height, in feet and how many seconds it takes to hit the ground.
Differentiating the given equation, we get
dh/dt=-32t + 84
Putting dh/dt = 0, we get,
-32t + 84 = 0
t = 84/32 = 21/8 seconds
Putting t = 21/8, we will get the maximum height that the ball will reach.
Hence,
[tex]h(21/8)=-16(21/8)^2+84(21/8)+72[/tex]
h(21/8) = -16(441/64)+84(21/8)+72 = -110.25 + 220.50 +72 = 182.25 feet
At h = 0, the ball will have hit the ground.
Hence, we can write,
[tex]h(t) = 0 = -16t^2+84t+72[/tex]
Dividing -4 from the equation, we get,
[tex]4t^2-21t-18=0[/tex]
Using middle term split theorem, we can write,
[tex]4t^2-24t+3t-18=0\\[/tex]
4t(t-6)+3(t-6) = 0
(t-6)(4t+3) = 0
Hence, the values of t can be:-
t = 6, -3/4
As the time cannot be negative, hence the ball will hit the ground after 6 seconds.
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10 in.What is the volume of atriangular pyramid that is10 in. tall and has a basearea of 9 square in.?9cubic inchesVolume of a pyramid: V = {Bh (Where "B" is the area of the pyramid's base.)=
You have to calculate the volume of a pyramid with a height of 10in and a base area of 9 in²
The volume of a pyramid is equal to one third the product of the area of the base (B) and the height (h), following the formula:
[tex]V=\frac{1}{3}Bh[/tex]Replace the values on the formula and calculate the volume:
[tex]\begin{gathered} V=\frac{1}{3}\cdot9\cdot10 \\ V=30in^3 \end{gathered}[/tex]The volume is equal to 30 cubic inches.
What are all of the x-intercepts of the continuousfunction in the table?Х-4-20246f(x)02820-20 (0,8)O (4,0)O (4,0), (4,0)O (4,0), (0, 8), (4,0)
The x-intercepts of any function f(x) occur when f(x)=0.
As a reminder, f(x) corresponds to the y coordinate for any given x.
So, we need to focus on the parts of the table where f(x)=0 and look at the x value, that will give us the coordinates of the x-intercepts.
We can see the first entry in the table has f(x)=0 and x= -4.
The only other entry in the table where f(x)=0 has x=4.
As such, the x-intercepts of the given function are (-4,0) and (4,0), which are the coordinates presented in the third option.
In general, what points can have coordinates reversed and still have the same location?Choose the correct answer below.O the points with x-coordinates 0o the points with y-coordinates 0o the points with the same x- and y-coordinatesO the points with opposite coordinates
SOLUTION
The Point of a co-ordinate is always written as
[tex](x,y)[/tex]Giving a point
[tex]\begin{gathered} A(x,y) \\ \text{if the coordinates of x and y are the same } \end{gathered}[/tex]For instance x=2 and y=2, the point will be
[tex](2,2)[/tex]If the coordinate of x and y are reversed, the point will remain the same
Hence
the points with the same x- and y-coordinates will give the same location if the coordinate is reversed.
Therefore The Third option is correct (c)
can someone please help me find the mesauser of the following?
Answer:
The measure of the given arcs are;
[tex]undefined[/tex]Given the figure in the attached image.
we want to find the measure of the given arcs.
For arc ED.
The measure of arc ED is equal to the measure of arc AB;
[tex]\begin{gathered} ED=AB=\measuredangle AOB=50^{\circ} \\ ED=50^{\circ} \end{gathered}[/tex]To get the measure of BC, we can see that AB, BC, and CD will sum up to 180 degrees.
[tex]\begin{gathered} AB+BC+CD=180^{\circ} \\ 50^{\circ}+BC+40^{\circ}=180^{\circ} \\ BC=180^0-(50^{\circ}+40^{\circ}) \\ BC=90^{\circ} \end{gathered}[/tex]To get arc BED;
[tex]\begin{gathered} \text{BED}=BE+ED \\ \text{BED}=180+50 \\ \text{BED}=230^{\circ} \end{gathered}[/tex]which function has an inverse that is also a function horizontal line test
If the graph of a function y = f(x) is such that no horizontal line intersects the graph at more than one point, then f has an inverse function.
A. The absolute value function f(x) = | x | is intersected twice by any horizontal line at y > 0. Thus this function does not have an inverse
B. The quadratic function f(x) = x^2 has a graph called parabola. If we plot any horizontal line at y>0, that line will intersect the function twice. This function has no inverse function
What is the equation of this line?
A. y=4/3x−5
B. y=3/4x−5
C. y=−43/x−5
D. y=4/3x+5
I need help on this showing step by step work
Solution
Notice that we have two solid shapes and we want to find the surface area of the composite.
We have a triangular prism on a cuboid.
Note: Formula For Finding the Surface Area Of A Cuboid
[tex]Surface\text{ }Area=2(lw+lh+wh)[/tex]From the question, we have that
[tex]\begin{gathered} Length(l)=12cm \\ Width(w)=4cm \\ Height(h)=14cm \end{gathered}[/tex]The area will be
[tex]\begin{gathered} Surface\text{ A}rea=2(lw+lh+wh) \\ \\ Surface\text{ A}rea=2(12(4)+12(14)+4(14)) \\ \\ Surface\text{ A}rea=2(48+168+56) \\ \\ Surface\text{ A}rea=2(272) \\ \\ Surface\text{ A}rea=544cm^2 \end{gathered}[/tex]Now, we find the Area of the Triangular Prism
Note: Formula To Use
From the question, we have
[tex]\begin{gathered} b=4cm \\ h=2\sqrt{3}\text{ \lparen since the triangle is an equilateral triangle\rparen} \\ L=12cm \\ S_1=S_2=S_3=4cm \end{gathered}[/tex]Substituting we have
[tex]\begin{gathered} Surface\text{ }Area=bh+L(S_1+S_2+S_3) \\ \\ Surface\text{ }Area=4(2\sqrt{3})+12(4+4+4) \\ \\ Surface\text{ }Area=(8\sqrt{3}+144)cm^2 \end{gathered}[/tex]Therefore, the total surface area of the composite is
[tex]\begin{gathered} Surface\text{ }Area=544+8\sqrt{3}+144 \\ \\ Surface\text{ }Area=(688+8\sqrt{3})cm^2 \\ or\text{ if we want to write the answer in decimal point, we have} \\ Surface\text{ }Area=701.8564065cm^2 \end{gathered}[/tex]What interest will be earned if $11,000.00 is invested for 3 years at 11% compounded semi-annual?You would earn $ in interest. (Round to 2 decimal places.)
Answer:
$4,167.27
Explanation:
The amount, A(n) in an account for a Principal invested at compound interest is calculated using the formula:
[tex]\begin{gathered} A(n)=P(1+\frac{r}{k})^{nk}\text{ }where=\begin{cases}P=Prin\text{cipal} \\ r=\text{Annual Interest Rate} \\ k=\text{Compounding Period}\end{cases} \\ n=nu\text{mber of years} \end{gathered}[/tex]In the given problem:
• P = $11,000.00
,• r=11% = 0.11
,• n= 3 years
,• k=2 (semi-annual)
Substitute these into the formula:
[tex]\begin{gathered} A(n)=11,000(1+\frac{0.11}{2})^{2\times3} \\ =11,000(1+0.055)^6 \\ =11,000(1.055)^6 \\ =\$15,167.27 \end{gathered}[/tex]Next, we find the interest earned.
[tex]\begin{gathered} \text{Interest}=\text{Amount}-\text{Prncipal} \\ =15167.27-11000 \\ =\$4,167.27 \end{gathered}[/tex]You would earn $4,167.27 in interest (rounded to 2 decimal places).
Use the given instructions to answer question 17 to question 20.
Given
The boxplot.
And, the total number of students in the class is 60.
To find:
a) The percentage of students who received one or more moving violation.
b) The number of parking violations received by at least 50% of students.
c) How many students received two or more parking violation.
Explanation:
a) From the figure,
The percentage of students who received one or more moving violation is,
[tex]Percentage\text{ of students}=75\%[/tex]Because the number of students having minimum moving violation is 0, and the number of students having maximum moving violation is 4.
b) The number of parking violation received by at least 50% of students is,
[tex]\begin{gathered} Number\text{ }of\text{ }parking\text{ }violation\text{ received by at least 50}\%\text{ of students } \\ is\text{ }2\text{ }or\text{ }more. \end{gathered}[/tex]c) The number of students who received two or more parking violation is,
[tex]\begin{gathered} Number\text{ of students}=75\%\times60 \\ =\frac{75}{100}\times60 \\ =45 \end{gathered}[/tex]Hence, the number of students who received two or more parking violation is 45.
ok so I understand the first 2 steps of solving this but I dont entirely get it........
You have the following equation:
2x² - 12x + 16 = 0
in order to solve the previous equation, first divide by 2 both sides:
x² - 6x + 8 = 0
next, consider that the factors of the previous expression has the form:
(x - )(x - ) = 0
consider the first number inside the first factor is the result of the sum of two numbers, and the number of the second factor is the product of the same numbers. Such numbers are:
(2)·(4) = 8
2 + 4 = 6
hence, the factorized expression is:
(x - 8)(x - 2) = 0
the solutions of the equations are:
x = 8
x = 2
- 9 = 12 what is the value of K?
For this case we have the following expression given:
k/3 -9 = 12
We can add 9 in both sides and we got:
k/3 = 12+9
k/3= 21
And if we multiply in both sides by 3 we got:
k = 21*3 = 63
Which is an equation of the line with a slope of2323 passing through the point (4,-1).Group of answer choices=14+23 =−4+23 =23−53 =23−113
Given that the slope of a line is 2/3, that passes through the point (4, -1), i.e
[tex]\begin{gathered} m=\frac{2}{3} \\ (x_1,y_1)\Rightarrow(4,-1) \end{gathered}[/tex]The formula to find the equation of straight line is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m is the slope of the line} \end{gathered}[/tex]Substitute the values into the formula of the equation of a straight line
[tex]y-(-1)=\frac{2}{3}(x-4)[/tex]Solve for y i.e make y the subject
[tex]\begin{gathered} y-(-1)=\frac{2}{3}(x-4) \\ y+1=\frac{2}{3}(x-4) \\ \text{Open the bracket} \\ y+1=\frac{2}{3}x-\frac{2}{3}(4) \\ y+1=\frac{2}{3}x-\frac{8}{3} \\ y=\frac{2}{3}x-\frac{8}{3}-1 \\ y=\frac{2}{3}x-(\frac{8}{3}+1) \\ y=\frac{2}{3}x-(\frac{8+3}{3}) \\ y=\frac{2}{3}x-\frac{11}{3} \end{gathered}[/tex]Thus, the answer is
[tex]y=\frac{2}{3}x-\frac{11}{3}[/tex]Thus, the answer is the last option.
Esmeralda rents a car from a company that rents by the hour. she has to pay an initial fee of $50, and they charge her $8 per hour. she has $150 available to spend on car rental. what is the greatest number of hours for which she can rent the car?A. 18 hoursB. 12.5 hoursC. 12 hoursD. 13 hours
Let the number of hours be x,
Initial fee is $50,
Amount charged per hour is $8
The charge for a number of x hours is'
[tex]x\times8=8x[/tex]The total amount Esmeralda has is $150,
Therefore,
[tex]8x+5\leq150[/tex]Solving for x to find the greates number of hours,
[tex]\begin{gathered} 8x+50\leq150 \\ \text{Collect like terms,} \\ 8x\leq150-50 \\ 8x\leq100 \\ \text{Divide both sides by 8} \\ \frac{8x}{8}\leq\frac{100}{8} \\ x=12.5\text{ hours} \end{gathered}[/tex]Hence, the greates number of hours is 12.5 hours.
Option B is the right answe
I would like to make sure my answer is correct ASAP please
step1: Write out the formula for exponential growth
[tex]y=a(1+r)^n[/tex][tex]\begin{gathered} a=\text{initial population} \\ r=\text{rate} \\ n=\text{years} \end{gathered}[/tex]Hence we have
[tex]a=800,r=3\text{ \%, n=x}[/tex]Step2: substitute into the formula in step 1
[tex]\begin{gathered} y=800(1+\frac{3}{100})^x \\ y=800(1+0.03)^x \\ y=800(1.03)^x \end{gathered}[/tex]Hence the right option is A
2)Find the missing coordinate (5, 7) and (8,y); m= 4/3
Answer:
y = 11
Step-by-step explanation:
Hello!
We can utilize the slope formula to create the equation for y:
[tex]\frac{y - 7}{8 - 5} = \frac{4}{3}[/tex]Solve for y[tex]\frac{y - 7}{8 - 5} = \frac{4}{3}[/tex][tex]\frac{y - 7}{3} = \frac{4}{3}[/tex] => Simplifyy - 7 = 4 => Multiply both sides by 3y = 11 => Add 7 to both sidesThe value of y is 11.
14) A positive number is two fifths of another positive number. The sum of the numbers is 49. What arethe two numbers?
Let's use the variable x to represent the second number. The first number is two fifths of x, so the first number is 2x/5.
If the sum of the numbers is 49, we can write the following equation:
[tex]\frac{2}{5}x+x=49[/tex]Now, solving the equation for x, we have:
[tex]\begin{gathered} \frac{2}{5}x+\frac{5}{5}x=49\\ \\ \frac{7}{5}x=49\\ \\ \frac{1}{5}x=7\\ \\ x=7\cdot5\\ \\ x=35 \end{gathered}[/tex]Let's calculate the first number:
[tex]\frac{2}{5}x=\frac{2}{5}\operatorname{\cdot}35=2\cdot7=14[/tex]Therefore the numbers are 14 and 35.
