The given equation is expressed as
4(x - 3)= 16 - 3x
The first step is to expand the parentheses on the left by multiplying the terms inside the parentheses with the term outside. We have
4x - 12 = 16 - 3x
The nest step is to add 3x and 12 to both sides of the equation. We have
4x + 3x - 12 + 12 = 16 + 12 - 3x + 3x
7x = 28
Dividing both sides of the equation by 7, we have
7x/7 = 28/7
x = 4
What is the equation of the line that passes through the point (2,-2) and has aslope of -1/2
Concept
Use slope and a point form to find the equation of the line.
Method
Given data
slope = -1/2
Given point = (2,-2)
Next, write the equation of a slope-point form to find the equation of a line.
[tex]\begin{gathered} \text{Slope}-po\text{int equation of a line} \\ m\text{ = }\frac{y-y_1}{x-x_1} \end{gathered}[/tex]Next, label the given data
m = -1/2
x1 = 2 and y1 = -2
Substituting m, x1 and y1 into the equation we get
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ \frac{-1}{2}\text{ = }\frac{y\text{ -(-2)}}{x\text{ - 2}} \\ \frac{-1}{2}\text{ = }\frac{y\text{ + 2}}{x\text{ -2}} \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} 2(\text{ y + 2 ) = -1 ( x - 2 )} \\ 2y\text{ + 4 = -x + 2} \\ \text{collect like terms} \\ 2y\text{ = -x + 2 - 4} \\ 2y\text{ = -x - }2 \\ \text{Divide through by 2} \\ \frac{2y}{2}\text{ = }\frac{-1}{2}x\text{ - }\frac{2}{2} \\ y\text{ = }\frac{-1}{2}x\text{ - }1 \end{gathered}[/tex]Final answer
[tex]\text{Equation of a line is: y = }\frac{-1}{2}x\text{ - 1}[/tex]I know what to do but im confused of what the answer is
a) It is known that the area of Indian ocean is 25 million square miles.
Lets take the unknown ocean percentage as x, which is bigger than the Indian ocean.
So comparing to the size of that unknown x ocean, Indian ocean is just a small part (39%) of the area.
So,
[tex]\begin{gathered} \frac{39}{100}x=25 \\ x=\frac{25\times100}{39} \\ x=\frac{2500}{39} \\ x=64.1 \end{gathered}[/tex]Now, we have to compare the value of x with the data given in the table. It matches with the Pacific ocean.
Hence Indian ocean is a small part (39%) of Pacific ocean.
b) Given that the area of artic ocean is 5 million square miles. It is just a small percentage (16%) of some bigger ocean given in the table. Let's take the unknown ocean as y.
[tex]\begin{gathered} \frac{16}{100}y=5 \\ y=\frac{5\times100}{16} \\ y=\frac{500}{16} \\ y=31.25 \end{gathered}[/tex]A hurricane is approaching land. At 3:00 p.m. it is 487 miles off the coast, and at 8:00 p.m. it is 372 miles off the coast, as shown below. Assuming the hurricane continues on the same path at the same speed, which equation represents the distance, in miles, between the hurricane and the coast as a function of time, in hours, since 8:00 pm?
Answer:
[tex]d(t) = -23t +556[/tex]
Step-by-step explanation:
Assuming the hurricane continues on the same path at the same speed means the relationship between speed and time will be linear. This means our function can be written in slope-intercept form, [tex]y=mx+b[/tex]. For our function, it will be written as [tex]d(t)=mt+b[/tex], where t is time, d is distance, m is the slope of the line, and b is the y-intercept. We can solve for slope by using the formula [tex]\frac{y_{2}-y_1 }{x_2-x_1}[/tex], where x2 and x1 are the times 8 and 3, respectively, and y2 and y1 are the distances 372 and 487, respectively. This gives us a slope of -23.
We can solve for b by inputting the values we've been given and using algebra.
[tex]d(t)=mt+b\\487 =-23(3)+b\\487=-69+b\\b=556[/tex]
This gives us the equation [tex]d(t) = -23t +556[/tex]
Something to note, since we let 3:00 pm and 8:00 pm be the values x=3 and x=8, 12:00 pm would be x=0, and values in the morning would be negative, like 9:00 am would be x=-3.
I will give brainliest
Answer:
x⁴ or 2x³
Step-by-step explanation:
According to the BODMAS rule
brackets go first
then Order which is the powers basically
next is division....multiplication, addition and finally Subtraction
A 5K is roughly 3.1 miles long. Which equation could be used to determine the time, t, ittakes to run a 5K as a function of the average speed, s, of the runner where t is in minutesand s in miles per minute?
Explanation:
Given in the question:
[tex]\begin{gathered} distance=3.1mile \\ speed=s \end{gathered}[/tex]The formul for time is given below as
[tex]t=\frac{distance}{speed}[/tex]By substituting the values, we will have
[tex]\begin{gathered} t=\frac{d\imaginaryI stance}{speed} \\ t=\frac{3.1}{s} \\ \end{gathered}[/tex]Hence,
The final answer is
[tex]t=\frac{3.1}{s}[/tex]given: angle a is comp to angle b. angle c is comp to angle b. angle a = (3x+y), angle b = (x+4y+2), angle c = (3y-3) find: angle b
Complementary angles are the angles whose sum is 90° thus measure of angle b will be 54°.
What is the complementary angle?A complementary angle is an angle in which the sum of both angles will be 90°.
A complementary angle is just a denotation that we have an angle that is how much bigger than 90.
The sum of two complementary angles is 90°
Given that, angles a and b are complementary.
∠a + ∠b = 90°
3x + y + x + 4y + 2 = 90
4x + 5y = 88
Also, angles b and c are complementary.
∠c + ∠b = 90°
3y - 3 + x + 4y + 2 = 90
x + 7y = 91
By solving both equations,
4(91 - 7y) + 7y = 91
364 - 28y + 7y = 91
364 - 91 = 21y
y = 13 so, x = 91 - 7(13) = 0
So,
∠b = 0 + 4(13) + 2 = 54°.
Hence "Complementary angles are the angles whose sum is 90° thus measure of angle b will be 54°".
For more about the complementary angle
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Complete the statement to describe the expression abc + def.The expression consists ofterms, and each term containsfactors.Stuck? Review related articles/videos or use a hint.Report a probl
Factors are separated by a product and terms are separated by + or - signs.
In this case, we have two terms, abc and def , each term has three factors a, b and c for the first term and d, e and f for the second term.
Then, the given expression has two terms with three factors
TU has a midpoint at M(7,5). Point T is at (9,8). Find the coordinates of point U.
(5,2)
Explanation
Step 1
if you have 2 points P1 and P2 , the midpoint is given by:
[tex]\text{Midpoint}=(\frac{x_1+x_{2,}}{2},\frac{y_1+y_2}{2})[/tex]where
[tex]\begin{gathered} P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
T=(9,8)
Midpoint(7,5)
U=unknown
Step 2
replace
[tex]\begin{gathered} \text{Midpoint}=(\frac{x_1+x_{2,}}{2},\frac{y_1+y_2}{2}) \\ (7,5)=(\frac{9+x_{u,}}{2},\frac{8+y_u}{2}) \\ \text{then} \\ 7=\frac{9+x_u}{2} \\ \text{and} \\ 5=\frac{8+y_u}{2} \end{gathered}[/tex]Step 3
solve for x and y
[tex]\begin{gathered} 7=\frac{9+x_u}{2} \\ 14=9+x_u \\ x_u=14-9 \\ x_u=5 \end{gathered}[/tex]and
[tex]\begin{gathered} 5=\frac{8+y_u}{2} \\ 10=8+y_u \\ 10-8=y_u \\ y_u=2 \end{gathered}[/tex]I hope this helps you
Evaluar la expresión numérica. -8.5 (9.4 a 6.1) en
En la expresión:
[tex]-8.5(9.4a6.1)[/tex]Sustituye la letra "a" por diferentes signos de operaciones para ver si el resultado coincide con alguna opción.
Comenzando por un signo "+":
[tex]\begin{gathered} -8.5(9.4+6.1)=-8.5(15.5) \\ =-131.75 \end{gathered}[/tex]El cual, no se encuentra entre las opciones.
Intentando ahora con el signo "-":
[tex]\begin{gathered} -8.5(9.4-6.1)=-8.5(3.3) \\ =-28.05 \end{gathered}[/tex]Dicho número sí se encuentra entre las opciones.
Por lo tanto, la expresión correcta es -8.5(9.4-6.1), y la respuesta es:
[tex]B)-28.05[/tex]find the values of x and y
Answer:
x = 8 degrees ; y= 12 degrees
Step-by-step explanation:
what is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters? Write Your Answer In Terms Of pi.
Given the word problem, we can deduce the following information:
1. The diameter of the circle is 3 meters.
2. The side length of the square is 3 meters.
To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:
[tex]A_{circle}=\frac{\pi d^2}{4}[/tex]where:
d=diameter
[tex]\text{A}_{square}=d^2[/tex]where:
d=side length
The figures are shown below:
Based on this, the difference of areas would be:
[tex]\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ \end{gathered}[/tex]Next, we plug in d=3:
[tex]\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ =(3)^2-\frac{\pi(3)^2}{4} \\ =9-\frac{9\pi}{4} \end{gathered}[/tex]Therefore, the difference in areas is:
[tex]9-\frac{9\pi}{4}[/tex]Which of the following functions exhibit the end behavior f(x) —>infinite as x—> -infinite and f(x) —> -infinite as x—>infinite? Select all that apply. Please help me out! Nobody wants to help :(
The end behavior f(x) → ∞ as x → -∞ means that x-value is negative and y-value is positive. If this is the case, the other end part of the function is located in the 2nd quadrant.
The end behavior f(x) → -∞ as x → ∞ means that the x-value is positive and the y-value is negative. The other end part of the function is located in the 4th quadrant.
Looking at the choices, Option 1 and 4 exhibits these characteristics.
The temperature for five hours in Queens, New York is shown in the graph below y 80 70 60 50 Temperature (°F) 40 30 20 10 0 Х 1 2 3 4 5 Hours What is the range of this set of data? 1) OSXs5 2) 56
Range is the set of output values of the function.
In the given question : The temperature for five hours in Queens, New York is shown
So, the tempreature is the output of the graph and time is the set of input values :
From the graph the tempreature for five hours
Intital at 0 hours the tempreature is 56 and at five hours temperature is 70
Since x axis represent the time and y axis represent the temperature
So. Range will be : 56 ≤ y ≤ 70
Answer : 4) 56 ≤ y ≤ 70
Solve 272 - 10 = r2 using square roots. Select the solution(s).
Calculate the square root in both sides of the calculation:
Distribute the square roots
Simplify the square roots.
[tex]\begin{gathered} 272=16\cdot17 \\ \sqrt[]{272}=\sqrt[]{16}\cdot\sqrt[]{17} \\ \sqrt[]{272}=4\cdot\sqrt[]{17} \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sqrt[]{r^2}=\sqrt[]{272-10} \\ r=\sqrt[]{272}-\sqrt[]{10} \\ r=4\sqrt[]{17}-\sqrt[]{10} \end{gathered}[/tex]Share £400 in a ratio of 3.5
Answer:
£150 and £250
Step-by-step explanation:
When you share something in the ratio a:b the fraction of each to the total is given by a/(a+b) and b/(a+b)
Here the ratio is 3:5
So the fractions of the share are 3/(3+5) = 3/8 and 5/8
So actual amounts are
3/8 x 400 = £150
5/8 x 400 = £250
a motorboat travels 190 miles in 5 hours going upstream. It travels 270 miles going Downstream in the same amount of time what is the rate of the boat in still water and what is the rate of the current
To find the rate of the boat you divide the distance by the time:
[tex]r=\frac{d}{t}[/tex]Going upstream is s
Question / OT 8What is the value of p?140"90-OAnswer hereSUBMIT
From the problem, we have a triangle and we need to find the measurements of the angles marked in blue.
Note that angles adjacent to each other in a straight line have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \theta+140=180 \\ \theta=180-140 \\ \theta=40 \end{gathered}[/tex]The other angle is :
[tex]\begin{gathered} \theta+90=180 \\ \theta=180-90 \\ \theta=90 \end{gathered}[/tex]Now we have the two angles in a triangle, 40 and 90 degrees, and the sum of interior angles in a triangle is always 180 degrees.
That will be :
[tex]\begin{gathered} p+40+90=180 \\ p+130=180 \\ p=180-130 \\ p=50 \end{gathered}[/tex]ANSWER :
p = 50 degrees
Linda uses the simple interest formula to calculate the interest fee on her recent loan. Her interest rate is 5%.What value will Linda use for r, interest rate, in her calculation?
Since the interest rate is 5%. She needs to express the percentage as a decimal.
In order to do it, she needs to divide 5 by 100, so:
[tex]\frac{5}{100}=0.05[/tex]Answer:
r = 0.05
A rectangle has vertices at (0, 0), (3, 0), and (0,6). What is the area of the rectangle?
First, set the coordinate points on a graph, and joint them to form a graph
By looking at the graph we can see that:
width : 3
length: 6
Area of a rectangle : Length x width : 6 x 3 = 18
solve for measure of arc dg and the angle DHG
I just need help with part B please. I have part A correct
Given the expression:
[tex]\frac{-3-2i}{6i}[/tex]Dividing complex numbers:
[tex]\frac{-1}{3}+\frac{1}{2}i[/tex]Finding the conjugate:
[tex]-\frac{1}{3}-\frac{1}{2}i[/tex]Find the distance traveled by a bullet that has a mullet velocity of 3800ft/s and a total flight time of 2.3 seconds. Express your final answer on miles.
Find the distance traveled by a bullet that has a mullet velocity of 3800ft/s and a total flight time of 2.3 seconds. Express your final answer on miles.
To find out the distance, multiply the velocity by the time
d=3,800*2.3
d=8.740 ft
Convert to miles
Remember that
1 mile=5,280 ft
so
8,740 ft=8.740/5,280=1.66 miles
You are going to build a new garage similar to the rectangular one you currently have. The current dimensions are 18 feet wide by 24 feet lorig You need to stake and rope off where the concrete will be poured. If the new igarage is going have a width of 24 feet, how much rope are you going to need?-60 ft-120 ft-112 ft -56 ft
By definition, if two figures are similar, then their corresponding angles have the same measure and the length of their corresponding sides are in the same ratio.
In this case, you know that the new garage and the current garage are similar. Then, using the information given in the exercise you can set up the following proportion (Where "l" is the length in feet of the new garage):
[tex]\frac{24}{18}=\frac{l}{24}[/tex]Solving for "l", you get:
[tex]\begin{gathered} (24)(\frac{24}{18})=l \\ \\ \frac{576}{18}=l \\ \\ l=32 \end{gathered}[/tex]Since you need to stake and rope off where the concrete will be poured, you need to find the perimeter of the rectangle, in order to calculate the amount of rope (in feet) you are going to need.
Knowing the length and the width of the new garage, you get that its perimeter is:
[tex]\begin{gathered} P=2(32ft)+2(24ft) \\ P=64ft+48ft \\ P=112ft \end{gathered}[/tex]The answer is: Third option.
By convention if only the common logarithm are used throughout a discussion the base _______ is not written:
A.e B.10 C.1 D.0
Answer:
B 10
Step-by-step explanation:
MODELING REAL LIFE The height of the house is 26 feet. What is the height x of each story?T61tThe height x of each story isfeet
The total height of the building in the picture has been shown as
x + x + 6
That is, the first two storys have been shown as x feet each and the total height is 26 feet.
That means the two x are actually 20 feet, (if you deduct the 6 feet given)
Total height = x + x + 6
26 = x + x + 6
26 = 2x + 6
Subtract 6 from both sides of the equation
26 - 6 = 2x + 6 - 6
20 = 2x
Divide both sides of the equation by 2 and you now have,
20/2 = 2x/2
10 = x
Therefore, te height of each story is 10 feet!
30. Determine an equation for a line that is parallel to the y-axis and passes through the point (-7,9).(1 point)31. Determine an equation for the line that passes through the points (1,22) and (7,4). (1 point)Can I Get Help with question 30 and 31?
Given:-
The line passes through (-7,9).
To find:-
Equation for a line that parallel to y-axis and passes through the point (-7,9).
The images of line which is parallel to y-axis is,
So if the line is parallel towards the y-axis then, the value of x-axis is equal.
That is,
[tex]x=k[/tex]And the value of k here is the x-axis value of the point the line passes through.
So,
[tex]x=-7[/tex]So the equation of the line which is parallel to y-axis and passes through the point (-7,9) is,
[tex]x+7=0[/tex]So the required equation is x+7=0.
(ii) Find p if 3P =
3 square root 9/3
P = 9/3 is the formula for the power of three.
3p = 3
When the power of 3 is P = the power of 3 is 1, the outcome is p = 1.
A hospital conducted a random sample of its patients by asking each to report the number of colds they had experienced over the last year. The results are shown in the bocks plot and the histogram
We are given a boxplot and a histogram of the number of colds patients had experienced over the last year.
Let us analyze each of the given statements.
Statement 1: Both displays show the data is skewed right.
The above statement is correct.
Notice that the peak of the histogram is at 2 and the long tail of values is to the right of the peak.
Hence, the histogram is skewed right.
Now, notice the boxplot, the whisker is longer on the right side of the box.
Hence, the distribution of the boxplot is skewed right.
Statement 2: Both displays show the data is skewed left.
The above statement is incorrect. (because statement 1 is correct)
Statement 3: Only the histogram indicates the number of patients in the sample.
The above statement is correct.
You can calculate the total number of patients in the sample by adding up the heights of all bars in the histogram.
On the other hand, there is no indication of the number of patients in the boxplot.
Statement 4: The box plot shows the mean number of colds was 2.
The above statement is incorrect because a box plot gives us the median value, not the mean.
Statement 5: The box plot shows the median number of colds was 2.
The above statement is correct.
The median of the box plot is the middle value of the box which is exactly 2.
Hence, the median of the box plot is 2.
Summary:
Statements 1, 3, and 5 are correct.
how many sixths are equivalent to 6/12
Answer:
3/6
Step-by-step explanation:
6/12 divided by 2 is 3/6
Hope that helped!!
The odds against the horse Bucksnot winning the race are 8:7. What is the probability that Bucksnot will win the race?
We have to find the probability that Bucksnot wins the race, which has odds that are 8:7.
The odds 8:7 means that out of 8+7 = 15 races, Bucksnot is expected to win 8.
Then, the probability can be calculated as:
[tex]P=\frac{8}{15}\approx0.533[/tex]Answer: the probability is approximately 0.533.