For this type of question the first step is to calculate the slope of the line given by th equation x+2y=7, for this we recall the slope intercept form ( y=mx+b) and put the equation in that form
[tex]y=-\frac{x}{2}+\frac{7}{2}[/tex]Then, m=-1/2. Now, since the equation of the line we are looking for is parallel to the previous line the slope must be the same, now we recall the point slope equation
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ \end{gathered}[/tex]Substituting m=-1/2, and recalling that the line is passing through (-3,4) we get that the point slope equation the line is :
[tex]\begin{gathered} y-4=-\frac{1}{2}(x-(-3)) \\ y-4=-\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]Finally to put it in the slope intercept form, we solve the equation for y:
[tex]y=-\frac{1}{2}x+\frac{5}{2}[/tex]For part b) we recall that the standard form of the equation of a line is:
[tex]\begin{gathered} C=Ax+By \\ \text{where C, A and B are real and whole numbers if possible} \end{gathered}[/tex]Now, we solve for the constant of the equation:
[tex]\begin{gathered} \frac{5}{2}=y+\frac{1}{2}x \\ 5=2y+x \end{gathered}[/tex]The last equation is the standard form of the equation of the line.
BC has endpoints at B(2, 9) and C(8, 7). Find the midpoint M of BC.
Answer:
Midpoint, M is (5,8)
Step-by-step explanation:
To find the midpoint, average the x's (add and divide by2) then average the y's.
The x's are the first numbers (2+8)/2 is
10/2 which is 5.
The y's are the second numbers in the parentheses, (9+7)/2 is 16/2 which is 8.
So the x of the midpoint is 5 and the y is 8.
The midpoint is (5,8)
Two parallel lines e, and f, are crossed by two transversals. What is the measure of <15?
m<15 = 77
m<15= 83
m<15= 93
m<15= 97
The measure of the angle 15 is 97°
How to find the measure of an angle?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles.
The parallel lines are e and f. These parallel lines are cut across by the transversal lines c and d. The transversal line d is the line that forms the angle 15 with the parallel lines e and f.
Therefore, the angle 97 degrees and the angle 15 are alternate exterior angles.
Alternate exterior angles are congruent.
Therefore,
∠15 = 97 degrees.
Hence, the measure of ∠15 is 97 degrees.
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What is the correct answer to this question
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: State the Angle-Arc relationship
STEP 2: Interpret the given image
[tex]\angle HIJ=\frac{1}{2}HJ[/tex]STEP 3: Find the required angle
By substitution
[tex]\begin{gathered} \angle HIJ=\frac{1}{2}\cdot100 \\ \\ HJ=100 \\ \angle HIJ=\frac{1}{2}\cdot100=50\degree \end{gathered}[/tex]Hence, the answer is 50°
6. Find the value of x. 12 x + 3
Answer:
[tex]x = - 0.25[/tex]
Step-by-step explanation:
[tex]12x + 3[/tex]
[tex]12x = - 3[/tex]
[tex] \frac{12x}{12} = \frac{ - 3}{12} [/tex]
[tex]x = - \frac{1}{4} \: or \: - 0.25[/tex]
A science experiment has a catapult launch a ball. The result of the experiment is shown in the table. experiment is shown in the table.
a. What is the average distance of the 5 attempts? Show your work.
B. How far does the ball have to travel on the sixth attempt so that the average of all 6 of the attempts is 50.9 meters? Explain
please help!!
The data on the attempts and distances of the science experiment on the launch of a ball by a catapult, presented in a tabular form gives the following;
a. The five attempts have an average distance of 50.58
b. The distance the sixth ball has to travel so as to give an average distance traveled of 50.9 meters is 52.5 meters
What is an average of a data set?An average is a descriptive statistics that tends to describe the values in a dataset. An average or the mean of a dataset is obtained by summing the data values and dividing the result by the number of data points
Please find attached, the Attempt to Distance table obtained from a similar question online
a. The formula for average, [tex] \bar{x} [/tex] of a set of data or observations is presented as follows;
[tex] \displaystyle{\bar x = \frac{Sum \: of \: observations}{Number \: of \: observations}} [/tex]
Mathematically, we have;
[tex] \displaystyle{\bar x = \frac{\sum x}{N}} [/tex]
Which gives from the attached table;
[tex]\displaystyle{\sum {x} =50.7+49.4 +52.3 + 48.9 + 51.6 = 252.9}[/tex]
N = 5
Which gives;
[tex] \displaystyle{\bar x = \frac{252.9}{5} = 50.58}[/tex]
The average distance of the 5 attempts is 50.58 metersb. The distance, d, the ball has to travel on the sixth attempt to get an average of 50.9 meters is found as follows;
The new total number of attempts, N = 6
Which gives;
[tex] \displaystyle{\bar x = 50.9 = \frac{d + 252.9}{6} }[/tex]
6 × 50.9 = d + 252.9
Therefore;
d = 6 × 50.9 - 252.9 = 52.5
The distance the ball has to travel in the sixth attempt to have an overall average of 50.9 meters is 52.5 metersLearn more about the average of a dataset here:
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Will equation 2/5 + 3 squared be rational or irrational? Why?
The short answer is [tex]\frac{2}{5}+3^2[/tex] will be considered rational.
Why you ask? Continue reading below for a deeper explanation.
_____________________________________________________
| Rational and Irrational Numbers |"What Are They?" - Descriptions and Examples
Rational Numbers are numbers in which can be expressed as an integer or the quotient of an integer divided by a nonzero integer. For example, the number can be represented in the form of [tex]\frac{p}{q}[/tex] , where P and Q are integers and Q ≠ 0.
Example ( [tex]\frac{1}{3}, \frac{2}{4}, \frac{1}{5}, ...[/tex]are all considered rational.Irrational Numbers on the other hand cannot be written in the form of simple fractions. In other words, it is a real number the isn't able to be made by dividing two integers.
Example ([tex]\sqrt{2}, \sqrt{3} , \sqrt{5},...[/tex] are all considered irrational._____________________________________________________
Hope this helps! If I missed anything, feel free to ask any further questions you may have regarding the topic below in the comments and I'll see what else I can do to assist you further. However, if this did help, feel free to lmk. Thank you for your time and I wish you the best of luck on the rest of your studies!
which of the following is the graph of the function f(x)=1/2Ix+4I-3
we have the function
f(x)=1/2Ix+4I-3
the vertex of the given function is the point
(-4,-3) ---------> III quadrant
therefore
the answer is the option Ca recipe calls for 15 oz of flour for every 8 fl oz of milk
if you use 15 fl oz of milk, how much flour should you use
Work Shown:
(15 oz of flour)/(8 fl oz of milk) = (x oz of flour)/(15 fl oz of milk)
15/8 = x/15
15*15 = 8*x
225 = 8x
8x = 225
x = 225/8
x = 28.125
the net decimal equivalent of 48 27 12
In a lab experiment, 260 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 26 hours. How long would it be, to
the nearest tenth of an hour, until there are 350 bacteria present?
It will take about 8.7 hours until there are 350 bacteria present using exponential growth.
What is exponential growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
The formula is as follows:
P = [tex]initial (rate)^x[/tex]
Given that 260 bacteria are placed in a petri dish.
initial value = 260
growth factor = 2
growth factor's associated time period = 26 hours
Exponential growth equation can be written as
[tex]n = 260(2^(t/26))[/tex]
For n=350, we can put the value and take log on both sides.
[tex]350=260(2^{(t/26)} )[/tex]
[tex]1.3 = 2^{t/26}[/tex]
log 1.3 = (t/26) log(2)
26×log(1.3)/log(2) = t
t ≈ 8.7 hours
Therefore, it will take about 8.7 hours until there are 350 bacteria present.
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Find the number of zeros at the end of (51! −50!).
The City Pool needs a new cover for its circular toddler pool. The diameter of the pool is 25 ft. Which size cover will fit the pool?
Answer:
it’s 20 feet
Step-by-step explanation:
just took the test
what is the value of 6a+9b?
D) Simplify the expression.
7/12- 11/12 + 5/12=
Answer: 1/12
step by step equation:
Suvinder spends £ 26 on 100 postage stamps. If x of them are 20 p stamps and the remaining y are 35p stamps, write down two equations in x and y and solve them.
Solving a system of equations, we will see that Suvinder bought 60 of the £0.20 stamps and 40 of the £0.35 stamps.
How to write and solve the equations for x and y?We know that Suvinder spent £26 on 100 postage stamps, defining:
x = number of £0.20 stamps bought.y = number of £0.35 stamps bought.Then we can write the system of equations:
x + y = 100
x*0.20 + y*0.35 = 26
Isolating x on the first equation we get:
x = 100 - y
Replacing that in the other equation we get:
(100 - y)*0.20 + y*0.35 = 26
Solving that for y, we get:
20 - y*0.20 + y*0.35 = 26
20 + y*0.15 = 26
y*0.15 = 26 - 20 = 6
y = 6/0.15 = 40
Then:
x = 100 - y = 100 - 40 = 60
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if 1kg=2,2ib(pounds),convert 300g into pounds
1 kg = 1000g
Hence,
[tex]1000g\equiv2.2\text{ pounds}[/tex]This implies that,
[tex]1g\equiv\frac{2.2}{1000}[/tex][tex]300g\equiv\frac{2.2}{1000}\times300=\frac{6.6}{10}=0.66\text{ pounds}[/tex]The diagram shows two quadrilaterals graphed on a coordinate plane. 4 5 6 7 8 Which transformation on quadrilateral 1 can be used to verify that is similar to quadrilateral
dilation, k=0.5
Explanation
Step 1
as we can see, the quadrilaterals have different size. it means we can discard a traslation
Step 2
now, we can see both quadrilateral have similar shape, so we can check for a dilation.
A dilation is a type of transformation that changes the size of the image. The scale factor measures how much larger or smaller the image is
[tex]A(x,y)\rightarrow Dilation\rightarrow A^{\prime}(kx,ky)[/tex]in this case, quadrilateral 1 is bigger than quadrilateral 2, it means it suffered a compresion, so k is smaller than 1
[tex]A(x,y)\rightarrow A^{\prime}(kx,ky)\text{ for k}<1[/tex]we can find k,
let
A=a point of the quadrilateral
[tex]\begin{gathered} A(-6,0)\rightarrow A^{\prime}(-6k,0k)\rightarrow A^{\prime}(-3,0) \\ so \\ -6k=-3 \\ k=\frac{-3}{-6} \\ k=\frac{1}{2} \end{gathered}[/tex]I hope this helps you
Question
Find the equation of a line that contains the points (-7,-4) and (−2, 3).
(Write the equation in standard form.)
Answer:
y=1.4x+5.8
You have to do y2-y1 over x2-x1.
Please help me factor.
49 - 9x²
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
7
and
b
=
3
x
.
(
7
+
3
x
)
(
7
−
3
x
)
Answer: -(3x - 7)(3x + 7)
Step-by-step explanation:
1. Rewrite the formula:
-[tex]9x^{2} + 49[/tex]
2. Factor -1 out of [tex]-9x^{2} + 49[/tex]
[tex]-(9x^{2} - 49)[/tex]
3. [tex]9x^{2} - 49 = (3x)^{2} - 7^{2}[/tex]
[tex]((3x)^{2} - 7^{2})[/tex]
4. Factor the difference of two squares. [tex](3x)^{2} - 7^{2} =[/tex]
[tex](3x-7)(3x+7)[/tex]
5. Add back negative:
Answer: [tex]-(3x-7)(3x+7)[/tex]
Which is the best approximate solution to the linear system? (Use the graphing calculator tool to graph the
system. Round to the nearest tenth.)
2x - y = //
-2y + 2x =
O (0.7, -1)
(0.8,-1)
O (1.4,-0.3)
O (1.4,-0.4)
The best approximate solution to the linear system is x= 3/4 y = -1
What is linear system?
linear system are system of equations in which the variables are never multiplied with each other but only with constants and then summed up.
Reorder the equation:2x-y =5/2
2x-2y = 7/2
Subtract the two equations:
2x-y -(2x-2y)=5/2 - 7/2
Remove parentheses:
2x-y -2x +2y =5/2-7/2
Cancel one variable:
-y +2y =5/2-7/2
Combine like terms:
5/2-7/2
Write the numerators over common denominator:
Y= 5-7/2
Calculate the sum or difference:-2/2
Rewrite the fraction:-2/2
Cross out the common factor:-1
Substitute into one of the equations:2x-(-1)=5/2
Remove the parentheses:2x+1=5/2
Multiply both sides of the equation by the common denominator:2x×2+2=5×2/2
Reduce the fractions:2x×2+2=5
Rearrange unknown terms to the left side of the equation:4x=5-2
Calculate the sum or difference:4x=3
Divide both sides of the equation by the coefficient of variable:
The solution of the system is:x=3/4
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Points A, B, and C are collinear. Point B is between A and C. Find the value of x.
AC = 4x − 29
AB = 2x − 18
BC = 19
A ball is thrown in the air. The function
h = 30t-5t²
can be used to find the height (h) of the ball in meters after 6 seconds. How long does it take the ball to reach a height of 45 meters?
Using given function, we conclude that it will take 3 seconds the ball to reach a height of 45 meters.
In this question, we have been given a function h = 30t - 5t²
This function is used to find the height (h) of the ball in meters after 6 seconds.
We need to find the amount of time required to reach ball to a height of 45 meters.
here, height h = 45 meters
to find : time t
h = 30t - 5t² ........................(Given function)
45 = 30t - 5t²
30t - 5t² - 45 = 0
5t² - 30t + 45 = 0
t² - 6t + 9 = 0
(t - 3)² = 0
t - 3 = 0
t = 3 seconds
Therefore, it will take 3 seconds the ball to reach a height of 45 meters.
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Choose the correct simplification of (5xy^7)^2(y^4)^3.
25x^2y^22
10x^2y^14
25x^2y^14
10x^2y^20
The simplified form of the given expression is 25 x² y ²⁶.
What is the simplified form of the expression?
Simplifying expressions mean rewriting the same algebraic expression in a compact form such that there are no like terms.
What are the exponent rules?
The different Laws of exponents used to solve the above mentioned question are:
[tex]x^{m}.x^{n} = x^{m+n} \\\frac{x^{m} }{x^{n} } = x^{m-n} \\(x^{m})^{n} } = x^{mn }[/tex]
According to the given question.
We have an expression (5xy⁷)²(y⁴)³
To simplify the above expression we use the exponent rules.
Therefore,
(5xy⁷)²(y⁴)³
(5² x² y²×⁷) (y ⁴׳)
(25 x² y¹⁴ ) (y¹²)
25 x² y¹⁴⁺¹²
25 x² y ²⁶
Therefore, the simplified form of the given expression is 25 x² y ²⁶
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The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random
variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl
in 10 births is a significantly low number of girls.
Use the range rule of thumb to identify a range of values that are not significant.
The maximum value in this range is ___
Number ofGirls x
0
1
2
3
4
5
6
8
9
10
P(x)
0.004
0.015
0.036
0.116
0.201
0.245
0.196
0.115
0.041
0.012
0.019
The maximum value in this range is 8.3 girls. The range of a set of numbers is the difference between its highest and lowest values. To find it, subtract the lowest number from the highest in the distribution.
What is maximum value?The maximum value of a function is the point on a graph where the function reaches its highest point, or vertex. In this image, for example, the maximum value of the function is y equals 5. To find the maximum, we must locate the point on the graph where it changes from increasing to decreasing. We look at the second derivative and see when the value changes from positive to negative to determine the rate at which the graph shifts from increasing to decreasing. The min is simply the smallest observation, while the max is the largest. Obviously, determining the min and max is easier if the data is ordered from lowest to highest. So, for our data, the minimum is 13 and the maximum is 110To learn more about maximum value, refer to:
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The length of a rectangle is four times its width.
If the perimeter of the rectangle is 60 ft , find its area.
A rectangle has a perimeter of 60 feet. The rectangle's length is four times its width. The area of rectangle is 144 square feet.
Given that,
A rectangle has a perimeter of 60 feet.
The rectangle's length is four times its width.
We have to find the area of rectangle.
Let us take length as x
The width will be 4x
The perimeter =2(4x+x)
2(4x+x)=60
4x+x=60/2
5x=30
x=30/5
x=6
The length will be 6.
The width will be 4×6=24.
The area of rectangle is length×width
=6×24
=144 square feet.
Therefore, the area of rectangle is 144 square feet.
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Below is the graph of f’(×), the derivative of f(x), and has x-intercepts at x =-3, x = 1, and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5.Which of the following statement is false?
Answer:
Option 1:
Explanation:
In order for f(x) to be concave up in an interval, the graph of the derivative would have to be increasing in that interval.
In the given graph, from x=-1.5 to x=1.5, the graph of the derivative is decreasing, therefore, the statement that "f is concave up from x=-1.5 to x=1.5" is false.
Next, for f to have an inflection point at any x-value the slope of the derivative, f'(x) must change signs at that x-value. Therefore, the statement "f has an inflection point at x=1.5" is true.
Finally, for f(x) to have a relative minimum at x=2, the value of the derivative must be 0, which is as seen on the graph.
Therefore, the first option is False.
the bear family has an average age of 58. if john is two years younger than tom and lisa is 16 years older than john, what are the ages of john,tom and lisa ?
The ages of John, Tom and Lisa are 52 years, 54 years and 68 years respectively.
According to the question,
We have the following details:
The average age of the Bear family is 58 years.
Now, let's take Tom's age to be x years, Lisa's age to be y years and John's age to be z years.
So, we have the following expression:
(x+y+z)/3 = 58
(x+y+z) = (58*3)
(x+y+z) = 174 .... (1)
Now, John is two years younger than Tom, so we have:
z = (x-2) ....(2)
Lisa is 16 years older than John. So, we have:
y = (z+16) ....(3)
Now, putting the values of y and z in equation 1,
x+z+16+x-2 = 174
Now, again putting the value of z from equation 2,
x+x-2+16+x-2 = 174
3x+12 = 174
3x = 174-12
3x = 162
x = 162/3
x = 54 years
Now, putting the value of x in equation 2,
z = x-2
z = (54-2) years
z = 52 years
Now, putting the value of z in equation 3,
y = z+16
y = (52+16)
y = 68 years
Hence, the ages of John, Tom and Lisa are 52 years, 54 years and 68 years respectively.
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Indira and Jean begin their hike at 10 a.m. one morning. They plan to hike from the 2 2/5-mile marker to the 8 1/10-mile marker along the trail. They plan to hike at an average speed of 3 miles per hour. Will they reach the 8 1/10 -mile marker by noon? Explain your reasoning.
Please hurry this is due tomorrow. I would really appreciate it. And if you can, please send a photo of how you solved the problem. Lastly, make sure the explanation is clear. Again, thank you sm. <3
Step-by-step explanation:
the initial distance is 2 2 /5mile or 2.4 mikes and the final is 8 1/10 or 8.1 mile . Therefore total distance to hike is
Distance=8.1 - 2.4 = 5.7miles
since they will trek at 3 miles per hour the time needed is : 5.7 MILE/ 3MILES PER hour
time: 1.9HOURS
since they started at 10am and there is 2 HOURs ALLOWANCE from noon ,THEREFORE they will reach the marker by noon 0.10 hour left
THAT'S ALL MISS
Insert parenthesis in the proper place so that the given value of the expression is obtained. Show all WORK. You may have to insert more then one set of parenthesis.
6+9/3+16-4*2; 29
36/4+2-4; 2
5-3*2+8*5-2; 28
Applying precedence of operations, the parenthesis on the operations are inserted as follows:
(6+9)/3+(16-4)*236/(4 + 2) - 4.(5-3)*2 + 8*(5 - 2).What is the precedence of operations?The acronym PEMDAS defines the precedence of operations, from highest to lowest, as follows:
P: Parentheses.E: Exponent.M: Multiplication.D: Division. (same precedence as multiplication).A: Addition.S: Subtraction. (same precedence as addition).For the first item, we want a result of 29, hence the expression will be of:
(6+9)/3+(16-4)*2.
As the equivalent result will be of:
(6+9)/3+(16-4)*2 = 15/3 + 12 x 2 = 5 + 24 = 29.
For the second item, we want a result of 2, hence the expression will be of:
36/(4 + 2) - 4.
As the equivalent result will be of:
36/6 - 4 = 6 - 4 = 2.
For the third item, we want a result of 28, hence the expression will be of:
(5-3)*2 + 8*(5 - 2)
As the equivalent result will be of:
(5-3)*2 + 8*(5 - 2) = 2 x 2 + 8 x 3 = 4 + 24 = 28.
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Express 36 cookies divided equally among 24 students as a fraction and a decimal.
Answer:
3/2, 1.5
Step-by-step explanation:
When you put 36 cookies divided amongst 24 students, each student cookies one and a half cookies