[tex]5x + 5x = - 2 + 9 \\ 10x = 7 \\ \frac{10x}{10} = \frac{7}{10} \\ x = \frac{7}{10} [/tex]
ATTACHED IS THE SOLUTION
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 CIn 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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for 1 and 2 draw front side and top views of each stack of unit blocks
1.
2.
3.
In the figure of the second exercise there is one block which is not visible.
4.
We can see that the figure is made with 8 blocks
5.
The maximum length of the figure would be 6. You need 3 blocks to get a heigth of 3 units. Then you can add the other 5 blocks to the one which is in the base to make the figure with a length of 6 units.
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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Find the number of zeros at the end of (51! −50!).
Question 10
What is the equation of a line parallel to y = 3x + 2 and passes through the point (2, 1)?
Oy = 3x - 5
Oy=2x+3
Oy=3x + 7
Oy=1/3x+7
10 pts
The equation for a line parallel to y = 3x + 2 that passes through the point (2, 1) is y = 3x - 5.
What exactly is Point Slope Form?The point slope form is used to calculate the equation of a straight line that is inclined to the x-axis at a given angle and passes through a given point.
What are the methods for solving the line equation?Depending on the information available, the equation of a line can be found using a variety of methods. Among the methods are:
Point slope formSlope-intercept formIntercept formTwo-point formThe given equation of line is y = 3x + 2.
We need to find the equation of line parallel to the given line and it passes through the point (2, 1).
Slope of line y = 3x + 2 is given as:
By comparing the given equation with y = mx + c, we can say that the slope(m) = 3
Let, a point with coordinates (x, y) be on the line parallel to given line.
Finding slope again we get,
[tex]\frac{y-1}{x-2}[/tex] = 3
y-1 = 3x - 6
∴ y = 3x - 5
As a result, a line parallel to y = 3x + 2 that passes through the point (2, 1) has the equation y = 3x - 5.
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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]
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
The difference between 7 times a number and 9 more than 2 times the number.
Answer:
Step-by-step explanation:
Equation: 7x - 9 = 5 (x+2) 7x - 9 = 5x + 10 2x = 19 x = 9.5
Act 3 of the 2003 Leonid meteor shower was expected to last 24 hours. The margin of error for this prediction was
0.7 days. Set up and solve an absolute value equation to find the limits of the range for the length of time that Act 3
could last. Show your work.
The limits of the range for the length of time that Act 3 could last is 33.6
What is limit ?The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category. In general, integrals are divided into two categories: definite integrals and indefinite integrals.
A 24-hour period was predicted for Act 3 of the 2003 Leonid meteor shower. This prediction had a 0.7-day error window. How long could Act 3 potentially last, in the range
Lower Limit: 24-0.7(24) = 0.3(24) = 7.2 hrs
Upper Limit: 24+0.7(24) = 40.8 hrs
Range = Upper Limit - Lower Limit
= 40.8 - 7.2
=33.6
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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)
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]
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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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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Find the area of the sector of the circle.
Answer:
D
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{\frac{5\pi }{8} }{2\pi }[/tex]
= π × 12.8² × ([tex]\frac{5}{8}[/tex] ÷ 2)
= π × 163.84 × [tex]\frac{5}{16}[/tex]
≈ 160.8 cm² ( to the nearest tenth )
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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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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uppose that the rela
S={(-1, -9), (-9, 1), (3, 1)}
ve the domain and range of S.
rite your answers using set notation.
domain =
range =
Answer:
Domain = {-9, -1, 3}Range = {-9, 1}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
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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Help me solve this please
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
11=t/-12. Find the value of T
Answer:
t=-132
Step-by-step explanation:
multiply -12 on both sides.
-12x11=t
t=-132
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
D) Simplify the expression.
7/12- 11/12 + 5/12=
Answer: 1/12
step by step equation:
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
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.
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
the net decimal equivalent of 48 27 12
what is the value of 6a+9b?
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°
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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