Answer:
[tex] \sf \large \: x≤6 \: or \: x≥10[/tex]
Step-by-step explanation:
Let's solve your inequality step-by-step.
x2−16x+60≥0
Let's find the critical points of the inequality.
x2−16x+60=0
(x−6)(x−10)=0(Factor left side of equation)
x−6=0 or x−10=0(Set factors equal to 0)
x=6 or x=10
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x≤6(Works in original inequality)
6≤x≤10(Doesn't work in original inequality)
x≥10(Works in original inequality)
This table displays the height of a balloon as it floats away. A 2-column table with 6 rows. Column 1 is labeled Time (minutes) with entries 10, 11, 12, 13, 14, 15. Column 2 is labeled Height (feet) with entries 64, 73.5, 83, 92.5, 102, 111.5. What is the rate of change for the height as the time increases by 1 minute? Rate of change = Which table shows a constant rate of change of –3? A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6. Column 2 is labeled y with entries negative 8, negative 5, negative 2, 1. A 2-column table with 4 rows. Column 1 is labeled x with entries 15, 16, 17, 18. Column 2 is labeled y with entries 12, 9, 7, 4. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 1. Column 2 is labeled y with entries negative 9, negative 12, negative 16, negative 20. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 22, negative 21, negative 20, negative 19. Column 2 is labeled y with entries 2, negative 1, negative 4, negative 7.
Using the average rate of change concept, we have that:
The rate of the height is of 9.5 feet per minute.The table with a rate of -3 is given by: A 2-column table with 4 rows. Column 1 is labeled x with entries negative 22, negative 21, negative 20, negative 19. Column 2 is labeled y with entries 2, negative 1, negative 4, negative 7.What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item 1, when the time in minutes changes by 1, the height changes by 9.5 units, hence the rate is given by:
r = 9.5/1 = 9.5 feet per minute.
For item 2, we want a table with a rate of -3, hence, when the first column changes by 1, the second column should always change by -3, hence the table is:
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 22, negative 21, negative 20, negative 19. Column 2 is labeled y with entries 2, negative 1, negative 4, negative 7.
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Find the slope of the line graphed below.
GUYS WHAT HELPPP MEEE
ILL LOVE YOU FOREVER PLEASEHELP MEE
Answer:
75°
Step-by-step explanation:
[tex]m\angle KLM=m\angle KLQ+m\angle QLM \\ \\ 173=x+105+x+82 \\ \\ 173=2x+187 \\ \\ 2x=-14 \\ \\ x=-7 \\ \\ \implies m \angle QLM=-7+82=75^{\circ}[/tex]
Answer:
75
Step-by-step explanation:
Points A and B lie on plane M. Does line AB lie in plane M? Justify your answer using a postulate.
The line AB joining the points A and B on the plane M lies in plane M.
Say there are two points A and B which lies on the plane M.
Through any two points, there is only one line. Then there is exactly one line joining the two points A and B which is the line AB
Since both the points lies on the plane M, the line joining them should also lie on the plane M.
The postulate which verifies this is:
If two points lie on a plane, then the line joining the points also lies on the same plane.
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What is the graph of this function
A statement, rule, or regulation that establishes the relationship between an independent variable and a dependent variable is known as a function.
A network can be represented mathematically as a graph, which explains the connection between lines and points. A graph consists of some points with connecting lines.
Consider the function,
[tex]f(x)=\frac{||x||+2}{2}[/tex] and 0 ≤ x ≤ 6
To graph the function we will find the points on the graph for different values of x.
When x = 0,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(x)=\frac{||0||+2}{2}=1[/tex]
When x = 1,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(1)=\frac{||1||+2}{2}\\ f(1)=\frac{3}{2}[/tex]
When x = 2,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(2)=\frac{||2||+2}{2}[/tex]
[tex]f(2)=2[/tex]
When x = 3,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(3)=\frac{||3||+2}{2}[/tex]
[tex]f(3)=\frac{5}{2}[/tex]
When x = 4,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(4)=\frac{||4||+2}{2}\\ f(4)=3[/tex]
When x = 5,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(5)=\frac{||5||+2}{2}[/tex]
[tex]f(5)=\frac{7}{2}[/tex]
When x = 6,
[tex]f(x)=\frac{||x||+2}{2}[/tex]
[tex]f(6)=\frac{||6||+2}{2} \\f(6)=4[/tex]
Therefore, the points on the graph of the function [tex]f(x)=\frac{||x||+2}{2}[/tex] are ( 0, 1 ), ( 1, ( 3/2 ) ), ( 2, 2 ), ( 2, ( 5/2 ) ), ( 4, 3 ), ( 5, ( 7/2 ) ), and ( 6, 4).
Hence, the graph of the function is:
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The area of a square tin plate is 7056 square inches. Find the length of a side of the plate.
whatre the values of x and y
By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).
What are the values of two variables associated with two angles from a right triangle?
In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:
(x + 20) + 90 + 30 = 180 (1)
20 + 90 + (y + 30) = 180 (2)
By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).
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Evaluate x/2-5y+1.5z when x = 10, y = 8, and z = 4
Answer:
-29
Step-by-step explanation:
x/2 - 5y + 1.5z
(10)/2 - 5(8) + 1.5(4)
5 - 40 + 6
-35 + 6
-29
Answer:
=10/2-5×8+1.5×4
=5-40+6.0
=-29
A salesperson earns a commission of $510 for selling $3000 in merchandise find the commission rate
Step 1) : Based on the given conditions, formulate
[tex] \large\bf \longrightarrow \frac{510}{3000} [/tex]
Step 2) : Calculate
[tex] \bf \longrightarrow\frac{51 \cancel{0}}{{300 \cancel{0}} } \: = \frac{51 \div 3}{300 \div 3} = \frac{17}{100} [/tex]
Step 3) : Convert to percentage
[tex] \bf\longrightarrow{\frac{17}{100} = 0.17}[/tex]
Hence, the commission rate is 17%.Suppose [tex]f[/tex] is an even function and [tex]\int\limits^7_{-7} {f(x)} \, dx =18[/tex].
a. Evaluate [tex]\int\limits^7_0 {f(x)} \, dx[/tex]
b. Evaluate [tex]\int\limits^7_{-7} {xf(x)} \, dx[/tex]
a. Because [tex]f[/tex] is even,
[tex]\displaystyle \int_{-7}^7 f(x) \, dx = 2 \int_0^7 f(x) \, dx = 18 \\\\ ~~~~ \implies \int_0^7 f(x) \, dx = \frac{18}2 = \boxed{9}[/tex]
b. The product of an even function [tex](f)[/tex] by an odd function [tex](x)[/tex] is an odd function, whose integral over a symmetric interval is zero.
[tex]\displaystyle \int_{-7}^7 xf(x) \, dx = \boxed{0}[/tex]
Ritzie has 80 metres of fencing wire which she wants to use to fence a rectangular plot for gardening. She wished to get the right length and width such that the area enclosed is the maximum. Let x to represent length and y to represent width.
1) Write two equations one for perimetre and the other for area using X and Y
2)Obtain only one equation in terms of area from the equations in 1
Step-by-step explanation:
1)
the perimeter P
P = 2x + 2y = 80 m
the area A
A = x × y
2)
2x + 2y = 80
2y = 80 - 2x
y = 40 - x
and we use that in the equation for area
A = x × (40 - x) = 40x - x²
we find the maximum (or minimum) of a function by finding the 0s of the first derivative.
A' = 40 - 2x = 0
40 = 2x
x = 20
y = 40 - x = 40 - 20 = 20
and just to be sure :
if the second derivative at that point x is negative, we have a maximum, if it is positive, we have a minimum.
A'' = -2
so, it is negative for all x incl. x = 20.
therefore, we have a maximum.
the rectangle with perimeter of 80 m and the max. area is a square of 20 m side length.
Let F(x)=x2-19 and G(x) = 14-x
Find (F/G)(-3)
Value of (F/G)(-3) with the given functions F(x)=x² -19 and G(x) = 14 - x is equal to (-10/17).
As given,
Given functions
F(x)=x² -19
G(x)=14 - x
Substitute the values in the required function:
( F/G )(x)=( x² -19 )/( 14 - x)
Now substitute x= -3
( F/G )( -3) =[ (-3)² -19 ] /[ 14 - (-3) ]
⇒ ( F/G )(-3) =( 9-19) / (14+ 3)
⇒ ( F/G )(-3) =( -10/17)
Therefore, value of (F/G)(-3) with the given functions F(x) = x² -19 and G(x) = 14 - x is equal to (-10/17).
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Please help i really need this done :) I added 50 p[oints
A) Matching the stages of a business life cycle in the correct order is as follows:
ExistenceSurvivalSuccessTake-off Pivot or persistResource MaturityExit Plan.B) Matching the business life cycle to its description is as follows:
Life Cycle DescriptionExit Plan The owner decides to sell.
Success A business owner gets it running and introduces it
to the market in its attempt to catch the competition.
What is the business life cycle?The business life cycle refers to the gradual progress of a business over its lifetime.
A business life cycle can be divided into five broad stages: launch, growth, shake-out, maturity, and decline. Some management gurus classify the life cycle of a business into the following stages: Existence, Survival, Success, Take-off, and Resource Maturity.
Thus, a successful business declines after its maturity stage.
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A chord of a circle 9cm long if it's distance of the centre of the circle is 5 cm calculate the radius of the circle
considering the distance between the center of the circle and the chord is perpendicular, pythagorean theorem can be applied to calculate the radius of the circle.
[tex]r^2=a^2+b^2[/tex] , r=radius, a=half of the chord length, b the distance between the center of the circle and the center of the chord
[tex]r^2=(4.5cm)^2+(5cm)^2\\r^2=20.25cm^2+25cm^2\\r^2=45.25cm^2\\r=\sqrt{45.25cm^2}\\r=6.7268cm[/tex]
Researchers wanted to determine if there was an association between the level of trauma of an individual and their risk
of diabetes. The researchers studied 1544 people over the course of 12 years. During this 12-year period, they
interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition,
hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews
were videotaped and studied to assess the emotions of the individuals. The researchers also determined which
individuals in the study experienced any type of diabetes over the 12-year period. After their analysis, the researchers
concluded that the trauma-free individuals were less likely to experience diabetes. Complete parts (a) through (c).
(a) What type of observational study was this? Explain.
This was a
because information was collected about a group of individuals
The observational study is the Cross-sectional studies.
What is an observational study?It should be noted that an observational study is simply used to answer a research question that is based on what the researcher observes.
This is a cross-sectional studies because it analyzes a population of study at a specific point in time. It should be noted that this involves narrowing previously collected data to one point in time to test the prevalence of a theory.
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BF is dilated to created WH. The center of dilation is point A where BF=15, WH=20
What is the scale factor that was used to create WH
Answer:
The scale factor is 4/3
Step-by-step explanation:
Let x = the scale factor
15x = 20 Divide both sides by 15
x =20/15 Which simplifies to 4/3
The scale factor that was used to create WH will be 4/3.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image decision-making. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
Given that BF is dilated to create WH. The center of dilation is point A where BF=15, WH=20
The scale factor will be calculated as below:-
Let x = the scale factor
15x = 20
Divide both sides by 15
x =20/15
Which simplifies to 4/3.
x = 4 / 3
Therefore, the scale factor that was used to create WH will be 4/3.
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A technician repaired 18 laptops and
24 desktops last month. What is the
ratio of laptops to total computers?
Therefore, the ratio of the number of laptops to total computers is 2:7
Number of laptops repaired by a technician = 18
Number of desktops repaired by a technician = 24
Total number of computers = no of laptops + no of desktops
= 18 + 24
= 42
We have to determine the ratio of laptops to total computers as
= no of laptops / total no of computers
= 18 / 42
= 6 / 14
= 2 / 7
Therefore, the ratio of the number of laptops to total computers is 2:7
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what is 50 pounds in kilograms
Answer:
22.6796 kg.
Step-by-step explanation:
The answer is 22 i am sure about this
The bill for dinner was $77.12. You left $15.88 for the tip. What percentage of the original bill was the tip?
Answer:
The tip was 20.6% or 20.59% of the original bill
Step-by-step explanation:
Question: The bill for dinner was $77.12. You left $15.88 for the tip. What percentage of the original bill was the tip?
Step-by-step:
To find the percentage of how much a part ($15.88) is or a whole ($77.12), the formula of part = percentage * whole is used.
It is usually written as a = p*w
In this case, $15.88 is a and $77.12 is w.
so, 15.88 = p*77.12
However, we need to find p. To do so, we need to get p by itself. Divide 77.12 on both sides so that it cancels out on the right side.
15.88 divided by 77.12 is about 0.2059
We need to make the decimal a percentage by multiplying 100
0.2059 * 100 = 20.59%
You could probably round it up to 20.6% if you wanted to
Therefore, the tip was 20.6% or 20.59% of the original bill.
simplify 18/42 to lowest terms
Answer: 3/7
The factors of 18 are 1,2,3,6,9,18;
The factors of 42 are 1,2,3,6,7,14,21,42.
Find the coordinates of the point 3/10 of the way from A to B. The points given are A(-3,-5) , B(9,6)
[tex]\displaystyle\\Answer:\ (-\frac{3}{13},-2\frac{6}{13} )[/tex]
Step-by-step explanation:
[tex]\displaystyle\\\frac{3}{10} =0.3\\\\(-3,-5)\ \ \ \ \ (9,6)\\\\\boxed {x=\frac{x_1+\lambda x_2}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \ \boxed {y=\frac{y_1+\lambda y_2}{1+\lambda} }\\\\x_1=-3\ \ \ \ \ x_2=9\ \ \ \ \ y_1=-5\ \ \ \ \ \ \ y_2=6\\\\x=\frac{-3+0.3*9}{1+0.3} \\\\x=\frac{-3+2.7}{1.3} \\\\x=\frac{-0.3}{1.3}\\\\ x=-\frac{0.3*10}{1.3*10}\\\\ x=-\frac{3}{13} \\\\[/tex]
[tex]\displaystyle\\y=\frac{-5+0.3*6}{1+0.3} \\\\y=\frac{-5+1.8}{1.3} \\\\y=\frac{-3.2}{1.3} \\\\y=-\frac{3.2*10}{1.3*10} \\\\y=-\frac{32}{13} \\\\y=-2\frac{6}{13} \\[/tex]
Study the red pre-image and the associated blue dilation image. The center of dilation is (2, 2). What is the scale factor of the dilation? 1/3 StartFragment, 1/3, 8 StartFragment, 8, 12 StartFragment, 12, 3
Answer: 3
Step-by-step explanation:
The required scale factor of the given dilation is 3. Option D is correct.
Given that,
The center of dilation is (2, 2).
To determine the scale factor of the dilation.0
The scale factor is defined as the ratio of modified change in length to the original length.
Here,
Length of one side of triangle former dilation = 2 units
Length of one side of triangle later dilation = 6 units
Scale factor = later dimensions / former dimensions = 6 / 2 = 3
Thus, the required scale factor of the given dilation is 3. Option D is correct.
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How you solve this??
Answer:— 36, 20-29 years, 20-29 years, Total confirmed cases in ages 20-29 over the 14 day period ... 707, 01/03/2022, 1151692, 36278, 18031.4286.
Step-by-step explanation:
In a recent year, a university had an enrollment of 15,363 male and 19,512 female undergraduate students. The total number of full-time instructional faculty was 1,849. Find the ratio of students to full-time instructional faculty as a unit ratio. Round to the nearest whole number.
The required ratio of students to teachers is 19: 1.
Given that,
The total enrollment of male students and female students is 15,363 male and 19,512 female respectively.
The total number of full-time instructional faculty was 1,849.
To determine the ratio of students to teachers.
Here,
Total students = 15363 + 19512 = 34875
Number of teachers = 1849
Now,
Ratio = total students / teacher
Ratio = 34875 / 1849
Ratio = 19 : 1
Thus, the required ratio of students to teachers is 19 : 1.
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7 + (4 + 8) = (7 + 4) + 8
Answer:
true
Step-by-step explanation:
Suppose 3
plss helppp
?
The side-by-side stemplot below displays the arm spans, in centimeters, for two classes.
A stemplot titled Arm Span (centimeters). For Class A, the values are 148, 151, 153, 155, 156, 159, 161, 162, 164, 165, 169, 169, 170, 171, 175, 176, 179, 179, 180, 182, 183, 186, 186, 190. For Class B, the values are 153, 155, 16, 160, 162, 162, 162, 163, 163, 165, 166, 167, 170, 173, 180, 181, 182, 189, 192, 202.
Which statement correctly compares the arm spans for Class A to those of Class B?
The mean arm span for Class A is much lower than Class B’s.
The mean arm span for Class B is much lower than Class A’s.
The mean arm span for Class A is much higher than Class B’s.
The mean arm span for Class B is about the same as Class A’s.
Answer:
D
Step-by-step explanation:
I got it right!
Answer:
d
Step-by-step explanation:
took the test
leanna cuts some roses in her front garden and another 20 in her back garden. she uses one quarter of her roses to make a bouquet of a dozen flowers. how many roses did leanna cut in her front yard?
The roses that Leanna cut in her front yard is 28 roses.
How to calculate the value?From the information, she uses one quarter of her roses to make a bouquet of a dozen flowers. Therefore, the total flowers will be:
= 12 ÷ 1/4
= 12 × 4
= 48 flowers
Since she cuts some roses in her front garden and another 20 in her back garden, the number that she cut in the front garden will be:
= 48 - 20
= 28 flowers.
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A rectangular garden plot measures 12 feet by 25.6 feet.
Answer:
Do I calculate the area?
Step-by-step explanation:
A label for a drug indicates that each milliliter contains 7 milligrams of the drug. How many milligrams are in 8 milliliters?
There are 56 milligrams in 8 milliliters of the drug if the drug's label says each milliliter contains 7 milligrams of the substance.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Let x milligrams would in 8 milliliters.
We can write this as a ratio as
As per the given information,
1 milliliter : 7 milligrams = 8 milliliter : x milligrams
⇒ 1 / 7 = 8 / x
⇒ x = 8 × 7
⇒ x = 56 milligrams
Hence, there are 56 milligrams in 8 milliliters of the drug.
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