Answer:
n < 6
Step-by-step explanation:
n/-3 + 8 > 6
Subtract 8 from each side
n/-3 + 8 -8> 6-8
n/-3 > -2
Multiply each side by -3 to isolate n. Remember to flip the inequality since we are multiplying by a negative
n/-3 * -3 < -2 *-3
n < 6
How do you do this problem
Answer:
[tex]\large\boxed{\text{Factored Form:}\ f(x)+-(x-1)(x-5)}\\\boxed{\text{Vertex Form:}\ f(x)=-(x-3)^2+4}\\\boxed{\text{Standard Form:}\ f(x)=-x^2+6x-5}[/tex]
Step-by-step explanation:
(look at the picture)
Factored form:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]
x₁, x₂ - zeros
Vertex form:
[tex]f(x)=a(x-h)^2+k[/tex]
(h, k) - vertex
Standard form:
[tex]f(x)=ax^2+bx+c[/tex]
If from the vertex we go 1 unit down (up) and 1 unit left (right) and we get the point on the parabola, then a = 1.
The parabola is open down, therefore a < 0 → a = -1.
The zeros are [tex]x_1=1[/tex] and [tex]x_2=5[/tex]. Therefore the Factored Form is:
[tex]f(x)=-(x-1)(x-5)[/tex]
The vertex is V(3, 4). Therefore the vertex form is:
[tex]f(x)=-(x-3)^2+4[/tex]
Convert it to a standard form using (a - b)² = a² - 2ab + b²
[tex]f(x)=-(x^2-2(x)(3)+3^2)+4=-x^2+6x-9+4=-x^2+6x-5[/tex]
Write an equation to match the statement “10 is 2 times as many 5” show the work pleaseeeeeee
Identify the center and the radius of each.
x^+y^+26x-22y+281=0
Answer:
Center (-13,11) , radius 3
Step-by-step explanation:
The given circle has equation
[tex]x^2+y^2+26x-22y+281=0[/tex]
We compare this to the general equation.
[tex]x^2+y^2+2ax+2by+c=0[/tex]
where (-a,-b) is the center.
This implies that;
2a=26
[tex]\Rightarrow a=13[/tex]
2b=-22
b=-11
The center is therefore (-13,11)
The radius is given by
[tex]r=\sqrt{a^2+b^2-c}[/tex]
[tex]r=\sqrt{13^2+(-11)^2-281}[/tex]
[tex]r=\sqrt{9}[/tex]
The radius is 3
Given F(x)=1/3(4-x)^2 What is the value of f(16)
Answer:
48
Step-by-step explanation:
Wherever you see an x on the right, you put a 16. That's what f(16) means.
f(16) = 1/3 (4 - 16)^2
f(16) = 1/3 (- 12)^2
f(16) = 1/3 (144)
f(16) = 48
What is the Y-value of the vertex of4x^2+8x-8
Answer:
-12
Step-by-step explanation:
y = 4x^2 + 8x - 8
Put brackets around the first 2 terms and pull out the common factor
y = (4x^2 + 8x) - 8
y = 4(x^2 + 2x) - 8
Take 1/2 of the linear term (2x) and square it. Put the square inside the brackets.
y = 4(x^2 + 2x + (2/2)^2 ) - 8
y = 4(x^2 + 2x + 1) - 8
You have added 4*1 inside the brackets. You must subtract that amount outside the brackets.
y = 4(x^2 +2x + 1) - 8 - 4
Notice that the trinomial inside the brackets is a perfect square. Combine the terms outside the brackets.
y = 4(x + 1)^2 - 12
You have completed the square and you are finished.
The vertex is (-1, - 12)
The y value is - 12.
Just to confirm this, I have included the graph.
The amount of money that high school students spend on fast food each month is usually between $50 and $200. However, there are a few students who do not eat fast food at all. What measure of spread would be most appropriate to measure the amount of money that high school students spend on fast food per month?
Answer:
B) Interquartile Range
Answer:
IQR, interquartile range
Step-by-step explanation:
thats what i got on algebra nation, lmk if you want an explanation :)
Which of the following statements is true about this situation?
ZOOMIN
Hello there! The correct answer is C. The electric car is not moving at 0 seconds and 12 seconds.
In the question description it says that y represents the car's speed in miles. Now looking back at the chart, wherever the x values are at when y = 0, the car isn't moving at this time, because if the car is going at 0 miles per hour, it is not moving. Looking at the chart, you can see the car is going 0 miles per hour when x = 0 and x = 12. This means that C is your answer.
I hope this helps and have a great day!
A statement that is true about this situation include the following: C. The electric car is not moving at 0 seconds and 12 seconds.
In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
Generally speaking, a physical object is considered as being static (not moving or in motion) when its speed is equal to zero (0).
In this context, we can reasonably infer and logically deduce that this new electric car is not moving at 0 seconds and 12 seconds because the speeds (y-avlues) at this time interval are equal to zero (0).
Complete Question;
Marcel is performing the first test on his company's new electric car During the test, the electric car reaches a maximum speed of 81 mph.
The performance test results of the electric car can be modeled by the following table, where x represents time, in seconds at the start of the test, and y represents the speed, in miles per hour.
Which of the following statements is true about this situation?
A. The electric car is not moving at 6 seconds and 12 seconds.
B. The electric car is not moving at 4 seconds and 8 seconds.
C. The electric car is not moving at 0 seconds and 12 seconds
D. The electric car is not moving at 0 seconds and 6 seconds
William allots 2.5 minutes to read each page of his novel. How is the total time related to the number of pages he reads?
Answer:
2.5 mins per page
Step-by-step explanation:
2.5 x [page's Read] = Awnser
The total time William needs to read his novel is calculated by multiplying the number of pages by 2.5 minutes per page. This method allows efficient time management and scheduling for reading. By dividing the total pages by available days, one can manage the reading workload more effectively.
The total time William takes to read his novel is directly proportional to the number of pages he reads. This means that if William allots 2.5 minutes to read each page of his novel, then for every page he reads, he will spend 2.5 minutes. To find the total time spent reading, you simply multiply the number of pages by 2.5 minutes.
For example, if William wants to read 40 pages, he would calculate his total reading time as 40 pages × 2.5 minutes per page = 100 minutes. This approach allows William to plan how much time he needs to set aside for reading based on the number of pages.
Additionally, dividing the total page count by the number of available days can help in managing the reading workload efficiently. By knowing how long it takes to read a set number of pages, William can also estimate the time required for larger sections and manage his schedule accordingly.
If y=2x+7 were changed to y=5x+7 how would the graph of the new function compare with the original?
Answer:
If y=2x+7 were changed to y=5x+7, then the graph of the new function would be steeper than the graph of the original function. On the other hand, the y-intercept would be unchanged; ( 0, 7)
Step-by-step explanation:
If y=2x+7 were changed to y=5x+7, then the graph of the new function would be steeper than the graph of the original function. On the other hand, the y-intercept would be unchanged; ( 0, 7)
During a 3 day street fair, 159 woman and 177 men attended. At that rate, how many more men than women will attend a 7 day street fair?
Please Help!!
awnser: 42
step by step:
1. find the racio of both
2.multiply the awnsers by 7
3.finally subtract
The answer is 42 because to find how meant men and women started at on the the first day you do
177/3=59 and 159/3=53
Then you times those numbers separately by 7. So 59*7=413 and 53*7=371
Then you do 413 men-371 women=42 more men then women.
How to solve this problem in math
Step-by-step explanation:
Well you got a good start. #16 = 105°, #17 = 27°, and #15 = 48°.
Inscribed angles are half the arc angle, so #3 = #10 = 21°, and #4 = #5 = 39°.
That means #14 = #12 = 120°, and #11 = #13 = 60°.
The sum of the angle arcs is 360°, and AD is the diameter, so it splits it in half. So arc BC is 180 - 78 - 42 = 60°, so #1 = 30°.
Therefore, #2 = 90°.
AG and FG are both radii, so AGF is an isosceles triangle. Therefore, #8 = #9 = 66°.
Similarly, FG and DG are both radii, so FGD is an isosceles triangle. So #6 = #7 = 24°.
That means #18 = 129°. So #20 = 129° and #19 = #21 = 51°.
That's all of them.
what would 7/8 of an hour be? please explain how you got your answer
I think the answer is 52.5.
Terry has three pairs of pants black khaki and brown and four shirts yellow red blue and white he does not care which colors he wears together if Terry chooses one pair of pants and one shirt randomly what is the probability that the outfit will be black pants and yellow shirt
the answer would be 0.08333… or 1/12
(from my own work it would be ,I'm not saying its right or wrong though)
The probability that Terry randomly chooses an outfit with black pants and a yellow shirt is 1 out of 12, calculated by dividing the number of favorable outcomes (1) by the total possible outcomes (12).
The question revolves around basic probability. Terry has three pairs of pants and four shirts, meaning there are a total of 3 x 4 = 12 possible outfits. Since only one outfit consists of black pants and a yellow shirt, the probability of selecting this combination is therefore 1 out of 12.
The formula used to calculate this probability is the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcome (black pants with a yellow shirt) is just one, and the total number of possible outfits is twelve.
radical symbol non examples
The radical symbol √ indicates the root extraction operation in mathematics. Non-examples of the radical symbol could include any symbol not associated with this concept, such as the minus sign (-), division sign (÷), or the Greek letter alpha (α).
Explanation:The radical symbol √, used in mathematics, represents the operation of root extraction. A non-example of the radical symbol would be anything outside this context. Here are a few:
Minus sign (-): This symbol is related to subtraction, which is a different operation from root extraction. Division sign (÷): This sign indicates the operation of division, not root extraction. Alpha (α): This is a Greek letter used in various mathematics and science contexts, but it is not related to root extraction.
In summary, symbols unrelated to root extraction do not serve as examples of the radical symbol, since their usage and meaning in a given context significantly differ.
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Final answer:
In chemistry, a radical is a molecule with an odd number of valence electrons, such as the chlorine atom and the hydroxyl radical, which makes the molecule highly reactive and typically paramagnetic.
Explanation:
The term radical in chemistry usually refers to a molecule that has an odd number of valence electrons, rendering it highly reactive. These radicals do not follow the conventional complete octets in terms of electron configuration; they are typically short one or more electrons, which gives them an odd number of electrons in total. A familiar example of a radical is the gaseous chlorine atom, which has seven valence electrons and is denoted by its elemental symbol with a dot (Cl·). This makes the chlorine atom a radical because the unpaired electron can easily participate in chemical reactions.
Another example is the hydroxyl radical (OH·), which contains an unpaired electron. Radicals are generally considered to be paramagnetic due to their odd electrons, which can align with a magnetic field. The presence of these unpaired electrons makes radicals highly reactive and an important subject in chemical reactions.
How do you solve for x?
Answer:
x = 8
Step-by-step explanation:
The two angles are complementary angles, which means they add to 90 degrees
6x + (4x+10) = 90
Combine like terms
10x+10 = 90
Subtract 10 from each side
10x+10-10=90-10
10x = 80
Divide each side by 10
10x/10=80/10
x = 8
What is the sum of 6 dm, 40 mm, 2 m, and 10 cm in meters?
Answer: 800
Step-by-step explanation:
Answer: 2.74 m
Step-by-step explanation:
You need to make the following conversions:
From 6 dm to m (Remember that [tex]1m=10dm[/tex]), then you get:[tex](6dm)(\frac{1m}{10m})=0.6m[/tex]
From 40 mm to m (Remember that [tex]1m=1,000mm[/tex]), then you get:
[tex](40mm)(\frac{1m}{1,000mm})=0.04m[/tex]
From 10 cm to m (Remember that [tex]1m=100cm[/tex]), then you get:
[tex](10cm)(\frac{1m}{100cm})=0.1m[/tex]
Now you need to add all the values to get the sum. This is:
[tex]0.6m+0.04m+2m+0.1m=2.74m[/tex]
Plz read question and tell answer
Answer:
Lin has not proven that the probability is not 1/2 because there are only two possible outcomes when flipping a coin and each side has a 50% chance of facing up. Liz flipping the coin 10 times and not getting equal results for both sides is just a random occurrence and it does not effect the 50% chance.
kevin bought 4.6 pounds of pecans for $50.89. About how much was the cost per pound
Answer:
Step-by-step explanation:
4.6 pounds of pecans 1 pound of pecans
_________________ = ______________
50. 89 dollars x dollars
Set up an equation like this.
Cross multiply
4.6(x)=50.89(1)
divide both sides by 4.6
x=11.06 (about)
So I pound of pecans costs about 11.06 dollars
Answer:
11.06 is the one correct :)
]
write a polynomial function of least degree with integral coefficients that has the given zeros. -(1/3), -i
Answer:
[tex]f(x)=3x^3+x^2+3x+1[/tex]
Step-by-step explanation:
If a real number [tex]-\frac{1}{3}[/tex] is a zero of polynomial function, then
[tex]x-\left(-\dfrac{1}{3}\right)=x+\dfrac{1}{3}[/tex]
is the factor of this function.
If a complex number [tex]-i[/tex] is a xero of the polynomial function, then the complex number [tex]i[/tex] is also a zero of this function and
[tex]x-(-i)=x+i\ \text{ and }\ x-i[/tex]
are two factors of this function.
So, the function of least degree is
[tex]f(x)=\left(x+\dfrac{1}{3}\right)(x+i)(x-i)=\left(x+\dfrac{1}{3}\right)(x^2-i^2)=\\ \\ =\left(x+\dfrac{1}{3}\right)(x^2+1)=\dfrac{1}{3}(3x+1)(x^2+1)=\dfrac{1}{3}(3x^3+x^2+3x+1)[/tex]
If the polynomial function must be with integer coefficients, then it has a form
[tex]f(x)=3x^3+x^2+3x+1[/tex]
Graph the linear equation x-3y=-6
Answer:
Step-by-step explanation:
One of the easier approaches to graphing a linear equation such as this one is to solve it for y, which gives us both the slope of the line and the y-intercept.
x-3y=-6 → -3y = -x - 6, or 3y = x + 6.
Dividing both sides by 3, we get y = (1/3)x + 2.
So the slope of this line is 1/3 and the y-intercept is 2.
Plot a dot at (0, 2). This is the y-intercept. Now move your pencil point from that dot 3 spaces to the right and then 1 space up. Draw a line thru these two dots. End.
Alternatively, you could use the intercept method. We have already found that the y-intercept is (0, 2). To find the x-intercept, let y = 0. Then x = -6, and the x-intercept is (-6, 0).
Plot both (0, 2) and (-6, 0) and draw a line thru these points. Same graph.
Answer: Not sure if this is right but here we go.
Step-by-step explanation:
to solve for x
x-3y=-6
Add 3y on both sides, and that should give you x=-6+3y
Solve for y:
y=x/3+2
Solve for X and solve for Y step by step
Answer:
x = 4, y = 1
Step-by-step explanation:
Given the 2 equations
4x + y = 17 → (1)
2x + y = 9 → (2)
Subtract (1) from (2) term by term
(4x - 2x) + (y - y) = (17 - 9)
2x = 8 ( divide both sides by 2 )
x = 4
Substitute x = 4 into (1) and solve for y
4(4) + y = 17
16 + y = 17 ( subtract 16 from both sides )
y = 1
Giggles the clown gave every 10th child a balloon animal and paints every 3rd child’s face. If there are 105 kids at the party, how many kids will get balloon animals and have their faces painted?
it should be 31.5 kids get balloon animals
Answer:
Balloon Animals: 10 children
Face Paint: 35 children
Step-by-step explanation:
To find out how many children get balloon animals, divide 105 by 10. Your answer will be 10.5, but ten and a half children can't get balloon animals (it's physically impossible) so we would have to round down to 10. To find out how many children get their faces painted, you would divide 105 by 3, which would give you 35. So 35 children would get their faces painted.
Hope this helps ya :D
Which of the following is a trinomial with a constant term?
Answer: D. x+2y+10
Trinomial refers to the fact that the polynomial has 3 pieces (x, 2y, and 10)
Constant term means there is a term with no variable (a number with no letters attached to it: In this example, that number is 10)
The trinomial with a constant term is D. x + 2y + 10.
What are Trinomials?Trinomials are polynomials which consists of three terms in total.
Given are four polynomials.
A trinomial consists of three terms.
The only polynomials in the option which contains three terms are,
B. y⁶ + 8y³ + 64y
D. x + 2y + 10
The polynomial with constant is D.
Hence the correct option is D.
Hence the trinomial with a constant term is option D.
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A system of equations is shown below. y = 5x + 10 y = 10x – 5 What is the value of x + y? A. 25 B. 28 C. 72 D. 75
Answer:
B. 28
Step-by-step explanation:
We are given the following system of equations
[tex]y=5x+10\\y=10x-5[/tex]
We can substitute in one of the equations for y. This will give us an equation that we can solve for x.
[tex]5x+10=10x-5\\\\5x=15\\\\x=3[/tex]
Next we can substitute in our value for x in order to find the y value.
[tex]y=5(3)+20\\\\y=15+20\\\\y=25[/tex]
Now we can check with the other equation to see if our x and y values are correct
[tex]25=10(3)-5\\\\25=30-5\\\\25=25[/tex]
Now we are certain that x=3 and y=25
[tex]x+y=?\\\\3+25=28[/tex]
Which measure of the ages has the greatest value?
A- mean
B- median
C- mode
D- range
Final answer:
The mean usually has the greatest value among measures of central tendency like the median and mode, particularly in skewed distributions. The range is not a central tendency measure but represents the difference between the highest and lowest values.
Explanation:
When comparing different measures of central tendency, the mean usually has the greatest value in a skewed distribution. The mean is the arithmetic average of all the numbers, while the median is the middle value when the numbers are sorted, and the mode is the number that appears most frequently. Examples given show that in various cases, the mean tends to be larger than the median and mode, especially when the data set is right-skewed, which is when there are values that are significantly higher than the rest. Range, however, represents the difference between the highest and lowest values in the set, and is not a measure of central tendency, but rather a measure of spread.
What is the complete factorization of the polynomial below ?
Answer:
(x - 2i)(x + 2i)(x + 1)
Step-by-step explanation:
Factor x³ + x² + 4x + 4.
Note that x² is common to the first two terms, and that 4 is common to the last two terms.
Thus: x³ + x² + 4x + 4 = x²(x + 1) + 4(x + 1).
We see that x + 1 is common to both terms. Thus, we have:
(x² + 4)(x + 1).
Note that x² + 4 has two imaginary roots: 2i and -2i. Thus, the complete
factorization of the polynomial is (x - 2i)(x + 2i)(x + 1).
Answer:
[tex](x+1)(x+2i)(x-2i)[/tex]
Step-by-step explanation:
[tex]x^3+x^2+4x+4[/tex]
Factor the given polynomial
Group first two terms and last two terms
[tex](x^3+x^2)+(4x+4)[/tex]
Factor out GCF from each group
[tex]x^2(x+1)+4(x+1)[/tex]
Factor out x+1
[tex](x^2+4)(x+1)[/tex]
Now factor out x^2+4 that is x^2 + 2^2
[tex]x^2+4= (x+2i)(x-2i)[/tex]
[tex](x+1)(x+2i)(x-2i)[/tex]
What is the solution to this inequality: 8x < -32
Answer:
x < -4 or (-∞,-4)
Step-by-step explanation:
to solve 8x < -32, we treat the inequality symbol as an = sign and solve it like we would any other equation: get x alone
8x < -32 < divide both sides by 8 to isolate x
8x/8 = x
-32/8 = -4
x < -4 is our solution
in interval notation this can be written as (-∞, -4)
A jar contains 3 pennies, 5 nickels, 4 dimes, and 6 quarters. If a coin is selected at random, what is the probability of selecting a penny?
Answer:
1/6
Step-by-step explanation:
We know this because we have to first add up all of the coins, bringing us to 18. Then, to make the fraction of the probability of selecting a penny at random, we'd simply do 3/18. This simplified would be 1/6
The probability of selecting a penny is 1/6.
Given that, a jar contains 3 pennies, 5 nickels, 4 dimes, and 6 quarters.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Total number of outcomes =3+5+4+6
= 18
Number of favourable of outcomes = 3
So, probability of an event =3/18
= 1/6
Hence, the probability of selecting a penny is 1/6.
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How do you compare two-way frequencies in a relative frequency table
Final answer:
To compare two-way frequencies in a relative frequency table, calculate the relative frequency by dividing each frequency by the total number of data values, and find the cumulative relative frequency by summing up the previous relative frequencies.
Explanation:
To compare two-way frequencies in a relative frequency table, you start by calculating the relative frequency. This is done by dividing the frequency by the total number of data values for that group. For cumulative relative frequency, add the relative frequencies of all preceding rows to the relative frequency of the current row. Let's clarify using an example.
In the first row, if the relative frequency is .15, this is the cumulative frequency as well since it's the first value. For the second row, if the relative frequency is .25, we add this to the .15 from the first row to get a cumulative relative frequency of .40. Continue this process down each row.
When constructing a histogram using these frequencies, scale the x-axis in increments suitable to the data range (e.g., $50 widths) and plot relative frequencies on the y-axis. The sum of the relative frequency column should total 1 (or 100% if in percentage form), as it represents the entire sample.
The difference between relative frequency and frequency is that frequency is the absolute count of occurrences, while relative frequency expresses this count as a proportion of the total number of data values. Cumulative relative frequency is the sum of all previous relative frequencies, showing the accumulation of data up to that point.
Find the 10th term in the following geometric sequence 1/3,1,3,9
[tex]\bf \cfrac{1}{3}~~,~~\stackrel{\frac{1}{3}(3)}{1}~~,~~\stackrel{1(3)}{3}~~,~~\stackrel{3(3)}{9}~~...\qquad \qquad \impliedby \textit{3 is the common ratio} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ r=3\\ a_1=\frac{1}{3}\\ n=10 \end{cases}\implies a_{10}=\cfrac{1}{3}\left(3^{10-9} \right) \\\\\\ a_{10}=\cfrac{1}{3}\cdot 3^9\implies a_{10}=\cfrac{1}{3}\cdot 19683\implies a_{10}=6561[/tex]
Answer:
19683
Step-by-step explanation: