Answer: -7.2
Step-by-step explanation:
The vertex form of quadratic equation :[tex]f (x) = m(x - a)^2 + b,[/tex] where (a,b) is the vertex.
Given: The quadratic function g(x) has a vertex at (-5, 0).
Put (a,b)= (-5,0) for function g(x), we get
[tex]g(x)=m(x-(-5))^2+0\\\\\Rightarrow\ g(x)=m(x+5)^2[/tex]
Also, its y-intercept is (0, -5).
Put x= 0 and g(x) =-5
[tex]-5=m(0+5)^2\\\\\Rightarrow\ -5=m(25)\\\\\Rightarrow\ m=\dfrac{-5}{25}\\\\\Rightarrow\ m=\dfrac{-1}{5}[/tex]
so, [tex]g(x)=-\dfrac{1}{5}(x+5)^2[/tex]
For g(1), put x=1
[tex]g(1)=-\dfrac{1}{5}(1+5)^2\\\\=-\dfrac{1}{5}(6)^2=-\dfrac{1}{5}(36)\\\\=-7.2[/tex]
Hence, g(1) is -7.2.
what is −10x + 1 + 7x = 37
Answer:
x = -12
Step-by-step explanation:
−10x + 1 + 7x = 37
Combine like terms
-3x+1 = 37
Subtract 1 from each side
-3x +1-1 = 37-1
-3x = 36
Divide each side by -3
-3x/-3 = 36/-3
x = -12
Answer:
x = -12
Step-by-step explanation:
[tex]-10x+1+7x=37\\\\\mathrm{Group\:like\:terms}\\-10x+7x+1=37\\\\\mathrm{Add\:similar\:elements:}\:-10x+7x=-3x\\-3x+1=37\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\-3x+1-1=37-1\\\\Simplify\\-3x=36\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{36}{-3}\\\\x =-12[/tex]
which line of best fit should not have been drawn. Give a reason for your answer
Answer:
Diagram B
Step-by-step explanation:
This is because the line only goes through two points and many are dispered from the line, however diagram A and C have points fairly close to them
Visually inspecting the three scatterplots, the line of best fit does not accurately fit the points on the second graph. Hence, line of best fit should not have been drawn for the second graph as the relationship isn't linear.
The line of best fit minimizes the sum of the square of the mean distance between each point. Hence, the distance between the line and the best fit line should be as small as possible.
However, the second graph isn't linear, hence , a linear line cannot model the relationship.
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Which measure of center best represents this set of data?
12, 13, 13, 15, 15, 15, 16, 16, 17
•Mean
•Mode
•Median
•Symmetric
Answer:
Mean: 14.67
Mode: 15
Median: 15
Symmetric: Idk
Answer:
Median P.S. The median is 15
Step-by-step explanation:
It is a median because you cross out the highest and lowest numbers out at a time.
Which fraction is equivalent to
2/5
Answer:
To make equivalent fractions, what we have to do is multiplicate or divide the numerator or denominator by the same number.
In our case:
[tex]\frac{2}{5}=\frac{2*2}{5*2}=\frac{4}{10}[/tex]
[tex]\frac{2}{5}=\frac{2*6}{5*6}=\frac{12}{30}[/tex]
[tex]\frac{2}{5} = \frac{2*12}{5*12}=\frac{24}{60}[/tex]
That are only three examples, but there are infinite.
We could also obtain equivalent fractions dividing, for example, [tex]\frac{3}{9}[/tex]:
[tex]\frac{3}{9}=\frac{\frac{3}{3}}{\frac{9}{3}}[/tex] = [tex]\frac{1}{3}[/tex]
A golfer recorded the following scores for each of four rounds of golf: 86, 81, 87, 82. The mean of the scores is 84. What is the sum of the squared deviations of the scores from the mean?
Answer:
26
Step-by-step explanation:
The mean of a set of number is the average the set of number, it is the ratio of the total sum of the terms to the sum of terms.
The standard deviation is the variation of a set of numbers to their mean. A low standard deviation means the value are close to the mean and a high standard deviation means the values are far from the mean. The standard deviation is given as:
[tex]\sigma=\sqrt{\frac{\Sigma (x_i-\mu)^2}{n} }\\ \\\mu=mean,n=number\ of\ terms, \sigma=standard\ deviation[/tex]
Given the numbers:
86, 81, 87, 82. mean = μ = 84
[tex]\Sigma(x_i-\mu)^2=(86-84)^2+(81-84)^2+(87-84)^2+(82-84)^2=4+9+9+4=26[/tex]
Sum of squared deviations = 26
The sum of the squared deviations of the scores from the mean is 26.
-----------------------
The observations are: 86, 81, 87 and 82.The mean of the observations is 84.The sum of the squared deviations of the scores from the mean is the sum of the differences squared of each observation and the mean.Thus:
[tex]S_{ds} = (86-84)^2 + (81-84)^2 + (87-84)^2 + (82-84)^2 = 4 + 9 + 9 + 4 = 26[/tex]
The sum of the squared deviations of the scores from the mean is 26.
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Explain how you could use the construction tool or a compass and straightedge to create a line segment that is twice as long as A and B
So far, segment CD is the same length as AB. So we can say AB = CD.
Let's keep going
Step 6) Place the nonpencil part of the compass at point D and draw another arc to intersect line CD. Make sure you do not intersect at point C, but rather the point on the other side of D. Call this point E. Step 7) Use a marker or pen to highlight everything from C to E. So you'll highlight segment CE. Erase everything else.Segment CE is composed of CD and DE, both of which are equal to AB. In other words, AB = CD = DE. Because CD = DE, and the two segments add up to CE, this must mean that CE is twice as long as CD. Therefore, CE is twice as long as AB.
See the diagram below for a visual summary.
Please help! I have very limited time to answer, but I am really stumped!
Answer:
A
Step-by-step explanation:
So we have the function:
[tex]f(x)=y=\sqrt[3]{x-2}+8[/tex]
To find the inverse of the function, we can flip x and y and then solve for y. Therefore:
[tex]x=\sqrt[3]{y-2}+8[/tex]
Solve for y to find our inverse.
Subtract 8 from both sides:
[tex]x-8=\sqrt[3]{y-2}[/tex]
Cube each side. The right cancels:
[tex](x-8)^3=y-2[/tex]
Add 2 to both sides:
[tex]y=(x-8)^3+2[/tex]
Therefore, our inverse is:
[tex]f^{-1}(x)=(x-8)^3+2[/tex]
The answer is A
I really need their answers!!!!!!!
Answer:
1.c 1875cm squared.
Step-by-step explanation:
if the area of the park is the area if pool 3 times ... which is 625
so 625×3
=1875cm squared
Answer:
B, C, B
Step-by-step explanation:
24
area of A'B'C'D' = 3 × ABCD = 3 × 625 = 1875 m²
Thus area of park = 1875 - 625 = 1250 m² → B
25
A tangent has only one point of contact with the circle. Thus does not pass through the centre.
26
The inscribed angle subtended by a semi- circle is 90° not 180°
What is the value of 3 minus (negative 2)?
Answer:
5 I think I'm pretty sure
The number of private investigators is expected to increase from 25,000 in 2009
to 30,000 in 2019. If there are 312,500 police officers in 2009, how many police
officers must there be in 2019 to have a greater percent increase than that of
private investigators? *
Answer:
[tex]375001[/tex] police officers
Step-by-step explanation:
[tex]\frac{30,000}{25,000} = \frac{30}{25} = \frac{120}{100} = 1.2[/tex]
That's a 20% increase.
So increase the police by 20% gets you:
[tex]312500 * 1.2 = 375000[/tex]
Based on the wording of the question, if you want a greater percentage, the answer should be a single policeman more, thus 375,001.
What are composite numbers
Answer:
When a number can be divided up exactly and is not a prime number , it is a Composite Number.
The first few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16,........
Hope it helps.
Find the domain and range of the function represented by the graph. A Domain: {−2,−1,1,2} Range: {−2,1,2}{−2,1,2} B Domain: −2≤x≤2 Range: −2≤y≤3 C Domain: {−2,1,2} Range:{−2,−1,1,2} D Domain: −4≤x≤4 Range: −4≤y≤4
Answer:
B) Domain: -2≤x≤2 Range: -2≤x≤3
Step-by-step explanation:
The domain is the x-values, in this case all the numbers between -2 and 2. The range is the y-values, which are the numbers between -2 and 3. So the answer is
B) Domain: -2≤x≤2
Range: -2≤x≤3
Which value is larger -17 or -23
Answer: -17
Step-by-step explanation:
Simplify (please show work if possible) HELP!!
Answer:
See below.
Step-by-step explanation:
So we have the expression:
[tex]\sqrt{125a^2b^2}[/tex]
This is the same as:
[tex]=\sqrt{(5ab)^2\cdot5}[/tex]
Expand:
[tex]=\sqrt{(5ab)^2}\cdot\sqrt5[/tex]
The left term cancels:
[tex]=5|ab|\sqrt5[/tex]
Note that we need the absolute value bars because if a and/or b was negative in the original equation, they will turn positive. Thus, to keep things consistent, we must use the absolute value to make sure that a and b stays negative :)
Answer:
there is google!
Step-by-step explanation:
Please help me on this question :(
The main table is at the top. This is what it would look like if you filled out your blank boxes. The second section below shows scratch work to help form the more complicated columns.
=========================================================
Explanation:
We have two atomic variables p and q. They can each take on values of True (T) or False (F).
There are 2*2 = 4 combinations of T and F as shown below
T,T ... both trueT,F ... p is true but q is falseF,T ... p is false, but q is trueF,F ... both are falseThat takes care of the first two columns of the table. Note how there aren't any other ways to have two truth values together.
The third column ~q is where we flip everything in the q column. So if q is true, then ~q is false, and vice versa. A similar situation happens with the ~p column as well.
The ~p v q column is where we apply a disjunction to ~p with q. The V stands for "or". It means either ~p is true or q is true. If either are true, then (~p v q) is true. Otherwise it's false. Put another way, (~p v q) is only false when both ~p and q are false together.
The last column is the entire expression ~q ^ (~p v q). We apply a conjunction to the ~q column and the (~p v q) column. Both expressions must be true for the entire ~q ^ (~p v q) to be true, otherwise it's false.
Let me know if you have any questions. It's probably tricky to wrap your head around at first, but hopefully the table clears things up.
The scratch work section is to show how the fifth and sixth columns are formed.
1. Which words represent ADDITION
less than
sum
more than
times
Answer:
more than
Step-by-step explanation:
What is the factored form of the expression 9x2 + 6x + 1?
O (3x - 1)2
O (3x + 1)2
O (9x + 1)2
O (9x - 1)
Answer:
(3x + 1)²
Step-by-step explanation:
Given
9x² + 6x + 1 ← is a perfect square of the form
(ax + b)² = a²x² + 2abx + b²
Compare like terms to find a and b
a²x² = 9x² ⇒ a² = 9 ⇒ a = [tex]\sqrt{9}[/tex] = 3
b² = 1 ⇒ b = [tex]\sqrt{1}[/tex] = 1
and 2ab = 2 × 3 × 1 = 6
Thus
9x² + 6x + 1 = (3x + 1)²
Answer:
(3x + 1)^2
Step-by-step explanation:
The first and last terms are perfect squares. From its structure, this is a perfect square trinomial.
All of the symbols in the expression 9x2 + 6x + 1 are positive, so use the rule for the square of the sum of two terms.
In the given expression, a2 = 9x2 and b2 = 1, so a = 3x and b = 1.
2ab = 2(3x)
= 6x
This result matches the middle term in the polynomial expression, 6x, so apply the rule for the square of the sum of two terms.
The expression 9x2 + 6x + 1 is equal to (3x + 1)2.
A school of salmon was swimming in the river 5 feet below the surface. To escape a hungry bear, they went down another 3 feet. What is the position of the salmon now relative to the surface?
Answer:
8 Feet below the surface
Step-by-step explanation:
If the salmon were initially 5 feet below the surface, and then travelled down an additional 3 feet from the initial 5, then the new position would be 8 feet down relative to the surface.
You can write this as -5 + -3 = -8, assuming that 0 represents surface level.
Cheers.
The distance of salmon from the surface of the water is 8 feet.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Given that,
The distance of school of salmon for the surface of the river = 5 feet.
Since, to escape a hungry bear, the school of salmon went down to 3 feet.
The position of the salmon to the surface = 5 + 3 = 8 feet.
The required distance of school of salmon from the surface of water is 8 feet.
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Sophie opens a new restaurant. The function f ff models the restaurant's net worth (in thousands of dollars) as a function of time (in months) after Sophie opens it.
Based on the graph given, the point of the graph that corresponds with the shop's net worth when Sophie opened it is -5.
What is the minimum of a quadratic function?
The minimum value of the function is the place where the graph has a vertex at its lowest point. In the real world, you can use the minimum value of the quadratic function to determine the minimum cost and area.
What is the minimum amount?
we use minimum to describe an amount which is the smallest that is possible, allowed, and required.
What was the shop worth when it was opened?
The point of the shop were opened is represented by the value of the y axis when it was first crossed.
Looking at the graph, the line first intercepted the y axis at -5 which means that this was the shop's net worth when it was opened by Sophie.
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(8 x 106 ) / (4 x 103 ) = ?
(the 10 stands for the 0 in scientific notation)
Answer:
3.2 x 10^12
Step-by-step explanation:
80000000/40000
Answer:
Answer:
3.2 x 10^12
Step-by-step explanation:
80000000/40000
The square of a whole number is between 6400 and 7000. The number must be between ?
Answer:
The number must be between 80 and 83.666002653408
Step-by-step explanation:
The square root of 6400 is 80 and the square root of 7000 is 83.666002653408 so it would be between those numbers.
what is 16-(-)24+4 and does it equal 44
Answer:
yes, it equals 44
Step-by-step explanation:
16-(-)24+4=44
Answer:
it is 44
Step-by-step explanation:
2 minus's right by each other turn into a plus sign.
square root of 141 '
Find sin of theta when you only know cos of theta. You have to use the Pythagorean Identity!
Answer:
[tex]\huge\boxed{B. \ sin \theta = \frac{\sqrt{35} }{6} }[/tex]
Step-by-step explanation:
We'll use the following Pythagorean Identity:
[tex]cos ^ 2 \theta + sin^2 \theta = 1[/tex]
Finding sin θ , we'll rearrange the formula as:
[tex]sin \theta = \sqrt{1 - cos^2 \theta}[/tex]
Given that cos θ = - 1 / 6
[tex]sin \theta = \sqrt{1 - (-\frac{1}{6} )^2} \\sin \theta = \sqrt{1-\frac{1}{36} } \\sin \theta = \sqrt{\frac{36-1}{36} } \\sin \theta = \sqrt{\frac{35}{36} } \\sin \theta = \frac{\sqrt{35} }{\sqrt{36} }\\ sin \theta = \frac{\sqrt{35} }{6}[/tex]
A pound of raisins costs $2.00, and a pound of almonds costs $5.00. Six pounds of a trail mix contains 2 more pounds of raisins than almonds. What is the cost of the 6 pounds of trail mix?
Answer:
18.00 because 1 pound is 5.00, 1 plus 2 is 3 so 5 x 3 = 18
Step-by-step explanation:
6 pounds of a trail mix contains 2 more pounds of raisin than almonds
i.e.
Suppose:
raisins = r; andalmonds = a6 pounds of trails will contain a pound of almond (a) and two more pounds of raisin i.e. (a +2)
∴
a + (a+2) = 6
2a + 2 = 6
2a = 6 -2
2a = 4
a = 2
It implies that there are:
2 pounds of almond; and= (a +2) pounds of raisins
= (2+2) pounds of raisins
= 4 pounds of rasins
Provided that:
a pound of raisins costs = $2.00 a pound of almonds costs = $5.00∴
The total cost of the 6 pounds of trails mix will be:
= 2($4.00) + 2($5.00)
= $8.00 +$10.00
= $18.00
Therefore, we can conclude that the total cost of 6 pounds of trail mix is $18.00
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The width of a rectangle measures (3.1s-1.6)(3.1s−1.6) centimeters, and its length measures (7.2s-4.6)(7.2s−4.6) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? A. −6.2+10.3s B. −12.4+20.6s C. 1.5s+2.6 D. 5.2+3s
Answer:
B. -12.4 + 20.6s.
Step-by-step explanation:
Perimeter = 2*length + 2 * width
= 2(3.1s - 1.6) + 2(7.2s - 4.6)
= 6.2s + 14.4s - 3.2 - 9.2
= 20.6s - 12.4
= -12.4 + 20.6s.
[tex]\boxed{-12+20.6s}[/tex]
To find the perimeter of a shape, we add length + width + length + width (or length * 2 + width *2). So we would multiply the width, (3.1s - 1.6), and the length, (7.2s - 4.6), by 2, and then add them together to find the perimeter.
2(3.1s - 1.6) + 2(7.2s - 4.6)
This is equal to:
6.2s + 14.4s - 3.2 - 9.2
Simplified, this is equal to:
20.6s - 12.4
(We have to switch it around, but this answer is equal to option b.)
-12.4 + 20.6s
Tip: To simplify an equation, you add like terms. Like terms are numbers that have the same variables or exponents; for example, -4 and 3 are like terms, as well as 5^2 and 8^2. (Keep in mind, the variables and/or exponents have to be the same if you combine the like terms. Numbers with different variables and exponents can never be combined!)
The water level as a river recedes after a flood is measured at regular intervals, and its height relative to normal, in inches, follows the sequence below. If the sequence continues, what do you expect the 7th measurement to be? 16, 9, 2, –5, ...,
Answer:
-26
Step-by-step explanation:
Given the sequence:
16, 9, 2, –5, ...,
To find:
7th measurement, if the above sequence continues:
Solution:
Let us examine the given sequence first:
First term is 16
Second term = 9
Third term = 2
Fourth term = -5
Difference between 2nd and 1st term = 9 - 16 = -7
Difference between 3rd and 2nd term = 2 - 9 = -7
Difference between 4th and 3rd term = -5 - 2 = -7
We can see that there is a common difference of -7 between each term.
That means, the sequence is in Arithmetic Progression.
whose first term, [tex]a=16[/tex]
Common difference, [tex]d=-7[/tex]
To find:
7th term i.e. [tex]a_7=?[/tex]
Solution:
Formula for [tex]nth[/tex] term of an Arithmetic Progression is given as:
[tex]a_n=a+(n-1)d[/tex]
Let us put [tex]n=7[/tex]
[tex]a_7=16+(7-1)\times (-7)\\\Rightarrow a_7=16+6\times (-7)\\\Rightarrow a_7=16-42\\\Rightarrow \bold{a_7=-26}[/tex]
7th measurement will be -26.
Answer:
7th measurement= -26
Step-by-step explanation:
The sequence is 16, 9, 2, –5, ...,
First term( a)= 16
Second term=9
Common difference (d) = 9-16
Common difference= -7
The sequence is a arithmetic progression
For AP's ,the terms formula is
Term(n) = a + (n-1)d
Where n represent the term to be found
In this case,we Are looking for the 7th term , so n= 7
Term(7) = 16+ (7-1)-7
Term(7)= 16 +6(-7).
Term (7) = 16-42
Term(7) = -26
7th term =-26
what is -3d + 8d - 5d simplified?
Answer:
0
Step-by-step explanation:
-3d + 8d - 5d
Combine like terms
5d -5d
0
Answer:
[tex]\Huge \boxed{0}[/tex]
Step-by-step explanation:
[tex]-3d + 8d - 5d[/tex]
Combining like terms:
[tex]\Rightarrow 5d- 5d[/tex]
[tex]\Rightarrow 0[/tex]
Which fraction is equivalent to 80%?
Answer:
4/5
Step-by-step explanation:
80% is equivalent to 80/100
80/100 can be simplified into 8/10 by dividing both sides by 10
8/10 can be further simplified into 4/5 by dividing both sides by 2
4/5 can not be simplified any further
1.A five pack of theater tickets cost $88.75 what is the unit price per ticket?
2.A 4 pack of monster cards costs $6.56, what is the unit price per card?
3.An 8 pack of stickers cost $0.64, what is the unit price per sticker?
4. An 9 pack of apple cost $6.30, what is the unit price per apple?
5. A 5 pack of muffins costs $6.25, what is the unit price per muffin?
6. A 9 pack of lollipops costs $5.85, what is the unit price per lollipop?
7. A 3 pack of batteries costs $ 4.65, what is the unit price per battery?
8. A 6 pack of pencils cost $4.80, what is the unit price per pencil?
9. A 2 pack of books costs $24.80, what is the unit price per book?
10. A 5 pack of stamps cost $5.95, what is the unit price per stamp?
11. An 8 pack of eggs costs $4.80, what is the unit price per eggs?
12. A 10 pack of candy bars costs $5.70, what is the unit price per candy bar?
Answer:
1. 17.75 per ticket
2. 1.64 per card
3. 0.08 per sticker
4. 0.07 per apple
5. 1.25 per muffin
6. 0.65 per lolipop
7. 1.55 per battery
8. 0.80 per pencils
9. 12.40 per book
10. 1.19 per stamp
11. 0.60 per egg
12. 0.57 per candy bar
Step-by-step explanation:
price divided by ammount