Answer:
-9
Step-by-step explanation:
her error was that -9 can't add up to -4
Answer:
she needs to find factors of -45 that add to -4
Step-by-step explanation:
You want to know the error involved when looking for factors of 5x²-4x-9 by considering only factors of -9.
Quadratic factorsConsider the product of factors (ax +b)(x +d):
(ax+b)(x +d) = ax² +adx +bx +bd = ax² +(ad+b)x +bd
You will notice the two parts of the sum that is the middle term coefficient have the product abd, which is also the product of the first and last coefficients.
Sarah needs to be looking for factors of (5)(-9) = -45 that have a sum of -4.
__
Additional comment
The factors Sarah needs are -9 and 5. These will give Sarah the equation ...
5x² -9x +5x -9
which can be factored pairwise to ...
x(5x -9) +1(5x -9) = (x +1)(5x -9)
Identify the slope of the line that passes through the given points.
(1,3) and (6,1)
The slope of the line that passes through the given points,
(1,3) and (6,1)= -0.4
How slope is calculated?
The formula of the slope of a line between two points:[tex]\text{slope of a line between }(x_{1} ,y_{1} ) \text{ and } (x_{2} ,y_{2})=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substituting the given values,[tex]\text{slope of a line between }(1,3 ) \text{ and } (6,1)=\frac{1-3}{6-1}=-\frac{2}{5}=-0.4[/tex]
What is a slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's and Todhunter's versions of the equation for a straight line, respectively, where they are written as y = mx + b and y = mx + c.To learn more about slope, refer:
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normal body tem varies by the time of day. a series of readings was taken of the body temperature of a subject. the mean reading was found to be 36.5 C with a standard deviation of 0.3 C. if you wanted to convert the temp to the Fahrenheit scale, what would the new mean and standard deviation be?
Answer: 97.7 F 32.54 F
Step-by-step explanation:
So the equation to go from Celsius to Fahrenheit is 9/5(C)+32
So it would be 9/5(36.5)+32=97.7 F
And 9/5(0.3)+32=32.54 F
The new mean is 97.7 F and new standard deviation is 32.54 C.
what is Standard Deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean.
Given:
Mean = 36.5 C
Standard deviation = 0.3 C
Now, converting Celsius to Fahrenheit as
= 9/5(C)+32
So, the new mean is
=9/5(36.5)+32
=97.7 F
and, new standard deviation is
= 9/5(0.3)+32
=32.54 F
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A rectangular room is
1.4
1.4
times as long as it is wide, and its perimeter is
27
27
meters. Find the dimension of the room.
The length is : meters and the width is meters. Enter the dimensions as decimals rounded to at least one decimal place.
The length of the rectangle is 7.875 meters and the width of the rectangle is 5.625 meters.
Perimeter of a rectangleLength of the rectangle = 1.4xWidth of the rectangle = xPerimeter of the rectangle = 27 metersPerimeter of a rectangle = 2(length + width)
27 = 2(1.4x + x)
27 = 2(2.4x)
27 = 4.8x
divide both sides by 4.8x = 27/4.8
x = 5.625
Therefore,
Length of the rectangle = 1.4x
= 1.4(5.625)
= 7.875 meters
Width of the rectangle = x
= 5.625 meters
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Your teacher invested 5000 in three funds. After a year they had 5450 . The growth fund had a return rate of 12% , the income fund had a return rate of 8% , and the money market fund had, a return rate of 5 \% . Your teacher invested twice as much in the income fund as in the money market fund. How much money was invested in each fund?
Using a system of equations, the amounts invested in each fund are given as follows:
Growth: $2,000.Income: $2,000.Market: $2,000.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: amount invested into the growth fund.Variable y: amount invested into the income fund.Variable z: amount invested into the market fund.The teacher invested 5000, hence:
x + y + z = 5000.
After a year, the amount was of $5,450, hence, considering the return rates:
1.12x + 1.08y + 1.05z = 5450.
The teacher invested twice as much in the income fund as in the money market fund, hence:
y = 2z.
Then, replacing y = 2z in the first two equations:
x + 3z = 5000 -> x = 5000 - 3z.1.12x + 3.21z = 5450.Replacing the first equation into the second.
1.12(5000 - 3z) + 3.21z = 5450.
0.15z = 150
z = 150/0.15
z = 1000.
Hence:
y = 2z = 2000.x = 5000 - 3z = 2000.The amounts invested in each fund are given as follows:
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d. Could the triangle have 110 cans? 140 cans? Explain.
NO, for such a triangle to exist is impossible.
We are given two angles of 110° and 140°.
We have to find whether Triangle with given angles (110° and 140°) is possible or not.
We will utilize the basic knowledge of triangles and their angles to solve this problem. As we know, the sum of all triangle angles is 180°.
If
let the third angle be x
110° + 140° + x = 180
according to the angle sum property of triangles
then,
x = 180° - 250°
which is not possible.
And if we add 110 and 140, we will get 250° as a resultant, which is much greater than the sum of the three angles.
Therefore, a triangle with 110° and 140° as two of its angles is not possible.
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For the geometric sequence 3,12,48,192, . . . . . , find the indicated term.20 th term
The 20th term of the given geometric sequence, 3, 12, 48, 192, . . . , is 8.246337208 x 10^11.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
r = ratio
Given the geometric sequence 3, 12, 48, 192, . . .
Find the ratio,
r = a(n)/a(n-1)
r = a(2)/a(1)
r = 12/3
r = 4
Notice that the ratio between two succeeding terms is always 4.
Use the formula to find the 20th term of the geometric sequence.
a(20) = a r^(20-1)
a(20) = 3[4^(20-1)]
a(20) = 3(4^19)
a(20) = 8.246337208 x 10^11
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Solve for x.
I need help with this geometry problem
1. How would you write 2 × 2 × 2 using exponents?
(1 point)
02×3
023
032
2. Rewrite the following expression using exponents.
3×3 × 3× 3 × 3 x3
(1 point)
036
035
O
63
3. What is the value of 44? (1 point)
016
064
0256
4. What is the value of 92? (1 point)
018
081
0729
5. What is the value of 83? (1 point)
024
064
0512
In the pressure equation, P represents the pressure on the object in pascals (Pa), F represents the force applied on the object in newtons (N), and A represents the area, in square meters, of the object over which the pressure is applied.
The pressure inside the container is 81.625 pascals
Calculating pressureFrom the question, we are to determine the pressure applied inside the container
From the Pressure equation, we have that
P = F/A
Where P is the pressure
F is the force
and A is the area
From the given information,
F = 1306 N
A = 16 m²
P = 1306/16
P = 81.625 pascals
Hence, the pressure inside the container is 81.625 pascals
Here is the complete question:
In the pressure equation, P represents the pressure on the object in pascals (Pa), F represents the force applied on the object in newtons (N), and A represents the area, in square meters, of the object over which the pressure is applied. What is the pressure applied inside a container having an inner area of 16 square meters over which a force of 1,306 newtons is applied?
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Explain how to do long division within 5 minutes.
Let's say 125 / 5
5 can't go into 1 so we move on to 12(if it doesn't work for twelve you move on to the next number). 5 goes into 12 twice because 5*2=10.
So the first number to our answer is 2 and we do 12-10=2. Then we bring down the 5 in 125 to make 25(from 12-10=2).
Since we are dividing by 5, 5 goes into 25 five times, so the next number to our answer is 5. 25-25=0 which means we can't divide by 5 any further so our answer is 25.
I think it's confusing but just for the points :)
which is the value of (1.8 x 10^8) (8.3 x 10^-3)
Answer:
О C 1.494*10⁻⁶
Step-by-step explanation:
1.8*10⁸ = 180000000
8.3*10⁻³ = 0.0083
180000000 * 0.0083 = 1494000
= 1.494*10⁶
Show ur work please and thank you I’ll give brainilest
Answer:
7
Step-by-step explanation:
If he made 6 in the first game and 34 total, then we cant subtract 34 from 6 to find how many he made in the 4 remaining games.
34 - 6 = 28
Now simply divide 28 by 4 to figure out how much he made in each game
28 / 4 = 7
PLEASE HELP ASAP
ykdlydkyskyskystksltsylelyellyslyspyslsu dyllglgzlgsls xlykx
Answer:
There is nothing to answer.
At a football game half time show the marching band was in 3 sections each with 8 rows of 8 players. The dancers were in 2 sections each with 6 rows of 7 dancers. What
is the total number of band members and dancers in the halftime show?
Answer:
276
Step-by-step explanation:
so since there is 3 section we know that it will be the same answer for the three sections then if it's 8 rows with 8 in each it would be 8x8=64 then since it's three sections 64 x 3= 192 that's the total of band then you repeat the process with dancers with will give you the total of 276
215,36,6 find the seventh term
Pls help
Answer: 216, 36, 6, 1, 1/6, ...
Step-by-step explanation:
216, 36, 6, ...
[tex]b_1=216\\b_2=36\\b_3=6\\\displaystyle\\q=\frac{b_2}{b_1} \\\\q=\frac{36}{216} \\\\q=\frac{1}{6} \\\\q=\frac{b_3}{b_2} \\\\q=\frac{6}{36} \\\\q=\frac{1}{6} \\\\Hence,\\\\b_n=b_1q^{n-1}\\\\b_5=216*(\frac{1}{6})^{5-1}\\\\b_5=216*(\frac{1}{6} )^4\\\\b_5=216*\frac{1}{6^4}\\\\b_5=6^3 *\frac{1}{6^4} \\\\b_5=\frac{6^3}{6^4} \\\\b_5=6^{3-4}\\\\b_5=6^{-1}\\\\b_5=\frac{1}{6}[/tex]
.............................................
Answer:
The value would be 100
Step-by-step explanation:
Determine whether each sequence is arithmetic. If so, identify the common difference. 100,10,1,0.1, ...........
The given sequence 100,10,1,0.1, ........... does not form an AP as the common difference is not same.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two mathematical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few key concepts in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be referred to in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows:Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the stated sequence is; 100,10,1,0.1, ...........
The series comprises of four defined terms.
Consider the initial term be 'a₁' = 100.
Consider the second term be 'a₂' = 10.
Consider the third term be 'a₃' = 1.
And, consider the fourth term is 'a₄' = 0.1.
The AP must have the equal common difference. So,
d₁ = a₃ - a₂
Substitute the values.
d₁ = 1 - 10
d₁ = -9
Thus, the computed common difference is -9.
or d₂ = a₄ - a₃ (Substitute the values)
d₂ = 0.1 - 1
d₂ = -0.9.
As, for the result it is clear that the value of both common difference is not same. That is,
d₁ ≠ d₂.
Therefore, the given sequence doesn't not form an arithmetic sequence.
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The total height of the cubes stacked on top of each other is 2f + 3g^2.
The cubes have a combined volume that is the same as a rectangular prism of the same height. What is the area of the base of the rectangular prism? (Recall: V = Bh)
A: 2f + 3g^2
B: 8f^3 + 27g
C: 2f - 6fg^2 + 3g^2
D: 4f^2 - 6fg + 9g^4
(And pls be fast)
The area of the base of the rectangular prism will be D. 4f² - 6fg + 9g⁴.
How to illustrate the information?it should be noted that from the information given, the cubes have a combined volume that is the same as a rectangular prism of the same height.
The total height of the cubes stacked on top of each other is 2f + 3g²
Therefore, the area will be:
= (2f)² - 2(3fg) + (3g²)²
= 4f² - 6fg + 9g⁴
Therefore, the area of the base of the rectangular prism will be 4f² - 6fg + 9g⁴.
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the stage wich is 35 feet wide in real life is 5 inches wide in the drawing . what is the scale of the drawing
Answer: 20 feet
Step-by-step explanation:
The scale is 3 inches to is to 2 feet
As a ratio, it would be:
The question is what is the actual length of the stage if the drawing is 30 inches. All we need to do is find a ratio proportional to the scale ratio:
Now to find the missing number, cross multiply the fractions first:
Then solve for x:
The answer is 20 feet
A bee flies at 6 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 11 minutes, and then flies directly back to the hive at 4 feet per second. It is away from the hive for a total of 15 minutes. a. What equation can you use to find the distance of the flowerbed from the hive? b. How far is the flowerbed from the hive?
Answer:
576 feet
Step-by-step explanation:
The bee is at the flowerbed for 11 minutes so we can subtract that form the 15 minutes. The bee travels for 4 minutes.
So now we have that it flew to the flowerbed at 6 feet per second and back at 4 feet per second.
We have a total of 4 minutes or 240 seconds. we now have two speeds where one is 50% faster than the other. We then find the two percents that one is 50% greater than the other percent and both add up to 100. 40% +50% of 40% is 60. 60%+40% is 100%
We know it spent 40% of 240 seconds flying to the flowerbed at 6 feet per second.
40% of 240 is 96
96 seconds at 6 feet per second is 576 feet
if a box contains 200 tissues and we take 3/5 of these tissues, work out how many tissues we take
Answer:
120 tissues
Step-by-step explanation:
3/5 x 200 tissues
X（´∀｀ ）
Answer:
We take 120 tissues
Step-by-step explanation:
[tex]\frac{200}{1} *\frac{3}{5} = \\\\\frac{600}{5} = 120[/tex]
I now understand how to get y.. But how do I get x?
Answer:
x = 3.6
Step-by-step explanation:
since the 2 figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{AD}{EH}[/tex] = [tex]\frac{AB}{EF}[/tex] ( substitute values )
[tex]\frac{x}{2.4}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
2x = 7.2 ( divide both sides by 2 )
x = 3.6
Miranda purchased a coat for $101.50 that was regularly priced at $145, not including tax. what percentage did miranda save by purchasing a coat on sale?
If Miranda purchased a coat for $101.50 that was regularly priced at $145, not including tax then the percentage Miranda saved by purchasing the coat on sale is equal to 30%.
Percentage in mathematics can be described as a number expressed as a fraction of 100. The symbol % is used to indicate a percent.
The percentage Miranda saved by purchasing the coat on sale can be calculated as follows,
First, subtract the regular price from the price at which she purchased
145 - 101.50 = 43.5
Now, divide this number by the regular price of the coat,
43.5 ÷ 145 = 0.3
Now, the percentage Miranda saved can be calculated by multiplying the result by 100,
0.3 × 100 = 30%
Hence, the percentage Miranda saved by purchasing the coat on sale is calculated to be 30%.
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FIND x
log(x)+ log (x+3)=1
The statistical analysis of economic phenomena is defined as:_________
a) standard deviation.
b) econometrics.
c) confidence intervals.
d) variance.
The correct option out of all these is option B: Econometrics.
Now to clear our confusion further, we will look at the basic definitions of these concepts,
A confidence interval in statistics is the probability that a population parameter falls within a range of values for a specified percentage of the time.
Variance and standard deviation are very different measures from the mean, so we expect to see significant differences in how they are estimated.
Econometrics is a statistical and mathematical analysis of economic relations and is often the basis for economic forecasting. Governments may use such information to set economic policies and private companies to support pricing, inventory, and production decisions. However, economists mainly use it to study relationships between economic variables.
So, option B is Correct Econometrics.
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Simplify (1+1/3)^2-2/9
The simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.
What is the simplified form of the given expression?Given the expression in the question;
( 1 + 1/3 )² - 2/9
Add the two terms inside the parenthesis
( (3+1)/3 )² - 2/9
( 4/3 )² - 2/9
Apply product rule to 4/3
4²/3² - 2/9
Raise 4 and 3 to the power of 2
16/9 - 2/9
Combine the numerators over common denominator
( 16 - 2 ) / 9
14/9
Therefore, the simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.
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Write an equation of a circle with the given center and radius. Check your answers.
center (-4,-6) , radius 7
The equation of the circle with radius 7 and center at (-4 , -6) is (x + 4)^2 + (y + 6)^2 = 49.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-4 , -6)
r = 7
(x - -4)^2 + (y - -6)^2 = 7^2
(x + 4)^2 + (y + 6)^2 = 49
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Determine the range of f(x) = |x + 5|.
if right ill award u pls need fast pretty pls
Answer:it
Step-by-step explanation:
it should be 10 i think
Please help I don't understand!!
1. Use the graph at right to answer the following questions. (Hint: rate of change = slope).
Calculate the average rate of change from x = 1 to x = 4
2. Use the graph at right to answer the following questions. (Hint: rate of change = slope).
Calculate the average rate of change from x = 2 to x = 5
1. Average rate of change = -1/3
2. Average rate of change = 4/3
How to the Average Rate of Change?Average rate of change = change in y /change in x.
1. Average rate of change from x = 1 to x = 4
When x = 1, y = 5
When x = 4, y = 4
Average rate of change = (4 - 5)/(4 - 1)
Average rate of change = -1/3
2. Average rate of change from x = 2 to x = 5
When x = 2, y = 3
When x = 5, y = 7
Average rate of change = (7 - 3)/(5 - 2)
Average rate of change = 4/3
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Complete the square. x² +14 x+ ____
The complete expression of the given quadratic function is:
x² + 14x + 49
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:
(a + b)² = a² + 2ab + b²
x² + 14x + ?
where:
x² = a²14x = 2abb = ?Substitute and find b
14x = 2xb
2b = 14
b = 7
Let's complete the square
x² + 14x + 7²
x² + 14x + 49
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