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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14 POINTS!!!!!!!!!!!!!
PLS HELP
Answer:
1) y = 6
2) Paul has 20 quarters
Step-by-step explanation:
PLEASE HELP ASAP
ykdlydkyskyskystksltsylelyellyslyspyslsu dyllglgzlgsls xlykx
Answer:
There is nothing to answer.
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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An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $2,600 1.7%
Municipal Bond $3,700 3.2%
Preferred Stock $575 12.9%
Common Stock A $1,225 −5.6%
Using technology, calculate the weighted average ROR of the investments. Round to the nearest tenth of a percent.
2.1%
3.1%
5.9%
7.5%
Using technology, the weighted average ROR of the investment, rounded to the nearest tenth of a percent is 2.1%
What is the weighted average ROR?
The weighted average ROR means the rate of return of the four investments combined together to give a single return, which is computed as the sum of the RORs multiplied by the percentage of total portfolio invested in each security.
total investment=$2600+$3700+$575+$1225
total investment=$8100
% invested in each security=amount invested in each security/total investment
weighted average ROR=(1.7%*$2600/$8100)+(3.2%*$3700/$8100)+(12.9%*$575/$8100)+(-5.6%*$1225/$8100)
weighted average ROR=2.1%
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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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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 :)
What is £40 shared in the ratio of 1:4
the ratio of tomatoes to red apples is2:5 if there are 20 tomatoes how many red apples are there
Answer:
50 red apples
Step-by-step explanation:
If the ratio is 2:5
20 tomatoes ( 2 ratio)
20 ÷ 2 = 10 ( 1 ratio)
5 x 10 = 50 (5 ratio)
then there would be 50 red apples.
(o´▽`o)ﾉ x
Answer:
50 red apples
Step-by-step explanation:
the 2 part of the ratio applies to tomatoes of which there are 20, then
20 ÷ 2 = 10 ← value of 1 part of the ratio, then
5 parts = 5 × 10 = 50 red apples
y varies directly with x .
If y=6 when x=2 , find x when y=12 .
The required value of x is 4 by using constant of proportion.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Now, find k for given x = 2 and y = 6, we need to put these values in equation 1, i.e.
6 = k(2)
k = 6/2
k = 3
Further calculate x for given y = 12 and constant of variation = 3 i.e.
12 = (3)x
x = 4
Hence, the required value of x is 4.
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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
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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Find the common ratio for each geometric sequence. 64,48,36,. . . . . .
The infinite geometric series has the general form a1 + a1r + a1r² + a1r³ +…, where r is the common ratio and a1 is the first term. The common ratio of the geometric sequence 64, 48, 36,.... is 3/4.
What is meant by geometric series?The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³ +…, where r is the common ratio and a1 is the first term.
The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.
Given: a1 = 64 and a2 = 48
The common ratio(r) is:
r = a2/a1 = 48/64
r = 6/8 = 3/4
Therefore, the common ratio of the geometric sequence 64, 48, 36,.... is 3/4.
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Booker owns 85 video games. He has 3 shelves to put the games on.
Each shelf can hold 40 video games. How many more video games does he have room for? (Brainliest Question)
Answer:
5
Step-by-step explanation:
it's because one shelf is 40 then the second shelf is 80 and then the third is 5.
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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Solve for x in terms of y
4x+2y=7
Answer:
x= -(2y+7)/(4)
Step-by-step explanation:
4x+2y=7
4x = -2y+7
x= -(2y+7)/(4)
Answer:
x = [tex]\frac{7-2y}{4}[/tex]
Step-by-step explanation:
4x + 2y = 7 ( subtract 2y from both sides )
4x = 7 - 2y ( divide both sides by 4 )
x = [tex]\frac{7-2y}{4}[/tex]
.............................................
Answer:
The value would be 100
Step-by-step explanation:
The diameter of the trunk of a bush is 7.62 × 10^-2 meters. The diameter of the trunk of a tree is 3.81 × 10^–1 meter. How many times larger is the diameter of the trunk of the tree?
2 times larger
3 times larger
4 times larger
5 times larger
The diameter of the trunk of a tree is 5 times larger than the diameter of the trunk of a bush.
How to find the number of times larger the diameter of the trunk of the tree is when compared with the diameter of the trunk of a bushGiven data
diameter of the trunk of a bush is 7.62 × 10^-2 meter
diameter of the trunk of a tree is 3.81 × 10^–1 meter
To achieve the comparison we divide the diameter of the trunk of a tree with the diameter of the trunk of a bush, as follows:
= 3.81 × 10^–1 meter ÷ 7.62 × 10^-2 meter
= 5
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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
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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PLEASE HELP!!!
Noor needs to build a pen for her chickens. She wants the pen to be rectangular, 3 meters longer than it is wide. Write the equation Noor should use to determine the width of a pen which has an area of 70 square meters
Given the area, the equation that Noor should use to determine the width of pen is x² + 3x = 70.
The length and width of the rectangular pen are 10m and 7m respectively.
What is the width of the rectangular pen?The area of a rectangle is expressed as;
A = l × w
Where l is length and w is width.
Given the data in the question;
Let the width of the rectangular pen be 'x'
Width = w = xLength = l = x + 3Area = 70m²To determine the equation that Noor will use to find the width of the pen, plug the values into the equation above.
A = l × w
70 = (x+3) × x
70 = x² + 3x
x² + 3x = 70
We can go further and solve for the width of the pen.
x² + 3x = 70
x² + 3x - 70 = 0
Factor sing AC method; find two integer whose addition gives 3 and multiplication gives -70.
-7 and 10
(x-7) (x+10) = 0
x - 7 = 0, x + 10 = 0
x = 7, x = -10
But the dimension of the width can not be negative.
Hence
x = 7
Width = x = 7m
Length x + 3 = 7 + 3 = 10m
Given the area, the equation that Noor should use to determine the width of pen is x² + 3x = 70.
The length and width of the rectangular pen are 10m and 7m respectively.
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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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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
Graph the line with the equation y = -4/3x+1
Answer: coordinates would be 0,1 and 3,-3
Step-by-step explanation:
a₁ is the first term of a sequence, r is a common ratio, and d is a common difference. Write the first five terms. a₁=3, d=7
The first five terms of an arithmetic sequence with first term 3 and common difference 7 are 3, 10, 17, 24, 31
The given parameters:
a₁ = 3, d = 7
d is the common difference, hence, the given sequence is an arithmetic sequence.
In an arithmetic sequence, the formula for the nth term is given by:
a(n) = a(1) + (n - 1) . d
We can also find the terms using recursive formula. The nth term of an arithmetic sequence is equal to the (n-1)th term plus the common difference, d. Mathematically,
a(n) = a(n -1) + d
Let us start from n = 1
a(1) = 3 (given)
a(2) = a(1) + d = 3 + 7 = 10
a(3) = a(2) + d = 10 + 7 = 17
a(4) = a(3) + d = 17 + 7 = 24
a(5) = a(4) + d = 24 + 7 = 31
Thus, the first five terms are 3, 10, 17, 24, 31
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Determine whether the following statements are sometimes, always, or never true. Explain.
How can triangle classifications help you prove triangle congruence?
Triangle classification will always help us to prove congruency in triangle. Each of the three angles in an acute triangle is acute. One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle.
What is triangle congruence?The triangles are congruent when two sets of corresponding sides and the corresponding angles between them are in agreement. Two triangles that have a congruent angle in the middle and two congruent sides.
Instead of using the unit measure, it is based on the proportion of the side lengths to one another. As a result, triangles are categorized according to how many of their sides are the same length as one another or not at all equal.
Angles are another way to categorize triangles. Each of the three angles in an acute triangle is acute (less than 90 degrees). One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle (greater than 90 degrees).
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Solve for x.
I need help with this geometry problem
write 1875/100 in its lowest terms
Answer:
hii
Step-by-step explanation:
18.75 answer
is
correct
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
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]
