Use the diagram below for the expression x^2+10x+6 to answer the following questions?
What value needs to be added to x^2+10x+6 to complete the square?
Using your answer above rewrite the perfect square trinomial as a squared binomial?
Answers
The value needs to be added to x²+10x+6 to complete the square is 19.
What is Perfect square trinomials?Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)².
In the presented trinomial, we can immediately find that a = x, and b² = c,
We know that a = x, and , 2ab = 2bx.
Now, 2bx and 30x are corresponding terms, 2bx = 30x.
Take the coefficient of x = 10
Divide by 2
10/2 =5
Then Square it
5 x 5=25
Add this to make a perfect square trinomial;
x² + 10x + 25
In the given equation we need to add 19 to make the perfect square trinomial; x² + 10x + 25.
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Related Questions
some pennies are arranged in rows. the number of pennies in each row is the same as the number of rows. after 10 pennies are removed, the remaining pennies can be arranged into 2 fewer rows, but with 1 additional penny in each row. how many pennies were there originally?
Answers
Answer:
22
Step-by-step explanation:
Which equation represents this sentence?
Half the difference of a number and 5 is−2.
Responses
12(5−x)=−2
1 half left parenthesis 5 minus x right parenthesis equals negative 2
12x−5=−2
1 half x minus 5 equals negative 2
12(x−5)=−2
1 half left parenthesis x minus 5 right parenthesis equals negative 2
5−12x=−2
Answers
The equation which represents the sentence given; Half the difference of a number and 5 is−2 is; 1/2(x - 5) = -2; 1 half left parenthesis x minus 5 right parenthesis equals negative 2.
Word phrases from Algebraic expressions.It follows from the task content that the expression which best represents the given algebraic expression is to be determined.
First, the difference of a number, x and t is represented as; (x - 5).
Hence, the word phrase; Half the difference of a number and 5; is best represented algebraically as; 1/2(x - 5).
Ultimately, the whole word phrase; Half the difference of a number and 5 is -2 can best be represented as; 1/2(x - 5) = -2.
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⦁ The function p (w) = 230(1.1)w represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period. 10 points
⦁ During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
⦁ Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
⦁ When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
you will get 10 points
Answers
The increasing exponential functions are described as follows:
f(t) = a(1 + r)^t.
In which the parameters are listed as follows:
a is the initial value.r is the growth rate.For the old factory, the function is of:
p (w) = 230(1.1)^w.
Hence:
During week 0, 230 items are produced.The growth rate is of 10%.For the new factory, from the graph given at the end of the answer, the parameters are given as follows:
a = 190, which is the intercept.b = 1.1578, as 220/190 = 1.1578.Hence the function is:
pn(w) = 190(1.1578)^w.
The new factory overtakes the old factory when:
pn(w) > p(w)
190(1.1578)^w > 230(1.1)^w
(1.1578/1.1)^w > 230/190
wlog(1.1578/1.1) > log(230/190)
w > log(230/190)/log(1.1578/1.1)
w > 3.73 weeks.
Missing InformationThe graph for the second factory is given by the image presented at the end of the answer.
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Replace the star astrict (*) with a digit that allows you to reduce the fraction. If there are two * in the same fraction, replace them with the same digit. Find all possible values of * in each fraction. This is the one that I got stumped in...
12*/23* This is a fraction. Fill it in. Remember, you have to fill it in, so it can get reduced.
Please answer by 3:00PM Pacific time Sunday november 6th 2022
Answers
The star asterisk in the fraction 12*/23* is being replaced by all the possible values as outlined
1 to be 11/21
2 to be 61/116
4 to be 62/117
5 to be 25/47
6 to be 63/118
8 to be 64/119
0 to be 12/23
What are fractions?In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a chunk or section taken from a whole, which can be any number, and can represent any amount.
The fractions with different numerators and denominators when compared with another fraction but the same value with the fraction are said to be equivalent fractions.
The asterisk value is replaced with digit in each case, and the fraction formed is reduced to their equivalent forms as below
12*/23* * replaced by 1 and reduced to be 11/21
12*/23* * replaced by 2 and reduced to be 61/116
12*/23* * replaced by 4 and reduced to be 62/117
12*/23* * replaced by 5 and reduced to be 25/47
12*/23* * replaced by 6 and reduced to be 63/118
12*/23* * replaced by 8 and reduced to be 64/119
12*/23* * replaced by 0 and reduced to be 12/23
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What is the
y-intercept of the function f(x)=-2/9x+1/3?
Answers
Answer:
1/3
Step-by-step explanation
We can immediately tell the y-intercept is 1/3.
Slope intercept form:
y = mx + b
m = slope
b = y-intercept.
Answer: the y - intercept is 1/3
Step-by-step explanation: trust
Each of PQ and RS represents a 2-digit number. Different letter represent different digits, chosen from 6, 7, 8 and 9. What is the greatest product that PQx RS can have?
Answers
The greatest product that PQ x RS can have: 96 * 87 = 8352
In this question, we have been given PQ and RS represents a 2-digit numbers. Different letter represent different digits, chosen from 6, 7, 8 and 9
We need to find the greatest product that PQ x RS can have.
Consider P = 9, Q = 6, R = 8 and S = 7
So the two digit numbers would be,
PQ = 96 and RS = 87
PQ x RS
= 96 * 87
= 8352
Therefore, the greatest product that PQ x RS can have: 96 * 87 = 8352
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Deandre is studying metals. He finds out that the ratio of chromium to nickel in stainless steel is 9 to 4.
Deandre adds 27 pounds of chromium and 12 pounds of nickel to his forge. Did he add the metals correctly
(is this a proportional relationship)? Show your work
Answers
9:4 27:12 27/9=3 12/4=3 3=3
Please someone help me. Number 7 and 8. Thank you.
Answers
7. The composite functions are given as follows:
a. f(g(x)) = [tex]\frac{3x}{-x^2 + 3x - 1}[/tex].
b. g(f(x)) = [tex]\frac{3x(x - 1)}{9x^2 + x - 1}[/tex]
c. (f(g(3)) = -9.
8. The inverse function is given as follows:
[tex]f^{-1}(x) = \frac{4 + x}{3 - x}[/tex]
How to obtain the composite function?The composite functions are obtained using the inner function as the input to the outer function.
In this problem, the functions are defined as follows:
f(x) = x/(x - 1).g(x) = 3x/(x² + 1).The composite of f and g is:
[tex]f(g(x)) = f\left(\frac{3x}{x^2 + 1}\right) = \frac{\frac{3x}{x^2+1}}{\frac{3x}{x^2+1} - 1} = \frac{\frac{3x}{x^2+1}}{\frac{-x^2 + 3x - 1}{x^2 + 1}} = \frac{3x}{-x^2 + 3x - 1}[/tex]
At x = 3, the numeric value of the composite function is given as follows:
f(g(3)) = 9/(-9 + 9 - 1) = -9.
The composite function of g and f is given as follows:
[tex]g(f(x)) = g\left(\frac{x}{x - 1}\right) = \frac{\frac{3x}{x - 1}}{\left(\frac{3x}{x - 1}\right)^2 + 1} = \frac{3x}{x - 1} \times \frac{(x - 1)^2}{9x^2 + x - 1} = \frac{3x(x - 1)}{9x^2 + x - 1}[/tex]
Inverse functionThe function is given as follows:
y = (3x + 4)/(x - 1)
The find the inverse, the variables x and y are exchanged, and then y is isolated, as follows:
x = (3y + 4)(y - 1)
xy - x = 3y + 4
3y - xy = 4 + x
y(3 - x) = 4 + x
y = (4 + x)/(3 - x)
[tex]f^{-1}(x) = \frac{4 + x}{3 - x}[/tex]
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Find the perimeter of \triangle PQR△PQR. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answers
154.5
Step-by-step explanation:
left triangle and right triangle has the same degree.
M to Q 107/2 = P to R 53.5
O to N 110/2 = R to Q 55
Find X
M to N 92/2 = P to Q 46
Perimeter- 53.5+ 55+ 46= 154.5
Describe the transformation of
f(x) = -2|x + 1 + 5
Shift Up__units.
Shift Down__units.
Shift Right__units.
Shift Left__units.
Compress by a factor of__
Stretch by a factor of__
Reflect over__axis.
Answers
The transformation of the equation f(x) = -2|x + 1| + 5 is
Shift Left 1 units
Shift Up 5 units
Compress by a factor of 2
Reflect over x axis
Interpretation of the transformationsTransformation involves movements of image or object usually described in a cartesian plane
starting from |x| at the origin
|x + 1| is a shift to the left 1 unit
|x + 1| + 5 is a shift on the y axis, it represents a shift up 5 units
2|x + 1| + 5 is a vertical compression by a factor of 2
-2|x + 1| + 5 the negative sign shows reflection over x axis turning the graph over
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a study is designed to test whether there is a relationship between natural hair colors and eye colors. if a significant chi-square value is obtained, this suggests that:
Answers
Using the concepts of hypothesis test, we got that something is happening that wasn’t accounted for as a result when a significant chi-square value is obtained.
A chi-squared test (symbolically represented as χ2) is basically the data analysis on the basis of the observations of a random set of variables. Usually, it is the comparison of two statistical data sets. This test was introduced by Karl Pearson in the 1900 for categorical data analysis and distribution. So it was mentioned as a Pearson’s chi-squared test.
The chi-square test is actually used to estimate how likely the observations that are made would be, by considering assumption of the null hypothesis as true.
Hence, a study is designed to test whether there is a relationship between natural hair colors and eye colors, in that case if a significant chi-square value is obtained it suggests that something is happening that wasn’t accounted for .
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An isosceles right triangle has a hypotenuse length that can be modeled with the function . the combined length of the legs can be modeled with the function l(x) = 2x. which function, p(x), can be used to find the perimeter of the triangle?
Answers
The perimeter of the isosceles triangle will be P(x) = x√2 + 2x.
A polygon with three sides is known as a triangle. The angles of a triangle add up to form 180° and the sum of all sides of a triangle is known as the perimeter. In an isosceles triangle, the two sides are equal and their opposite angle too. In an isosceles triangle, the hypotenuse side of the triangle can be written as h(x) = x√2. The combined length comes out to be L(x) = 2x. Using this information the perimeter of the triangle comes out to be,
P(x) = h(x) + L(x).
P(x) = x√2 + 2x
Hence the perimeter of the triangle comes out to be P(x) = x√2 + 2x
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Suppose that A and B are points on the number line.
If AB=5 and B lies at 12, where could A be located?
If there is more than one location, separate them with commas.
:0
Location(s) of A :
0.0....
X
Answers
Answer:
locations of A are 7, 17
Step-by-step explanation:
since B is positioned at 12 and AB = 5 , then
A = 12 - 5 or 12 + 5 = 7 , 17
2/7 x 2 1/4 write your answers in simpliest form
Answers
Answer:
the answer is 9/14
Step-by-step explanation:
2/7× 2 1/4 = 2/7× 9/4
= 2 × 9 / 7 × 4
= 18/28
= 9/14
Colin buys a car for £45500. It depreciates at a rate of 6% per year. How much will it be worth in 3 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
The answer is 33,710 euros.
Step-by-step explanation:
Start by multiplying 45,550 by 6%. This will give 2,730. over the next three years the price decreases, so multiply 2,730 by 3, which is 8,190. Finally, subtract 45,550 by 8,190 to get 33,710.
sally purchases some apples and oranges for $5.25. oranges cost 51 cents each and apples costs 42 cents each. sally purchased 11 pieces of fruit in total. how many oranges did sally purchase? g
Answers
Sally purchased 7 pieces of orange .
Conversion applied :
1 dollar = 100 cents
Cost of 1 piece of orange = 51 cents
Cost of 1 piece of apple = 42 cents
Let pieces of orange purchased be x .
⇒ pieces of apples purchased = 11 - x .
The following linear equation becomes ,
51 x + 42 ( 11 - x ) = 5.25 * 100
Solving linear equation in 1 variable given above ,
9 x = 63
x = 7
⇒ no. of oranges purchased = 7
Therefore Sally purchased 7 pieces of orange .
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(b) Work out the value of (2.3 × 10³) × (5.9 × 105)
Give your answer in standard form.
Answers
Answer: 1424850
Step-by-step explanation:
2.3 x 10³ = 2300
5.9 x 105 = 619.5
2300 x 619.5 = 1424850
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1. which of these variables are discrete and which are continuous random variables? (a) the number of new accounts established by a salesperson in a year. (b) the time between customer arrivals at a bank atm. (c) the number of customers at big nick's barber shop. (d) the amount of fuel in your car's gas tank. (e) the number of minorities on a jury. (f) the outside temperature today.
Answers
The discrete and continuous random variables are-
a) Discrete; (b) Continuous; (c) Discrete; (d) Continuous; (e) Discrete; (f) Continuous
Define the term discrete and continuous random variables?Discrete variables are those whose values may be measured through counting. Contrarily, random variables which it reflect something are designated continuous variables.(a) So because number of new accounts is counted, (a) discrete (like, non-negative integers).
(b) Continuous, given that the interval between customer arrivals may have decimal values (like 2.9 minutes or 27.75 seconds).
(c) Because the quantity of clients is counted, (c) discrete (like, non-negative integers).
(d) Continuous, as the fuel consumption can have decimal values (like 15.5 gallons).
(e) Since this number of minorities is counted, (e) discrete (like, non-negative integers).
(f) Continuous since the outdoor temperature can be expressed in decimal degrees (e.g., 7.78 C).
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The radius of a circle is 15 inches. What is
the circumference of the circle? Write
your answer using T.
Answers
Answer:
C = 30pi inches
Step-by-step explanation:
The radius is 15 inches (said so in the question)
The diameter is 30 inches (The diameter is twice the radius)
The circumference is
C = pi•d
C = pi•30
C = 30pi
The circumference is 30pi inches.
Write an equation in slope-intercept form
to represent the relationship between x
and y shown in the table.
X
Y
-10 -5 0 5
55
20
-15
-50
10
-85
Answers
Answer:
665-09
Step-by-step explanation:
its easy but im lazy please helppppp
Answers
y=1/58x
because in 3 hours its 174 miles.
let y=miles
x=time
so 174y=3x
divide by 3 on both sides
58y=x
isolate y by dividing by 58 on both sides
therefore you get the answer
Graph the points of the given function with the x-values x=−4 , x = 0, and x = 5. f(x)=−2x+4−−−−√
Answers
The graph is attached and the table of value of the graph is as follows
x y
-4 12
0 4
5 -6
How to get the table of valuesThe function y = −2x + 4 is a linear function and will have a straight line graph
The table of values is gotten form the equation y = −2x + 4
solving for x = -4,
y = −2 * -4 + 4 = 12
solving for x = 0
y = −2 * 0 + 4 = 4
solving for x = 5,
y = −2 * 5 + 4 = -6
x y
-4 12
0 4
5 -6
The graph is plotted by finding the points in the table in the Cartesian plane and joining the points together
Other values are solved for in similar step
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Answer:Here is your answer
Step-by-step explanation:
22. A train travels 3 hours at 20km per
hour. How long will it take another
train to travel the same distance at
10km per hour?
(a) 6²/³ hours
(b) 6¹/2hours
(c) 6 hours
(d) 3 hours
(e) 2 hours
ans
Answers
6 hours will it take another train to travel the same distance .
What is speed?
Speed indicates the rate of movement of something or someone. If you know the distance traveled and the time it took, you may calculate an object's average speed. Speed is calculated as distance times speed.Average speed = Total distance/Total time
A train travels 3 hours at 20km per hour.
train travels 20 km in 1 hours.
then in 3 hours train travels = 3 * 20 = 60 km
total speed = 10 km/hr
t = distance/speed
= 60/10 = 6 hours
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How do you write 5 11/16 and 7 24/25 as a decimal?
Answers
Answer:
5 11/16 as a decimal = 5.6875
7 24/25 as a decimal is 7.96
Step-by-step explanation:
Answer:
5 11/16 = 5.6875
7 24/25 = 7.97
Step-by-step explanation:
you keep the whole numbers then you turn the fractions into decimals so to do that you divide 100 by the denominator and whatever the answer is you multiply it by the numerator to get your answer, 100 divided by 16 is 6.25 and 6.25 multiplied by 11 is 68.75 but since the 5 is already the whole number you basically just forget the decimal in 68.75 ( I hope that makes sense)
And for 7 24/25 you do 100 divided by 25 and that’s 4 so now you multiply 24 by 4 and that’s 96 so that goes after the decimal so it’s 7.96 (I hope that helped and all made sense.)
Solve for x:-
[tex]\sf -10 + x + 4 - 5 = 7x - 5[/tex]
Answers
Answer:
x = -1
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ -10 + x + 4 - 5 = 7x - 5
Then the value of x will be,
→ -10 + x + 4 - 5 = 7x - 5
→ -11 + x = 7x - 5
→ 7x - x = -11 + 5
→ 6x = -6
→ x = -6/6
→ [ x = -1 ]
Hence, the value of x is -1.
how many cards must be selected from the standard 52 deck to guarantee that at least 3 cards of the same suit are chosen
Answers
Nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.
What is the pigeon-hole approach?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. For instance, if one possesses three gloves but none of them are ambidextrous or reversible, then there must be at least two right-handed gloves or at least two left-handed gloves since there are three items but only two categories of handedness. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
The standard 52 deck has 4 suits of 13 cards each, thus as per n pigeons need to be extracted from p = 4 pigeon-holes; as per established literature above.
∴ [(n - 1) / p] + 1 = 3 ⇒ [(n - 1) / 4] + 1 = 3 ⇒ n - 1 = 8 ⇒ n = 8 + 1 ⇒ n = 9
Therefore, nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.
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Two integers, a and b, have different signs. They absolute value of integer a is divisible by the absolute value of integer b. Find two integers that fit this description. Then decide if she product of the integers is greater than or less than the quotient of the integers. Show your work.
Answers
Answer:
Step-by-step explanation:
One example is a=-6 and b=3
-6/3=-2
-6*3=-18
-2 is greater than -18; the quotient is greater than the product in this case.
Another example is a=6 and b=3
6/3=2
6*3=18
2 is smaller than 18; the quotient is smaller than the product in this case.
What are some ways we have learned to solve percent increase or percent decrease problems? How are these ways related to one another?
Answers
The different ways of solving percent increase or percent decrease problems has been described below
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
One way to solve the percentage increase or decrease problem is by multiplying the original number by the percentage given and then adding the result with the original number.
Another method is by multiplier method
Here, the original number is taken as 1 and the given percentage has to be converted to decimal and then 1 and the percentage obtained as decimal is added or subtracted. The result obtained has to be multiplied by the original number to get the required number after increase or decrease
For the first method
Suppose the number is n and it is increased by p%
Required result is
[tex]n + \frac{p}{100}\times n\\n( 1 + \frac{p}{100})[/tex]
For the second method
Suppose the number is n and it is increased by p%
Here n is taken as 1 and p% is converted to decimal
then 1 and p% in decimal form is added
we get (1 + 0._p)
Now the result is obtained is multiplied by n
Required result is
n(1 + 0._p)
[tex]n(1 + \frac{p}{100})[/tex]
In this way the two methods are related
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Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Which expression can you use to find 23% of 52?
0.23 × 52
23% of $52 is $
11.96
.
An easy way to check your answer is to use the friendly
50%
and divide 52 by
2
to get
13
.
Am i right???
Answers
Answer:
yeah i think so
Answer:
$11.96
Step-by-step explanation:
Now we have to,
→ find the 23% of $52.
Let's solve the problem,
→ 23% of $52
→ (52/100) × 23
→ 0.52 × 23
→ $11.96
The similar expression is,
→ 0.23 × 52
→ $11.96
Hence, answer is $11.96.
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Wilson paints 40% of a bookcase in 20 minutes.
Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase.
Answers
The time it takes to paint the whole bookcase is 50 minutes.
How to calculate the value?From the information, Wilson paints 40% of a bookcase in 20 minutes.
Let the time taken to paint the whole bookcase be x. This will be illustrated as:
20/x = 40/100
Cross multiply
40x = 100 × 20
40x = 2000.
Divide
x = 2000 / 40
x = 50
The time taken is 50 minutes.
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