Complete the expression so it forms a perfect-square trinomial.
x² - 5x +
✔ 25/4
x² +
x + 49
Answers
Answer:
Second question in Assignment = A) 14
Step-by-step explanation:
x^2 = 14x +49
Answer: 14
Step-by-step explanation:
The first one is 25/4 then 14
Related Questions
The sales tax rate in El Paso, TX is 6.25%. Morris wants to buy a coat with a $56.00 price tag. He has a gift card to the store he wants to use. Create a proportionor equation. Use x for your variable.
Answers
Data:
Tax: T
Price tag: P
Total cost: x
Gift card: G
T=6.25/100
P=$56.00
The total cost will be:
x will be equal to the cost of the coat plus the tax (6.25 of the ccost of the coat) less the gift card.
\(x=P+TP-G\)\(x=56.00+56.00(\frac{6.25}{100})-G\)\(x=56.00+\frac{7.00}{2}-G\)\(x=\frac{119.00}{2}-G\)\(x=59.5-G\)Number List 1: X=1,2,3,4,5 Y=3,6,9,12,15 Number List 2: X=1,2,3,4,5 Y=2,4,6,8,10 Scenario 1: You go to the movie theaters and buy x tickets how much do you pay when you buy 6 tickets? Which set of numbers does this match? Scenario 2: At the vet for every dog there is 2 cats. Which set of numbers does this match?
pls help!!
Answers
The set of numbers that matches each scenario is given as follows:
Scenario 1: Number list 1.Scenario 2: Number list 2.How to match each number list for a scenario?For the number list 1, the rate between the output variable y and the input variable x is given as follows:
k = 15/5 = 12/4 = 9/3 = 6/2 = 3/1 = 3.
Hence the proportional relationship that models this scenario is of:
y = 3x.
The rate is different of two, hence the scenario modeled is scenario 1, meaning that the cost of each movie ticket is of $3, and thus the cost of six tickets is of $18.
For the number list 2, the rate between the output variable y and the input variable x is given as follows:
k = 10/5 = 8/4 = 6/3 = 4/2 = 2/1 = 2.
Hence the proportional relationship that models this scenario is of:
y = 2x.
Hence the scenario modeled is given by scenario 2, as a situation in which for every dog there would be two cats would also be modeled by a proportional relationship with a rate of change of 2.
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is this the right answer to it?
Answers
Answer:
Yes
Hope i helped
what’s the slope lol
Answers
Step-by-step explanation:
From the figure , assume that OAB is a right angle triangle and angle OAB is alpha
\(Slope = \tan( \alpha ) \)
\( = \frac{opposite \: side}{adjacent \: side} \)
\( = \frac{ - 3}{ - 1} \)
\( = 3\)
Simplify.
1. \(\frac{3y-2}{5}\)
2. \(\frac{6x-3}{3}\)
3. \(\frac{4}{2}\)
Answers
Answer:
\( 1. \frac{3y - 2}{5} = \frac{3y}{5} - \frac{2}{5} \\ \\ 2. \frac{6x - 3}{3} = \frac{6x}{3} - \frac{3}{3} \\ = 2x - 1 \\ \\ 3. \frac{4}{2} = 2\)
15PTS PLEASE HELP ASAP!
(dont write random answers pls!)
Answers
Answer:
52
Step-by-step explanation:
.................................
Answer:
52
Step-by-step explanation:
its too hard to explain
Solve the system by substitution. x=-y-9 6x-5y=1
Answers
Answer:
x= -64, y= 55
Step-by-step explanation:
x=-y-9
6(y-9)-5y=1
6y-54-5y=1
y=55
x=-55-9
x=-64
Answer:
{x=-4
{x= -5
Step-by-step explanation:
Substitute into one of the equations:6(- y -9) - 5y=1
Apply Multiplicative Distribution Law:- 6y-54-5y=1
Rearrange unknown terms to the left side of the equation:-6y -5y = 1+54
Combine like terms:- 11y= 1+54
Calculate the sum or difference:-11y=55
Divide both sides of the equation by the coefficient of variable:y= 55÷(-11)
Remove the parentheses:y = -55÷11
Calculate the product or quotient:y=-5
Substitute into one of the equations:x=-(-5)-9
Remove the parentheses:x=5-9
Calculate the sum or difference:x=-4
The solution of the system is:{x=-4
{x=-5.
Which polynomial correctly combines the like terms and puts the given polynomial in standard form? one-thirdx 8x4 – two-thirdsx2 – x 8x4 – one-thirdx2 – x 8x4 two-thirdsx2 two-thirdsx 8x4 – two-thirdsx2 – two-thirdsx 8x4 – two-thirdsx2 – x.
Answers
Polynomial equation is a equation which is formed with coefficients variables and exponents with basic mathematics operation and equality sign. From the given option the option C correctly combines the like terms and puts the given polynomial in standard form which is,
\(8x^4-\dfrac{2}{3}x^2-\dfrac{2x}{3}\\\)
Hence the option C is the correct option.
Given information-The given polynomial equation in the problem is,
\(\dfrac{1}{3} x+8x^4-\dfrac{2}{3}x^2-x\)
Polynomial equationPolynomial equation is a equation which is formed with coefficients variables and exponents with basic mathematics operation and equality sign.
In the above polynomial equation the variable are x and the highest power of the variable x is four.
Arrange the given polynomial equation in the power of the variable x. Thus,
\(8x^4-\dfrac{2}{3}x^2+\dfrac{1}{3} x-x\)
Make the group of the same power of the variable x. Therefore,
\(8x^4-\dfrac{2}{3}x^2+(\dfrac{1}{3} x-x)\)
\(8x^4-\dfrac{2}{3}x^2+\dfrac{x-3x}{3}\\\)
\(8x^4-\dfrac{2}{3}x^2-\dfrac{2x}{3}\\\)
From the given option the option C correctly combines the like terms and puts the given polynomial in standard form which is,
\(8x^4-\dfrac{2}{3}x^2-\dfrac{2x}{3}\\\)
Hence the option C is the correct option.
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In the given figure ABCD, prove that
angleBCD= angleBAD+ angle ABC+angle ADC.
[Hint: Join A and C then extended AC to the point E]
Answers
We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:
Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.
Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.
Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).
Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.
Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).
Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.
Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.
Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.
Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.
Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
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Given: Quadrilateral \(\displaystyle\sf ABCD\)
To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)
Proof:
1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).
2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).
3. In triangle \(\displaystyle\sf ACD\):
- \(\displaystyle\sf \angle ACD = \angle BAD + \angle ADC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).4. In triangle \(\displaystyle\sf BCE\):
- \(\displaystyle\sf \angle BCE = \angle BAD + \angle ABC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):
- \(\displaystyle\sf \angle BCE = \angle BCD\).6. Combining the equations from steps 3 and 4:
- \(\displaystyle\sf \angle BCD = \angle ACD = \angle BAD + \angle ADC\). - \(\displaystyle\sf \angle BCD = \angle BCE = \angle BAD + \angle ABC + \angle ADC\).Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
HELP ASAP
A picture is 7 inches wide and 9 inches long. A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long. What scale factor was used to enlarge the picture?
9/7
7/9
31.5/7
7/31.5
Answers
By simply taking the width after it was enlarged and dividing it by the width before it was enlarged we can find the scale factor that was used. In this case it would be 31.5 (width after)/ 7 (width before) which gives us a scale factor of 31.5/7. Simplifying would yield a scale factor of 4.5 times.
The Scale factor was used to enlarge the picture is 7/ 31.5.
What is Scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
A picture is 7 inches wide and 9 inches long.
A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.
So, scale factor is
= Original dimension / Enlarged dimension
= 9/ 40.5
= 90/ 405
= 10/45
= 2/9
Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.
= 7/ 3.15
= 70/31.5
= 2/9
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there is one line on the graph and its asking what is in the solution set?
Answers
Answer: you
Step-by-step explanation:
they are 8,756 students that attend middle schools in the city of Johnson. Of the students, 3,252 are picked up by car, 2,549 ride the bus home, and 2,955 students walk home. How many students leave school by bus or car?
Answers
The number of students that leave by bus or car is given as follows:
5801 students.
How to obtain the union and intersection set of the two sets?The union and intersection sets of multiple sets are defined as follows:
The union set is composed by the elements that belong to at least one of the sets.The intersection set is composed by the elements that belong to at all the sets.The or operation is equivalent to the union operation, meaning that we add the number of students that leave by bus to the number of students that leave by car.
Hence the number of students that leave by bus or car is given as follows:
3232 + 2549 = 5801 students.
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What is the radius of a
cylinder with a
diameter of 18 cm?
Answers
Since a diameter is twice the size of a radius.
Hope this helps
IF U HELP U GET BRAINLISTED the difference of a number and six is the same as five times the sum of a number and 2 what is the number
Answers
Answer:
\(let \: the \: number \: be \: x \\ x - 6 = 5(x + 2) \\ x - 6 = 5x + 10 \\ 4x = - 16 \\ x = - \frac{16}{4} \\ x = - 4 \\ the \: number \: is \: - 4\)
In the exponential growth model P(t)=P_0 e^kt, what does the variable P0 represent?
A. The variable P0 represents the present value.
B. The variable P0 represents the initial amount.
C. The variable P0 represents the proportionality constant.
D. The variable P0 represents the principal.
Answers
The variable P0 represents the initial amount.
In the exponential growth model, P(t) represents the population at time t, P0 represents the initial population at time t=0, k represents the growth rate, and e is the mathematical constant, approximately equal to 2.71828. Therefore, P0 represents the initial amount or the starting point of the population.
The correct answer is B, the variable P0 represents the initial amount.
B. The variable P0 represents the initial amount.
In the exponential growth model P(t) = P0 * e^(kt), the variables are defined as follows:
- P(t): The population size at time 't'
- P0: The initial population size (i.e., the population size at the beginning, when t=0)
- e: The base of the natural logarithm (approximately 2.71828)
- k: The growth rate constant
- t: Time
In this model, P0 is the population size at the beginning of the observed period (when t=0). Therefore, it represents the initial amount.
The variable P0 in the exponential growth model P(t) = P0 * e^(kt) represents the initial amount of the population or quantity being studied.
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Which of the following lists all the roots of x^4 =x^3 +x^2 + x+2?
F {−1, 2}
H {−2, −1}
G {−1, 2, i, −i}
J {−2, −1, i, −i}
Answers
Answer:
G
Step-by-step explanation:
\(x^4-x^3-x^2-x-2=0 \\ \\ (x+1)(x^3+x-2x^2-2)=0 \\ \\ (x+1)(x(x^2+1)-2(x^2+1))=0 \\ \\ (x+1)(x-2)(x^2+1)=0 \\ \\ (x+1)(x-2)(x-i)(x+i)=0 \\ \\ x=-1, 2, i, -i\)
3x-1 /x+k=3-7/x+k
what is the value of k?
Answers
Answer:
The answer is k=2.
Step-by-step explanation:
Explanation: Let f(x)=x3+kx2+x+5. When f(x) is divided by (x+ 2) , the remainder is =3.
If you are standing 75 ft away from a tree and looking up at the top at a 40° angle, what is the height of the tree?
Answers
Answer:
Step-by-step explanation:
The lower and upper estimates of a car coming to a stop six seconds after the driver applies the brakes are as follows: Lower estimates = 122 Upper estimates = 298 Question: On a sketch of velocity against time, show the lower and upper estimates.
Answers
These lines will be parallel to the initial line and will intersect the final velocity line at the corresponding values (122 for the lower estimate and 298 for the upper estimate)
To sketch the velocity against time, you can take the following steps:
First, calculate the acceleration using the given data by using the formula;
acceleration = (final velocity - initial velocity)/time
Where; Initial velocity is the velocity before applying the brakes
Final velocity is the velocity at which the car comes to stop
Time is the time it takes to stop the car (6 seconds in this case)
Now, calculate the lower and upper estimates using the formula;
Lower estimate = initial velocity + (acceleration x time)
Upper estimate = initial velocity + (2 x acceleration x time)
Sketch the graph using the following steps;
On the vertical axis, plot the velocity of the car
On the horizontal axis, plot the time
Start from the initial velocity and draw a straight line with the calculated acceleration until the end of the time (6 seconds)This straight line will give you the final velocity (0 in this case)
Now, draw two more lines, one with the lower estimate and the other with the upper estimate
Finally, label the axes and the lines with their corresponding values.'
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The postal service charges $2 to ship packages up to 5 ounces in weight, and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce. What is the domain of this relation?
Answers
Answer: x > 0 x = (0, ∞)
Step-by-step explanation:
The domain (x-values) are the number of ounces the package weighs.
The package must weigh greater than 0 but there doesn't appear to be a maximum weight. Therefore, x > 0
The domain is the set of values for which the given function is defined. The domain of the given relation is (0,∞).
What is the domain and range of a function?The domain is the set of values for which the given function is defined.
The range is the set of all values which the given function can output.
Given the postal service charges $2 to ship packages up to 5 ounces in weight and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce. Therefore, the independent variable in this relationship is the weight of the postal.
Since the weight of the postal can be anything greater than 0.
Therefore, the domain of the relation is (0,∞).
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The area of a rectangle is 26.88 square centimeters. The length of the rectangle is 9.6 centimeters. What is the width of the rectangle in centimeters?
Answers
Answer:
26.88 divided by 9.6 is 2.8
Meaning that the width is 2.8 cm
It rained 0.8 inches on Monday. On Tuesday, it rained 0.34 inches less than on Monday. How much did it rain on Tuesday?
Answers
PLEASE HELP it’s literally easy
Answers
Answer:
it would be 4 right (the last one)
Step-by-step explanation:
suppose a political advisor is interested in the proportion of the vote an opponent will receive. if he samples voters randomly and tests hypotheses regarding p, the population proportion, what should he do to reduce his risk of making a type ii error? increase the number of voters he will sample decrease the number of voters he will sample increase the significance level decrease the significance level
Answers
So, on solving the provided question, we can say that to decrease that the Type II error, it is necessary to increase both the significance level and the sample size of voters.
A Type II mistake is what?When the experimenter fails to rule out a false null hypothesis, they commit a type II error, also referred to as a false-negative.Type II errors can also be decreased by increasing the significance level used throughout the testing method.
By employing more stringent criteria, the power of the testing technique can be increased while significantly reducing a type II error.
By raising the significance level employed throughout the testing procedure, Type II mistakes can also be reduced.
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the smith family consists of a mother, father, and some children. the average age of the family is 20 yrs. old. the father is 48 yrs. old, and the average age of the mother and children is 16. how many children are in the smith family?
Answers
This is a contradiction, which means that our initial assumption that there are n children is incorrect. Therefore, there is no solution to this problem that satisfies the given conditions.
Let's assume that there are n children in the Smith family.
We know that the father is 48 years old, so the sum of the ages of the mother and children is:
Total age = (n + 1) * 20 (as there are n children and 1 father)
And we also know that the average age of the mother and children is 16, so we can write:
Total age / (n + 1) = 16
Combining these two equations, we get:
(n + 1) * 20 / (n + 1) = 16
Simplifying, we get:
20 = 16
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I need steps to find the equation of the inverse of the function f(x) = log2 (9x).
Answers
Answer:
f⁻¹(x) = 2ˣ / 9
Step-by-step explanation:
f(x) = log₂ (9x)
y = log₂ (9x)
swap y and x: x = log₂ (9y)
solve y: 9y = 2ˣ y = 2ˣ / 9
f⁻¹(x) = 2ˣ / 9
The equation of the inverse of the function f(x) = log2 (9x) should be considered as the \(f^{-1}(x) = 2^x / 9\)
Calculation of the equation of the inverse of the function:Since
f(x) = log₂ (9x)
So,
y = log₂ (9x)
Now
swap y and x so x = log₂ (9y)
And, now we have to solve for y
9y = 2ˣ
y = 2ˣ / 9
f⁻¹(x) = 2ˣ / 9
Hence, The equation of the inverse of the function f(x) = log2 (9x) should be considered as the \(f^{-1}(x) = 2^x / 9\)
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What is the sum of the infinite series 1−( 2
π
) 2
3!
1
+( 2
π
) 4
5!
1
−( 2
π
) 6
7!
1
+⋯+( 2
π
) 2n
(2n+1)!
(−1) n
+⋯ ? 0 π
2
1 (D) 2
π
Answers
The given series can be written as:
sum = sin(2π) = 0
The sum of the infinite series is 0.
To find the sum of the infinite series 1 - (2π/2!)^2/1 + (2π/4!)^2/1 - (2π/6!)^2/1 + ⋯ + (2π)^(2n)/(2n+1)!*(-1)^n + ⋯, we can use the concept of the Taylor series expansion of a function.
The given series resembles the expansion of the sine function, sin(x), where x = 2π. The Taylor series expansion of sin(x) is:
sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ⋯ + (-1)^n * x^(2n+1)/(2n+1)! + ⋯
Comparing the given series with the expansion of sin(x), we can see that the terms are similar, except for the factor of (-1)^n.
Therefore, the given series can be written as:
sum = sin(2π) = 0
The sum of the infinite series is 0.
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Helpppp with this plssss
Answers
Answer:
26.411
Step-by-step explanation:
In 3a+bc-c you have to substitute
a=8.6, b=2.3, c=0.47
3*8.6 + 2.3*0.47 - 0.47 first do the multiplication then addition and subtraction
25.8 + 1.081 - 0.47=
26.411
ken and hamid run around a track it takes ken 80 seconds to complete a lap it takes hamid 60 seconds to complete a lap how many laps would they have won to both meet on the starting line
Answers
When Ken and Hamid race around a track, Ken completes a lap in 80 seconds while Hamid completes a lap in 60 seconds. ken will run 3 laps where as Hamid will run 4 laps.
Given that,
When Ken and Hamid race around a track, Ken completes a lap in 80 seconds while Hamid completes a lap in 60 seconds.
We have to find if they had faced off on the starting line, how many laps would they have won.
We have to find the LCM of the 80 and 60.
The prefix "LCM" stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.
LCM of 80 and 60 is 240
240=80×3
ken will complete 3 laps.
240=60×4
Hamid will complete 4 laps.
Therefore, ken will complete 3 laps where as Hamid will complete 4 laps.
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Help plis! Need process too
Answers
Answer:
Step-by-step explanation:
E