Answer:
Step-by-step explanation:
1) 9 x 4 = 36
9 + 4 = 13
2) 9 x -4 = -36
9 + (-4) = 5
3) 4 x3 = 12
4+ 3 = 7
4) -4 x 3 = -12
-4 + 3 = -1
Find the sum of the first 6 terms of the given sequence. The sequence is either arithmetic or geometric.
-1, 7, -49, ...
The Sum of the first six terms of the progression is 14706
What is Geometric Progression?
A geometric progression, also known as a geometric sequence, is a non-zero numerical series in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value known as the common ratio.
Solution:
On carefully observing
We can state that, the Common Ratio is -7
Sum(n) = a(\(r^{n}\) - 1) / r - 1
Sum(6) = -1 (-7^6 - 1) / -7-1
Sum(6) = -1(117648)/-8
Sum(6) = 14706
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. \text{a number raised to the third power.} a number raised to the third power.
Answer: #x^3
Step-by-step explanation:
"A number " is represented by the letter xA number (x) raised (^) the third power will be,x^3
note: An algebraic expression doesn't have an equal sign (=)
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please help i wasn’t taught this
Answer:
Step-by-step explanation:
B
you can rent time on computers at the local copy center for a $10 setup charge and an additional $2 for every 5 minutes. how much time can you rent for $25?
You can rent time on computers at the local copy center for 35 minutes with $25.
To find out how much time you can rent for $25 at the local copy center, follow these steps:
1. Subtract the $10 setup charge from the total amount you have: $25 - $10 = $15.
2. Now you have $15 left for renting time on the computers. Since it costs $2 for every 5 minutes, you need to find out how many 5-minute increments can be covered by $15.
3. Divide the remaining amount by the cost per 5-minute increment: $15 / $2 = 7.5. Since you can't have half an increment, round down to 7.
4. Multiply the number of 5-minute increments by the time per increment: 7 * 5 = 35 minutes.
So, you can rent time on computers at the local copy center for 35 minutes with $25.
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if alicia had been able to achieve the same percentage of visitors for the entire week as she does on monday, how many additional people would then visit cool beans?
Alicia want that 50 % of all people who visited one of the three coffee shops should visit her every week.
Total visitors to the other two coffee shops during one week = 840+1,220 i.e. 2,060
Total visits to Cool Beans should be 50 % of total visits i.e. equal to visits of the other two cafes combined
Visits to Cool Beans should be 2,060
Current Visits =548
Additional visits =2,060-548 i.e. 1,512 visits
Note for better understanding:
same or the demand of coffee will remain same, then the Additional people will be calculated as:
Total number of visits = 584+840+1,220 i.e. 2,608
Target number of visits =50 % of total visits i.e. 1,304 visit
Additional visits = 1,304-548 = 756 visits
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√125x^4y^2
simplify square roots
Answer:
5 x2 • sqrt(5y)
Step-by-step explanation:
Factor 125 into its prime factors
125 = 53
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
25 = 52
Factors which will remain inside the root are :
5 = 5
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
5 = 5
At the end of this step the partly simplified SQRT looks like this:
5 • sqrt (5x4y)
STEP
2
:
Simplify the Variable part of the SQRT
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x8)=x4
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x2•sqrt(x)
(4.2) sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(x4y) = x2 • SQRT(y)
Combine both simplifications
sqrt (125x4y) =
5 x2 • sqrt(5y)
Simplified Root :
5 x2 • sqrt(5y)
find the largest four-digit value of ${}t$ such that \[\sqrt{t-\sqrt{t-\sqrt{t-\sqrt{t-\cdots}}}}\]is an integer.
To find the largest four-digit value of t such that the expression is an integer, we need to set up an equation and solve for t.
Let's denote the given expression as x:
x = √(t - √(t - √(t - √(t - ...)))
To simplify the expression, we notice that the inner square root can be represented by x itself. So we can rewrite the equation as:
x = √(t - x)
Squaring both sides to eliminate the square root:
x^2 = t - x
Rearranging the equation:
x^2 + x - t = 0
To find the largest four-digit value of t, we can iterate through the values of t starting from 9999 and solve the quadratic equation for x. We are looking for a positive integer solution for x. Once we find the largest value of t that satisfies this condition, we have our answer.
By solving the quadratic equation for different values of t, the largest four-digit value of t that satisfies the condition is 9985.
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What portion of the Loop of Henley is impermeable to water?
The Loop of Henle, which is a part of the nephron in the human kidney involved in producing urine.
The Loop of Henle is divided into three parts:
The thin descending limb, the thick ascending limb, and the thin ascending limb.
The portion of the Loop of Henle that is impermeable to water is the thick ascending limb.
This segment actively transports ions such as sodium and chloride out of the tubular fluid and into the surrounding tissue, which creates a concentration gradient that allows for the reabsorption of water in the collecting ducts.
Unlike the thin descending limb, which is permeable to water and allows for the passive diffusion of water out of the tubular fluid, the thick ascending limb does not allow for the passive movement of water across its walls.
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Suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of 74 and a standard deviation of 8. On a separate sheet of paper, draw a Normal Curve and label the mean, standard deviations, and the associated percentages. Find the percent of juniors who score no more than 90.
PLEASE HELP AHHHH
Answer:
97.5%
Step-by-step explanation:
Solution:-
- Denote a random variable,
X: Scores of all juniors in a school district centralized test.
- The random variable ( X ) follows normal distribution with the corresponding parameters:
X ~ Norm ( μ , σ^2 )
Where, μ = Mean score
σ = standard deviation of scores secured
- The given parameters for the normal distribution are:
X ~ Norm ( 74 , 8^2 )
- To draw a Normal curve we need to draw a bell shaped curve and annotate the following descriptions:
Mean ( μ ) : The vertical center-line that bifurcates the normal curve
1st standard deviation ( μ ± σ ) : First small division to the left and right about the mean ( μ ). [ 74 - 8 , 74 + 8 ] = [ 66 , 82 ]
2nd standard deviation ( μ ± 2σ ) : Second small division to the left and right about the mean ( μ ). [ 74 - 16 , 74 + 16 ] = [ 58 , 90 ]
3rd standard deviation ( μ ± 3σ ) : Third small division to the left and right about the mean ( μ ) - tailed. [ 74 - 24 , 74 + 24 ] = [ 50 , 98 ]
- Mark the associated percentage of scores that lies between 1st, 2nd and 3rd standard deviations from the mean ( μ ). Apply the Empirical rule of statistics. Which states:
p ( μ - σ , μ + σ ) = p ( 66 , 82 ) = 67 %
p ( μ - 2σ , μ + 2σ ) = p ( 58 , 90 ) = 95 %
p ( μ - 3σ , μ + 3σ ) = p ( 50 , 98 ) = 99.7 %
- See the attachment for the complete diagram.
- To determine the percentage of students who scored no more than 90 on the test.
- Employ the use of standardizing the required probability by using the following relation:
p ( X < x ) = p ( Z < [ (x - μ) / σ ] )
p ( X < 90 ) = p ( Z < [ (90 - 74) / 8 ] )
= p ( Z < [ (90 - 74) / 8 ] )
= p ( Z < 2 )
- We will employ the use of Empirical rule of second deviation ( μ ± 2σ ) to evaluate the required percentage:
p ( μ - 2σ < X < μ + 2σ ) = p ( 58 , 90 ) = 95 %
1 - p ( 58 < X < 90 ) = 1 - 0.95 = 0.05
p ( X > μ + 2σ ) = p ( X > 90 ) = [ 1 - p ( 58 < X < 90 ) ] / 2
= [ 1 - 0.95 ] / 2
= 0.05 / 2
= 0.025
Hence,
p ( X < 90 ) = p ( Z < 2 ) = 1 - p ( X > 90 )
= 1 - 0.025
Answer = 0.975 ( 97.5 )%
max can mow a lawn in 45 minutes. jan takes twice as long to mow the same lawn. if they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together. 1/45 + 1/90 = 1/t
how long will it take them to mow the lawn?
It would take Max and Jan 30 minutes to mow the lawn together.
It will take Max 45 minutes to mow the lawn alone, and it will take Jan twice as long, so it will take her 90 minutes to mow the same lawn alone. Working together, we can use the equation 1/45 + 1/90 = 1/t to solve for t, where t is the number of minutes it would take to mow the lawn together.
First, we need to simplify the equation:
1/45 + 1/90 = 1/t
2/90 + 1/90 = 1/t
3/90 = 1/t
1/30 = 1/t
Now we can solve for t by cross-multiplying:
1/30 = 1/t
t = 30
So, it will take Max and Jan 30 minutes to mow the lawn together.
To find how long it would take Max and Jan to mow the lawn together, we can solve the equation 1/45 + 1/90 = 1/t for t.
First, find a common denominator for the fractions, which in this case is 90. Then, rewrite the equation as: (2/90) + (1/90) = 1/t.
Next, add the fractions on the left side: 3/90 = 1/t.
Now, to solve for t, take the reciprocal of both sides: t = 90/3.
Finally, simplify: t = 30.
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A firm issues three-month commercial paper with a $1000000
face value and pays an EAR of 7.4%. What is the amount the firm
receives?
If firm issues commercial paper with $1000000 face-value and pays EAR of 7.4%, then amount the firm will receive is $981500.
To calculate the amount the firm receives from issuing the three-month commercial paper, we need to determine the total interest earned over the three-month period.
The Effective Annual Rate (EAR) of 7.4% indicates the annualized interest rate. Since the commercial paper has 3-month term, we adjust the EAR to account for the shorter period.
To find the quarterly interest rate, we divide the EAR by the number of compounding periods in a year. In this case, since it is a 3-month period, there are 4-compounding periods in a year (quarterly compounding).
Quarterly interest rate = (EAR)/(number of compounding periods)
= 7.4%/4
= 1.85%,
Now, we calculate interest earned on "face-value" of $1,000,000 over 3-months,
Interest earned = (face value) × (quarterly interest rate)
= $1,000,000 × 1.85% = $18,500,
So, amount firm receives from issuing 3-month commercial paper is the face value minus the interest earned:
Amount received = (face value) - (interest earned)
= $1,000,000 - $18,500
= $981,500.
Therefore, the amount that firms receives is $981500.
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Find the area and the circumference of a circle with diameter 9 cm.
pls help
Answer:
63.62cm²
Step-by-step explanation:
please help due today;/
Enter the value of n so the expression (7y + 6) + (3y – 2) is equivalent to (ny + 4),
Answer:
10
Step-by-step explanation:
the third-degree taylor polynomial for a function f about x=4 is (x−4)3512−(x−4)264 (x−4)4 2. what is the value of f′′′(4)?
Answer: the value of f′′′(4) is 3/256.
Step-by-step explanation:
Given the third-degree Taylor polynomial:
f(x) = (x−4)³/512 − (x−4)²/64 + (x−4)⁴/2
To find the value of f′′′(4), we need to differentiate the polynomial three times and evaluate it at x = 4.
First derivative:
f'(x) = 3(x−4)²/512 − 2(x−4)/64 + 4(x−4)³/2
Second derivative:
f''(x) = 6(x−4)/512 − 2/64 + 12(x−4)²/2
Third derivative:
f'''(x) = 6/512 + 24(x−4)/2
Now, substitute x = 4 into f'''(x):
f'''(4) = 6/512 + 24(4−4)/2
= 6/512 + 0
= 6/512
= 3/256
Therefore, the value of f′′′(4) is 3/256.
4x-y=5 slope n y intercept
Step-by-step explanation:
4x - y = 5
You need to convert this equation to point intercept form: y = mx + b where m = slope and b = y-intercept.
4x - y = 5
subtract 4x from both sides:
4x - y - 4x = 5 - 4x
-y = 5 - 4x
divide both sides by -1:
(-y)/-1 = (5 - 4x)/-1
y = -5 + 4x
rearrange right side:
y = 4x - 5
Remembering that: y = mx + b where m = slope and b = y-intercept
slope = 4
y-intercept = -5 or (0 , -5)
I WILL GIVE BRANLISET
Answer:
y axis: (0, 12)
x axis: (18, 0)
Quadrant I: (4.5, 10.6)
Quadrant II: (-15, 21)
Quadrant III: (-3/4, -4 1/9)
Quadrant IV: (3, -7)
Step-by-step explanation:
Integers used for each Quadrant.
Quadrant one: x axis = positive, y axis = positive
Quadrant two: x axis = negative, y axis = positive
Quadrant three: x axis = negative, y axis = negative
Quadrant four: x axis = positive, y axis = negative
(0,12) = goes to the y axis
(3,-7) = goes to quadrant 4
(-15,21) = goes to quadrant 2
(18,0) = goes to the x axis
(4.5,10.6) = goes to quadrant 1
(-3/4, -4 1/9) = goes to quadrant 3
A bucket contains 72 red crayons, 48 green crayons, 48 blue crayons, and 48 yellow crayons. The art teacher also has 120 peices of drawing paper. What is the largest number of identical kits the art teacher can make using all the crayons and
All of the paper
The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.
To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.
The GCD represents the largest number that can divide all the quantities without leaving a remainder.
The GCD of the quantities of crayons can be found by considering the prime factorization:
\(72 = 2^3 * 3^2\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\\)
The GCD of the crayons is \(2^3 * 3\), which is 24.
Now, we need to find the GCD of the quantity of drawing paper:
120 = \(2^3 * 3 * 5\)
The GCD of the drawing paper is also \(2^3 * 3\), which is 24.
Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.
Each kit would contain an equal distribution of crayons and drawing paper.
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Find the measures of <1 and <2 if <3 = 78^0 and <4 = 102^0.
Assume the lines are parallel.
Figure is not drawn to scale.
Angle 78 102 12
<1
<2
Answer:
my acc just got yeeted by a penguin pfp
Step-by-step explanation:
Answer:
oops look in commments
Step-by-step explanation:
a survey has an error in departure (ed) of 0.35 ft, and error in latitude (el) of 0.82 ft. the total distance covered i the survey is 684.5 ft. compute the precision (choose the answer that is closest)
The correct value for the precision is found to be 0.0013 for the survey.
What is called the precision in surveying?Our measurement processes take into account accuracy and precision. How precisely a measurement or observation compares to a predetermined value or benchmark defines its accuracy. Contrarily, precision is the degree to which a measurement is repeatable precisely without reference to any specific significance or standard.The formula for finding the precision is-
Precision = E(closure)/ Perimeter
E(closure) = √(ed)² + (el)²
Where,
error in latitude (el) = 0.82 ft
error in departure (ed) = 0.35 ft.
Perimeter = 684.5 ft.
Find the E(closure)
E(closure) = √(0.82)² + (0.35)²
E(closure) = 0.89
Precision = 0.89/684.5
Precision = 0.0013
Thus, the correct value for the precision is found to be 0.0013 for the survey.
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Why does a method to swap two array elements work correctly when a method to swap two integer values does not?
A method to swap two array elements works correctly because it is designed to swap the entire elements at two different indexes in an array.
The method receives two integer values representing the indexes of the elements to be swapped and then proceeds to swap the elements themselves.
On the other hand, a method to swap two integer values does not work correctly because integers are passed by value, which means that the method receives a copy of the integer values rather than the original values themselves. Thus, the method only swaps the copies and not the original values, and as a result, the original values remain unchanged.
To overcome this issue, one can use a workaround such as passing the integer values as references instead of values. This way, the method receives a reference to the original value, and any changes made to the reference will affect the original value as well. However, this approach can be more complex and less efficient than simply swapping array elements.
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Write the equation that is parallel to y = -3x + 7 and passes through the point (2, -1). Write your answer in slope intercept form.
y =
The equation that is parallel to y = -3x + 7 and passes through the point (2, -1) is y=-3x+5.
What is slope Intercept form?The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.
y=mx+b
where m is the slope of the line and b is the y intercept.
The slope of the given equation,
y=-3x+7 is -3.
So, to write an equation parallel to the given equation and set of points, use point slope form and the slope of -3
y-y₁=m(x-x₁)
where (2,-1) are x₁, y₁
y-(-1)=-3(x-2)
y+1=-3(x-2)
Multiply with 3 on RHS side
y+1=-3x+6
We have to write in slope intercept form, so shift 1 to RHS.
y=-3x+6-1
y=-3x+5
As you can see, the slope of this line is -3
, which means that the two equations are parallel to each other.
Hence y=-3x+5 is the equation that is parallel to y = -3x + 7 and passes through the point (2, -1).
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Alejandro will deposit $1,750 in an account that earns 6.5% simple interest every year. His sister Anallency will deposit $1,675 in an account that earns 7.5% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which sibling will have more money at the end of four years?
Answer: Anallency
Step-by-step explanation:
First, lets make two equations for both siblings, using the base: SI = P(1 + rt) and CI = P(1 + r/n)^nt
Alejandro = 1750(1 + 0.065[4]) = 1750 + 455 = $2,205
Anallency = 1675(1 + 0.075/1)^4 = $2236.91
After 4 years, Alejandro will have $2,205, and Anallency will have $2236.91
Since $2236.91 > 2,205, Anallency will have more money after 4 years.
Answer:
Anallency will have mor money.
Step-by-step explanation:
Simple Interest:
I = Prt
I = $1750 × 0.065 × 4
I = $455
Total after 4 years: $1750 + $455 = $2205
Compound Interest:
F = P(1 + r/n)^(nt)
F = $1675(1 + 0.075)^(4)
F = $2236.91
Answer: Anallency will have mor money.
Colleen already owns 28 hair bands, and additional hair bands are priced at 1 for a dollar.
With $15 to spend on new hair bands, how many total hair bands can Colleen own?
Please help
Answer:
After buying additional hair bands, Colleen can own a total of 43 hair bands.
Step-by-step explanation:
Solving this problem entails of finding out the total number of hair bands Colleen can own, based on the amount she already owns and how many more she purchases. Start by reading the problem carefully to break down the information provided.
We know that Colleen already owns twenty eight hair bands. This is important to remember to include. The problem also states that she has a total of fifteen dollars and each individual hair band is priced at one dollar.
Because the hair bands are only a dollar, Colleen can purchase an additional fifteen hair bands.
Setting up an equation will help us solve. Here is how we could set up the equation:
(amount of hair bands already owned = 28) + (number hair bands bought = 15) = (total number of hair bands owned = x)
28 + 15 = x
The equation is now in place. Solve by adding both terms. This is how you will reach the answer.
28 + 15 = x
43 = x
This means that Colleen will have 43 hair bands in total, after purchasing fifteen hair bands.
Brandon rides his bike 7 miles south and then 24 miles west. About how far is he from his starting point
15 POINTS I was gone when we learned this and I’m very confused someone pls help
Make a table with quadratic equations
ps. any markings I wrote might be wrong
(Asking for help on the first problem)
The complete table of values is
x y
-2 10
-1 17
0 26
1 37
2 50
How to make a table with quadratic equationsFrom the question, we have the following parameters that can be used in our computation:
y = x^2 + 10x + 26
To generate a table of 5 values of y for the equation y = x^2 + 10x + 26, we can choose different values of x and evaluate the equation for each of those values.
x y = x^2 + 10x + 26
-2 10
-1 17
0 26
1 37
2 50
For the axis of symmetry, we have
y = x^2 + 10x + 26
Differentiate and set to 0
2x + 10 = 0
So, we have
x = -5
Substitute -5 for x
y = (-5)^2 + 10(-5) + 26
y = 1
So, we have
Axis of symmetry: x = -5
Vertex = (-5, 1)
The domain is the set of all real values while the range is y >= -5
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Find the average rate of change of the following line WITHOUT CALCULATING. y=18 on [1000,10000]
Answer
The average rate of change of the function y = 18 on the interval [1000, 10,000] is ZERO
SOLUTION
Problem Statement
The question wants us to find the average rate of change of the function y = 18 on the interval [1000, 10,000].
Method
- The function given is a constant function. This means that for every value of x from -∞ to +∞, the value of the function will always be y = 18.
- Since y is a function of x (albeit a constant function of x), it can be written as y = f(x).
- With these in mind, we can find the average rate of change of the function using the formula given below:
\(\begin{gathered} \bar{\Delta}=\frac{f(b)-f(a)}{b-a} \\ \text{where} \\ \lbrack a,b\rbrack\text{ is the interval for which we want to know the rate of change of the function }f(x) \end{gathered}\)- Note that since the function is a constant function, we should expect that its rate of change should be ZERO since the function is constant throughout despite the value of x.
Let us apply the formula above to find the average rate of change of the given function.
Implementation
The average rate of change of the function y = 18 is gotten below:
\(\begin{gathered} b=10,000,a=1000 \\ f(b)=f(10,000)=18\text{ (Since the function does not change)} \\ f(a)=f(1000)=18\text{ (Since the function is constant)} \\ \\ \therefore\bar{\Delta}=\frac{18-18}{10,000-1000}=\frac{0}{9,000} \\ \\ \therefore\bar{\Delta}=0 \end{gathered}\)Final Answer
The average rate of change of the function y = 18 on the interval [1000, 10,000] is ZERO
Starbucks wants to use the subjective approach to evaluate a new project. They are considering expanding their stores and renting office space to small business owners. They will have a separate reception area and online scheduling for those that want to use the office space. Starbucks has a WACC of 12%. What would be the WACC for this new project
The Weighted Average Cost of Capital (WACC) for Starbucks' new project can be determined by considering the subjective approach. To calculate the WACC, information such as the cost of equity and the cost of debt is required, along with their respective weights in the company's capital structure.
In this scenario, the given information only mentions Starbucks' overall WACC, which is 12%. However, to determine the WACC for the new project, additional details specific to the project, such as its risk profile and capital structure, are necessary. Without this specific information, it is not possible to calculate the WACC for the new project. The WACC is influenced by various factors, including the riskiness of the project, the expected return on equity and debt, and the proportion of equity and debt in the project's capital structure. Therefore, a comprehensive evaluation of the project's risk and financial structure is required to determine an accurate WACC for the new project.
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Помогите пж пж пж пж пж
Answer:
sorry i dont understand
Step-by-step explanation:
The difference of the square of a number and 21 is equal to 4 times that number. Find
the negative solution.
Answer:
-3
Step-by-step explanation:
Let the number be x.
x^2 - 21 = 4x
x^2 - 4x - 21 = 0
(x - 7)(x + 3) = 0
x - 7 = 0 or x + 3 = 0
x = 7 or x = -3
Answer: -3
Answer:
-3
Step-by-step explanation:
I got it right