The resultant answer of the given quadratic equation is x₁,₂ = -1 ± √61/6.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a, and b are the coefficients, and c is the constant term.So, solve 3x²+x-5=0 as follows:
Quadratic formula: x = -b ± √b²-4ac/2aNow, evaluate as follows:
x = -b ± √b²-4ac/2ax₁,₂ = -1 ± √1² - 4×3(-5)/2×3x₁,₂ = -1 ± √61/2×3x₁,₂ = -1 ± √61/6Therefore, the resultant answer of the given quadratic equation is x₁,₂ = -1 ± √61/6.
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Write your answer as an integer or decimal to the nearest 0.5. 5 4 3 NO -3 3 4 -1 А -3 -4 B -5 )
Answer:
(-2.5, 4.5)
Explanation:
To know the coordinates of point D, we need to identify the projection of this point on the x-axis and the y-axis. So:
Since the projection in the x-axis is a number between -2 and -3 and the projection in the y-axis is a point between 4 and 5, the coordinates of D are:
(-2.5, 4.5)
y = x sq+ 10 ; x = 3 find the value of the function rule
The value of the function is, y = 3.61
What is the value of the function?
The objective function's value at a solution is given by the value function of an optimization problem, which only depends on the problem's parameters.
Consider the given function,
[tex]y = \sqrt{x+10}[/tex]
We have to find the value of y at x = 3.
So, plug x = 3 in the above equation.
We get,
[tex]y = \sqrt{3 + 10} = \sqrt{13} = 3.61[/tex]
When we plug x = 3 then we get y = 3.61.
Therefore, the value of the given function is, y = 3.61
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Christina needs a new pair of basketball shoes for the upcoming season. The original price of the shoes she wants is $79.99. The tax on the shoes is
3.4%. What is the amount of tax Christina will pay?
Answer:
Christina will pay $82.71 after tax
60 POINTS!!! HELPFind any asymptotes or holes in the function below. Explain how you arrived at your answer. SHOW YOUR WORK AND THE STEPS YOU TOOK.
The function given is,
[tex]y=\frac{x-6}{(x-1)(x-6)}[/tex]Since , the leading coefficient of numerator is less than the leading coefficient of denominator .
Therefore, there is no horizontal asymptotes.
For finding the vertical asymptotes, substitute the denominator is equal to 0.
[tex](x-1)=0\text{ , }(x-6)=0[/tex][tex]x=\text{ 1,6.}[/tex]The vertical asymptotes are 1 and 6.
To find the hole in the function,
[tex](x-6)[/tex]is crossed out in numerator and denominator.
So, if we set up x-6 equals to 0.
The hole in the function is, when
[tex]x=6.[/tex]suppose each license plate in a certain state has three letters followed by three digits. The letters H and L and the digits 1, 2, and 9 are not used. So, there are 24 letters and 7 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format.
Number of license plates = 24 x 24 x 7 x 7 x 7
= 197568
What is the range of the function f(x) = x^2 - 2x -15?*
For this problem, we are given a certain function and we need to determine its range.
The function is:
[tex]f(x)=x^2-2x-15[/tex]This quadratic function has a minimum value in its range, which is represented by its vertex. The best way to determine the range is to find the coordinates of the vertex of this function, therefore we have:
[tex]\begin{gathered} x_{vertex}=\frac{-b}{2a}=\frac{2}{2}=1\\ \\ y_{vertex}=f(1)=(1)^2-2(1)-15=1-2-15=-16 \end{gathered}[/tex]The minimum value in the range is -16, which means that the range is:
[tex]\lbrace f(x)|f(x)\geqslant-16\rbrace[/tex]The correct option is the second one.
HELP IT'S DUE NOW! :(
The system of equations that can be used to find the number of black and white copies and color copies is b + c = 68 , 0.08b + 0.15c = 6.00 .
In the question ,
it is given that
the total amount paid by the customer at the print shop = $6.00
total number of copies that the customer made = 68
the cost for printing 1 black and white copy = $0.08
the cost of printing 1 color copy = $0.15
let the number of black and white copies be "b"
let the number of color copies be "c" .
So ,
b + c = 68
and
the cost of b black and white copies is = 0.08b
the cost of c color copies is = 0.15c
the total cost = cost of b black and white copies + cost of c color copies
6.00 = 0.08b + 0.15c
0.08b + 0.15c = 6.00
Therefore , The system of equations that can be used to find the number of black and white copies and color copies is b + c = 68 , 0.08b + 0.15c = 6.00 , the correct option is (d) .
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Convert 6 feet per hr to miles per year
We can convert this using the following conversion process:
[tex]\frac{6ft}{h}\cdot\frac{1mile}{5280.0196ft}\cdot\frac{1h}{0.0001141\text{year}}=9.9593\text{mile}/\text{year}[/tex]Therefore, the equivalent is 9.9593miles/year.
Return Submit et Income 10 1 point If Betty has a gross income of $3000 a month, what would her total deductions be for the table? Deduction Percentage of gross income 6.2% Type your answer... Social Security Medicare 1.45% Income tax 12.5% Medical $300 Submit Previous
The answer is very simple
The total deductions would be
total deductions = 3000*0.062 + 3000*0.0145 + 3000*0.125 + 300
total deductions = 904.5
Given the graph f(x)=4^x write a function that results from each given transformation. A. f(x)=4^x is shifted 4 units up. What is the equation of the new function?B. f(x)=4^x is shifted 3 units down. What is the equation of the new function?C. f(x)=4^x is shifted 2 units left. What is the equation of the new function?D. f(x)=4^x is shifted 5 units right. What is the equation of the new function?E. f(x)=4^x is reflected about the x-axis. What is the equation of the new function?F. f(x)=4^x is reflected about the y-axis. What is the equation of the new function?
Given:
There are given that the function:
[tex]f(x)=4^x[/tex]Explanation:
To find any transformation, we need to use the parent function which is given.
Then,
(A): Shifted 4 units up:
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^x+4 \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^x+4[/tex](B): Shifted 3 units down.
Then,
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^x-3 \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^x-3[/tex](C): Shifted 2 units left:
Then,
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^{x+2} \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^{x+2}[/tex](D): Shifted 5 units right.
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^x-5 \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^x-5[/tex](E); Reflected about x-axis:
[tex]\begin{gathered} f(x)=4^x \\ f(x)=-4^x \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=-4^x[/tex](F): Reflected about the y-axis:
Then,
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^{(-x)}_{} \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^{(-x)}_{}[/tex]
a cell phone tower cast a shadow 10 feet long at the same time that a 75-foot building casts a shadow 15 feet long. how tall is the cell phone tower?
Answer:
50 feet
Step-by-step explanation:
answer question below pls. If you do, I will mark it brainliest.
The expression in the blank spaces -3x, 5x-8, -4x+7, 3x-10, 4x-9 and -2x+5 represented with A, B, C, D, E and F respectively
What are the expressions in the blank space?
This is a problem involving algebraic expressions
Since the total for each row and column is the same
First, start from the second because it is complete. Add up all the expressions to get the total:
2x-3 + 3 + 2-x + x = 2x-2
Check the attached image. I labeled the boxes with alphabets for convenience.
A = 2x-2 -(1-2x) - (4x-1)-(3x-2) (Remember: 2x-2 is the total)
A = 2x-2 -1 +2x - 4x+1-3x+2 = -3x
B = 2x-2 -(8-3x) - (2x-3) -(1-2x)
B = 2x-2 -8+3x - 2x+3 -1+2x = 5x-8
C = 2x-2 -B -(6-5x) -(6x-7) where B = 5x-8
C = 2x-2 -5x+8 -6+5x -6x+7 = -4x+7
D = 2x-2 -3 -(4x-1) -(6-5x)
D = 2x-2 -3 -4x+1 -6+5x = 3x-10
E = 2x-2 -C -(2-x) -(3x-2)
E = 2x-2 +4x-7 -2+x-3x+2 = 4x-9
F = 2x-2 -A -x -(6x-7)
F = 2x-2 +3x -x -6x +7 = -2x+5
Therefore, the blank spaces should be filled with the expressions -3x, 5x-8, -4x+7, 3x-10, 4x-9 and -2x+5 represented with A, B, C, D, E and F respectively
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HINT: the table IS PROPORTIONAL, so that means we can compare any y/x value from the table to get r. r = y/x
r = ?
The given relation is not a proportional relationship, with proportional constant r =1.
What is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.
Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.
The proportionality constant is,
for 1st case, r = y/x = 1
for 2nd case, r =y/x = 1
for 3rd case, r = y/x = 1
Hence we can say that the given relation is not a proportional relationship, with proportional constant r =1.
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6x+7y=4x+4y6, x, plus, 7, y, equals, 4, x, plus, 4, y complete the missing value in the solution to the equation.
The missing value is 6.
As per the question, y = -4. Keeping the value of y in the equations to find the value of x.
6x + 7(-4) = 4x + 4(-4)
Performing multiplication on each side of the equation
6x - 28 = 4x - 16
Rewriting the equation with identical values on each side of the equation
6x - 4x = 28 - 16
Performing subtraction on each side of the equation to find the value of x
2x = 12
Shifting 2 to Right Hand Side of the equation
x = 12 ÷ 2
Performing division on Right Hand Side of the equation
x = 6
Hence, the value of x is 6.
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The complete question is -
6x+7y=4x+4y
Complete the missing value in the solution to the equation.
(__,-4)
10.Which of these operations should be completed firstwhen solving an equation?a. xb. +c. ()d. +
Given the list of symbols:
x, +, ( ), ÷
Let's determine the operations that should be completed first when solving an equation.
To solve an equation, we are always required to apply the PEMDAS theorem.
PEMDAS is an acronym for:
0. P,arentheses
,1. E,xponents
,2. M,ultiplication
,3. D,ivision
,4. A,ddition
,5. S,ubtraction.
This shows the order in which the operations in an equation should be solved.
We can see that the first operation which is to be completed is the parenthesis.
Therefore, using the PEMDAS theorem, the operation that should be first completed when solving an equation is the parenthesis ().
ANSWER:
C. ( )
PLEASE HELP ME OUT WITH THIS X^2+10x+25
Answer:
(x+2)(x+5)
Step-by-step explanation:
20(4. 12)6.Cost($)Weight (kg)Use the graph to find the rate of change of the function m
Rate of change of the function, dC/dW = 3
Explanations:Let the cost be represented as C
Let the wight be represented as W
[tex]\begin{gathered} (W_1,C_1)\text{ = (1, 3)} \\ (W_2,C_2)\text{ = (4, 12)} \end{gathered}[/tex]The rate of change of the function can be calculated using the formula:
[tex]\begin{gathered} \frac{dC}{dW}=\text{ }\frac{C_2-C_1_{}}{W_2-W_1} \\ \frac{dC}{dW}=\text{ }\frac{12-3}{4-1} \\ \frac{dC}{dW}=\text{ }\frac{9}{3} \\ \frac{dC}{dW}=\text{ 3} \end{gathered}[/tex]Mrs. publinsky and her husband, xander, are planning their dream house. the lot for the house sits high on a hill with a beautiful view of the white mountains. the plans show the size of the house to be 2,900 square feet.
The estimated cost if they use a contractor to complete the house would be $435,000.
How to calculate the cost of the house?The cost of the house is based on what home builders typically charge for a house similar to the one Mrs. Pavlinski and her husband Zander have in mind.
In this case, the contractor's price is $150 per square foot of her home while the area of the house is given as 2,900 square feet.
Total cost = Cost per square feet x Area of house
Solving for the estimated cost gives:
= 150 x 2,900
= $435,000
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The given question is incomplete and the complete question is as follows.
"Mrs. Publinsky and her husband, Xander are planning their dream house. The lot for the house sits high on a hill with a beautiful view of the White Mountains. The plans show the size of the house to be 2,900 sq ft. The average price for a lot and house similar to this one has been 150 per sq ft. Fortunately, Xander is a retired plumber and feels he can save money by installing the plumbing himself. Mrs Publinsky feels she can take care of the interior decorating. They both feel they can complete the exterior painting with the help of their two sons."
What is the value of x when the Richter
scale rating is 7.5? Round your answer
to the nearest hundredth.
The value of x = 31622776.6.
To find what is the value of x when the Richter scale rating is 7.5.
To round your answer to the nearest hundredth.
if no base is stated, then assume base 10
[tex]log(x) = log_{10} (x)[/tex]
Lets remember that [tex]a = log_{b}(c)[/tex] translates to [tex]b^{a} = c[/tex]
so
[tex]r = log(x)[/tex]
or
[tex]r = log_{10}(x)[/tex] translates to [tex]10^{r} = x[/tex]
so when r=7.5, what is x
[tex]10^{r} = x\\\\10^{7.5} = x[/tex]
31622776.60168379 = x
round to nearest ???
thousandth? 31622776.601 = x
hundredth? 31622776.60 = x
tenth? 31622776.6 = x
Hence the answer is the value of x = 31622776.6.
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Can someone help? :)
Average rate of change of [tex]y = x^2 + 4x - 1\\[/tex] over the interval [tex]-4 \leq x \leq 1[/tex] is 1
What is average rate of change of a curve?
Average rate of change of a curve is equal to the slope of the curve and is obtained by dividing the change in functional value by the change in the value of the domain.
Here,
[tex]y = x^2 + 4x - 1\\[/tex]
At x = -4,
[tex]y = (-4)^2+ 4(-4)-1\\y = -1[/tex]
At x = 1
[tex]y = (1)^2 + 4(1) -1\\y = 4[/tex]
Average rate of change of [tex]y = x^2 + 4x - 1\\[/tex] over the interval [tex]-4 \leq x \leq 1[/tex]
= [tex]\frac{4 - (-1)}{1- (-4)}\\\\\\\frac{5}{5}\\\\1[/tex]
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1. These are added to a picture to make it look more realistic.
Ospaces
Ohorizon lines
Oshadows
O sketches
(C) Shadows are added to a picture to make it look more realistic by enhancing the aesthetics of the picture.
How does adding shadows affect a picture?For images to be properly balanced, light and shadow contrast is crucial. Shadow can provide drama to a certain area of the composition of an image while light makes an image appear brighter. For black-and-white images, using shadows to add contrast is extremely important because you won't be using color to add interest or contrast. With the addition of depth and realism, shadows can significantly enhance the overall aesthetics and usability of any design. Shadows in design should effectively integrate into the overall design and mimic the real-world, organic behavior of light and shadow-casting.Therefore, (C) shadows are added to a picture to make it look more realistic by enhancing the aesthetics of the picture.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Which equation demonstrates the distributive property? Responses A (3 + 8)5 = 5(3 + 8)(3 + 8)5 = 5(3 + 8) B 15 + 40 = 5(3 + 8)15 + 40 = 5(3 + 8) C 15 x 40 = 40 x 1515 x 40 = 40 x 15 D 15 + 40 = 55
The correct equation which demonstrates the distributive property will be;
⇒ 15 + 40 = 5 (3 + 8)
What is Distributive property?
By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.
Given that;
There are some equations.
Now,
We know that by the definition of distributive property,
⇒ a (b + c) = ab + ac
So, By the equation (ii);
⇒ 15 + 40 = 5 × 3 + 5 × 8
= 5 (3 + 8)
Thus, The correct equation which demonstrates the distributive property will be;
⇒ 15 + 40 = 5 (3 + 8)
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Similar figures have sides that are proportional and corresponding angles 1 that are to each other * Cooresponding Similar O Congruent O Proportional O None of the above
Similar figures have sides that are proportional and corresponding angles are congruent to each other
Match each system of linear equations with the correct number of solutions.
1) Linear equation has no solutions.
2) It has one solution.
3) It has many solutions.
Define linear equation.The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
Given,
Linear equations:
1) 3x - y = 4
6x - 2y = 8
Multiplying 3x - y = 4 by 2
6x - 2y = 8
6x - 2y = 8
0 = 0
It has no solutions.
2) -3x + y = 7
2x - 4y = -8
2(x - 2y ) = -8
x - 2y = -4
Multiplying x - 2y = -4 by 3
-3x + y = 7
3x - 12y = -12
-11y = -5
y = 5/11
It has one solution.
y = -4x -5
y = -4x + 1
It has many solutions.
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michael is running for president. the proportion of voters who favor michael is 0.8. a simple random sample of 100 voters is taken. (a) what is the expected value of the sampling distribution of p?
The expected value of the sampling distribution of p is 0.8.
A statistic's probability distribution is called a sampling distribution when it is calculated from a larger number of samples taken from a particular population. The distribution of frequencies for a variety of outcomes that could possibly occur for a statistic of a population is known as the sampling distribution of that population.
The normal distribution, which is also known as the Gaussian distribution, is symmetric about the mean. It demonstrates that data close to the mean occur more frequently than data far from the mean. The normal distribution is depicted graphically as a "bell curve."
the sampling distribution of sample proportion will be a normal distribution with mean
[tex]\mu_{p}[/tex] = p = 0.8
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If f(x) = x + 4 and g(x) = x ^ 2 - 1 , what is big(g f big) big(x big) ?
Given
[tex]\begin{gathered} f\mleft(x\mright)=x+4 \\ g\left(x\right)=x^2-1 \end{gathered}[/tex]Find
[tex](g\circ f)(x)[/tex]
Explanation
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ (g\circ f)(x)=g(x+4) \\ (g\circ f)(x)=(x+4)^2-1 \\ (g\circ f)(x)=x^2+16+8x-1 \\ (g\circ f)(x)=x^2+8x+15 \end{gathered}[/tex]Final Answer
Therefore , the correct option is C.
Marty can make four modifications to his car. He chooses to upgrade the tires, fuel, engine, and driver using the expression 4t + 2f + 3e + 1d to calculate the total cost. Which of these values represents the total cost of these upgrades?
The total cost of the upgrades is $3280.
What is the total cost?It is an economic measure that sums all expenses paid to the product, purchase, and investment. It refers to the overall cost of a product which includes both fixed and variable components of the cost. It works by allocating all the costs of doing business to the goods or services for sale. These are composed of both total fixed costs and total variable costs.
The given expression is 4t+2f+3e+1d
From the table, The values of t, f, e, and d in the cost column are 50, 40, 600, and 1200.
Substituting the values in the above equation.
4(50) + 2(40) + 3(600) + 1(1200) = 3280
Therefore, the total cost is $3280.
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The complete question is:
two shirts cost 12:40$ how much will it cost to buy five of the shirts?
Answer:
12.50/26.256.25×5 31.25
Step-by-step explanation:
the difference between 75% of a number and 20% of the same number is 378.9 what is 40% of that number?
Thus, the 40% of the number is
[tex]688.909\cdot0.4=275.563[/tex]