Answers
For a general quadratic polynomial of the form:
[tex]ax^2+bx+c=0[/tex]the solution is
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]this formula is called "the quadratic formula". There are 2 solutions indicated by the subindex 1 and 2 in x.
In our case, by comparing polynomials, we can see that
[tex]\begin{gathered} a=2 \\ b=-1 \\ c=-6 \end{gathered}[/tex]becuase our polynomial is
[tex]2x^2-x-6=0[/tex]in which we moved 1 to the left hand side as -1.
Then, by applying the quadratic formula, we have
[tex]x_{1,2}=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(2)(-6)}}{2(2)}[/tex]Then ,the first solution is
[tex]x_1=\frac{-(-1)+\sqrt[]{(-1)^2-4(2)(-6)}}{2(2)}[/tex]and the
Related Questions
Sheila is making a model of a stadium using a scale where 3 centimeters equal 20 feet. If the model is 30.5 centimeters wide, what is the actual width of the stadium, in feet?
Answers
Answer:
answer is in the explanation
Step-by-step explanation:
first w have to get from 3cm to 30.5cm
to do that we can multiply by 10 1/6
3*10=30
1*3=3
30 3/6
the scale factor, like I said is 10 1/6.
20*10 1/6=20*10+20*1/6=200+20/6=203 2/6, or 203 1/3, or 203.3333333, or 610/3
How do i get the proportionality on this❓❓
Answers
Step by step
Finding the constant of proportionality is the same as finding rate of change, or slope.
Here we have the given point of (1, 4)
y /x = 4 /1 or 4
We can see another possible point on the graph, (2, 8)
y /x = 8 /2 or 4
The laboratory technician can combine L of the pure acid solution with L of the 10% acid solution to get the desired concentration.A laboratory technician needs to make a 33-liter batch of a 40% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid wi is 10% to get the desired concentration?
Answers
The laboratory technician has to combine 11 L acid solution to get the desired concentration .
What is concentration in a solution?The volume of solute that has been dissolved in a specific volume of solvent or solution is known as the concentration of a solution. A solution with a significant concentration of dissolved solute is one that is concentrated. When there is just a minimal amount of dissolved solute in a solution, it is said to be diluted. The amount of a solute, or dissolvable substance, combined with the solvent, or other substance, determines the concentration of a solution in chemistry. C = m/V, where m is the mass of the solute dissolved and V is the total volume of the solution, is the accepted formula. Among the quantitative units of concentration are molarity, molality, mass percentage, parts per thousand, parts per million, and parts per billion.
The33 L batch is 40% acid, so 33 x 0.4 = 13.2 L of pure acid in the batch.
Let P = the number of liters of pure acid required, D = the number of liters of the 10 % solution.
Then P + 0.10 x D = 13.2.
Also, P + D = 33
This equation can be solved simultaneously by substitution.
P = 33 - D
33 - D + 0.10 x D = 16.8
-D (1 - 0.10) = 13.2 - 33
-D = -19.2/ 0.9
D = -22
P = 33 - 22
= 11 L
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The x-intercept of 2x – y = 6 is -6.
True
False
Answers
Answer:
False
Step-by-step explanation:
The [tex]x[/tex] intercept is when [tex]y=0[/tex].
Substituting [tex]y=0[/tex], we get [tex]2x=6[/tex], meaning that [tex]x=3[/tex].
So, the [tex]x[/tex] intercept is 3, not -6.
arc TQ =arc QR =arc TS =arc SQR =arc RQTBackNext
Answers
[tex] - 10 - (5 - 9) {}^{2} [/tex]How would you solve this problem?
Answers
You have the following expression:
-10 - (5 - 9)²
In order to simplify the previous expression you proceed as follow:
- 10 - (5 - 9)² simplify terms inside parenthesis
= -10 - (-4)² solve the parenthesis
= -10 - 16 simplify
= -26
Hence, the simplified expression is -26.
10. Given: ABED, AD = EBProve: AABD AEDBLook at the proof. Name the postulate you would use to prove the two triangles are congruent.Given: AB ED, AD EBProve: AABD = AEDBAB EDGivenAD EBGivenBD BDReflexive Propertyof CongruenceAABD AEDB?BDE
Answers
In the problem, we are already given 2 pairs of sides that are congruent: AB and ED, and AD and BE.
Using the reflexive property of congruence, we also know that segment BD is congruent to itself.
We have therefore used three pairs of sides that are congruent to prove that △ABD ≅ △EDB.
This means that we used the SSS Postulate to prove the congruence of the two triangles.
help me please
thank you
Answers
Answer:
Domain: [-8, 2]
Range: [-4, 0]
Function: Yes
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A relation is a function if each x value corresponds to only one y-value.
Consider the expression. (-3)^-3 divided by 1/-6^2Which Three choices are equivalent to the expression givenA. 4/3B. 1/-(6)^2(-3)^3C. 36/-27D. -6^2/-27E. -36/(-3)^3
Answers
Solution
For this case we have the following:
[tex]3^{-3}=\frac{1}{3^3}=\frac{1}{27}[/tex][tex](\frac{1}{-6})^2=\frac{1}{36}[/tex]When we apply the division we got:
[tex]\frac{\frac{1}{27}}{\frac{1}{36}}=\frac{36}{27}=\frac{4}{3}[/tex]Option A is correct
Option D is correct
Option E is correct
Final answer: A, D, E
4x-3 x=2 4(2)-3 the blank property is used here
Answers
From the information given above, The substitution property is used here. See further explanation below.
What is substitution property?The substituted property of equality states that one value may be substituted for another in an expression or equation and the result will be the same.
If the values of x and y are equivalent, then x and y may be substituted for one another. The property's opposite is likewise true.
For exmaple,
If x=y for any real integer x and y, then y may be replaced for x in any statement.
In the above instance, x = 2 and hence can be substituted for x in the first expression given as:
4x -3.
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Full Question:
4x-3
x=2
4(2)-3
The _____ property is used here.
Hello, stuck on this practice problem. I also need to show all work.
Answers
Given the model for the height of a ball:
[tex]h(t)=-16t^2+5t+15[/tex]To hit the ground, the height must be h(t) = 0. Then:
[tex]\begin{gathered} -16t^2+5t+15=0 \\ \Rightarrow16t^2-5t-15=0 \end{gathered}[/tex]We use the general solution for a quadratic equation:
[tex]ax^2+bx+c=0\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=16 \\ b=-5 \\ c=-15 \end{gathered}[/tex]Using the formula:
[tex]\begin{gathered} t=\frac{5\pm\sqrt{25+4\cdot15\cdot16}}{2\cdot16}=\frac{5\pm\sqrt{985}}{32} \\ \\ \Rightarrow t_1=1.137 \\ \Rightarrow t_2=-0.825 \end{gathered}[/tex]We only take the positive value (because the time is always positive!). Then, the answer is:
[tex]1.137\text{ seconds}[/tex]Simplify.(5+squartrt3)225 + sqrtrt1010 + 28sqrtrt328 + 10sqrtrt3
Answers
The given expression is,
[tex](5+\sqrt[]{3})^2[/tex]We have the algebraic expansion,
[tex](a+b)^2=a+2ab+b^2[/tex]Therefore we have,
[tex]\begin{gathered} (5+\sqrt[]{3})^2=5^2+(2\times\sqrt[]{3}\times5)+(\sqrt[]{3})^2 \\ \text{ =25+10}\sqrt[]{3}+3=28+10\sqrt[]{3} \end{gathered}[/tex]Thus, the correct option is 28 + 10sqrt3.
The difference between nine times a number and one more than six times the number.
the algebraic expression?
Answers
The required algebraic expression is: 9n - (6n +1)
What is an algebraic expression and how is it formed?
Variables and constants are used to create algebraic expressions using a variety of techniques. It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc. When operations like addition, subtraction, multiplication, division, etc. are performed on any variable, the resulting equations are called algebraic expressions. An algebraic expression (or variable expression) is a grouping of terms that have undergone operations like addition, subtraction, multiplication, division, etc.
Let the given number be = n
Therefore, nine times the number = 9n
Also, six times the number = 6n
Again, one more than six times the number = 6n + 1
Given, difference between nine times a number and one more than six times the number.
Using all of the expressions derived above, we curate the algebraic expression as:
Algebraic expression: 9n - (6n +1)
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Triangles G H L and K H J are connected at point H. Angles Angles L G H and H K J are congruent. Sides G H and H K are congruent. Which congruency theorem can be used to prove that △GHL ≅ △KHJ?
Answers
1) Considering that in these triangles, there is one pair of vertical angles
∠GHL and ∠JHK and two congruent angles ∠JKH and ∠HGL,
2) We can tell that these triangles fall within the following congruence case:
[tex]ASA[/tex]Select the three equations that pass through the points (–4, –16) and (5, 2):
y + 4 = 2(x – 16)
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
Answers
The equations of the line are:
y – 2 = 2(x – 5)
y + 16 = 2(x + 4)
y = 2x – 8
How to Find the Equation of a Line that Passes through two Points?The equation of a line, in point-slope form, that passes through two points can be expressed as y - b = m(x - a).
To find the equation, first, we will need to find the slope of the line. Next, we will use a point and the slope to write the equation by simply substitute their values in y - b = m(x - a), where the slope is m and a point is (a, b).
Given the points:
(–4, –16) (5, 2)Find the slope of the line (m):
Slope of the line (m) = change in y / change in x = (-16 - 2)/(-4 - 5)
Slope of the line (m) = -18/-9
Slope of the line (m) = 2
Substitute m = 2 and (a, b) = (5, 2) into y - b = m(x - a):
y - 2 = 2(x - 5)
Or, substitute m = 2 and (a, b) = (-4, -16) into y - b = m(x - a):
y + 16 = 2(x + 4)
Any of the above equations can be rewritten in slope-intercept form as:
y = 2x - 8.
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Does the geometric sequence converge or diverge? Explain.
320,-40, 5, -0.625,...
O The sequence diverges because r = -8, which is less than one.
O The sequence diverges because |r | = 8, which is greater than one.
The sequence converges because || = 0.125, which is less than one.
O The sequence converges because r = 0.125, which is less than one.
Answers
The sequence converges because |r| = 0.125, which is less than one. The correct answer would be option (C).
What is geometric series?The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.
The nth term of a geometric progression is expressed as
Tₙ = arⁿ⁻¹
Where a is the first term, r is the common ratio
We have been given that geometric sequence as:
320, -40, 5, -0.625,...
To determine whether the geometric sequence converges or diverges
We have to find the common ratio of the given sequence.
|r | = | -40/320 |
|r | = 0.125 < 1
Since the common ratio of the sequence is less than 1,
Therefore, the given sequence converges.
Hence, the correct answer would be an option (C).
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2. Invasive weed species can grow quickly. One variety grows up to 1.65 ft per day. How fast in inches per minute can this weed grow? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
Show you work please :)
Answers
Answer:
0.825 inches per hour
Step-by-step explanation:
Invasive weed species can grow quickly. One variety grows up to 1.65 ft per day. How fast in inches per minute can this weed grow?
FACTS:
the weed grows up to 1.65 feet per day
there are 12 inches in 1 foot
there are 24 hours in 1 day
First, lets figure how many inches the weed can grow in one day:
= daily growth in feet per day * inches in 1 foot
= 1.65 feet * 12 inches
= 19.8 inches a day
If the weed can grown 19.8 inches a day, and there are 24 hours in a day:
= growth in inches per day/24 hours in 1 day
=19.8/24
= 0.825 inches per hour
Determine the slope and the y-intercept of the line.
12 = 3 y
Slope: 0; y-intercept: (0,4)
Slope: 0; y-intercept: (4, 0)
Slope: undefined; y-intercept: (4,0)
Slope: 1; y-intercept: (0,4)
Answers
Answer:
Slope = 0, y int = (0,4)
If there is no x variable, slope is 0. y = 4 so no matter what x is (which it will always be 0) the y intercept will always be 4
Evaluate the expression 2x + 5 for x = 10
Answers
Answer:
[tex]2x + 5 \\ (2 \times 10) + 5 \\ 20 + 5 \\ = 25[/tex]
Which polynomials are prime? Check all of the boxes that apply.
x² +9
0²-9
Ox²+3x+9
O-2x² +8
Answers
x² +3x+9 and x² + 9 are prime polynomials.
Define prime numbers.A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components. A prime number is one that can only be divided without leaving a residue by itself and one.
Given Data
x² +9
x² + 9 cannot be divided into factors of rational numbers. It is a prime polynomial as a result.
x²+3x+9
It is impossible to factorize x² + 3x + 9 using rational values. It is a prime polynomial as a result.
x²-9
Factoring x² - 9 results in (x - 3)(x + 3). It is not a prime polynomial, therefore.
-2x² +8
The factorization of -2x² + 8 results in -2(x - 2)(x + 2). It is not a prime polynomial, therefore.
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The weight of 8 eggs is 496 grams. Identify the constant of proportionality of total weight to number of eggs.
Group of answer choices
60
56
62
58
Answers
The constant of proportionality of total weight to number of eggs having the weight of 8 eggs as 496 grams is 62.
How can the constant of proportionality of total weight to number of eggs be determined?The weight of 8 eggs is given as 496 grams
The equation can be written as :
w=n
where n= number of the eggs
we= weight of the eggs
then the equation can be written as
w∝n
Then we can introduce the proportionality constant sign as ;
then w=kn
where k is the proportionality constant
then we can substitute the given figures as ;
496=k *8
then k=496/8 = 62.
Therefore third option is correct.
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Select that two values of x that are roots of thi equation
Answers
ANSWER:
B.
[tex]x=\frac{5+\sqrt{17}}{4}[/tex]C.
[tex]x=\frac{5-\sqrt{17}}{4}[/tex]EXPLANATION:
Given:
[tex]2x^2+1=5x[/tex]To find:
The two values of x that are roots of the equation
Let's subtract 5x from both sides of the equation;
[tex]\begin{gathered} 2x^2+1-5x=5x-5x \\ 2x^2-5x+1=0 \end{gathered}[/tex]Recall that a quadratic equation is generally given in the below form;
[tex]ax^2+bx+c=0[/tex]Comparing both equations, we can see that;
[tex]\begin{gathered} a=2 \\ b=-5 \\ c=1 \end{gathered}[/tex]Let's go ahead and use the below quadratic formula to solve for the values of x;
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} x=\frac{-(-5)\pm\sqrt{(-5)^2-4*2*1}}{2*2} \\ \\ x=\frac{5\pm\sqrt{25-8}}{4} \\ \\ x=\frac{5\pm\sqrt{17}}{4} \\ \\ x=\frac{5+\sqrt{17}}{4},\frac{5-\sqrt{17}}{4} \end{gathered}[/tex]A moving company charges a one-time and a cost per mile for its service. The relationship between the mileage and the cost is displaying in the graph. Which equation best represents the relationship between the total cost, C, and miles traveled, m?*
Answers
This is a linear relation. For linear relations, we have the general form:
[tex]y=ax+b[/tex]Where 'a' is the slope and 'b' is the intercept.
In this problem, we have that the intercept b is 200, because that's the point where the line crosses the y-axis. For now we have something like:
[tex]C=am+200[/tex](here y is C and x is m)
To find the slope we have to use the intercept point (0, 200) and another point on the line. We can see that one of those points is (200, 500).
For a line with points (x1, y1) and (x2, y2), the slope is find like:
[tex]a=\frac{y_2-y_1}{x_2-x_1}[/tex]In this problem, the slope is:
[tex]a=\frac{500-200}{200-0}=\frac{300}{200}=\frac{3}{2}=1.5[/tex]Then, we have the equation that represents the relationship between the mileage and the cost:
[tex]C=1.5m+200[/tex]NEED HELP NOW!!!!!!!!Find the number that should be added to the expression to create a perfect square trinomial. x^2-8x-161664-64
Answers
From a perfect square trinomial
[tex]a^2+2ab+b^2[/tex]We know that:
[tex]2ab=2\cdot\sqrt[]{a^2}\cdot\sqrt[]{b^2}[/tex]Now, let's use this for the trinomial given:
[tex]x^2-8x+b^2[/tex]We know that:
[tex]-8x=2\cdot x\cdot b^2[/tex]Solving for b,
[tex]\begin{gathered} -8x=2xb \\ \rightarrow b=-\frac{8x}{2x}\Rightarrow b=-4 \end{gathered}[/tex]This way, the complete perfect square trinomial is:
[tex]x^2-8x-16[/tex]Ans: Option A
What is the sum of + 5 16 000 ? 9 B 13. 32 o c. 9 16 D. 13 16
Answers
Answer:
The sum of the fractions is;
[tex]\frac{13}{16}[/tex]Explanation:
We want to find the sum of the fraction;
[tex]\frac{1}{8}+\frac{5}{16}+\frac{3}{8}[/tex]The least common multiple is 16;
[tex]\begin{gathered} \frac{1}{8}+\frac{5}{16}+\frac{3}{8} \\ =\frac{2+5+6}{16} \\ =\frac{13}{16} \end{gathered}[/tex]The sum of the fractions is;
[tex]\frac{13}{16}[/tex]Come onnnnSimplify fast help
Answers
Answer:
i know that if i just answered the question quick then it would have been better for you but i also need help with something but i know something that will help you
Step-by-step explanation: go to cymath ans type it in it will help you and you can use it on school laptops so im kind of helping future you
Answer the question in the picture below please someone help me
Answers
Answer:
here is the Answer The population will be 799,500 people
Step-by-step explanation:
Fill in the frequency distribution below
Answers
The frequency for the given distribution of the class interval 1.00 - 1.09 is 3, which are 1.07, 1.05 and 1.07.
What is frequency?The frequency of a repeating event is its number of instances per unit of time. In some cases, it is also referred to as temporal frequency or ordinary frequency to emphasise differences with spatial and angular frequencies, respectively. One (event) per second is equal to one hertz (Hz), which is how frequency is expressed.
The period is the reciprocal of the frequency because it is the length of time for one cycle in a repeating event. For instance, the period, T—the space between beats—of a heart beating at a frequency of 120 beats per minute (2 hertz), is equal to 0.5 seconds (60 seconds divided by 120 beats).
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a. 2а + 4(7 + 5а) (simplify)
Answers
Answer
22a + 28
Explanation
The question asks us to simplify the given expression
2a + 4(7 + 5a)
The first step is to open the bracket
2a + 4(7 + 5a)
= 2a + 28 + 20a
= 2a + 20a + 28
= 22a + 28
Hope this Helps!!!
A carpenter spend his 40-hour workweek as follows: 1/4 of his ordering materials; 1/2 of his time doing the wooodwork; and 1/8 of his time talking to customers. The rest of his time devoted to cleanup. What is the approximately percentage of time the carpenter spend doing cleanup?
Answers
The forty hours of the workweek of the carpenter are distributed as follows:
Then, the time that the carpenter spends cleaning up is (what remains from the 40 hours after subtracting the time he spends in the other activities):
[tex]40h-10h-20h-5h=5h\text{.}[/tex]The question now is, what percentage does 5h represent in 40h? We need to use the percentage formula:
[tex]\begin{gathered} 5=\frac{\%}{100}\cdot40.\leftarrow\begin{cases}\%=\text{ Percentage that 5 represents in 40}\end{cases} \\ \\ \end{gathered}[/tex]Solving this equation, we get
[tex]\begin{gathered} 5=\frac{\%}{100}\cdot40, \\ \\ 5=\frac{\%\cdot40}{100}, \\ \\ 100\cdot5=\%\cdot40, \\ \\ 500=\%\cdot40, \\ \\ \frac{500}{40}=\%, \\ \\ \%=\frac{500}{40}, \\ \\ \%=12.5. \end{gathered}[/tex]AnswerThe percentage of time that the carpenter spends cleaning up is 12.5%.
