Answers
The quotient is x² + 4x + 3
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
Explanation:[tex](x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2)}[/tex][tex]\begin{gathered} x\text{ - 2 = 0} \\ x\text{ = 2} \\ \\ \text{coefficient of }x^3+2x^2\text{ - 5x - 6:} \\ 1\text{ 2 -5 -6} \\ \\ We\text{ will divide the coefficients by 2} \end{gathered}[/tex]Using synthetic division:
[tex]\begin{gathered} (x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2) = }\frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}} \\ \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}\text{ = quotient + }\frac{remai\text{ nder}}{\text{divisor}} \\ \\ The\text{ coefficient of the quotient = 1 4 3} \\ \text{The last number is zero, so the remainder = 0} \end{gathered}[/tex][tex]\begin{gathered} \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}=1x^2\text{ + 4x + 3 + }\frac{0}{x\text{ - 2}} \\ \text{quotient }=\text{ }x^2\text{ + 4x + 3} \end{gathered}[/tex]For a (x - 2) to be a factor of x³ + 2x² - 5x - 6, it will not have a remainder when it is divided.
Since remainder = 0
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
Related Questions
50 gramos de pechuga de un pollo contiene 10.4 g de proteínas, 0.5 g de carbohidratos y 1.6 g de grasas. Los valores medios de energía alimentaria de esas sustancias son de 4.0 kcal/g para las proteínas y los carbohidratos, y de 9.0 kcal/g para las grasas. a) Al jugar baloncesto, una persona representativa consume energía a una potencia de 420 kcal/h. ¿Cuánto tiempo debe jugar para “quemar” esa pechuga?
Answers
Tenemos lo siguiente:
Lo primero es calcular las kilocalorías para las proteínas y para los carbohidratos y grasas, de la siguiente día:
[tex]\begin{gathered} \text{Protenas} \\ 10.4\text{ g}\cdot4\frac{\text{ kcal}}{g}=41.6\text{kcal} \\ \text{Carbohidratos} \\ 0.5\text{ g}\cdot4\frac{\text{ kcal}}{g}=2\text{kcal} \\ \text{Grasas} \\ 1.6\text{ g}\cdot9\frac{\text{ kcal}}{g}=14.4\text{kcal} \end{gathered}[/tex]Ahora sumamos todas las kilocalorías y nos queda lo siguiente:
[tex]41.6+2+14.4=58[/tex]Es decir que en total en los 50 gramos de pechuga hay en total de 58 kilocalorías, ahora debemos calcular el tiempo dividiendo el numero de kilocalorías por la cantidad de consumo de kilocalorías al jugar baloncesto
[tex]\frac{58\text{ kcal}}{420\text{ kcal/h}}=0.138\text{ h}[/tex]Es decir que debe jugar 0.138 horas o un total de:
[tex]0.138\text{ h}\cdot\frac{60\text{ min}}{1\text{ h}}=8.28\text{ min}[/tex]Es decir que debe jugar 8.28 minutos
Set up the equation for the following word problem and solve the equation. Let x be the unknown number. -26 times a number minus 5 is equal to 56 less than the number. Step 2 of 2: Solve the equation for x. Express your answer as an integer, a reduced fraction, or a decimal number rounded to two pl Answer
Answers
Answer:
Step 1 of 2:
-26x - 5 = x - 56
Step 2 of 2:
17/9 or 1.89
Step-by-step explanation:
1. Putting word statement in algebraic form
Step 1:
Let x be the unknown number ==> x is the unknown variable to be used in the equation and to be solved for
Step 2:
-26 times a number minus 5 ==> -26x - 5
Step 3:
is equal to 56 less than the number ==> = x - 56
Putting it all together:
-26x - 5 = x - 56
2. Solving the equation
-26x - 5 = x - 56
1. Subtract x from both sides:
-26x - 5 - x = x - x -56
-26x -x - 5 = -56
-27x - 5 = -56
2. Add 5 to both sides
-27x - 5 + 5 = -56+ 5
-27x = -51
x = -51/-27 (dividing both sides by -27)
x = 51/27 (negative divide by negative results in positive)
Reduce 51/27 by dividing numerator and denominator by 3
x = (51 ÷ 3)/(27 ÷ 3) = 17/9
= 1.88888.... = 1.89 rounded to two decimal places
in this quadratic trinomial 20 is the _____. 3x^2 -7x-20
Answers
A trinomial has three terms. The first term contains the squared variable, the second term contains the variable with an exponent of 1, and the third term does not have any variable. That term is called the independent term.
In the polynomial:
[tex]3x^2-7x-20[/tex]The term -20 is the independent term because it does not depend on the value of the variable x.
Algebra 1B CP find the zeros of the function by factoringexercise 2 please
Answers
2) y = 8x² +2x -15
(4x -5)(2x +3)
S={-3/2, 5/4}
3) y= 4x² +20x +24
(4x +8)(x +3)
S={-2,3}
1) Factoring these quadratic functions we have:
2) y = 8x² +2x -15
Let's call u, and v two factors.
Multiplying 8 by -15 = we have u*v = -120 Adding u + v= 2, so u = 12 and v =-10
12 x -10 = -120
12 +(-10) = 2
So, now we can rewrite it following this formula:
(ax² + ux) +(vx +c)
(8x² +12x) +(-10x-15) Rewriting each binomial in a factored form
4x(2x +3) -5(2x+3)
(4x -5)(2x +3)
Equating each factor to zero to find out the roots:
(4x -5) =0
4x =5
x=5/4
(2x +3) = 0
2x = -3
x= -3/2
Hence, the solution set is S={-3/2, 5/4}
3) y= 4x² +20x +24
Proceeding similarly we have:
u * v = 96
u + v = 20
So u = 12, and v =8 12x 8 = 96 12 +8= 20
Rewriting into (ax²+ux)+(vx +c)
(4x²+12x) +(8x+24) Factoring out each binomial
4x(x+3) +8(x+3) As we have a repetition we can write:
(4x +8)(x +3)
3.2) Now to find out the roots equate each factor to zero, and solve it for x:
4x +8 = 0
4x = -8
x =-2
x+3 =0
x=-3
4) Hence, the answers are:
2) y = 8x² +2x -15
(4x -5)(2x +3)
S={-3/2, 5/4}
3) y= 4x² +20x +24
(4x +8)(x +3)
S={-2,3}
Convert 255 to base 2
Answers
We can count the number of zeros and ones to see how many bits are used to represent 255 in binary i.e. 11111111. Therefore, we have used 8 bits to represent 255 in binary.
Convert 255 to base 2?
255 = 8 bits
255 in Binary: 255₁₀ = 11111111₂
Binary is a system used in mathematics and computer science where values and numbers are stated as 0 or 1.Binary is base-2, which means that there are just two digits or bits used.For computers, 1 denotes truth or "on," while 0 denotes falsehood or "off." Computers communicate and represent information using binary code.Everything you see on a computer, including letters, numbers, and pictures—basically everything—is made up of multiple 0s and 1s combinations. One of the four different kinds of number systems is the binary number system.When used in computer programs, binary numbers are solely represented by the digits 0 (zero) and 1. (one).Here, the base-2 numeral system is used to represent the binary numbers.One binary number is (101)2, for instance. The modern binary number system was first suggested and refined by Gottfried Leibniz in the 17th century in his article Explication de l'Arithmétique Binaire [1].The system was created by Leibniz about 1679, although it wasn't published until 1703.He had already used 0 and 1.To learn more about binary refer
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Determine the effect on the graph of the parent f(x)=x
Answers
To answer this question we first graph the parent function
Now we compare the two graphs. We notice that the graph shown is translated two units up.
To translate the graph of function we have to add the ammount we want to translate, then in this case
[tex]g(x)=f(x)+2[/tex]Therefore the answer is J.
Given ABC below, with m B=25°, a = 9, and c = 16, find the area of the triangle.
Answers
It is given that the sides of the triangle are a =9 and c=16 . The angle is given mB=25 degree.
The area of triangle is determined as
[tex]A=\frac{1}{2}a\times c\times\sin B[/tex][tex]A=\frac{1}{2}\times9\times16\times\sin 25=72\sin 25^{\circ}[/tex][tex]A=30.428sq\mathrm{}\text{unit}[/tex]Thus the area of triangle is 30.428 sq.unit.
a. Create a perfect square trinomial.
b. Factor the perfect square trinomial you created in 1a.
a. Create a difference of two squares.
b. Factor the difference of two squares you created in 2a.
a. Describe at least one similarity between the perfect square trinomial and the difference of squares. You can use either the form you wrote in 1a and 2a, or you can use their factored form from 1b and 2b. Write your answer using complete sentences.
b. Describe at least one difference between the perfect square trinomial and the difference of squares. You can use either the form you wrote in 1a and 2a, or you can use their factored form from 1b and 2b. Write your answer using complete sentences.
A factored perfect square might look like (x+a)(x+a) or (x-a)(x-a) [or (ax+b)(ax+b) but keep it simple]. Then, distribute.
A factored difference of two squares might look like (x+a)(x-a). Then, distribute.
(pick a number for a)
Answers
1.
a. One example of a perfect square trinomial is: x² + 6x + 9.
b. The factored trinomial above is: (x + 3)².
2.
a. One example of a difference of two squares is: x² - 4.
b. The factored difference of squares above is: (x - 2)(x + 2).
3.
a. The similarity is that the first term is positive for both cases.
b. The difference is that the final term is positive for perfect square trinomials and negative for the difference of squares.
Perfect square trinomialsThere are two examples of perfect square trinomials, the square of the sum and the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².Square of the subtraction: (a - b)² = a² - 2ab + b².The left side is the factored form and the right side is the expanded form.
Hence one example of a perfect square trinomial is given as follows:
(x + 3)² = x² + 6x + 9.
Difference of two squaresA difference of two squares is factored as follows:
x² - y² = (x + 2)(x - 2)
Hence one possible example is:
x² - 4 = (x + 2)(x - 2).
Compared to the perfect square trinomial, we have that:
The similarity is that the first term in any of the two polynomials will always be positive.The difference is in the last term, for the perfect square it will always be positive (+ b²) and for the difference of two squares it will always be negative (- b²).More can be learned about perfect square trinomials at https://brainly.com/question/14584348
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Assume the hold time of callers to a cable company is normally distributed with a mean of 4.0 minutes and a standard deviation of 0.4 minute. Determine the percent of callers who are on hold between 3.4 minutes and 4.5 minutes. % (Round to two decimal places as needed.)
Answers
According to the problem, we have
[tex]\begin{gathered} \mu=4.0\min \\ \sigma=0.4\min \end{gathered}[/tex]We have to find the percent of callers who are on hold between 3.4 minutes and 4.5 minutes.
First, we find the z-score
[tex]z=\frac{x-\mu}{\sigma}[/tex]For x = 3.4
[tex]z=\frac{3.4-4.0}{0.4}=\frac{-0.6}{0.4}=-1.5[/tex]For x = 4.5
[tex]z=\frac{4.5-4.0}{0.4}=\frac{0.5}{0.4}=1.25[/tex]The probability we have to find is
[tex]P=(3.4Using a z-table, we have[tex]\begin{gathered} P(3.4Then, we multiply by 100 to express it in percetange.[tex]0.2351\cdot100=23.51[/tex]Hence, the probability is 23.51%.Deter mine the intervals for which the function shown below is increasing
Answers
Answer:
The interval at which the function is increasing is from x = -2 to x = 0. In interval notation, it is (-2, 0).
Explanation:
See the graph below for the pattern of the function.
As you can see above, from x = -∞ until x = -2, the value of the function decreases from y = +∞ to y = -7.
Then, starting at x = -2 to x = 0, the value of the function increases from y = -7 to y = -3.
Lastly, starting at x = 0 to +∞, the value of the function decreases again from y = -3 to -∞.
Hence, the interval at which the function is increasing is at (-2, 0).
estimate 328 divided by 11=?
Answers
Answer:
30
Step-by-step explanation:
You have a piggy bank containing a total of 66 coins in dimes and quarters. If the piggy bank contains $10.20, how many dimes are there in the piggy bank?
Answers
I have 42 dimes in my piggy bank according to the given condition of 66 coins and amount $10.20 and used the system of equation as well as substitution method.
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations.
What is substitution method?Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. Applying the substitution method begins with this.
Here,
x+y=66 ......(1)
1 dime values 10 cents.
1 quarter values 25 cents.
10x+25y=1020 ........(2)
x=66-y
10(66-y)+25y=1020
660-10y+25y=1020
15y=360
y=360/15
y=24
x=66-24
x=42
I used the system of equations and the substitution method to determine that I have 42 dime coins in my piggy bank in accordance with the requirement of 66 coins totaling $10.20.
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set up a trigonometric ratio for angle H and solve for X
Answers
According to the picture, it is necessary to use cosine, which is the ratio between the side that is adjacent to a given angle and the hypotenuse.
In this case, the angle would be H, the adjacent side to it would be x and the hypotenuse 14. It means that cos H is the ratio between x and 14:
[tex]\cos H=\frac{x}{14}[/tex]The following triangles are not similar. Determine the ratio between AMCD and AOLN. Howcould you change the measurement(s) to make them similar?
Answers
The ratio between MD and DC IS
[tex]\frac{MD}{DC}=\frac{14}{6}=\frac{7}{3}[/tex]The ratio of ON to LN
[tex]\frac{ON}{LN}=\frac{49}{21}=\frac{7}{3}[/tex]The ratio CM to CD
[tex]\frac{CM}{CD}=\frac{12}{6}=\frac{2}{1}[/tex]The ratio of OL to LN
[tex]\frac{OL}{LN}=\frac{40}{21}[/tex]To make the
a1. The amount of milk in a one-gallon milk container has a normal distribution with a meanof 1.07 gallons and a standard deviation of 0.12 gallons.Calculate and interpret the z-score for exactly one gallon of milk.
Answers
The z-score formula is given to be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} x=score \\ \mu=mean \\ \sigma=standard\text{ }deviation \end{gathered}[/tex]From the question given, the mean and standard deviations are provided as:
[tex]\begin{gathered} \mu=1.07 \\ \sigma=0.12 \end{gathered}[/tex]Therefore, the z-score of exactly 1 gallon is calculated to be:
[tex]\begin{gathered} x=1 \\ \therefore \\ z=\frac{1-1.07}{0.12}=\frac{-0.07}{0.12} \\ z=-0.583 \end{gathered}[/tex]Therefore, the z-score is -0.583.
This tells us that a container with exactly one gallon of milk lies 0.583 standard deviations below the mean.
Hello,Can you help me with question 1: Evaluate the given binomial coefficient
Answers
Solution:
Given the expression below
[tex](^8_3)[/tex]Applying the combination formula below
[tex]^nC_r=\frac{n!}{r!(n-1)!}[/tex]The binomial coefficient will be
[tex]=\frac{8!}{3!(8-3)!}=\frac{8!}{3!5!}=\frac{8\times7\times6\times5\times4\times3\times2\times1}{3\times2\times1\times5\times4\times3\times2\times1}=56[/tex]Hence, the answer is 56
Pls help me with this I will give brainless thank u <3
Answers
15.sum,neg
16.sum,neg
17.diff,neg
18.sum,neg
19.sum,pos
20.neg
21.pos
22.neg
23.pos
24.neg
Given a family with four children, find the probability of the event. All are boys. The probability that all are boys
Answers
Answer:
0.0625
Explanation:
The number of children in the family = 4
The possible combination of genders:
[tex]|\Omega|=2^4=16[/tex]The event that all are boys, |A|=1
Therefore, the probability that all are boys:
[tex]\begin{gathered} P(A)=\frac{1}{16} \\ =0.0625 \end{gathered}[/tex]Solve for u.u + 8 = 16
Answers
In this case the answer is very simple. .
We must apply algebraic rules to find the solution.
u + 8 = 16
u = 16 - 8
u = 8
The answer is:
u = 8
Please help I need to graph this and i can only have two points
Answers
Given the function:
[tex]f\mleft(x\mright)=\mleft(x+2\mright)\mleft(x-4\mright)[/tex]You can rewrite it as follows:
[tex]y=\mleft(x+2\mright)\mleft(x-4\mright)[/tex]You need to remember that the y-value is zero when the function intersects the x-axis. Then, you need to make it equal to zero, in order to find the x-intercepts:
[tex]\begin{gathered} 0=\mleft(x+2\mright)\mleft(x-4\mright) \\ (x+2)(x-4)=0 \end{gathered}[/tex]Solving for "x", you get these two values:
[tex]\begin{gathered} x+2=0\Rightarrow x_1=-2 \\ \\ x-4=0\Rightarrow x_2=4 \end{gathered}[/tex]In order to find the vertex, you can follow these steps:
1. Find the x-coordinate of the vertex with this formula:
[tex]x=-\frac{b}{2a}[/tex]To find the value of "a" and "b", you need to multiply the binomials of the equation using the FOIL Method. This states that:
[tex]\mleft(a+b\mright)\mleft(c+d\mright)=ac+ad+bc+bd[/tex]Then, in this case, you get:
[tex]\begin{gathered} y=(x)(x)-(x)(4)+(2)(x)-(2)(4) \\ y=x^2-4x+2x-8 \end{gathered}[/tex]Add the like terms:
[tex]y=x^2-2x-8[/tex]Notice that, in this case:
[tex]\begin{gathered} a=1 \\ b=-2 \end{gathered}[/tex]Then, you can substitute values into the formula and find the x-coordinate of the vertex of the parabola:
[tex]x=-\frac{(-2)}{2\cdot1}=-\frac{(-2)}{2}=1[/tex]2. Substitute that value of "x" into the function and then evaluate, in order to find the y-coordinate of the vertex:
[tex]\begin{gathered} y=x^2-2x-8 \\ y=(1)^2-2(1)-8 \\ y=1-2-8 \\ y=-9 \end{gathered}[/tex]Therefore, the vertex of the parabola is:
[tex](1,-9)[/tex]Knowing the x-intercepts and the vertex of the parabola, you can graph it.
Hence, the answer is:
a loaf of sandwich bread contains 24 slices. which of these tables correctly shows the ratios of different of loaves of bread to the number of total slices they contain
Answers
We have that a loaf of sandwich bread contains 24 slices, then we have that the ratio must be constant between the loaves and the slices. If we have 1 loaf: 24 slices, this ratio must be equal in the table.
Therefore, we have that the only table that follows this is the table that has:
If we have:
2/48 = 1/24
3/72 = 1/24
4/96 = 1/24
The ratio of loaves to slices is the same, that is, 1 / 24.
log(x) + log(x + 3) = 7
Answers
Answer:
[tex]x=3160.778016...[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log(x)+\log(x+3)=7[/tex]
[tex]\textsf{Apply the product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \log(x(x+3))=7[/tex]
[tex]\implies \log(x^2+3x)=7[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies x^2+3x=10^7[/tex]
[tex]\implies x^2+3x-10000000=0[/tex]
Solve the quadratic equation by using the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=3,\quad c=-10000000[/tex]
Substitute the values of a, b and c into the quadratic formula:
[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(-10000000)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{9+40000000}}{2}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{40000009}}{2}[/tex]
[tex]\implies x=3160.778016..., \quad x=-3163.778016...[/tex]
As logs of negative numbers cannot be taken, the only valid solution is:
[tex]\boxed{x=3160.778016...}[/tex]
Referring to the figure, find the value of x in circle C.
Answers
The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
Graphically,
[tex]PA\cdot PB=(PD)^2[/tex]In this case, we have:
[tex]3x\cdot5=10^2[/tex]Now, we can solve the equation for x:
[tex]\begin{gathered} 3x\cdot5=10^2 \\ 15x=100 \\ \text{ Divide by 15 from both sides of the equation} \\ \frac{15x}{15}=\frac{100}{15} \\ \text{Simplify} \\ x=\frac{20\cdot5}{3\cdot5} \\ x=\frac{20}{3} \\ \text{ or} \\ x\approx6.67 \end{gathered}[/tex]Therefore, the value of x is 20/3 or approximately 6.67.
A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that no two of the civil engineers will sit together? [ 9! × 10!/4!)]
Answers
The software engineers can be seated on a round table with no two civil engineers sitting together is 9!×10!/4!
Given, a company has 10 software engineers and 6 civil engineers.
we need to determine in how many ways can they be seated around a round table so that no two civil engineers will sit together.
10 software engineers can be arranged around a round table in :
=(10-1)!
= 9! ways .... eq(A)
Now, we must arrange the civil engineers so that no two can sit next to one another. In other words, we can place 6 civil engineers in any of the 10 *-designated roles listed below.
This can be done in ¹⁰P₆ ways ...(B)
From A and B,
required number of ways = 9!×¹⁰P₆
= 9! × 10!/4!
Hence the number of ways the engineers can be seated is 9! × 10!/4!.
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Find the volume of each prism. Round your answers to the nearest tenth, if necessary. Do not include units (i.e. ft, in, cm, etc.). (FR)
Answers
EXPLANATION:
Given;
We are given the picture of an isosceles trapezoidal prism.
The dimensions are as follows;
[tex]\begin{gathered} Top\text{ }base=4 \\ Bottom\text{ }base=9 \\ Vertical\text{ }height=4.3 \\ Height\text{ }between\text{ }bases=6 \end{gathered}[/tex]Required;
We are required to find the volume of this trapezoidal prism.
Step-by-step solution;
The area of the base of a trapezium is given as;
[tex]Area=\frac{1}{2}(a+b)\times h[/tex]For the trapezium given and the values provided, we now have;
[tex]\begin{gathered} a=top\text{ }base \\ b=bottom\text{ }base \\ h=height \\ Therefore: \\ Area=\frac{1}{2}(4+9)\times4.3 \\ Area=\frac{1}{2}(13)\times4.3 \\ Area=6.5\times4.3 \\ Area=27.95 \end{gathered}[/tex]The volume is now given as the base area multiplied by the length between both bases and we now have;
[tex]\begin{gathered} Volume=Area\times height\text{ }between\text{ }trapezoid\text{ }ends \\ Volume=27.95\times6 \\ Volume=167.7 \end{gathered}[/tex]ANSWER:
The volume of the prism is 167.7
Send me Answers for Questions A, B, and C
Answers
Answer: A) 4 B) 30 C) 6
Step-by-step explanation:
For question A, you subtract the highest number and the lowest number (10-6)
For question B, you add all the frequency numbers together
For question C, you use your answer on B and divide it by 5
Dejah is comparing two numbers shown in scientific notation on her calculator. The first number was displayed as 7.156E25 and the second number was displayed as 3.498E-10. How can Dejah compare the two numbers?
Answers
The first number is about
2 x 10¹⁵
2 x 10³⁵
2 x 10‐¹⁵
2 X 10‐³⁵
times bigger than the second number.
Answers
Answer:
2 x [tex]10^{35}[/tex]
Step-by-step explanation:
7 ÷ 3 is about 2
[tex]\frac{10^{25} }{10^{-10} }[/tex] = [tex]10^{35}[/tex] When you are dividing powers with the same bases, you subtract the exponents
25 - -10 = 25 + 10 = 35
Angela bought a calculator on sale for 15% off. Sales tax is 7.5%. If the calculator cost x dollars, which expression represents the total cost of the calculator?A). (x-0.15) (0.075)B). (x-0.15) (1.075)C). (x-0.15x) (0.075)D). (x- .015x) (1.075)
Answers
Original price = x
Price with 15% off = x - 0.15x
Price with 15% off and 7.5% tax = (x - 0.15x)(1.075)
Answer:
Option B: (x - 0.15x)(1.075)
A ball is thrown from an initial height of 1 meter with an initial upward velocity of 7 m/s. The balls height h (in meters) after t seconds is given by the following. h=1+7t-5t^2Find all values of t for which the balls height is 2 meters.Round the answer(s) to the nearest hundredth
Answers
Solution
To find the values of t for which the ball's height is 2 meters
we set h = 2
=> 2 = 1 + 7t - 5t^2
=>5t^2 - 7t + 1 = 0
Using the quadratic formula,
[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \Rightarrow t=\frac{7\pm\sqrt{\left(-7\right)^2-4\left(5\right)\left(1\right)}}{2\cdot5} \\ \\ \Rightarrow t=1.24s\text{ or }0.16s \end{gathered}[/tex]Therefore, t = 1.23s or 0.16s
|x|=-5 why is there no solution?
Answers
Absolute value is the distance a number is from zero.
Because distance cannot be negative, an absolute value can never be a negative.
Therefore,
|x| = -5 has no solutions
