In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
8x² - x - 9 = (x + 1) ( ? )
Step 02:
We must find the missing root to solve the exercise.
x1 = - 1
x2 :
a = 8
b = -1
c = -9
[tex]x\text{ = }\frac{-(-1)\pm\sqrt[]{(-1)^2-4\cdot8\cdot(-9)}_{}}{2\cdot8}[/tex][tex]x\text{ = }\frac{1\pm17}{16}[/tex][tex]x\text{ = }\frac{1+17}{16}=\frac{18}{16}=\frac{9}{8}[/tex]x2 = 9 / 8
The answer is:
( x - 9/8)
8x² - x - 9 = (x + 1) ( x - 9/8 )
If f(1) = 2 and f(n) = f(n - 1)^2 – 5 then find the value of f (4).
We are asked to calculate f(4) by means of the following function:
f(n) = f(n - 1)² - 5
As you can see, in order to calculate f(n) first we have to specify the value of f(n - 1), we are given the value of f(1), so we can calculate the value of f(2), then f(3) and finally f(4), like this:
f(2) = f(2-1)² - 5 = f(1)² - 5 = 2² - 5 = 4 - 5 = -1
Then, f(2) = -1, now we can calculate f(3) like this:
f(3) = f(3 - 1)² - 5 = f(2)² - 5 = (-1)² - 5 = -4
Then f(3) = -4, now we can calculate f(4) like this:
f(4) = f(4 - 1)² - 5 = f(3)² - 5 = (-4)² - 5 = 16 - 5 = 11
Then, f(4) equals 11
Kiran read for x minutes, and Andre read 5/8 more than that. Write an equation that relates the number of minutes Kiran read with Y ,the number of minutes Andre read. "Use decimals in the equation.DO NOT ROUND"
The time for which Kiran read is x minutes.
Determine the time for which Andre read.
[tex]\begin{gathered} Y=x+\frac{5}{8}\cdot x \\ =x+0.625x \\ =\text{1}.625x \end{gathered}[/tex]Thus answer is Y = 1.625 x.
Customers can pick their own blueberries at Blueberry Hill. They pay $5 toenter the patch and $4 per pound for the blueberries they pick. Write anequation to model the total cost, y, for x pounds of blueberries.
SOLUTION
Step1; Write out the parameters
[tex]\begin{gathered} \text{entry fe}e=\text{ \$5} \\ \cos t\text{ of blueberries per pound=\$4} \end{gathered}[/tex]Step2: Write out the variables
[tex]\text{let y=total cost and x=number of bluerries}[/tex]Step3: write out the model
[tex]\begin{gathered} \text{The total cost=number of blueberries}\times\text{\$}4+\text{ the entry fe}e \\ y=4x+5 \end{gathered}[/tex]There
Write the equation to represent the following relationship. y varies inversely with x. When y = 4, x = 3.
EXPLANATION
The relationship that represents the equation is the following:
[tex]y=\frac{k}{x}[/tex]Plugging in x=3 and y=4 into the equation:
[tex]4=\frac{k}{3}[/tex]Multiply 3 to both sides:
[tex]3*4=k[/tex]Multiplying numbers:
[tex]12=k[/tex]Switching sides:
[tex]k=12[/tex]Therefore, the equation is the following:
y= 12/x
In order to pass a science lab, you have to measure a beaker (container) of water with 5% error or less. The beaker has 12 ounces of water in it. You measure 13.2 ounces of water. Did you pass the lab? Why or why not?
Data:
Error: 5%
Volume of water in the Beaker: 12oz
Your measure: 13.2oz
As the error is 5% it means that the measure can be actually 5% more or 5% less.
Then, you calculate the 5% of the measure you have to measure: 12oz
[tex]12\cdot\frac{5}{100}=0.6oz[/tex]Then, the measure you need to take to pass the lab is between: 11.4oz and 12.6oz
[tex]12oz\pm0.6oz[/tex][tex]\begin{gathered} 12oz+0.6oz=12.6oz \\ 12oz-0.6oz=11.4oz \end{gathered}[/tex]Then, your measure of 13.2oz is not between the 5% of error. You didn't pass the lab.
Hello am I correct, if not can you help me understand?
total kilometer of journey = 353miles
she stopped at mile 36
-7.9 cm 26.2 cm 6.2 cm 19.1 cm 2.8 cm The perimeter of the figure is (Type a whole number or a decal.) .
ANSWER
The perimeter is 81.5 cm
EXPLANATION
The perimeter of any polygon is the sum of the length of its sides. The perimeter of this figure is:
[tex]P=7.9+26.2+6.2+22.8+18.4=81.5\operatorname{cm}[/tex]A quality control worker at a factory selects the first 10 items she sees as her sample for the day.What type of sample is this?
This is a convinience sample because the first 10 items are easy to select.
9(m - 3) + 3m = 7m + 43
For a winter-themed Valentine's Day party, Mr. Rivera made 12 cups of hot chocolate. Does he have enough hot chocolate to give 26 kids 1/2 of a cup each?
Multiply the number of kids by the number of cups for each kid. This is 26 times 1/2.
[tex]26\cdot\frac{1}{2}=\frac{26}{2}=13[/tex]It means 13 cups are needed to give each of the 26 kids 1/2 of a cup of chocolate.
Mr. Rivera does not have enough hot chocolate to give 26 kids 1/2 of a cup of chocolate.
Given `lim_(x -> 2) 2x - 3 = 1`, use the formal definition of a limit to find the value of δ that corresponds to ε = 0.3.
A. 0.05
B. 0.15
C. 0.30
D. 0.50
Answer: B. 0.15
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Estimate the local minimum of y = −³ − 5x² − 3x + 9.-OA. (1.5,-10.25)OB. (-3,0)C. there is no local minimumOD. (-0.33,9.48)Reset Selection
Given: The function below
[tex]y=-x^3-5x^2-3x+9[/tex]To Determine: The local minimum
Solution
The graph of the function is as shown below
Hence, the local minimum from the graph above is (- 3, 0), OPTION B
Convert the Fahrenheit temperature to the equivalent Celsius temperature round to 1 decimal Places if necessary
Given
[tex]19^0F[/tex]To convert the given to Celsius
Solution
The formula connecting Fahrenheit and degree Celsius is given as
[tex]\begin{gathered} =\frac{5(F-32)^{}}{9} \\ =\frac{5(19-32)}{9} \\ =\frac{5(-13)}{9}=-7.222^0C \end{gathered}[/tex]Hence
19⁰F = -7.2⁰C
The product of 5 – 2i and i is1) 72) 2 + 5i3) 5 – 2i4) -2 + 5i
Answer:
2) 2 + 5i
Explanation
Fom the given question, we are find the product of 5-2i and i
i(5-2i)
Expand
= 5i - 2(i^2)
From complex number i^2 = -1
Substitute
= 5i - 2(-1)
= 5i + 2
= 2 + 5i
Hence the product is 2 + 5i
Allen is choosing a 2 letter password from the letters ABCD. the password cannot be the same letter repeated in it .how many such passwords are possible?
Since we can choose 2 letters and they can not be the same, we have the following possibilities:
[tex]{}\lbrace AB,AC,AD,BC,BD,BA,CB,CA,CD,DA,DB,DC\rbrace[/tex]As we can note, there are 12 possible combinations of 2 different letters. So, How many such passwords are possible? The answer is 12 passwrods
A system of equations is given below.x + 2y = 24x − 5y = 8Identify the constant that can be multiplied by both sides of the first equation to eliminate the variable x when the equations are added together.thenWrite the revised system of equations.
Answer:
[tex]constant\rightarrow-4[/tex]Explanation: We have to find the constant that when multiplied to the first equation and added to the second, the variable x gets canceled out, the two equations are as follows:
[tex]\begin{gathered} x+2y=2\rightarrow(1) \\ 4x-5y=8\rightarrow(2) \end{gathered}[/tex]Multiplying the equation (1) by -4 and adding it to the equation (2) gives the following answer:
[tex]\begin{gathered} -4\times(x+2y)=-4\times2\rightarrow-4x-8y=-8 \\ \begin{equation*} -4x-8y=-8 \end{equation*} \\ + \\ \begin{equation*} 4x-5y=8 \end{equation*} \\ ---------------------- \\ -3y=0 \end{gathered}[/tex]Therefore the value of the constant is -4.
Use a graphing utility to find or to approximate the x-intercepts of the graph of the function.y=3x2−8x+
Answer:
The x-intercepts are x = 0.6667, 2
Explanation:
The graph of the function y = 3x² - 8x + 4 is:
Then, the x-intercepts are the points where the graph crosses the x-axis.
So, an approximation for the x-intercepts are x = 0.6667 and x = 2
Therefore, the answer is:
The x-intercepts are x = 0.6667, 2
This statics question has me stumped if you could hope me I would rlly appreciate it! Have a nice night :).
Spinner A
Sample space = 1,2,3,4,5,6
Number of total outcome = 6
Odd numbers = 1,3,5
Number of odd numbers = 3
[tex]\text{Probability = }\frac{n\text{umber of required outcomes}}{\text{total number of possible outcome}}[/tex]Probability of spinning an odd number = 3/6 = 1/2
Spinner B
Sample space = yellow, brown, red
Number of total outcome = 3
Not yellow = brown, red
Number of not yellow = 2
Probability of not yellow = 2/3
Since the two spinners are independent events, then the probability that you spin an odd number and not yellow are multiplied together
Thus we have,
Probability of spinning an odd number X Probability of not yellow
[tex]\frac{1}{2}\text{ X }\frac{2}{3}\text{ = }\frac{2}{6}[/tex]Final answer is 1/3.
The data are at the ordinal level of measurement.What is wrong with the given calculation?Identify the level of measurement of the data, and explain what is wrong with the given calculation.In a set of data, blood lead levels are represented as 10 for low, 20 for medium, and 30 for high. The average (mean) of the 595 blood lead levels is 25.4.A. One must use a different method to compute the average (mean) of such data.B. Such data should not be used for calculations such as an average (mean).C. The true average (mean) is 18.2.D. There is nothing wrong with the given calculation.
Answer: Blood lead levels are represented as 10 for low, 20 for medium, and 30 for high.
The average (mean) of the 595 blood lead levels is 25.4, assuming that each blood lead level is also known, then:
[tex]A=\frac{\sum_i^{595}x_i}{595}=25.4\Rightarrow\text{ Average}\rightarrow(1)[/tex]As (1) is the perfectly reasonable mathematical approach to calculating the average, however, the blood lead levels are reported in 10 20 30 levels only, therefore, the answer is:
[tex]\text{ Such data should not be used for calculations such as an average \lparen mean\rparen}\Rightarrow\text{ Option\lparen B\rparen}[/tex]Or the Option(B).
Train A travels 30 miles in 20 minutes at a constant speed. Train B travels 20 miles in 15 minutes at a constant speed. Redo Which train is going faster? Circle your answer and show how you figured it out below, Train A Train B
Write a quadratic inequality represented by the graph.
The quadratic inequality represented by the graph is y > -x².
What is meant by quadratic inequality?Simply put, an equation of the type with the highest degree of two and no equal sign is known as a quadratic inequality. There is a technique for resolving quadratic inequalities called the wavy curve approach. It is the same to solve quadratic equations as it is solving quadratic inequalities. When plotted, quadratic inequalities show a parabola, much like quadratic equations do. Quadratic inequalities can be solved to provide a variety of solutions. For instance, the quadratic equation x²+6x+5=0 has two solutions: x² + 6 x + 5 = 0 and x² + 6x + 5 = 0. A second-degree equation with a quadratic inequality substitutes an inequality sign for an equal sign. The quadratic inequalities x- 6x - 16 0, 2x² - 11x + 12 > 0, x² + 4> 0, and x² - 3x + 20 are some examples.
From the graph, we can see that it is a parabola with vertex points (0,-9)
Thus, y= -3² is the equation at the vertex and the equation of the parabola will be y= -x².
The graph is an increasing function, so the inequality will be
y > - x²
To know more about quadratic inequality, visit:
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A bag contains:• 3 red marbles• 2 orange marbles• 1 yellow marble• 4 green marblesRico will randomly choose a marble. Then he will put itback and randomly choose another marble. What isthe probability that he will choose a red and then anorange marble?
The probability is given by the following formula:
Probability = number of favorable outcomes / total number of outcomes
The total number of outcomes is 10, 3 of the initial number of marbles are red and 2 of them are orange.
The probability of getting a red marble in the first draw is:
Probability = 3/10
The probability of getting an orange marble in the second draw is:
Probability = 2/10 = 1/5
the probability that he will choose a red and then an orange marble can be calculated by multiplying the probabilities that we found, then we get:
Probability = 3/10 × 1/5 = 3/150 = 1/50
Then, the answer is 1/50
Learning Diagnostic Analytics Recommendations Skill plans Social stu La Language arts All Science Math Eighth grade ) T.11 Volume of cones YYR A cone has a height of 14 meters and a diameter of 12 meters. What is its volume? Use A 3.14 and round your answer to the nearest hundredth. cubic meters Submit
The volume of a cone is calculated as follows:
[tex]V=\pi\cdot r^2\cdot\frac{h}{3}[/tex]where r is the radius and h is the height of the cone.
Given that the diameter of the cone is 12 meters, then its radius is 12/2 = 6 meters
Substituting into the equation with h = 14 m, and r = 6 m, we get:
[tex]\begin{gathered} V=3.14\cdot6^2\cdot\frac{14}{3} \\ V=3.14\cdot36\cdot\frac{14}{3} \\ V=527.52m^3 \end{gathered}[/tex]Need help with this exercise. It’s from a review the real test is next week need more explanation so I already know what to do on the test.
ANSWER
Options 1 and 4
EXPLANATION
First, let us find the length of the third side of the right triangle. To do this apply the Pythagoras theorem.
Let the length of the third side of the triangle be x.
It implies that:
[tex]\begin{gathered} x^2+8^2=17^2 \\ x^2=17^2-8^2 \\ x^2=289-64=225 \\ x=\sqrt[]{225} \\ x=15 \end{gathered}[/tex]Now, we can find the value of sinA, tanA, and sinC.
According to trigonometric ratios, SOHCAHTOA, we have that:
[tex]\begin{gathered} \sin A=\frac{\text{opposite}}{\text{hypotenuse}} \\ \tan A=\frac{\text{opposite}}{\text{adjacent}} \\ \sin C=\frac{\text{opposite}}{\text{hypotenuse}} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \sin A=\frac{15}{17} \\ \tan A=\frac{15}{8} \\ \sin C=\frac{8}{17} \end{gathered}[/tex]Hence, the correct options are options 1 and 4.
10 Students share 1 hour to give their science reports
Answer:
1/10
Explanation:
If 10 students share 1 hour, we need to divide 1 hour into 10 students. So, the fraction is
[tex]\frac{1\text{ hour}}{10\text{ students}}=\frac{1}{10}[/tex]It means that each student has 1/10 hour to give the science report.
I need help with this questionthe question to this question is below is a graph of a logarithmic function, identify it key characteristics. match accordingly
The answers to the problem :
[tex]\begin{gathered} 1.\text{ Domain : x >-6} \\ 2\text{ Range : -}\infty\text{ to +}\infty \\ 3.\text{ Aymptote : x = -6} \\ 4\text{. Transformation : left 6, down 1} \\ 5.\text{ End behaviour : As x approaches }\infty,\text{ f(x) approaches }\infty.\text{ As x approaches -6, f(x) approaches -}\infty \\ 6.\text{ x-intercept : (-4,0)} \end{gathered}[/tex]Find the difference. (10m+ 3) - (4m-2) O A. 14m-1 OB. 6m+ 5 O C. 6m-1 D. 14m + 5
(10m + 3) - (4m -2)
Firstly, use the negative sign to open the parenthesis
(10m + 3) -1 x 4m -1 x (-2)
minus x minus = plus
(10m + 3) -4m + 2
10m + 3 - 4m + 2
Collect the like terms
10m - 4m + 3 + 2
m(10-4) + 5
m(6) + 5
6m + 5
The answer is OPTION B
Each person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of ancestors a person has, going back five generations? twelve generations?
62
8190
1) Gathering the data:
So Adding the 2 + 4 +8 +16+32 Then we can write that up to the 5th generation each person has 62 ancestors.
2) Or we can check. Let's write out considering that the ratio is 2 and the first term is 2 since the person per se is not counted.
[tex]\begin{gathered} S=\frac{a_1(1-r^n)}{1-r} \\ S_5=\text{ }\frac{2(1-2^5)^{\square}}{1-2}=62 \\ S_{12}=\frac{2(1-2^{11})}{1-2}=8190 \end{gathered}[/tex]3) Hence, each person has counting back up to the 5th generations 62 ancestors and 4094 when it comes to 11 generations
Triangle ABC shown below has m B = 38°, a = 8, and c = 16. Find the area of the triangle. Round your answer to the nearest tenth and do not include units in your answer.
The area of triangle is determined as
[tex]A=\frac{1}{2}a\times c\times\sin B[/tex][tex]A=\frac{1}{2}\times8\times16\times\sin 38=64\sin 38^{\circ}[/tex][tex]A=39.4\text{ squnit}[/tex]Thus the area of triangle is 39.4 sq.unit.
Solve the equation.g−37=27g− 73 = 72 g, minus, start fraction, 3, divided by, 7, end fraction, equals, start fraction, 2, divided by, 7, end fractiong=g=g, equals
ANSWER
[tex]\text{ g = }\frac{5}{7}[/tex]EXPLANATION
We want to solve for g in:
[tex]g\text{ - }\frac{3}{7}=\frac{2}{7}[/tex]Collect like terms by moving 3/7 to the right hand side:
[tex]\begin{gathered} g\text{ = }\frac{2}{7}+\frac{3}{7} \\ \Rightarrow\text{ g = }\frac{5}{7} \end{gathered}[/tex]