The first question
[tex]\frac{5x^2-28x-12}{x-6}[/tex]can be rewritten by polynomial division since the quadratic polynomial is not easy to factorize by inspection
The 2nd question
[tex]\frac{x^2+11x+28}{x+4}=\frac{(x+7)(x+4)}{x+4}=x+7[/tex]so, it can be solved by inspection.
The 3rd question
[tex]\frac{6x^2+2x+7}{3x-2}[/tex]can be rewritten by polynomial division since the quadratic polynomial is not easy to factorize by inspection
Finally, 4th question
[tex]\frac{x^2-x-35}{x-6}[/tex]can be rewritten by polynomial division.
Please help!! slope-intercept form!!
Answer: y=1x+4
Step-by-step explanation: the b (y-intercept) is 4 and when you go up 1/1 (1) it crosses the lines
The following chart below represents the bedtimes of 100 students at Waller Junior High in a recent survey Number of Students Bedtime 8:00 PM 22 8.30 PM 17 9:00 PM 36 9:30 PM 25 If all 750 students at WJH were surveyed, what is the best prediction of the number of students who would have a bedtime of 9:00 PM in
Answer
The predicted number of students with bedtime of 9:00 PM
= 270 students
Explanation
For surveying and sampling, the fraction of a particular case in the sample is generalized for the entire population to predict that case for the population.
So, if we want the number of students who would have a bedtime of 9:00 PM, we first find the percentage of students with bedtime of 9:00 PM in the sample.
Number of students with bedtime of 9:00 PM in the survey = 36
Total number of students in the survey = 22 + 17 + 36 + 25 = 100
Percentage of students with bedtime of 9:00 PM in the survey = (36/100) = 0.36
So, in the population of 750 students,
The predicted number of students with bedtime of 9:00 PM = (0.36) (750) = 270 students
Hope this Helps!!!
Use the drawing tools to form the correct answers on the graph Consider function f(x)= ( 1 2 )^ x ,x<=0\\ 2^ x ,&x>0 Complete the table of values for function and then plot the ordered pairs on the graph. - 2 -1 1 2 f(x)
See explanation and graph below
Explanation:For x less than or equal to zero, we would apply the function f(x) = (1/2)^x
For x greater than zero, we would apply the function f(x) = 2^x
when x = - 2 (less than 0)
This falls in the 1st function
[tex]\begin{gathered} f(-2)\text{ = (}\frac{1}{2})^{-2} \\ f(-2)=\frac{1}{(\frac{1}{2})^2}\text{ = 1}\times\frac{4}{1} \\ f(-2)=2^2\text{ = 4} \end{gathered}[/tex]when x = -1 (less than 0)
This falls in the 1st function
[tex]\begin{gathered} f(-1)\text{ = (}\frac{1}{2})^{-1} \\ f(-1)\text{ = }\frac{1}{(\frac{1}{2})^1}\text{ = 2} \end{gathered}[/tex]when x = 0 (equal to 0)
This falls in the 1st function
[tex]\begin{gathered} f(0)\text{ = (}\frac{1}{2})^0 \\ f(0)\text{ = 1} \end{gathered}[/tex]when x = 1 (greater than 0)
This falls in the 2nd function
[tex]\begin{gathered} f(1)=2^1 \\ f(1)\text{ = 2} \end{gathered}[/tex]when x = 2 (greater than 0)
THis falls in the 2nd function
[tex]\begin{gathered} f(2)\text{ = }2^2 \\ f(2)\text{ = 4} \end{gathered}[/tex]Plotting the graph:
The end with the shaded dot reresent the function with equal to sign attached to the inequality [f(x) = (1/2)^x].
The end with the open dot represent the function without the equal to sign [f(x) = 2^x)
What is the solution to -1-7? + 4 5 6 9 10 2 -10-9-8-7 6-5- 4 -3
Solution
To find the best expression, we need to first approximate the values before dividing it
[tex]\begin{gathered} 6\frac{3}{4}=6.75 \\ \\ We\text{ approximate to get} \\ 6.75\cong7 \end{gathered}[/tex]Similarly
[tex]\begin{gathered} 1\frac{2}{3}=1.6666666666667 \\ \\ we\text{ approximate to get} \\ \\ 1.6666667\cong2 \end{gathered}[/tex]Therefore, the answer is
[tex]7\div2[/tex]101987006HR5SrOL4.3ON21.1 2 345 6 78 9 10Which of these statements are true for the scatter plot? Select all that apply.The scatter plot shows a negative association.The scatter plot shows a linear association.The scatter plot shows a positive association.The scatter plot shows no association.
The scatter plot shows a linear association.
The scatter plot shows a positive association.
Which of the following is the closet approximation to 3√20?A) 3B) 5C) 2D) 4
The given expression is:
[tex]\sqrt[3]{20}[/tex]This can also be written as:
[tex]20^{(\frac{1}{3})}[/tex]The result = 2.71
Since 7 is greater than 5, it will become 0 and add 1 to 2 to become 3
Therefore, the closest approximation is 3
1.Given the graph, find the following:A: Identify the slope of the lineB.Identify the y-intercept of the lineC.Identify the x-intercept of the lineD. Write the equation of the line in slope-intercept form (y = mx+b)
A.
The slope of a line is the rate of change of the dependent variable (y) with respect to the independent variable (x).
Notice that for each increase of 3 units in the variable x, the variable y decreases 2 units. Then, the change in y is -2 when the change in x is 3. Then, the rate of change is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{-2}{3}[/tex]B.
The y-intercept of a line is the value of y in which the line crosses the Y-axis. In this case, the line crosses the Y-axis at y=4. Then, the y intercept is:
[tex]4[/tex]C.
Similarly, the x-intercept is the value of x in which the line crosses the X-axis. In this case, we can see that the x-intercept is:
[tex]6[/tex]D.
Since the slope m is equal to -2/3 and the y-intercept b is equal to 4, then the equation of the line is:
[tex]y=-\frac{2}{3}x+4[/tex]can someone please help me find the answer to the following?
Answer:
1077.19 ft
Explanation:
Using the depression angle, we get that one of the angles of the formed triangle is also 18° because they are alternate interior angles, so we get:
Now, we can relate the distance x, the angle of 18°, and the height of the tower using the trigonometric function tangent, so:
[tex]\begin{gathered} \tan 18=\frac{Opposite}{Adjacent} \\ \tan 18=\frac{350}{x} \end{gathered}[/tex]Now, solving for x, we get:
[tex]\begin{gathered} x\cdot\tan 18=x\cdot\frac{350}{x} \\ x\cdot\tan 18=350 \\ \frac{x\cdot\tan18}{\tan18}=\frac{350}{\tan 18} \\ x=\frac{350}{\tan 18} \end{gathered}[/tex]Using the calculator, we get that tan(18) = 0.325, so x is equal to:
[tex]x=\frac{350}{0.325}=1077.19\text{ }ft[/tex]Therefore, the forest ranger is at 1077.19 ft from the fire.
write a ratio that is equivalent to 12:36 using the collums for 2 and 6
The given ratio is 12:36, which can be expressed as a fraction 12/36. An equivalent expression to this one can be obtained by simplifying
[tex]\frac{12}{36}=\frac{6}{18}[/tex]Therefore, the answer is 6/18.write an equation of the circle that passes through (2, 8) with center (-3 4)
we have, the equation is of the form
[tex](x-h)^2+(y-k)^2=r^2[/tex]then, first calculate the radius of the circle
[tex]\begin{gathered} r=\sqrt[]{(x2-x1)^2+(y2-y1)} \\ r=\sqrt[]{(14-14)^2+(-8-1)^2} \\ r=\sqrt[]{0+(-9)^2} \\ r=\sqrt[]{81} \\ r=9 \end{gathered}[/tex]so, (h,k) is the center and the equation is
[tex]\begin{gathered} (x-14)^2+(y-(-8))^2=9^2 \\ (x-14)^2+(y+8)^2=81 \end{gathered}[/tex]1. d decreased by three
We need to write the expression:
d decreased by three
So. the new value will be less than the old value by 3
The word decreased mean the negative sign
So, the expression will be:
[tex]d-3[/tex]
the measure of an interior angle of an equilateral triangle is given as 3n-6. solve for the value of nA. 22B. 60C.6D. 2
11. A map is drawn so that 2 inches represents 700 miles. If the distance betweentwo cities is 3850 miles, how far apart are they on the map?a. 5.5 inchesb. 11 inchesc. 22 inchesd. 6 inchese. 12 inches
Given:
• 2 inches represents 700 miles on the map.
,• Actual distance between two cities = 3850 miles
Let's find the distance on the map.
Let's first find how many miles 1 inch represent.
We have:
[tex]\frac{700}{2}=350\text{ miles}[/tex]This means on the map, 1 inch represent 350 miles.
Now, to find the distance between the two cities on the map, we have:
[tex]\frac{3850}{350}=11\text{ inches}[/tex]Therefore, the distance between the two cities on the map is 11 inches.
ANSWER:
b. 11 inches
Find the length of the leg x. enter the exact value, not a decimal approximation x1210x=
We can solve for the value of x using pythagorean theorem
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse ( in this case is 15) and a, b are the other legs of the triangle ( in this case is 8 and x).
Let's substitute the given values to the formula
[tex]\begin{gathered} c^2=a^2+b^2 \\ 15^2=8^2+x^2 \\ 225=64+x^2 \\ x^2=225-64 \\ x^2=161 \\ x=12.69 \end{gathered}[/tex]Now please follow this solution to solve for x in:
1. According to the story of Pythagoras's discoveries and your own exploration during the lesson,
when does the relationship a² + b² = c² hold true?
The given relationship using the Pythagorean theorem holds true for a right-angled triangle.
We are given a mathematical relationship using the Pythagorean theorem. The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between the three sides of a right triangle in Euclidean geometry. The equation is given below.
a² + b² = c²
We need to describe the situation when this relationship holds true. The variables "a", "b", and "c" represent the sides of a triangle. The Pythagorean theorem is applicable to a right-angled triangle. It states that the sum of the squares of the base and the perpendicular is equal to the square of the hypotenuse.
Here a, b, and c denote the lengths of the base, the perpendicular, and the hypotenuse of the triangle, respectively.
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Complete the table for y = 2x + 2 and graph the resulting line.
Answer
The table is
x | y
-2 | -2
0 | 2
2 | 6
4 | 10
6 | 14
The graph is then
Explanation
In the absence of the table, I will use a couple of values for x to obtain corresponding values of y.
Then, these points will be marked on the graph and the line connecting the points is drawn.
y = 2x + 2
when x = -2
y = 2x + 2
y = 2(-2) + 2
y = -4 + 2
y = -2
The point will then be (-2, -2)
when x = 0
y = 2x + 2
y = 2(0) + 2
y = 0 + 2
y = 2
The point will then be (0, 2)
when x = 2
y = 2x + 2
y = 2(2) + 2
y = 4 + 2
y = 6
The point will then be (2, 6)
when x = 4
y = 2x + 2
y = 2(4) + 2
y = 8 + 2
y = 10
The point will then be (4, 10)
when x = 6
y = 2x + 2
y = 2(6) + 2
y = 12 + 2
y = 14
The point will then be (6, 14)
The full table and graph will then be presented under 'Answer'.
Hope this Helps!!!
Which of the qqq-values satisfy the following inequality?6−3q≤16−3q≤16, minus, 3, q, is less than or equal to, 1Choose all answers that apply:Choose all answers that apply:(Choice A)Aq=0q=0q, equals, 0(Choice B)Bq=1q=1q, equals, 1(Choice C)Cq=2q=2q, equals, 2
Given -
6 - 3q ≤ 1
To Find -
The q-values that satisfy inequality =??w
Step-by-Step Explanation - ion
We will check for each of the given values;
A) q = 0
Putting q = 0, we get:
6 - 3(0) ≤ 1
6 ≤ 1
But, Six is greaterr than onee
So, this is the incorrect option.
B) q = 1
Putting q = 1, we get:
6 - 3(1) ≤ 1
3 ≤ 1
But, three is greater than one
So, this is the incorrect option.
C) q = 2
Putting q = 2, we get:
6 - 3(2) ≤ 1
0 ≤ 1
zero is less than one.
So, this is the correct option.
Final Answer -
Option (C) q = 2
which of the following is equivalent to the expression below? In(e^7)
Answer: C. 7
Explanation
When the exponent of a natural logarithm has an exponent, we can do the following:
[tex]\ln(e^7)=7\ln(e)[/tex]Additionally, we are given a natural logarithm, and the base for the natural logarithm is the mathematical constant e. When the argument of the logarithm is equal to the base, then it is equal to 1:
[tex]7\ln(e)=7\cdot1[/tex][tex]=7[/tex]ty-qy+p=r solve for y
A robot can complete 10 tasks in hour. Answer in fraction form.How many tasks can the robot complete in 1 hour?How long does it take the robot to complete one task?hoursIf you have a mixed number put a space between the whole number and fraction. Ex 7=7 1/2tasks
Hello!
We know that the robot can complete 10 tasks in 3/4 hour.
To solve this exercise, we can use the rule of three, look:
How many tasks can the robot complete in 1 hour?[tex]\frac{\frac{3}{4}h\rightarrow10\text{ tasks}}{1h\rightarrow x\text{ tasks}}[/tex]So, we have:
[tex]\begin{gathered} \frac{3}{4}x=10 \\ \\ x=\frac{10}{1}\div\frac{3}{4}\rightarrow\frac{10}{1}\times\frac{4}{3}=\frac{40}{3} \\ \\ \end{gathered}[/tex]Let's write it as a mixed number:
Answer:
[tex]13\text{ }\frac{1}{3}\text{ tasks}[/tex]How long does it take the robot to complete one task?We'll solve it in a similar way, look:
[tex]\frac{\frac{3}{4}h\operatorname{\rightarrow}10\text{ tasks}}{x\text{ }h\operatorname{\rightarrow}1\text{ task}}[/tex][tex]\begin{gathered} 10x=\frac{3}{4} \\ \\ x=\frac{3}{4}\div\frac{10}{1}\rightarrow\frac{3}{4}\times\frac{1}{10}=\frac{3}{40}\text{ hours} \end{gathered}[/tex]Answer:
[tex]\frac{3}{40}\text{ hours}[/tex]Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=x−−√+4 , g(x)=x2+1
We have a case of composite functions, we must evaluate or replace one function as x value of the other one. In other words and doing the calculations
[tex]\begin{gathered} f(g(x))=f(x^2+1)=\sqrt{x^2+1}+4 \\ g(f(x))=(\sqrt{x})^2+8\sqrt{x}+16+1=x+8\sqrt{x}+17 \end{gathered}[/tex]Thus, the answer to the exercise is
f(g(x))=√(x^2+1) +4
g(f(x))=x+8√x+17
what is 10+5 rounded to the nearest thousand
the given expression is,
10 + 5 = 15
now we will round off it to the nearest
2. Given the degree and zero of a polynomial function, identify the missing zero and then find the standard form of the polynomial
Degree: 2; zero: -7 + 2i
The missing zero is:
+
i
The expanded polynomial is:
The expanded quadratic equation with real coefficients is y = x² + 14 · x + 45.
How to determine the least polynomial that contains a given root
In this problem we need to determine the expanded quadratic equation with real coefficients such that one of its roots is - 7 + i 2. According with the quadratic formula, quadratic equations can have two conjugated complex roots, that is:
r₁ = α + β, r₂ = α - β
Then, the complete set of roots of the quadratic equation are r₁ = - 7 + i 2 and r₂ = - 7 - i 2. Then, the factor form of the polynomial is:
y = (x + 7 - i 2) · (x + 7 + i 2)
y = x · (x + 7 + i 2) + (7 - i 2) · (x + 7 + i 2)
y = x² + 7 · x + i 2 · x + (7 - i 2) · x + 7 · (7 - i 2) + i 2 · (7 - i 2)
y = x² + 7 · x + i 2 · x + 7 · x - i 2 · x + 49 - i 14 + i 14 - i² 4
y = x² + 14 · x + 45
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Hi i need help with unit rate fractions and ill show an example i need to have this figured out by thurday for a test and i have no clue so pls help
To find the rate in teaspoons per cup we divide the number of teaspoons by the cups:
[tex]\frac{4}{\frac{2}{3}}=\frac{12}{2}=6[/tex]Therefore, the unit rate is 6 teaspoons per cup.
7. Solve 3(x-4)=-5 for x.
Explantion:
3(x-4) = -5
Expand the bracket:
3x -12 = -5
Collect like
Find the zeros of the function. You may want to view the graph of the function to help you identifythe real root, then use it to depress the polynomial & find the remaining roots.I
We must find the zeros of the following function:
[tex]f(x)=x^3-x^2-11x+15.[/tex]1) First, we plot a graph of the function:
From the graph, we see that the function crosses the x-axis at x = 3, so x = 3 is one of the zeros of the function.
2) Because x = 3 is a zero of the function, we can factorize the function in the following way:
[tex]f(x)=x^3-x^2-11x+15=(x^2+b\cdot x+c)\cdot(x-3)\text{.}[/tex]To find the coefficients b and c, we compute the product of the parenthesis and then we compare the different terms:
[tex]f(x)=x^3-x^2-11x+15=x^3+(b-3)\cdot x^2+(c-3b)\cdot x-3c.[/tex]To have the same expressions at both sides of the equality we must have:
[tex]\begin{gathered} -3c=15\Rightarrow c=-\frac{15}{3}=-5, \\ b-3=-1\Rightarrow b=3-1=2. \end{gathered}[/tex]So we have the following factorization for the function f(x):
[tex]f(x)=(x^2+2x-5)\cdot(x-3)\text{.}[/tex]3) To find the remaining zeros, we compute the zeros of:
[tex](x^2+2x-5)\text{.}[/tex]The zeros of this 2nd order polynomial are given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2a},[/tex]where a, b and c are the coefficients of the polynomial. In this case we have a = 1, b = 2 and c = -5. Replacing these values in the formula above, we get:
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Identify the underlined place and 27.3856. Then round the number to that place.
Based on the positiion of the underlined decimal places, the underlined number is in the hundredths place.
Rounding it off, next to 8 in the hundredths place is 5 in the thousandths place.
If the number is 5 or greater, we add 1 to the previous decimal place therefore it is rounded to 27.39
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 16 gallons of fuel, the airplane 2104. When carrying 48 gallons of fuel, it weighs 2312. How much does the airplane weigh if it is carrying 66 gallons of fuel?
Let 'y' be the weight of the airplane corresponding to when the amount of fuel is 'x'.
Given that the airplane weighs 2104 when fuel is 16 gallons, this can be represented as the ordered pair,
[tex](16,2104)[/tex]Also, given that the airplane weighs 2312 when fuel is 48 gallons.The corresponding ordered pair will be,
[tex](48,2312)[/tex]It is mentioned that there is a linear relationship between the amount of fuel (x), and the weight of airplane (y).
Consider that the equation of a straight line passing through two given points is given by,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot(x_2-x_1)[/tex]As per the given problem,
[tex]\begin{gathered} (x_1,y_1)=(16,2104) \\ (x_2,y_2)=(48,2312) \end{gathered}[/tex]Substitute the values,
[tex]\begin{gathered} y-2104_{}=\frac{2312-2104}{48-16}\cdot(x-16) \\ y-2104_{}=\frac{13}{2}\cdot(x-16) \\ y-2104=\frac{13}{2}x-104 \\ y=\frac{13}{2}x-104+2104 \\ y=\frac{13}{2}x+2000 \end{gathered}[/tex]At the instant when the fuel is 66 gallons,
[tex]x=66[/tex]The corresponding weight of airplane is calculated as,
[tex]\begin{gathered} y=\frac{13}{2}(66)+2000 \\ y=429+2000 \\ y=2429 \end{gathered}[/tex]Thus, the airplane weighs 2429 if it is carrying 66 gallons of fuel.
1. ABC Bank offers a certificate of deposit (CD), where you deposit money and are required to leaveit in the account for a set amount of time. You will be penalized if you withdraw your money fromit early. Suppose you want to deposit $6,000 in a 5-year CD where interest is accrued daily (1 year= 365 days).(a) How much money will you have in the account after 5 years if the APR is 2.12%? Round yourfinal answer to 2 decimals.(b) What is the annual percentage yield (APY) on this account? Round your final answer to 2decimals.
To calculate the ampount of money in the account after 5 years, we will use the formula:
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]where A is the final amount
P is the initial amount or principal
r is the rate
n is the number of times the interest is applied
t is the time in years
From the question,
P = $6000 r = 2.12/100 = 0.0212 t= 5 n=365
substitute the values ibto the formula and evaluate
[tex]A=6000(1+\frac{0.0212}{365})^{365\times5}_{}[/tex][tex]A=6000(1+\frac{0.0212}{365})^{1825}[/tex][tex]A=6670.91[/tex]The amount is $6670.91
b)
To find the annual percentage yield (APY) on this account, we will use the formula:
[tex]APY=(1+\frac{r}{n})^n-1[/tex]Write 6.546 x 10 ^-6 in standard notation
The given number in scientific notation is:
[tex]6.546\times10^{-6}[/tex]In order to write it in standard notation, first take a look at the power: -6.
As it is a negative number, it means we need to move the dot to the left 6 units.
Therefore, we need to fill the blank places with zeros:
[tex]6.546\times10^{-6}=0.000006546[/tex]