Express (5/6x + 4) 2 as trinomial in simplest form (2 is an exponent)
Answers
We are given the expression (5/6x + 4)^2 and we are asked to express it as a trinomial in the simplest form.
To do this, we will be using the FOIL method. FOIL stands for First-Outer-Inner-Last.
The product will then be:
[tex]\begin{gathered} (\frac{5}{6}x+4)^2=(\frac{5}{6}x+4)(\frac{5}{6}x+4) \\ \\ (\frac{5}{6}x+4)^2=(\frac{5}{6}x)^2+(\frac{5}{6}x)(4)+(4)(\frac{5}{6}x)+4(4) \\ \\ (\frac{5}{6}x+4)^2=\frac{25}{36}x^2+\frac{10}{3}x+\frac{10}{3}x+16 \\ \\ (\frac{5}{6}x+4)^2=\frac{25}{36}x^2+\frac{20}{3}x+16 \end{gathered}[/tex]So, the final answer is 25/36 x^2 + 20/3 x + 16.
Related Questions
Given the equation of the circle, identify the center and radius (x + 1) ^ 2 + (y - 1) ^ 2 = 36
Answers
The form of the equation of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex](h, k) is the center
r is the radius
Let us compare it with the given equation to find the center and the radius
[tex](x+1)^2+(y-1)^2=36[/tex]From the comparing
h = -1
k = 1
r^2 = 36
Find the square root of 36 to get r
[tex]\begin{gathered} r=\sqrt[]{36} \\ r=6 \end{gathered}[/tex]The center is (-1, 1) and the radius is 6
If the graph of f(x) passes through the point (2, -1), then the graph of g(x) = -f(x - 2) + 4must pass through the point whose r coordinate is and whose y coordinate is
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If the graph of f(x) passes through the point (2, -1), then the graph of g(x) = -f(x - 2) + 4must pass through the point whose r coordinate is and whose y coordinate is
In this problem the transgormation of f(x) ------> g(x) is equal to
(x,y) --------> (x+2,y+4)
so
(2,-1) -------> (2+2,-1+4)
(2,-1) -------> (4,3)
but remembe
a toy car is a scale model of a real car
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If the two objects are on the same scale, then as the toy size increases the real size should increase on the same proportion. This means that these two variables, toy size and real car size, are directly proportional and we have to solve the rule of three on the following manner:
[tex]\begin{gathered} \frac{3}{x}=\frac{120}{5} \\ 120\cdot x=3\cdot5 \\ 120\cdot x=15 \\ x=\frac{15}{120}=\frac{1}{8} \end{gathered}[/tex]The door handle toy size is 1/8 of an inch, which is equal to 0.125 inches.
The sphere is _____ cubic centimeters bigger than the cube. (Round to the nearest cubic centimeter.)
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ANSWER
The sphere is 10762 cubic centimeters bigger than the cube.
EXPLANATION
We want to find the difference in the volumes of the sphere and the cube.
To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.
The volume of a sphere is given as:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r = radius
The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:
[tex]\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot15^3 \\ V\approx14137\operatorname{cm}^3 \end{gathered}[/tex]The volume of a cube is given as:
[tex]V=s^3[/tex]where s = length of the side
The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:
[tex]\begin{gathered} V=15^3 \\ V=3375\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the difference in the volumes of the sphere and cube is:
[tex]\begin{gathered} V_d=V_s-V_c \\ V_d=14137-3375 \\ V_d=10762\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the sphere is 10762 cubic centimeters bigger than the cube.
URGENT I NEED IT NOWW!! What is 7 1/2-4 3/4
Answers
The given expression is
[tex]7\frac{1}{2}-4\frac{3}{4}[/tex]First, we transform each mixed number into a fraction
[tex]\begin{gathered} 7\frac{1}{2}=\frac{7\cdot2+1}{2}=\frac{14+1}{2}=\frac{15}{2} \\ 4\frac{3}{4}=\frac{4\cdot4+3}{4}=\frac{16+3}{4}=\frac{19}{4} \end{gathered}[/tex]Then, we subtract
[tex]\frac{15}{2}-\frac{19}{4}=\frac{15\cdot4-2\cdot19}{2\cdot4}=\frac{60-38}{8}=\frac{22}{8}=2\frac{3}{4}[/tex]Hence, the answer is 2 3/4.200023.14 in scientific notation (round to two digts after the decimal
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we convert 200023.14 to scientific notation
we count the number of movement after the decimal point towards the left to the first number
we moved the point 5 times. It becomes:
2.0002314 × 10 raised to the number of times point was moved
[tex]=2.0002314\times10^5[/tex][tex]\begin{gathered} \text{Rounding to two digits after the decimal point:} \\ =2.00\times10^5 \end{gathered}[/tex]A coffee shop receives a box of cups and lids. The box weighs less than 42 ounces. Each cup weighs 0.5 ounce, and each lid weighs 0.25 ounce.
Choose the inequality that shows the possible contents of the box.Use c for
the number of lids
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The inequality that shows the possible contents of the box is 0.5c + 0.25l < 42
What is inequality?Inequality, defined as "the state of not being equal, particularly in status, rights, and opportunities," is a central concept in social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.
The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It's an example of inequity. This means that the left part, 5x 4, is greater than the right part, 2x + 3. We'll be looking for x values for which the inequality holds true.
The definition of inequality is that two things are not equal.
One of the things could be less than, greater than, less than or equal to the other things, or greater than or equal to the other things.
p ≠ q means that p is not equal to q
p < q means that p is less than q
p > q means that p is greater than q
p ≤ q means that p is less than or equal to q
p ≥ q means that p is greater than or equal to q
Therefore, The inequality that shows the possible contents of the box is 0.5c + 0.25l < 42
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Given the following probabilities, algebraically determine if Events A and B are:• mutually exclusive or non-mutually exclusive• independent or dependent.P(A) =P(B) 0.75P(A U B)'U0.15
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We know that:
[tex]\begin{gathered} P(A\cup B)^{\prime}=1-P(A\cup B) \\ P(A\cup B)^{\prime}=1-P(A)+P(B)-P(A\cap B) \end{gathered}[/tex]Plugging the values given we have that:
[tex]\begin{gathered} 0.15=1-0.8+0.75-P(A\cap B) \\ P(A\cap B)=1-0.8+0.75-0.15 \\ P(A\cap B)=0.8 \end{gathered}[/tex]Now, since the probability of the intersection is not zero this means that the events are non-mutually exclusive.
4(2x + 3) = 3x + 3 + 2x
Answers
We operate as follows:
[tex]4(2x+3)=3x+3+2x\Rightarrow8x+12=5x+3[/tex][tex]\Rightarrow3x=-9\Rightarrow x=-3[/tex]The value of x is -3.
A store's sales grow according to the recursive rule Pr = Pn-1 7 12000, with initial sales Po = 27000.(a) Calculate P1 and P2.P1 = $ 39000P2 = $ 51000(b) Find an explicit formula for Pn.Pn - 27000 + 12000n(c) Use the explicit formula to predict the store's sales in 10 years.Pio = $ 147,000(d) When will the store's sales exceed $97,000? Round your answer to the nearest tenth of a year.Afteryears.Enter an integer or decimal number (more..
Answers
Given that,
The equation is,
[tex]P_n=P_{n-1}+12000[/tex]withg initial sales,
[tex]P_0=27000[/tex]a) To calculate P1 and P2
Put n=1 in the given equation
[tex]P_1=P_0+12000[/tex]Substitute the values, we get,
[tex]=27000+12000=39000[/tex]d)To find the time (n) store's sales exceed $97,000
Let Pn=97000
we get,
[tex]97000=27000+12000n[/tex][tex]12000n=97000-27000[/tex][tex]n=5.8[/tex]Answer is: 5.8 years
According to the graph, what is the value of the constant in the equation below?A.2B.0.667C.3D.1.5
Answers
Solution
- The constant being asked for is the slope of the graph.
- The formula for finding the slope of a graph is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ where, \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the points on the line} \end{gathered}[/tex]- The points on the graph that we will use are:
[tex]\begin{gathered} (x_1,y_1)=(2,3) \\ (x_2,y_2)=(4,6) \end{gathered}[/tex]- Thus, we can find the constant as follows:
[tex]\begin{gathered} m=\frac{6-3}{4-2} \\ \\ m=\frac{3}{2}=1.5 \end{gathered}[/tex]Final Answer
The constant(slope) is 1.5 (OPTION D)
Given function g, which is defined by g(x)=x3−x, what is the value of g(3)?Enter a number in the box.
Answers
Given:
There are given the function:
[tex]g(x)=x^3-x[/tex]Explanation:
To find the value of g(3), we need to put 3 for x into the given function:
So,
From the function:
[tex]\begin{gathered} g(x)=x^{3}-x \\ g(3)=(3)^3-3 \end{gathered}[/tex]Then,
[tex]\begin{gathered} g(3)=(3)^3-3 \\ g(3)=27-3 \\ g(3)=24 \end{gathered}[/tex]Final answer:
Hence, the value is 24.
use your formula to determine the height of a trapezoid with an area of 24 square centimeters and base length of 9 cm and 7 cm
Answers
Answer
The height of the trapezoid = 3 cm
Explanation
The area of a trapezoid is given as
Area = ½ (a + b) h
where
a and b = base lengths of the trapezoid
a = 9 cm
b = 7 cm
h = height of the trapezoid = ?
Area = 24 cm²
Area = ½ (a + b) h
24 = ½ (9 + 7) h
24 = ½ (16) h
24 = 8h
8h = 24
Divide both sides by 8
(8h/8) = (24/8)
h = 3 cm
Hope this Helps!!!
The data set below provides the monthly rent (in dollars) paid by 7 tenants.990, 879, 940, 1010,950, 920, 1430Suppose the rent for one of the tenants changes from $1430 to $1115.What is the mean before the rent change?What is the mean after the change?
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To solve this question, we need to find the mean for both cases. The mean is given by summing the given values and then dividing them by the number of values (or given cases).
We have that, before the rent chance, we have the following monthly rent (in dollars):
990, 879, 940, 1010,950, 920, 1430
There are seven (7) values. Then, the mean, in this case, is:
[tex]m_{\text{before}}=\frac{990+879+940+1010+950+920+1430}{7}=\frac{7119}{7}\Rightarrow m=1017[/tex]Therefore, the mean, in this case, is equal to $1017.
Now, we have that the rent change for the one with $1430 to $1115, now the values are:
990, 879, 940, 1010,950, 920, 1115.
We can proceed as before to obtain the mean:
[tex]m_{\text{after}}=\frac{990+879+940+1010+950+920+1115}{7}=\frac{6804}{7}\Rightarrow m_{after}=972[/tex]Thus, the mean after the change is equal to $972.
In summary, we have that:
• The mean before the rent change is equal to $1017
,• The mean after the rent change is equal to $972.
Can anyone help me? I don't know the answer.
Answers
By means of the area formula for a square, the square has an area of 4 / 49 square meters (approx. 0.0816 square meters).
What is the area of the square?
Herein we find a representation of a solid square in the figure, whose side length measure (l), in meters, is known, and whose area (A), in square meters, has to be found. Dimensionally speaking, the area unit is the square of length unit.
The area formula of the square is shown below:
A = l²
If we know that the side length of the square has a measure of 2 / 7 meters (l = 2 / 7 m), then the area of the triangle is equal to:
A = (2 / 7 m)²
A = 4 / 49 m²
A ≈ 0.0816 m²
The area of the square is 4 / 49 square meters (approx. 0.0816 square meters).
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no5 Diana and Becky were on the samesoccer team and took turns being thegoalie. They stopped 9 out of every10 shots made against them. If theother team scored 3 points, how manyballs did Diana and Becky stop fromgoing into the net?balls
Answers
ANSWER
27 balls
EXPLANATION
The points scored by the other team are the number of balls Diana and Becky didn't stop.
We know that if the other team would make 10 attempts of goal, only 1 would result in a point. The ratio of scored points to stopped balls is 1:9
Let x be the number of balls they stopped in this match. The other team scored 3 points, so the ratio is 3:x. We know that the ratio should be constant, which means,
[tex]\frac{1}{9}=\frac{3}{x}[/tex]To solve this, we have to multiply both sides by x. On the right side, the x cancels out,
[tex]\begin{gathered} \frac{1}{9}x=\frac{3x}{x} \\ \frac{1}{9}x=3 \end{gathered}[/tex]And then multiply both sides by 9,
[tex]\begin{gathered} \frac{1}{9}\cdot9x=3\cdot9 \\ x=27 \end{gathered}[/tex]Hence, Diana and Becky stopped 27 balls.
Find the two dimensional diagonal. Round to the nearest tenth.
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Given the value of b and c, we want to get the value of a
The three sides represent the sides of a right triangle
By the use of Pythagoras' theorem, we can get the value of a
From the diagram, the disgonal represents the hypotenuse of the right triangle
According to Pythagoras' theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
Thus, we have it that;
[tex]\begin{gathered} c^2=a^2+b^2 \\ 6^2=3^2+a^2 \\ 36=9+a^2 \\ a^2\text{ =36-9} \\ a^2\text{ = 27} \\ \text{a = }\sqrt[]{27} \\ a\text{ = 5.2 units} \end{gathered}[/tex]The triangle shown below are similar. which line segment corresponds to RS?
Answers
B) TS
1) Since these triangles are similar then we can write out the following ratios according to the Thales Theorem:
[tex]\frac{RS}{TS}=\frac{RO}{TU}[/tex]2) So these line segments must share the same ratio
3) Hence, the answer is TS
Answer:
TS
Step-by-step explanation:
You pick a card at random. Without putting the first card back, you pick a second card at rando 4 5 6. What is the probability of picking an odd number and then picking an odd number? Simplify your answer and write it as a fraction or whole number.
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Given data:
The three numbers on the cards are 4, 5, 6.
The probability of picking an odd number and then picking an odd number is,
[tex]\begin{gathered} P=\frac{1}{3}\times\frac{0}{2} \\ =0 \end{gathered}[/tex]Thus, the probability of picking an odd number and then picking an odd number is 0.
Find the slope of the line below. Enter your answer as a fraction or decimal.Use a slash mark (/) as the fraction bar if necessary.(4,4)6(-4,-2)8Answer here
Answers
slope = 3/4
Explanation:We would apply the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]The points of the graph: (-4, -2) and (4, 4)
[tex]\begin{gathered} x=-4,y_1=-2,x_2=4,y_2\text{ = }4 \\ \text{slope = }\frac{4-(-2)}{4-(-4)} \end{gathered}[/tex][tex]\begin{gathered} \text{Multiplication of same sign gives a positive sign} \\ \text{slope = }\frac{4+2}{4+4} \end{gathered}[/tex][tex]\begin{gathered} \text{slope = 6/8} \\ To\text{ the lowest term:} \\ \text{slope = 3/4} \end{gathered}[/tex]of the trains that recently pulled into Westford Station, 16 were full and 4 had room for morepassengers. What is the experimental probability that the next train to pull in will be full?Write your answer as a fraction or whole number
Answers
The formula for probabilty is given by; the Probability of an event(A) is the number of favorable outcomes divided by the total number of outcomes possible in a scenario. It can also be denoted by the formula:
[tex]P(A)=\frac{Number\text{ of Favorable Outcome}}{\text{Total Number of }Outcome}[/tex]In our problem we have 16 trains that are full and 4 which are not, therefore there are a total number of 20 trains in the Westford Station.
The number of favorable outcome is equal to the number of trains that are full since it is the one asked in our question as the one which is more favored to come, according to the question.
Therefore, the number of favorable outcome = number of full trains = 16, and
The Total number of Outcome = total number of trains that may pull over to Westford Station = 20
Therefore the experimental probability that a full train will pull over in the station is;
[tex]\begin{gathered} P(A)=\frac{Number\text{ of Favorable Outcome}}{\text{Total Number of Outcome}}\text{ = }\frac{16}{20} \\ P(A)=\frac{16}{20}=\frac{4}{5} \\ P(A)=\frac{4}{5} \end{gathered}[/tex]Therefore there is a probabilty of 4/5 or 80% that a full train will pull over the station.
What is the exponential form of the logarithmic equation?5= log base .9 .59049
Answers
Given:
[tex]5\text{ }=\text{ log}_{0.9}0.59049[/tex]To find:
to convert from logarithmic form to exponential form
[tex]\begin{gathered} If\text{ logarithmic form:} \\ a\text{ = log}_bC \\ E\text{xponential form:} \\ b^a\text{ = C} \\ \\ The\text{ base of the log will become the base of the expoenent on the other side} \\ \text{The exponent will be the number of the other side of the equation} \end{gathered}[/tex][tex]\begin{gathered} Applying\text{ same rule:} \\ 0.9^5\text{ = 0.59049} \end{gathered}[/tex]Use vertical multiplication to find the product of: x2 + 3x + 2 x x - x2-1 O - A. ** - 3x4 – x2-3x+ - *- 2 O B. x + 2x4 – x2-3x2 – 3x-2 - C. + 3x4 - X2-3x2-3x O D. +2x4- *° - 3x2 - 3x-2 x
Answers
Use vertical multiplication as shown below
Therefore, the answer is x^5+2x^4-x^3-3x^2-3x-2, option B
Which of the following scenarios describes independent events from disjoint sets?
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Two events are independent if one does not depend on the other to occur.
The correct option here is B because frieddie chooses one fruit out of six is an even that does not depend on the other
f(x) = x ^ 2 + ax + bf(x) has m zeros, and f[f(x)] has M zeros,So M - m will never be ____A. 0B. 1C. 2D. 3
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First, notice that the expression for f(f(x)) is the following:
[tex]f(f(x))=(x^2+ax+b)^2+a(x^2+ax+b)+b[/tex]notice that the first term is a quadratic expression with exponent 2. This means that f(f(x)) has 4 zeros.
Since f(x) has 2 zeros (since its quadratic), we have that M-m = 4-2 = 2, thus, M-m will never be 0, 1 or 3
In a normal distribution, about 0.1% 2.2% 13.6% 1 SD % of the data lies between 1 and 3 standard deviations of the mean. Mean 13.6% 1 SD 2.2% 0.1% 3 SD
Answers
Solution:
Given a normal distribution table;
The % of data that lies between 1SD and 3SD is
[tex]=13.6\%+2.2\%=15.8\%[/tex]Hence, the answer is 15.8%
I need help with my school final and I am very lostFind the resultant and the angle
Answers
We have the triangle below:
The value of x can be found using Pythagoras theorem:
[tex]hypothenuse^2\text{ = opposite}^2\text{ + adjacent}^2[/tex]Substituting we have:
[tex]x^2\text{ = 16}^2\text{ + 36}^2[/tex]Solving for x:
[tex]\begin{gathered} x^2\text{ = 1552} \\ x\text{ = }\sqrt{1552} \\ x\text{ = 39.39} \end{gathered}[/tex]Answer: 39.4 feet
The value of the angle can be found using the formula:
[tex]\begin{gathered} \theta\text{ = }\tan^{-1}(\frac{16}{36}) \\ \theta\text{ = 23.96 } \\ \theta\text{ }\approx\text{ 24}^0 \end{gathered}[/tex]Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters highand have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer thanits width.The volume of a rectangular prism is found using the formula V= / w- h, where / is the length, w is the width, and h is the height.
Answers
Explanation
The volume of a rectangular prism is given by
[tex]v=length\times breadth\times height[/tex]We have the information:
h =3cm
v=252 cm³
If the width is x
And the length is 5cm longer than the width
L =5+x
Then, we will have
[tex]volume=252=l\times w\times h=(5+x)(x)(3)[/tex]Thus, we will have
[tex]\begin{gathered} 252=3x(5+x) \\ 252=15x+3x^2 \\ 3x^2+15x-252=0 \end{gathered}[/tex]Simplifying further
[tex]x^2+5x-84=0[/tex]Thus, the equation that models the tray will be
[tex]x^2+5x=84[/tex]Part B
To check if a with of 7.5 is possible, we will put x = 7.5c and check if the equation holds true
[tex](7.5)^2+5(3.5)=93.75[/tex]since
[tex]\begin{gathered} 93.75\ne84 \\ The\text{ is false} \\ \end{gathered}[/tex]Therefore, the answer is NO.
It is not possible for the width to be 7.5cm
Your mom paid $8 for 10 Granny Smithapples and bought some Golden Deliciousat 60 cents an apple. If her average cost is$0.66 per apple, how many GoldenDelicious apples did she buy?
Answers
First, let's calculate the price of each Granny Smith apples, by dividing the cost by the number of apples:
[tex]undefined[/tex]e dist Since the radius is an imaginary value, the equation is not a real circle. the cece - 4x + 2) + ( + 8y + (-2) + + 4) = -5 2-5 r-rs-115 lisch Pe squares for each quadratic, list the center and radius, then graph each circle ahs 12.3 llowing: it tort 'onics Ibolas It wh 121, the at of anslated center: 2 - 40 = 4 (b) x² + y2 - 4x = 0 2 27 822
Answers
The general equation of a circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center of the circle and r is the radius
x² + y² -2x - 8y = 8
x² - 2x + y² - 8y = 8
(x² - 2x + ) + (y² -8y + ) = 8
Add square of half of the coefficient of x in the first paenthesis and the half of the square of the coefficient of y in the second parenthesis
Then add the two squaes at the right-hand side of the equation
(x² -2x +1 ) + (y² -8y + 16 ) = 8 + 1+ 16
(x-1)² + (y-4)² = 25
comparing this with the general equation
Center is ( 1, 4)
Radius is 5