Answer:
[tex](5d^4-8)^2[/tex]
Step-by-step explanation:
[tex]\textsf{Let }\:u=d^4[/tex]
[tex]\implies 25d^8-80d^4+64=25u^2-80u+64[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex] :
[tex]\implies ac=25 \cdot 64=1600[/tex]
[tex]\implies b=-80[/tex]
Two numbers that multiply to 1600 and sum to -80 are:
-40 and -40
Rewrite b as the sum of these two numbers:
[tex]\implies 25u^2-40u-40u+64[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 5u(5u-8)-8(5u-8)[/tex]
Factor out the common term (5u - 8):
[tex]\implies (5u-8)(5u-8)[/tex]
Simplify:
[tex]\implies (5u-8)^2[/tex]
Substitute back [tex]u=d^4[/tex]
[tex]\implies (5d^4-8)^2[/tex]
Therefore:
[tex]25d^8-80d^4+64=(5d^4-8)^2[/tex]
Let's see
25d⁴-80d⁴+645²(d⁴)²-2(5)(d⁴)(8)+8²(5d⁴)²-(2)(5d⁴)(8)+8²(5d⁴-8)²Used formula
(a+b)²={a²+2ab+b²)GEOMETRY)
Fill in the blanks:
How many degrees is arc PA?
How many degrees is angle PRA?
Line PR is a diameter of the circle. How many degrees is arc PAR?
How many degrees is arc AR?
(The picture is below and Q is the one above the circle and A at the bottom of the circle)
Part 1
By the inscribed angle theorem, arc PA measures 62 degrees.
Part 2
Angles inscribed in the same arc are congruent, so angle PRA measures 31 degrees.
Part 3
Diameters form semicircles, and the arc of a semicircle measures 180 degrees, so arc PAR measures 180 degrees.
Part 4
Subtracting arc PA from arc PAR, we get arc AR measures 118 degrees.
Please help me with Algebra 2 questions (2).
#8: Simplify the expressions. Assume all variables are positive.
#11: Solve the equation.
8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]
11. The value of x is 4
Simplifying an expressionFrom the question, we are to simplify the give expression
The given expression is
[tex]y^{3}\sqrt[5]{32x^{4} } - 7\sqrt[5]{x^{4}y^{15} }[/tex]
[tex]y^{3} (32x^{4} )^{\frac{1}{5} } - 7(x^{4}y^{15} )^{\frac{1}{5}[/tex]
[tex]y^{3} \times 32^{\frac{1}{5} } x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{\frac{15}{5}}[/tex]
[tex]y^{3} \times 2^{5 \times} ^{\frac{1}{5} } \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]
[tex]y^{3} \times 2 \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]
[tex]2 x^{\frac{4}{5} } y^{3} - 7 x^{\frac{4}{5}}y^{3}[/tex]
[tex]= - 5 x^{\frac{4}{5}}y^{3}[/tex]
11. [tex]\frac{1}{2}(5x+7 )^{\frac{2}{3} } =\frac{9}{2}[/tex]
Multiply both sides by 2
[tex]2 \times \frac{1}{2}(5x+7 )^{\frac{2}{3} } =2 \times \frac{9}{2}[/tex]
[tex](5x+7 )^{\frac{2}{3} } =9[/tex]
Multiply both sides by a power of 3/2
[tex](5x+7 )^{\frac{2}{3} \times {\frac{3}{2} } } =9^{\frac{3}{2} }[/tex]
[tex](5x+7 )=3^{2 \times} ^{\frac{3}{2} }[/tex]
[tex]5x+7 =3^{3}[/tex]
[tex]5x+7 =27[/tex]
[tex]5x =27-7[/tex]
[tex]5x = 20[/tex]
[tex]x = \frac{20}{5}[/tex]
x = 4
Hence,
8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]
11. The value of x is 4
Learn more on Simplifying expressions here: https://brainly.com/question/11688560
#SPJ1
Can someone help me pls
Answer:
(d) x = (5±√53)/2
Step-by-step explanation:
The given quadratic equation is in standard form, so the coefficients are readily identified. The solution is given by the quadratic formula based on those coefficients.
Quadratic formulaThe solution to the quadratic equation ax² +bx +c = 0 is given by the formula ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
ApplicationThe given equation has coefficients a = 1, b = -5, c = -7, so the solutions given by the formula are ...
[tex]x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(1)(-7)}}{2(1)}=\dfrac{5\pm\sqrt{25+28}}{2}\\\\\boxed{x=\dfrac{5\pm\sqrt{53}}{2}}[/tex]
Given that a= 3, b= -2 and c= -4, evaluate the following expression. 3a-b/2c + 3a-c/c-b
The value of the given algebraic expression is -63/8.
To evaluate an algebraic expression, we substitute the values of the variables in the expression, and then follow the rules of solving a numeral expression.
In the question, we are asked to evaluate the algebraic expression:
{(3a - b)/2c} + {(3a - c)/(c - b)}, given the values of a = 3, b = -2, and c = -4.
To evaluate the expression {(3a - b)/2c} + {(3a - c)/(c - b)}, given the values a = 3, b = -2, and c = -4, we substitute these values in the expression and solve as follows:
{(3(3) - (-2))/2(-4)} + {(3(3) - (-4))/((-4) - (-2))}
= {(9 + 2)/(-8)} + {(9 + 4)/(-4 + 2)}
= {-(11/8)} + {-(13)(2)}
= -(11/8) - (13/2)
= -(11/8) - (52/8)
= -(63/8).
Thus, the value of the given algebraic expression is -63/8.
Learn more about algebraic expressions at
https://brainly.com/question/723406
#SPJ4
7
Solve the system of inequalities by graphing.
2x + 5y < 25
y < 3x-2
5x - 7y < 14 DUE NOW
The solution to the inequality 2x + 5y < 25, y < 3x-2 and 5x - 7y < 14 is the dark triangular region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality shows the non equal comparison of two or more numbers and variables.
The solution to the inequality 2x + 5y < 25, y < 3x-2 and 5x - 7y < 14 is the dark triangular region shown in the graph.
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
What is the decimal expansion of the following fraction? 1/5
Answer:
0.2
Step-by-step explanation:
Answer:
0.2
Step-by-step explanation:
1 divided by 5 = 0.2
heeelpp mee please !!!!!
Answer:
210 yd²
Step-by-step explanation:
If we rotate the shape we get a right angle triangle with a hypotenuse of 29 yd :
The area of a right angle triangle is given by the formula :
A = [tex]\frac{ab}{2}[/tex]
Substituting the 2 values given in diagram gives us :
A = [tex]\frac{(20)(21) }{2}[/tex] = 420÷2 = 210
Our units will be yd² as we are dealing with area
Amy simplified this complex fraction problem.
Negative 2 and one-half divided by five-fourths = Negative five-halves divided by five-fourths = negative five-halves (five-fourths) = negative StartFraction 10 over 8 EndFraction. The quotient is negative five-fourths.
What errors did Amy make? Select all that apply.
Reciprocal the second fraction and perform multiplication instead addition.
What is fraction?
A number expressed as a quotient, in which a numerator is divided by a denominator.
Given:
Negative 2 and one-half divided by five-fourths = Negative five-halves divided by five-fourths = negative five-halves (five-fourths) = negative StartFraction 10 over 8 EndFraction.
As we see the calculations there is mistake which had amy made.
Amy should have reciprocal the second fraction before multiplication. As division is now allowed in fraction.
Also, She perform addition instead of multiplication.
Learn more about this concept here:
https://brainly.com/question/14520050
#SPJ1
hi who know how to do this 3 question?,I will mark brainlest for good answer.
Answer:
its answer is 36
.
.
.
.
.
.
.
.
.
.
.
.
......
.
.
.
.
.
.
if a researcher counting how many seconds each bystander helps a stranger struggling to pick up a heavy box fan varying amounts of time but i 10 seconds and 15 seconds equally as much in the data. all the restaurant under 10 seconds. this means the data are
The mean of the data about researcher counting of seconds each by stander helps a stranger struggling to pick up a heavy box fan varying amounts of time is 11.67 seconds.
Given if a researcher counting how many seconds each by stander helps a stranger struggling to pick up a heavy box fan varying amounts of time but is 10 seconds and 15 seconds equally as much in the data. all the restaurant under 10 seconds.
We have to calculate mean of the data.
Mean is the sum of numbers divided by total numbers included.
Mean=∑X/n
where n is the numbers.
Mean =(10+15+10)/3
=35/3
=11.67
Hence mean of the data about researcher's counting is 11.67.
Learn more about mean at https://brainly.com/question/1136789
#SPJ4
HALP
x =x=x, equals
^\circ
∘
Answer:
90°+x = 180°(angles on a straight line)x=180°-90°x=90°THERE ARE A LOT OF WAYS TO WORK THE ANSWER OUT BUT THAT ONE IS SIMPLE AND EASY TO UNDERSTANDStep-by-step explanation:
HOPE THIS HELPS!!1. Please answer the question on exponential growth or decay. Round to
the nearest whole number or penny if the question is concerning money if
necessary.
A country pledges to reduce its annual
CO₂ emissions by 2% per year. If the
emissions in 2022 are 4,200 Mt (metric
megatons), what are the maximum
allowable emissions in the year 2031?
The maximum value of allowable emissions in the year 2031 is equal to 3,502.
How to calculate the maximum value?In order to determine the maximum value of allowable emissions in the year 2031, we would use an exponential function which also relates to compound interest as follows:
A = P(1 - r)^t
For the time, we have:
Time, t = 2031 - 2022
Time, t = 9
Substituting the given parameters into the formula, we have;
A = 4,200(1 - 0.02)^9
A = 4,200(0.98)^9
A = 4,200 × 0.8338
A = 3501.7 ≈ 3,502.
Read more on exponential functions here: https://brainly.com/question/27866047
#SPJ1
Write the first five terms of the sequence. an = n 2 + 2 2, 3, 6, 11, 18 3, 6, 9, 12, 15 3, 6, 11, 18, 27
The first five terms of the sequence will be 3, 6, 11, 18, 27. Then the correct option is C.
What are sequence and series?A sequence is a list of elements that have been ordered sequentially, such that members come either before or after.
The equation will be given below.
[tex]\rm a_n = n^2+2[/tex]
Then the first five terms of the sequence will be
For n = 1, we have
a₁ = 1² + 2
a₁ = 3
For n = 2, we have
a₂ = 2² + 2
a₂ = 6
For n =3, we have
a₃ = 3² + 2
a₃ = 11
For n = 4, we have
a₄ = 4² + 2
a₄ = 18
For n = 5, we have
a₅ = 5² + 2
a₅ = 27
Then the sequence will be 3, 6, 11, 18, 27.
Then the correct option is C.
More about the sequence link is given below.
https://brainly.com/question/21961097
#SPJ1
help me pls
4/3(6/4/5)
Answer:
0.4
Step-by-step explanation:
4/3(1.5/5)
4/3(0.3)
1.33333333333(0.3)
0.4
−6i⋅(6−2i)=minus, 6, i, dot, left parenthesis, 6, minus, 2, i, right parenthesis, equals Your answer should be a complex number in the form a+bia+bia, plus, b, i where aaa and bbb are real numbers.
The solution to the given product is:
-6i*(6 - 2i) = -12 - 36i
How to solve the given expression?
Here we want to solve:
-6i*(6 - 2i)
Here the thing that you need to remember is that i² = -1.
Expanding the product, we get:
-6i*(6 - 2i) = (-6i)*6 + (-6i)*(-2i)
= -36i + (6i)*(2i) = -36i + 12i² = -36i - 12
Then we conclude:
-6i*(6 - 2i) = -12 - 36i
That is the solution to the given expression.
If you want to learn more about complex numbers:
https://brainly.com/question/10662770
#SPJ1
You walk into a room. 2 dogs, 4 horses 1 giraffe and a duck on the bed. 3 chickens flying over a chair. How many legs are on the floor?.
Answer:
8+16+2=28
Step-by-step explanation:
I have $230 and I’m at a bookstore. I love books, so I want to buy as many as I can. The books I want to buy each cost $17. At most, how many books can I buy and still have at least $25 left for dinner?
Answer:
12 books
Step-by-step explanation:
Lets set aside $25 for dinner first.
Amount left = $230 - $25 = $205
Number of books able to buy = amount left ÷ cost per book
= $205 ÷ $17
= 12.058 books
Of course, you cant buy .058 books , that wont make sense, so you take the highest possible WHOLE number, which in this case, is 12 books.
help me please i give you brainly
Answer:
the answer is false .
Step-by-step explanation:
Some families spend their incomes according to budget plans. If a family used the plan
below as a basis, about how much would it spend for clothing?
Shelter.
Food
Clothing
Operation
Savings
Other Expenses.
$525
Monthly
Income
.26%
.28%
7%
. 10%
. 9%
20%
100%
O $35.75
O $36.75
O $53.20
$75.00
O none of these
Using proportions, it is found that the family would spend $36.75 on clothing.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The family has a budget of $525, and spends 7% of it in clothing, hence the amount is given by:
A = 0.07 x 525 = $36.75.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
HELPS I NEED THE ANSWER PLSSSSSSSSSSSS!
Answer:
5.5x+7.146 (the six is repeating)
Step-by-step explanation:
Answer:
5.5x + 7.25
Step-by-step explanation:
5.5(x+6.5)-(x+9.5)-(19-x) Convert the fractions to decimal
5.5x+35.75 -x - 9.5 - 19 +x Expand
(5.5x - x + x) +(35.75 - 9.5 - 19) Group like terms
5.5x + 7.25 Combine like terms
Solve the system, enter the smallest x coordinate first
The solutions to the system of equations are given as follows: (1, -3) and (-4,2).
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The equations are given as follows:
(x + 3)² + (y + 2)² = 17.x + y = -2.From the second equation:
y = -2 - x.
Replacing in the first:
(x + 3)² + (y + 2)² = 17.
(x + 3)² + (-2 - x + 2)² = 17
x² + 6x + 9 + x² = 17
2x² + 6x - 8 = 0
2(x² + 3x - 4) = 0
2(x + 4)(x - 1) = 0.
Then the solutions for x are:
x + 4 = 0 -> x = -4.x - 1 = 0 -> x = 1.The solutions for y are:
When x = 1, y = -2 - 1 = -3.When x = -4, y = -2 -(-4) = 2.Hence the solutions are:
(1, -3) and (-4,2).
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 490 and 560
[tex]P(490 < X < 560)[/tex]= 0.3133
Given: μ = 560
σ = 90
To find: P (490 < X < 560)
Normal distributions are symmetric, unimodal, and asymptotic. A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. It's always easy to solve questions in terms to standard normal
Hence, converting normal distribution to standard normal gives:
P(490 < X < 560) = [tex]P(\frac{560-560}{90}[/tex]≤ [tex]\frac{X-\mu}{\sigma} < \frac{640-560}{90})[/tex]
= P(0 ≤ Z < 0.888)
= P (z<0.89) - P(z ≤ 0)
Using standard normal table,
= 0.8133 - 0.5
P(490 < X < 560) = 0.3133
To learn more about Normal Distribution, visit:
https://brainly.com/question/4079902
#SPJ4
A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, find the probability that a blue marble will be drawn. a. One-third c. StartFraction 1 Over 7 EndFraction b. StartFraction 1 Over 11 EndFraction d. StartFraction 3 Over 14 EndFraction Please select the best answer from the choices provided A B C D
The probability of selecting a blue marble is 3/14. Hence, option D is the right choice.
The probability of any event is the chance of the occurrence of that event. It is given as the ratio of the number of favorable outcomes to the event to the total number of outcomes possible in the experiment.
If we consider an event A, the number of favorable outcomes to event A be n, and the total number of outcomes be S, then the probability of event A is given as:
P(A) = n/S.
Let us take the event of selecting a blue marble from the experiment of selecting a marble randomly from the bag be A.
The number of outcomes favorable to event A (n) = 3 {3 blue marbles}.
The total number of outcomes (S) = 14 {Total number of marbles in the bag = 4 red + 3 blue + 7 green = 14 marbles}.
Therefore, the probability of selecting a blue marble is,
P(A) = n/S = 3/14.
Hence, option D is the right choice.
Learn more about the probability of an event at
https://brainly.com/question/7965468
#SPJ10
help me pls and if u can explain too.
Part 1
The gradient of the line is [tex]\frac{11-1}{-3-2}=-2[/tex], so the equation is [tex]y=-2x+5[/tex].
This means the system is
[tex]y=-2x+5\\\\y=ax^2 +b[/tex]
Part 2
Substituting in the coordinates (-3,11) and (2,1) into the equation of the parabola,
[tex]11=9a+b\\\\1=4a+b[/tex]
Subtracting the equations, we get 10=5a, and thus a = 2
Substituting a = 2 back into the system, we get b = -7
Part 3
The equation of the parabola is [tex]y=2x^2 - 7[/tex], and the turning point is at [tex]x=0[/tex]. Therefore, the value of y is -7
Alice, Bob, and Carol were riding their bikes along the same path at different speeds. Alice's speed was twice Bob's speed, and Carols' speed was one-third that of Alice's speed. What was Carol's speed, in miles per hour, if Bob's speed was 9 miles per hour
Carol's speed is computed to be 6 miles/hour, solved using the equation (3x)/2 = 9.
We assume Carol's speed to be x miles/hours.
Carol's speed is given to be one-third of Alice's speed.
Then Alice's speed is three times Carol's speed, that is, Alice's speed = 3x miles/hour.
Alice's speed is given to be twice Bob's speed.
Then Bob's speed is half of Alice's speed, that is, Bob's speed = (3x)/2 miles/hour.
But, Bob's speed is given to be 9 miles per hour.
Therefore, we get the equation:
(3x)/2 = 9.
To find Carol's speed, we solve this equation as follows:
(3x)/2 = 9,
or, {(3x)/2}*2 = 9*2 {Multiplying both sides by 2},
or, 3x = 18 {Simplifying},
or, 3x/3 = 18/3 {Dividing both sides by 3},
or, x = 6 {Simplifying}.
Therefore, Carol's speed is computed to be 6 miles/hour, solved using the equation (3x)/2 = 9.
Learn more about solving equations at
https://brainly.com/question/27952911
#SPJ4
A loaded 8-sided die is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency. what is the expected value of this die
Answer:
4.4
Step-by-step explanation:
The sum of the probabilities of all possible outcomes is 1.
As the die is loaded so that the number 4 occurs 3/10 of the time, and the other numbers occur with equal frequency, then the probability of numbers 1, 2, 3, 5, 6, 7 and 8 being rolled is 1/10.
Create a probability distribution table for X, where X is the score on the loaded 8-sided die:
[tex]\begin{array}{ | c | c | c | c | c | c | c | c | c |}\cline{1-9}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\cline{1-9} & & & & & & & &\\ \text{P}(X=x) & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{3}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10} & \dfrac{1}{10}\\& & & & & & & &\\\cline{1-9}\end{array}[/tex]
Add a product row and a totals column:
[tex]\begin{array}{ | c | c | c | c | c | c | c | c | c | c |}\cline{1-10}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 &\text{Total} \\ \cline{1-10} &&&&&&&&& \\ \text{P}(X=x) & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{3}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & 1\\ &&&&&&&&&\\ \cline{1-10} &&&&&&&&&\\\text{Product} & \frac{1}{10} & \frac{2}{10} & \frac{3}{10} & \frac{12}{10} & \frac{5}{10} & \frac{6}{10} & \frac{7}{10} & \frac{8}{10} & \frac{44}{10} \\ &&&&&&&&&\\\cline{1-10}\end{array}[/tex]
(The Product is row is the product of the score on the die and its probability).
The expected value (EV) is the sum of the product of each outcome and its probability.
Therefore, the expected value (EV) of this die is 44/10 = 4.4
a parabola passes through the points (2,8), (6,2), and (8,8). what is the x-coordinate of its vertex?
a) 4
b) 5
c) 7
d) cannot be determined
The x-value of the vertex of the given parabola is x = 5, so the correct option is b.
How to get the x-value of the vertex?
If we define the parabola by f(x), by looking at the table, we can read:
f(2) = 8f(6) = 2f(8) = 8So, notice that:
f(2) = f(8).
Then the x-coordinate of the vertex is the midpoint between 2 and 8.
x = (2 + 8)/2 = 5
The x-value of the vertex of the given parabola is x = 5, so the correct option is b.
If you want to learn more about parabolas:
https://brainly.com/question/4061870
#SPJ1
Ms. johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about acceleration due to gravity. the program reports =31.5 and . what is the variance of the data? round to the nearest tenth.
Since the variance is the square of the standard deviation, the variance here is 6.3.
A commonly used measure of dispersion is the standard deviation, which is simply the square root of the variance. Therefore, we just raise the standard deviation to the power of 2 to get the answer. We do as follows:
s = √v
(2.5)² = (√v)²
v = 6.25 = 6.3
So, Since the variance is the square of the standard deviation, the variance here is 6.3.
DISCLAIMER: The question was incomplete. Please find the full content below.
Question
Ms. Johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about the acceleration due to gravity. The program reports a mean of 31.5 and a standard deviation of 2.5. What is the variance of the data?
Learn more about VARIANCE here https://brainly.com/question/15858152
#SPJ4
Answer: D). 6.3
Step-by-step explanation:
WILL GIVE BRAINLIEST IF YOU HELP MEE
Answer: A: Whole Number B:Integer and C: Rational are all correct.
For the question: In the figure, AB is divided into equal parts. The coordinates of point A are (2, 4), and the coordinates of point B are (10, 6). Match each pair of coordinates to the corresponding point on AB.
Answer:The coordinates of the point are (6 , 5).
For the question: Imani and Abedi drive to work. Imani drives 66 miles in 1.5 hours. Abedi drives 56 km in 1 hour 15 min. Work out the difference between their average speeds in km/h. 1 mile = 1.6 km
Answer:25.6 km/h
I couldn't help you on all of them, but I helped you on some. Hope this helps :D
Find m/HFG if m/EFG = 2x + 52, m/EFH = 21°, and
m/HFG = x + 31.
Answer:
31°
Step-by-step explanation:
Given Angle EFG = Angle EFH + Angle HFG (based on the diagram)
[tex]2x+52 = 21 + (x+31)\\2x+52 = 21+x+31\\2x+52=x+52\\2x-x+52=52\\x+52=52\\x=52-52\\x=0[/tex]
From here we can see the value of x is non-existent.
Substitute x to find Angle HFG.
x+31 = 0 + 31 = 31°