By theorem we have the following:
[tex]h^2=a^2+b^2[/tex]And, we are given:
[tex]A=\frac{a\cdot b}{2}\Rightarrow2A=a\cdot b[/tex]Then:
[tex]\Rightarrow4A^2=a^2b^2\Rightarrow4A^2=a^2(h^2-a^2)[/tex][tex]\Rightarrow a^4-h^2a^2+4A^2=0[/tex]Now, we replace h and A:
[tex]a^4-(25)^2a^2+4(54)^2=0[/tex]And solve for a:
[tex]a^4-625a^2+11664=0[/tex]Then, the possible values for a are:
[tex]a=\begin{cases}a_1=-\frac{29}{2}-\frac{\sqrt[]{409}}{2} \\ a_2=\frac{29}{2}-\frac{\sqrt[]{409}}{2} \\ a_3=\frac{\sqrt[]{409}}{2}-\frac{29}{2} \\ a_4=\frac{29}{2}+\frac{\sqrt[]{409}}{2} \\ \end{cases}[/tex]We can see that a1, and a2 are not solutions, therefore a2 and a4 are.
So, the two possible b sides are then:
[tex]b_2=\sqrt[]{25^2-(\frac{29}{2}-\frac{\sqrt[]{409}}{2})^2}\Rightarrow b_2\approx24.99[/tex]and:
[tex]b_4=\sqrt[^{}]{25^2-(\frac{29}{2}+\frac{\sqrt[]{409}}{2})^2}\Rightarrow b_{4\approx}15.50[/tex]So, the lengths of the two sides can be:
a = 4.38 and b = 24.99
or
a = 24.61 and b = 15.50
Fill in the blank to correctly complete the sentence.
Consider the following function.
f(x)
=
2x4+6x3−4x2+2x+12
=
x−2)2x3+10x2+16x+34+80
By inspection, we can state that f(2)=
The value of f(2) would be 80 which is determined by substituting the value of x = 2in the given function f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80.
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The given function below is:
f(x) = 2x⁴ + 6x³ −4x² +2x + 12
f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80
We have to determine the value of f(2).
⇒ f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80
Substitute the value of x = 2 in the given function,
⇒ f(x) = (2 −2)(2(2)³ + 10(2)² + 16(2) + 34) + 80
⇒ f(x) = (0)(2(2)³ + 10(2)² + 16(2) + 34) + 80
⇒ f(x) = 0 + 80
⇒ f(x) = 80
Therefore, the value of f(2) would be 80.
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I'll give brainliest!
Answer:
=1/1024
Step-by-step explanation:
4^-5
=1/4^5
=1/1024
Rate as brainliest
11 – 8 (5 – 2) help
Answer
11 - 8 (5 -2) = -13
Explanation
11 - 8 (5 -2)
To solve this, we will first solve the one in the bracket
11 - 8 (5 -2)
= 11 - 8 (3)
= 11 - 24
= -13
Hope this Helps!!!
Roots of Quadratics 50 PTS!!!
The values of k for the different quadratic equation solutions are as follows
a the equation 2x² - x + 3k = 0 has two distinct real roots
k < 1/24b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots
k = 3/5ci the equation -x² + 3x + (k + 1) = 0 has real roots
k > -3.25d the equation 3kx² - 3x + 2 = 0 has no real solutions
k < ± 1.633How to solve quadratic equations to get different answersQuadratic equations of the form ax² + bx + c = 0 is solved using the formula
[tex]-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex] OR [tex]-b-\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
The equation b² - 4ac is called the discriminant and it is used as follows
To solve the equation and get two real roots: 2x² - x + 3k = 0
b² - 4ac > 0substituting the values gives
(-1)² - 4 * 2 * 3k > 0
1 - 24k > 0
1 > 24k
divide through by coefficient of k
k < 1/24
To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0
b² - 4ac = 0substituting the values gives
(-2)² - 4 * 5 * (2k - 1) = 0
4 - 40k + 20 = 0
-40k = -24
divide through by coefficient of k
k = 3/5
To solve the equation and get real roots -x² + 3x + (k + 1) = 0
b² - 4ac > 0substituting the values gives
(3)² - 4 * -1 * (k+1) > 0
9 + 4k + 4> 0
4k > -13
divide through by coefficient of k
k > -3.25
To solve the equation and get no real solutions 3kx² - 3x + 2 = 0
b² - 4ac < 0substituting the values gives
(-3)² - 4 * 3k * 2 < 0
9 - 24k² > 0
9 > 24k²
divide through by coefficient of k²
k² < 24/9
k < ± 1.633
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Answer:
ax² + bx + c = 0 is solved using the formula
Step-by-step explanation:
The entire graph of the function g is shown in the figure below.
Write the domain and range of g using interval notation.
(a) domain=
(b) range =
which number is a rational number?A. √3B. √36C. √7D. π
We have to identify the rational number.
Any number that can be expressed as a fraction is a rational number.
In this case the options are:
A. The square root of 3. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.
B. The square root of 36, unlike the square root of 3, does have a rational solution: 6. So the square root of 36 is a rational number.
C. The square root of 7. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.
D. The number π has an infinite number of decimals, so it can not be represented as a fraction. Thn, it is not a rational number.
nswer: O√36 [ption B]
Given{x=7y-9 2x-14y= -18I think the solution is b? Am I correct?
there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)
Explanation:Given:
x = 7y - 9 . . .(1)
2x - 14y = -18 . . . (2)
To find:
the solution of the system of equations
To determine the value of x and y, we will apply the substitution method:
we will substitute for x in equation (2):
2(7y - 9) - 14y = -18
2(7y) + 2(-9) - 14y = -18
14y - 18 - 14y = -18
14y - 14y - 18 = -18
0 - 18 = -18
-18 = -18
The left-hand side of the equation is equal to the right side of the equation.
when this happens, it is called infinitely many solutions.
Hence, there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)
2, 4, 5, 6, 6, 7
What is the mean of the list of numbers above?
Answer: 5
Step-by-step explanation: add up the numbers to get 30 then divide by 6 (the amount of numbers) to get 5
Answer: 5
Step-by-step explanation:
the mean is the average. add the numbers together then divide by how many addends you have.
2 + 4 + 5 + 6 + 6 + 7 = 30
30/6 = 5
:)
a student measures which method of taking notes improves grades more, using a computer or a pencil and paper. what type of study is described?Sample StudyExperiment Observational Study Cluster Study
Since the student is meausuring something we conclude that this is an experiment.
m^2+5mn+5n^2factor each polynomial completely. If a polynomial is prime, state this.
m²+5mn+5n²
To factor the above, we need two factors of 5n², such the sum gives 5n and the product gives 5n²
No such factors exists, hence the polynomial is prime.
which of the relations has a domain of (-5, 0, 5)
Choice A
Is the answer
9m^2 - 49factor each expression. Be sure to check for the greatest common factor first.
We need to factor the following polynomial:
[tex]9m^2-49[/tex]We can see that:
[tex]9m^2=3^2m^2=(3m)^2[/tex]And
[tex]49=7^2[/tex]Then, we can use the following factor rule:
[tex]x^2-y^2=(x-y)(x+y)[/tex]We have that:
[tex]x=3m,y=7[/tex]Then, we can factor the polynomial as follows:
[tex]9m^2-49=(3m)^2-(7)^2=(3m-7)(3m+7)[/tex]In summary, we have:
[tex]9m^2-49=(3m-7)(3m+7)[/tex]Catalina is moving to a new house. Her old house is 3.5 miles away from her new house. How many feet are between Catalina’s old and new house?
18480 feet are between her old and new house
Look Ahead To find the new temperature, you found the sum of a positive anda negative integer. You can use a number line to help you think about addinga. During the day, the temperature at another weather station is 4°C. Overnight,it changes by-9°C Enrico models the situation on the number line below.Hasina says she can model it with one arrow. How can she model the situationLook Back whalHow do you know?positive and negative numbers.with just one arrow?434520 1-3 -2 -1
Let's begin by listing out the information given to us:
The sales tax in Arizona is 7.5%. The price tag on a T-shirt in Arizona says $11.50. What is the sales tax, in dollars, for this item?
Answer:
$0.8625
Explanation:
The sales tax for the t-shirt will be 7.5% of the price. So, 7.5% of $11.50 can be calculated as:
[tex]\text{ \$11.50 }\times\text{ 7.5\% = 11.50}\times\frac{7.5}{100}=\text{ \$0.8625}[/tex]So, the sales tax for this item is $0.8625
yasir received a 50% increase in his allowance this year. He now receives £33 a week. What was his weekly allowance last year?
Answer:
£22
Step-by-step explanation:
x+1/2x=33
1.5x=33
33/1.5=22
The weekly allowance for Yasir last year is £22.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Yasir received a 50% increase in his allowance this year. He now receives £33 a week.
The weekly allowance for last year will be calculated as,
1.5 x (X) = £33
X = £33 / 1.5
X = £330 / 15
X = £22
Therefore, Yasir's weekly allowance for last year is £22.
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I need this answered From my prep guid, pre calc
Given:
The equation of the ellipse is,
[tex]\frac{(x-2)^2}{36}+\frac{(y+3)^2}{12}=1[/tex]Explanation:
The general equation of ellipse with center (h,k) is,
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]The center of te given ellipse is (2,-3).
Determine the value of a and b.
[tex]\begin{gathered} a=\sqrt[]{36} \\ =6 \end{gathered}[/tex][tex]\begin{gathered} b=\sqrt[]{12} \\ =2\sqrt[]{3} \end{gathered}[/tex]The value of a is more than b. so major axis is horiontal and minor axis is vertical.
The coordinates of endpoints of major axis are,
[tex](2+6,3)=(8,-3)[/tex]and
[tex](2-6,3)=(-4,-3)[/tex]The coordinates of endpoints of minor axis,
[tex](2,-3+2\sqrt[]{3})[/tex]and
[tex](2,-3-2\sqrt[]{3})[/tex]or we can expressed coordinates of endpoints of minor axis as,
[tex](2,-3\pm2\sqrt[]{3})[/tex]a crew can clear 1/2 ton of dirt in 30 minutes. how many tons can they clear in 4 hours
Answer: 4 tons
Step-by-step explanation:
Since the crew can clear 1/2 ton in 30 minutes, 4 hours has eight 30 minutes, which means that 8x1/2 = 4
Answer: 4 tons
Step-by-step explanation:
30 minutes multiplied by 2 is 1 hour and 1 half times 2 is 1 ton, so the crew can clear one ton every hour. 4 hours times 1 ton is 4 tons an hour.
PLS HELP ME WITH THIS QUESTION ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of (x) will be equal to → x = 16 - K.
What is the perimeter?
Perimeter is the measure of the length of the boundary of any two dimensional shape.
Given is a quadrilateral with its sides given.
The perimeter of this quadrilateral will be the sum of the length of its sides. Since, in the question, the final value of perimeter is not given, therefore we will assume it as K. The perimeter will be equal to -
(7x - 1) + (- 8x - 5x) + (6x + 13) + (4 - x) = K
7x - 1 - 8x - 5x + 6x + 13 + 4 - x = K
16 - x = K
x = 16 - K
Therefore, the value of (x) will be equal to → x = 16 - K.
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6.Landscaping Calculate the area (in square feet) of a flower garden shaped like a circularsector with radius 60 ft and central angle 40 degrees.
The area of the circular sector is given as:
[tex]\begin{gathered} \text{Area}=\frac{\theta}{360}\times\pi r^2 \\ \end{gathered}[/tex]Given that, radius= 60ft and angle =40 degrees
[tex]\begin{gathered} \text{Area}=\frac{40}{360}\times3.14\times60\times60 \\ \text{Area}=\frac{452160}{360} \\ \text{Area}=1256\text{square f}eet \end{gathered}[/tex]Find sin S, sin R, cos S, cos R.sin S =sin R =cos S =cos R =
From the basic knowledge of Trignometry,
We are meant to find sin S , sin R , cos S and cos R:
sin S = opposite / Hypoteuse = 18 / 26
sin R = opposite / Hypotenuse = 16 / 26
cos S = Adjacent / Hypotenuse = 16 / 26
cos R = Adjacent / Hypotenuse = 18 / 26
A person invests $6,750 in an account that earns 5.25% annual interest compounded continuously. Findwhen the value of the investment reaches $15,000. If necessary round to the nearest tenth.The investment will be reach $15,000 in approximatelyyears.
Recall the formula for the Future value of a principal amount, compounded continuously.
[tex]\begin{gathered} A=Pe^{rt} \\ \text{where} \\ A\text{ is the Future Value} \\ P\text{ is the Principal amount} \\ r\text{ is the rate in decimals} \\ t\text{ is time in years} \end{gathered}[/tex]Rearrange the equation so that we can solve for time t.
[tex]\begin{gathered} A=Pe^{rt}^{} \\ \frac{A}{P}=\frac{Pe^{rt}}{P} \\ \frac{A}{P}=e^{rt} \\ e^{rt}=\frac{A}{P} \\ \ln e^{rt}=\ln \mleft(\frac{A}{P}\mright) \\ rt\ln e^{}=\ln \mleft(\frac{A}{P}\mright) \\ rt^{}=\ln \mleft(\frac{A}{P}\mright) \\ \frac{rt}{r}=\frac{\ln (\frac{A}{P})}{r} \\ t=\frac{\ln(\frac{A}{P})}{r} \end{gathered}[/tex]Now substitute the following given and we have
[tex]\begin{gathered} t=\frac{\ln(\frac{A}{P})}{r} \\ t=\frac{\ln (\frac{15000}{6750})}{0.0525} \\ t=\frac{\ln (\frac{20}{9})}{0.0525} \\ t=15.2096704\text{ years} \end{gathered}[/tex]Rounding the answer to the nearest tenth, the investment will reach $15000, in approximately 15.2 years.
Evaluate the expression.3 – 5 (11 + 4) = 52
In order to evaluate this expression, let's calculate the operations in the left side and compare the final value with the value in the right side:
[tex]\begin{gathered} 3-5(11+4)=52 \\ 3-5\cdot15=52 \\ 3-75=52 \\ -72=52 \end{gathered}[/tex]Since the values don't match, so the expression is FALSE.
2 PointsMULTIPLE CHOICEQuestion 42: PracticeWhich statements are true for the decimals 0.04 and 0.004?Choose two correct answers.in Base TenA0.04 is 10 times as much as 0.004.B.0.04 is 100 times as much as 0.004.Etice Solvingс0.004 is 10 the amount of 0.04.uizD0.004 is 100 the amount of 0.04
From the question;
we are given the decimal numbers
[tex]0.04\text{ and 0.004}[/tex]If we consider dividing 0.04 by 0.004 we will have
[tex]\frac{0.04}{0.004}=10[/tex]Therefore, 0.04 is 10 times as much as 0.004
Also, if we consider dividing 0.004 by 0.04 we will get
[tex]\frac{0.004}{0.04}=0.1=\frac{1}{10}[/tex]Therefore, 0.004 is 1/10 the amount of 0.04
Hence
Given the decimals 0.04 and 0.004 we have
1. 0.04 is 10 times as much as 0.004
2. 0.004 is 1/10 the amount of 0.04
If a car moves along a perfectly straight road at a velocity of 24 m/s, how far will the car go in 35 minutes?
Answer:
distance = rate x time
Step-by-step explanation:
distance = ?
rate = 24 m/s
time = (35 x 60) = 2100 s
thus,
distance = 24 x 2100 = 50400 m
Can someone tell me how to solve it with a picture on how you did it. Teacher told me to show my work. It hard pls Helppp
The solution to the given inequality in interval notation is: -6 ≤ v ≤ 3
How to solve the given inequality?In this exercise, you're required to determine all the values of v that simultaneously satisfy given inequality. First of all, we would have to eliminate the fraction on the left-hand side of the inequality by adding using an appropriate lowest common denominator of 3 as follows:
(2 × |4v + 6|)/3 - 2/1 ≤ 10
[(2 × |4v + 6|) - (3)2]/3 ≤ 10
[(2 × |4v + 6|) - 6]/3 ≤ 10
Cross-multiplying, we have:
(2 × |4v + 6|) - 6 ≤ 10 × 3
(2 × |4v + 6|) - 6 ≤ 30
Adding 6 to both sides, we have:
(2 × |4v + 6|) - 6 + 6 ≤ 30 + 6
(2 × |4v + 6|) ≤ 36
Dividing both sides by 2, we have:
(2 × |4v + 6|)/2 ≤ 36/2
|4v + 6| ≤ 18
Evaluating the absolute value function, we have:
4v + 6 ≤ ±18
For the positive interval, we have:
4v ≤ 18 - 6
4v ≤ 12
v ≤ 12/4
v ≤ 3.
For the negative interval, we have:
4v ≥ -18 - 6
4v ≥ -24
v ≥ -24/4
v ≥ -6
Lastly, we would express the solution as an interval notation as follows:
-6 ≤ v ≤ 3
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Use the inverse trigonometric keyson a calculator to find the measureof angle A
ANSWER
A = 51°
EXPLANATION
ABC is a right triangle. We know the length of the hypotenuse, AB = 44 m, and the length of the adjacent leg to angle A, AC = 28 m. To find the measure of angle A we have to use the cosine of that angle,
[tex]\cos A=\frac{AC}{AB}[/tex]Solving for A,
[tex]A=\cos^{-1}\left(\frac{AC}{AB}\right)[/tex]Replace with the known values and solve,
[tex]A=\cos^{-1}\left(\frac{28}{44}\right)=\cos^{-1}\left(\frac{7}{11}\right)\approx50.4788\degree\approx51\degree[/tex]Hence, the measure of angle A is 51°, rounded to the nearest whole number.
The tree diagram represents an experiment consisting of two trials
What is P(A)
The value of probability P(A) is 0.60
How to determine the probability?The clear tree diagram is added as an attachment
The given parameters from the tree diagram are:
Probability of event A: P(A only) = 0.6Probability of event A: P(A and C) = 0.3Probability of event A: P(A and D) = 0.7The probability is calculated using the following probability formula
P(A) = P(A and D) + P(A and C)
Substitute the known values in the above equation
P(A) = 0.6 * 0.7 + 0.6 * 0.3
Evaluate the products
P(A) = 0.42 + 0.18
Evaluate the sum
P(A) = 0.60
Hence, the value is 0.60
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Tracy's Termite Control has a net worth of $750,000. The assets total $980,235. Find the amount of the liabilities.$1,730,235$730,235$229,765$230,235None of these choices are correct.
Tracy's Termite Control has a net worth of $750,000.
The assets total $980,235.
Recall that the assets are the sum of liabilities and equity.
[tex]Assets=Liabilities+Equity[/tex]For the given case,
Assets = $980,235
Equity = $750,000
Let us substitute these values into the above formula and solve for liabilities
[tex]\begin{gathered} Assets=Liabilities+Equity \\ 980,235=Liabilities+750,000 \\ Liabilities=980,235-750,000 \\ Liabilities=\$230,235 \end{gathered}[/tex]Therefore, the amount of the liabilities is $230,235
The 4th option is the correct answer.
What is the equation of the
line that goes through
(-1, 3) and is perpendicular
to y = 4x - 7?
Answer:
Step-by-step explanation:Perpendicular lines have a slope that is the negative reciprocal of the given line.
For example, if a given line has the slope 3/2, the the perpendicular line would have the slope -2/3.
For the given line: y = 4x - 7, the perpendicular line would have a slope of -1/4
There isn't enough info in the question to determine the y-intercept. Literally, any y-intercept could work and the line would still be perpendicular. Is the line supposed to pass through a certain point?
Your answer would be something like: y = -1/4 x + b
b is the y-intercept...if your question paper is multiple choice, choose the answer with the slope of -1/4. If it's supposed to pass through a certain point (x,y) replace x and y with the values in that point and solve for b to get the y-intercept.