Answer:
90 degrees
Step-by-step explanation:
We can take a look at that each these triangles are in truth right triangles, seeing that the two angles of and both have measures of 90 degrees.
(02.01, 02.02 HC)Vanessa and William are stuck simplifying radical expressions. Vanessa has to simplifyx3William has to simplify 15xx.x4. Usingx6full sentences, describe how to fully simplify Vanessa and William's expressions. Describe if Vanessa and William started with equivalentexpressions or if they started with expressions that are not
ANSWER:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=x^{\frac{1}{2}} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the given expression is the following:
[tex]\frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}[/tex]The other expression is the following:
[tex]\sqrt[16]{x\cdot \:x^3\cdot \:x^4}[/tex]We simplify in each case:
[tex]\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{4}{3}-\frac{5}{6}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=\sqrt[16]{x^{1+3+4}}=\sqrt[16]{x^8}=x^{\frac{8}{16}}=x^{\frac{1}{2}} \end{gathered}[/tex]This means that the expressions are equal
Use the graph to write the factorization of x2 + 4x - 5.10+y = x2 + 4x-5-1010-10O A. (x + 1)(x - 5)B. (x + 5)(x-1)C. (x-3)(x-2)D. (X+6)(x-2)
Solution
From the given graph
The zeros of the given graph are
[tex]x=-5,1[/tex]Converting the zeros to roots gives
[tex]\begin{gathered} x=-5,1 \\ x=-5 \\ x+5=0 \\ x=1 \\ x-1=0 \end{gathered}[/tex]The factorized form of the equation of the given graph is
[tex](x+5)(x-1)[/tex]Hence, the answer is option B
Please help me I’m miserable because I was sick.It’s 2:00AM and this is due at 8 somebody please help me
Answer:
see explanation
Step-by-step explanation:
(a)
the angles shown are alternate interior angles and are congruent
(c)
since they are congruent , then
- 1 + 8x = 7x + 11 ( subtract 7x from both sides )
- 1 + x = 11 ( add 1 to both sides )
x = 12
(d)
then
7x + 11 = 7(12) + 11 = 84 + 11 = 95
- 1 + 8x = - 1 + 8(12) = - 1 + 96 = 95
A rectangle is 4 meters longer than it is wide. Find the dimensions of the rectangle if its area is 165 sq-meters.
Answer:
width = 11 and length = 15
Step-by-step explanation:
→ Find algebraic length and width
width = x ∴ length = x + 4
→ Find area
x ( x + 4 ) = x² + 4x
→ Equate to area
x² + 4x = 165
→ Solve
x = 11
→ Find length and width
width = 11 and length = 15
K is the midpoint of JL. If JK = 6x and JL = 13x − 7, what is JK?
The length of JK is 42.
JL is a line and K is the mid-point of that line.
J____________.___________L
K
From this we get:
JK = KL
JL = JK + KL
JL= 2JK = 2KL
Here it is given that,
JK = 6x and JL = 13x - 7
JL = 2JK
13x - 7 = 2× 6x
13x - 7 = 12x
x = 7
We have to find the length of JK
JK = 6x
=6× 7
= 42
Therefore the length of JK is 42.
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Maddox has $100 and plans to spend $20 each time he goes to the movies. At this rate,how many times can Maddox go to the movies?O $5O 5 timesО 4 timesO $120
ANSWER
EXPLANATION
addox has $100.
He plans to spend $20 each time he goes to the movies.
To find out how many times he can go to the movies,
In the box below, explain why this is an error. What should he have done?
He should have divided both sides by -10.
Write a quadratic function given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
y=(x+3)(x=2)
y=(x-3)(x+2)
y=3(x-3)(x-2)
y=3(x-3)(x+2)
Quadratic function is 3(x+3)(x-2) given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).
What is quadratic function?In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
Standard form, vertex form, and intercept form are three alternative ways a quadratic function can be expressed. The basic forms of each of them are as follows:
f(x) = ax² + bx + c in standard form, where a 0.
Vertex form: (h, k) is the vertex of the parabola representing the quadratic function, and f(x) = a(x - h)² + k is the equation.
The quadratic function's x-intercepts are (p, 0) and (q, 0), and its intercept form is f(x) = a(x - p)(x - q), where a 0.
Given Data
Roots (-3,0) and (2,0)
Point (1,-12)
y = a(x-(-3) (x-2)
y = a(x+3)(x-2)
Equating points
-12 = a(1+3)(1-2)
-12 = a(4)(-1)
-12 = -4a
a = 3
f(x) = 3(x+3)(x-2)
Function is 3(x+3)(x-2).
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Can i get some help
Answer:
Explanation:
iven the function:
Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{3}{8}-\frac{1}{6}
8
3
−
6
1
Step-by-step explanation:
A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. To simplify a fraction: divide the top and bottom by the greatest number that will divide both numbers exactly.
I hope this helps.
Step-by-step explanation:
8/3
8-3=6
6/3
6-3=
3The sun is shining on a house and fence. The roof of the house is 16 feet from the ground and makes a shadow 24 feet long. The fence is 4 feet tall. How long is the fence's shadow?
The length of the shadow of fence will be equal to 6 feet.
Proportionality may be defined as the term which can be used to describe or denote a relationship between two entities which are always in the same ratio. For example, the number of bananas is proportional to the number of trees with the proportionality being average number of bananas per number of trees. Here, we are given the height of house = 16 feet and length of its shadow = 24 feet and also the height of fence = 4 feet. Since, both house and fence lie in the same area they both are proportional. Let the length of shadow be x. Since, they are proportional
16/24 = 4/x
2/3 = 4/x
=> x = 12/2
=> x = 6 feet.
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Evaluate: - 2 to the third power - 45(15+10-23)
1. Remember
[tex]2^3[/tex]Means
[tex]2\times2\times2[/tex]Therefore,
[tex]2^3=2\times2\times2=8[/tex]2. Remember that we have to solve what's inside the parenthesis first. Therefore,
[tex]45(15+10-23)=45(2)=90[/tex]If Alejandra estimates that one outfit welghs two pounds and one pair of shoes welghs three pounds, which graph represents the number of
outfits and shoes that Alejandra can pack while staying under the weight limit?
A graph which represents the number of outfits and shoes that Alejandra can pack while staying under the weight limit is shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In this scenario, the x-axis represents the number of outfits while the y-axis represents the number of shoes. Additionally, since one pair of shoes weighs three (3) pounds and one outfit weighs two (2) pounds, the x and y coordinates would be given by this inequality:
2x + 3y < 30
Making y the subject of formula, we have:
3y < -2x + 30
Dividing all through by 3, we have:
3y/3 < -2x/3 + 30/3
y < -2x/3 + 10
Note: For 30 pounds, there would be 10 shoes (0, 10) while for 30 pounds, there would be 15 outfits (15, 0).
In conclusion, the boundary line is dashed or dotted to indicate that the boundary is not part of the solution because the inequality symbol is less than (<).
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Element X is a radioactive isotope such that every 70 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 610 grams, how much of
the element would remain after 17 years, to the nearest whole number?
The element would remain 515 grams after 17 years.
What is isotope?Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.
Given Data
the initial mass of a sample of Element X is 610 grams
Element X is a radioactive isotope such that every 70 years, its mass decreases by half.
Since the half-life, or the number of years after which an isotope decays to half its original level, is stated to be 70 years.
k = [tex]\frac{2}{70}[/tex]
k= 0.0099
Equation-
N = 610e⁻⁰°⁰⁰⁹⁹ˣ
x = time
time = 17
N = 610 e⁻⁰°⁰⁰⁹⁹⁽¹⁷⁾
N = 610(0.845)
N = 515.49
The element would remain 515 grams after 17 years.
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Select the three pairs of numbers that 403 is between.
Answer:
1 and 403 13 and 31 13 and 31
Step-by-step explanation:
Evalúe the limit. Show steps
Answer: sqrt{3} over 2, this also equivalent to 0.866025
6. A certificate of deposit (CD) is a savings instrument that many banks offer. It usually gives a
higher interest rate, but you cannot access your investment for a specified length of time.
Suppose you deposit $3000 in a CD paying 6% interest, compounded monthly. How much will
you have in the account after 20 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases} \\\\\\ A=3000\left(1+\frac{0.06}{12}\right)^{12\cdot 20} \implies A=3000(1.005)^{240}\implies A \approx 9930.61[/tex]
At the neighborhood grocery, 0.5 pounds of chicken thighs cost $3.14 Taub spent $29.83 on chicken thighs. How many pounds of chicken thighs did she buy, to the nearest hundredth of a pound?
Taub bought 4.75 pounds of chicken thighs at the neighborhood grocery.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying direct proportion, we have:
0.5 pounds of chicken thighs = 3.14 dollars
X pounds of chicken thighs = 29.83 dollars
Cross-multiplying, we have:
3.14X = 0.5 × 29.83
3.14X = 14.915
X = 14.915/3.14
X = 4.75 pounds of chicken thighs.
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Find the product.
(b-na)(4b+9na)
Enter the correct answer.
The product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².
How do you find the product of an expression?Algebraic expressions can be multiplied using the following procedures. You can start by calculating the algebraic sum of the like and unlike terms, multiplying the term coefficients, and adding the variable powers with the same base.
Given:
To find the product of (b-na)(4b+9na).
To determine the product, multiply each term of the first expression by each term of the second expression.
(b-na)(4b+9na)
= 4b² + 9abn - 4abn - 9a²n²
= 4b² + 5abn - 9a²n²
Therefore the product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².
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i need help with this asap Consider the following equations.Approximate the solution to the equation f(x) = g(x) using three iterations of successive approximation. Use the graph below as a starting point.
we have the equations
[tex]\begin{gathered} f(x)=\frac{x+1}{x^2} \\ \\ g(x)=\frac{x-1}{x+1}+1 \end{gathered}[/tex]equate both equations
[tex]\frac{x+1}{x^2}=\frac{x-1}{x+1}+1[/tex]First iteration
For x=1
[tex]\begin{gathered} \frac{1+1}{1^2}=\frac{1-1}{1+1}+1 \\ \\ 2=1 \end{gathered}[/tex]For x=2
[tex]\begin{gathered} \frac{2+1}{2^2}=\frac{2-1}{2+1}+1 \\ \\ \frac{3}{4}=\frac{1}{3}+1 \\ \\ \frac{3}{4}=\frac{4}{3} \\ 0.75=1.33 \end{gathered}[/tex]For x=1.5
[tex]\begin{gathered} \frac{1.5+1}{1.5^2}=\frac{1.5-1}{1.5+1}+1 \\ \\ \frac{\frac{5}{2}}{\frac{9}{4}}=\frac{\frac{1}{2}}{\frac{5}{2}}+1 \\ \\ \frac{20}{18}=\frac{1}{5}+1 \\ \frac{10}{9}=\frac{6}{5} \\ 1.11=1.2 \end{gathered}[/tex]the answer must be less than 1.5 and greater than 1
so
Verify each option
A ----> 13/8=1.625 -----> is not a solution
B ----> 23/16=1.4375 ---> could be an approximate solution
C ---> 25/16=1.5625 ----> is not a solution
D ---> 7/4=1.75 ----> is not a solution
therefore
The answer is option BThe midpoint of AB is M (−6, 2). If the coordinates of A are (-5, -2), what are
the coordinates of B?
Answer:
(-7,6)
Step-by-step explanation:
Midpoints
x = (x1 + x2)/2
y = (y1 + y2)/2
-6 = (-5 + x2)/2
x2 - 5 = -12
x2 = -7
2 = (-2 + y2)/2
y2 - 2 = 4
y2 = 6
An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 44% probability of winning the first contract. If they win the first contract, the probability of winning the second is 66%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 54%.
A. What is the probability that they win both contracts?
B. What is the probability that they lose both contracts?
C. What is the probability that they win only one contract?
A) The probability that the Aerospace Company wins both contracts is 29.04%.
B) The probability that the Aerospace Company loses both contracts is 70.96%.
C) The probability that the Aerospace Company wins only one contract is 23.76%.
What is the probability?Probability describes the chance or likelihood of an expected event occurring out of many outcomes.
Probability is a ratio of an outcome versus many possible events.
Probability is represented as a percentage, fraction, or decimal, like a ratio.
How the probabilities are calculated:The probability of winning the first contract = 44%
The probability of losing the first contract = 56% (1 - 44%)
The probability of winning the first and the second contract = 66%
The probability of losing the first and the second contract = 34% (1 - 66%)
The probability of losing the first contract and winning the second = 54%
A) The probability that they win both contracts = the probability of winning the first contract multiplied by the probability of winning the second contract.
= 29.04% (44% x 66%)
B) The probability that they lose both contracts = 1 minus the probability of winning both contracts.
= 70.96% (1 - 29.04%)
C) The probability that they win only one contract = the probability of winning the first contract multiplied by the probability of winning only the second contract.
= 23.76% (44% x 54%)
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ƏR Ər Find for the following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x ADSER y, w = 2xy
The chain rule tells us how to find derivative of a composite function., The following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x-y, w = 2xy ƏR/Əx= 9/7 and ƏR/Əy = 9/7.
What is chain rule?The Chain Rule is a mathematical method to differentiate a composition of the functions. From this composition of the functions, we can discern the functions' derivatives and their relationships.
In other words, the derivative of composite function = derivative of the outside function × derivative of the inside function.
The Chain Rule gives:
ƏR/Əx= ƏR/Əu × Əu/Əx + ƏR/Əv × Əv/Əx + ƏR/Əw × Əw/Əx
= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *1 + \frac{2v}{u^{2}+v^{2}+w^{2} } *2+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2y[/tex]
When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so
ƏR/Əx = 6/14 × 1+ 2/14 ×2+ 4/14×2 = 18/17 = 9/7
ƏR/Əy= ƏR/Əu × Əu/Əy + ƏR/Əv × Əv/Əy + ƏR/Əw × Əw/Əy
= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *2 + \frac{2v}{u^{2}+v^{2}+w^{2} } *(-1)+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2x[/tex]
When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so
ƏR/Əy = 6/14 × 2 + 2/14 × (-1) + 1/14 × 2= 18/14 = 9/7
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HELP! ALgebra 2
A soccer ball is kicked into the air so that its height, h, in feet, after t seconds is given by the function:
h(t)= -16t^2+96
What is the maximum height the ball reaches?
How long is the ball in the air?
The maximum height reached by the ball in discuss as described is; 96 while the time spent by the ball in the air is; 0 seconds.
What is the maximum height the ball reaches and how long was the ball in the air?It follows from the task content that the maximum height of the ball in the air is to be determined and so.is the time spent by the ball in the air.
Therefore, since the correct form of the function given is;
h(t) = -16t² + 96
By expressing the function above in vertex form; it follows that we have;
h(t) = -16 (t - 0)² + 96.
This vertex form function above therefore translates to the fact that the point, (0, 96) represents the vertex of the balls motion curve.
Ultimately, the maximum height reached by the ball is; 96 and the time it takes to reach this height is; 0 seconds.
PS; The scenario above in real life situation would translate to dropping a ball from the top.
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(-8.8)(-9) = ? im confused?
Answer: 79.2
Step-by-step explanation: if you take -8.8 x -9 take out the negative completely because we are multiplying 2 negatives you never have to worry about the them. 8.8 x 9 = 79.2
side note: + x + = + - x - = + - x + = - + x - = -
Meghan has her own business. When she makes money, it is called income. When she spends money, it is called expenses. Choose the phrases below to explain how to use positive or negative integers to represent income and expenses.
You would use
Choose...
integers to represent income because it is a
Choose...
amount.
You would use
Choose...
integers to represent expenses because they are
Choose...
income.
The positive integer represents an addition to the income while.a negative integer represents a subtraction.
How to illustrate the information?Positive integers are used to represent income since they indicate an increase rather than a decrease in the financial value of the company. In other words, cash is coming in rather than leaving. A positive number 10 is used as an example to illustrate an increase in operating revenue when there is profit on items sold, say $10.
When you express an expense with a negative number, you're actually subtracting money value rather than adding it. In other words, money is leaving the company rather than being brought in. For instance, when a transportation expense is incurred to deliver items to the customer, it is recorded as an expense deducted from, let's say, the business' revenue sales. Since they are already identified and recognized as expenses and deducted nonetheless, they are typically shown in brackets in accounting to signify negative worth.
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What are the dimensions of a right triangle with an eight-inch hypotenuse and an area of 16 square inches?
The dimensions of the given right triangle would be 5.66 inches and 11.31 inches.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Let the legs of the triangle be x and y
Using the Pythagorean theorem:
c² = a²+b²
So the hypotenuse will be:
x² + y² = 8²
x² + y² = 64
x² = 64 - y²
So the area of the triangle is:
A = 1/2bh
A = 1/2xy
⇒16 = 1/2xy
32 = xy
x = 32/y
x² = 1024/y²
Substitute the above value in x² = 64 - y² and solving for y we get:
1024/y² = 64 - y²
1024 = 64y²- y⁴
This can be written as:
y⁴ - 64y² + 1024 = 0
Thus y = 4√2 = 5.66
x = 64/(4√2)= 16/√2 = 8√2 = 11.31
Therefore, the dimensions of the given right triangle would be 5.66 inches and 11.31 inches.
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Write the quadratic equation whose roots are -6 and 5, and whose leading coefficient is 2 .
Answer: y = 2x² + 2x - 60
Step-by-step explanation:
We will write this in factored form since we are given the roots and leading coefficient. This will be written in the form y = c(x - a)(x - b) where c is the coefficient and a & b are the roots.
y = c(x - a)(x - b)
y = 2(x + 6)(x - 5)
Now, we will distribute so we end up with the standard quadratic equation form.
y = 2(x + 6)(x - 5)
y = 2x² + 2x - 60
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Find the equation of the graph given below. Notice that the cosine function is used in the answer template, representing a
cosine function that is shifted and/or reflected.
When entering in your answer, use the letter a rather than the multiplication symbol.
Provide your answer below:
Answer:
y = 1/2cos(x/2 -5π/4) -1
Step-by-step explanation:
You want the equation of the shifted and scaled cosine function shown in the graph.
TranslationA point on a function f(x) will be translated (right, up) = (h, k) by the transformation ...
g(x) = f(x -h) +k
ScalingA function will be vertically expanded by a factor of p and horizontally expanded by a factor of q by the transformation ...
g(x) = p·f(x/q)
Graphed functionThe graph shows a cosine function with a peak-to-peak amplitude of 1, which is 1/2 the parent function's amplitude, so p=1/2.
The period is (9π/2 -π/2) = 4π, which is twice the period of the parent cosine function, so q=2.
The first peak of the graphed waveform is at x=5π/2, and the midline of the graphed waveform is y=-1, so we have (h, k) = (5π/2, -1).
Putting these transformations together, we find the equation of the graph to be ...
y = 1/2cos((x - 5π/2)/2) -1 . . . . . . scaling applied before translation
y = 1/2cos(x/2 -5π/4) -1
can someone help me with this
If each of the 4 sloping side ahs length 10 cm
This implies they have length 40 cm altogether
To find the base length, simply subract the 40 cm from the total length of 68cm
68 - 40 = 28
each base length = 28/4 = 7cm
Area of the square base is = l x l = 7 x 7 = 49 cm²