Answer:
[tex](5+3\sqrt{2} )^{2} =43+30\sqrt{2}[/tex]
≈85.43
Step-by-step explanation:
apply the binomial theorem to the square
[tex]=(5)^{2} +2(5)(3\sqrt{2} )+(3\sqrt{2} )^{2}[/tex]
[tex]=25+30\sqrt{2} +18\\[/tex]
[tex]=43+30\sqrt{2}[/tex]
≈85.43
Hope this helps
Hello!
Here, we apply the algebraic identity :
[tex]\boxed {(a + b)^{2} = a^{2} + 2ab + b^{2}}[/tex]
Let's solve!
⇒ (5 + 3√2)²
⇒ (5)² + 2(5)(3√2) + (3√2)²
⇒ 25 + 30√2 + 18
⇒ [tex]\boxed {43 + 30\sqrt{2}}[/tex]
∴ The final answer will be 43 + 30√2.
please help me i am struggling
The Equation is represented as [tex]\rm F = \dfrac{9}{5} (K -273.15 ) +32[/tex]
Option B is the answer.
What is an Equation ?An equation is am mathematical statement formed when an algebraic expression is equated by an equal sign with another algebraic expression or a constant.
A Equation is given in the question
[tex]\rm K = \dfrac{5}{9}(F -32) +273.15[/tex]
where K denotes temperature in Kelvins and F denotes Fahrenheit .
To convert the equation in terms of K it can be rewritten as follows
[tex]\rm K = \dfrac{5}{9}(F -32) +273.15\\\\K -273.15 = \dfrac{5}{9}(F -32) \\\\\dfrac{9}{5} (K -273.15 ) = F - 32\\\\F = \dfrac{9}{5} (K -273.15 ) +32[/tex]
Therefore Option B is the right answer.
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the probability that Luis will pass his test is 0.82. find the probability that he will fail his statistic test
The probability of failure for Luis will be 0.18.
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability of passing is = 0.82
We know that the maximum probability of happening any event is 1 or 100 per cent if the probability of passing of the person is 0.82 then the probability of failure will be calculated as:-
Probability of failing = 1 - probability of passing
Probability of failing = 1 - 0.82
Probability of failing = 0.18
Therefore the probability of failure for Luis will be 0.18.
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a dog is moving at a constant speed of 8 m/s. what is the dog’s acceleration
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Acceleration_{dog} = 0[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
A dog is moving at a constant speed of 8 m/s, that concludes that there's no change in its speed with respect to time.
And Acceleration is define as rate of change in velocity, but since velocity/speed is constant. change in velocity = 0
Henceforth, Acceleration of dog is 0 as well.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer: Acceleration = 0 ✅
Step-by-step explanation:
Hii, let me help you out! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 1Acceleration means "change in speed (which is also known as velocity, V, in physics) per a specific amount of time.
Part 1 is Successfully completed!
↪
Part 2Our Dog ProblemNow let's focus on finding the acceleration of the dog.
Like I said above, [tex]\sf Acceleration=change\;in\;speed\;per\;a\;specific\;amount\;of\;time[/tex]
Well, we are provided with the information that the dog's speed is constant. This means that it doesn't change. So the dog keeps on moving at a speed of 8 m/s. This means that its speed doesn't change, so the change in speed is 0. And this means that its acceleration is 0.
Voila! There's our answer, cheers! (:
___________________Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
the price for each ticket is 7.99 one person thinks the total for all eight people will be around 50.00 is this a reasonable estimate. why?
Answer:
No
Step-by-step explanation:
no because just muiltiplying 7.00 * 8 is 56 not inculuding the 99 cents it is already over 50. The answer is 63.92 so a reasonable estimate would be around $60
Find an equation for the line that passes through the point P(-5,-3) and is parallel to the line
7x + 4y
10. Use exact values.
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -1.75x - 11.75}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: We need to first solve for y in the equation that was provided so we can determine the slope. Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.
Subtract 7x from both sides
[tex]\textsf{7x - 7x + 4y = 10 - 7x}[/tex][tex]\textsf{4y = 10 - 7x}[/tex]Divide both sides by 4
[tex]\textsf{4y/4 = (10 - 7x)/4}[/tex][tex]\textsf{y = (10 - 7x)/4}[/tex][tex]\textsf{y = 10/4 - 7x/4}[/tex][tex]\textsf{y = 2.5 - 1.75x}[/tex]Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-3) = -1.75(x - (-5))}[/tex]Simplify and distribute
[tex]\textsf{y + 3 = -1.75(x + 5)}[/tex][tex]\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}[/tex][tex]\textsf{y + 3 = -1.75x - 8.75}[/tex]Subtract 3 from both sides
[tex]\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 11.75}[/tex]Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75
(X+p)(x+q) what part of the trinomial will equal the product of p and q?
The part of the trinomial that will equal the product of p and q is the constant part
How to determine the part?The expression is given as:
(x + p)(x + q)
From the expression, p and q are both constants.
When a constant is multiplied to another, the result is a constant
This means that:
pq = constant
Hence, the part of the trinomial that will equal the product of p and q is the constant part
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The graph of (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of (in red).
The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation h(x) = -1/2(x -3)² + 4
Translation of coordinates and functionThe given graph is a quadratic graph. Given the function of the blue parabola expressed as:
f(x) = -1/2x²
The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation
h(x) = -1/2(x -3)² + 4
Note that the upward translation will be positive while the horizontal shift to the right will be negative
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i need help please very fast thanks
Outside of the United States, many countries use ____ for their accounting standard.
A. the Common Market accounting methods
B. the international agreement on taxes and tariffs
C. the International Financial Reporting Standards
D. generally accepted accounting practices
Which equation has a constant of proportionality equal to 1/2
Choose 1 answer:
Can anyone Help I have 25 questions, 2hr 40mins remaining,
Combining the like-terms, the result of the addition of polynomials f(x) and g(x) is given by:
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
How do we add polynomials?We add polynomials combining the like-terms, that is, adding terms with the same exponent.
In this problem, the polynomials are:
[tex]f(x) = 3x^{\frac{1}{2}} + 7x^{-\frac{1}{4}} + 8x^{-4}[/tex][tex]g(x) = -\frac{7}{4}x^{\frac{1}{2}} + 12x^{-\frac{1}{4}} - 21x^3[/tex]Combining the like terms, the addition is given by:
[tex]f(x) + g(x) = \left(3 - \frac{7}{4}\right)x^{\frac{1}{2}} + (7 + 12)x^{-\frac{1}{4}} + 8x^{-4} + 21x^3[/tex]
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
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Find the domain and range of the following graph
Write your answer as an interval.
Answer:
Domain: [1, infinity)
Range: All real numbers or (- infinity, + infinity)
Step-by-step explanation:
Hope this helps
In your own words, explain the discriminant test. Use the discriminant test to decide whether the equation represents a parabola, ellipse or a hyperbola and explain why you know this is true. x^2 − 4xy + 3x + 25y − 6 = 0
A discriminant test is one that tells whether a formula has one, two or no solutions.
The equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
What is a discriminant test?A discriminant test is a test that tells whether there are one, two or no solutions for a formula.
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac.
The discriminant of a quadratic equation is given as ax2 + bx + c = 0
A discriminant is said to be a parabola either x or y is squared and not both unlike that of an eclipse and a hyperbola.
With the given equation, x^2 − 4xy + 3x + 25y − 6 = 0, only x is squared and not both x and y.
Thus, the equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
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How much is Bob's net salary for the week? Question 32
Answer:
A. $152.00
Step-by-step explanation:
I'm 99% sure the net salary is just the 220 (gross salary) minus everything else taken away which is (42 + 7 + 15 + 4) = 68. 220 - 68 = 152 so Bob's net salary would be 152
DRaw the graph of f (x) = 1/2 x² -2x where -2 < x < 4
Answer:
Graphs Attached Below
Step-by-step explanation:
Hello!
Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]
From our Equation:
a = 1/2b = -2c = 0There are several values that are needed to drawing a parabola:
y - interceptAxis of Symmetry (AOS)Vertexx - interceptsY-interceptStandard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]
The y-intercept is the "c" value. Given that our equation has a "c" value of 0, the y -intercept is 0.
Axis of SymmetryA parabola is always symmetrical vertically. The line in which the fold happens is the Axis of Symmetry.
To calculate the AOS, we use the formula [tex]AOS = \frac{-b}{2a}[/tex], from the values of the equation.
Calculate
[tex]AOS = \frac{-b}{2a}[/tex][tex]AOS = \frac{-(-2)}{2(0.5)}[/tex][tex]AOS = \frac{2}{1}[/tex][tex]AOS = 2[/tex]The Axis of Symmetry is a vertical line, so the AOS is the line x = 2.
VertexThe vertex is the highest or lowest point on the graph of a parabola. It resides on the AOS of the graph.
To calculate the vertex, we simply have to find the y-value, given that we have the x-value from the AOS. We can find the y-value by plugging in the AOS for x in the original equation.
Calculate
[tex]f(x) = \frac12x^2 - 2x[/tex][tex]f(x) = \frac12 (2)^2 - 2(2)[/tex][tex]f(x) = 2 - 4[/tex][tex]f(x) = -2[/tex]The y-value is -2. The vertex is (2, -2).
X-interceptsThe x-intercepts are the points where the graph intersects the x-axis (y = 0).
Solve by Factoring
[tex]f(x) = \frac12 x^2 - 2x[/tex][tex]0 = \frac12x(x - 4)[/tex][tex]x = 0, x = 4[/tex]The roots are (0,0) and (4,0).
GraphNow we just draw the y-intercept, vertex, AOS, and the x-intercepts, and draw a curved line between them.
Image Attached
Domain RestrictionsThe Domain (x-values) are being restricted to all x-values that are greater than or equal to -2 and less than 4.
That means we remove the parts of the line that don't belong in that domain.
Image Attached
21% of hospital patients stay for less than 1 day. If 1,134 patients in January stay less than 1 day what total of number of patients did the hospital treat in January?
g(x)=f(x)-3 which statement best describes the graph of g(x) with the graph of f(x)
Answer: The graph of g(x) is the graph of f(x) shifted 3 units down.
What amount would u have if u deposited 1800 a year for 30 years at 7% compounded annually
Answer: $183,731
Step-by-step explanation:
After 30 years, the interest is $183,731
The Candle Factory is producing a new candle. It has a radius of 3 inches and a height of 5 inches. How much wax is needed to make the candle? Use 3.14 for Pi. Round to the nearest whole cubic inch.
A cylinder with a radius of 3 inches and height of 5 inches.
Recall the formulas S A = 2 pi r squared + 2 pi r h and V = pi r squared h.
141 cubic inches
236 cubic inches
443 cubic inches
565 cubic inches
Answer:
141 cubic inches
Step-by-step explanation:
The candle can be modeled as a cylinder.
To find how much wax is needed to make the candle, calculate the volume of the cylinder.
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 3 inh = 5 inπ = 3.14Substitute the given values into the formula and solve for V:
[tex]\implies \sf V=3.14 \cdot 3^2 \cdot 5[/tex]
[tex]\implies \sf V=3.14 \cdot 9 \cdot 5[/tex]
[tex]\implies \sf V=28.26 \cdot 5[/tex]
[tex]\implies \sf V=141.3\:in^3[/tex]
Therefore, the amount of wax needed to make the candle is 141 cubic inches (nearest whole cubic inch).
PLEASE HELP WITH THIS PROBLEM!
Answer: Options 1 and 2
Step-by-step explanation:
To model exponential decay, the base of the exponential has to be less than 1.
Model exponential decay equation are
y = 0.34(0.98)^x
y = 8 (0.28)^x
Model exponential decay equation
Model exponential decay equation has the base value which is less than 1.Exponential decay is the process of reducing amount by consistent percentage rate over a time period. It can be expressed by the equation y=a(1-b)x where y is the final amount, a original amount, b decay factor, and x is the amount of time that has passed.Option C and D have the base value greater than 1. So it can't be model exponential decay equation.
Hence, the model exponential decay equation are
y = 0.34(0.98)^x
y = 8 (0.28)^x
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Help me with this question please and thank you!! :)
Question 1
The complement of set B is all the elements in S but that are not in B, which is [tex]\{2, 4, 5, 9, 10, 11, 12, 13, 14, 17, 19\}[/tex].
We want to find the intersection of set A and the complement of set B, which is the set of all elements that both sets contain.
This is {2, 9, 10, 12}, meaning there are 4 elements.
Question 2
Following a similar logic as the last problem, the complement of set A is [tex]\{1,3,4,5,6,7,11,13,14,15,17,18,19\}[/tex].
Therefore, the desired set is [tex]\{1,3,6,7,15,18\}[/tex], and thus there are 6 elements.
From this diagram, select the
pair of lines that must be
parallel if 24 = 23. If there
is no pair of lines, select
"none."
O is parallel to q
let's take the angle opposite to angle 4 is alpha
angle 4 = angle alpha ( vertically opposite angles)
angle alpha = angle 3 ( as angle 4 = angle 3).
hence o is parallel to q as both the angles are equal
Mitch needs to do his laundry. It takes him 75 minutes to do each load
when he washes and dries the load. It takes him 43 less minutes if he
hangs up his laundry to dry. He decides to hang up one load of laundry
to dry.
Mitch writes the equation 75r -43 = 332, where x is the number of loads
of laundry he needs to do in order to determine how long it is going to
take him.
The next step Mitch wrote to solve the equation is shown here: 75r = 375
Which property did he use to get to this step?
A
addition property of equality
B
distributive property
C
subtraction property of equality
D
combining like-terms
Answer: [A] addition property of equality
Step-by-step explanation:
Mitch used the addition property of equality because he added 43 to both sides of the equation.
75r - 43 = 332
43 + (75r - 43) = (332) + 43
75r = 375
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A medication states that the odds of having an allergic reaction are 2 in 200. What is that probability states as a percent?
Help asap !………………………
Answer:
c
Step-by-step explanation:
dvdywuwhfuwi eurue wuid
if the relationships below are given in the form(input, output) which paring always describes a function
The function among the given option is height of a building in feet, height of the building in inches , Option B is the correct answer.
What is a Function ?
A function is a law that relates a dependent and an independent variable.
The options mentioned below needs to be studied to determine which forms a function.
Option A , C and D doesn't really form a function ,
For two variables need to be a function then they have to be dependant on each other and have only one output for a given input.
height of a building in feet, height of the building in inches
Height of building in feet = (height of building in inches/12)
so this is a function
Therefore Option B is the right answer.
The missing options are
If the relationships below are given in the form (input, output), which pairing always describes a function?
A) (number of doors in a car, number of cup holders in the car)
B) (height of a building in feet, height of the building in inches)
C) (beverage charge on a bill, total meal charge on the bill)
D) (distance from home during a trip, time elapsed during the trip)
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What is the simplified form of √ 144x36?
Answer:
12x^18
Step-by-step explanation:
Fill in the blank. In the triangle below, y=? Round your answer to two decimal places.
Answer:
z= 38°
Step-by-step explanation:
z= 90(from right angle)+52=142
180-142=38°
se the distributive property to remove the parentheses.
-(-3v-4w+1)
Hii!
[tex]\leadsto\parallel\boldsymbol{Answer.}\parallel\gets[/tex]
_________________________________________________________
3v+4w-1
__________________________________________________________
[tex]\leadsto\parallel\boldsymbol{Explanation.}\parallel\gets[/tex]
We use the distributive property to "distribute" the minus sign.
[tex]\sf -(-3v-4w+1)=-1\cdot(-3v)+(-1)\cdot(-4w)+(-1)\cdot1}[/tex].
Simplify!
[tex]\sf 3v+4w-1}[/tex]. Which is our final answer.
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]
[tex]\boldsymbol{-Greetings!-}[/tex]
_________________________________________________________
Four students were asked to write an expression which has terms that have a greatest common factor of ab. The
expressions provided by the students are shown below.
Olivia
20ab-14abc
Michelle
16a+3b
Michelle
Naomi
Which student wrote the correct expression?
O Olivia
O Peyton
Naomi
18abc-13abc
Peyton
15abc+ 14ab
Answer: Peyton
Step-by-step explanation:
Michelle: Greatest common factor is 1
Naomi: Greatest common factor is abc
Olivia: Greatest common factor is 2ab
Peyton: Greatest common factor is ab
