Answer:
The given equation is expansion of (a-b)² = a²-2ab+b²
[tex]\sqrt{81-18\sqrt{7}+7} \\ \sqrt{ {9}^{2} -2 \times 9 \times \sqrt{7}+ { \sqrt{7} }^{2} } \\ \sqrt{ {(9 - \sqrt{7})}^{2} } \\ {(9 - \sqrt{7})}[/tex]
hope that help.
Answer:
[tex]9-\sqrt{7}[/tex]
Step-by-step explanation:
Given expression: [tex]\sqrt{81-18\sqrt{7}+7}[/tex]
To simplify the given expression, use the "A minus B Whole Square" identity.
A minus B Whole Square identity
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Comparing [tex]81-18\sqrt{7}+7[/tex] to the right side of the identity:
[tex]a^2=81 \implies a=\sqrt{81}=9[/tex][tex]b^2=7\implies b=\sqrt{7}[/tex][tex]-2ab=-18\sqrt{7}=-2 \cdot 9\sqrt{7}[/tex]Therefore:
[tex](9-\sqrt{7})^2=81-18\sqrt{7}+7[/tex]
Finally:
[tex]\sqrt{81-18\sqrt{7}+7}=\sqrt{(9-\sqrt{7})^2}=9-\sqrt{7}[/tex]
Fractional Area
What fraction of the square's total area
is shaded?
Answer:
7/32
Step-by-step explanation:
O
1) Complete the square to determine the maximum or minimum value of the function defined by the expression.
x² - 2x-5
A) minimum value at 1
B) minimum value at -6
C) minimum value at -1
D) maximum value at -6
please help ASAP
tthankyou
answer is below in attachment
Answer:
10, 13, 15.Step-by-step explanation:
Solve all possible equations:
8 + 10 + 1 + 9 + 2Adding them all up we get:8 + 10= 18 + 1= 19 + 9= 28 + 2= 3030 < 40.10 will be used for the next equation:
2nd equation:
10 + 12 + 1 + 13 + 2Solve:10 + 12= 22 + 1= 23 + 13= 36 + 2= 3838 < 40.13 will be used for the final equation:
Final equation:
10 + 13 + 1 + 15 + 2= 10 + 13= 23 + 1= 24 + 15= 39 + 2= 41.41 > 40.The 3 digits are 10, 13, 15.According to the rational root theorem, negative seven-eighths is a potential rational root of which function? f(x) = 24x7 3x6 4x3 – x – 28 f(x) = 28x7 3x6 4x3 – x – 24 f(x) = 30x7 3x6 4x3 – x – 56 f(x) = 56x7 3x6 4x3 – x – 30
According to the rational root theorem, -7/8 is a potential rational root of: A. f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28.
What is a rational root theorem?A rational root theorem is also referred to as rational root test and it states that when the coefficients of a polynomial are integers, all of the possible rational roots can be determined by dividing each factor of the constant term by each factor of the coefficient of the highest power (leading coefficient).
In Mathematics, the canonical form for a polynomial in one variable (x) is given by:
[tex]a_n x^n + a_{n-1} x^{n-1} +a_1 x^1 +a_0=0[/tex]
Therefore, the potential rational root of the above polynomial is ±factors of a₀ dividided by ±factors of [tex]a_n[/tex] i.e ([tex]\pm a_0/\pm a_n[/tex]).
For this exercise, -7/8 is a potential rational root of f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28 in accordance with rational root theorem;
Factors of the leading coefficient are: 24: ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.Factors of the constant term are: 28: ±1, ±2, ±4, ±7, ±14, ±28.Potential rational root is: ±7/8.Read more on rational root theorem here: https://brainly.com/question/10937559
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Help me please it’s l haven’t learnt it
the horizontal axis is the bottom (____), the title is usually hiden in the task name
Luke gets paid $13/hour. He got an
additional bonus of $50 for staying late one
day. He got paid $641.50 this month.
Write an equation, define your variable and
solve. How many hours did he work?
Answer: Luke spent 45.5 hours working
Step-by-step explanation:
let x = hours worked
[tex]641.5 = 13x + 50\\\\641.5-50 = 13x\\\\591.5 = 13x\\\\\frac{13x}{13}=\frac{591.5}{13} \\\\x=45.5[/tex]
We can conclude Luke spent 45.5 hours working
660 miles on 20 gallons or 850 miles on 25 gallons which is greater
ethan sorts shapes into two groups as shown what mistakes does ethan make use the drop down menus to explain the mistakes ethan makes
Using the bottom rules, we can conclude that Ethan's mistakes are: shapes C and F are placed in the wrong groups.
How to spot mistakes?The image showing the two groups is as shown in the brainly link attached at the end.
From the attached file in the brainly link, we see that the shapes are grouped using the following criteria:
All the shapes in group 1 have 4 square corners.All the shapes in group 2 have exactly 1 square corner.Using the above rules, we can conclude that Ethan's mistakes are: shapes C and F are placed in the wrong groups.
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Subtract and simplify. What is the restriction on x?
[tex]x\neq[/tex]
[tex]\frac{2}{x^2-25} - \frac{3x}{x^2-4x-5}[/tex]
[tex]\cfrac{2}{x^2-25}~~ - ~~\cfrac{3x}{x^2-4x-5}\implies \cfrac{2}{\underset{\textit{difference of squares}}{x^2-5^2}}~~ - ~~\cfrac{3x}{(x+1)(x-5)} \\\\\\ \cfrac{2}{(x-5)(x+5)}~~ - ~~\cfrac{3x}{(x+1)(x-5)}\implies \cfrac{(x+1)2~~ - ~~(x+5)3x}{\underset{\textit{using this LCD}}{(x+1)(x-5)(x+5)}} \\\\\\ \cfrac{2x+2-3x^2-15x}{(x+1)(x-5)(x+5)}\implies \cfrac{2-3x^2-13x}{(x+1)(x-5)(x+5)}\qquad x\ne -1,\pm 5[/tex]
why can't it be -1 or 5 or -5? if it ever does become that, the denominator will go poof and the fraction undefined.
Brendon walsh wants to borrow $50,000 from the bank. the interest rate is 6% and the term is for 5 years.
what is the monthly payment amount?
o $3,000
o $10,600
o $600
$883.33
Brendon has to pay $1083.33 as monthly payment.
What is Interest ?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan.
This percentage is known as the interest rate on the loan.
Brendon walsh wants to borrow $50,000
P = $50,000
The interest rate is 6%
and the term is for 5 years
S.I. = (P*R*T)/100 = (50000*6*5)/100 = 15,000
AMOUNT = 50000+15000
Amount = $65000
This amount has to be paid in 5 years , Therefore
65000/5=13000
monthly 13000/12 = $1083.33
Brendon has to pay $1083.33 as monthly payment.
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I am in dire need. helpp
the lengths of the side of a triangle are 8,10,12 is the triangle acute, right, or obtuse?
Answer:
acute triangle
Step-by-step explanation:
because (12)^2 = 144 while [tex]8^{2}[/tex] + [tex]10^{2}[/tex] = 164 which means the sum of it's smaller angles are greater than it's greatest angle so it's an acute triangle
Answer:
take the two smaller sides, call them a and b. call the longest side c.
if a^2 + b2 = c^2 you have a right triangle
if < c^2 it's acute
if > c^2 it's obtuse
in addition, if you can find a,b,c such that
a=b=c it's equilateral
a=b≠c it's isosceles
a≠b≠c it's scalene
plug in your numbers and make your choice.
Step-by-step explanation:
What are the coordinates of the image
of (-3, -7) after the translation
(x, y) - > (x-9, y + 9)?
F (-6, 16)
H (12, -2)
G (6, -16)
J (-12, 2)
here my Answer:)))))))
H (12, -2)
Which of the following are true? Select all that apply.
1. 9 m = 9000 mm
2. 8 km = 8000 m
3. 10 cm = 100 mm
4. 890 cm = 8900 m
5. 2000 m = 20 km
6. 4 m = 40 cm
The following are true:
1. 9 m = 9000 mm
2. 8 km = 8000 m
3. 10 cm = 100 mm
What is unit conversion?Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.
1. 9m in mm
1 m = 1000 mm
9 m = 9000 mm
2. 8 Km in m
1 Km = 1000 m
8 Km = 8000 m
3. 10 cm in mm
1 cm = 10 mm
10 cm = 100 mm
4. 890 cm in m
1 cm = 1/100 m
890 cm = 8.9 m
5. 2000 m in Km
i m = 1/1000 Km
2000 m= 2 Km
6. 4 m in cm
1 m = 100 cm
4 m = 400 cm
From the above discussion (1), (2), (3) are true.
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Mitch is making a target for the beanbag toss at his school's fall fun-run and carnival. the target is a short round basket divided evenly into 4 sections. the player wins a prize for each section the beanbag lands in. there is 1 section that wins the player a rubber ball. there are 3 sections that win the player a teddy bear. what fraction of the target wins the player a teddy bear?
Answer:
3/4 is your fraction because 3 out of the four sections gives you the bear
Step-by-step explanation:
[SOLVED] The following data values are amperage outputs from electrical testing.
60, 60, 61, 62, 63, 63, 65, 65, 70, 72, 73, 98
Use the drop-down menus to identify the key values.
What is the median? ✔ 64
What is Q1, the median of the lower half of the data? ✔ 61.5
What is Q3, the median of the upper half of the data? ✔ 71
What is the interquartile range, or Q3 – Q1? ✔ 9.5
The median of the data is 64, the value of Q1 is 61.5, the value of Q2 is 71, and the value of Q3-Q1 is 9.5
What is the median?A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.
We have data:
60, 60, 61, 62, 63, 63, 65, 65, 70, 72, 73, 98
The median = (63+65)/2 = 64
Q1 = (61+62)/2 = 61.5
Q2 = (70+72)/2= 71
Q3 - Q1 = 71 - 61.5 = 9.5
Thus, the median of the data is 64, the value of Q1 is 61.5, the value of Q2 is 71, and the value of Q3-Q1 is 9.5
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Answer:
Use the drop-down menus to identify the key values.
What is the median? ✔ 64
What is Q1, the median of the lower half of the data? ✔ 61.5
What is Q3, the median of the upper half of the data ✔ 71
What is the interquartile range, or Q3 – Q1? ✔ 9.5
Step-by-step explanation:
edge 2023
help me PLEASE FIND THE VOLUME
Answer:
1. 519.75 cm^3
2. 19.22 cm^3
3. 613.6 cm^3
4. 1365.68 cm^3
Step-by-step explanation:
Hello again, similar to the other questions, these problems use the same formulas.
1. volume of a rectangular prism is: V = lwh, where l = length, w = width, h = height. Substitute known values into this equation: V = 4.5 x 7 x 16.5 and we get V = 519.75 cubic cm.
2. V = (1/2)bhl, where the base and height are dimensions of the triangle. V = (1/2)6.2 x 2 x 3.1 and we get V = 19.22 cubic cm
3. V = Bh, where B is the base area and h is the perpendicular height. Substitute known values into equation: V = 52(11.8). So, V = 613.6 cubic cm.
4. And again, V = Bh. Substitute given values into this equation: V = 79.4(17.2), which means V = 1365.68 cm^3
What is Surface area for 5ft, 16ft, and 8ft
The surface area of the given rectangular prism is:
S = 496 square feet.
How to find the surface area?
For a rectangular prism of length L, width W, and height H is:
S = 2*(L*W + W*H + L*H).
In this particular case, we have:
L = 5ftW = 16ftH = 8ft.If we replace that in the surface area equation, we will get:
[tex]S = 2*(5ft*16ft + 5ft*8ft + 16ft*8ft) = 496 ft^2[/tex]
The surface area of the rectangular prism is 496 square feet.
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Find the surface area of the sphere. Use 3.14 for π. Round your answer to the nearest tenth.
Show work and explain it please.
[tex]s = 4\pi {r }^{2} [/tex]
13.6/2=6.8
4×3.14×(6.8×6.8)=580.7
QUESTION ON THE IMAGE
Answer:
660 cubic cm
Step-by-step explanation:
Volume= bhl/2
PLEASE PLEASE I BEG YOU FOR HELP
Answer:
False
Ab is not perpendicular bisector to bc
( i will give brainlist ) please help is the following equation linear, quadratic, exponential or none of these?
Answer:
exponential
Step-by-step explanation:
It is exponential because the variable is in the exponent
the quation is 8=z/6 please help me solve this algebraic equation......
Answer:
to find z
Step-by-step explanation:
8=z/6
z=6 x 8
z= 48
A
B
21
48°
6x-24
D
[?] << <[ ]
11
C
The shape in the figure is a composite shape with two triangles, and the inequality is 4 < x < 12
How to determine the range of value of x?In the given figure, the side lengths AB and AD are equivalent.
This means that, we have the following angle relationship:
CAD < CAB
Substitute known values
6x - 24 < 48
Add 24 to both sides
6x < 72
Divide both sides by 6
x < 12
Also, we have the following angle relationship:
CAD > 0
Substitute known values
6x - 24 > 0
Add 24 to both sides
6x < 24
Divide both sides by 6
x < 4
This means that:
x < 4 and x < 12
Combine both inequalities
4 < x < 12
Hence, the inequality is 4 < x < 12
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How do I turn this 10(0j + 40 + 4j) into a verbal expression?
I NEED HELP!!!!1
Answer:
See below
Step-by-step explanation:
You could say "10 times the sum of 0j, 40, and 4j" because that is exactly what you are doing in the algebraic expression.
Anyone please help me this I can't solve so I need help.༎ຶ‿༎ຶ waaaaaahhhhhh
This is your answer. I keep hope it will help you
which grade are you studying
By about how many years did life expectancy increase in the us between 1960 and 2010? 7 years 17 years 27 years
Answer:
The closest answer would be 7 years
Step-by-step explanation:
In the '60s, the life expectancy was approximately 70 years, and in 2010 it was approximately 78.
Answer: answer would be 7 years
Step-by-step explanation:
just did it
109, 94, 87, 103, 89, 112, 98, 115, 99 Find the minimum.
ANSWER ASAP PLEASE
Answer:
The minimum is 87
Step-by-step explanation:
The minimum is the lowest number that you can see. 87 is the minimum because it is the lowest of all numbers listed
Answer:
87
Step-by-step explanation:
Put them in order
87, 89, 94, 98, 99, 103, 109, 112, 115
Minimum = The least
The least = 87
4. Write 2 trinomials that when you add them together you will get 5x2 + 9x + 3.
Trinomial A
Trinomial B
An expression is defined as a set of numbers, variables, and mathematical operations. The two trinomial whose sum will get 5x²+9x+3 are 3x²+5x+2 and 2x² + 4x + 1.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The two trinomial whose sum will get 5x²+9x+3, therefore, the trinomial will be,
Trinomial A = 3x²+5x+2
Trinomial B = 2x² + 4x + 1
Hence, The two trinomial whose sum will get 5x²+9x+3 are 3x²+5x+2 and 2x² + 4x + 1.
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A mining company is mining silver. The relationship between the mass of the material mined in metric tons and the number of carts required to transport the material is given by the function V(n) = 0.5n. Additionally, the relationship between the amount of silver and the material mined is given by the function G(V) = 0.00001V.
Which function can be used to determine the mass of silver in metric tons as a function of the number of carts required to transport the materials out of the mine?
A)G(V(n))
B)V(G(n))
C)n(G(V))
D)n(V(G))
Answer:
G(V(n))
Step-by-step explanation:
As V(n)=0.5nWhere V is carts and n is material
So vRnAnd
G(v)=0.00001VWhere G is silver found and v is material
GRvOn combininf
GRv =>(G,v)€RVRn=>(v,n)€RSo as per transitive property
GRn=>( G,n)€RR is relation
G is related to n
So G will stay outside and the relationship become GoV(n)