Answer:
A
Step-by-step explanation:
y = x² - 6x - 4
(x - 3)² - 3² - 4 = 0
(x - 3)² - 13 = 0
(x - 3)² = 13
x - 3 = ±√13
x = 3 ± √13
Brian invests £6600 into his bank
account.
He receives 0.6% per year compound
interest.
How much will Brian have after 6 years?
Give your answer to the nearest penny
where appropriate.
O
→ £ 1
Answer:
See Below
Step-by-step explanation:
The equation for this scenario would be ( compounded annually)
6600 ( 1 + .006)^6 = £ 6841.19
Answer:
Brian will have £6841.19 after 6 years.
Step-by-step explanation:
The compound interest formula is:
[tex]A = P( 1 +\frac{r}{100} )^{n}[/tex] ,
where A is the final amount, P is the initial (principal) amount invested (£6600), r is the interest rate (0.6%) and n is the number of years the money is kept for (6 years).
Using the formula:
[tex]A = 6600(1 + \frac{0.6}{100} )^{6}\\\\A = 6841.19[/tex]
(X-5)\(3x^2-14x-5) solve by polynomial long division
Answer: 3x+1
Step-by-step explanation: See attachment
(12 ÷ 3) + 3+ (16-7) × 4
Answer: 43
Step-by-step explanation:
Step 1: Simplify inside the parenthesis
(12 ÷ 3) + 3+ (16-7) × 4
4 + 3 + 9 × 4
Step 2: Multiply 9 by 4
4 + 3 + 36
Step 3: Combine Like Terms
43
same side interior angles are _____ congruent
A.always
B.never
C.sometimes
Answer:
B. Never
Step-by-step explanation:
that's just what my math teacher told us...
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The domain of the function f(x) = 3x3 is {2, 5}. What is the function’s range?
The range of the function f(x) = 3x3 when its domain is {2, 5} is
The range of the function f(x) = 3x3 when its domain is {2, 5} is {24, 375}
Domain and range of a functionThe domain is the independent value for which a function exists.
Given the function below;
f(x) = 3x^3
If the domain of the function is {2, 5}, the range are;
If x = 2
f(2) = 3(2)^3
f(2) = 3(8)
f(2) = 24
If x = 5
f(5) = 3(5)^3
f(5) = 3(125)
f(5) = 375
Hence the range of the function f(x) = 3x3 when its domain is {2, 5} is {24, 375}
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A scale model of a statue has a height of 20 cm. The real statue has a height of 2 m. The model and statue are both made of the same stone which has a density of 1.8 g/cm3. The mass of the real statue is 104.4 kg. Find the volume of the model in cm3
The volume of the model in cm³ is 52.2 if the scale model of a statue has a height of 20 cm. The real statue has a height of 2 m
What is density?It is defined as the mass-to-volume ratio. The density indicates the object's density and is represented by the symbol. The density is measured in kilograms per cubic meter.
A scale model of a statue has a height of 20 cm.
The formula for density:
D = mass/volume
Volume = base area×hieght
104.4 kg = 104400 grams
2 m = 200 cm
Volume = Mass/D
Volume(real statue) = 104400/200 = 522 cubic cm
Scale factor = 20/200 = 1/10
Volume of model statue = 522(1/10) = 52.2 cubic cm
Thus, the volume of the model in cm³ is 52.2 if the scale model of a statue has a height of 20 cm. The real statue has a height of 2 m
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The equation of a circle is (x-2)2+(y-6)2=25. What is the radius of the circle?
Answer:
radius = 5
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
(x - 2)² + (y - 6)² = 25 ← is in standard form
with r² = 25 ( take the square root of both sides )
r = [tex]\sqrt{25}[/tex] = 5
Loss = 10% VAT=13% SP WITH VAT=25,425 now calculate CP
The cost price of the product will be 25000.
How to calculate the price?From the information given, the cost price is 25000. The loss is 10%. This will be:
= 25000 - (10% × 25000)
= 25000 - 2500
= 22500
The tax is 13%. This will be:
= 22500 + (13% × 22500)
= 22500 + 2925
= 25425
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Considering the activity series given below for metals and nonmetals, which reaction will occur? al > mn > zn > cr > fe > cd > co > ni > sn > pb > h > sb > bi > cu > ag > pd >hg > pt f > cl > br > i 2nabr i2 right arrow. 2nai br2 2fe al2o3 right arrow. 2al fe2o3 2agno3 ni right arrow. ni(no3)2 2ag pb zn(c2h3o2)2 right arrow. zn pb(c2h3o2)2
The activity series is an arrangement of species in order of reactivity.
What is the activity series?The activity series is an arrangement of species in order of reactivity. The position of a specie in the series determines the possibility of certain reactions.
The following are the fates of these reactions;
2NaBr + I2--------->2NaI + Br2 - Not possible2Fe + Al2O3 ----------> 2Al + Fe2O3 - Not possible2AgNO3 + Ni ----------> Ni(NO3)2 + 2Ag - possiblePb + Zn(C2H3O2)2 ----------> Zn + Pb(C2H3O2)2 - Not possibleLearn more about activity series:https://brainly.com/question/18080147
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$50 item discounted 30%
Answer:
$15 is the answers
Step-by-step explanation:
please mark me as brainlest
Answer:
$ 35.00 is what you pay $15.00 off original price
Step-by-step explanation:
30 % discount means you pay 70 %
$ 50 * .70 = $ 35 .00
Paolo and Monika are both travelling by train.
Paolo's train travels 70 km in 35 minutes.
Monika's train travels 684 km.
It leaves at 16:15 and arrives at 20:45.
Work out the difference, in km/h, between the average speed of their trains.
Answer:
32 km/hr
Step-by-step explanation:
Firstly, you need to find the speed of both trains in km/hr.
Paolo's train= (70km x 60hr)/35= 120 km/hr
Monika's train= 684km/4.5hr= 152 km/hr
Then find the difference in speed:
152-120=32 km/hr
What are the asymptote and the y-intercept of the function shown below?
f(x) = 6(0.5)x + 2
A curve declines through (negative 0 point 5, 10), (0, 8), (1, 5), (3, 2 point 9), (4, 2 point 3) and extends linearly through (6, 2), (7, 2), (8, 2) and (9, 2) on the x y coordinate plane.
A.
asymptote: y = 2
y-intercept: (0,8)
B.
asymptote: y = 1
y-intercept: (0,5)
C.
asymptote: y = 2
y-intercept: (0,5)
D.
asymptote: y = -2
y-intercept: (0,8)
The asymptote and the y-intercept of the function is asymptote: y = 2
y-intercept: (0,8) , Option A is the answer.
What is an Asymptote ?Asymptote is a straight line that approaches the curve but does not meet even at infinite distance.
It is given that f(x) = 6 (0.5)ˣ +2
The horizontal asymptote is at y = c
y = 2
From the curve it can be seen that
The intercept of y axis is determined when x = 0
then f(0) = 6 * (0.5)⁰ + 2
f(0) = 8
Therefore the y intercept is at (0,8)
Therefore Option A is the right answer.
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Answer:
C
Step-by-step explanation:
thats what i got
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
Answer:
Step-by-step explanation:
Convert kilometer to miles:1 km = 0.62 mi
So, to convert 6 km to mi, multiply 6 by 0.62.
6km = 6* 0.62
= 3.72 mi
Convert liter to gallon:1 L = 0.26 gal
To convert 2.5 L to gallon, multiply 2.5 by 0.26.
2.5 L = 2.5 * 0.26
= 0.65 gal
Convert pound to kilogram:1 lb = 0.45 Kg
To convert 90 lb to Kg, multiply 90 by 0.45.
90 lb = 90 *0.45
= 40.5 Kg
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 1-√6 , 1+ √6 , and 7-i
Step-by-step explanation:
Use this algebra 2 theorem:
If r and q are roots of a polynomial function then
the polynomial function can be expressed as
[tex](x - r)(x - q)[/tex]
Here the roots are
1- root of 6, 1+ root 6, and. 7-i so our. function can be expressed as
[tex](x - (1 - \sqrt{6} ))(x - (1 + \sqrt{6} ))(x - (7 - i))[/tex]
The first two binomials are difference off squares so the we have
[tex] {x}^{2} + x( - 1 + \sqrt{6} ) + x( - 1 - \sqrt{6} ) + ( - 5)[/tex]
[tex] {x}^{2} - 2x - 5[/tex]
The other root is (7-i).
Also note since (7-i) is a root, then (7+I) is also a root.
So
[tex](x - (7 - i)(x - (7 + i)( {x}^{2} - 2x - 5)[/tex]
[tex]( {x}^{2} - 14x + 50)( {x}^{2} - 2x - 5)[/tex]
Simplify and it gives us
[tex] {x}^{4} - 16 {x}^{3} + 73 {x}^{2} - 30x - 250[/tex]
What is the value of the expression 4 x (2a - 1) if a = 3?
16
20
23
25
Answer:
20
Step-by-step explanation:
⇒ Multiply 2 by 3
2 * 3 = 6
4 (6 - 1)
⇒ Distribute terms
4 * 5
20
Hence, the answer is 20.
Round 38.856 to the nearest tenth
Answer:38.9
Step-by-step explanation:
Andy spent $55 in all to purchase 20 two-dollar and five-dollar toys. How many two-
dollar toys did he buy? How many five-dollar toys did he buy?
can u give the direct answer of 1 and 2
[tex] {a}^{3} . \\ \\ {a}^{5}. \\ \\ {a}^{9} . \\ \\ {a}^{m + n}. \\ \\ {x}^{1} = x.\\ \\ {x}^{3}. \\ \\ {x}^{3}. \\ \\ {x}^{m - n} . \\ \\ {y}^{6} . \\ \\ {y}^{12} . \\ \\ {y}^{18} . \\ \\ {y}^{ab}. \\ \\ 1. \\ \\ 1. \\ \\ {px}^{1} = px.[/tex]
••••••••••••••••••••••••••••••••••••••[tex]343 .\\ \\ 16 .\\ \\ 3125 .\\ \\ \frac{ - 8}{27} .[/tex]
What is the measure of \angle x∠xangle, x?
Angles are not necessarily drawn to scale.
Answer:
x=135°
Step-by-step explanation:
WZ is 180 degrees. Simply subtract 48 from 180.
180-45=135.
Hope this helps!
If not, I am sorry.
Answer:
The answer is 132
Step-by-step explanation:
For khan academy
PLEASE HELP GEOMOTRY"the ratio of the angles of a pentagon is 1:2:2:3:4 find the largest angle"
The largest angle of the pentagon with the given ratio of angles is: 180°.
What is a Pentagon?A pentagon is a 5-sided polygon with 5 interior angles that have a sum of 540 degrees.
If the ratio of the angles are: 1:2:2:3:4, then the largest angle would be calculated as shown below:
4/(1+2+2+3+4) × 540
4/12 × 540 = 180°
The largest angle is: 180°.
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what is the value of x in the equation
(3x+5)/2=(5x+3)/3
Answer:
x=9
Step-by-step explanation:
Find cos (330°). Your answer MUST be in radical form.
Step-by-step explanation:
square root 3 divided by
2
Given the function f(x) = −5x2 − x + 20, find f(3).
Answer:
123icuxxiffatjtjfug8utkxi93hkgodo c office c 8f
The work of a student to solve the equation 2(3x-4)= 8 + 2x + 4 is shown below.
Step 1: 2(3x-4)= 8+2x+4
Step 2: 5x6 = 12 + 2x
Step 3: 5x-2x = 12 +6
Step 4: 3x = 18
Step 5: x = 6
In which step did the student first make an error and what is the correct step?
O Step 2; 6x6 = 2(6+ x + 2)
O Step 2; 6x8 = 12 + 2x
O Step 3; 5x-2x = 12-6
O Step 3; 5x + 2x = 12 +6
21. What is the perimeter of the triangle?
18.2 units
18.3 units
9 units
15.5 units
(1,6)
(3, 1)
(6, 1)
Answer:
C) 15.5 units
Step-by-step explanation:
On a number line, 2.5 would be located ______. Choose all answers that make a true statement.
2.5
《----|----|----|----|----|----|----|----|----|----|----》
A. to the right of 2.52
B. between 2.45 and 2.55
C. to the left of 2.3
D. between of 2.4 and 2.6
Answer:
It is both answers B and D
Consider the transformation shown. 2 triangles are shown. The first is labeled pre-image and the second is labeled image. Both triangles have congruent angle measures. The pre-image has side lengths of 6, 10, and 8. The image has side lengths of 3, 5, and 4. Use the drop-down menus to complete the sentence. The transformation is because the preserved
The transformation is nonrigid because the segment lengths are not preserved.
How to determine the transformation?The image related to the question cannot be found. However, the question can still be solved
The given parameters are:
Triangle 1: 6, 10 and 8Triangle 2: 3, 5 and 4From the question, we understand that the side lengths are not equal.
This means that the triangles are dilated.
And the scale factor of dilation is
Scale factor = 6/3 = 10/5 = 8/4
Scale factor = 2
The scale factor of dilation is 2
Dilation is a non rigid transformation.
Hence, the transformation is nonrigid because the segment lengths are not preserved.
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Answer:
The transformation is nonrigid because the segment lengths are not preserved.
a paperweight has height 4cm and volume 38.4cm3.
a mathematically similar paperweight has height 7cm.
calculate the volume of this paperweight.
The similar paperweight has a volume of 67.2 cubic cm if the height is 7 cm.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
As we know,
Volume = base area×height
38.4 = base area×4
base area = 38.4/4 = 9.6 square cm
A mathematically similar paperweight has a height of 7 cm.
Volume = base area×height
Volume = 9.6×7 = 67.2 cubic cm
Thus, the similar paperweight has a volume of 67.2 cubic cm if the height is 7 cm.
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Using p as the variable for the problem below, solve for p. Submit your answer
as an inequality, using "<=" for < or ">" for ≥ if necessary. Round to two
decimal places.
Hosting a dinner party for 38 people, you plan to serve peach pie for dessert.
Each pie has 8 slices. How many pies must you buy to ensure each guest
gets 1 slice?
Answer:
Step-by-step explanation:
As host, we want to insure each guest has at least one slice of pie. We can say (1 Slice/Guest) and use this as a conversion factor. We also know each pie has 8 slices: (8 Slices/1 Pie). Since this is a conversion factor, we can invert it to (1 Pie/8 Slices). We expect 38 people and want to convert that number of people to the number of pies, p, we need.
p (pies) [tex]\geq[/tex] (38 Guests)*(1 Slice/Guest)*(1 Pie/8 Slices)
We use the [tex]\geq[/tex] sign to note that we need a minimum of pies to be sure everyone is served.
p (pies) [tex]\geq[/tex] (38 )*(1 /)*(1 Pie/8 )
Note how the units cancel:
Guests and Slices both cancel and we are left with pies as the only remaining unit, as we hoped we'd see.
p [tex]\geq[/tex] (38/8) pies
p = 4 +(6/8) pies
Since we cannot purchase 6/8 of a pie, we need to round up to 5 pies.
5 pies, at 8 slices per pie, will provide 40 servings, enough for the 38 guests.
Find the equation of the line through point (8,−9) and perpendicular to 3+8=4.
The equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.
We are aware that any straight line's equation can be expressed as
y = mx + c,
where m denotes the slope and c denotes a constant.
Also, two perpendicular lines' slopes are the negative reciprocals of one another.
Here, the equation of the given straight line is
3x+8y=4
i.e. 8y = 4 -3x
i.e. y = (4/8) - (3/8)x
Now the negative reciprocal of - 3/8 is 8/3.
Then we can write the equation of the perpendicular line is
y = (8/3)x + c ...(1)
Since (1) passes through the point (8, -9), so we can put x = 8 and y = -9 in (1) to get the value of c.
So, -9 = (8/3)*8 + c
i.e. -9 = 64/3 + c
i.e. c = -9 -64/3 = - (27 + 64)/3 = - 91/3
(1) can be written as
y = (8/3)x - (91/3)
i.e. 3y = 8x - 91
i.e. 8x - 3y = 91
Therefore the equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.
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