Answer:
[tex]g(x) = \frac14x^2[/tex]
Step-by-step explanation:
Since f(x) and g(x) share the same top at (0,0), their difference is only a scale factor, so g(x) = ax² but we need to find a.
To find it, we use the given point of g, (2,1)
So g(2) = 1
meaning that
a·2² = 1
4a = 1
a = 1/4
Write in figures;Nine million twenty thousand four hundred and six and twenty seven thousandths.
Answer:
9,020,406.27
Step-by-step explanation:
Answer:
9,020,406.27
Step-by-step explanation:
Ewen has 48 whistle tiles and 16 blue tiles the cost of each white tile was £2 and the cost of each blue tile was £4 Work out the ratio of the total cost of the white tiles to the total cost of the blue tiles
Answer:
3:2
Step-by-step explanation:
Ewen has 48 white tiles and 16 blue tiles
The cost of each white tile was £2
The cost of each blue tile was £4
Therefore the total cost of 48 white tiles is
= 48×2
= £96
The total cost of 16 blue tiles is
= 16×4
= £64
The ratio of the total cost of the white tiles and blue tile can be calculated by dividing the cost of both tiles by their greatest common factor
The greatest common factor of £96 and £64 is 32
96/32 = 3
64/32= 2
Ratio= 3:2
Hence the ratio of the total cost of the white tiles to the blue tiles is 3:2
4⋅f(6)−6⋅g(5) need help asap
Answer:
6
Step-by-step explanation:
From the blue graph of f(x) we can see that the function value is -6 when x = 6. Similarly, g(5) = -5.
Then: 4*f(6) - 6*g(5) becomes:
4*(-6) - 6*(-5), or
-24 + 30 = 6
The value of ⋅f(6)−6⋅g(5)= 6
What is Composition of function?An operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).
Given:
From the blue graph we can see that
f(x)= -6 when x = 6.
Similarly, g(5) = -5.
thus,
4*f(6) - 6*g(5)
=3 4*(-6) - 6*(-5)
=-24 + 30
= 6
Learn more about this concept here:
https://brainly.com/question/20379727
#SPJ2
How many 4-digit numbers divisible by 5, all of the digits of which are odd, are there?
Answer:
I guess that we want to create 4 digit numbers that are divisible by 5, only using the odd numbers in the image.
We know that a number is divisible by 5 only if the last digit (the units digit) is a zero or a five, in the image we only have a five, so our 4-digit numbers need to end with a five, so we have a digit fixed in five and the other 3 digits can be other numbers.
We have two different approaches to this:
First, if each odd number can be used only once, we already used the five, so we can use the other 4 numbers.
Then, for the first digit, we have 4 options.
for the second digit, we have 3 options (because we already used one)
for the third digit, we have 2 options (because we already used 2)
then the number of combinations is equal to the product of the number of options for each selection:
C = 4*3*2 = 24 combinations.
The second approach is If the numbers in the image can be repeated (for example, 5555 or 3435 are allowed)
we still have our last digit fixed in 5, and for the first digit we have 5 options, for the second we also have 5 options, and for the third, we also have 5 options, then, with the same reasoning as above, we have:
C = 5*5*5 = 25*5 = 125 combinations.
12. Where do the lines y = 5 and x = -7 intersect?
Answer:
(-7,5)
Step-by-step explanation:
y = 5 and x = -7
The lines intersect at the point x=-7 and y =5
(-7,5)
Three angles of an octagon are equal and the sum of the remaining angles is 705⁰. find the size of one of the equal angles.
Answer:
125°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 8 (octagon), thus
sum = 180° × 6 = 1080°
let x represent one of the equal angles, then
3x + 705 = 1080 ( subtract 705 from both sides )
3x = 375 ( divide both sides by 3 )
x = 125
Thus the size of one equal angle = 125°
7. In 2015 a club has 250 members who each
pay
$95 annual subscription.
In 2016 the membership increases by 4% and the annual subscription is
increased by 6%. What is the total income from subscriptions in 2016?
2015:
250 members
$95 annual subscription
2016
250 members + 4%
$95 annual subscription + 6%
Work:
250 x 1.04 = 260
95 x 1.06 = 100.7
260 x 100.7 = 26,182
Thus, the club makes $26,182 from 260 members who pay a subscription of $100.7
A chemist is using 367milliliters of a solution of acid and water. If 18.4% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
Answer:
For this case we know that the total amount of solution including water and acid is V=367 ml
And we know that the % of acid in the solution is 18.4% so then we can find the number of ml of acid witht this operation:
[tex] Acid = 0.184 *367 ml = 67.528 ml \approx 67.5 ml[/tex]
Step-by-step explanation:
For this case we know that the total amount of solution including water and acid is V=367 ml
And we know that the % of acid in the solution is 18.4% so then we can find the number of ml of acid witht this operation:
[tex] Acid = 0.184 *367 ml = 67.528 ml \approx 67.5 ml[/tex]
please help me Which of the following choices will evaluate the function ƒ(x) = -(-x), when x = -3? 3 -1 -3 None of these choices are correct.
Answer:
-3
Step-by-step explanation:
Given the function f(x) = -(-x)
we want to evaluate f(-3)
What we do simply here is substitute the value of -3 for x in the equation
That would be ;
f(-3) = -(-(-3)) = -(3) = -3
Find the slope of the line that passes through (3, 6) and (6, 10). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
4/3
Step-by-step explanation:
To find slope use the formula (y2-y1)/(x2-x1)
In this case it is (10-6)/(6-3)
4/3
A taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional $0.20 for each mile traveled. The rule c = 0.20m + 2.00 describes the relationship between the number of miles m and the total cost of the ride c. What is the charge for a 1-mile ride? A)$0.20 B)$0.02 C) $2.20 D)$2.00
Answer:
c
Step-by-step explanation:
Any ride takes $2.00 and one mile takes $0.20.
Cost = $0.20 + $2.00
Cost = $2.20
Sphere A has a diameter of 12 and is dilated by a scale factor of one half to create sphere B. What is the ratio of the volume of sphere A to sphere B?
Answer:
VA/VB = 8
Step-by-step explanation:
You have a sphere A with diameter 12, that is, radius 6, which can be written as follow:
[tex]V_A=\frac{4}{3}\pi r_A^3=\frac{4}{3}\pi (6)^3=288\pi[/tex] (1)
The sphere A is dilated by a scale factor of one half to sphere B. Then, you have:
[tex]V_B=\frac{4}{3}\pi r_B^3=\frac{4}{3}\pi (\frac{6}{2})^3=36\pi[/tex] (2)
From the results of equation (2) and (1) you can calculate the ratio VA/VB:
[tex]\frac{V_A}{V_B}=\frac{288\pi}{36\pi}=8[/tex]
The ratio of the volumes of both sphere A and B is 8
Answer:
8:1
Step-by-step explanation:
hope this helps
In arguing against the death penalty, Amnesty International has pointed out supposed inequities, such as the many times a black person has been given the death penalty by an all-white jury. If jurors are selected randomly from an adult population, find the probability that all 12 jurors are white when the population is (a) 90% white and (b) 50% white.
Answer:
(a) 0.2824
(b) 0.0002441
Step-by-step explanation:
Assuming that the population is large enough to behave as a binomial distribution (between whites and non-whites), the probability of 12 out of 12 juros being white is:
[tex]P(w=12) = p(w)^{12}[/tex]
Where p(w) is the proportion of the population that is white:
(a) for p = 0.90
[tex]P(w=12) = 0.90^{12}\\P(w=12) =0.2824[/tex]
The probability is 0.2824.
(b) for p = 0.50
[tex]P(w=12) = 0.50^{12}\\P(w=12) =0.0002441[/tex]
The probability is 0.0002441.
What are the coordinates of point P on the directed line segment from A to B such that P is One-fourth the length of the line segment from A to B?
Answer:
The answer is explained below
Step-by-step explanation:
The location of point A = (-5, -1) and point B = (4, 1).
To find the coordinate of the point that divides a line segment PQ with point P at [tex](x_1,y_1)[/tex] and point Q at [tex](x_2,y_2)[/tex] in the proportion a:b, we use the formula for the x and y coordinates:
[tex]x-coordinate:\\\frac{a}{a+b}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{a}{a+b}(y_2-y_1)+y_1[/tex]
P is One-fourth the length of the line segment from A to B, Therefore AB is divided in the ratio 1:4. The location of point A = (-5, -1) and point B = (4, 1).Therefore:
[tex]x-coordinate:\\\frac{1}{1+3}(4-(-5))+(-5)=\frac{1}{4}(9)-5=-\frac{11}{4} \\\\While \ for\ y-coordinate:\\\frac{1}{1+3}(1-(-1))+(-1)=\frac{1}{4}(2)-1=\frac{-1}{2}[/tex]
Therefore the coordinate of P is (-11/4, -1/2)
Answer:
the coordinate of P is (-11/4, -1/2)
x= -11/4
y= -1/2
c on edu
Step-by-step explanation:
edu 2021
Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below. Table showing 3 steps to solve an equation using the quadratic formula. What are the solutions to the equation?
Answer:
[tex]\underline{x\in\left\{-6\,,\ 1\right\}}[/tex]
Step-by-step explanation:
[tex]x^2+5x-6=0\\\\a=1\,,\ \ b=5\,,\ \ c=-6\\\\x_1=\dfrac{-5-\sqrt{5^2-4\cdot1\cdot(-6)}}{2\cdot1}=\dfrac{-5-\sqrt{25+24}}2=\dfrac{-5-\sqrt{49}}2=\dfrac{-5-7}2=-6\\\\x_2=\dfrac{-5+\sqrt{5^2-4\cdot1\cdot(-6)}}{2\cdot1}=\dfrac{-5+7}2=1[/tex]
Answer:
Step-by-step explanation: Answer is B-6,1
I need help with this problem, the picture is attached below. Select the following numbers that cannot represent the area of a polygon.
Answer:
-200, 0 and -5
Step-by-step explanation:
Area can never be zero or negative.
first chance you get the best marks
Answer:
First box and last box.Step-by-step explanation:
It is the first box.Distribute 7 to the first number
7 * -3/4 = -21/4
-21/4 = 5 -1/4
Distribute 7 to the second number
7 * -3
= -21
Put the numbers together
5 -1/4x -21 is the answer.It is also the last box.They separated the parenthesis.
So it is still 7 * -3/4
and
7*-3.
Hope this helps,
Kavitha
Please answer this question fast in two second
Answer:
it could be angle DGF or CGA (they are both supplementary to angle CGD)
Step-by-step explanation:
A box has a volume of 5m³. The box will be enlarged by a scale factor of 2. What will the volume of the new box be?
Answer:
40m³
Step-by-step explanation:
[tex]\sqrt[3]{5}[/tex] = 1.709975947
1.709975947 × 2 = 3.419951893
3.419951893³ = 40
Answer:
volume of the box multiply scale factor
=5 × 2
=10m
Use the Factor Theorem to determine which of the following are NOT factors of 3x^4 - 5x^3 - 71 x^2 + 157x + 60 a. x - 3 c. x - 2/3 b. x + 1/3 d. x - 4
Answer:
c. x - 2/3
Step-by-step explanation:
The given equation is f(x) = [tex]3x^4 - 5x^3 - 71 x^2 + 157x + 60[/tex]
To test if the given equations are factors of the polynomial, check if the remainder is equal to zero if substituted into the equation.
For x - 3, x = 3
Substituting x = 3 into the given polynomial:
[tex]f(3) = 3(3)^4 - 5(3)^3 - 71 (3)^2 + 157(3) + 60\\f(3) = 0[/tex]
x - 3 is a factor
For x - 4, x = 4
Substituting x = 4 into the given polynomial:
[tex]f(4) = 3(4)^4 - 5(4)^3 - 71 (4)^2 + 157(4) + 60\\f(4) = 0[/tex]
x - 4 is a factor
For x - 2/3, x = 2/3
Substituting x = 2/3 into the given polynomial:
[tex]f(2/3) = 3(2/3)^4 - 5(2/3)^3 - 71 (2/3)^2 + 157(2/3) + 60\\f(2/3) = 132.22[/tex]
x - 2/3 is not a factor
For x + 1/3, x = -1/3
Substituting x = -1/3 into the given polynomial:
[tex]f(-1/3) = 3(-1/3)^4 - 5(-1/3)^3 - 71 (-1/3)^2 + 157(-1/3) + 60\\f(-1/3) = 0[/tex]
x + 1/3 is a factor
Mariano puede despachar periódicos 2 veces el tiempo que le toma a Alberto. ¿Cuánto tiempo le llevará a cada uno si juntos pueden hacer el trabajo en 3h?
Answer:
El tiempo le llevara a Mariano es 2 horas y el tiempo que le llevara a Alberto es de una hora
Step-by-step explanation:
Para calcular el tiempo que le llevará a cada uno si juntos pueden hacer el trabajo en 3h, tenemos que primero segun los datos considerar lo siguiente:
Segun los datos tenemos que Mariano puede despachar periódicos 2 veces el tiempo que le toma a Alberto, por lo tanto:
2X=Mariano puede despachar periódicos 2 veces el tiempo que le toma a Alberto
X=El tiempo que le toma a Alberto.
Por lo tanto calculando la siguiente ecuacion, podremos hallar el valor de X:
2X+X=3 horas
3X=3 horas
X=1 hora
Entonces, tenemos que el tiempo le llevara a Mariano es 2 horas y el tiempo que le llevara a Alberto es de una hora
?
Match each ratio to an equal ratio. Drag the items on the left to the
correct location on the right.
1:4
4:48
1:3
4:6
2:3
2:8
1:12
2:6
Answer:
2:8 is the ratio to an equal ratio
A box contains 10 red , 3 blue, and 7 white balls , two balls are drawn at random from the box on after the other without replacement. What is the probability that both balls are of the same colour
Answer:
P(XX) = 69/190
Step-by-step explanation:
Given:
20 balls, 10R, 3B, 7W.
Two taken without replacement.
Find probability of two identical colours.
P(XX)
Solution:
We use the multiplication rule for the probability of each of the 2 draws
P(RR) = 10/20*9/19 = 90/380
P(BB) = 3/20*2/19 = 6/380
P(WW) = 7/20*6/19 = 42/380
Probability of drawing two identical coloured balls
P(XX) = (90+6+42)/380 = 138/380 = 69/190
If, 3a/b= 12 what is the value of (-a/-b)
Answer:
A ; -4
Step-by-step explanation:
3a = 12b then a = 4b (dividing by 3)
we put 4b in the equation instead of a:
(-4b / b) = -4
.. ..
Answer:
A. -4
Step-by-step explanation:
3a/b = 12
Let b = 2
3a/2 = 12
3a = 24
a = 8
( - a/b)
( - 8/2)
( - 4)
Change 80265 gram to kilogram
Hey there! :)
Answer:
80.265 kg.
Step-by-step explanation:
1 kilogram = 1000 grams. Therefore:
[tex]\frac{80265g}{1} * \frac{1 kg}{1000g} = \frac{80265kg}{1000} = 80.265 kg[/tex]
80265 grams = 80.265 kg.
Answer:
80.265 kg
Step-by-step explanation:
1 kilogram is equivalent to 1,000 g. Therefore, the decimal point goes 3 spaces to the left to divide by 1,000, which is one rack ayyy.
If Tanø =a/b Find the value of sinø+cosø/sinø-cosø
Answer:
[tex]\frac{b+a}{b-a}[/tex]
Step-by-step explanation:
Tan θ = [tex]\frac{perpendicular}{base}[/tex] = [tex]\frac{b}{a}[/tex]
So, Perpendicular = b, base = a
Finding hypotenuse by Pythagorean Theorem:
[tex]c^2 = a^2+b^2[/tex]
=> So, hypotenuse = c
Sin θ = [tex]\frac{perpendicular}{hypotenuse}= \frac{b}{c}[/tex]
Cos θ = [tex]\frac{base}{hypotenuse}= \frac{a}{c}[/tex]
So, Now finding [tex]\frac{sin\theta+cos\theta}{sin\theta-cos\theta}[/tex]
=> [tex]\frac{b}{c} + \frac{a}{c}[/tex] ÷ [tex]\frac{b}{c} - \frac{a}{c}[/tex]
=> [tex]\frac{b+a}{c}[/tex] ÷ [tex]\frac{b-a}{c}[/tex]
=> [tex]\frac{b+a}{c} * \frac{c}{b-a}[/tex]
=> [tex]\frac{b+a}{b-a}[/tex]
If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b − a) ≤ b f(x) dx a ≤ M(b − a). Use this property to estimate the value of the integral. π/9 5 tan(3x) dx π/12 (smaller value) (larger value)
Answer: the value of the integral is in the range:
0.006 ≤ int ≤ 0.008
Step-by-step explanation:
First, we have the function
5*tan(3x), and the range in this case is: pi/12 ≤ x ≤ pi/9
Then, the first step is find the maximum and minimum of f(x) in this range.
We know that between 0 and pi/2, tan(x) is a growing function, then
then the limits are
5*tan(3*pi/9) = 5*tan(pi/3) = M= 0.091
5*tan(3*pi/12) = 5*tan(pi/4) =m = 0.069
Then the value of the integral is between:
0.069*(3.14/9 - 3.14/12) ≤ int ≤ 0.091*(3.14/9 - 3.14/12)
0.006 ≤ int ≤ 0.008
Plssssssssssssss help me it’s due tomorrow I really need help I will mark brainliest!!!
Answer:
∠BAD = 100°
∠ADC = 105°
∠DCB = 50°
∠ABC = 105°
Step-by-step explanation:
∠BAD is given.
∠ADC is supplementary to the 75°, so it is 180-75 = 105°
∠DCB is 50° just like its opposite angle
The sum of all angles in a quadrilateral must be 360, so ∠ABC = 360-100-105-50 = 105.
Please help me……………………………………………………………
Hey there! :)
Answer:
x = -6.
Step-by-step explanation:
Given:
[tex]\sqrt[3]{5x-4} = \sqrt[3]{7x + 8}[/tex]
Cube both sides:
5x - 4 = 7x + 8
Subtract 5x from both sides:
-4 = 2x + 8
Subtract 8 from both sides:
-12 = 2x
x = -6.
Plz please help❤️ With only 5 please
Answer:
4. -1/2 and 2
5. N and R
Step-by-step explanation:
Well if you want me too do 5 I’ll do 4 too.
So for #4 it’s actually pretty simple we just have to seperate y that’s it.
So first we have to get y by itself by subtracting 3x to the other side so the equation looks like this now [tex]6y=-3x+12[/tex].
Now we have to take away the 6 and to do that we divide it to all the numbers and variables. Which gets us [tex]y=-1/2x+2[/tex].
So m and b are -1/2 and 2.
So we have to graph y = -1/2x + 2 so look at the image below.
So looking at the image we can see it passes through the points N and R.
Answer:
The line passes through points N and R.
Step-by-step explanation:
I graphed the equation on the graph below.