Answers
Answer:
When x = -1, f(x) = 2
Step-by-step explanation:
f(x) = (1/2)^x
When x = -4
f(x) = (1/2)^x
f(x) = (1/2)^-4
= 1 ÷ (1/2)^⁴
= 1 ÷ 1^⁴/2^⁴
= 1 ÷ 1/16
= 1 × 16/1
= 16
When x = -1
f(x) = (1/2)^x
= (1/2)^-1
= 1 ÷ 1/2^1
= 1 ÷ 1/2
= 1 × 2/1
= 1 × 2
= 2
When x = -1, f(x) = 2
Related Questions
Write the equation for a parabola with a focus at (-4,-2) and a directrix at y = 3.
Answers
Answer:
[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]
Step-by-step explanation:
By definition, any point (x, y) on the parabola is equidistant from the focus and the directrix.
The distance between a point (x, y) on the parabola and the focus can be described using the distance formula:
[tex]d=\sqrt{(x-(-4))^2+(y-(-2))^2[/tex]
Simplify:
[tex]d=\sqrt{(x+4)^2+(y+2)^2}[/tex]
Since the directrix is an equation of y, we will use the y-coordinate. The vertical distance between a point (x, y) on the parabola and the directrix can be described using absolute value:
[tex]d=|y-3|\text{ or } |3-y|[/tex]
The two equations are equivalent. Therefore:
[tex]\sqrt{(x+4)^2+(y+2)^2}=|y-3|[/tex]
Solve for y. We can square both sides. Since anything squared is positive, we can remove the absolute value:
[tex](x+4)^2+(y+2)^2 = (y-3)^2[/tex]
Expand:
[tex](x^2+8x+16)+(y^2+4y+4)=(y^2-6y+9)[/tex]
Isolate:
[tex]x^2+8x+11=-10y[/tex]
Divide both sides by -10. Hence, our equation is:
[tex]\displaystyle y=-\frac{1}{10}x^2-\frac{4}{5}x-\frac{11}{10}[/tex]
Can anyone do this thanks
Answers
2) sept.
4) aug. &' sept
Not 100% though .
How many x-intercepts appear on the graph of this polynomial function?
f(x) = x - 5x?
O 1 x-intercept
O 2 x-intercepts
O 3 x-intercepts
O 4 x-intercepts
Answers
Answer: B
Step-by-step explanation:
There are two x-intercepts: x = -√5 and x = √5. The answer is: 2 x-intercepts.
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.
To find the x-intercepts of the polynomial function f(x) = x⁴ - 5x², we set f(x) equal to zero and solve for x.
Setting f(x) = 0:
x⁴ - 5x² = 0
Factoring out the common term x²:
x²(x² - 5) = 0
Now we have two factors: x² = 0 and x² - 5 = 0.
For x² = 0, we have a double root at x = 0.
This means the graph touches the x-axis at x = 0 but does not cross it.
For x² - 5 = 0, we can solve for x by taking the square root:
x² = 5
x = ±√5
Therefore, there are two x-intercepts: x = -√5 and x = √5.
The answer is: 2 x-intercepts.
Learn more about the x-intercept here:
https://brainly.com/question/14180189
#SPJ7
The distance an airplane travels depends on how much time it spends flying. Which expression represents the distance the airplane flies in 20 minutes?
a. 20(distance)
b. distance-20
c. distance+20
d. distance(20)
Answers
Answer:
D distance(20)
Step-by-step explanation:
The notation to express a dependent variable is given by :-
, where Y is depending variable which is dependent upon x ( independent variable).
The given statement : The distance an airplane travels depends on how much time it spends flying.
Here , Independent variable : Time
Dependent variable : Distance
Then , the notation to express distance (dependent variable) the airplane flies in 20 minutes is given by :-distance(20).
If the measures of Arc=122 find the measure of angle b
Answers
Answer:
∠ B = 61°
Step-by-step explanation:
The inscribed angle B is half the measure of its intercepted arc, then
∠ B = [tex]\frac{1}{2}[/tex] × 122° = 61°
Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 10 right angle0,−10 in the directions parallel to and normal to the plane that makes an angle of theta equals tangent Superscript negative 1 Baseline (StartFraction StartRoot 3 EndRoot Over 3 EndFraction )θ=tan−1 3 3 with the positive x-axis. Show that the total force is the sum of the two component forces. What is the component of the force parallel to the plane? left angle nothing comma nothing right angle , What is the component of the force perpendicular to the plane? left angle nothing comma nothing right angle , Find the sum of these two forces. left angle nothing comma nothing right angle
Answers
Solution :
Let [tex]$v_0$[/tex] be the unit vector in the direction parallel to the plane and let [tex]$F_1$[/tex] be the component of F in the direction of [tex]v_0[/tex] and [tex]F_2[/tex] be the component normal to [tex]v_0[/tex].
Since, [tex]|v_0| = 1,[/tex]
[tex]$(v_0)_x=\cos 60^\circ= \frac{1}{2}$[/tex]
[tex]$(v_0)_y=\sin 60^\circ= \frac{\sqrt 3}{2}$[/tex]
Therefore, [tex]v_0 = \left<\frac{1}{2},\frac{\sqrt 3}{2}\right>[/tex]
From figure,
[tex]|F_1|= |F| \cos 30^\circ = 10 \times \frac{\sqrt 3}{2} = 5 \sqrt3[/tex]
We know that the direction of [tex]F_1[/tex] is opposite of the direction of [tex]v_0[/tex], so we have
[tex]$F_1 = -5\sqrt3 v_0$[/tex]
[tex]$=-5\sqrt3 \left<\frac{1}{2},\frac{\sqrt3}{2} \right>$[/tex]
[tex]$= \left<-\frac{5 \sqrt3}{2},-\frac{15}{2} \right>$[/tex]
The unit vector in the direction normal to the plane, [tex]v_1[/tex] has components :
[tex]$(v_1)_x= \cos 30^\circ = \frac{\sqrt3}{2}$[/tex]
[tex]$(v_1)_y= -\sin 30^\circ =- \frac{1}{2}$[/tex]
Therefore, [tex]$v_1=\left< \frac{\sqrt3}{2}, -\frac{1}{2} \right>$[/tex]
From figure,
[tex]|F_2 | = |F| \sin 30^\circ = 10 \times \frac{1}{2} = 5[/tex]
∴ [tex]F_2 = 5v_1 = 5 \left< \frac{\sqrt3}{2}, - \frac{1}{2} \right>[/tex]
[tex]$=\left<\frac{5 \sqrt3}{2},-\frac{5}{2} \right>$[/tex]
Therefore,
[tex]$F_1+F_2 = \left< -\frac{5\sqrt3}{2}, -\frac{15}{2} \right> + \left< \frac{5 \sqrt3}{2}, -\frac{5}{2} \right>$[/tex]
[tex]$=<0,- 10> = F$[/tex]
find the area of the circle. leave your answer in terms is pi.
a. 9
b. 324
c. 82
d. 18
Answers
Answer:
9
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
9×2 =18 or 9+9=18 I haven't done this since 6 grade sorry if I got it wrong
1+2+3+4+5+6+7+8+9+2000+1000000
Answers
Please help!
Find the length of the triangle.
Answers
Answer: 12.
Step-by-step explanation: Use Pythagorean Theorem. We that a = 9, b = ?, and c = 15. Plugging that in gives us 9^2 + b^2 + 15^2. Solving for b gets us b^2 = 144. Taking the square root of both sides gets us b = 12.
Find three consecutive even integers such that the product of the second and
third integers is equal to 35.
Answers
Step-by-step explanation:
first number=x
second number=x+2
third number=x+4
(x+2)(x+4)=35
x(x+4)+2(x+4)=35
x²+4x+2x+8=35
x²+6x+8=35
x²+6x=35-8
x²+6x=33
x²+6x-33=0
using that, you can find the first number,
then use the data to find the other two.
PLs! 100 points the integers 1,2,3,4,5,6,7,8 are placed in a list so that each value is either bigger than all the numbers it precedes or smaller than all the numbers it precedes. How many such lists are possible? 100 points!
Answers
2
Hope this helps! :)
______________
Answer:
you can know by the minimum number or the maximum e.g minimum 1 maximum 20 answer 20
Step-by-step explanation:
so in this kind it is 2
hope its useful
Find the 10th term in the following geometric sequence.
8, 4, 2, 1,
Answers
[tex]\huge\mathfrak\green{ please \: help \: ...} \\ \\ \huge\mathfrak\red{5 ^{2} + 6 ^{2} = {?} }[/tex]
Answers
61
Answer:
5²+6²=5*5+6*6=25+36=61 is a required answer.
Answer:
61 is the answer
Step-by-step explanation:
[tex] {5}^{2} = 5 \times 5 = 25 \\ {6}^{2} = 6 \times 6 = 36 \\ \\ {5}^{2} + {6}^{2} = 25 + 36 \\ = 61[/tex]
if a person gives you their card number and they say you can spend a certain amount of money and u spend more is it considered stealing? or is it not because they gave u their card willingly and all u did was go over the limit.
Answers
Answer:
It would be considered stealing.
Step-by-step explanation:
They did willingly give you their card BUT, they trusted you to only spend a certain amount and not go over that certain limit. You went over the limit even though they specifically told you not to go over it so yes, it would be classified as stealing.
Triangle ABC is on a coordinate plane.
If its rotated 180 degrees around a specific point to create A'B'C'
Which characteristics are true for both the original triangle and the triangle's image?
Question 11 options:
The measures of
The coordinates of B' will be the same as B.
The coordinates of A' will be the same as A.
The Area of ABC will be the same as A'B'C'
The perimeter of ABC will be the same for A'B'C'
The length of segment AB will be the same as Segment A'B'
Answers
Answer:
The last 3 choices are correct
Step-by-step explanation:
A rotation of 180 degrees has the rule (x,y) →(-x,y) , so the coordinates will not be the same. The shape's size doesn't change.
Answer the question pleaseeeee
Answers
Can anyone help ? :) thanks
Answers
no se ingles xd asi que la verdad sorry aun que dime si es potensiacion
Which expression can be used to find 80% of 120?
80% of 120
20%
20%
20%
20%
20%
Answers
Answer:
96
Step-by-step explanation:
80*120=9600 divided by 100
Mathssssssssssssssssssssssssss
Answers
Answer:
The value of x is 5
The value of Kelsey's car will depreciate (decrease) by a rate of 15% each year. She wants to write an exponential equation to find out what it will be worth in 6 years. What is the multiplier for this situation?
Answers
So if you multiply 15 by 6 you get 90 and the 6 is from every years she has saved. So if you take any number 95000 and 15 percent of 95000 is 14250 so try breaking it down and divide as much as you can but not to much and slowly at a time and then when you get that try to get close to 9500 as much as you can cause 90 percent of 95000 is 9500.
the price of a ring was increased by 30% to £325 what was the price before the increase
Answers
Answer is : Price before increase is £250
Explaination:
Let the Original price of a ring = x
Increase price( g) = 30%
New price(n) = £325
x = ( 100*n)/ (100+g)
x= (100*325)/(100+30)
x= (200*325)/130
x= 250
Therefore price before increase is £250
Another method:
Given that after 30% increases,
the cost of the ring is £325 so we can assume that 130% (100+30) is £325.
Now, we have to form an expression in term of x where x represents the original cost :
130/100*x=325
Solving x
x= 250
So the original price or price before the increase is £250
A cube that is used as a table is 2ft on each side. how many square feet will be painted if all sides are painted
A. 24ft²
B. 48ft²
C. 36ft²
Answers
Answer:
a = 24 ft²
Step-by-step explanation:
Area of 1 side
a = 2 * 2
a = 4 ft²
Cubes have 6 sides
a = 6 * 4
a = 24 ft²
Answer:
A. 24 ft²
Step-by-step explanation:
The faces of a cube are squares. We know that the squares have a side length of 2 ft. Therefore, the area of a square will be 4 ft². There are 6 faces/squares on a cube, so we take the 4 ft² and multiply it by 6. This gives us 24 ft².
what is the solution to the equation 1/4 x + 2 -5/8 x - 5? i
Answers
Answer:
work sh bf nd diu xd vs a wish even den dvs dneirgrvvdndkddvdvndkdosuehebdno he be bes be nah be even be bed buddy be end
A surveyor leaves her base camp and drives 42km on a bearing of 032degree she then drives 28km on a bearing of 154degree,how far is she from her camp base and what is her bearing from it
Answers
Answer:
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).
Step-by-step explanation:
The final position of the surveyor is represented by the following vectorial sum:
[tex]\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3}[/tex] (1)
And this formula is expanded by definition of vectors in rectangular and polar form:
[tex](x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2})[/tex] (1b)
Where:
[tex]x, y[/tex] - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.
[tex]r_{1}, r_{2}[/tex] - Length of each vector, in kilometers.
[tex]\theta_{1}, \theta_{2}[/tex] - Bearing of each vector in standard position, in sexagesimal degrees.
If we know that [tex]r_{1} = 42\,km[/tex], [tex]r_{2} = 28\,km[/tex], [tex]\theta_{1} = 32^{\circ}[/tex] and [tex]\theta_{2} = 154^{\circ}[/tex], then the resulting coordinates of the final position of the surveyor is:
[tex](x,y) = (42\,km)\cdot (\cos 32^{\circ}, \sin 32^{\circ}) + (28\,km)\cdot (\cos 154^{\circ}, \sin 154^{\circ})[/tex]
[tex](x,y) = (35.618, 22.257) + (-25.166, 12.274)\,[km][/tex]
[tex](x,y) = (10.452, 34.531)\,[km][/tex]
According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:
[tex]\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}[/tex]
[tex]\theta \approx 16.840^{\circ}[/tex]
And the distance from the camp is calculated by the Pythagorean Theorem:
[tex]r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}[/tex]
[tex]r = 36.078\,km[/tex]
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).
Can someone please help me?the question is in the picture. Thank you
Answers
Answer:
It would be 9π
Step-by-step explanation:
(x-1)²π
(x-1)(2x-4)
ann and betty shared a sum of money in the ratio 2 : 3. ann received $120. what was betty's share?
Answers
Answer:
Betty got $180
Step-by-step explanation:
If its 2:3 and 2 is 120, that means 120/2 equals 60. 60*3=180
Step-by-step explanation:
the answer is 180 as the other person stated
Mr. Ali cut a wooden plank into three parts in the ratio 2:3:8. The longest part was 72 centimeters
Answers
Answer:
117 centimeters
Step-by-step explanation:
Since the longest pieces is 72 centimeters and it’s ratio is 8, that means the individual unit of the ratio is 9 (72/8=9). You can multiply each part of the ratio by 9
2x9=18
3x9=27
We already know the third part of the ratio is 72. Add all of it together to get the original length.
18+27+72=117 cm
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.
If one of the longer si
des is 6.3 centimeters, which equation can be used to find the length of the base
Answers
Answer:
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 3.1
Thank you please shwo your work if you can<3 !!!!
x=
y=
Answers
Answer:
x = 2, y = - 1
Step-by-step explanation:
Given the 2 equations
y = - 7x + 13 → (1)
y = - 1 → (2)
Substitute y = - 7x + 13 into (2)
- 7x + 13 = - 1 ( subtract 13 from both sides )
- 7x = - 14 ( divide both sides by - 7 )
x = 2
y = - 1 is already given in (2)
Then x = 2, y = - 1
So the equation will be: -1 = -7x + 13
Now we solve from here, start by subtracting 13 on both sides:
-14 = -7x
Divide -7 on both sides:
2 = x
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.
y=−9x^2+571x−3884