Answer:
d) -3
Step-by-step explanation:
The equation of a parabola in vertex form is given as:
y = a(x - h)² + k. Where (h, k) is the vertex of the parabola.
Given that the vertex of the parabola is at (4,-3) i.e h = 4 and k = -3.
The equation of the parabola is given as:
y = a(x - 4)² + (-3)
y = a(x² - 8x + 16) - 3
y = ax² - 8ax + 16a - 3
Given that when x = 5, y = -6. i.e:
-6 = a(5)² - 8a(5) + 16a - 3
- 6 = 25a - 40a + 16a - 3
-6 + 3 = a
a = -3
Find the angle measures given the figure is a rhombus.
Answer:
1 = 90°, 2 = 66°
Step-by-step explanation:
Since the diagonals of a rhombus are perpendicular, ∠1 = 90°. Using the Exterior Angles Theorem (exterior angle = sum of remote interior angles, we see that ∠2 = 90 - 24 = 66°.
Type the correct answer in each box. Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes. (graph below) The function with the lowest output values as x approaches infinity is ____ . The function with the greatest output values as x approaches infinity is ____ .
As x approaches infinity,
The function with the lowest output is graph A
The function with the greatest output is graph B
===========================================================
Explanation:
As the graphs head to the right, they go up forever. However, the growth rate (how fast they go upward) varies. The red straight line (line A) goes up the slowest. The growth rate is the same throughout the entire function. The rate is the slope of the line. In contrast, the purple curve B goes up the fastest as it has the steepest increase among the four graphs. The graph steadily gets steeper as you move to the right.
The exponential graph will grow the fastest compared to a linear one or parabolic one. Graphs B and C are exponential, where graph B has a steeper curve compared to graph C.
Answer: The function with the lowest output values as x approaches infinity is Graph A.
The function with the greatest output values as x approaches infinity is Graph B.
Step-by-step explanation: I can’t give you a step-by-step explanation, but this is right!
Which number line represents the solution set for the inequality
3(8-4x)<6(x-5)?
Answer:
B. x > 3
Step-by-step explanation:
Well we first simplify the following inequality,
3(8 - 4x) < 6(x - 5)
Distribute
24 - 12x < 6x - 30
Communicative property
-6x
24 - 18x < -30
-24
-18x < -54
Divide -18x by both sides
Which flips the < to a >.
x > 3
Thus,
the answer is B. x > 3.
Hope this helps :)
what is the explicit formula for this sequence ?
Answer:
B
Step-by-step explanation:
common difference is 3
explicit formula is
first term + ( n-1 ) * common difference
= -7 + ( n-1) * 3
Which triangle with side lengths given below is a right triangle? Select Yes or No.
A. 10, 15, 20
B. 10, 24, 25
C. 9, 40, 41
D. 11, 60, 61
Answer:
C, or 9,40,41
Step-by-step explanation:
Find the least number which must be subtracted from the following numbers to make it a perfect square i) 2361 ii) 26535 iii)16160 iv) 4401624
PLEASE HELP
For his long distance phone service, David pays a $5 monthly fee plus 9 cents per minute. Last month, David’s long distance bill was $10.58. For how many minutes was David billed?
Subtract the monthly fee:
10.58 -5 = 5.58
Divide the remaining amount by cost per minute:
5.58/ 0.09 = 62
He was billed for 62 minutes.
Um reservatório possui inicialmente R litros de água, por conta de um vazamento, perde 5 litros a cada minuto. Indique a lei de formação de uma função que expressa a quantidade de água no reservatório em função do tempo
Answer:
A(t) = R -5(t)
t in minuto
Step-by-step explanation:
Nesta questão, estamos preocupados em estabelecer uma lei que forneça a quantidade de água presente no reservatório a qualquer momento, usando a quantidade inicial de água no reservatório e a taxa de perda de água do reservatório.
Agora, sabemos que a taxa de perda de água é de 5 litros por minuto.
Assim, podemos estabelecer a lei da seguinte forma; vamos chamar a quantidade de água a qualquer momento no reservatório A (t);
A lei é assim; A (t) = R -5t onde t representa o tempo que estamos considerando e é em minutos, enquanto R é o volume inicial de água no tanque.
triangular park ABC has sides 3 m, 5 m, and 6 m. a gardener ravi wants to put a fence all around it and also plant grass inside. how much area does he need to plant?
Step 1) Check if the given triangle lengths form a right triangle
3^2 + 5^2 = 6^2
9 + 25 = 36
36 = 36
Step 2) Solve for the area of the triangle
Formula: A = 1/2 x base x height
A = 1/2 x 3 x 5
A = 1/2 x 15
A = 7.5 m^2
Step 3) Solve for the perimeter of the triangle
Formula: P = sum of all sides
P = 3 + 5 + 6
P = 14 m
Ravi needs to plant 7.5m^2 of grass and put up a fence that is 14m in total length.
Hope this helps!! :)
Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes. How many square meters could he make with 4 cloaks of fabric
Answer:
14 square meters of fabricStep-by-step explanation:
[tex]21\: square\:meters = 6 \:wizard \:cloak\\x\:square\:meters\:\:=4 \:wizard\:cloaks\\\\Cross\:Multiply\\6x = 84\\\frac{6x}{6} =\frac{84}{6} \\\\x = 14 \:square\:meters[/tex]
Answer:
14.0 square meters
Step-by-step explanation:
What is the center and radius of the circle? (x-4)^2 + (y-7)^2 =49
Answer:
The center of circle is: (-7,4) and Radius is 7 units
or (-4,7) and Radius is 7 units
We have to compare the given equation of circle with standard equation of circle
Given equation is:
2nd pic
down below
Standard equation of circle is:
3rd pic
down below
Here
h and k are coordinates of center of circle
So,
comparing
1st pic
down below
Hence,
The center of circle is: (-7,4) and Radius is 7 units
Keywords: Circle, radius
Answer:
The center is ( 4 , 7)The radius is 7Step-by-step explanation:
First expand the equation
That's
( x - 4)² + ( y - 7)² = 49
x² - 8x + 16 + y² - 14y + 49 - 49 = 0
x² + y² - 8x - 14y + 16 = 0
Comparing with the general equation of a circle
x² + y² + 2gx + 2fy + c = 0
2g = - 8 2f = - 14
g = - 4 f = - 7 c = 16
Center of a circle is ( - g , - f)
( --4 , --7)
Which is ( 4 , 7)
The radius of the circle is given by
r = √g² + f² - c
Where r is the radius
r = √ (-4)² + (-7)² - 16
= √16 + 49 - 16
= √49
= 7Hope this helps you
write the recurring decimal 0,101010101... . as a fraction in its simplest form.
Answer:
[tex]\frac{10}{99}[/tex]
Step-by-step explanation:
Answer:
[tex]\frac{10}{99}[/tex]
Step-by-step explanation:
We require to create 2 equations with the repeating decimal after the decimal point.
let x = 0.10101.... → (1)
Multiply both sides by 100
100x = 10.10101.... → (2)
Subtracting (1) from (2) eliminates the repeating decimal, thus
99x = 10 ( divide both sides by 99 )
x = [tex]\frac{10}{99}[/tex]
URGENT!!!!!!
Identify the sequence graphed below and the average rate of change from n = 0 to n = 3 . (2, 10) (3, 5) (4, 2.5) (5, 1.25)
A) a_n=8(1/2)^(n-2); average rate of change is -3
B) a_n=10(1/2)^(n-2); average rate of change is -(35/3)
C) a_n=8(1/2); average rate of change is 3
D) a_n=10(1/2)^(n-2); average rate of change is 35/3
Answer: Choice B
a_n = 10(1/2)^(n-2) is the nth term
average rate of change = -35/3
=======================================================
Explanation:
Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.
If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.
Use the slope formula to find the slope of the line through (0,40) and (3,5)
m = (y2-y1)/(x2-x1)
m = (5-40)/(3-0)
m = -35/3
The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3
The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.
In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.
Evaluate the function from the graph! PLEASE I NEED HELP!!
Hey there! I'm happy to help!
When it says f(1), that simply means to look for the x-coordinate 1 and then see what y-value of the function.
If we go to the x-value of 1 and look up a bit, we see where the function is at 1, it is at the y-value of 1!
Therefore, f(1)=1.
Using this, we can see that f(7) is 5, f(0)=2, etc.
Have a wonderful day!
DONT EXPLAIN just help me with the answer pleaseeee !
Answer:
A.928.20 is the answers..
Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8
Answer:
b=4
Step-by-step explanation:
So, we have the function [tex]f(x)=1/x[/tex]. We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).
f(2) = 1/(2) = 1/2
So, we have the point (2, 1/2)
At point b, f(b) = 1/b.
Let's plug this into the slope formula:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8[/tex]
Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).
[tex]\frac{.5b-1}{2b-b^2} =\frac{-1}{8}[/tex]
Now, cross multiply.
[tex]4b-8=b^2-2b[/tex]
[tex]b^2-6b+8=0[/tex]
Solve for b. Factor using the numbers -4 and -2.
[tex]=(b-4)(b-2)=0[/tex]
Thus, b=4 or b=2.
However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.
We want to find an interval such that the given equation, f(x) = 1/x, has an average rate of change of -1/8 in that interval.
We will see that the interval is [2, 4]
-------------------------------
For a function f(x), the average rate of change in the interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Here we have:
[tex]f(x) = 1/x[/tex]
And the interval is [2, b] such that r in that interval is -1/8, so we need to solve:
[tex]r = -1/8 = \frac{f(b) - f(2)}{b - 2} = \frac{1/b - 1/2}{b - 2}[/tex]
We can rewrite it to:
[tex]-1/8 *(b - 2)= 1/b - 1/2\\\\-1/8 *(b - 2)= 2/2b - b/2b = (2 - b)/2b = -(b - 2)/2b[/tex]
Now we can remove the term (b - 2) because it appears on both sides, so we get:
[tex]-1/8 = -1/2b\\1/8 = 1/2b\\2/8 = 1/b\\1/4 = 1/b\\b = 4[/tex]
Then we found that b must be equal to 4, so the interval is [2, 4]
If you want to learn more, you can read:
https://brainly.com/question/23483858
HELP!! Fiona races BMX around dirt course. If the radius of the course is 70 meters, what is the total distance Fiona covers in two laps of the race?
Answer:
879.64 (C)
Step-by-step explanation:
Answer:
879.2
Step-by-step explanation:
How do the areas of triangle ABC and DEF compare? The area of △ABC is 1 square unit less than the area of △DEF. The area of △ABC is equal to the area of △DEF. The area of △ABC is 1 square unit greater than the area of △DEF. The area of △ABC is 2 square units greater than the area of △DEF.
Answer:
The area of △ABC is equal to the area of △DEF
Step-by-step explanation:
On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (4, 2), (7, 2), (4, 6). Triangle D E F has points (negative 2, negative 1), (4, negative 3), and (4, negative 1).
How do the areas of triangle ABC and DEF compare? The area of △ABC is 1 square unit less than the area of △DEF. The area of △ABC is equal to the area of △DEF. The area of △ABC is 1 square unit greater than the area of △DEF. The area of △ABC is 2 square units greater than the area of △DEF.
Answer: The length of the sides of the triangle ABC are given below:
[tex]AB=\sqrt{(7-4)^2+(2-2)^2} =3\ unit\\\\BC=\sqrt{(4-7)^2+(6-2)^2} =5\ unit\\\\AC=\sqrt{(4-4)^2+(6-2)^2} =4\ unit[/tex]
The area of triangle ABC is given as:
Area = 1/2 × base × height = 1/2 × 3 × 4 = 6 unit²
The length of the sides of the triangle DEF are given below:
[tex]DE=\sqrt{(4-(-2))^2+(-3-(-1))^2} =\sqrt{40} \ unit\\\\EF=\sqrt{(4-2)^2+(-1-(-3))^2} =2 \ unit\\\\DF=\sqrt{(4-(-2))^2+(-1-(-1))^2} =6 \ unit[/tex]
The area of triangle DEF is given as:
Area = 1/2 × base × height = 1/2 × 2 × 6 = 6 unit²
The area of triangle ABC is equal to 6 unit² and the area of triangle DEF is equal to 6 unit² , therefore The area of △ABC is equal to the area of △DEF
Answer:
b
Step-by-step explanation:
edge exam
A town currently has a population of 1,000,000, and the population is increasing 6 percent every year
a) using standard function notation , next = nowx1.06, starting at 1,000,000 use p to denote current population, r for the rate of population growth, and t for the number of years explain answer
b)is the function you wrote in the previous task recursive or non recursive?
c)compare the benefits of representing a situation using a recursive function versus using a regular function
Answer:
a) [tex]1,000,000 \times (1.06)^{t}[/tex]
b) The function is recursive
c) The benefits includes;
1) Simplification of information
2) Faster data access
3) Lesser storage requirement
4) Good for forecasting
5) Simplifies information analysis.
Step-by-step explanation:
The given information are;
The current population = 1,000,000
The rate of increase of the population = 6%
a) With the standard function notation is [tex]P_f[/tex] = [tex]P_p[/tex] × [tex](1 + r)^{t}[/tex]
Where;
[tex]P_f[/tex] = Future population
[tex]P_p[/tex] = Present population
r = Rate of population increase
t = The number of years
Therefore, we have;
[tex]P_f[/tex] = 1,000,000 × [tex](1 + 0.06)^{t}[/tex] = 1,000,000 × [tex](1.06)^{t}[/tex]
The population increases by a factor of [tex](1.06)^{t}[/tex] given the number of years, t
b) The function is recursive as it takes account of the number of years and the previous population to calculate the future population
c) The benefits includes;
1) Simplification of the relationship of a given data with time
2) Provides a more faster way to access data that is recursive than using complex regular function with more variables
3) Reduces data storage space for statistical calculations as several particular data can be accessed using one function
4) Provides improved forecasting
5) Enables detailed information analysis.
A garden has an area of 264ft^2. Its length is 10 ft more than its width. What are the dimensions of the garden?
Answer:
Length = 22 ftWidth = 12 ftStep-by-step explanation:
Let length of the garden be ' x + 10 '
Let breath of the garden be ' x '
Area of the garden = 264 ft²
Now, let's find the breath of the garden 'x'
[tex]x(x + 10) = 264[/tex]
Distribute X through the parentheses
[tex] {x}^{2} + 10x = 264[/tex]
Move constant to left and change its sign
[tex] {x}^{2} + 10x - 264 = 0[/tex]
Write 10x as a difference
[tex] {x}^{2} + 22x - 12x - 264 = 0[/tex]
Factor out X from the expression
[tex]x(x + 22) - 12x - 264 = 0[/tex]
Factor out -12 from the expression
[tex]x(x + 22) - 12(x + 22) = 0[/tex]
Factor out X +22 from the expression
[tex](x + 22)(x - 12) = 0[/tex]
When the products of factors equals to 0 , at least one factor is 0
[tex]x + 22 = 0[/tex]
[tex]x - 12 = 0[/tex]
Solve for X
[tex]x + 22 = 0[/tex]
[tex]x = 0 - 22[/tex]
[tex]x = - 22[/tex]
Again,
[tex]x - 12 = 0[/tex]
[tex]x = 0 + 12[/tex]
[tex]x = 12[/tex]
(The dimensions can't be negative. )
So, width = 12 ft
Now, let's find the length of the garden ' X + 10 '
[tex]x + 10[/tex]
Plug the value of X
[tex]12 + 10[/tex]
Calculate the sum
[tex] = 22 \: ft[/tex]
Therefore,
Length = 22 ftWidth = 12 ftHope this helps..
Best regards!
4x-5 /6- 2x-1 /6 = 2/3
Answer:
x = [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Given
4x - [tex]\frac{5}{6}[/tex] - 2x - [tex]\frac{1}{6}[/tex] = [tex]\frac{2}{3}[/tex]
Multiply through by 6 to clear the fractions
24x - 5 - 12x - 1 = 4
12x - 6 = 4 ( add 6 to both sides )
12x = 10 ( divide both sides by 12 )
x = [tex]\frac{10}{12}[/tex] = [tex]\frac{5}{6}[/tex]
Lines m and p are parallel. If the slope of line m is 1/25 the
slope of line p?
Answer:
1/25
Step-by-step explanation:
Parallel lines have equal slopes.
So,
Slope of m = Slope of p = 1/25
Answer:
[tex]\boxed{\frac{1}{25}}[/tex]
Step-by-step explanation:
The lines are parallel. Two lines that are parallel have the same slopes.
slope of line [tex]m[/tex] = slope of line [tex]p[/tex]
[tex]slope= \frac{1}{25}[/tex]
Will ran 1 2/3 laps of a 1/4 mile track. How far, in miles, did Will run on that track?
Answer:
[tex]\boxed{\frac{5}{12} \ miles}[/tex]
Step-by-step explanation:
Will ran = [tex]1 \frac{2}{3} \ of \ a \frac{1}{4} \ miles \ track[/tex]
Will ran = [tex]\frac{5}{3} * \frac{1}{4}[/tex] [of means to multiply]
=> [tex]\frac{5*1}{3*4}[/tex]
=> 5/12 miles
Given: x + 2 < -5. Choose the solution set.
Answer:
x < -7
Step-by-step explanation:
to isolate x we need to subtract 2 from both sides. -5-2 is -7, so the answer is x < -7
Answer:
x< −7
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
x+2-(-5)<0
Step by step solution :
STEP 1:
Solve Basic Inequality :
1.1 Subtract 7 from both sides
x < -7
Inequality Plot :
1.2 Inequality plot for
x + 7.000 < 0
Six friends went to a restaurant and agreed to share the bill equally. However, two people forgot their wallets so the other four friends' portions of the bill went up by $7 each. How many dollars was the total bill?
Answer:
The total bill was $84
Step-by-step explanation:
Ok so we know a few things, we know that the total cost of the bill is divisible by both 6 and 4, and we know that if we call the total cost of the bill x and the amount each person would pay if it was divided for 6 people y we can write these equations:
[tex]\frac{x}{6}=y[/tex]
[tex]\frac{x}{4}=y+7[/tex]
Now we can substitute the first equation into the second and solve for x
[tex]\frac{x}{4}=\frac{x}{6}+7\\\frac{x}{4}-\frac{x}{6}=7\\\frac{x}{12}=7\\x=7*12=84[/tex]
Therefore, the total bill was $84
Given that the quadrilateral is a trapezoid, XW ≅ YZ and m∠Z = 44° , what is m∠X?
Answer:
angle X = 136 degrees
Step-by-step explanation:
Given XYZW is a trapezoid means XY || WZ.
Given XW ≅ YZ means that base angles are equal
=>
XWZ = YZW = 44
Since interior angles between parallel lines are supplementary,
angle X = YXW = 180-XWZ = 180-YZW = 180-angle Z = 180-44 = 136 degrees
Answer:
Angle X =136 degrees
Step-by-step explanation:
i. For any uniform probability distribution, the mean and standard deviation can be computed by knowing the maximum and minimum values of the random variable.
a) true
b) false
ii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.
a) true
b) false
iii. The uniform probability distribution's shape is a rectangle
a) true
b) false
Answer: I. True
II. True
III. True
Step-by-step explanation:
Uniform probability distributions, this are probability distributions which have equally likely outcomes. There are two known types of uniform distributions:
1. discrete
2. continuous.
In the first type of distribution, each outcome is discrete. In a continuous distribution, outcomes are continuous this means they are usually infinite.
HELP ASAP THANK YOU!!!!!!!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
If (x + h) is a factor of f(x) then remainder is zero and x = - h is a root
Since division of 2x² + 2x + 9 by (x + 3) is zero , then
(x + 3) is a factor and x = - 3 is a root of the polynomial → C
Please answer this question now
Answer:
Step-by-step explanation:
The side y is across from the angle Y which is 68 degrees. Angle Y is next to both the hypotenuse (14 units) and adjacent to the side XY (5 units). If we are finding side y, we need to use one of the trig ratios that relates the angle Y to the side across from it. That would be either the sin of Y which is the side opposite y) over the hypotenuse (14) or the tan of Y which is the side opposite over the side adjacent. Either one will get you the side lengths within a tenth or hundredth of each other. Let's do both, just because. First the sine:
[tex]sin(68)=\frac{y}{14}[/tex] and
14sin(68) = y so
y = 12.98 and rounded to the nearest tenth is 13.0
Now the tangent:
[tex]tan(68)=\frac{y}{5}[/tex] and
5tan(68) = y so
y = 12.37 and rounded to the nearest tenth is 12.4.
As an integer, your answer would be 13; as a decimal it would be the 12.4
Apparently, either is fine.
Help please!!!!!!!!!!!
Answer:
B. 2/3
Step-by-step explanation:
To solve this we have to take into account this axioms:
- The total probability is always equal to 1.
- The probability of a randomly selected point being inside the circle is equal to one minus the probability of being outside the circle.
Then, if the probabilities are proportional to the area, we have 1/3 probability of selecting a point inside a circle and (1-1/3)=2/3 probability of selecting a point that is outside the circle.
Then, the probabilty that a random selected point inside the square (the total probability space) and outside the circle is 2/3.