Answer:
[tex]\log_5(\frac{x}{4})^2 = 2\log_5(x) - 2\log_5(4)[/tex]
Step-by-step explanation:
Given
[tex]\log_5(\frac{x}{4})^2[/tex]
Required
The equivalent expression
To do this, we apply the following law of indices:
[tex]\log_a(b)^c = c\log_a(b)[/tex]
So, we have:
[tex]\log_5(\frac{x}{4})^2 = 2\log_5(\frac{x}{4})[/tex]
To further simplify:
[tex]\log(\frac{a}{b}) = \log(a) - \log(b)[/tex]
So, we have:
[tex]\log_5(\frac{x}{4})^2 = 2(\log_5(x) - \log_5(4))[/tex]
Open brackets
[tex]\log_5(\frac{x}{4})^2 = 2\log_5(x) - 2\log_5(4)[/tex]
Answer:
C.
Explanation:
Edge 2021
Determine where the PHD Mathematicians live.
The Mathematicians who live within the enclosure made by
the parabola
y = x2 +2x-3
and the line
y = -x + 1
have all earned their PHD in Mathematics. The following mathematicians live at the following coordinates:
Annie Easley:
Benjamin Banneker:
Fan Chung
Joan Clarke
A (-3,5)
B (6, 5)
C (5,5)
D(-1,-3)
Sophie Germain
Elbert Frank Fox:
Emmy Noether
Jama Musse Jama:
E (3,6) David Blackwell:
F (-2,-2) Mary Somerville:
G (-1,-4) Grace Hopper:
H(-6,8) Nalini Joshi
I (-1, -1)
J (3,-2)
K(-1,-2)
L (0, -1)
a) Plot the points given above on the grid. *Label each point with the given letter
b) Graph the line
y = -x + 1
Slope=__: y-intercept=
c) Factor and then find the x-intercepts.
y=x2+2x-3
Answer:
the answer to A,B,C
Step-by-step explanation:
all the points are on the graph
all answers
b) slope -1
intercept 1
c)(x+3)(x-1)
intercepts (-3,0),(1,0)
vertex (-1,-4)
The graph of the function f(x) = (x + 2)(x − 4) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 2, 0), has a vertex at (1, negative 9), and goes through (4, 0). Which describes all of the values for which the graph is negative and increasing? all real values of x where x < −2 all real values of x where −2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0
Answer:
c
Step-by-step explanation:
all real values of x where 1 < x < 4
Answer:
c
Step-by-step explanation:
trust me
Which function vertex form is equivalent to f(x)=x^2+6x+3?
Answer:
y = (x + 3)² - 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
f(x) = x² + 6x + 3
Using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² + 6x
f(x) = x² + 2(3)x + 9 - 9 + 3
= (x + 3)² - 6 ← in vertex form
Find the lengths of the missing pieces of the triangle. (Picture attached). Thank you!!
Step-by-step explanation:
my answer is in the image above
Answer:
I've attached the Answer here
What will be the remainder when 6x + 4x4 - 27x³
- 7x² + 27x + 3/2 is divided by (2x² – 3)?
Answer: The remainder is 0.
Step-by-step explanation:
We are given:
Dividend polynomial = [tex]6x^5+4x^4-27x^3-7x^2+27x+\frac{3}{2}[/tex]
Divisor polynomial = [tex]2x^2-3[/tex]
We divide the dividend by the divisor using the long division method.
In this method, the final answer written in the bottom is considered as remainder and the uppermost polynomial is considered as the quotient.
The long division of the two polynomials is attached in the image below.
From the image, we can say that the remainder of the two is 0
i have no idea what to do can someone pls help me quick
The ratio of goldfish to gallons of water is 7 to 2. How many goldfish can you get if you have 16 gallons of water? __________ and How many gallons of water do you need to keep 28 fish? ____________.
Answer: 56, 8
Step-by-step explanation:
Given
The ratio of goldfish to gallons of water is 7:2
If there is 16 gallons of water. For x goldfish, We can write
[tex]\Rightarrow \dfrac{7}{2}=\dfrac{x}{16}\\\\\Rightarrow x=7\times8\\\Rightarrow x=56[/tex]
If there are 28 fish, for y gallons of water we can write
[tex]\Rightarrow \dfrac{7}{2}=\dfrac{28}{y}\\\\\Rightarrow y=2\times 4\\\Rightarrow y=8\ \text{gallons}[/tex]
the sum of the digits of a two-digit number is 15. the unit digit is one less than the tens digit. find the number. let x be the tens digit. show the equation!
Answer: 87.
Step-by-step explanation:
Let x be the tens digit, then (x - 1) - unit digit.
x + x - 1 = 15
2x - 1 = 15
2x = 15 + 1
2x = 16
x = 16 ÷ 2
x = 8 - the tens digit.
8 - 1 = 7 - the units digit.
87 - the number.
Which system of equations has one solution?
Based on these results, express the probability that the next customer will pay with something other than a credit card as a fraction in simplest form.
Answer: 99/130
Payment made by any method except credit card is 95+4=99 and altogether there is three payment method including a credit card which sums up to 130.
So the probability is 99/130.
write the formula for the coefficient of quartile deviation
Step-by-step explanation:
How to Calculate the Semi Interquartile Range / Quartile Deviation. As the SIR is half of the Interquartile Range, all you need to do is find the IQR and then divide your answer by 2. Note: You might see the formula QD = 1/2(Q3 – Q1). Algebraically they are the same.
help pleaseee and thank you
Answer:
-2x-11=0
1) Add 11 to both sides
Dividde both sides by - 2
X= _11/2
Drcimal form: - 5.5
If k is a non-zero constant, determine the vertex of the function y = x2 - 2kx + 3 in terms of k.
Answer:
Set y = 0, evaluate the quadratic at h=−b2a and solve for k.
k=9 I think..... I'm not completely sure but I think that's how it is
Answer:
[tex]\displaystyle \text{Vertex} = \left(k, 3-k^2\right)[/tex]
Step-by-step explanation:
We are given the quadratic equation:
[tex]y=x^2-2kx+3[/tex]
Where k is a non-zero constant.
And we want to determine the vertex of the parabola in terms of k.
The vertex of a parabola is given by the formulas:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -2k, and c = 3.
Find the x-coorinate of the vertex:
[tex]\displaystyle x=-\frac{(-2k)}{2(1)}=\frac{2k}{2}=k[/tex]
To find the y-coordinate, we substitute the value we acquired back into the equation. So:
[tex]\displaystyle \begin{aligned} y(k)&=(k)^2-2k(k)+3\\&=k^2-2k^2+3\\&=3-k^2\end{aligned}[/tex]
Therefore, our vertex in terms of k is:
[tex]\displaystyle \text{Vertex} = \left(k,3-k^2\right)[/tex]
In ΔOPQ, PQ = 14, QO = 13, and OP = 20. Which list has the angles of ΔOPQ in order from smallest to largest?
Answer:
The answer is A, that's the correct one
In a standard deck of cards, there are 26 different red cards. How many possible combinations of 5 red cards
are there from those 26 cards?
Step-by-step explanation:
It doesn't matter what order they are drawn in, so youi have a combination problem
26C5
My calculator gives the answer directly,
It is 65780
Express x^2 + 4x - 7 in the form (x + a)^2 - b where a and b are intergers
Answer:
[tex]a = 2 \\ b = 11[/tex]
Step-by-step explanation:
[tex] {x}^{2} + 4x + 4 - 4 - 7 = {(x + 2)}^{2} - 11[/tex]
PLZZ HELPPP
Which matrix equation can be used to solve the system?
x+y=21
5x+4y=20
Answer:
[tex]X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\[/tex]
Step-by-step explanation:
Given the simultaneous equation
x+y=21
5x+4y=20
To write in matrix form, it must be in the form AX= b
X = A⁻¹b
A⁻¹ is the inverse of matrix A
A is a 2by2 matrix
X is the variables
b is a column matrix
The expression will therefore be written as;
[tex]A=\left[\begin{array}{ccc}1&1\\5&4\\\end{array}\right] \\\\|A| = 1(4)- 5(1)\\|A| = 4-5\\|A| = -1\\A^{-1} = -\left[\begin{array}{ccc}4&-1\\-5&1\\\end{array}\right] \\\\A^{-1} = \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \\[/tex]
Hence the required product matrix that represent X is;
[tex]X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\[/tex]
5) Last week a Pizza Hut sold 36 cheese pizzas, 64 pepperoni pizzas, and 20 veggie pizzas. Based on these data, which number is closest to the probability that the next customer will order a cheese pizza?
Answer:
[tex]P(Cheese) = 0.30[/tex]
Step-by-step explanation:
Given
[tex]Cheese = 36[/tex]
[tex]Pepperoni = 64[/tex]
[tex]Veggie = 20[/tex]
Required
[tex]P(Cheese)[/tex]
This is calculated as:
[tex]P(Cheese) = \frac{Cheese}{Total}[/tex]
[tex]P(Cheese) = \frac{36}{36+64+20}[/tex]
[tex]P(Cheese) = \frac{36}{120}\\[/tex]
[tex]P(Cheese) = 0.30[/tex]
Over what interval is the function in this graph constant?
Answer:
[tex]\text{A. }1\leq x \leq6[/tex]
Step-by-step explanation:
A constant intervals occurs when the function is neither increasing or decreasing. In the graph, we see this occurs from [tex]x=1[/tex] to [tex]x=6[/tex]. Therefore, the interval in which the graph is constant is [tex]\boxed{\text{A. }1\leq x \leq6}[/tex]
THIS IS TO HELP OTHER PEOPLE IF THEY FIND THIS QUESTION THIS QUESTION IS ALREADY CORRECT
What is the value of this expression?
[(3+5)⋅2−5]⋅3
Enter your answer in the box.
Which glide reflection describes the mapping ABC to DEF?
(x, y) (x + 6, y – 1) and reflected across x = 0
(x, y) (x + 6, y − 1) and reflected across y = 0
(x, y) (x, y + 6) and reflected across y = 0
(x, y) (x + 7, y) and reflected across x = 0
Answer:
Option (2)
Step-by-step explanation:
To get the transformation applied in triangle ABC to map triangle DEF we will apply the following rules.
If a point A of triangle ABC maps the point D of triangle DEF,
Coordinates of point A → (-4, -5)
Coordinates of point D → (2, 6)
First point A is shifted to quadrant (4) from quadrant (3),
Rule for the translation,
A(x, y) → A'(x + 6, y - 1)
A(-4, -5) → A'(2, -6)
Followed by reflection across x-axis (y = 0)
A'(x, y) → D(x, -y)
A'(2, -6) → D(2, 6)
Therefore, Option (2) will be the answer.
help me..........
only 23...
Question 23
Recall that a kite in geometry is any four sided figure where we have two different pairs of adjacent sides that are the same length.
We're told that PS = 4.5 and RS = 6. So this isn't an adjacent pair of congruent sides. But we can say that PS and PQ are one pair of adjacent congruent sides. That makes PQ to be 4.5 cm long.
Similarly, RS = RQ = 6 is the other pair of adjacent congruent sides. Notice that triangle PQR reflects over line PR to get triangle PSR.
See the diagram below.
I need help finding the distince.
Answer:
guessing that the area of the inner rectangle is 10m²
and the other rectangle is 16m*10m= 160m²
we can say that
(16-x) * (10-x) = 10
for the area of the inner rectangle
let's calculate the lefthand side of the equation
160 - 16x -10x + x² = 10
160 -26x +x² = 10
subtract 10 on both sides
150 -26x +x² = 0
rearrange
x² -26x + 150 = 0
looks like something we can throw the pq formula on to solve for x
with p = -26 and q = 150
[tex]x = - \frac{ - 26}{2} \frac{ + }{ - } \sqrt{( \frac{ - 26}{2})^{2} - 150 } [/tex]
[tex]x = 13 \frac{ + }{ - } \sqrt{169 - 150 } [/tex]
[tex]x = 13 \frac{ + }{ - } \sqrt{19 } [/tex]
[tex]x1 = 8.64[/tex]
[tex]x2 =17.36 [/tex]
we need to interpret this solutions
but to be sure on this, I need the unreadable text of the photographed problem
Need help quick easy problem to solve pls help!
Answer:
C
Step-by-step explanation:
12b + 30f = 240
7b + 10f = 125
Multiply the second equation by -3
12b + 30f = 240
-21b -30f = -375
Add up the two equations
-9b = -135
b = $15
Substitute this value in one of the two equations
12 * 15 + 30f = 240
180 + 30f = 240
30 f = 60
f = $2
An economist tracks the relationship between the change in the value of the U.S. dollar (a measure known as the dollar index) and the price of corn per bushel. The relationship is modeled by a quadratic function whose values are also shown in the table. For what change in the dollar index is the minimum corn price
how long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above?
Answer:
39.24 sec
How long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above? All tutors are evaluated by Course Hero as an expert in their subject area. Answer is t = 39.24 sec
Step-by-step explanation:
It will take the motor 39.2 seconds to lift the piano to the sixth-story window.
Given the following data;
Power = 1500 WattsMass = 300 kgHeight = 20 metersWe know that acceleration due to gravity is equal to 9.8 m/s².
To find how long it will take to lift the piano to the sixth-story window;
First of all, we would have to determine the gravitational potential energy required to lift the piano up.
Mathematically, gravitational potential energy is given by the formula;
[tex]G.P.E = mgh[/tex]
where:
G.P.E is the gravitational potential energy of an object.m is the mass of the object.g is the acceleration due to gravity.h is the height of the object.Substituting into the formula, we have;
[tex]G.P.E = 300*9.8*20[/tex]
G.P.E = 58,800 Joules
Next, we would determine the time using the following formula;
[tex]Time = \frac{Energy}{Power}[/tex]
Substituting the values into the formula, we have;
[tex]Time = \frac{58800}{1500}[/tex]
Time = 39.2 seconds.
Therefore, it will take the motor 39.2 seconds to lift the piano to the sixth-story window.
Find more on power, time and energy here: https://brainly.com/question/20488953
What is the equation of the following line written in slope-intercept form?
Answer:
C
Step-by-step explanation:
y=-7x-11
**PLEASE HELP**The frequency table below represents the 30 best battling averages for a semi pro baseball league. Which ranges of battling averages were least common among the players
The lower the frequency the least common the average.
There are two frequencies that are 1, which would be the least common.
The answer is C. 0.320-0.329 and 0.360 -0.369
Answer:
option C
Step-by-step explanation:
option c is contains the two batting averages which have a frequency of 1, this means that they both only occurred once which is the least amount of times any of the batting averages has occurred.
You get 11 points if you answer a.s.a.p
Answer:
Have you got it now?
Step-by-step explanation:
Anyone know the answer?
Answer:
Determine AC with the pythagorean theorem, then you can find CD by subtracting AD.
with DC and BC, you can find BD. again, with the pythagorean theorem
Answer:
20
Step-by-step explanation:
Find AC
[tex]\sqrt{65^{2} -16^{2} } = 63[/tex]
Substract
63 - AD = 12
Find "?"
[tex]\sqrt{12^{2} +16^{2} } = 20[/tex]