For the function, y = log₄ (x + 16) - 1, it has x-intercept of -12 and y-intercept of 1.
What are Logarithmic Functions?Logarithmic functions are functions expressed in another way for exponential functions. It is the power to which any number should be raised to yield other values.
Logₐ x = n can be written in exponential form as x = aⁿ.
y = log₄ (x + 16) - 1
x-intercept is the x-coordinate of the point when y = 0.
0 = log₄ (x + 16) - 1
For the left hand side to be equal to 0, the term log₄ (x + 16) must be equal to 1.
log₄ (x + 16) = 1
⇒ x + 16 = 4 (∵ logₐ a = 1)
⇒ x = -12
y-intercept is the y-coordinate of the point where x = 0.
y = log₄ (0 + 16) - 1
y = log₄ (16) - 1
y = log₄ (4²) - 1
logₐ mⁿ = n logₐ m
⇒ y = 2 log₄ (4) - 1
⇒ y = 2 - 1 (∵ log₄ (4) = 1)
⇒ y = 1
Hence, the function y = log₄ (x + 16) - 1 has x-intercept of -12 and y-intercept of 1.
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A 12-ounce box of cereal costs $4.80. Which equation relates the price, p, to the weight, w, in ounces, of the cereal correctly?
Responses
The correct equation is [tex]P = 2.5w[/tex] .
What is cost and equation ?The average cost is the ratio of the total of cost of all the products to the total number of products.
The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
An equation says that two things are equal. It will have an equals sign "=" .
A 12-ounce box of cereal costs $4.80.
The price be 'P' and weight be 'w'.
$4.80 is the price of box with weight 12-ounce
i.e. 4.80P = 12w
Divide both side by 4.80
[tex]\frac{4.80P}{4.80} = \frac{12w}{4.80}[/tex]
[tex]P = 2.5w[/tex]
Therefore, the correct equation is [tex]P = 2.5w[/tex] .
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A line passes through the point (3, 7) and has a slope of 4.
Write an equation in point-slope form for this line.
Answer:
Step-by-step explanation:
4y=3x+7
divide both sides by 4
y= 0.75x+1.75
or in fraction
y=3/4x+7/4
Write an equation for the nth term of the sequence 12, 5, -2, -9,...
Is x^4+2x^3-x^2+7x+11 a quintic binomial
The category of the expression x⁴ + 2x³ - x² + 7x + 11 is not quintic binomial
How to determine the category of the expression?From the question, we have the following expression that can be used in our computation:
x^4+2x^3-x^2+7x+11
Rewrite this expression properly
So, we have the following representation
x⁴ + 2x³ - x² + 7x + 11
The degree of the above polynomial is 4
As a general rule, a quintic binomial is any polynomial that has a degree of 5
A degree of 5 and a degree of 4 are not the same
Hence, the expression is not a quintic binomial
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Suppose you have two options from which to choose a pay raise for each of the next two years.
Option A: You received a $6,000 raise in year 1 and then 4% raise in year 2.
Option B: You receive a 4% raise for 1 year and then a $6,000 raise in year 2.
Which option will result in you making more money? Explain.
We see that under option B, you will make more money than under option A.
What is a percentage?
A relative value indicates the hundredth part of any quantity. One percent (symbolized 1%) is the hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
To compare the two options and determine which one will result in you making more money, we need to find the total amount of money you will make under each option.
Under option A, you will receive a $6,000 raise in year 1 and a 4% raise in year 2. Let's call your base salary S. After the first year, your salary will be S + $6,000. After the second year, your salary will be (S + $6,000) * 1.04 = S + $6,240.
Under option B, you will receive a 4% raise in year 1 and a $6,000 raise in year 2. After the first year, your salary will be S * 1.04 = S + $480. After the second year, your salary will be (S + $480) + $6,000 = S + $6,480.
Comparing the two options, we see that under option B, you will make more money than under option A. This is because option B includes a $6,000 raise in the second year, while option A includes a smaller 4% raise in the second year.
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is 0.25 L less than or greater than 2,500 ML
Answer:
Equal to.
Step-by-step explanation:
there's 1000 ML in one L
so .25 x 1000 =
2500
which would mean they're equal
Hello please graph this with steps thank you
Graph f(x)=-x^4+1
The graph of the quartic function f(x) = -x⁴ + 1 is attached below with points at (-1 ,0), (0, 1) and (1, 0)
Graph of a Quartic ExpressionQuartic polynomials are continuous curves like the cubic polynomials. This means that you can draw the graph of the quartic without lifting your pencil from the page. There are no holes or jumps in the curve but, unlike the cubic graph, a graph of the quartic looks like a W or an M.
The general form of quartics of this form is y = a(x − h)⁴ + k The turning point is at (h, k). When sketching quartic graphs of the form y = a(x − h)⁴ + k, first identify the turning point. To add further detail to the graph, the x-axis and y-axis intercepts are found.
In this function given;
f(x) = -x⁴ + 1
This quartic function has points at (-1 ,0), (0, 1) and (1, 0)
Kindly find the attached graph below
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Simplify 5a
8c + b + 3c-9a6b. (1 point)
Answer:
11c-63ab
Step-by-step explanation:
8c +b+3c-9a6b
( b n 6b are common)
8c + 3c-9a7b
(8c and 3c are also common)
11c-9a7b
11c-63ab
Calculate the quotient and enter it below.
19 ÷ (-1)
Answer here
Answer:
-19
Step-by-step explanation:
Use a calculator
There are 28 student desks in ms. Johnson's. Each desk measures 26. 17 inches long. If you were to line up all the desks end-to-end, how long would all the desks be? do not include units.
Answer: 732.76
Step-by-step explanation: 28 x 26.17 = 732.76, and if by units you mean decimals, then its 732
8/3x+1/3x=3 1/3+ 7/3x
find value of x
An equation is a formula that expresses the equality of expressions, with the aid of using connecting them with the equals signal =. The value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x is x = 1.
The required details for equation in given paragraph
The word equation and its cognates in different languages can also additionally have subtly extraordinary meanings; for example, in French an equation is described as containing one or more variables, whilst in English, any well-shaped formula which includes expressions associated with an equals signal is an equation. Solving an equation containing variables includes figuring out which values of the variables make the equality true. The variables for which the equation must be solved also are called unknowns, and the values of the unknowns that fulfill the equality are called solutions of the equation.
To find the value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x, we need to first get all of the terms with x on the same side of the equation.
We can start by moving the 3 1/3 to the right side of the equation by subtracting it from both sides:
8/3x + 1/3x - 3 1/3 = 7/3x - 3 1/3
Next, we can combine the coefficients of x on the left side of the equation:
(8/3 + 1/3) x = (7/3 - 3 1/3)
4/3 x = 4/3
Finally, we can divide both sides of the equation by 4/3 to find the value of x:
(4/3) x / (4/3) = (4/3) / (4/3)
x = 1
Therefore, The value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x is x = 1.
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Answer:
x = 5
Step-by-step explanation:
8/3x+1/3x=3 1/3+ 7/3x
find value of x
8/3x + 1/3x = 3 1/3 + 7/3x
3x = 7/3x + 10/3
2/3x = 10/3
x = 5---------------------------
check8/3 x 5 + 1/3 x 5 = 3 1/3 + 7/3 x 5
15 = 15
the answer is good
A square coaster has a side length of 5/12 feet on each side.
What is the area of the coaster???
HELP!!! FAST!!
Answer:
[tex]\frac{25}{144}[/tex] ft
Step-by-step explanation:
We can find the area by multiplying 2 sides together
Multiply [tex]\frac{5}{12}[/tex] × [tex]\frac{5}{12}[/tex] to find the area
[tex]\frac{5}{12}[/tex] × [tex]\frac{5}{12}[/tex] = [tex]\frac{25}{144}[/tex]
The area of the coaster would be [tex]\frac{25}{144}[/tex] ft
Please help me!
Thank you
The required measures of the angle are given as,
∠JKL = 72° ∠MLK = 108° ∠JMK = 36°
∠MJL = 54° ∠KNL = 90°
Given that.
The measure of the rhombus is given, we have to determine the measure of the angles,
orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as angle.
Here,
∠JKL= 2 × ∠JKM = 72°
∠MLK = 180 - 2 × ∠JKM = 108°
∠JMK = ∠JKM = 36°
∠MJL = ∠MLK/2 = 54°
The diagonal of the rhombus bisect each other at an angle of 90°
So,
∠KNL = 90°
Thus, all the measure of the angles is shown above.
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Which of the following equations have exactly one solution?
Choose all answers that apply:
(Choice A)
A
-5x+12=5x-5
(Choice B)
B
-5x+12=-5x-12
(Choice C)
C
-5x+12=5x+12
(Choice D)
D
-5x+12=-12x-12
Option A and D are appropriate.
What does the one solution mean?There is just one correct answer to some equations. There is only one value for the variable in these equations that causes the equation to be true. If you solve an equation and the result is a variable equal to a number, the problem has just one solution.
To date,
1) x has just one solution since -5x + 12 = 5x -5
-5x -5x = -5 -12
-10x = -17
x = 1.7
2) -5x+12=-5x-12 -5x + 5x = -12-12
0x (not possible)
3) -5x+12=5x+12 -5x + 5x = +12-12
0x ( not possible)
4) The equation -5x+12=-12x-12
-5x + 12x = -12 -12
7x = -24
x = -24/7, indicating that x has just one solution.
Option A and D thus have a single solution.
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£11000 is invested in an account paying 2.25% per annum. How much will interest will be in the account at the end of 4 years?
Answer:
£990
Step-by-step explanation:
£11000 * 2.25% * 4 = £990
please help me. thanks.
The angles which makes 45° and 90° in square are shown below.
What is square?The square is a 4 sided figure, each side of the square is equal and make a right angle.
The area of square having sided a unit can be given by a² square unit.
Given that,
ABCD is a square,
The angles which are 45°,
∠ CAD, ∠ CAB, ∠ DBA, ∠ DBC, ∠ ACB, ∠ ACD, ∠ BDA, ∠ BDC
The angle which are 90°,
∠ DAB, ∠ ABC, ∠ BCD, ∠ ADC
And central angles also make 90°,
∠ AEB, ∠ BEC, ∠ CED, ∠ DEA
In square there is no angle that neither makes 45° nor 90°.
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Angles categorized in 45° and 90° are ∠DBC = ∠BDC =∠BAC = 45° and
∠ABC = ∠AED = 90° respectively.
What is a square?Square is a polygon which has 4 sides. All four sides of square are equal length and perpendicular to each other that means the angle between two adjacent side is 90°.
Given that ABCD is a square surface. And diagonal of square creates two isosceles triangles.
So the ∠ABC = ∠BCD = ∠CDA = DAB = 90°
Here, BD and AC are two diagonals of a square ABCD and E is the intersection point of diagonals.
Diagonals cut each other perpendicular.
So, ∠AED = 90° and ∠EAD = ∠EDA = 45°
Now to find ∠BAC;
we have ∠ABC = 90° so from the property of isosceles triangle
∠BAC = ∠BCA = 45°
In isosceles triangle BCD,
∠BCD = 90° and ∠DBC = ∠BDC = 45°
Therefore, the angles categorized in 45° and 90° are ∠DBC = ∠BDC =∠BAC = 45° and ∠ABC = ∠AED = 90° respectively.
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Hooke’s Law for springs states that the distance a spring is
stretched or compressed from rest is directly proportional to the force applied to
the spring. Suppose a force of 16 lbs stretches a spring 5 inches from rest. What
force is required to stretch the same spring 13 inches from rest, if it’s possible
According to Hooke's law, a material's strain will increase in direct proportion to its applied stress up to its elastic limit. When elastic materials are stretched, atoms and molecules deform up to a point of stress, after which they return to their original shape.
What is Hooke's law?Hooke's law only approximates in first-order linear terms how springs and other elastic bodies actually react to applied forces. Since no material can be stretched or squeezed beyond a given size without permanently deforming or changing its condition, it must inevitably fail once the forces reach a certain threshold.
Many substances will diverge from Hooke's law clearly before they reach such elastic limits.
On the other hand, as long as the forces and deformations are small enough, Hooke's law provides a close approximation for the majority of solid bodies. Since it is the basis of many fields including seismology, molecular mechanics, and acoustics,
Hooke's law is widely applied in all branches of science and engineering. It.
Hence, a material's strain will increase in direct proportion to its applied stress up to its elastic limit. When elastic materials are stretched, atoms and molecules deform up to a point of stress, after which they return to their original shape.
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regarding antipoverty programs intended to supplement family income, One adjustment that can be made is to gradually reduce benefits as incomes rise. However, the more gradual the phase-out of benefits, the _____ the burden on taxpayers.
Safety net policies like food assistance, housing assistance, and family tax credits keep millions of Americans from poverty each year and reduce hardship for millions more.
What are some examples of policies that have been created to address poverty in the United States?The interaction of labor supply and demand on the market determines wage rates. The business will hire as much labor as its marginal labor cost equals its marginal labor revenue output.The interaction of labor supply and demand on the market determines wage rates. The business will hire as much labor as its marginal labor cost equals its marginal labor revenue output. The definition of a wage rate is the amount paid to employees. It is one of the major topics covered in human resource studies. It depends on two things: either the amount of production hours or productivity at work. This field of research is called wage rate economics. Wage rates quantify the fundamental compensation for each unit of output or of time.Contrarily, in a wage system, a person is paid according to the current wage rate, which is subject to change.To learn more about demand refer to:
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What is 5x-2+7x-5 simplified?
Answer:
12x -7
Step-by-step explanation:
3. Given that x = 3 and y = 4, find the value of the following
expression (3x + 4y)^2 + (8x + 7y)² + 24xy
Answer: 3353
Let's solve this equation:
[(3)(3)+(4)(4)]2+[(8)(3)+(7)(4)]2+(2)(3)(4)
=(9+(4)(4))2+((8)(3)+(7)(4))2+(2)(3)(4)
=(9+16)2+((8)(3)+(7)(4))2+(2)(3)(4)
=252+((8)(3)+(7)(4))2+(2)(3)(4)
=625+((8)(3)+(7)(4))2+(2)(3)(4)
=625+(24+(7)(4))2+(2)(3)(4)
=625+(24+28)2+(2)(3)(4)
=625+522+(2)(3)(4)
=625+2704+(2)(3)(4)
=3329+(2)(3)(4)
=3329+(6)(4)
=3329+24
=3353
Hope this helps!!
Solve the following compound inequality. 5x+7<-3 or 3x-4>11
Answer:
X <-2 or X > 5
Step-by-step explanation:
Find the slope of the line y=14x–1.
Write your answer as an integer or as a simplified proper or improper fraction.
The slope of the line y = 14x – 1 is 14.
To find the slope of a line, we need to know two points on the line. We can choose any two points, as long as they are not the same. For example, we can choose the points (0, -1) and (1, 13):
y = 14x – 1
y = 14(0) – 1 = -1 when x = 0
y = 14(1) – 1 = 13 when x = 1
The slope of the line is the change in y divided by the change in x between these two points. In this case, the change in y is 13 – (-1) = 14, and the change in x is 1 – 0 = 1. Therefore, the slope of the line is 14/1 = 14.
We can also write the slope as a simplified fraction. In this case, 14 is already a simplified fraction, so we don't need to simplify further. Therefore, the slope of the line y = 14x – 1 is 14.
please give a reasonable answer please and thank you!
The inequality on the graph is a linear inequality, and it can be written as:
y > 2x - 4
What inequality is shown in the graph?On the graph, we can see a linear inequality, we can see a dashed line with a positive slope, and the shaded area is above that line, so the inequality is of the form:
y > line.
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
We can find two points on the graph, we can see that the line passes through (0, -4) and (2, 0), then the y-intercept is -4 and the slope is:
a = (0 + 4)/(2 - 0) = 2
y = 2x - 4
then the inequality is:
y > 2x - 4
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If light strikes a plate mirror at a 36° angle of incidence, what would you expect the resulting angle of reflection to be?
According to the angle of incidence, the angle of reflection will also be 36°
Angle of incidence:
In math it means the angle which an incident line or ray makes with a perpendicular to the surface at the point of incidence.
Given,
Here we need to find the If light strikes a plate mirror at a 36° angle of incidence, then what would you expect the resulting angle of reflection to be.
Here we know that, the incident ray, the reflected ray and the normal ray at the point of incidence all lies in the same plane.
Then the angle of incidence is equal to the angle of reflection
And it can be written as,
=> Angle of incidence = angle of reflection
As per the 2nd law given above, we say that if a light ray incident at 45°, then the reflected angle will also be 45°
Here we know that the value of,
=> Angle of incidence = 36°
Therefore, the Angle of reflection = 36°
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Can you help me thank you
Answer:
A.) [tex]\frac{1}{5^6}[/tex]
Step-by-step explanation:
To simplify [tex](5^2)^3[/tex], use the exponent rule that states [tex](a^m)^n=a^{mn}[/tex]
So,
[tex](5^2)^3=5^{2*3}=5^6[/tex]
Use the same exponent rule to begin simplifying [tex](5^4)^{-3}[/tex]:
[tex](5^4)^{-3}=5^{4*(-3)}=5^{-12}[/tex]
To further simplify [tex]5^{-12}[/tex], use the exponent rule that states [tex]a^{-m}=\frac{1}{a^m}[/tex]
So,
[tex]5^{-12}=\frac{1}{5^{12}}[/tex]
Then multiply the two new expressions as indicated in the original problem:
[tex](5^6)(\frac{1}{5^{12}})=\frac{5^6}{5^12}=\frac{1}{5^6}[/tex]
Alternatively, you could use the exponent rule that states [tex]a^m*a^n=a^{m+n}[/tex]
where
[tex]a^m=5^6\\a^n=5^{-12}[/tex]
So,
[tex](5^6)(5^{-12})=5^{6+(-12)}=5^{-6}=\frac{1}{5^6}[/tex]
an experienced bricklayer can build a small wall in 3 hours. her apprentice can complete the job in 6 hours. find how long it takes if they work together.
For both the experienced bricklayer and her apprentice working together it will take 2 hours to complete the work.
This is type of combined rate or time and work problem. Here, the experienced bricklayer takes 3 hours and apprentice take 6 hours to complete the job. So the experienced bricklayer completes 1/3rd of work in an hour and her apprentice completes 1/6th of work in an hour.
Let us consider they would take x hours to complete the work together. The work done is the summation of product of time taken by each person to do the work and the rate of work done by each person.
x (1/3 + 1/6) = 1
x = 1/(1/3 + 1/6)
=18/9
=2
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What is the slope of the line that passes through the points (-4, 5) and (-7,8)?
rite your answer in simplest form.
Answer:
m= -1
Step-by-step explanation:
Line A passes through the points (-1, 5) and (3, 21). Line B passes through the points (4, -2) and (-3, 19). Find the point where line A intersects line B. A. B. C. D.
A line's angle of slope between two points is (5, -4)
How to calculated the line's Angles?A line's angle of slope between two points is given as follows:
m = y2-y1/x2 - x1
A line passing through a given point and having the following equation:
y - y₁ = m(x - x₁)
Line A:
m = -1 - 5 /3- (-1) = -6 /4 = -3/2
y - 5 = -3 / 2(x +1)
y = -3/2 (x + 1) + 5.
Line B:
m = -1-2/6-7 = -3 / -1 = 3
y - 2 = 3 (x - 7)
y = 3(x -7) + 2.
Point of intersection denotes identical x and y coordinates.
So:
3(x - 7)+ 2 = -3/2 (x + 1 ) +5
3x - 21 + 2 = -3/2x - 3/2 +5
3x - 19 = -3/2x + 7/2
6x - 38 = 3x +7
6x + 3x = 7 + 38
9x =45
x = 5
y = 3(5 - 7) + 2 = 3(-2) + 2 = -4.
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A condo is listed for $230,000. After a year, It’s marked down to $200,000. What was the percent change?
Answer:
13.0434782609%
Step-by-step explanation:
200000 - 230000
-----------
230000
x 100% = 13.0434782609% - 100 = 86.9565217
86.9565217 x 230,000 = 200,000
If 1000K is 5T How many K's do i need for 4200 T's
Answer:
840000 K's
Step-by-step explanation:
Since 5T = 1000K then T = 1000K/5 which is T = 200K. Multiply both sides by 4200 so you can find how many K's needed for 4200T's.
[tex]\displaystyle{4200T=200K\cdot 4200}\\\\\displaystyle{4200T=200K\cdot 4200}\\\\\displaystyle{4200T=840000K}[/tex]
Therefore, you need 840000 K's for 4200T's.
Answer:
840 000 K
Step-by-step explanation:
5 T = 1000k
4200 T = ? K
⇒4200 × 1000 ÷ 5
⇒840 000 K answer.
hope that helps...