For this case we must find an expression equivalent to:
[tex]log_ {5} (\frac {x} {4}) ^ 2[/tex]
So:
We expanded [tex]log_ {5} ((\frac {x} {4}) ^ 2)[/tex]by moving 2 out of the logarithm:
[tex]2log_ {5} (\frac {x} {4})[/tex]
By definition of logarithm properties we have to:
The logarithm of a product is equal to the sum of the logarithms of each factor:
[tex]log (xy) = log (x) + log (y)[/tex]
The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.
[tex]log (\frac {x} {y}) = log (x) -log (y)[/tex]
Then, rewriting the expression:
[tex]2 (log_ {5} (x) -log_ {5} (4))[/tex]
We apply distributive property:
[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]
Answer:
An equivalent expression is:
[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]
Answer: the answer is c
Step-by-step explanation: 2log5x-2log54
Write the equation in standard form of the circle whose center is at (0, 0) and that is tangent to x + y = 6
Answer:
[tex]x^2 + y^2 =18[/tex]
Step-by-step explanation:
The standard equation of a circumference has the following formula.
[tex](x-h) ^ 2 + (y-k) ^ 2 = r ^ 2[/tex]
Where the point (h, k) is the center of the circle and r is the radius.
If in this case we know that the circle has center at point (0,0), then its equation will have the following form
[tex]x ^ 2 + y ^ 2 = r ^ 2[/tex]
The radius of the circumference will be the distance from the center of the circumference to the point where the circumference is tangent to the line [tex]Ax + Bx + C = 0[/tex]
The radio is:
[tex]r=\frac{|Ah + Bk +C|}{\sqrt{A^2+B^2}}[/tex]
In this case, the line is
[tex]x + y = 6[/tex]
And the center of the circumference is (0, 0)
So
[tex]A = 1\\B = 1\\C = -6\\h = 0\\k = 0[/tex]
The radio is:
[tex]r=\frac{|1*0 + 1*0 -6|}{\sqrt{1^2+1^2}}\\\\r=\frac{|-6|}{\sqrt{1^2+1^2}}\\\\r=\frac{6}{\sqrt{2}}[/tex]
Finally the equation of the circumference is:
[tex]x^2 + y^2 =(\frac{6}{\sqrt{2}})^2\\\\x^2 + y^2 =18[/tex]
Final answer:
The standard form equation of the circle centered at (0, 0) and tangent to the line x + y = 6 is x² + y² = 18, after determining the radius using the distance formula.
Explanation:
The question asks for the standard form equation of a circle centered at (0, 0) that is tangent to the line x + y = 6. To find the standard form of the circle, we first need to determine the radius of the circle, which is equal to the distance from the center of the circle to the tangent line. Since the center of the circle is at the origin (0,0), we can use the distance formula for a point to a line:
d = |Ax + By + C| / √(A² + B²), where A, B, and C are the coefficients from the line equation Ax + By + C = 0.
In this case, the line x + y = 6 can be rewritten as x + y - 6 = 0 (A = 1, B = 1, C = -6). Plugging these into the distance formula we get:
d = |1 · 0 + 1 · 0 - 6| / √(1² + 1²) = 6 / √2 which simplifies to √18.
The standard form equation of a circle with center at (h, k) and radius r is (x - h)² + (y - k)² = r². With a center at (0, 0) and a radius of √18, the equation becomes:
x² + y² = 18.
This is the standard form equation of the circle which is tangent to the line x + y = 6 at one point.
i need help please ill give 20 points
If this helps you please mark brainliest. As it helps me out.
Output = Input - 2
Input = Output + 2
So
-3 - 2 = -5
And
-1 - 2 = -3
And
0 - 2 = -2
Hope this helps!
What's the area of this rectangle?
The area of this rectangle is 18 square units. What is the unit of measurement?
Answer:
Step-by-step explanation:so first you need to find the sides 6*3 so it is 24
Five years after jari's age now doubles, he will be 27. How old is jari now
Answer:
8 or 8.5
Step-by-step explanation:
27 divided by 2 = 13.5
13.5 take away 5 = 8.5
The age of Jari now if the age after 5 years doubles is 11.
Given that:
Five years after jari's age now doubles, he will be 27.
Let x be the age of Jari now.
An equation can be formed with the given information.
When the age doubles, the age is 2x.
Five years after this age can be written as 2x + 5.
Now, it is given that this age is 27.
So,
2x + 5 = 27
Subtract both sides by 5.
2x = 27 - 5
2x = 22
Divide both sides by 2.
x = 22/2 = 11
Hence Jari is now 11 years old.
Learn more about Equations here :
https://brainly.com/question/30940948
#SPJ2
I WILL MARK BRAINIEST IF CORRECT!
Answer:
I believe I would be the last one D
Answer:
Last choice
Step-by-step explanation:
He spins the spinner and can get Red, White, or Blue.
For each of those three outcomes, the coin can land on Heads or Tails.
The sample space has the following 6 possible outcomes.
Red, Heads
Red, Tails
White, Heads
White, Tails
Blue, Heads
Blue, Tails
The answer is the last choice.
Please HELP !!
Each granola bar costs $1 write an expression that shows the total costs of the granola bars using the variable J
Answer:
Expression for the total cost is $1J.
Step-by-step explanation:
Given that each granola bar costs $1.
Now we need to write an expression that shows the total costs of the granola bars using the variable J.
So let's assume that the number of granola bars = J
then total cost of g granola bars = (J)($1) = $1J
Hence required expression for the total cost is 1J dollars.
9x^2-4=0 find two real solutions
Answer:
The two real solutions are [tex]x=\frac{12}{18} = 0.6667[/tex] and [tex]x=-\frac{12}{18} =-0.6667[/tex]
Step-by-step explanation:
The equation [tex]9x^{2} -4=0[/tex] is a quadratic function of the form [tex]ax^{2} +bx+c=0[/tex] that can be solved by using the Quadratic Formula.
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
The plus and minus mean that the equation has two solution.
In order to identify is the equation has two real solutions we use the discriminant equation [tex]b^{2} -4ac[/tex]. Depending of the result we got:
1. If the discriminant is positive, we get two real solutions.
2. if the discriminant is negative, we get complex solutions.
3. If the discriminant is zero, we get just one solution.
Solution:
The equation [tex]9x^{2} -4=0[/tex] has a=9, b=0, and c=-4
Using the discriminant equation to know if the quadratic equation has two real solutions:
[tex]b^{2} -4ac[/tex]
[tex]0^{2} -4(9)(-4)=144[/tex] The discriminant is positive which mean we get two real solutions.
Using the Quadratic Formula
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
[tex]x=\frac{-0±\sqrt{0^{2} -4(9)(-4)} }{2(9)}[/tex]
[tex]x=\frac{±\sqrt{144} }{18}[/tex]
[tex]x=±\frac{12}{18}[/tex]
then
[tex]x=\frac{12}{18} = 0.6667[/tex] and [tex]x=-\frac{12}{18} =-0.6667[/tex]
To solve the equation 9x^2-4=0, we simplify and take the square root of both sides, resulting in two real solutions: x = 2/3 and x = -2/3.
To find two real solutions to the equation 9x^2-4=0, we can approach this by simplifying it into a form that can use the square root method for solving. Here are the steps:
Add 4 to both sides of the equation: 9x^2 = 4.Divide both sides by 9: x^2 = 4/9.Take the square root of both sides: x = ±2√(4/9).Simplify the square root: x = ±2/3.Therefore, the two real solutions are x = 2/3 and x = -2/3.
A rectangle container that has a length of 25cm,a width of 37cm, and a height of 21cm a is filled with water to a depth of 18 cm. When an additional 7 liters of water are poured into the container, some water overflows.How many liters water overflows the container?use words,pictures,and numbers to explain your answer.(Remember:_1cm3=1 mL.)
Answer:
4.225 L
Step-by-step explanation:
The box has a height of 21 cm. After the box is filled to 18 cm, there's 3 cm left of space. The volume of this space is:
V = lwh
V = (25 cm) (37 cm) (3 cm)
V = 2775 cm³
1 cm³ is the same as 1 mL, so the volume of the space is 2775 mL.
1 L is 1000 mL, so this volume is 2.775 L.
7 L of water is then poured in. The box can hold 2.775 L. The rest overflows. The overflow volume is:
7 L - 2.775 L = 4.225 L
Final answer:
The volume of water that overflows from the container after pouring an additional 7 liters is 4,225 mL or 4.225 liters.
Explanation:
The question involves calculating the volume of water that overflows from a rectangular container when additional water is poured in. The existing water depth, dimensions of the container, and the volume of the additional water are given. We know that 1 cm³ of water is equivalent to 1 mL, and there are 1000 mL in 1L.
The initial water volume in the container is the product of the length, width, and depth filled with water. Thus, the initial volume is:
25 cm (length) × 37 cm (width) × 18 cm (depth) = 16,650 cm³ (or mL)
When an additional 7 liters (which is 7,000 mL) of water is added to the container, the total volume of water becomes:
16,650 mL + 7,000 mL = 23,650 mL.The full capacity of the container is calculated by multiplying its length, width, and height:
25 cm × 37 cm × 21 cm = 19,425 cm³ (or mL).By subtracting the full capacity from the total volume after pouring:
23,650 mL - 19,425 mL = 4,225 mL (or 4.225 liters)We find that 4,225 mL (or 4.225 liters) of water overflows.
It is hard to calculate the volume of a mountain but several estimates put the volume of Mount Everest at around 2,413 cubic kilometers. The Dallas Cowboys Stadium (currently the largest football stadium in the U.S.) has a volume of 140 million cubic feet. How many Cowboy stadiums could fit inside of Mount Everest?
Estimate an answer to this question and explain your estimation process. Be sure to state what facts or ideas you used to help.
Answer:
About 609,000 Cowboy stadiums could fit inside of Mount Everest
Step-by-step explanation:
we have
The estimate volume of Mount Everest is at around [tex]2,413\ km^{3}[/tex]
The Dallas Cowboys Stadium has a volume of [tex]140,000,000\ ft^{3}[/tex]
step 1
Convert ft³ to km³
we know that
1 km=3,280.84 ft
so
[tex]140,000,000\ ft^{3}=140,000,000*(1/3,280.84)^{3}=0.003964\ km^{3}[/tex]
step 2
To find how many Cowboy stadiums could fit inside of Mount Everest, divide the volume of Mount Everest by the volume of the Dallas Cowboys Stadium
[tex]2,413/0.003964=608,729[/tex]
Round to the nearest Thousands
[tex]608,729=609,000[/tex]
The volume of Mount Everest is about 609,000 times greater than the volume of the Dallas Cowboys Stadium
To estimate how many Dallas Cowboys stadiums could fit inside Mount Everest, we converted the volume of the stadium to cubic kilometers and then divided Mount Everest's volume by this number, resulting in approximately 608,845 stadiums.
Explanation:Calculating the Volume of Mount Everest Compared to the Dallas Cowboys Stadium
To estimate how many Dallas Cowboys stadiums could fit inside of Mount Everest, we need to convert the volume of both structures to the same units and then perform a division.
We have the volume of Mount Everest as approximately 2,413 cubic kilometers. To convert the volume of the Dallas Cowboys Stadium from cubic feet to cubic kilometers, we use the conversion factor of 1 cubic kilometer equals 35.3147 million cubic feet:
Cowboys Stadium volume in cubic kilometers = 140 million cubic feet × (1 cubic kilometer / 35.3147 million cubic feet) = 3.9642 × 10-3 cubic kilometers.
Now, we can find how many Cowboys stadiums fit into Mount Everest:
Mount Everest volume / Cowboys Stadium volume = 2,413 cubic kilometers / 3.9642 × 10-3 cubic kilometers ≈ 608,845.
Therefore, approximately 608,845 Dallas Cowboys stadiums could fit inside of Mount Everest's volume.
Ms. Redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented. The next student presents a monologue that is about 0.5 minutes long. What effect will this have on the graph? The median will decrease. The mean will decrease. The median will increase. The mean will increase.
Answer:the awnser is:B the mean will decrease
Step-by-step explanation:
The effect it would have on the dot plot graph is that: B. The mean will decrease.
What is the Mean of a Dot Plot?The mean of a dot plot is found by simply adding up all data points on the dot plot and divide by the number of data points we have on the dot plot.
Mean of the first 10 monologues = (1.5 + 1.5 + 2 + 2.5 + 2.5 + 2.5 + 3 + 3.5 + 3.5 + 4)/10 = 2.65
Mean of the first 10 monologues + 0.5 minutes = (1.5 + 1.5 + 2 + 2.5 + 2.5 + 2.5 + 3 + 3.5 + 3.5 + 4 + 0.5)/11 = 2.45
Therefore, the effect it would have on the dot plot graph is that: B. The mean will decrease.
Learn more about the mean on:
https://brainly.com/question/11015069
Can someone please help me out
Answer:
5/2 or 5:2
Step-by-step explanation:
Answer:
6*5=30 to 2*6=12
Step-by-step explanation:
6:5 and 2:6 for smaller hexagon
(X-2) is a factor of x^4+2x^3-7x^2-8x+12. The other factors are ____, ____, and _____
We have
[tex]\dfrac{x^4+2x^3-7x^2-8x+12}{x-2}=x^3+4x^2+x-6[/tex]
The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that [tex]x=-2[/tex] is a root, since [tex](-2)^3+4(-2)^2+(-2)-6=0[/tex], so [tex]x+2[/tex] is also a factor and we have
[tex]\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3[/tex]
Finally, we can factorize the remaining quotient easily:
[tex]x^2+2x-3=(x+3)(x-1)[/tex]
so the other factors are [tex]x+2[/tex], [tex]x+3[/tex], and [tex]x-1[/tex].
4. How many different bikes
5.how many different meals?
Answer:
4. 30
5. 108
Step-by-step explanation:
4. There are 2 styles, 3 sizes and 5 colors
2 * 3 * 5 = 20
There are 30 different bikes
5. There are 4 appetizers, 9 entrees, and 3 desserts
4*9*3 = 108
We can order 108 different combinations
Any and all answers get 5 stars.
Correct answers get a thanks,
Best answer gets brainliest.
Kim wants to know if the number of words on a page in her math book is generally more than the number of words on a page in her poetry book. She takes a random sample of 25 pages in each book, then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.
Book Mean Median Mean absolute deviation
Math 49.9 43 10.2
Poetry 41.5 42 1.1
Kim claims that because the mean number of words on each page in the math book is greater than the mean number of words on each page in the poetry book, the math book has more words per page. Based on the data, is this a valid inference?
A: No, because there is a lot of variability in the math book data
B: No, because the mean is larger in the math book
C: Yes, because the mean is larger in the math book
D: Yes, because there is a lot of variability in the math book data
Answer:
the answer is A I'm 80% sure
Find the Quotient: 6/ 27L 600ML
Answer:
400mL/3l
Is the correct answer
Step-by-step explanation:
To find the quotient of 6 liters by 27 liters and 600 milliliters, convert both to milliliters and divide. The quotient is approximately 0.21739.
To find the quotient of 6 liters (L) divided by 27 liters and 600 milliliters (mL), we first need to convert the amounts to the same unit. Since there are 1,000 milliliters in a liter, we can convert 27 liters into milliliters:
27 L × 1,000 mL/L = 27,000 mL
Now we add the 600 mL:
27,000 mL + 600 mL = 27,600 mL
Rewrite the problem with both measurements in milliliters:
6,000 mL / 27,600 mL
We now divide 6,000 by 27,600:
6,000 mL / 27,600 mL = 0.21739 (rounded to five decimal places)
So, the quotient is approximately 0.21739.
A cylinder has a volume of 288 pie cubic meters and a height of 9 meters. What is the area of the base?
Answer:
32 m²
Step-by-step explanation:
V(cylinder) = Area(base)*height
288 = Area(base)*9
Area(base)= 288/9=32 m²
Answer: [tex]32\pi\ m^2[/tex]
Step-by-step explanation:
We know that the volume of cylinder is given by :-
[tex]\text{Volume}=\text{Area of base * height}[/tex]
Given: The volume of cylinder = [tex]288\pi\text{ cubic meters}[/tex]
Height of the cylinder= 9 meters
[tex]\Rightarrow\ 288\pi=\text{Area of base }\times9\\\\\Rightarrow\ \text{Area of base }=\dfrac{288\pi}{9}=32\pi[/tex]
Hence, the area of the base = [tex]32\pi\ m^2[/tex]
Which has the least value 2 2/3,2.45,2 2/5
Answer:
2 2/5
Step-by-step explanation:
First, lets convert these all to decimals.
2 2/3 = 8/3 = 2.66666666.....
2.45 = 2.45
2 2/5 = 12/5 = 2.4
Thus, the smallest decimal here is 2.4, or, 2 2/5.
I hope this helps!
Answer:
the least value is 2 2/5
Step-by-step explanation:
Can somebody pls tell me which statement is true ?
Answer:
B
Step-by-step explanation:
Since the probability of an animal being blue isn't affected by the animal having two heads, the two events are independent.
Please help me with these !!!! asapppp!!!! they all go from 0-9 on the drop downs
Answer:
6x + 1
3x + 3
6x + 9
Step-by-step explanation:
1)
To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are different, then the equation has no solutions.
2x + 9 + 3x + x = _x +_
6x + 9 = _x + _
6x + 9 = 6x + 1
2)
To find the missing number, compare both sides of the equation. If the variable terms are the different and the constant terms are either different or same, then the equation has one solution.
2x + 9 + 3x + x = _x + _
6x + 9 = _x + _
6x + 9 = 3x + 3
3)
When equation is true for every possible value of x.
To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are same, then the equation has no solutions.
2x + 9 + 3x + x = _x + _
6x + 9 = _x + _
6x + 9 = 6x + 9
6x = 6x +9 -9
6x = 6x
6x/6 = x
x = x
5. Solve (2x - 1)2 = 8 using the quadratic formula.
The solution to the equation by using quadratic formula is [tex]x = \dfrac{1 + 2\sqrt{2}}{2} \ or \ \dfrac{1 - 2\sqrt{2}}{2}[/tex]
Solving quadratic equation using formula.
Quadratic equation can be solved by using the quadratic formula [tex]x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
The given equation (2x - 1)² = 8 can be written as 4x² - 4x - 7 = 0. where:
a = 4b = -4c = -7Replacing the values into the quadratic formula, we have:
[tex]x = \dfrac{-(-4) \pm \sqrt{(-4)^2 -4(4)(-7)}}{2(4)}[/tex]
[tex]x = \dfrac{4 \pm \sqrt{16 + 112}}{8}[/tex]
[tex]x = \dfrac{4 \pm \sqrt{128}}{8}[/tex]
[tex]x = \dfrac{4 \pm 8\sqrt{2}}{8}[/tex]
Divide the right hand side by 4;
[tex]x = \dfrac{1 \pm 2\sqrt{2}}{2}[/tex]
[tex]x = \dfrac{1 + 2\sqrt{2}}{2} \ or \ \dfrac{1 - 2\sqrt{2}}{2}[/tex]
If the scale on a map is 1 cm for every 117 km and Washington, D.C., and Baghdad, Iraq, are 85.26 cm apart on the map, then approximately how far apart are they really?
If 1 cm represents 117 Km.
Then, 85.26 cm represents 117×85.26=9975.42 Km
therefore, the given places are 9975.42 Km apart from eachother.
The distance between Washington, D.C., and Baghdad, Iraq, are approximately 9,764.82 km apart in real life.
What is the scale factor?The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.
We are given that;
11cm=117km
Distance of baghdad and iraq= 85.26cm
Now,
If the scale on a map is 1 cm for every 117 km and Washington, D.C., and Baghdad, Iraq, are 85.26 cm apart on the map, then we can use the scale to find the actual distance between the two cities.
We can set up a proportion to solve for the actual distance:
1 cm / 117 km = 85.26 cm / x
To solve for x, we can cross-multiply:
1 * x = 117 * 85.26
x = 9,764.82 km
Therefore, by the scale factor the answer will be 9,764.82 km.
Learn more about scale factor here:
https://brainly.com/question/11178083
#SPJ3
Claudine traded U.S. dollars for Mexican pesos at an exchange rate of 1 U.S. dollar = 12.6577 Mexican pesos. She gave the exchanger a total of 2300 U.S. dollars and was charged a flat fee of 55 U.S. dollars. Approximately how many Mexican pesos does Claudine have?
Answer:
Step-by-step explanation:
You have to start by taking away $55 from the 2300. The 55 does not get exchanged.
2300 - 55 = 2245
1 US dollar = 12.6577 pesos
2245 US dollars = x Cross multiply
x = 12.6577 * 2245
x = 28416.54 pesos. (rounded to 2 places)
Answer:
$28,416.54 Mexican pesos
Step-by-step explanation:
That $2,300 will be divided into two parts: 1) $55 fee and 2) equivalent amount in Mexican pesos:
The amount exchanged into pesos is $2,300 - $55, or $2,245.
Converting this into pesos:
$2,245 12.6577 Mex pesos
------------ * ------------------------------- = $28,416.54 Mexican pesos
1 $1
PLEASE HELP ME WITH STUDYISLAND!!!
Answer: is A
Step-by-step explanation: so I did 1×3/12+1×4/12 (3+4)/12 =7/12
Answer:
D. 7/36 pounds
Step-by-step explanation:
Combine the two using like terms so 1/3 and 1/4 = 4/12 and 3/12 so 4+3=7 so 7/12.
Next you divide by 3. To do this, find a larger denominator with a number that can be divided by 3.
7/12 to 14/24 and 21/36. 21 can be divided by 3.
Divide 21/36 by 3 and get 7/36. This can not be simplified any further.
Therefore your answer is D. 7/36.
Hope I helped!
Evaluate the expression. Express the result in scientific notation.
(9.08 × 106) – (2.25 × 105)
To evaluate the expression (9.08 × 10⁶) - (2.25 × 10⁵), align the exponents and then subtract the base numbers, resulting in (8.855 × 10⁶) expressed in scientific notation.
To evaluate the expression (9.08 × 10⁶) - (2.25 × 10⁵) and express the result in scientific notation, we will align the exponents and then subtract the base numbers. Since the exponents are not the same, we need to adjust the smaller exponent to match the larger one.
First, we rewrite (2.25 × 10⁵) with a base of 10⁶, which becomes (0.225 × 10⁶). Now we can subtract:
(9.08 × 10⁶) - (0.225 × 10⁶) = (9.08 - 0.225) × 10⁶
Performing the subtraction, we get:
(8.855 × 10⁶)
Janelle invested $13000 into two mutual funds. Fund A earned 6% profit during the first year, well fund B suffered a 3.5% loss. If she received a total of 324$ profit, how much had she invested in each mutual fund?
Answer:
amount invested in mutual fund B; $4,800
amount invested in mutual fund A; $8,200
Step-by-step explanation:
Let the amount invested in mutual fund B be x. Then the amount invested in fund A would be;
(13000-x)
The loss emanating from fund B would be;
3.5% of x
=(3.5/100)*x
=0.035x
The profit resulting from investment in fund A would be;
6% of (13000-x)
= (6/100)*(13000-x)
=0.06(13000-x)
=780-0.06x
The total profit earned from funds A and B in terms of x will be;
780 - 0.06x + (-0.035x)
=780 - 0.095x
The total profit earned was 324, thus;
780 - 0.095x = 324
solving for x;
780 - 324 = 0.095x
456 = 0.095x
x = 4800
Then the amount invested in fund A would be;
13000 - 4800 = 8200
If f(x)= x^2-1 and g(x)=2x-3, what is the domain of (fog)(x)
Answer:
[tex]\large\boxed{\text{The domain is the set of all real numbes}\to x\in\mathbb{R}}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2-1,\ g(x)=2x-3\\\\(f\circ g)(x)-\text{instead of x in the function equation f(x) put}\ 2x-3:\\\\(f\circ g)(x)=(2x-3)^2-1\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(f\circ g)(x)=(2x)^2-2(2x)(3)+3^2-1=4x^2-12x+9-1\\\\(f\circ g)(x)=4x^2-12x+8\\\\\text{the domain is the set of all real numbes}\to x\in\mathbb{R}[/tex]
if 6 squared x =1 what is the value of x
Question: 6^x = 1 (finding x)
Answer: x = 0
Explanation: Any non-zero expression raised to the power of 0 equals 1. Since we are trying to find 1, 0 would be an appropriate vale for x.
Help me answer this question please
Answer:
The answer is C.
Step-by-step explanation:
Just go to Desmos.com and plug it in.
For this case we have:
Let k> 0:
To graph[tex]y = f (x) + k,[/tex] the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
Let h> 0:
To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.
To graph [tex]y = f (x + h),[/tex] the graph moves h units to the left.
So, we have:
[tex]y = f (x) = \sqrt [3] {x}[/tex]
Shifted 1 unit down and 4 to the left means:
[tex]k = 1\\h = 4[/tex]
[tex]y = f (x) = \sqrt [3] {x + 4} -1[/tex]
Answer:
Option D
Determine the answer to 3 + (−5) and explain the steps using a number line.
Answer:
[tex]\boxed{ -2}[/tex]
Step-by-step explanation:
On a number line
Adding a positive number means moving to the right Adding a negative number means moving to the leftUsing the number line,
Add 3 + (-5)
Step 1. Find 3 on the number line
Start at 0 and move three units to the right (see Image below).
This takes you to 3.
Step 2. Add (-5)
Start at 3 and move five units to the left.
This takes you to -2.
[tex]\boxed{\textbf{3 + (-5) = -2}}[/tex]
The value of the expression 3 + (-5) is - 2
Given the value :
3 + (-5)
From the operation rule :
+ and - = -
Hence,
3 + (-5) = 3 - 5 = - 2
Using the number line analogy :
Positive values (+) lies to the right of a number line while negative (-) are positioned on the left.
To perform 3 + (-5) using a number line ;
From +3 taking 5 points backwards to the left (-5) ; takes us to the point - 2
Hence, the value of the expression 3 + (-5) = - 2
Learn more : https://brainly.com/question/16191404
For a class picnic two teachers went to the same store to the purchase drinks. one teacher purchased 18 juice boxes and 32 bottles of water and spent $19.92. the other teacher purchased 14 juice boxes and 26 bottles of water and spent $15.76 write a system of equations to represent the costs of a juice box j and a bottle of water w.
18j + 32w = $19.92
14j + 26w = $15.76
HAVE A GREAT DAY MA DUDE!
The system of equations that represent the costs of a juice box j and a bottle of water w are :
18j + 32w = 19.92 ....(1)
14j + 26w = 15.76 ....(2)
As per the given information, Consider that the cost of a juice box be represented by j and the cost of a bottle of water be represented by w.
The teacher who purchased 18 juice boxes and 32 bottles of water spent $19.92, we can write the equation as follows:
18j + 32w = 19.92
Similarly, the other teacher who purchased 14 juice boxes and 26 bottles of water spent $15.76, we can write the equation as :
14j + 26w = 15.76
Hence, the system of equations is:
18j + 32w = 19.92 ....(1)
14j + 26w = 15.76 ....(2)
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ6