Which answer represents the domain of the logarithmic function given below?F(x) = log7 xA.x 0B.x < 0C.x > 0D.All real numbers
Answers
ANSWER
C. x > 0
EXPLANATION
The argument of a logarithm must be positive - i.e. it is not defined for negative values or zero.
In this case, the argument of the logarithm is x so, the domain of this function is x > 0.
Related Questions
Find the midpoint of points A (2,4) and B(-2,9) graphically
Answers
To find the midpoint of points A and B graphically, we need to start by drawing the given points.
A(2,4) and B(-2,9).
The graph looks like this:
To find the coordinates of the midpoint, add the x-coordinates and divide by 2, and do the same for the y-coordinates, then:
[tex]\text{Midpoint: (}\frac{2+(-2)}{2},\frac{4+9}{2})=(\frac{0}{2},\frac{13}{2})=(0,6.5)[/tex]Thus, the midpoint is at (0,6.5). In the graph it is at:
What is the value of 1 unit as a fraction?
Answers
The Solution:
From the given information in the picture.
Half of 10 units = 5 units
[tex]\frac{1}{2}of\text{ 10}=\frac{1}{2}\times10=5\text{ units}[/tex]We are asked to find the value of 1 unit as a fraction.
That is one unit out of ten units.
[tex]1\text{ unit =}\frac{1}{10}[/tex]Thus, the correct answer is
[tex]\frac{1}{10}[/tex]play adult dosage of a medication is 15 mg per day what is the Pediatric dosage of that same medication for a child weighing 52 lb
Answers
If the child is given 15 mg of medicine and weights 52 pounds, we can calculate the pediatric dosage as:
[tex]d=\frac{15mg}{52lb}\approx0.288\text{ mg/lb}[/tex]Answer: 0.288 mg/lb
3. Jada's sister earns a commission. She makes 3.5% of the amount she sells. Last week, she sold $7,000 worth of furtniture. How much was her commission? (don't forget the $)
Answers
The commission made was $245 from the sales
Here, we want to get the value of the commission made
From the question, we are told that the commission is 3.5% of the amount sold
We have this as;
[tex]\frac{3.5}{100}\times\text{ 7000 = \$245}[/tex]using the tables above, identify the point of intersection for the system.One point of intersection is?The other point of intersection is?
Answers
Remember that
a point of intersection is an ordered point where the value of x and the value of y is the same in both equations of the system
so
One point of intersection is (-3,4)
and
the other point of intersection is (0,1)
I need help this question and I need the answer asap please
Answers
Answer:
what is the question?
Step-by-step explanation:
what is the question?
THE HYPOTHESIS RED AND THE CONCLUSIONIf the weather is cold and wet, then the season is winter.
Answers
In this problem
The Hypothesis is: The weather is cold and wet
The conclution: The season is winter
For the polynomial function below: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of |x|
Answers
ANSWER
[tex]\begin{gathered} x\text{ = 0 (multiplicity of 2)} \\ x\text{ = }\sqrt[]{7}\text{ (multiplicity of 1)} \\ x\text{ = - }\sqrt[]{7}\text{ (multiplicity of 1)} \end{gathered}[/tex]
EXPLANATION
[tex]\begin{gathered} f(x)=-7x^2(x^2-7) \\ \text{set }-7x^2(x^2-7)\text{ = 0} \\ x^2\text{ = 0} \\ x\text{ = +-}\sqrt[]{0} \\ x\text{ = 0}\ldots\ldots..\ldots..\ldots\ldots.(1) \\ x^2\text{ - 7 = 0} \\ x^2\text{ = 7} \\ x\text{ = +-}\sqrt[]{7} \\ x\text{ = }\sqrt[]{7}\text{ or x = -}\sqrt[]{7}\ldots\ldots\ldots....\ldots\ldots\text{....}\mathrm{}.(2) \end{gathered}[/tex]The final solution is all the values that make -7x^2(x^2 -7) = 0 true.
while the multiplicity of a root is the number of times the root appears.
for the multiplicity:
[tex]\begin{gathered} x\text{ = 0 (multiplicity of 2)} \\ x\text{ = }\sqrt[]{7}\text{ (multiplicity of 1)} \\ x\text{ = - }\sqrt[]{7}\text{ (multiplicity of 1)} \end{gathered}[/tex]Law of Sines; B ≈ 42.7°, C ≈ 102.3°, c ≈ 18.7Law of Sines; B ≈ 102.3°, C ≈ 42.7°, c ≈ 18.7Law of Cosines; B ≈ 106.2°, C ≈ 38.8°, c ≈ 18.7Law of Cosines; B ≈ 38.8°, C ≈ 106.2°, c ≈ 18.7
Answers
The sine rule is used when we are given either
a) two angles and one side, or
b) two sides and a non-included angle.
The cosine rule is used when we are given either
a) three sides or
b) two sides and the included angle.
For the given problem, we are given a non-included angle and two sides. Hence, we have to solve the problem using the law of sines.
The sine rule states that:
[tex]\frac{\sin\text{ A}}{a}\text{ =}\frac{\sin\text{ B}}{b}\text{ }[/tex]We have:
A = 35 degrees, b = 13, a = 11
Substituting we have:
[tex]\begin{gathered} \frac{\sin35^0}{11}=\text{ }\frac{\sin \text{ B}}{13} \\ \text{Cross}-\text{Multiply} \\ \sin \text{ B }\times11=sin35^0\times13 \end{gathered}[/tex]Divide both sides by 11 and solving for B:
[tex]\begin{gathered} \sin \text{ B = }\frac{\sin \text{ 35 }\times13}{11} \\ \sin \text{ B = 0.677863} \\ B\text{ = 42.68} \\ \approx\text{ 42.7} \end{gathered}[/tex]Using the property of triangles, we can find the angle C:
[tex]\begin{gathered} \angle\text{ A + }\angle\text{ B + }\angle\text{ C =180 (sum of angles in a triangle)} \\ \angle\text{ C = 180 - 42.7 - 35} \\ \angle C\text{=1}02.3 \end{gathered}[/tex]Using the sine rule, we can solve for the unknown side c. We have:
[tex]\begin{gathered} \frac{\sin\text{ C}}{c}=\text{ }\frac{\sin \text{ B}}{b} \\ \frac{\sin\text{ 102.3}}{c}=\text{ }\frac{\sin \text{ 42.7}}{13} \\ \text{Cross}-\text{Multiply} \\ c\text{ }\times\text{ sin 42.7 = sin 102.3 }\times\text{ 13} \\ c\text{ = }\frac{\sin \text{ 102.3 }\times13}{\sin \text{ 42.7}} \\ c\text{ = 18.7295} \\ c\text{ }\approx\text{ 18.7} \end{gathered}[/tex]Answer summary
Law of Sines; B ≈ 42.7°, C ≈ 102.3°, c ≈ 18.7
Passes through (-1,-1), slope-2
Answers
1) Since we need a Linear function that passes through point (-1,-1) with a slope of -2
Let's use the slope-intercept formula y=mx+b an plug the slope and point (-1,-1)
to find the linear coefficient (b)
y =mx +b
-1=-2(-1) +b
-1=2+b
-1-2=b
b=-3
2) Therefore we can write our function as
y= -2x -3
please help me ASAP!!!
Answers
for being an exponential decay b must be less than 1 so in this case the aswer are:
[tex]\sqrt[]{0.9}\text{ and }2^{-1}[/tex]hi, can you help me answer this question, please, thank you:)
Answers
If the number of tablets in a shipment is sufficiently large, we can consider the testing procedure you describe (selecting a random sample of 21 ibuprofen tablets and counting the number of defective tablets in the sample) to be a binomial probability experiment.
Let X = (Number of defective ibuprofen tablets in a random sample of 21 tablets.) Then we may reasonably assume that X follows a binomial distribution. For each "trial" (that is, each tablet selected), there are two possible outcomes, "success" (the tablet is defective), or "failure" (the tablet is not defective).
Note that the word success as used in the binomial distribution does not carry the connotation of being a "good" outcome. A "success" is simply the outcome you are interested in counting, which in this case is the number of defectives in the sample.
The important parameters for a binomial distribution are n (the number of trials) and p (the probability of success on any one trial.)
For this situation, we have p= 0.01 (since we are told 1% of the tablets in the shipment are defective) and n = 21.
The general formula for the binomial distribution is
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]Where x is the number of successes in n trials (In this problem, x is the number of defectives in a random sample of 21 tablets.)
The symbol nCx is the "number of combinations of n things taken x at a time". This is the number ways of choosing x distinct objects from a set of n objects, without regard to order.
It is given by
[tex]^nC_x=\frac{n!}{x!(n-x)!}[/tex]where ! is the factorial symbol.
We want to find the probability that the shipment is accepted. We are told that a shipment will be accepted if at most one tablet doesn't meet the required specifications. That is, the number of defectives must be less than or equal to one.
P(Shipment accepted) = P(x ≤ 1). (In this case, x ≤ 1 if and only if x=0 or x=1) =P(0) + P(1)
So we calculate P(0) (the probability of 0 defective tablets in the shipment),
and P(1) (the probability of 1 defective.)
Using the formula for the binomial distribution, we have
[tex]\begin{gathered} P(0)=^{21}C_0(0.01)^0(1-0.01)^{21-0} \\ P(0)=\frac{21!}{0!(21-0)!}\times1\times0.99^{21} \end{gathered}[/tex][tex]\begin{gathered} P(0)=\frac{21!}{1\times21!}\times1\times0.809728 \\ P(0)=1\times1\times0.809728 \\ P(0)=0.809728 \end{gathered}[/tex][tex]\begin{gathered} P(1)=^{21}C_1(0.01)^1(1-0.01)^{21-1} \\ P(1)=\frac{21!}{1!(21-1)!}\times0.01\times0.99^{20} \end{gathered}[/tex][tex]\begin{gathered} P(1)=\frac{21!}{1\times20!}\times0.01\times0.817907 \\ P(1)=\frac{21\times20!}{20!}\times0.01\times0.817907 \\ P(1)=21\times0.00817907 \\ P(1)=0.171760 \end{gathered}[/tex]Finally, then, we have:
P(Shipment accepted)= P(0) + P(1)
[tex]\begin{gathered} P(0,1)=0.809728+0.171760 \\ P(0,1)=0.981488 \\ P(0,1)\approx0.9815(4decimal\text{ place)} \end{gathered}[/tex]Hence, the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 1% rate of defects is 0.9815 corrected to 4 decimal places
what is 6x2/5 and 5x2/3 and 6x2/10
Answers
When multiplying fractions we need to multiply the numerator of one of the fractions by the numerator of the other and the denominator of one to the denominator of the other. This is done below.
[tex]6\cdot\frac{2}{5}=\frac{12}{5}[/tex][tex]5\cdot\frac{2}{3}=\frac{10}{3}[/tex][tex]6\cdot\frac{2}{10}=\frac{12}{10}=\frac{6}{5}[/tex]I’m trying to figure out this compare functions to pass summerschool I just can’t get it
Answers
Answer:
B. The y-intercept of item I is less than the y-intercept of item II.
Explanation:
The y-intercept of a function is the value of y when x = 0.
In item I, from the pair (0,3), the y-intercept of item I = 3.
In Item II:
[tex]\begin{gathered} y=5x+9 \\ \text{ When x=0} \\ y=9 \end{gathered}[/tex]The y-intercept of item II is 9.
Thus, the y-intercept of item I is less than the y-intercept of item II.
Option B is correct.
The kitchen has 5 pots, 4 pans and 2 baking sheets. write the ratio of baking sheets to pots. show all three forms of ratio
Answers
SOLUTION
From the question, the kitchen has 5 pots, 4 pans and 2 baking sheets.
This means the ratios of pots to pans to baking sheets is
[tex]\begin{gathered} 5\text{ pots : 4 pans : 2 baking sheets } \\ =5:4:2 \end{gathered}[/tex]Ratio of baking sheets to
a.The amount of money invested in a retirement fund is an example of which of the followinginvestment assetb. liquid assetC. long term assetd. use asset
Answers
Answer:
It is an investment asset.
Step-by-step explanation:
It is an investment asset.
An investment asset are itens, tangible or intangible, that are used to produce additional income, or held based on speculation. Examples are mutual funds, stocks or retirement funds.
May I please get help with the graphing and figuring out weather it is a triangle, trapezoid, square, or if it is none of them.
Answers
We need to graph each point and then we connect them
As we can see we have a trapezoid
Luis exercises by running 5km. each day. The course he runs is ¼ km. long. How many times does he run the course each day?
Answers
Given:
it is given that Luis exercises by running 5 km each day. and course he runs is 1/4 km long.
Find:
we have to find that how many times he runs the course each day.
Explanation:
The number of time Luis runs the course each day is = Total distance run/ length of the course
i.e.
[tex]\frac{5}{\frac{1}{4}}=5\times4=20\text{ times}[/tex]Therefore, Luis runs the course 20 times each day.
How is 3 2/5 expressed as a percent?
Answers
First, express as a simple fraction:
3 2/5 = (3x5+2) /5 = 17/5
then, multiply by 20 both numerator and denominator
17x20 / 5x 20 = 340/100
multiply by 100
340/100 x 100 = 340%
Joanna is wrapping a present in the box shown. Find the amount of wrapping paper in square inches that Joanna needs, not counting overlap.
Answers
Recall
[tex]1\text{ foot = 12inches}[/tex]Given parameters
Length =12inches
Breadth = 8inches
Height =6 inches
Step 1
Formula
The total surface area of a cuboid
[tex]\text{The total surface area }of\text{ a cuboid =2(lb+bh+hl)}[/tex]Step 2
Substitute the given parameters
[tex]\begin{gathered} \text{The total surface area }of\text{ a cuboid =2((}12\times8)\text{+(8}\times6)\text{+(6}\times12)\text{)} \\ \text{The total surface area }of\text{ a cuboid =2((96})\text{+(48})\text{+(72})\text{)} \\ \text{The total surface area }of\text{ a cuboid =2(216)} \\ \text{The total surface area }of\text{ a cuboid =}432in^2 \end{gathered}[/tex]The final answer
The amount of wrapping paper that Joanna needs is 432 square inches
if the point is on the unit circle what is X
Answers
The question can be represented by:
where
[tex]y=\frac{\sqrt[]{3}}{2}[/tex]Note that the Hypotenuse is 1 because a unit circle has a radius of 1.
Considering the triangle from the diagram above, we can find x using the Pythagorean Theorem:
[tex]\begin{gathered} 1^2=x^2+y^2 \\ 1=x^2+(\frac{\sqrt[]{3}}{2})^2 \\ 1=x^2+\frac{3}{4} \end{gathered}[/tex]Solving for x, we have
[tex]\begin{gathered} x^2=1-\frac{3}{4} \\ x^2=\frac{1}{4} \\ x=\sqrt[]{\frac{1}{4}} \\ x=\frac{1}{2} \end{gathered}[/tex]The value of x is 1/2.
Rewrite the expressionas asingle rational number,480 + (-2215)
Answers
We will investigate how to evaluate percentages in decimal as a fraction.
We are to find the following:
[tex]22\text{\% of 300}[/tex]We will first convert the percentage in the decimal form then multiply the second number:
[tex]\frac{22}{100}\cdot300[/tex]We will simplify the reslult of dividing 300 by 100. We are left with:
[tex]\begin{gathered} 22\cdot3 \\ 66\ldots\text{ Answer} \end{gathered}[/tex]What’s is the the meaning of the y-value on the line when x=1 ?
Answers
So,
Since the graph is a prediction, we can say that the meaning of the y-value on the line when x=1 means a prediction of a student's quiz score if they spent 1 hour on they homework.
The students in class are building a rectangular float for a homecoming parade. The float will be 6 feet wide by 10 feet long. The students made a scale drawing of the float that is 14 inches long. What is the approximate width of the scale drawing of the float?
Answers
The scale drawing of the float is shown to be 14 inches long. The actual float has its length as 10 feet long. That means the scale used is;
[tex]\begin{gathered} \text{Scale}=\frac{14}{120} \\ \text{Note that 10 f}eet\text{ equals (10 x 12) 120 inches } \\ \text{Scale}=\frac{7}{60} \\ \text{For the width of the scale drawing, we use the scale as follows;} \\ \text{Scale}=\frac{7}{60}\times\text{actual} \\ \text{Scale}=\frac{7}{60}\times72 \\ \text{Scale}=\frac{7}{5}\times6 \\ \text{Scale =}\frac{42}{5} \\ \text{The width of the scale drawing is 8}\frac{2}{5} \\ \text{The approx}imate\text{ width therefore is 8 inches} \\ \text{This is because }\frac{2}{5}\text{ or 0.4 cannot be approx}imated\text{ to a whole number} \end{gathered}[/tex]Use transformations of the graph of f(x)=x^2 to determine the graph of the given function. h(x)= -(x+4)^2
Answers
Given:
[tex]f(x)=x^2[/tex]To determine the graph of the given function f(x) using transformations:
[tex]h(x)=-(x+4)^2[/tex]Since the function f(x) is an upward parabola, the function h(x) is in negative so the function h(x) is drawn a downward parabola.
Also the graph h(x) is shifted 4 units to the left since the graph is adjusted +4 units.
The graph of f(x) is drawn as:
Now, this graph is shifted 4 units to the left and drawn taking reflection along x-axis and is drawn a downward parabola, that is,
This is the graph of h(x) .
the greatest common factor of 28x²y and34x³y.
Answers
Given:
[tex]28x^2y\text{ and 34x}^3y[/tex]Find : the greatest common factor
Explanation: The greatest common factor of 28 and 34 is 2.
the greatest common factor
[tex]x^2y\text{ and x}^3y[/tex]is
[tex]x^2y[/tex]hence the greatest common factor of
[tex]28x^2y\text{ and 34x}^3y\text{ }[/tex]is
[tex]2x^2y[/tex]Henry stores the arrowheads he has found in a box the shape of a rectangular prism. The box is 14 inches long, 12 inches wide and 2 inches high. He plans to paint the exterior of the box. How many square inches does he have to paint? 2 in. 14 in. 12 in.
Answers
Side areas
The box in the image has six sides, each one consisting of rectangles
Note the sides come in pairs of equal areas
For example, the front and the back sides have the same dimensions, thus their areas are equal. Let's calculate them
Area of front side = 12 in * 2 in = 24 square inches
The sum of the front and back areas is:
2 * 24 = 48 square inches
Now for the lateral sides. Again, we have two similar shapes with identical areas:
Area of one lateral side = 14 in * 2 in = 28 square inches
Area of both lateral sides = 2 * 28 = 56 square inches
Finally, the top and bottom areas are equal:
Area of top side = 12 in * 14 in = 168 square inches
Area of top and bottom sides = 2* 168 = 336 square inches
The total area is
48 + 56 + 336 = 440 square inches
Henry has to paint 440 square inches
list the 6 exponent rules with names and formulas
Answers
To list the 6 exponent rules with names and formulas.
Explanation:
The 6 exponent rules are,
1) Product with the same bases
[tex]a^m\times a^n=a^{m+n}[/tex]2) Quotient with same bases,
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]3) Power raised to a power.
[tex](a^m)^n=a^{mn}[/tex]4) Product to a power.
[tex]a^nb^n=(ab)^n[/tex]5) Quotient to a power
[tex]\frac{a^n}{b^n}=(\frac{a}{b})^n[/tex]6) Zero power
[tex]a^0=1[/tex]Use parallelogram to find
Answers
Take into account that the measure of the angle XYZ is the same that angle ZWY:
m∠XYZ = M∠ZWY = 105°
next, consider the sum of the interior angles of the parallelogram is 360°, moreover, angle WZY and angle WXY are congruent.
Then, you have:
2m∠XYZ + 2m∠WZY = 360°
solve the previous equation for m∠WZY:
2m∠WZY = 360 - 2m∠XYZ
2m∠WZY = 360 - 2(105)
2m∠WZY = 360 - 210
2m∠WZY = 150
m∠WZY = 150/2
m∠WZY = 75
Hence, the measure of the angle WZY is 75°
the smallest female spider measures about 3/5 millimeter in lenght.The smallest male spider measures about 1/5 millimeter in lenght. How much longer,n, is the smallest female spider than the smallest male spider
Answers
Female spider length = 3/5 mm
Male spider length = 1/5 mm
Get the difference between the lengths of female and male spider :
[tex]\frac{3}{5}-\frac{1}{5}=\frac{2}{5}[/tex]Therefore, the female spider is longer by 2/5 mm than the male spider.