Answers
The given expression is;
[tex]6^{-10}[/tex]A)
[tex]6^{-5}\cdot6^2_{}[/tex]Since bases of both the terms are same i.e., 6
So, when multiplying two powers that have the same base, you can add the exponents.
[tex]\begin{gathered} 6^{-5}\cdot6^2_{}=6^{-5+2} \\ 6^{-5}\cdot6^2_{}=6^{-3} \\ \text{Since, 6}^{-3}\ne6^{-10} \end{gathered}[/tex]So, Option A is not the right answer;
B)
[tex](\frac{1}{6^2})^5[/tex]Apply the power rule of exponents;
[tex]\begin{gathered} (\frac{1}{6^2})^5=(6^{-2})^5^{} \\ (\frac{1}{6^2})^5=6^{-10} \\ \text{ Since, the given expression is 6}^{-10} \\ So,6^{-10}=6^{-10} \end{gathered}[/tex]Thus, Option B is the right answer
C)
[tex](6^{-5})^2[/tex]Apply the exponents rule;
[tex]\begin{gathered} (6^{-5})^2=6^{-10} \\ \text{ Since, the given expression is; 6}^{-10} \\ 6^{-10}=6^{-10} \end{gathered}[/tex]Therefore, Option C is the right answer
D)
[tex]\frac{6^5\cdot6^{-3}}{6^{-8}}[/tex]Simplify the expression;
since the bases are same so the in the multiplication the exponent value will be add up and during division, the exponent value will be subtract;
[tex]\begin{gathered} \frac{6^5\cdot6^{-3}}{6^{-8}}=\frac{6^2}{6^{-8}} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=6^{2-(-8)} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=6^{2+8} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=6^{10} \\ \text{ Since, the given expression is 6}^{-10} \\ and6^{-10}\ne6^{10} \end{gathered}[/tex]Therefore, Option D is not the right answer
E)
[tex]\frac{6^{-3}}{6^7}[/tex]Simplify the expression by using division rule of exponent;
To divide exponents (or powers) with the same base, subtract the exponents:
[tex]\begin{gathered} \frac{6^{-3}}{6^7}=6^{-3-7} \\ \frac{6^{-3}}{6^7}=6^{-10} \\ \text{ Since, the given expression is 6}^{-10} \\ 6^{-10}=6^{-10} \end{gathered}[/tex]So, option E is the correct answer
Answer : B, C,
Related Questions
Liam says – (2) is equivalent to - 2. Explain if Liam is correct by completing thestatements below.Click the arrows to choose an answer from each menu.The fraction - G) can be described as the opposite of a positive number divided by a positivenumber. A positive number divided by a positive number results in a Choose...quotient, and its opposite is always choose...The fraction - 2 can be described as a positive number divided by a negative number, whichalways results in a Choose... quotient.The fractions haveChoose...value, so LiamChoose...correct.
Answers
-(5/12) is equivalent to (5/-12).
The fraction -(5/12) can be described as the opposite of a positive number divided by a positive number. a positive number divided by a positive number results in a Positive Quotient and its opposite is always Negative.
The fraction 5/-12 can be described as a positive number divided by a negative number, which always results in a Negative quotient.
The fraction have the same value, so Liam is correct.
Write the percent as a decimal. Round to the nearest thousandth if the division does not terminate. 2/16%
Answers
Answer:
0.00125
Explanation:
We can express 2/16% as a fraction by dividing it by 100 as shown below;
[tex]\frac{\frac{2}{16}}{100}=\frac{2}{16}\times\frac{1}{100}=\frac{1}{8}\times\frac{1}{100}=\frac{1}{800}=0.00125[/tex]Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.-10-8-6-4-2246810-10-8-6-4-2246810xyEFGHE'=,F'=,G'=,H'=,SubmitQuestions
Answers
We have a quadrilateral given by the following vertices:
• E = (1, -4),
,• F = (10, -4),
,• G = (10, 0),
,• H = (1,0).
A rotation of the coordinates of the vertices in 270° counterclockwise around the origin, is equivalent to the following transformation of the coordinates:
[tex]P=(x,y)\rightarrow P^{\prime}=(y,-x).[/tex]Applying this transformation to the points above, we get:
• E' = (-4,-1),
,• F' = (-4,-10),
,• G' = (0,-10),
,• H' = (0,-1).
Answer
• E' = (-4,-1),
,• F' = (-4,-10),
,• G' = (0,-10),
,• H' = (0,-1).
Verification
Find h(3)+d(2) if h(x)= x-1 and d(x) = 7x + 3A.2 B.5 C.14 D.19
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I NEED HELP ASAP! with questions 9-18 ( Yes it might be a lot but you don't have to answer all of them! <3 ) I will give brainly, all stars, thanks, and a comment to whoever helps me the most!Question 9- Which statement best describes the expression 3 + 2 ÷ y?The quotient of y and the sum of 3 and 2The quotient of the sum of 3 and 2 and yThe sum of 3 and the quotient of 2 and yThe sum of 3 and the quotient of y and 2Question 10- If x = 2.3, 5x = ____. (Input decimals only, such as 12.7.)There no answer choicesQuestion 11-What is the value of fraction 1 over 3 x3 + 5.2y when x = 3 and y = 2?3.416.419.428.4Question 12-The expression to find the perimeter of a rectangle is 2(length + width). What is the perimeter, in units, of a rectangle of length fraction 1 over 3 unit and width fraction 1 over 2 unit?fraction 2 over 5 unitfraction 4 over 5 unitfraction 1 and 1 over 3 unitsfraction 1 and 2 over 3 unitsQuestion 13- Which of these shows 7 + 2y rewritten using the commutative property of addition?7y + 22y + 77 − 2y2y − 7Question 14-Which algebraic property is used to rewrite 2(4y + 1) as (4y + 1)(2)?Distributive propertyAssociative propertyCommutative property of multiplicationCommutative property of additionQuestion 15-The work of a student to find the dimensions of a rectangle of area 8 + 16x and width 4 is shown below:Step 1: 8 + 16xStep 2: 4(4) + 4(12x)Step 3: 4(4 + 12x)Step 4: Dimensions of the rectangle are 4 and 4 + 12xIn which step did the student first make an error and what is the correct step?Step 3; 4 + (4 + 12x)Step 3; 4 + (4 ⋅ 12x)Step 2; 4(2) + 4(4x)Step 2; 4(2) + 4x(2)Question 16-Which expression is equal to 4y?y + 3y2 + y23y + 1y + y + y + yQuestion 17- Which expressions are equivalent to 2(2x + 4y + x − 2y)?2(x + 6y) and 2x + 12y2(x + 2y) and 2x + 4y2(3x + 2y) and 6x + 4y2(3x + 6y) and 6x + 12yQuestion 18-Which expression is equivalent to 12x − 8x + 3 and why?3 + 4x, because (12x − 8x) + 3 = 4x + 3 = 3 + 4x7x, because 12x − 8x + 3 = 4x + 3 = 7x12x
Answers
Question 9
Given the expression:
[tex]3+2\div y[/tex]Following the order of operations BODMAS, we take dividion into account first:
ben is studying photography and he was asked to submit 5 photographs from his collection to exhibit at the fair. he has 13 photographs that he thinks are show worthy. in how many ways can the photographs be chosen?
Answers
Given:
The total number of photographs is, n = 13.
The number of photographs to be submitted is, r = 5.
The objective is to find the number of ways of choosing the photograph.
Explanation:
The general formula to find the number of ways is,
[tex]^nC_r=\frac{n!}{(n-r)!\times r!}[/tex]On plugging the given values in the above equation,
[tex]\begin{gathered} \frac{n!}{(n-r)!\times r!}=\frac{13!}{(13-5)!\times5!} \\ =\frac{13!}{8!\times5!} \\ =\frac{13\times12\times11\times10\times9\times8!}{8!\times5\times4\times3\times2\times1} \\ =1287 \end{gathered}[/tex]Hence, the number of ways in seleting the 5 photographs is 1287 ways.
Which graphs represent functions?w4-2Graph AуGraph Bу4-X+4X-2GraphGraph DА. Graph B and Graph DB. Graph C and Graph DC. Graph A onlyDGraph D only
Answers
For a function, there is only one value for x.
The graph of the linear function is shown on the coordinate grid. 102 What is the y intercept of the graph of the linear function?
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The y-intercept is the value of the variable y at which a function cuts the Y-axis. It is also the value of the function when x=0.
In this case, we can see that the line crosses the Y-axis at y=-3.
Therefore, the y-intercept is:
[tex]-3[/tex]need this in less than 5 minutes because it’s based on time ASAP PLEASE
Answers
We are asked to find the conditional probability that a flight arrives on time given that it departed on time.
Let event A = flight arrives on time
Let event B = flight departs on time.
We are given the following probabilities
P(A) = 0.92
P(B) = 0.87
P(A and B) = 0.84
Recall that the formula for conditional probability is given by
[tex]P(A|B)=\frac{P(A\; and\; B)}{P(B)}[/tex]Let us subs
I need help with this simple math question number 11 to 12
Answers
Notice that 8=4+4 and 4+4 is a double; therefore,
Finally, as for the last line, 7+4=11, and
The image above shows the whole solution.
which of the following is a solution to the equation
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A value of x that determines f(x)=g(x) means that for said value of x, f(x) and g(x) will have the same value. This is the point (or points, depending on the form of the functions) where both functions intercept.
Looking at the table you can see that
For x=-1
f(x)=1
g(x)=1
Is the only value of x where both functions have the same value.
plssss I need quick answers with tips I can understand
Answers
In a right traiangles, note that the longest side or the side facing the 90degrees is the hypotenuse.
Also, the side facing a given angle is the opposite
Then, the last side is adjacent.
Also, note the pythagorean theorem that;
[tex]\begin{gathered} h^2=o^2+a^2 \\ o^2=h^2-a^2 \\ a^2=h^2-o^2 \\ \text{Where h= hypotenuse} \\ a=\text{ adjacent} \\ o=\text{opposite} \end{gathered}[/tex]Also note the concept below;
[tex]\begin{gathered} \text{SOH, CAH and TOA} \\ \text{Where SOH means }\sin \theta=\frac{opposite}{hypotenuse} \\ \text{CAH means }\cos \theta=\frac{adjacent}{hypotenuse} \\ \text{TOA means }\tan \theta=\frac{opposite}{\text{adjacent}} \end{gathered}[/tex]As explained y represents the hypotenuse because it is the longest side,
x represents the opposite side because it faces the given angle,
so 13 is the adjacent.
First, using TOA concept to get x;
[tex]\begin{gathered} \text{Tan}\theta=\frac{o}{a} \\ \tan 45=\frac{x}{13} \\ x=13\tan 45 \\ x=13 \end{gathered}[/tex]On getting x=13, the pythagoream theorem can be used to get the third side called the hypotenuse.
[tex]\begin{gathered} h^2=o^2+a^2 \\ y^2=13^2+13^2 \\ y^2=169+169 \\ y^2=338 \\ y=\sqrt[]{338} \\ y=18.4 \end{gathered}[/tex]
Is this problem correct? If not how do you work it out?
Answers
We need to express this as a polynomial.
This is already expressed as a polynomial, but in a factorized form. We can express it in standard form by applying the distributive property:
[tex]\begin{gathered} (2x+6)(4x-7) \\ 2x\cdot4x+2x\cdot(-7)+6\cdot4x+6\cdot(-7) \\ 8x^2-14x+24x-42 \\ 8x^2+10x-42 \end{gathered}[/tex]Answer: 8x² + 10x - 42
3. Tom Holland who plays Spiderman has an action figure made of his character Tom'sactual height is 68 inches and his head measures 9.10 inches based on this informationset up a proportion to find the measurement of the action figure's head.15 cmThe action figure's head measures
Answers
Given:
• Tom's actual height = 68 inches
,• Tom's head measurement = 9.10 inches
,• Height of Tom's action figure = 15 cm
Let's set up a proportion to find the measurement of the action's figure head.
To find the proportion, we have:
Tom's actual height : Tom's action figure height
68 inches : 15 cm ==> 4.53 inches : 1 cm
Ther proportion of Tom's actual height to the height of Tom's action figure is:
4.53 inches : 1 cm
To find the measurement of the action figure's head, we have:
[tex]\frac{9.10\text{ inches}}{4.53\text{ inches }}=2.01[/tex]Therefore, the measurement of the action figure's head is = 2.01 cm
ANSWER:
2.01 cm
4.)If the circumference of a circle is 287 inches, then find its approximate area.
Answers
The circumference is given by:
[tex]\begin{gathered} C=2\pi r \\ so\colon \\ C=28\pi \\ 28\pi=2\pi r \\ r=\frac{28\pi}{2\pi} \\ r=14 \end{gathered}[/tex]Since we know the radius, we can find the area as follows:
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi(14)^2 \\ A=196\pi \\ A\approx615.75in^2 \end{gathered}[/tex]Answer:
615.75 in²
Select the place where the digit 2 sits in this number.428,031O A.hundred thousandsOB.onesO C.one thousandsODten thousandsE.tensOF. hundredsResetNext
Answers
Given the number 428,031, we can express this number as:
[tex]428031=400000+20000+8000+30+1[/tex]For digit 2, we have 20000, which corresponds to a multiple of ten thousand.
The line containing points E and G is a diameter. It ______ chord DF.Answer choice:A)never crossesB)intersects the endpoint ofC)runs parallel toD)bisects
Answers
Solution:
Concept:
If a diameter of a circle bisects a chord, then it must be perpendicular to the chord. If a diameter of a circle is perpendicular to a chord, then it bisects the chord. If two chords are congruent, then the center is equidistant from the two chords.
[tex]diameter=line\text{ }connecting\text{ }E\text{ }and\text{ }G[/tex]The chord given in the question is
[tex]chord=DF[/tex]Hence,
The final answer is
It BISECTS chord DF
OPTION D is the right answer
How many distinct committees of 3 people can be formed if the members are drawn from a pool of 15 people?
Answers
ANSWER
2730 groups
EXPLANATION
We want to find the number of distinct committees of 3 can be formed from a pool of 15 members.
To do this, we apply combination.
That is:
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]Therefore, we have:
[tex]\begin{gathered} ^{15}P_3=\frac{15!}{(15-3)!}=\frac{15!}{12!} \\ =\frac{15\cdot14\cdot13\cdot12!}{12!} \\ =15\cdot14\cdot13 \\ =2730\text{ groups} \end{gathered}[/tex]Use the fact that the sumof the angles in a triangle is 180 degrees for this question:Two angles of a triangle have the same measure and the third one is 36° greater thanthe measure of each of the other the. Find the measure of the 2 smaller angles and the measure of a larger angle
Answers
Information given
Use the fact that the sumo f the angles in a triangle is 180 degrees for this question:Two angles of a triangle have the same measure and the third one is 36° greater thanthe measure of each of the other the. Find the measure of the 2 smaller angles and the measure of a larger angle
Solution
Notation: Let x the measure of each of the two smaller angles
For this case we can set up the following equations:
[tex]x+x+(x+36)=180[/tex]And now we just need to solve for x and we got:
[tex]3x=144[/tex][tex]x=\frac{144}{3}=48º[/tex]And for the larger angle we got:
[tex]x+36=48+36=84º[/tex]A local community college has announced that they will be raising tuition costs from $36 per unit to $46 per unit. Determine the percent increase in tuition costs. Round your answer to the nearest tenth of a percent.
Answers
Solution
Determine the percent increase in tuition costs:
To calculate the percentage increase:
First: work out the difference (increase) between the two numbers you are comparing.
Increase = New Number - Original Number
Then: divide the increase by the original number and multiply the answer by 100.
New cost = $46
Original cost = $36
[tex]\begin{gathered} I\text{ncrease= New cost - Original cost} \\ Increase\text{ = 46-36} \\ Increase=\text{ \$}10 \end{gathered}[/tex][tex]\begin{gathered} \text{ \% increase = }\frac{10}{36}\times100 \\ =\frac{1000}{36} \\ =27.278 \\ \approx27.8\text{ \%} \end{gathered}[/tex]Therefore the percent increase in tuition costs = 27.8%
Solve for x. The triangles in each pair are similar please questions number 13
Answers
Answer:
x = 8
Explanation:
Two triangles are similar if the length of their sides is proportional, so we can write the following equation to find x:
[tex]\begin{gathered} \frac{SU}{SR}=\frac{ST}{SQ} \\ \frac{x+4}{4}=\frac{6}{2} \end{gathered}[/tex]So, we can solve for x:
[tex]\begin{gathered} \frac{x+4}{4}=3 \\ \frac{x+4}{4}\cdot4=3\cdot4 \\ x+4=12 \\ x+4-4=12-4 \\ x=8 \end{gathered}[/tex]Therefore, the answer is x = 8.
3a + 10b/4 + 5a-2b/4
Answers
We have the expression:
[tex]3a+\frac{10b}{4}+5a-\frac{2b}{4}[/tex]Add the coefficients with the same variable,
[tex]undefined[/tex]for every dollar of norevenue the government tales in, it paya 5 cents in interest on its debt. What is the ratio of debt interest to total revenue
Answers
Answer:
Choice D. 1 : 20
Explanation:
We know that if
Revenue = 1 dollar = 100 cents
interest debt = 5 cents
therefore, the ratio is
debt interest / revenue = 5 cents / 100 cents = 1 / 20
Hence, the correct answer is choice D
Hello, I need some help with this precalculus question for my homework, please HW Q2
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The logarithmic equation given is,
[tex]\log _4\left(11x\right)=2[/tex]Apply log rules
[tex]\log_4\left(11x\right)=\log_42^4[/tex]Cancel out the log₄
[tex]11x=2^4[/tex]Solve for x
[tex]\begin{gathered} 11x=16 \\ Divide\text{ both sides by 11} \\ \frac{11x}{11}=\frac{16}{11} \\ x=\frac{16}{11}=1\frac{5}{11} \end{gathered}[/tex]Hence, the solution set is
[tex]x=\frac{16}{11}or1\frac{5}{11}[/tex]A milkshake vendor sells shakes in three different flavors: see photo
Answers
Solution:
Let the price of mango, strawberry and chocolate flavors be x, y, and z respectively.
Thus,
[tex]\begin{gathered} mango\Rightarrow x \\ strwberry\Rightarrow y \\ chocolate\Rightarrow z \end{gathered}[/tex]From the table below:
Given that the total sales in shift 1 is $419, $649 in shift 2, and $96 in shift 3, this implies that
[tex]\begin{gathered} 16x+13y+29z=419\text{ ----- equation 1} \\ 26x+19y+45z\text{ = 649 ----- equation 2} \\ 6x+11y+0z\text{ = 96 ------ equation 3} \end{gathered}[/tex]From the above system of equations, we can resolve into matrices of the form:
[tex]A\cdot X=B[/tex]This gives:
[tex]\begin{bmatrix}{16} & {13} & {29} \\ {26} & {19} & {45} \\ {6} & {11} & {0}\end{bmatrix}\times\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {z} & {} & {}\end{bmatrix}=\begin{bmatrix}{419} & {} & {} \\ {649} & {} & {} \\ {96} & {} & {}\end{bmatrix}[/tex]Where:
[tex]\begin{gathered} A=\begin{bmatrix}{16} & {13} & {29} \\ {26} & {19} & {45} \\ {6} & {11} & {0}\end{bmatrix} \\ X=\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {z} & {} & {}\end{bmatrix} \\ B=\begin{bmatrix}{419} & {} & {} \\ {649} & {} & {} \\ {96} & {} & {}\end{bmatrix} \end{gathered}[/tex]To solve for the unknowns, we use the Cramer's rule expressed s
[tex]\begin{gathered} x=\frac{D_x}{D} \\ y=\frac{D_y}{D} \\ z=\frac{D_z}{D} \\ where\text{ D is the determinant of the matrix A} \end{gathered}[/tex]To evaluate the price of one chocolate, which is z, we have
[tex]\begin{gathered} z=\frac{D_z}{D}=\frac{det\begin{bmatrix}{16} & {13} & {419} \\ {26} & {19} & {649} \\ {6} & {11} & {96}\end{bmatrix}}{det\text{ A}} \\ =\frac{16\times\det\begin{pmatrix}19 & 649 \\ 11 & 96\end{pmatrix}-13\times\det\begin{pmatrix}26 & 649 \\ 6 & 96\end{pmatrix}+419\times\det\begin{pmatrix}26 & 19 \\ 6 & 11\end{pmatrix}}{578} \\ =\frac{16(-5315)-13(-1398)+419(172)}{578} \\ =\frac{5202}{578} \\ \Rightarrow z=9 \end{gathered}[/tex]Hence, the price of one chocolate is
[tex]\$9[/tex]The correct option is D
Choose the point which shows the correct location for the polar coordinate (1,5π/6)
Answers
Answer:
C
Explanation:
The polar coordinates have the following form
(r, θ)
Where r is the radius and θ is the angle. If the polar coordinate is (1, 5π/6), the point will be located in the first circle and an angle of 5π/6. Therefore, the point that shows the correct location is C.
So, the answer is C.
simplify the trig expression csc θ cot θ——————sec θ
Answers
To simplify:
[tex]\frac{\csc\theta\cot\theta}{\sec\theta}[/tex]We know that,
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin\theta} \\ \cot \theta=\frac{\cos\theta}{\sin\theta} \\ \sec \theta=\frac{1}{\cos \theta} \end{gathered}[/tex]Using this we get,
[tex]\begin{gathered} \frac{\csc\theta\cot\theta}{\sec\theta}=\frac{\frac{1}{\sin\theta}\cdot\frac{\cos\theta}{\sin\theta}}{\frac{1}{\cos\theta}} \\ =\frac{1}{\sin\theta}\cdot\frac{\cos\theta}{\sin\theta}\times\frac{\cos\theta}{1} \\ =\frac{\cos^2\theta}{\sin^2\theta} \\ =(\frac{\cos \theta}{\sin \theta})^2 \\ =\cot ^2\theta \end{gathered}[/tex]Hence, the answer is,
[tex]\cot ^2\theta[/tex]Ping's sister baked a plum pie yesterday. Ping ate 5.8 slices yesterday and 1.7 slices today. How many slices has Ping eaten so far?
Answers
Ping has eaten 7.5 slices so far.
Step - by - Step Explanation
What to find?
The number of slice ping has eaten.
Given:
• Amount Ping ate yesterday = 5.8 slices.
,• Amount Ping ate today = 1.7 slices.
To get the total number of slice she has eaten, add up the number of slice eaten yesterday and today.
That is;
Hence, she has eaten 7.5 slice so far.
Answer:
7.5
Step-by-step explanation:
5.8+1.7=7.5 (slices)
12y=156Solve for the variable
Answers
The variable y is 13
Given the equation:
12y = 156
To solve for the variable y, we divide both sides of the equation by the coefficient of y, which is 12.
Doing this, we have
[tex]\begin{gathered} \frac{12y}{12}=\text{ }\frac{156}{12} \\ \\ y\text{ = }13 \end{gathered}[/tex]The variable y is 13.
a system of equations is graphed here. which system of equations does the graph represent? A) y = 3x + 2y = -2x + 5 B) y = 3x - 2 y = 2x + 5 C) y = -3x + 2 y = 2x - 5 D) y = -3x - 2 y = -2x - 5
Answers
Notice that the line with negative slope has a y-intercept of 5 and the line with positive slope has a y-intercept of 2.
On the other hand, the slope of the line with negative slope is -2, while the slope of the line with positive slope is 3 (This can be identified since in one case, the value of y decreases by 2 for each increase of 1 unit in x, and in the other, the value of y increases by 3 for each increase of 1 unit in x).
Using the y-intercept form to represent each line, the system of equations represented by the graph must be equivalent to:
[tex]\begin{gathered} y=-2x+5 \\ y=3x+2 \end{gathered}[/tex]From the given options, the one that displays the correct system of equations is option A.
Therefore, the answer is:
[tex]\begin{gathered} A) \\ y=3x+2 \\ y=-2x+5 \end{gathered}[/tex]