Answer:
[tex]3x^2[/tex]
Step-by-step explanation:
First main thing to know is the product and quotient rule of exponents.
Product Rule:
[tex]x^a*x^b = x^{a+b}[/tex]
And if this doesn't make sense, you can think of the exponent like this:
[tex]x^a*x^b = (x*x*x*x...\text{ a amount of times}) * (x * x * x \text{ b amount of times})[/tex]
and since multiplication is commutative, we can just combine all these x's, and since the total amount on the left is "a", and the right is "b", the total combined x's should be a+b, which can be expressed as:
[tex]x*x*x... \text{ a+b amount of times}[/tex]
which can be expressed as an exponent (x^(a+b))
Quotient Rule:
[tex]\frac{x^a}{x^b} = x^{a-b}[/tex]
You can use similar reasoning for this, since if you write it out you get
[tex]\frac{x*x*x...\text{ a amount of times}}{x*x*x\text{ b amount of times}}[/tex]
and since you have an x in the numerator and the denominator, you can simply cancel the x's out. In doing this you want to remove the denominator, so you cancel out "b" x's. So there will be (a-b) x's left in the numerator, and a 1 in the denominator, so it's just x^(a-b)
Ok so now let's apply these to solve your question
[tex]\frac{(15x^{-4})*x^{15}}{(5x^4)*x^5}\\[/tex]
So let's combine the exponents in the numerator and denominator using the product rule
[tex]\frac{15x^{11}}{5x^9}\\[/tex]
Now we can divide the 15 by 5, and divide the x^11 by the x^9 using the quotient rule
[tex]3x^2[/tex]
Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship.
Enter the correct answer in the box by replacing the values of a and b
f(x) = a(b)^x
(PLATO)
The exponential equation modeling this relationship is given as follows:
f(x) = 8(0.5)^x.
What is an exponential equation?An exponential equation is modeled by:
f(x) = a(b)^x
In which:
a is the initial value, that is, the value of y when x = 0.b is the rate of change.For this problem, we have that when x = 0, y = 8, hence a = 8. Then:
f(x) = 8(b)^x.
When x = 1, y = 4, hence b is found as follows:
f(x) = 8(b)^x.
4 = 8b
b = 0.5.
Hence the equation is:
f(x) = 8(0.5)^x.
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0
According to the Nielsen Media Research, of all the U.S. households that owned at least one television set, 83% had two or more sets, A local cable
company canvassing the town to promote a new cable service found that the 300 randomly selected households visited, 240 had two or more
television sets. At 0.05 level of significance, is there sufficient evidence to conclude that the proportion is less than the one in the report?
Answer Questions 12-23.
The level of significance on 0.05 exists at 83%.
How to find the level of significance?The sample size (n) specified by the local cable company exists 300 which exists quite large.
According to the Central limit theorem, the sampling distribution of sample proportion observes a normal distribution with mean p and standard deviation
[tex]$\sqrt{\frac{p(1-p)}{n}}$[/tex]
Since the sampling distribution of sample proportions observes a normal distribution utilize the z-test for one proportion to execute the test.
The hypothesis is:
[tex]$H_{0}$[/tex]: The proportion of U.S. households that owned two or more televisions exists at 83 %, i.e. p = 0.83
[tex]$H_{1}$[/tex]: The proportion of U.S. households that owned two or more televisions exists less than 83 %, i.e. p < 0.83
Decision Rule:
At the level of significance [tex]$\alpha=0.05$[/tex] the critical region for a one-tailed z-test is:
[tex]$Z \leq-1.645[/tex]
By using the z table for the critical values.
So, if [tex]$Z \leq-1.645$[/tex] the null hypothesis will be rejected.
Test statistic value:
[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
Here [tex]$\hat{p}$[/tex] exists the sample proportion.
Compute the value of [tex]$\hat{p}$[/tex] as follows:
[tex]$&\hat{p}=\frac{X}{n} \\[/tex] [tex]$&=\frac{240}{300} \\[/tex]
= 0.80
To compute the value of the test statistic as follows:
[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]
[tex]$=\frac{0.80-0.83}{\sqrt{\frac{0.83 \cdot(1-0.83)}{3000}}}$[/tex]
The test statistic exists at -1.383 which exists more than -1.645.
Therefore, the test statistic lies in the acceptance region.
Thus we fail to reject the null hypothesis.
At a 0.05 level of significance, we fail to reject the null hypothesis noting that the proportion of U.S. households that owned two or more televisions exists at 83%.
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If log103 0.4771,
evaluate log100.0003.
Round your answer to four decimal
places.
Answer:
log(0.0003) = -3.5229
Step-by-step explanation:
The rules of logarithms tell you ...
log(ab) = log(a) +log(b)
Applicationlog(0.0003) = log(3×10^-4) = log(3) +log(10^-4)
= log(3) -4 = 0.4771 -4
log(0.0003) = -3.5229
__
Additional comment
If you do much work with logarithms, you find that negative logarithms are generally expressed using a positive mantissa with a negative add-on. Often, that negative add-on is -9, so this would be ...
5.4771-9
This helps when taking antilogs, as you look up 0.4771 in the table to see that the multiplier is 3.
If you were to look up 0.5229, you would find 3.333, meaning the multiplier is 1/3.333 and the antilog of -3.5229 is (10^-3)/3.333. This may not be a convenient value to work with.
The Black Pearl is following a course that is represented by the equation. + ? = 14. . The interception course of the Flying Dutchman is represented by the equation
Use the graphing method to determine the coordinate point where the two ships’ paths meet.
According to the graph, the ships’ paths do not meet at any point.
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the point where the two ships' path meet?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x = 5y - 40
-4x + 10y = 20
Make y the subject in the second equation, by adding 4x to both sides of the equation
4x -4x + 10y = 20 + 4x
This gives
10y = 20 + 4x
Divide both sides by 10
y = 2 + 0.4x
Substitute y = 2 + 0.4x in 2x = 5y - 40
2x = 5(2 + 0.4x) - 40
Expand
2x = 10 + 2x - 40
Subtract 2x from both sides of the equation.
2x - 2x = 10 + 2x - 2x - 40
Evaluate the like terms
0 = 10 - 40
Evaluate the like terms
0 = -30
The above equation is not true.
This means that the ships’ paths do not meet at any point.
This can be confirmed using the attached graph.
From the graph, we can see that the lines of 2x = 5y - 40 and -4x + 10y = 20 do not intersect
Hence, we can conclude that the ships’ paths do not meet at any point.
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What is the best estimate of the correlation for the data set
The best estimate for the correlation coefficient of the data is: C. 0.5.
What is Correlation?Correlation can be defined as a quantitative measure that describes the relationship between variables. Correlation coefficient, r, is a number that ranges from -1 to 1.
The farther the correlation coefficient from 0, the stronger the relationship between two variables, and also, the more closer the data points are on a plotted graph. Also, a negative correlation value will show a trendline on a plot that slopes downward, while positive correlation value will show a trendline that slopes upwards.
In the graph given, the points are moderately closer to each other. Also, the trendline slopes upward, which suggest a positive correlation.
Since the points are moderately spaced from each other, the correlation coefficient would positive and be approximately 0.5.
Therefore, the best estimate for the correlation coefficient of the data is: C. 0.5.
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Triangular prism advertising boards are being placed along the edge of the arena’s stage with the following dimensions: Select which of the nets below are labelled with the correct dimensions. What should the dimensions be of any advertisement that wants to fill the longest side of the shape?
The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m
According to the statement
we have given that the Triangular prism of size 0.75 m, 1m and length of 2m.
And we have to find the by which size of advertisement board need to fill the longest side of the shape.
A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
So, for this purpose,
we know that the longest side of triangular prism is 2m and we have to cover it with the advertising board.
Obviously the length of the advertising board is of 2m to cover the longest side of the shape.
So, The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m
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How many significant figures are in this number? 2.583 x 10^12
Answer:
2583000000000
Step-by-step explanation:
[tex]2.583*10^{12} = 2583000000000[/tex]
Tanya is a car saleswoman. Below are the number of cars that she sold in each of the last six months. 23, 21, 21, 20, 21, 20 Using this data, create a dot plot where each dot represents a month. 19, 20 ,21 Number of cars sold 22 ,23 pls
Answer: so there would be 1
23
3 21
2 20
Step-by-step explanation:
Which of the following fitness scores is the highest relative score?
a score of 39 on a test with a mean of 31 and a standard deviation of 6.1
a score of 1136 on a test with a mean of 1080 and a standard deviation of 67.8
a score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5
All scores are relatively equal.
Due to the higher z-score, the correct option regarding the highest relative score is:
A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.
What is the z-score formula?The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean, hence the higher the z-score, the higher the score X is relative to other scores.
The respective z-scores for this problem are given by:
(39 - 31)/6.1 = 1.31.(1136 - 1080)/67.8 = 0.83.(4730 - 3960)/555.5 = 1.39.Hence the correct option is:
A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.
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Definition of economic costs Gilberto lives in San Diego and runs a business that sells pianos. In an average year, he receives $701,000 from selling pianos. Of this sales revenue, he must pay the manufacturer a wholesale cost of $420,000; he also pays wages and utility bills totaling $247,000. He owns his showroom; if he chooses to rent it out, he will receive $9,000 in rent per year. Assume that the value of this showroom does not depreciate over the year. Also, if Gilberto does not operate this piano business, he can work as a financial advisor, receive an annual salary of $32,000 with no additional monetary costs, and rent out his showroom at the $9,000 per year rate. No other costs are incurred in running this piano business.
The wholesale cost for the pianos that Tim pays the manufacturer, wages and utility bills that Tim pays are counted as explicit cost. On the other hand, the salary that Tim could earn if he worked as an accountant and the rental income that Tim could earn from renting his showroom fall under implicit cost.
Difference between Implicit Cost and Explicit Cost:
These two expenses, implicit cost and explicit cost, both represent company activity. The connection between cost and business is what distinguishes these two.
An explicit cost is one that the owner bears directly; an implicit cost is one that the owner bears indirectly without paying or utilizing its own resources. However, the organization or corporation takes into account both expenses while making management decisions.
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classify the numbers in the image to be either a whole number integer rational number irrational number real number
Question
Which of the following equations is equivalent to 8x - 6y = 12?
y = ³x - 1²/2 3
y=x-2
y = 2x - 12
y = 8x - 6
The equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
What are Equivalent Equations?Equations that are equivalent to each other have the same value when evaluated or simplified.
Given the equation, 8x - 6y = 12, to determine which of the given equations in the options is equivalent to, rewrite the equation in slope-intercept form, as y = mx + b.
8x - 6y = 12
Subtract 8x from both sides of the equation
8x - 8x - 6y = -8x + 12
-6y = -8x + 12
Divide both sides of the equation by -6
-6y/-6 = -8x/-6 + 12/-6
y = 4x/3 + (-2)
y = 4x/3 - 2
Therefore, the equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
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consider a two-factor factorial design with three levels for facts a, three levels for factor b, and four replicates in each of the nine cells
a. how many degrees of freedom are there in determining the A variation and the factor B variation
b. how many degrees of freedom are there in dreaming the interaction variation
c. how many degrees of freedom are there in determining the random variation
d. how many degrees of freedom are there in determining the total variation
In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.
What is a two-factorial design?A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.
Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.
From the data given:
a.
In calculating the factor A variation, there are two degrees of freedom.
In determining the variation of factor B, there are two degrees of freedom.
b.
Finding the degree of freedom using the interaction variation, there are four degrees of freedom.
c.
In finding the random variable, there are 9(4-1) = 27 degrees of freedom.
d.
In calculating the total variable, there are 9*4-1 =35 degrees of freedom.
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Use the Divergence Theorem to evaluate the surface integral
The value of surface integral using the Divergence Theorem is [tex]729\pi[/tex] .
What is Divergence Theorem?Divergence Theorem states that the surface integral of a vector field over a closed surface, is equal to the volume integral of the divergence over the region inside the surface. Mathematically the it can be calculated using the formula:[tex]\int\int\int\limit{ }_V(\delta \cdot F)=\int\int(F \cdot n)dS[/tex]
The divergence of F is
[tex]div F=\frac{d}{dx}(2x^{3}+y^{3})+\frac{d}{dy}( y^{3} +z^{3})+\frac{d}{dz}3y^{3} z[/tex]
[tex]div F=6x^{2}+3y^{2}+3y^{2}[/tex]
Let E be the region [tex]{(x,y,z):0\leq z\leq 9-x^{2} -y^{2}[/tex] then by divergence theorem we have [tex]\int \int\limits^{}_s {F\cdot n\times dS} =\int\int\int\limits^{}_E divFdV=\int\int\int\limits^{}_E(6x^2+6y^2)dV[/tex]
Now we find the value of the integral:
[tex]=\int\limits^{2\pi}_0\int\limits^3_0\int\limits^{9-r^2}_0(6r^2)rdzdrd{\theta}\\=\int\limits^{2\pi}_0 \int\limits^3_0(9-r^2)6r^3drd{\theta}\\=2\pi\int\limits^3_0 {(54r^3-6r^5)} dr\\[/tex]
[tex]=2\pi\times \frac{729}{2}\\=729\pi[/tex]
Thus we can say that the value of the integral for the surface around the paraboloid is given by [tex]729\pi[/tex].
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Val’s whole-house central air conditioner uses 2,500 watts when running. Val runs the AC 7 hours per summer day. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Val’s AC costs to run for a summer month of 30 days?
The total cost to run Val’s AC costs for a summer month of 30 days is $94.5.
Cost of electricityQuantity of electricity used in kilowatts
1000 watts = 1 kilowatts
2,500 watts = 2.5 kilowatts
Number of hours Val runs AC per day = 7 hoursNumber of days = 30 daysCost of electricity = $0.18 kilowatts per hourCost of Val’s AC to run for a summer month of 30 days = Quantity of electricity used × Number of hours Val runs AC per day × Number of days × Cost of electricity
= 2.5 × 7 × 30 × 0.18
= $94.5
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A worker is constructing a concrete pad that has a radius of 6.3 metres, as shown below. Report a Problem ↻ Reload Image How many metres of wooden forming are needed for the circumference of the pad? 24.6 metres 31.5 metres 39.6 metres 249.2 metres
The circumference of the pad to the nearest tenth is 39.6 meters
Formula for calculating the circumference of a circle?The circumference of a circle is the arc length of the circle, as if it were opened up and straightened out to a line segment. It is also known as the perimeter of a circle.
The formula for calculating the circumference of a circle is expressed as;
C = 2πr
where
π = 3.14
r is the radius of the circle
Given the following parameters
π = 3.14
r = 6.3m
Substitute to have:
C = 2 * 3.14 * 6.3
C = 6.28 * 6.3
C = 39.564
Hence the circumference of the pad to the nearest tenth is 39.6 meters
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The data given to the right includes data from candies, and of them are red. The company that makes the candy claims that % of its candies are red. Use the sample data to construct a % confidence interval estimate of the percentage of red candies. What do you conclude about the claim of %?
Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:
[tex]n = 39, \pi = \frac{8}{39} = 0.2051[/tex]
Hence the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 - 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.0784[/tex][tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.3318[/tex]As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
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Solve by graphing. tan(30x - 90°) = -x³
The solution to the equation is 0.07, 0.17, 0.27, 0.38........
How to determine the solution to the trigonometry equation?The trigonometry equation is given as:
tan(30x - 90°) = -x³
We start by splitting the trigonometry equation as follows, by creating two different equations
y = tan(30x - 90°)
y = -x³
Next, we plot the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³
From the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³, we have the x coordinate of the point of intersection to be:
x = 0.07, 0.17, 0.27, 0.38........
Hence, the solution to the trigonometry equation is 0.07, 0.17, 0.27, 0.38........ .
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An investment pays 10% interest compounded monthly. What percent, as a decimal, is the effective annual yield? Enter your answer as a decimal rounded to four decimal places.
[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ APY=\left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12 \end{cases} \\\\\\ APY=\left(1+\frac{0.1}{12}\right)^{12}-1\implies APY=\left( \frac{121}{120} \right)^{12}-1\implies APY\approx 0.1047[/tex]
Which are valid pairs of opposite angle measures for a quadrilateral inscribed
in a circle? Select all that apply.
A. 72°, 108°
B. 66°, 114°
C. 80°, 90°
D. 64°, 106°
Answer:
A., B.
Step-by-step explanation:
Opposite angles of a quadrilateral inscribed in a circle are supplementary, so their sum must equal 180°.
A. 72° + 108° = 180° Answer: yes
B. 66° + 114° = 180° Answer: yes
C. 80° + 90° = 170° Answer: no
D. 64° + 106° = 170° Answer: no
Answer: A., B.
A right pyramid has a height of 3 inches and a square base with side length of 5 inches. What is the volume of the pyramid?
The volume of this pyramid is ______
cubic inches.
PLEASE MY LAST QUESTION
Answer: 25 in³
Step-by-step explanation:
We can calculate the volume of the pyramid by first calculating the volume of a prism with the same dimensions, and then dividing by 3 (all pyramids a volume that's [tex]\frac{1}{3}[/tex] of the volume of a prism with the same dimensions).
The volume of a prism is its base area times its height. The base would be a square, so its area is 5², which is 25. The height is 3 inches, making the prism's volume 75 in³.
The volume of the pyramid would be one-third of this value, which is 75[tex]75\div3[/tex] which is 25 in³.
Find P sophomore girl hint: p(a & b)/p(b)
Answer:
7/18
Step-by-step explanation:
P(sophomore girl) is 7 out of a total 30.
P(girl) is 18 out of 30.
(7/30) / (18/30) = 7/18
If you just look at the girls column you can see this immediately. A given is that we're looking for a girl (18 girls), then what is the chance that it's a sophomore. That is 7 out of 18.
Answer:
The answer would be 7 over 18 in fraction form fill in 7 then 18
Step-by-step explanation:
7/18
Two buses leave a station at the same time and travel in opposite directions. One bus travels 18 miles per hour faster than the other. If the two buses are 744 miles apart after 6 hours, what is the rate of each bus?
Answer:
53 mph and 71 mph
Step-by-step explanation:
bus 1 rate = x
bus 2 rate = x + 18
rate times time = distance
( x + x+18) * 6 = 744
(2x+18) * 6 = 744
2x + 18 = 124
2x = 106
x = 53 the other bus is 53 + 18 = 71 mph
If the measure of angle ABC is 68°, what is the measure of arc AB?
Answer:
136
Step-by-step explanation:
While there is no picture for this question, I was able to find this question online, so that should be the correct answer.
a mountain is 10,093 feet above sea level, and a valley is 111 feet below sea level. what is the difference in elevation between the mountain and the valley?
Answer: 10,204 feet
Step-by-step explanation: i would assume you would add the two together, seeing as if the mountain is 10,093 above sea level and the valley is 111 below, the difference in elevation is also the distance between each other.
if AC is parallel to DE, find X
Answer: x = 50
Concept:
Here, we need to know the idea of alternative interior angles and the angle sum theorem.
Alternative interior angles are angles that are formed inside the two parallel lines, and the values are equal.
The angle sum theorem implies that the sum of interior angles of a triangle is 180°
If you are still confused, please refer to the attachment below or let me know.
Step-by-step explanation:
Given information:
AC ║ DE
∠ABC = 85°
∠A = 135°
Find the value of ∠BAC
∠A + ∠BAC = 180° (Supplementary angle)
(135°) + ∠BAC = 180°
∠BAC = 45°
Find the value of ∠BCA
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)
(85°) + (45°) + ∠BCA = 180°
∠BCA = 50°
Find the value of x (∠EBC)
∠EBC ≅ ∠BCA (Alternative interior angles)
Since, ∠BCA = 50°
Therefore, ∠EBC = 50°
[tex]\Large\boxed{x=50}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What is the value of x in the equation −6 + x = −2? Answer A. 8 B. 3 C. -4 D. -8
someone help me
Answer:
x = 4
Step-by-step explanation:
You can solve for "x" by rearranging the equation and getting the "x" by itself on one side. Remember, whatever you do to one side of the equation, you must do to the other side.
-6 + x = -2 <----- Original equation
+6 +6 <----- Add 6 to both sides to isolate "x"
0 + x = 4 <----- After the addition
x = 4 <----- Rewrite
Answer:
None of the above (x = 4) [tex] \sf {} [/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ -6 + x = -2
Then the value of x will be,
→ -6 + x = -2
→ x = -2 + 6
→ [ x = 4 ]
Hence, the value of x is 4.
What is the measure of this line?
Answer:
2 and 1/16th inch
Step-by-step explanation:
the half inch mark would be 2 and 1/2 and you know half of half is 1/4 so the best answer is A.
F(v) =2x if g(x)=5x then f(g(x)
Answer:
10x
Step-by-step explanation:
g(x)=5x
f(x)=2x
f(g(x))=f(5x)
f(g(x))=2*5x=10x
The scouts packed 9 boxes of different kinds of chips for their trip. Each box had 10 bags of chips. These clues show what they had left at the end of the trip. They ate all the rest.
Clues:
2 full boxes of potato chips and 3 bags left over
1 fewer box of nacho chips than potato chips, with no bags left over
twice as many loose bags of barbecue chips than loose bags of potato chips, with no full boxes left over
How many bags of chips did the scouts eat on their trip?
The scouts eat 51 bags of chips on their trip
How to determine the number of bags of chips?The given parameters are:
Boxes = 9
Bag = 10 chips
2 full boxes of potato chips and 3 bags left over.
This represents:
Potato chips = 2 * 10 + 3
Potato chips = 23 i.e. 23 bags potato chips are left over
1 fewer box of nacho chips than potato chips, with no bags left over
This represents
Nacho chips = (2 - 1) * 10
Nacho chips = 10 i.e. 10 bags of nacho chips are left over
The loose bags of potato chips is 3.
So, we have:
Barbecue chips = 2 * 3 bags
Barbecue chips = 6 bags
At this point, we have:
Potato chips = 23 bagsNacho chips = 10 bags Barbecue chips = 6 bagsThe total number of bags left over is
Total = 23 + 10 + 6
Total = 39
The number of bags eaten is:
Eaten = 9 * 10 - 39
Evaluate
Eaten = 51
Hence, the scouts eat 51 bags of chips on their trip
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