The value x of the trapezoid is 3 units.
How to find the side of a trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides .
The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides.
The midsegment of a trapezoid is parallel to each base, and its measure is half the sum of the lengths of the bases.
Therefore,
29 = 1 / 2 × (23 + 11x + 2)
29 = 1 / 2 × (25 + 11x)
cross multiply
29 × 2 = 25 + 11x
58 = 25 + 11x
58 - 25 = 11x
33 = 11x
divide both sides by 11
x = 33 / 11
x = 3
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a population doubles in size every 15 years. assuming exponential growth, find the (a) annual growth rate (b) continuous growth rate
The annual growth rate is 4.73 %
The continuous growth rate is 4.62 %
What is exponential growth function ?
A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.
Let us assume:
The initial amount of 1, so results are 2.
Let x be the percent in decimal form
Growth rate per year:
[tex]1(1+x)^{15} = 2[/tex]
Take ln on both the sides
[tex]ln((1+x)^{15}) = ln(2)[/tex]
15*ln(1+x) =0 .693
ln(x+1) = 0.693/15
ln(x+1) = 0.04621
Take anti ln on both the sides
x+1 = 1.0473
x = 1.0473 - 1
x = .0473
x =4.73 % annual growth rate
Continuous growth rate:
[tex]1*e^{15x} = 2[/tex]
[tex]ln(e^{15x}) = ln(2)[/tex]
15x*ln(e) = ln(2)
ln(e) = 1
15x =0.693
x =0 .693/15
x = .0462
x = 4.62 %
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PLS HELP 50 pnts!!!!!!! giving brainliest!!! 1-4 (find the slope)
-attached pic
-unacceptable answers will result in 2 reports (2 warnings and the max is 3 then you will be banned)
Answer:
1) slope = 1/2 2) slope= -1 3)slope= 1/2 4) 5/4
Step-by-step explanation:
if you want y intercpt form
1) y=1/2x
2)y= -x-3
3) y= 1/2x-3.5
4) y= 5/4x - 1
Help please!! I need this answer!!
Answer: Store B and C sell at a lower unit price.
Step-by-step explanation:
Store B: $3.48/3 = $1.16 per pound.
Store C: $3.80/4 = $0.95 per pound.
PLS HELP ASAP!!!! 35pts!!
The hypotenuse - leg congruency can be applied in both right triangles.
How to find congruent triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.
In other words, if the hypotenuse and a leg of a right triangle are each congruent with the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.
Hence, the legs of the right triangle are congruent and one of the legs are congruent.
Therefore, the hypotenuse - leg congruency can be applied.
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a town’s january high temperatures average 36°f with a standard deviation of 10°, while in july the mean high temperature is 74° and the standard deviation is 8°. in which month is it more unusual to have a day with a high temperature of 55°? explain.
It is more unusual to have a high temperature of 55 degrees in July because the month's z-score is 2.375 standard deviations from its mean.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. Standard deviation is significant because it enables consumers to evaluate risk. Think about an investing strategy with a 10% average yearly return.
Here,
Calculations are attached in image.
A high temperature of 55 degrees is particularly rare since July's z-score is 2.375 standard deviations outside of its mean.
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Can someone check this plsss
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2: Suppose a sample of 782 suspected criminals is drawn. Of these people. 273 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.
The confidence interval is (0.309, 0.389).
Calculate a 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.
Sample size, n = 782
Sample proportion, p = x/n = 0.349105
Confidence level, 1 - α = 98% = 0.98 Implies
Level of significance, α = 0.02
At α = 0.02, the two-tailed critical value from the z-table, Zα/2 = 2.33
Then, the 98% confidence interval is,
It gives, 0.309≤ p ≤0.389
Lower endpoint = 0.309
Upper endpoint = 0.389
We are 98% confident that the proportion of all suspected criminals who were captured is within the confidence interval. If we were to take a large number of random samples of size 782, 98% of the resulting confidence intervals would contain the true proportion of all suspected criminals who were captured.
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If x = 6, what y? Please help
Answer: I think the answer is 2
Step-by-step explanation:
The smaller of the two shapes is 12, and the larger of the two shapes is 16,
I found that the difference between the two is 4 (or 16 - 12 =4). If x = 6 and the difference is 4, then subtract 4 from 6 and the answer will come out to be 2
16-12=6-4
y=2
To test the effectiveness of a liquid supplement that is supposed to help forgetful people with their memory, 400 college students are recruited for a study and divided into two groups. Group A with 250 students receives the supplement, while group B with 150 students receives some colored water. Neither group is told what they received. After several weeks, they are given a memory test. This study can best be described as: . a census a controlled placebo experiment a survey using quota sampling a survey using simple random sampling the placebo effect
This study can be best described as Controlled Placebo Experiment
What is a Controlled Placebo Experiment?
A controlled placebo experiment is a type of research method that is used to check the effectiveness of a drug in a patient. This is done by selecting a sample group, then randomly divide the two group into a placebo group (this are the group that will receive the drug treatment ) and the controlled group (these are the group that will receive a colored mixture that looks like the drug, but does not have any effect). Without the groups knowledge about the real drugs and the colored mixture, but are followed up and tested.
According to the given question:
This is a controlled placebo experiment, because 400 student has been chosen as the sample, and are divided into a placebo group and a controlled group, to check the effectiveness of a drug on their memory.
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carols buys 3 gallons of juice for a party. What is greatest number of cups of juice he can Surve
Answer:
24
Step-by-step explanation:
the answer is 24 because 3 gallons can definitely do more then 16 it also depends on how much water the cups can hold.
if gallup wishes to use a 95% confidence interval, compute the minimum number of american adults that they need to survey to ensure that the error bound, under no circumstances, is more than 0.01 before conducting the experiment?
the minimum number of american adults that they need to survey to ensure that the error bound is 16,867 with sample size
The sample size of a study is the number of subjects or observations that are included.Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.
The minimum sample size required to get a 95% confidence interval with an error bound of 0.01 is 16,867. This can be calculated using the formula:
n = (1.96 / 0.01)2 = 16,867.
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omg please help me with the ones with the red dot t’s for my math geometry class
a laboratory supply company produces graduated cylinders, each with an internal radius of 222 inches and an internal height between 7.757.757, point, 75 inches and 888 inches. what is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?
One possible volume of a graduated cylinder produced by the company is 98 cubic inch.
The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object. An object with a larger volume would occupy more space.
The volume of a cube can be found by multiplying the edge length three times. For instance, if the length of an edge of a cube is 4, the volume will be 4³. The formula to calculate the volume of a cube is given as,
Volume of a cube = s³, where 's' is the length of the side of the cube.
Given in the question:
Radius of cylinder = 2 inches.
Height of the cylinder = 7.75 to 8 inches.
We know that,
Volume of Cylinder = πr²
For minimum Volume 7.75 :
Volume = πr²× 7.75
= 3.14 × 4 × 7.75
= 97.34 cubic inches.
For maximum volume 8.00 inches
Volume = πr² × 8
= 3.14 × 4 × 8
= 100.81
Therefore, the possible volume could be between 97.34 cubic inches and 100.81 cubic inches.
Thus, the volume is 98 cubic inches.
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a research study reported that 10% of the people who are given a certain drug experience dizziness.if 15 people are selected at random, find the probability that none of them experience dizziness when given the drug.
Out of the 15 people the probability that none of the patients will experience dizziness is approximately 0.206 .
10% of the people experiences dizziness.
Probability that a random patient experiences dizziness = 0.1
Probability that the person does not experience dizziness = 0.9
Now this is in the form of a binomial distribution such that the probability is given by:
Sample = 15
P = 0.1
P' =0.9
Required probability :
= ¹⁵C₀ × P⁰ × P'¹⁵ (binomial distribution)
= 1 × 0.1⁰ × 0.9¹⁵
= 0.20589...
≈ 0.206
Hence the required probability is approximately 0.206 .
The binomial distribution is often used to predict the number of further successes in either a sample of size n drawn under replacement from either a population of size n.
If the sampling is carried out without replacement, the drawings are not independent, hence the resulting distribution is a hypergeometric one rather than a binomial one.
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Find the measure of A:
A
15x
31x-2
Answer:
30
Step-by-step explanation:
Triangles add up to 180.
Your known sides are: 15x, 31x-2, and 90 (the square on the corner of the angle tells you that it's a right angle or 90 degrees.)
First make an equation to find X
this looks like: 15x+31x-2+90=180
I just added the sides we know and set them to equal 180. Because triangles add up to 180.
Now solve this by first combining like terms
15x+31x-2+90=180 (do the numbers with x's) so 15x+31x
46x-2+90=180 (now combine the numbers without X's) so -2+90
46x+88=180 (now since 88 is positive, do the opposite and subtract it from 180. This is because 180 is on the other side of the = sign.)
46x=92 (now since 46x means 46 times x, you do the opposite of multiplication and divide 92 by 46.
This gives you x=2
Now the last thing you need to do is solve for angle A
Angle A says "15x" so you can substitute our x value (2) for the x
This looks like 15(2) 15 times 2 is 30
so 30 should be your answer
the planning board members for a city are debating whether to build a new municipal parking garage. the parking garage would be funded by the revenue the city collects from its existing parking meters. since the board members insist that the parking garage cannot be funded by raising property taxes, the mean daily parking revenue collected must be greater than $1,200. a random sample of 35 days was selected, and the parking revenue collected in dollars was recorded. based on previous research, the board members assume that the population standard deviation is $196. the board conducts a one-mean hypothesis at the 1% significance level, to test whether the mean daily parking revenue is greater than $1,200.
The required hypothesis for the given data of the problem is
Null hypothesis H₀: μ=$1200 , n = 35
Alternate hypothesis Hₐ : μ > 145
What is tailed test?In statistics, a two-followed test is a technique wherein the basic region of a dissemination is two-sided and tests whether an example is more noteworthy or under a scope of values. It is utilized in invalid speculation endlessly testing for measurable importance.
According to question:We have,
the board members insist that the parking garage cannot be funded by raising property taxes, the mean daily parking revenue collected must be greater than $1,200
So, Null hypothesis H₀: μ=$1200 , n = 35
Then, Alternate hypothesis Hₐ : μ > 145
Standard deviation = $196
Thus, It is right tailed hypothesis.
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mrs.rockwell lost money on an investment at a rate of $4 per day. what is the change in her investment, due to the lost money, after 4 weeks?
The change in her investment, due to the lost money is $112
How to determine the amount of money lost to the investment?From the question, we have the following parameters that can be used in our solution:
Rate of loss = $4 per day
Duration = 4 weeks
From the above parameter, we can calculate the amount of money lost to the investment using:
Amount lost = Duration * Rate of loss
Substitute the known values in the above equation
So, we have the following equation
Amount = 4 weeks * $4
Convert weeks to days
Amount = 28 * $4
Evaluate the quotient
Amount = $112
Hence, the amount is $112
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the residual is defined as the difference between the actual and predicted, or fitted values of the response variable. group of answer choices false true
The Residual is defined as the difference between the actual and predicted, or fitted values of the response variable. This statement is true.
Linear regression is a statistical tool that determines how well a straight line fits a set of paired data. The straight line that best fits that data is called the least squares regression line. This line can be used in a number of ways. One of these uses is to estimate the value of a response variable for a given value of an explanatory variable. Related to this idea is that of a residual.
Residuals are obtained by performing subtraction. All that we must do is to subtract the predicted value of y from the observed value of y for a particular x. The result is called a residual.
The formula for residuals is straightforward:
Residual = observed y – predicted y
It is important to note that the predicted value comes from our regression line. The observed value comes from our data set.
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When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
How many hours for one pipe to fill the pool? How many hours for the other pipe to fill the pool?
One pipe takes 6 hours to fill the pool and the other takes 12 hours.
Pipe A fills 1/x of the pool per hour, and Pipe B fills 1/y of the pool per hour. In other words, A takes x hours to fill the pool and B takes y hours to fill the pool.
Together, they fill 1/x + 1/y of the pool per hour. So, 4 hours times that rate should equal 1 full pool, since together they take 4 hours to fill the pool. That gives you your first equation:
4(1/x + 1/y) = 1
You're also told that if one pipe fills half the pool and the other takes over to fill the rest, it will take 9 hours. We don't know how long Pipe A works, so call that number of hours t. Pipe B must work for 9 - t hours.
So, Pipe A, working for t hours, fills half the pool:
t(1/x) = 1/2
And Pipe B, working for 9 - t hours, fills half the pool:
(9-t)(1/y) = 1/2
You now have a system of three equations (because this is an exceptionally complicated pipe-filling-pool problem):
4(1/x + 1/y) = 1
t(1/x) = 1/2
(9-t)(1/y) = 1/2
Solve for t in that second equation, then plug it into the third equation:
t(1/x) = 1/2
t = x(1/2)
t = x/2
(9 - x/2)(1/y) = 1/2
Now you've got a system of two equations:
4(1/x + 1/y) = 1
(9 - x/2)(1/y) = 1/2
Solve for y in the second equation, then plug that into the first equation:
(9 - x/2)(1/y) = 1/2
(9 - x/2) = y(1/2)
2(9 - x/2) = y
18 - x = y (this is a really nice-looking form of that equation; we'll use it again later)
4(1/x + 1/y) = 1
4(1/x + 1/(18-x)) = 1
4/x + 4/(18-x) = 1
(4(18-x))/(x(18-x)) + (4x)/(x(18-x)) = 1
(4(18-x) + 4x)/(x(18-x)) = 1
4(18-x) + 4x = x(18-x)
72 - 4x + 4x = 18x - x2
72 = 18x - x2
x2 - 18x + 72 = 0
(x - 6)(x - 12) = 0
x - 6 = 0 OR x - 12 = 0
x = 6 OR x = 12
So, Pipe A takes either x = 6 or x = 12 hours to fill the pool alone.
When Pipe A takes 6 hours to fill the pool, Pipe B takes 12. When Pipe A takes 12 hours to fill the pool, Pipe B takes 6.
These cases are equivalent, since the original problem makes no distinction between the pipes.
Hence, one pipe takes 6 hours to fill the pool and the other takes 12 hours.
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Morgan and her children went into a grocery store and she bought $10
worth of peaches and mangos. Each peach costs $1 and each mango
costs $2. She bought a total of 8 peaches and mangos altogether.
Graphically solve a system of equations in order to determine the
number of peaches, a, and the number of mangos, y, that Morgan
bought.
Answer:
The number of peaches and the number of mangos that Savannah bought
are 4 and 10 respectively.
The variable use to write the equation is x and it is the number of peaches
Savannah and her children bought
let
the number of peaches Savannah and her children bought = x
Therefore
the number of mangoes Savannah and her children bought = x + 6
The total worth of what they bought = $22
Therefore,
1.75x + 1.50(x + 6) = 22
1.75x + 1.50x + 9 = 22
3.25x + 9 = 22
3.25x = 22 - 9
3.25x = 13
x = 13 / 3.25
x = 4
Therefore,
number of peaches bought = 4
number of mangoes bought = 4 + 6 = 10
Step-by-step explanation:
Answer: 6 Peaches and 2 Mangos
Step-by-step explanation: If one peach is worth $1 and one mango is worth $2, to get $10 used you need to buy 6 peaches and 2 mangos since 2 + 2 = 4 and 6 + 4 = 10
Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)
It takes Bob 125.0633 seconds to cover the entire track.
Let the time taken by Bob to cover the track be x sec
Let the distance of the track be y m
Akira covers the whole track in 95 seconds
hence, his speed is y/95 m/s
Similarly, Bob's speed is y/x m/s
He has traveled to the Easternmost point in 22 seconds. Hence to meet Akira, he has to run for 4 more seconds.
In that time he will cover a distance of 4y/95 m
Similarly, in 26 seconds, Bob will cover
26 y/x m/s
Now Akira has started from the Northernmost point, and we all know that the distance between the Easternmost and Northernmost points of the track will be 1/4th of the whole track length.
Hence,
4y/95 + 26y/x = y/4
or, y(4/95 + 26/x) = y/4
or, 4/95 + 26/x = 1/4
or, (4x + 2470)/95x = 1/4
or, 4x + 2470 = 95x/4
or, 16x + 9880 = 95x
or, 79x = 9880
or, x = 125.0633 seconds
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help me for math..........
Answer:
A) -20
Step-by-step explanation:
[tex]4y(4y-4)-4(-4y+5+4y^2)\\\\16y^2-16y + 16y-20-16y^2\\\\-20\\[/tex]
write a different expression to model sean's order.eveluate not expressions to check that they are equivlent .How many cupcakes does sean have
The expression that represents the orders is 12 * (5 + 3.5)
Another expression is 12 * 8.5 The total order is 102How to determine the expression for Sean's purchase?From the question, we have the following parameters that can be used in our computation:
Number of cupcakes in a box = 12Number of boxes ordered for his sister’s graduation party = 5Number of boxes ordered for the Variety Show party = 3.5The above parameters mean that:
Expression for Sean's purchase = Number of cupcakes in a box * (Number of boxes ordered for his sister’s graduation party + Number of boxes ordered for the Variety Show party)
Substitute the known values in the above equation, so, we have the following representation
Expression for Sean's purchase = 12 * (5 + 3.5)
Hence, the expression is 12 * (5 + 3.5)
A different expressionIn (a), we have
Expression = 12 * (5 + 3.5)
Evaluate the sum
Expression = 12 * 8.5
Evaluate
Expression = 102
This means that the total number of box is 102
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Complete question
A baker packages 12 cupcakes to a box. Sean orders 5 boxes for his sister’s graduation party and 3.5 boxes for the Variety Show party. Write an expression that shows the calculations you could use to find the number of cupcakes Sean orders.
Write a different expression to model sean's order.eveluate not expressions to check that they are equivlent .How many cupcakes does sean have
An investment of $9,875 earns 4. 8% interest compounded monthly over 12 years. Approximately how much interest is earned on the investment?.
Using the compound interest formula, we know that $7,672 is the interest on investments earned.
What is compound interest?The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors.
The resulting value is subsequently deducted from the loan's entire original amount.
So, interest earned on investment:
A = 9,875 (1 + 0.048/12)^ 12(12)
A = $ 15,547
Interest on investments is the money received:
= $ 15,547 - $ 9,875
= $ 7,672
Therefore, using the compound interest formula, we know that $7,672 is the interest on investments earned.
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Complete question:
An investment of $9,875 earns 4.8% interest compounded monthly over 12 years. approximately how much interest is earned on the investment?
a. $4,740
b. $7,458
c. $7,672
d. $17,567
In cooking class, Lupita and Jacob each make a mixture of basil and oregano. Lupita uses 2 tsp basil for every 3 tsp oregano. Jacob uses 4 tsp basil for every 5 tsp oregano. Lupita says the two mixtures will taste the same. Jacob says his will have a stronger basil taste than Lupita’s. Who is correct? Explain.
Using ratio and proportions, Jacob has mixture with stronger basil taste
Ratios and ProportionRatio can be defined as a comparison between two or more numbers that shows their sizes in relation to each other. A ratio often compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Proportion can be defined as equality of two ratios. Two equivalent ratios are always in proportion. Proportion is an equation or statement that shows that the two ratios or fractions are equivalent.
In this case, we can compare the ratio and determine which will have a stronger basil taste.
Lupita mixed 2 tsp of basil for 3tsp of oregano
The ratio of basil to oregano = 2/3 = 0.67
Jacob mixed 4 tsp of basil for 5 tsp of oregano
The ratio of basil to oregano = 4/5 = 0.8
Comparing the ratios, Jacob ratio is higher compared to Lupita and makes Jacob have the strong basil taste.
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on your desk, there is a very special die with a prime number p of faces, and you throw this die once. show that no two events a and b can be independent unless either a or b is the whole sample space or the empty set.
We have proven that no two events a and b can be independent unless either a or b is the whole sample space or the empty set below.
A sample space can be defined as the set of all possible outcomes of any experiment.
We are already aware that the outcomes of this die are going to be (1,2,3,..p). If we have a pair of proper events A, B which are independent, this would mean that = A∩B={∅} (i)
This is a contradiction. So, now we suppose that = A∩B=C, for some proper event C (ii)
Using the values of (i) and (ii), we get -
= |C|p=P(A∩B)=P(A)P(B)=|A||B|p2.
= p|C|=|A||B|.
From this, we understand that neither A nor B are going to be full spaces and hence, no two events a and b are independent and 0<|A|<p and 0<|B|<p. Since |C| is also going to be less than 0 and p is prime, p divides either |A| or |B|. if p was not prime (say, p=4), then you would only need the factors of p to divide either |A|,|B|, so, it becomes necessary for p to be a prime number. Hence, proved.
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8(t+2) -3(t-4=6(t-7)+8
Answer: T-62
Step-by-step explanation: i think this is correct
The solution is, the value we get, t = 62.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
8(t+2) -3(t-4)=6(t-7)+8
or, 8t + 16 -3t +12 = 6t - 42 +8
or, 5t + 28 = 6t - 34
or, t = 62
Hence, The solution is, the value we get, t = 62.
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Given: Triangle ABC is isosceles with A as the vertex angle and segment AD bisects segment BC,
Prove: Segment AD bisects angle BAC.
Answer:
PAy Attention Triangle
Step-by-step explanation:
Triangle ABC is isolated True
my question is how do you write a simplified expression that is equivalent to 7/8+3/8x-1/4y+3/4y-1/2?
Answer:
1/8(3x+4y+3)
Step-by-step explanation:
can someone help me really quick
(please Explain how you know this is correct)
The answer is $12.50
You can see on the graph that if the weight is 20 pounds, it will cost $10. We are looking for how much it will cost to ship a 25 pound package. It can’t be $20.00 either.
hope this helps!
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