help me please :)
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Answer:
[tex]x = \frac{5}{3}[/tex]
Step-by-step explanation:
The expression under the square root is [tex]\sqrt{4x^2 - 20x + 25}[/tex]
This is equivalent of [tex](2x-5)^2[/tex]
We can check this by using the formula
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]
where [tex]\\a = 2x so a^2 = (2x)^2 = 4x^2\\\\b = -5 so b^2 = (-5)^2 = 25\\\\2ab = (2)(2x)(-5) = -20x\\[/tex]
So
[tex]\sqrt{4x^2 - 20x + 25} = \sqrt{(2x-5)^2}[/tex] which is [tex](2x-5)[/tex]
(The square root of the square of an expression is the expression itself)
So that gives us
[tex]2x - 5 = 5-2x\\[/tex]
Collecting like terms on each side gives us
[tex]2x + 2x = 5 -(-5)\\\\4x = 10\\\\x = 10/4 = 5/3[/tex]
Select the correct answer.
Which equation is true for the value b= 10?
O A. 2(b + 4) = 16
OB.
2(b + 2) = 40
OC. 316 - 2) = 24
OD. 2(8 + b) = 42
O E. 3(b - 4) = 20
Answer:
C. 3(b - 2) = 24Step-by-step explanation:
b = 10
Substitute b in every equation below and compare the results
A. 2(b + 4) = 16
2(10 + 4) = 2(14) = 28 ≠ 16, incorrectB. 2(b + 2) = 40
2(10 + 2) = 2(12) = 24 ≠ 40, incorrectC. 3(b - 2) = 24
3(10 - 2) = 3(8) = 24, correctD. 2(8 + b) = 42
2(8 + 10) = 2(18) = 36 ≠ 42, incorrectE. 3(b - 4) = 20
3(10 - 4) = 3(6) = 18 ≠ 20, incorrectAnswer:
C. 3(b - 2) = 24..
2+5xi-3y=14+3x-5yi.Find x and y
Question:
[tex]5x-3y=14[/tex]
[tex]3x-5y=2[/tex]
Find x and y
Answer:
[tex]x = 4[/tex]
[tex]y =2[/tex]
Step-by-step explanation:
Given
[tex]5x-3y=14[/tex] -- (1)
[tex]3x-5y=2[/tex] -- (2)
Required
Find x and y
We'll solve this using elimination method.
Multiply (1) by 3 and (2) by 5 to eliminate x
([tex]5x-3y=14[/tex]) * 3
([tex]3x-5y=2[/tex]) * 5
-------------------------------
[tex]15x - 9y = 42[/tex]
[tex]15x - 25y =10[/tex]
Subtract
[tex]15x - 9y = 42[/tex]
- ([tex]15x - 25y =10[/tex])
-----------------------
[tex]15x - 15x - 9y + 25y = 42 - 10[/tex]
[tex]- 9y + 25y = 42 - 10[/tex]
[tex]16y = 32[/tex]
Make y the subject
[tex]y = \frac{32}{16}[/tex]
[tex]y =2[/tex]
Substitute 2 for y in [tex]5x-3y=14[/tex]
[tex]5x - 3 * 2 = 14[/tex]
[tex]5x - 6 = 14[/tex]
Collect Like Terms
[tex]5x = 14+6[/tex]
[tex]5x = 20[/tex]
Make x the subject
[tex]x = \frac{20}{5}[/tex]
[tex]x = 4[/tex]
An item has increased by
23% to £58.
What was the original
price?
Answer:
The answer is 44.66
Step-by-step explanation:
Multiply 58 by 0.23. This will give you 13.34. Next, you subtract this from 58 to get your original price.
Find the indicated term of each sequence by repeatedly multiplying the first term by the common ratio.
Enter your answer to 5 decimal places if necessary. Use a calculator.
A
-50, 35, -24.5,..;5th term
The 5th term of the sequence is 70
Answer:
Step-by-step explanation:
The first term here is -50 and the common ratio is 0.70. Note that the second term is 0.70(50) = 35.
The formula a(n) = a(0)*r^(n -1) becomes a(n) = -50*0.70^(n -1), and so
the 5th term is a(5) = -50*0.70^4 = -12.005
Jermaine and Monica will usually both run 4.5 miles each time they go running. This month, Jermaine ran an additional 27 miles. Which answer choice shows an expression that represents the total distance Jermaine and Monica ran this month if j = the number of times that Jermaine ran and m = the number of times that Monica ran?
Answer:
4.5 (j + m) + 27
Step-by-step explanation:
how many HOURS are in d days and h hours?!
Answer:
24
Step-by-step explanation:
because its 24 gkrjkkmn lol
Which ordered pair is on the graph of 7x - y = 2?
Limit as x approaches 0 of (sin^2x)/x
Answer:
0Step-by-step explanation:
Given the expression
[tex]\lim_{x \to \ 0} \frac{sin^2x}{x}[/tex]
Substitute the value of x in the function
[tex]= \frac{sin ^2(0)}{0}\\= 0/0 (indeterminate) \\[/tex]
Apply l'hospital rule
[tex]\lim_{x \to \ 0} \frac{d/dx(sin^2x)}{d/dx(x)} \\= \lim_{x \to \ 0} \frac{(2sinxcosx)}{1} \\[/tex]
Substitute the value of x
= 2 sin(0)cos(0)
= 2 * 0 * 1
= 0
Hence the limit of the function is 0
An aircraft seam requires 20 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 16% of all seams need reworking, what is the probability that a rivet is defective
Answer:
probability that a rivet is defective is 0.00868
Step-by-step explanation:
given data
rivets = 20
all seam need reworking P = 16% = 0.16
solution
we consider here probability of a defective rivet = p
and 0.16 = P [Seam needs reworking) = P (at least one rivet in the seam is defective)
so that for non-defective = 1 - P [all the rivets are non-defective]
and that will be here as = 1 - P [rivet 1 is non-defective, rivet 2 is non-defective, rivet 3 is non-defective,...............,rivet 20 is non-defective]
= [tex]1 - (p})^{20}[/tex] ....................1
so
1-0.16 = [tex]1 - (p})^{20}[/tex]
0.84 = [tex]1 - (p})^{20}[/tex]
[tex]0.84^{\frac{1}{20}}[/tex] = 1 - p
solve it we get
p = 0.00868
so, probability that a rivet is defective is 0.00868
Sana bought a dress for $32.99 and two purses. The total cost for the three items was $57.97. What was the cost for one purse?
Answer:
$12.49
Step-by-step explanation:
cost of two purses = $57.97 - cost of dress = $57.97 - $32.99 = $24.98
cost of one purse = $24.98 ÷ 2 = $12.49
Sketch and shade the region in the xy-plane defined by the equation or inequalities.
|x| < 7 and |y| < 3 g
Answer:
attached below is the solution
Step-by-step explanation:
|x| < 7
= -7 < x < 7
| y | < 3
= -3< y < 3
attached below is the shaded region in the xy-plane
brainly the following stem-and-leaf plot shows the on-record attendance for regional charity drive meetings
What is the mode?
A.)48
B.)84
C.)70
D.)66
Answer:
what does the stem-and-leaf plot look like?
What is the slope of the line?
Answer:
2
Step-by-step explanation:
Answer:
First the line is positive so you can eliminate all negative choices for slope
Now start from a random point that lands on the graph
Now it can’t be 1 becuase it has am extra box but that line isn’t on a point
Now 1/2 it can’t be becuase if you rise 1 and go right 2 it’ll not land ona. Point
But for 2, you rise up 2 and right 1 and you land on a point on the graph so the final answer is 2
what is the answer? ;3
Kiran’s backpack weighs 3 pounds less than Clare’s backpack. Clare’s backpack weighs 14 pounds. How much does Kiran’s backpack weigh?
Answer:
well I have this question too if you are doing amplify math so I got the soulutions x+3=14 and x=14-3.
Step-by-step explanation:
And for the x= part its x=11
Question Help
9
s shown by the formula F= C+32. At what temperature will a Fahrenheit thermometer read the same as a Celsius thermometer
X
Answer:
It will read the same at F = -40.
Step-by-step explanation:
The relation between fahrenheit and celsius is given by the following equation:
[tex]C = \frac{5(F-32)}{9}[/tex]
At what temperature will a Fahrenheit thermometer read the same as a Celsius thermometer?
This is F for C = F. So
[tex]C = \frac{5(F-32)}{9}[/tex]
[tex]F = \frac{5(F-32)}{9}[/tex]
[tex]9F = 5F - 160[/tex]
[tex]4F = -160[/tex]
[tex]F = -\frac{160}{4}[/tex]
[tex]F = -40[/tex]
It will read the same at F = -40.
An integer between -1.6 and -0.4
b) Calculate the area of the trapezium
5.2cm
Not drawn accurately
6cm
4.5cm
10.8cm
Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}} : [/tex]
Height ( h ) = 4.5 cmBase 1 ( b ) = 5.2 cmBase 2 ( b ) = 10.8 cm[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
Area of the given trapezium[tex] \underline{ \underline{ \text{Solution}}} : [/tex]
[tex] \boxed{ \sf{Area \: of \: a \: trapezium = \frac{1}{2} h \: (b_{1} + b_{2})}}[/tex]
Plug the known values and then simplify !
⟶ [tex] \sf{ \frac{1}{2} \times 4.5 \times (5.2 + 10.8)}[/tex]
⟶ [tex] \tt{ \frac{1}{2} \times 4.5 \times 16}[/tex]
⟶ [tex] \tt{36 \: {cm}^{2} }[/tex]
[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \bold{ \tt{36 \: {cm}^{2} }}}}}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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Can someone please help me write an equation for this graph? This is a different one.
Answer:
The equation of a line passing through points [tex](x_1,y_1)[/tex]and [tex](y_1,y_2)[/tex] is given by:
[tex]y-y_1 = \frac{(y_2-y_1)}{x_2-x_1}(x-x_1)[/tex]
According to question, the passing points of the line are (1,1) and (3,-3). So, its equation is given by:
[tex]y-1 = \frac{-3-1}{3-1} (x-1) \\or, y-1 = \frac{-4}{2}(x-1)\\or, 2y-2 = -4x+4\\or, 4x + 2y = 2+4\\or, 4x+2y = 6\\or, 2x+y = 3 is the required equation.[/tex]
PLEASE HELP!
|−1.25| + |2.5|
Explanation
-1.25+2.5=1.25
Answer:
1.25 is the answer .......
Step-by-step explanation:
hello will u be friend with me
CAN SOMEONE HELP WALLAHI THIS IS SO HARDDDDDD
Answer:
3[tex]\sqrt{5}[/tex]
The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1300 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The value of the test statistic is t = 2.19.
Step-by-step explanation:
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Sample of 1300 voters:
This means that [tex]n = 1300[/tex]
Found that 45% of the residents favored construction.
This means that [tex]X = 0.45[/tex]
A political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%.
This means that [tex]\mu = 0.42[/tex], and by the Central Limit Theorem:
[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.42*0.58}{1300}} = 0.0137[/tex]
So, the test statistic is:
[tex]t = \frac{X - \mu}{s}[/tex]
[tex]t = \frac{0.45 - 0.42}{0.0137}[/tex]
[tex]t = 2.19[/tex]
The value of the test statistic is t = 2.19.
4. The ratio of the measures of the three angles in a triangle is 7:8:5, what is the
measure of the smallest angle?
Your answer
Step-by-step explanation:
let the angles be ' 7x, 8x and 5x'
as we know, the sum of all the angles of a triangle is 180 degree, so,
7x + 8x + 5x = 180
20 = 180
x = 180/2
x = 90 degrees
7x = 7 × 90 = 630 degree
8x = 8 × 90 = 720 degrees
5x = 5 × 90 = 540 degrees
therefore, 5x is the smallest degrees
javier is shopping for school supplies . he is buying 3 of the same notebooks and 2 pens that cost $1.75 each. His total, before tax, is $12.47. which equation below could be used to determine the cost of each notebook.
A. 3(1.75)+2x=12.47
B.3x+2(1.75)=12.47
C. 3(12.47)+2(1.75)+x
D. 3(1.75)+2(12.47)=x
PLEASE HELP
Answer:
3notebooks
2pens
the pens are 1.75 each
total is 12.47
i wouldnt use any of these
12.47-(2x1.75)=? then divide that by three and you get each notebook
but
c...
In a class of 26 students, 11 are female and 10 have an A in the class. There are 2 students who are female and have an A in the class. What is the probability that a student is a female given that they have an A?
The probability that a student is a female given that they have an A is 0.2
How to determine the probability?The given parameters are:
Female = 11
A= 10
Female and A = 2
The probability is calculated using:
P(Female given A) = P(female and A)/P(A)
This gives
P(Female given A) = 2/10
Simplify
P(Female given A) = 0.2
Hence, the probability that a student is a female given that they have an A is 0.2
Read more about probability at:
https://brainly.com/question/251701
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__+ (-4) = -1 what is the missing number
Answer:
3
Step-by-step explanation:
_+(-4) = -1
_-4 = -1
_ = 3
? x 3= 192 answer the question
Answer: 64
Step-by-step explanation:
i simply divided 192 by 3, because it's just the opposite of multiplying. it's a simple and easy way to get the missing number! :)
192 / 3 = 64
Answer:
n=64
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Cameron is a member of a national gardening club. She asked 200 of her fellow members whether they use compost to fertilize their plants, and
45% responded favorably.
What is the 90% confidence interval for the true proportion of club members who use compost?
Answer:
0.45 and 0.5
Step-by-step explanation:
plato/edmentum
The 90% confidence interval for the true proportion of club members who use compost is given as (0.4, 0.507)
What is Confidence Interval?
This refers to the probability of a parameter falling across a set of values around the mean.
To find the 90% confidence interval,
Probability= 45%= 0.45
Level of significance= 90%
1-0.90
= 0.10
[tex]z\alpha /2 = z(0.1/2) = 0.05[/tex]
The value of 0.05
P0.05= 1.645
P ± 1.645 x [tex]\sqrt{P0-p/n}[/tex]
0.45 ± 1.645 * [tex]\sqrt{0.48 (1-0.45)/200}[/tex]
0.45 ± 1.645 * 0.035178
0.45 ± 0.0578
0.45 - 0.0578, 0.45 + 0.0578
(0.4, 0.507)
Read more about confidence intervals here:
https://brainly.com/question/15712887
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Select all the correct locations on the map.
Identify the three trade routes used during the Hellenistic era.
SCYTHIA
EUROPE
SINAE
AFRICA
ARABIA
INDIA
—
PLS HELP IM BEGGING 39 POINT
Answer:
The Correct answers are, the top two (a and d), and the very bottom one (c).
Step-by-step explanation:
I got the answers right in my test!
Have a great day!!
