Answer:
Statement 1 is true; Statement 2 is false.
Step-by-step explanation:
Statement 1:
√12 - √8 = a
Let's use the given value of √12 + √8 ,that is, 4/ a.
If we multiply both the expressions such that their Left Hand Sides get multiplies together and Right Hand Sides together:
=> (√12- √8)(√12 + √8) = a × 4/a
On the LHS,
identity used:
(a-b)(a+b) = a²-b²
On the RHS:
a gets canceled due to its presence in both the numerator as well as the denominator.
=> 12 - 8 = 4
=> 4 = 4
That's it!
We got LHS = RHS, that approves the existence of the given statement.
___________________
Statement 2:
"a + √b is called the rationalizing factor of c + √d if their product is 1"
That's not entirely right!
The correct statement would be:
" a + √b is called the rationalizing factor of c + √d if their product is a rational number ."
Since, rationalizing has got nothing to do with 1, (1 is just another rational number), even if we get 2 by their multiplication, it will be called rationalizing as long as we're getting a rational number.
___________________
Answer:
Hence, I'd say:
Statement 1 is correct but Statement 2 isn't.
That's the third option.
Why is it useful to have different forms of linear equations?
Linear equation is the equation of a straight line.
Forms of a linear equation
The forms of a linear equation are:
Slope intercept form - [tex]\mathbf{y = mx + b}[/tex].Point slope form - [tex]\mathbf{y - y_1 = m (x - x_1)}[/tex].Standard form - [tex]\mathbf{Ax +Bx = C}[/tex].Slope intercept form
From the slope intercept form, one can easily deduce the slope and the y-intercept of the linear equation
Point slope form
From the point-slope form, one can easily deduce the slope and the points of the graph of the linear equation
Standard form
From the standard form, the values of x and y can be easily calculated.
Hence, the usefulness of having different forms of linear equation is that they all serve different purposes, even through they represent the same graph.
Read more about linear equations at:
https://brainly.com/question/17895632
Quadrilateral RSTU is a parallelogram. What must be the value of x?
2
4
5
10
Answer:
X=5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have. (Hint: one is the other simplified)
Answer:
(N)0.05 + (17-N)0.1 = M; M = amount of money I have.
Or 1.7-0.05N = M.
Step-by-step explanation:
Which table of ordered pairs represents a proportional relationship?
plss help!
Need help please with the step by step explanation
Answer:
exponential decay (0,8)
Step-by-step explanation:
the width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer:
Width: 160
Length: 80
Step-by-step explanation:
Width = 2x and length = x
X + 0.5x + 2x - 0.4x = 248
3.1x = 248
X = 248/3.1
X = 80
Width = (2)(80) and length = 80
Which is an exponential decay function
Answer:
Letter A is your answer
Step-by-step explanation:
mark me brainliest
Use the figure to find the radius.
Mrs. Sprott is planting a square garden in her backyard. The garden will
measure x feet on each side. Which function will give F(x), the area in
square feet of the garden?
Answer:
The answer the above question is f(x) = x²
Answer:
fdybg
gyani
2574387y
sngsrh
funddhhtffdsdnjjj
2. Use factoring to determine the x-intercepts and vertex of the quadratic function
y = 2x2 + 5x -3
(answer plsss)
Step-by-step explanation:
I solved for the x hope it's correct
Make a histogram, using a bin width of ten, to display the bowling scores for these 31 players: 87, 104, 79, 94, 117, 82, 72, 116, 105, 95, 88, 93, 109, 119, 75, 103, 112, 97, 73, 85, 91, 86, 102, 99, 106, 84, 98, 83, 81, 96, 92.
Step-by-step explanation:
Using R, I used the following code to create a histogram:
bowling.scores <- c(87, 104, 79, 94, 117, 82, 72, 116, 105, 95, 88, 93, 109, 119, 75,
103, 112, 97, 73, 85, 91, 86, 102, 99, 106, 84, 98, 83, 81, 96, 92)
data.frame(bowling.scores)
ggplot(data.frame(bowling.scores), aes(x=bowling.scores)) +
xlim(c(70, 120)) +
scale_y_continuous(breaks = seq(0, 10, by=1), "Frequency") +
geom_histogram(breaks=seq(70, 120, by=10), color="black", fill="grey60") +
labs(title="Histogram of Bowling Scores", x="Bowling Scores", y="Frequency")
Compare the value of the following expression with zero. 5a^3b^2/a+b, where a<0, b<0
Answer:
The given expression will be greater than zero.
Step-by-step explanation:
If a < 0 and b < 0, then 5a^3 is < 0 (5a^3) is negative;
but b^2 is > 0.
Then (5a^3)*(b^2) < 0
and if we divide this quantity by a + b (which is negative), the end result will be > 0.
Because of a problem in the program, the timer in a video player did not begin counting until the video had been playing for several seconds. The player began counting at 0 seconds even though the video had already played 190 frames The video plays 252525 frames per second. How many frames had the video already played when the time was equal to -3 3/5
Answer:
105 frames
Step-by-step explanation:
Given that 25 frames are played per second
25 frames= 1 sec
The video already played 3 and 2/5 seconds before the player started to count 0
Write 3 and 2/5 seconds as an improper fraction
=(5*3)+2 / 5 = 17/5 seconds
Multiply by 25 frames
17/5 *25 =85 frames
So according to the video counter,after 17/5 seconds,it should count 85 frames.However,at 0 seconds,it indicated a count of 190 frames.Thus,to get the number of frames that were already in count you subtract 85 frames from the 190 frames.
190-85=105 frames.
Step-by-step explanation:
Match the place value of each digit in 25.678.
Value: 5
:
Match the items.
a. Ones
b. Thousandths
C. Tens
d. Tenths
e. Hundredths
Match the place value of each digit in 25.678.
Match the place value of each digit in 25.678.Value: 5
5.000= ones......
Answer:
Ones
Step-by-step explanation:
In order the numbers are:
Tens
Ones
Tenths
Hundredths
Thousandths
EVALUATE: 10x – 2y3 (if x = 5 and y = 2)
Answer:
10*(5) - 2*(2)^3
= 50 - 2*8
= 50 - 16
=34
Answer:
Step-by-step explanation:
với x=5 và y=2
phương trinh trở th a
10* 5 - 2 * 2^ 3
=50 - 2*8
=50 - 16
=34
PLS HELP AND GET IT RIGHT IM ACTUALLY FAILING AND DONT WANNA FAIL MORE ITS PYTHAGOREAN THEOREM
Answer:
A = 10
Step-by-step explanation:
Use formula: c = sqrt of a^2 + b^2
1) Put in known numbers:
26 = sqrt of a^2 + 24^2
But instead of adding you would subtract and rearrange the formula bc you already have C:
2) Solve:
A = sqrt of 26^2 - 24^2
A = sqrt of 676 - 576
A = sqrt of 100
A = 10
Sqrt: square root
Therefore, out answer… I hope this helps! Best of Luck! (\^ v ^/)
1.2 m
1.2 m
Susie is 1.13 metres tall
She has a play tent in the shape of a triangular prism.
The diagram shows the front view of the tent.
The front of the tent has been drawn to scale below.
a) Complete the scale drawing.
1.5m
Not drawn accurately
b) Can Susie stand up in the
middle of the tent?
1.5m
Scale: 1 cm represents 60 cm
Split the triangle into 2 right in the middle so you have 2 identical right triangles. The base on one would be half the base of the triangle shown so, the base would be: 1.5/2 = 0.75 m.
Now using the Pythagorean theorem you can find the height:
Height - sqrt(1.2^2 - 0.75^2)
Height = sqrt(1.44 - 0.5625)
Height = sqrt(0.8775)
Height = 0.93675 meters
The height of the tent is smaller than the height of Suzie so she cannot stand up.
Evelyn earned a score of 86 on Exam A that had a mean of 71 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Evelyn score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
Answer:
580
Step-by-step explanation:
Assuming that the answer should be in terms of z scores, we can calculate the z score as
z = (observed value - mean)/(standard deviation)
For the first exam, the observed value is 86, the mean is 71, and the standard deviation is 20. The z score fot that exam is
z = (86-71)/20 = 0.75
Then, for the second exam, Evelyn has to do equivalently well, so the z score must be the same. Therefore, we have
0.75 = (observed score - 550)/40
multiply both sides by 40 to remove a denominator
0.75 * 40 = observed score - 550
add 550 to both sides to isolate the observed score
0.75 * 40 + 550 = observed score = 580
Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data.
A 3-row table with 10 columns. The first row is labeled essay rank with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The second row is labeled essay score with entries 9.7, 9.5, 9.5, 9.0, 8.9, 8.9, 8.5, 8.4, 8.2, 7.0. The third row is labeled word count with entries 324, 352, 337, 318, 299, 304, 290, 291, 278, 250.
How does the word count of an essay relate to its score in the contest?
Word count tends to decrease as the score decreases.
Word count tends to increase as the score decreases.
Word count tends to remain constant as the score decreases.
Word count has no apparent relationship to the score of the essay.
Unmark this question
Answer:
The word count tend to decrease as the score decreases
Step-by-step explanation:
The 3-row table is presented as follows;
[tex]\begin{array}{ccc}Essay \ Rank&Essay \ Score&Word \ Count\\1&9.7&324\\2&9.5&352\\3&9.5&337\\4&9.0&318\\5&8.9&299\\6&8.9&304\\7&8.5&290\\8&8.4&291\\9&8.2&278\\10&7.0&250\end{array}[/tex]
The relationship between the values on the Word Count column and the values on the Essay Score column is that as the Essay Score decreases from the top down to the last row, the values on the Word Count generally decreases in the same manner (top down decrease)
Therefore, the Word Count decreases as the Essay Score decreases.
AB←→||CD←→. Find the measure of ∠BFG.
Answer:
Value of ∠ BFG = 135°
Step-by-step explanation:
Given:
AB || CD
∠ AFG = (3x + 15)°
∠ FGD = (5x - 5)°
Find:
∠ BFG
Computation:
We know that;
∠ AFG = ∠ FGD
3x + 15 = 5x - 5
3x - 5x = - 5 - 15
- 2x = - 20
2x = 20
x = 10
Value of ∠ AFG = 3x + 15
Value of ∠ AFG = 3(10) + 15
Value of ∠ AFG = 45°
∠ BFG = 180° - Value of ∠ AFG
∠ BFG = 180° - 45°
∠ BFG = 135°
Value of ∠ BFG = 135°
The point M(-6, -4) is translated 2 units right. What are the coordinates of the resulting point, M′?
Answer:
(-4, -4)
Step-by-step explanation:
On a 2D graph, moving to the right means going up the x axis, to the left means down the x axis, up means up the y axis, and down means down the y axis.
The point is translated 2 units to the right. This means that it is going up the x axis by two units. As it is going up, we can say that it is increasing. Therefore, on a coordinate (x,y), going up the x axis means we add to the x value. For the point (-6, -4), we add 2 to the x value, or -6, to get -6+2 = -4 as our new x value.
Our new end value is (-4, -4)
HELPPPPPPPPP!!!!!!!!!!!!!!!!
Answer:
they are not similar. their one angle is only equal
4(2-3-1)+-5(6)--7to the power of 2
[tex]\\ \sf\longmapsto 4(2 - 3 - 1) + ( - 5)(6) - 7 {}^{2} \\ \\ \longmapsto 4( - 2) + ( - 30) - 7 {}^{2} \\ \\ \sf\longmapsto - 8 - 30 - 49 \\ \\ \sf\longmapsto - 38 - 49 \\ \\ \sf\longmapsto - 87[/tex]
what is the diameter of the circle shown?
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
[tex]a^2+b^2=c^2\\36+36 = c^2\\72=c^2\\c = 6\sqrt{2}[/tex]
Answer:
[tex]6\sqrt{2}[/tex] in
Step-by-step explanation:
this triangle is a right isosceles triangle. this means it is also a 45- 45- 90 triangle.
there is a special relation between the sides of a 45 45 90 triangle :
if the legs are 'x' then the hypotenuse is '[tex]x\sqrt{2}[/tex]'
so in this case, the legs are 6 in. the hypotenuse (or diameter of the circle) is
[tex]6\sqrt{2}[/tex]
If f(x) = [x]-5, what is f(8.6)?
O 3
O 4
O 8
O 9
Answer:
if the question wants you to round. the answer is 4.
Step-by-step explanation:
f(x)=[x]-5
where x= 8.6
substitute 8.6 for x and you have 8.6-5= 3.6= 4
Out of 120 students in exam, 2/3 of them passed. How many students passed?
Out of 120 students in exam, 2/3 of them passed. How many students passed?
now,
no of students passed = 2/3×120
= 0.66×120
=80...
therefore 80 students were passed....
Answer:
80
Step-by-step explanation:
The frequency table represents the job status of a number of high school students. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for job with entries 12, 38, 50. The third column is labeled not looking for a job with entries 28, 72, 100. The fourth column is labeled total with entries 40, 110, 150. Which shows the conditional relative frequency table by column? A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for a job with entries 0.3, nearly equal to 0.33, 1.0. The third column is labeled not looking for job with entries 0.7, nearly equal to 0.65, 1.0. the fourth column is labeled total with entries nearly equal to 0.27, nearly equal to 0.73, 1.0. A 4-column table with 3 rows titled job status. The first column is blank with entries currently employed, not currently employed, total. The second column is labeled Looking for a job with entries 0.12, 0.38, 050. The third column is labeled not looking for a job with entries 0.28, 0.72, 1.00. The fourth column is labeled total with entries 0.4, 1.1, 1.5. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for a job with entries 0.24, 0.76, 1.0. The third column is labeled not looking for a job with entries 0.28, 0.72, 1.0. The fourth column is labeled total with entries nearly equal to 0.27, nearly equal to 0.73, 1.0. A 4-column table with 3 rows titled job status. The first column has no label with entries currently employed, not currently employed, total. The second column is labeled looking for job with entries 0.08, nearly equal to 0.25, nearly equal to 0.33. The third column is labeled not looking for a job with entries nearly equal to 0.19, 0.48, nearly equal to 0.67. The f
Answer:
[tex]\begin{array}{cccc}{} & {Looking\ for\ job} & {Not\ looking} & {Total} & {Employed} & {0.24} & {0.28} & {0.27} & {Not\ Employed} & {0.76} & {0.72} & {0.73}& {Total} & {1} & {1} & {1} \ \end{array}[/tex]
Step-by-step explanation:
The question is not properly formatted (see attachment for the frequency table and the options)
Required
The conditional relative frequency table by column
We have:
[tex]\begin{array}{cccc}{} & {Looking\ for\ job} & {Not\ looking} & {Total} & {Employed} & {12} & {28} & {40} & {Not\ Employed} & {38} & {72} & {110}& {Total} & {50} & {100} & {150} \ \end{array}[/tex]
To get the conditional frequency by column, we simply divide each cell by the corresponding total value (on the last row)
So, we have:
[tex]\begin{array}{cccc}{} & {Looking\ for\ job} & {Not\ looking} & {Total} & {Employed} & {12/50} & {28/100} & {40/150} & {Not\ Employed} & {38/50} & {72/100} & {110/150}& {Total} & {50/50} & {100/100} & {150/150} \ \end{array}[/tex]
[tex]\begin{array}{cccc}{} & {Looking\ for\ job} & {Not\ looking} & {Total} & {Employed} & {0.24} & {0.28} & {0.27} & {Not\ Employed} & {0.76} & {0.72} & {0.73}& {Total} & {1} & {1} & {1} \ \end{array}[/tex]
A line with slope 3 intersects a line with slope 5 at the point (10, 15). What is the distance between the x-intercepts of these two lines?
Answer:
2
y = 3x-15
y=5x-35
x1=5
x2=7
distance between = 7-5 = 2
Step-by-step explanation:
Tìm x, biết:
2x.(x-1)-3.(x^2-4x)+ x.(x+2)= -3x
Answer:
X=0
Step-by-step explanation:
One angle on the base of an isosceles triangle is 30°. What is the measure of its vertical angle?
Answer:
120 degrees
Step-by-step explanation:
vertical angle of isoceles = 180 - 2(base angles) = 180 - 2(30) = 120
Answer:
isosceles triangle means both angle or sides equal so in this way
unknown angle + 30 + 30 = 180°
unknown angle+60=180
so unknown angle=120°
which is vertical angle
