Answer:
[tex]{ \bf{a).}} \\ { \tt{( \sqrt{6} + \sqrt{3} )( \sqrt{6} - \sqrt{3}) }} \\ { \tt{ = ( { \sqrt{6} )}^{2} - {( \sqrt{3}) }^{2} }} \\ { \tt{ = 6 - 3}} \\ { \tt{ = 3}} \\ \\ { \bf{b).}} \\ { \tt{( \sqrt{5} - \sqrt{2})( \sqrt{2} + \sqrt{5} )}} \\ { \tt{ = ( { \sqrt{5} }^{2}) - { (\sqrt{2} }^{2}) }} \\ { \tt{ = 5 - 2}} \\ { \tt{ = 3}}[/tex]
Answer:
(6-3)(5-2)=3×3=9
Step-by-step explanation:
[tex]x ^{2} - {y}^{2} = (x - y)(x + y)[/tex]
[tex]( \sqrt{6} - \sqrt{3} )( \sqrt{6} + \sqrt{3} ) = ( { \sqrt{6} }^{2} - { \sqrt{3} }^{2} ) = 6 - 3 = 3[/tex]
For the equation 3(7 + 2) = 3x + k, what value of k will create an equation with infinitely many solutions?
A)7
B)21
C)10
D)3
Answer:
ygftyhhhhgffyujhhgyjjjhhguj
Solve the equations and graph the solution
Given:
The inequalities are:
[tex]-5x<-3[/tex] or [tex]2x<-8[/tex]
To find:
The solution for the given inequalities and graph the solution.
Solution:
We have,
[tex]-5x<-3[/tex] or [tex]2x<-8[/tex]
Solve the above inequalities separately.
[tex]-5x<-3[/tex]
Divide both sides by -5.
[tex]x>\dfrac{-3}{-5}[/tex]
[tex]x>\dfrac{3}{5}[/tex] ...(i)
And,
[tex]2x<-8[/tex]
Divide both sides by 2.
[tex]x<\dfrac{-8}{2}[/tex]
[tex]x<-4[/tex] ...(ii)
From (i) and (ii). we get
[tex]x<-4[/tex] or [tex]x>\dfrac{3}{5}[/tex]
The interval notation of the solution is [tex](-\infty,-4)\cup \left(\dfrac{3}{5},\infty\right)[/tex].
The graph of the solution is shown below.
Ryan spent $3.25 on lunch every day, Monday through Friday. If he had $20 at the start of the week, how much money did he have left after Friday
Monday through Friday is 5 days.
Multiply the cost of lunch by number of days:
3.25 x 5 = $16.25
Subtract the total he spent on lunch from what he started with for money:
20 - 16.25 = 3.75
He had $3.75 left.
Answer:
He had $3.75 dollars left.
Step-by-step explanation:
He was spending launch money for five days so:
3.25*5 is the total amount of money he spent that week.
The amount of Mooney he had minus the amount of money he spent is the amount of money left.
20-3.25*5= 3.75
PLEASEE HELPP !
Over which interval is the graph of f(x) = { x2 + 5x +
10
6 increasing?
8
6 • (0,6)
4
(-6.5, 0)
0 (-5)
(0, -5)
0 ( 0, -6.5)
2
-10 48 -6 4
2
4
6
8
10
X
4.
(-5, -6.5)
16
-8
w 10
Answer:
Option B
Step-by-step explanation:
For increasing function in the interval (a, b),
"If we draw a tangent at any point on the graph in the given interval (a, b), slope of the tangent drawn will be positive"
Given function is,
[tex]f(x)=\frac{1}{2}x^2+5x+6[/tex]
In the interval (-∞, -5),
Graph is moving downwards therefore, tangents drawn at any point will have a negative slope and the function will decrease in this interval.
In the interval (-5, ∞),
In the given interval any tangent drawn at any point will have a positive slope and the function will be increasing.
Therefore, interval in which the function is increasing → (-5, ∞)
Option B is the answer.
The interval in which the function decreases is (-∞, -5).
In which interval the function decreases?The function decreases when, reading from left to right, the graph of the function goes downwards.
By looking at the graph, we can see that the graph goes downwards on the interval negative infinity and -5
Then we conclude that the function decreases on the interval (-∞, -5).
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Problem 6
Let Tn be the nth triangular number, Qn be the nth square number and
Pn be the nth pentagonal number.
(a) Show that 3Pn = T3n-1.
(b) Show that Pn - Qn = Tn-1 and hence that P3n - 3Pn = Q3n.
It has been shown that [tex]3P_{n} =T_{3n-1}[/tex], [tex]3P_{n} =T_{3n-1}[/tex] and hence [tex]3P_{n} =T_{3n-1}[/tex].
Given: [tex]T_{n}[/tex] is the nth triangular number. [tex]Q_{n}[/tex] is the nth square number. [tex]P_{n}[/tex] is the nth pentagonal number.
To show:
[tex]3P_{n} =T_{3n-1}[/tex] [tex]P_{n} -Q_{n} =T_{n-1}[/tex] and hence [tex]P_{3n} -3P_{n} =Q_{3n}[/tex]Triangular numbers are numbers formed by addition of consecutive natural numbers starting from 1. Square numbers are numbers formed by squaring natural numbers. Pentagonal numbers are numbers formed by distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex.
The formula for each of them is given by:
[tex]T_{n}=\frac{n(n+1)}{2}[/tex]
[tex]Q_{n}=n^{2}[/tex]
[tex]P_{n}=\frac{3n^{2}-n}{2}[/tex]
(a).
Now, put [tex]n=3n-1[/tex] in [tex]T_{n}=\frac{n(n+1)}{2}[/tex] to get,
[tex]T_{3n-1}=\frac{(3n-1)(3n)}{2}[/tex]
[tex]T_{3n-1}=3\frac{n(3n-1)}{2}[/tex]
[tex]T_{3n-1}=3\frac{3n^{2}-n}{2}[/tex]
Put [tex]P_{n}=\frac{3n^{2}-n}{2}[/tex] in [tex]T_{3n-1}=3\frac{3n^{2}-n}{2}[/tex] to get,
[tex]T_{3n-1}=3P_{n}[/tex]
So, [tex]3P_{n}=T_{3n-1}[/tex]
(b).
Now,
[tex]P_{n}-Q_{n}=\frac{3n^{2}-n}{2}-n^{2}[/tex]
[tex]P_{n}-Q_{n}=\frac{3n^{2}-n-2n^{2}}{2}[/tex]
[tex]P_{n}-Q_{n}=\frac{n^{2}-n}{2}[/tex]
Put [tex]n=n-1[/tex] in [tex]T_{n}=\frac{n(n+1)}{2}[/tex] to get,
[tex]T_{n-1}=\frac{(n-1)(n-1+1)}{2}[/tex]
[tex]T_{n-1}=\frac{(n-1)n}{2}[/tex]
[tex]T_{n-1}=\frac{n^{2}-n}{2}[/tex]
Comparing [tex]P_{n}-Q_{n}=\frac{n^{2}-n}{2}[/tex] and [tex]T_{n-1}=\frac{n^{2}-n}{2}[/tex], we get,
[tex]P_{n}-Q_{n}=T_{n-1}[/tex]
Now, put [tex]n=3n[/tex] in [tex]P_{n}-Q_{n}=T_{n-1}[/tex] to get,
[tex]P_{3n}-Q_{3n}=T_{3n-1}[/tex]
As shown in part (a), [tex]T_{3n-1}=3P_{n}[/tex]
Put [tex]T_{3n-1}=3P_{n}[/tex] in [tex]P_{3n}-Q_{3n}=T_{3n-1}[/tex] to get,
[tex]P_{3n}-Q_{3n}=3P_{n}[/tex]
[tex]P_{3n}-3P_{n}=Q_{3n}[/tex]
So, [tex]P_{n}-Q_{n}=T_{n-1}[/tex] and hence [tex]P_{3n}-3P_{n}=Q_{3n}[/tex]
Learn more about these kinds of numbers here:
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what is 18 7/8 -14 7/9
Answer:
295/72
Step-by-step explanation:
a telephone pole is 24 feet tall
Answer:i honestly dont know just trying to get points
Step-by-step explanation:
a rectangle and Square have equal perimeter .If the rectangle has width 8 and length 12 what the area of a square?
For each 70 mm of coloured fabric Alex uses to make his curtains, he also uses 20 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.
Answer:
20×10=200mm
70:200
70/10=7
200/10=20
7:20 is your answer in it's simplest form
I NEED THIS ASAP PLEASE
A ball is dropped from the height of 20 feet. the ball rebounds to 80% of his previous height. Let n represent the number of bounces of the ball.
The height of the ball after each bounce can be modeled by
A. H=20(1.80)^n
B. H=20(.80)n
C. H=20(.80)^n
D. H=20(.20)^n
Answer:
Step-by-step explanation:
This is modeled after an exponential function which, at its simplest, is
[tex]y=a(b)^x[/tex] where, for us and in this particular situation, y is the final height, a is the initial height, b is the rate of growth or decline, and x is the number of bounces. We know the initial height is 20, but we need to find the rate of decline. Rewriting the formula to model a rate of decay or decline is
[tex]y=a(1-r)^x[/tex], or more closely related to our circumstances:
[tex]H=20(1-.8)^n[/tex] and simplifying that a bit:
[tex]H=20(.2)^n[/tex], choice D.
A petrol can is a rectangular prism with base measurements 15 cm by 30 cm. If the can has capacity 18 liters, find its height.
Answer:
40
Step-by-step explanation:
The first step is to calculate the base area of the prism
= 15×30
= 450
The volume is then calculated as follows
= 450×h
= 450h
The capacity is 18 liters
= 18×1000
= 18,000
Therefore the height of the rectangular prism can be calculated as follows
450h= 18,000
h= 18,000/450
= 40
Hence the height is 40 cm
-1 1/4 + (-2 1/2)
anyone ty
Answer:
-3 3/4
Step-by-step explanation:
So we have:
-1 1/4 + (-2 1/2)
Before solving this, lets just clean it up.
First off, since we know that a + and - sign equals a - sign, we can rewrite it as:
-1 1/4 - (2 1/2)
We need to also get a common denominator, which would be 4. The first fraction already has a denominator of 4, so it doesnt change. However, the second fraction is 1/2, and we need to multiply both sides by 2 to change the denominator from 2 to 4:
-1 1/4 - (2 2/4)
Now lets solve:
I will do the fraction seperate from the whole number to make it simpler:
-1 - 2
A negative subtracted makes it a larger negative so:
-3
-1/4 - 2/4
Again, a negative subtracted makes it a larger negative:
-3/4
Now recombine the numbers:
-3 3/4
So this is your answer.
Hope this helps!
If a population consisted of 3200 people, a sample of the population could consist of which of the following numbers of people?
A. 320
B. 3,200,000
C.320,000
D.32,000
A survey is conducted in order to collect a piece of specific information. The number of people that can be considered as a sample for the given population is 320.
What is Survey?A survey is conducted in order to collect a piece of specific information from a group of people chosen from the entire population who denotes the entire population for those questions.
Given the population consist of 3200 people, therefore, the number of people that can be considered as a sample for the given population is 320.
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5 x 1/7
The question
Answer:
5/7 or 0.71 is the answer
What is the following sum?
4.5+2V5
O 6.10
O 8/10
O ENG
O ONE
Answer:
[tex]6 \sqrt{5} [/tex]
Step-by-step explanation:
Take out Square root 5 as common and then add numbers
[tex]4 \sqrt{5} + 2 \sqrt{5} \\ 6 \sqrt{5} [/tex]
How do i solve this plss helpp
Hope this helps!! :)))))))
Solve for x
-12 = 4(x – 5)
X =
Answer:
-12=4x-20
4x=12+20
4x=32
4 = 4
x=8
Answer:
[tex] - 12 = 4(x - 5) \\ - 12 = 4x - 4 \times 5(bracket \: multipiction) \\ - 12 = 4x - 20 \\ - 12 + 20 = 4x\\ 8 = 4x \\ x = \frac{8}{4} = 2 \\ x = 2 \\ thank \: you[/tex]
Complete the solution of the equation. Find the
value of y when x equals -8.
4x + 9y = -14
does anyone know what this is?
Answer:
Y is equal to 2
Step-by-step explanation:
X equals -8
So,
4(-8) + 9y = -14
-32 + 9y = -14
-32 + 32 + 9y = -14 + 32
9y = 18
1/9 × 9y = 18 × 1/9
y = 2
can someone explain on how to do it please thanks
Answer:
90=30+(x+10). remove blanket
90=30+x+10. correct like terms
90=30+10+x
90=40+x. 40 will cross the = and change from +ve to -ve sign
90-40=x.
therefore
x=40
Answer:
x = 50
Step-by-step explanation:
The 2 angles sum to 90° , that is
x + 10 + 30 = 90
x + 40 = 90 ( subtract 40 from both sides )
x = 50
Mr.Williams drew
△
A
B
C
on a coordinate grid and asked his students to determine the transformations that will result in a transformed figure
△
A
`
B
`
C
`
such that
△
A
`
B
`
C
`
is similar but NOT congruent to
△
A
B
C
.
Two student responses are shown below.
Student 1: Reflect
△
A
B
C
across the y-axis and then dilate it by a scale factor of 1 with the center of dilation at the origin.
Student 2: Dilate
△
A
B
C
by a scale factor of 2 and the center of dilation at the origin and then reflect it across the x-axis.
Which statement is true?
A.
Neither student 1 nor student 2, because dilations and reflections preserve both side lengths and angle measures.
B.
Both student 1 and student 2, because dilations and reflections preserve angle measures but not side lengths.
C.
Only student 2, because dilations preserve angle measures and side lengths are proportional.
D.
Only student 1, because this dilation preserves angle measures and side lengths.
Answer: Answer C , Only student 2, because dilation preserve angle measures and side lengths are proportional
The true statement is only student 2, because dilations preserve angle measures and side lengths are proportional.
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
In Reflection the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
Dilation preserves the angle measures, so the triangles will be similar.
Reflection, on the other hand, will result in congruent triangles.
Student 1 said that Reflect △ABC across the y-axis and then dilate it by a scale factor of 1 with the center of dilation at the origin.
If the scale factor is 1, then the dilated image will be the same as the original image.
So the resulting triangle will be congruent to the original triangle.
In the case of what student 2 said, scale factor is 2. Triangle is enlarged.
So the resulting image will be similar to the original one.
Hence student 2 is correct.
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which of the following indicates that triangle QRS and triangle TUV are similar? Btw I need a valid step-by-step on how you do this, if not I'll report your answer, and assume you're doing it for the points!!
Answer:
third option.
∼ means similar
≅ means congruent
≈ means approximate
= means equal
On the graph shown, what is f(-2)
Answer:
3 because when x=2 the lines are at y 1 and 3, but the y 1 isn't shaded, so the answer is 3
I will try my best to love you math, but I will never succeed in math, I will just die in math.
Answer:
your will becanswer $95.00
Answer:
105
Step-by-step explanation:
Price of a fridge is $1050instalment time 10 months
so from 1050÷10
105 ans
please mark as brainliestpls help what is 66 2/3 % of 9/10 of $45.00
*pls include steps tysm
Answer:
$27.00
Step-by-step explanation:
We first have to start at the base value of $45.00, as without that, we have nothing to go off of. We can work right to left because we start at the rightmost point of the problem.
Therefore, we start with finding 9/10 of 45.00 . This is as simple as multiplying 9/10 with 45.00, resulting in 40.5
To figure out a percentage relative to real numbers, we first have to turn that percentage into a fraction or decimal. To turn it into a decimal, we simply divide by 100, and 66 2/3 divided by 100 is roughly 0.6666 , or 2/3 . Multiplying our result of 40.5 by this, we get $27.00 as our answer.
3 vertices of a parallelogram ABCD are shown in the applet. What are the coordinates of point D?
Need ASAP
Answer:
D (0, 3)
Step-by-step explanation:
To go from B (8, 3) to C (3, 8)
subtract 5 from x, add 5 to y
A (5, -2)
subtract 5 from x, x = 0
add 5 to y, y = 3
D (0, 3)
What is the relative frequency (to the nearest percent) of boys among those who cannot bike to school
Answer:
29%
Step-by-step explanation:
From the two way table given : the relative frequency of boys among those who cannot bike to school ;
Here, we are only concerned with thilose who cannot Bikento school and not all of the data :
The relative frequency of boys among those who cannot bike to school is :
Number of boys who can't bike to school / total number of people who can't bike to school
Number of boys who can't bike = 4
Total who cannot bike = 14
Hence, 4 /14 = 0.2857142
0.2857142 * 100% = 28.57% = 29% (nearest percent)
please help! i think the answer is 12 but any verification would be greatly appreciated!
Answer:
13.9 or 14
Step-by-step explanation:
a^2 + b^2 = c^2
5^2 + 13^2 = c^2
25 + 169 = 197
square root 197 to get c
c = 13.9 (14 rounded up)
Helpful thing to note is that the hyptoenuse will always be longer than your "long side" of the triangle
A spinner with 12 equal sections is spun. Each section is numbered 1 to 12. What Is the probability of landing on an odd number. A) 25% B) 75% C) 100% D) 50%
Answer:
D
Step-by-step explanation:
The HCF and LCM of two numbers is 9 and 459 respectively if one the number is 27 the other number is (1)
Answer:
153
Step-by-step explanation:
[tex]other \: number = \frac{9 \times 459}{27} \\ \\ = \frac{459}{3} \\ \\ = 153[/tex]
Answer:
Other number is 153
Step-by-step explanation:
Usually, the product of the HCF and LCM will be the product of the 2 numbers in question.
The HCF and LCM are given as 9 and 459.
While one of the numbers used to find the HCF & LCM was 27.
Let the other number be y.
Thus;
27y = 459 × 9
y = 459 × 9/27
y = 153
(x-2)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15
Hope this may help you ☺