Answer:
y= 25/3 - x/3
Step-by-step explanation:
y= 25/3 - x/3
What is the nth term rule of the linear sequence below?
27, 25, 23, 21, 19, ...
Answer:
Step-by-step explanation:
Comment
This is an arithmetic series. It has the following givens.
a = 27 The first term
d = - 2 The difference between one term and the one behind it.
n = quite small
Tn = a + (n - 1)*d
tn = 27 - 2n + 2
tn = 29 - 2n
w and x are whole numbers
w>60
x<50
Work out the smallest possible value of x-z
Using the given information, the smallest possible value of x - z is 12
Evaluating an expressionFrom the question, we are to determine the smallest possible value of x - z
From the given information,
w and x are whole numbers
and
w > 60
x < 50
∴ w = 61, 62, 63, 63, 65, ...
x = 49, 48, 47, 46, 45, ...
Then,
The smallest possible value of x - z is
x - z = 61 - 49
x - z = 12
Hence, the smallest possible value of x - z is 12
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Find the simplified product. b-5/2b X b^2+3b/b-5
The simplified product of [tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5}[/tex] is [tex]\frac{(b+3)}{2}[/tex]
How to simplify a product?The products can be simplified as follows;
Multiplying fraction,
[tex]\frac{x}{y} . \frac{a}{b} = \frac{xa}{yb}[/tex]
Therefore,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)}[/tex]
Hence,
Let's reduce the fraction by dividing
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)}[/tex]
Therefore,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b}[/tex]
Hence,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b} = \frac{b+3}{2}[/tex]
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Answer:
A, b+3/2
Step-by-step explanation:
Simplify the exponential expression 48 ^1/2
O 2 (24^1/2)
O 3 (16^1/2)
O 4 (3^1/2)
O 16 (3^1/2)
Step-by-step explanation:
Hi There! Let me help you :)
To answer this question, we have to know about the way to simplify it. First, you find the factor of 48.
[tex] = {48}^{ \frac{1}{2} } [/tex]
[tex] = {(16 \times 3)}^{ \frac{1}{2} } [/tex]
[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]
[tex] \: [/tex]
—Use the general formula of the exponential, where a^m/n = ^n√a^m.
[tex] \: [/tex]
[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]
[tex] = \sqrt[2]{16} \times {3}^{ \frac{1}{2} } [/tex]
[tex] = 4 \times {3}^{ \frac{1}{2} } [/tex]
The answer is C.
a fence is 2m high by 33m long, if a gallon of paint is enough to paint 2.5m^2, how many gallons will be used to paint the entire fence?
The number of gallons of paint needed to paint the entire fence is 26.4 gallons.
Area of rectangleLength = 33 mWidth = 2 mArea = length × width
= 33 m × 2 m
= 66 square meter.
A gallon of paint = 2.5 m²Number of gallons of paint needed = 66 square meter / 2.5 m²
= 26.4 gallons
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In the Fig., if ABCD is a parallelogram, then the value of x is
Answer:
Value of x is 20.
Step-by-step explanation:
The angle opposite to 4x is also 4x.
Similarly, the angle opposite to 5x is also 5x.
So, 4x+4x+5x+5x=360
18x=360
x=360/18
x=20
Please give me brainlist.
4 kg 2 dag when converted in g gives you?
Answer:
4020 grams
Step-by-step explanation:
4kg=4000g
2 dag= 20g
Total: 4000g + 20g = 4020g
Answer:
4020 grams
Step-by-step explanation:
1 kg = 1000 g
1 dag = 10 g
4 x1000= 4000
2 x 10 = 20
4000 + 20
The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔA'B'C' is right because it is the image of ΔABC.
ΔADC is right because AA' intersects AC at A.
ΔBCC' is right because B lies of the line of reflection.
ΔBGC is right because Line E G is perpendicular-to CC'.
ΔDGC is right because Line E G is perpendicular-to CC', Option D is the correct answer.
What is Reflection ?Reflection along a line is plotting a new object as a mirror image of the original object .
It is given that the there are two Triangles , ABC and A'B'C' as an image.
The figure is attached with the answer.
D is the mid point of the line joining BB'
As the line of reflection is always perpendicular to the object and the image.
And as it is given that C G F is a right angle.
Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) , Line E G is perpendicular-to CC'.
Option D is the correct answer.
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Answer:
D
Step-by-step explanation:
Let f(x)=6/-2+2e^-0.3x. what is f(4)? enter your answer rounded to the nearest tenth
The value of the function f(x)=6/-2+2[tex]e^{-0.3x}[/tex] at x=4 after rounded to the nearest tenth is -2.4.
Given Function of x : f(x)=6/-2+2[tex]e^{-0.3x}[/tex]
The given function showing the relationship between x and f(x) is f(x)=6/-2+2[tex]e^{-0.3x}[/tex] where e is exponential and we have to find the value of f(4) by just putting the value of x=4 in the given function and round to the nearest tenth means replacing a number with an approximate value.
f(4)=6/-2+2[tex]e^{-0.3*4}[/tex] ( The value of e is 2.7812)
f(4)=-3+2[tex]e^{-1.2}[/tex]
f(4)=-3+2*0.30119 (The value of [tex]e^{-1.2}[/tex] is 0.30119)
f(4)=-3+0.60238
f(4)=-2.3972
Round -2.3972 to tenth is -2.4.
Hence the value of function of at x=4 is -2.4.
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The value of f(4) is -4.3.
The function is a relation between two different sets X and set Y which are in one-one or many-one relation. Here set X is called as the domain and set Y is called as the codomain.
For example: f(x)=3x+9
To get the value of the function at any point of x, we have to put the number in the function to get its function value.
For example the value of f(x) in above function at x=a will be f(a)=3a+9
Similarly given function in the question
[tex]f(x)=\frac{6}{-2+2e^{-0.3x}}[/tex]
to get the value of f(x) at x=4 put the value of x in the function,
[tex]f(x)=\frac{6}{-2+2e^{-0.3*4}}[/tex]
⇒[tex]f(x)=\frac{6}{-2+2e^{-1.2}}[/tex]
⇒f(x)=-4.3
Therefore the value of f(4) is -4.3.
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If function g has the factors (x − 7) and (x 6), what are the zeros of function g?
Two-thirds of the tokens in the box are red and 2/5 of the remaining tokens are blue.
If the remaining 24 tokens are green, how many tokens are there in the box?
Answer:
After solving this question I got and 120 tokens
What is the measure of angle AFR?
O 124 degrees
O 91 degrees
O 13 degrees
O 117 degrees
Answer:
13°Step-by-step explanation:
AFR = VFN (opposite angle rule)
7x + 33 = 9x + 7
33 - 7 = 9x - 7x
26 = 2x
x = 26 : 2
x = 13°
-----------------
check
7 * 13 + 33 = 9 * 13 + 7 (remember PEMDAS)
91 + 33 = 117 + 7
124 = 124
the answer is good
simplify algebraic equation x^2-4/x^2+2x
Answer:
Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]
Step-by-step explanation:
Simplify any algebric expression means to write an equivalent expression in which all similar terms combined and remove all symbols such as brackets.
The given algebraic equation is [tex]x^{2} -\frac{4}{x^{2} } +2x[/tex]
now for simplifying it
First of all take L.C.M of [tex]x^{2}[/tex]
= [tex]\frac{x^{2} (x^{2}) -4 + 2x(x^{2} )}{x^{2} }[/tex]
We get [tex]\frac{x^{2} -4+2x^{3}}{x^{2} }[/tex]
Further we can write it as [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]
Simplification of algebric expression is [tex]\frac{x^{2} - 2x^{3}-4 }{x^{2} }[/tex]
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Sketch the graph of y = x^2+2x-15 using your graphing calculator. What are the x-intercepts of this graph?
The intercept is 3 and 5
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
To find x- intercept, y=0
x² + 2x -15=0
x² -5x + 3x -15=0
x(x-5) - 3(x-5) = 0
(x-5)(x-3)=0
Hence, the x- intercept is 3 and 5.
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pe-intercept Equatic
Question 4 of 10
If f(x) = 5x - 12, what is f(2)?
Answer:
f(2) = 2
Step-by-step explanation:
Given function:
f(x) = 5x - 12
To Find:
f(2)
Solution:
Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.
[tex]f(x) = 5x - 12[/tex]
[tex]f(2) = 5(2)- 12[/tex]
[tex]f(2) = 10 - 12[/tex]
[tex]\boxed{f(2) = - 2}[/tex]
Hence,f(2) is equal to -2.
8.
36.2
22.3
- 30-
33
Find the value of x.
(Round answer to the nearest tenth when necessary)
44.6
33.2
Answer:
36.2
Step-by-step explanation:
Assuming that the dotted line is a perpendicular bisector, we can say that it splits the side that is 30 units long into 2 sets of 15 units. Then, we can use the pythaogrean theorem to solve (Leg A is 33 and Leg B: 15). a^2+b^2=c^2
33^2+15^2=c^2
1089+225=c^2
1314=c^2
Square root of 1314 = square root of c^2
36.2 aapproximately c
3.
The sides of a rectangle are x cm and (x + 1) cm. A circle has radius of (x + 2) cm. If the
22
sum of the area of the rectangle and the circle is 184 cm². Using n as 22/7find the value of x.
Answer:
x = 5.00 cm
Step-by-step explanation:
• area of the rectangle = [tex]x[/tex] x [tex](x + 1)[/tex]
= [tex]x^2 + x[/tex]
• area of the circle = π r²
= [tex]\frac{22}{7}[/tex] x [tex](x + 2)^2[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](x^2 + 4x + 4)[/tex]
∴ [tex]x^2 + x[/tex] + [tex]\frac{22}{7}[/tex] x [tex](x^2 + 4x + 4) = 184[/tex]
⇒ [tex]x^2 + x[/tex] + [tex]\frac{22}{7} x^2 \space\ + \space\ \frac{88}{7} x \space\ + \space\ \frac{88}{7} = 184[/tex]
⇒ [tex]\frac{29}{7}x^2 \space\ + \space\ \frac{95}{7}x \space\ - \frac{1200}{7} = 0[/tex]
• Using quadratic formula, where
a = [tex]\frac{29}{7}[/tex]
b = [tex]\frac{95}{7}[/tex]
c = [tex]\frac{-1200}{7}[/tex] ,
[tex]x=\frac{-b \pm \sqrt{b^2-4c}}{2}[/tex]
[tex]x = \frac{-\frac{95}{7}\pm \sqrt{(\frac{95}{7})^2 - 4(\frac{29}{7})(\frac{-1200}{7} ) } }{2(\frac{29}{7})}[/tex]
[tex]x = 5.00 \space\ \space\ \space\ or \space\ \space\ \space\ x = -8.28[/tex]
As length (x) cannot be a negative number,
x = 5.00 cm
Which of the following objects is considered to be one-dimensional because it ha length but no width or height?
A. Line segment
B. Point
C. Triangle
D.Cube
Which transformation would be a horizontal reflection and a dilation of scale factor ½ of the L shape?
The transformation which would be a horizontal reflection and a dilation of scale factor ½ of the L shape is as in the attached image.
What is horizontal reflection and dilation?The term horizontal reflection with respect to transformation in mathematical context simple means that the shape is reflected over the vertical axis(y-axis as mirror). The dilation of a scale factor of ½ simply means that the shape reduces to half it's original size.
Hence, it follows that the attached image represents the transformation.
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Find the variance of the given
data rounded to the nearest
hundredth.
3, 4, 5, 7, 10, 12, 15
Σ (x - mean)²
n
0²
0²
=
=
[?]
Enter
Answer:
17.14
Step-by-step explanation:
You have the data values {3, 4, 5, 7, 10, 12, 15}
To find the mean, [tex]\frac{3+4+5+7+10+12+15}{7} =8[/tex], yay a whole number, my favorite.
Then, [tex](3-8)^2+(4-8)^2+(5-8)^2+(7-8)^2+(10-8)^2+(12-8)^2+(15-8)^2=120[/tex].
Since n=7, σ^2≈[tex]17.14[/tex]
Get a similar question You can retry this question below
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the
third angle is 35 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Find the Largest angle:
Sum of triangle angles = 180
smallest angle = x
second angle = 3x
third angle = x +35
180 = x + 3x + x + 35
145 = 5x
x = 29 is the smallest
the second is 87
the third is 64
Identify a pair of overlapping congruent triangles in the
diagram. Then use the given information to write a proof
to show that the triangles are congruent.
Proof
Given: AC = BC, LA = LB
Answer:
overlapping congruent triangles:
ΔACE ≅ ΔBCD
Proof:
given: AC ≅ BC, angle A ≅ angle B
angle ACB ≅ angle BCA by the reflexive property
ΔACE ≅ ΔBCD by the ASA triangle congruence property
help grade 5 math please only answer if you know and if it’s right ill mark brainliest and please fast extra points who explain it
Answer:
[tex]\frac{42}{8}[/tex]
Step-by-step explanation:
7/8 <> 0.875
0.875 * 6 = 5.25
5.25 <> 42/8
(<> is used to show decimal to fraction and vice versa [the other way around])
Which choice is equivalent to the fraction below when x is an appropriate
value? Hint: Rationalize the denominator and simplify.
2
2-√6x
A.
2+√6x
2-6x
B. 2+√6x
4-3x
C. 2+√6x
2-3x
D. 2+√6x
4-6x
A fraction is a way to describe a part of a whole. The correct option is C.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The choice that is equivalent to the fraction can be found by rationalizing the denominator of the fraction. Therefore, we can write,
[tex]\dfrac{2}{2-\sqrt{6x}}\\\\\\=\dfrac{2}{2-\sqrt{6x}} \times \dfrac{2+\sqrt{6x}}{2+\sqrt{6x}}\\\\\\= \dfrac{4+2\sqrt{6x}}{4-6x}\\\\\\=\dfrac{2(2+\sqrt{6x})}{2(2-3x)}\\\\\\= \dfrac{2+\sqrt{6x}}{2-3x}[/tex]
Hence, the correct option is C.
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which greek geometer founded a philosophical society that devoted itself to study of mathematics
Answer:
Pythagoras was the Greek geometer .
Please mark me as the brainliest.
Matt is trying to measure the height of a tree using
trigonometry. He is having trouble because of the
terrain around the tree. The horizontal distance
from the tree to Matt's eyes is 120 feet. The angle
of depression from the horizontal is 30°. Matt's
angle of sight to the top of the tree is 23°. What is
the height of the tree? (Round to the nearest foot.)
The height of the tree will be 18.35 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Matt is trying to measure the height of a tree using trigonometry.
He is having trouble because of the terrain around the tree.
The horizontal distance from the tree to Matt's eyes is 120 feet.
The angle of depression from the horizontal is 30°.
Matt's angle of sight to the top of the tree is 23°.
The diagram is given below.
Let x be the height of tree and AM be h.
The value of (h + x) will be
tan 30° = (x + h) / 120
x + h = 69.288
Then the value of h will be
tan 23° = h / 120
h = 50.94 feet
Then the height of the tree will be
⇒ h + x – h
⇒ 69.29 - 50.94.
⇒ 18.35 feet
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can someone please help and explain its due in a littleee
Answer:
slope = 3
y-intercept: -4
explanation on how to graph given in step-by-step explanation
Step-by-step explanation:
y=3x-4 is given in slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept (when x = 0)
So the first coordinate that is easy to graph is the y-intercept since it's just (0, b) or in this case (0, -4). So that's the first point you graph. Now from here you can use the slope to graph all the other points. The slope is 3, which essentially means every time x increases by 1, the y-value increases by 3. So from the y-intercept (0, -4) you're going to go one unit to the right and three units up which should give you the coordinates (1, -1). Then from that coordinate go one unit to the right and three units up which should get you (2, 2) then from that coordinate go one unit to the right and three units up which should get you to (3, 5). Now go back the y-intercept (0, -4) and instead of going to the right 1 and up 3 you're going to do the inverse and instead go left 1 and down 3. So from (0, -4) go to the left one unit and down 3 units which should get you to (-1, -7). And now with all these points plotted draw a line through all of them
what is the equation of a line that has a slope of -5 and a y intercept of -7
Answer:
y=(-5x)+(-7)
Step-by-step explanation:
The equation for slope is y=mx+b
so you would say -5x as the mx in the equation and -7 as the u intercept.
Hii!
_________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
y=-5x-7
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
For this question we will use the slope intercept form equation, because we are provided with the slope and the y-intercept.
The slope intercept form equation is [tex]\large\textsf{y=mx+c}[/tex]. In this formula m denotes the slope and c denotes the y-intercept.
Since we have both m and b, we can stick them into the formula. Upon doing this we obtain
[tex]\twoheadrightarrow\sf y=-5x+(-7)[/tex]
[tex]\bullet[/tex] Simplify
[tex]\twoheadrightarrow\sf y=-5x-7[/tex]
[tex]\bullet[/tex] Great job! We found the equation
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
In a 19 sided polygon what is the sum of the exterior angles ??
Answer:
the sum of all exterior angle is 360 degree
How many solutions does the following equation have?
7(y+3)=5y+8
A. No Solution
B. Exactly One Solution
C. Infinitely many solutions
Answer:
B. Exactly One Solution
Step-by-step explanation:
Given:
[tex]7(y+3)=5y+8[/tex]
Expand the brackets:
[tex]\implies 7y + 21 = 5y + 8[/tex]
Subtract 21 from both sides:
[tex]\implies 7y + 21-21 = 5y + 8-21[/tex]
[tex]\implies 7y=5y-13[/tex]
Subtract 5y from both sides:
[tex]\implies 7y-5y=5y-13-5y[/tex]
[tex]\implies 2y=-13[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2y}{2}=\dfrac{-13}{2}[/tex]
[tex]\implies y=-\dfrac{13}{2}[/tex]
Therefore, the equation has exactly one solution.