Answer:
x = 10 / 7 (or) 1.43 <rounded to 2 decimal place>
y = - 54 / 7 (or) -7.71 <rounded to 2 decimal place>
Step-by-step explanation:
Another way to rewrite (5x-3y, 3x-y) = (16, 12),
5x - 3y = 16 -- (1)
3x - y = 12 -- (2)
Rewriting (1), y = -5/3x - 16/3 -- (1)'
Substituting (1)' into (2),
3x + 5/3x + 16/3 = 12
14/3x = 20/3
x = 10 / 7 -- (3)
Substituting (3) into (2),
3(10/7) - y = 12
30/7 - y = 12
-y = 54 / 7
y = - 54/7-- (4)
Therefore,
x = 10 / 7 (or) 1.43 <rounded to 2 decimal place>
y = - 54 / 7 (or) -7.71 <rounded to 2 decimal place>
if this helps you, please mark brainliest!
find the value of k if the line 2x-y+k=0 may touch the circle x^2 + y^2=5
Answer:
k = ±4
Step-by-step explanation:
Equation of the circle is:
x² + y² = 5
This means from the general form of equation of a circle;
Centre coordinates is (0, 0) and radius is; √5.
The line 2x - y + k = 0 touches the circle. Thus, perpendicular distance from centre of the circle to this line is equal to the circle radius;
Thus;
|((2 - 0) - (1 × 0) + k)|/(√(2² + 1²)) = √5
|(1 + k)|/√5 = √5
Multiply both sides by √5 to get;
|1 + k| = 5
|k| = 5 - 1
k = ±4
Which equation describes the
function table?
A b = a - 1
B a = b - 1
C b = 3a + 3
D b = 2a + 1
Answer:
The answer is no.d b= 2a + 1
Explanation:
Each time b goes up by 4, 'a' goes up by 2. The rate of change or slope is 4/2 = 2. This lets us see that the answer must be choice D, as no other answer choice has 2 as a slope.
If the side lengths of a cube are 15 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form? (2 points)
Group of answer choices
15 ⋅ 15 ⋅ 15
15 ⋅ 3
315
153
The expression to represent the volume of the cube in exponential form is 15^3
How to write the expression to represent the volume of the cube in exponential form?The length is given as:
Length = 15 feet
The volume of the cube is calculated as:
Volume = Length^3
So, we have:
Volume = 15^3
Hence, the expression to represent the volume of the cube in exponential form is 15^3
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What is the simplified value of the expression below?
3(8-4)+2x5.5
31
Оооо
47
15. In the diagram AB is parallel to CD.
Calculate the value of a.
NOT TO
SCALE
Step-by-step explanation:
sorry can't help u because I can't see any picture
What type of function is represented by the table of values below? X:1,2,3,4,5 X:4,8,12,16,20 A.cubic B.exponential C.quadratic D. Linear
Answer:
c
Step-by-step explanation:
8. Find TN, MP, TQ, PT
Please and thank you!
Answer:
TN = 13 units
MP = 22 units
TQ = 6.93 units
PT = 13 units
Step-by-step explanation:
If T is a circumcenter of the given triangle MNP,
Measure of TN = Measure of TM = Measure of TN
By applying Pythagoras theorem in ΔMRT,
MT² = TR² + MR²
MT² = (12)² + 5²
MT = [tex]\sqrt{169}[/tex]
MT = 13
Measure of TN = 13 units
Since, TQ, TS and RT are the perpendicular bisectors of the sides MP, NP and MN respectively,
Measure of MP = 2(PQ)
= 2(11)
= 22 units
By applying Pythagoras theorem in ΔTQM,
MT² = TQ² + MQ²
(13)² = TQ² + (11)²
TQ = [tex]\sqrt{169-121}[/tex]
TQ = [tex]\sqrt{48}[/tex]
TQ = 6.93
Measure of PT = Measure of TN = 13 units
Someone please help me ASAP
Answer:
(4, 0)
Step-by-step explanation:
D is clearly (1, 2).
so, for D' we have (1+3, 2-2) = (4, 0).
that's it. there is nothing more to it.
If I had 15 acres and I got $237,000 for it, how much is each acre?
For the price per acre do 237,000 / 15 = $15800 per acre
The diagram below represents the net of a triangular prism.
3
6 cm
12 cm
6 cm
8 cm
10 cm
6 cm
(not drawn to scale]
What is the surface area of the triangular prism?
A
288 square centimeters
B
312 square centimeters
с
336 square centimeters
D
368 square centimeters
Answer:
yes
Step-by-step explanation:
Answer:
336cm2
Step-by-step explanation:
The diagram is divided ninto 5 parts that is rectangles ABCD, CHGD, GFEH and triangles CIH and DGJ.
Area of rectangle ABCD= lxb
=12x6=72cm2
Area rectangle CDHG=lxb
12x8=96cm2
Area rectangle HGFE= lxb
=10x12=120cm2
Area of triangles CIH and DIG= 2x1/2xbxh
=6x8=48cm2
Surface area of the triangular prism=Area of rectangle ABCD+Area rectangle CDHG+Area rectangle HGFE+Area of triangles CIH and DIG
72+96+120+48=336cm2
Complete parallel side 2
Height = 8mm
parallel side 1= 5mm
parallel side 2=?
Area = 72 mm
Step-by-step explanation:
Assume length of side 2 = L
Area of parallelogram is Height x L
So, 72 = 8 x L
L = 9
Please help
Sketch the graph of y = (x – 1)2 + 2 and identify the axis of symmetry.
Answer:
The axis of symmetry is (0,0)
Step-by-step explanation:
This is the picture
An object starts at position 12 on a horizontal line with a reference point of 0. What is the position of the object if it
moves 14 units to the left?
0-26
-2.
02
O 26
Answer:
The answer would be B
Answer:
-2
Step-by-step explanation:
We know that the object is at 12 on a horizontal line.
The horizontal line of a graph is the x axis, so lets think of 12 as 12x
On a graph, left is negative, and right is postive.
In this case we need to move 14x to the right, or -14x.
We start at 12x, so its going to be:
12x-14x=-2x
So -2 is the postition of the object on the x axis.
This is answer B.
Hope this helps!
Move point b some more as you move point b the angle formed between ab and cd varies if you want to make an perpendicular to cd what do you need to do explain in terms of BEC
Answer:
Following are the response to the given question:
Step-by-step explanation:
Move b a bit further if the angle between cd and ab changes when you move b if you want to make a perpendicular point to cd The angle BEC is 90 ° for making the AB line perpendicular to the line CD to transfer point B to the angle between the two lines.
The box part of the box plot contains all the values between which numbers?
25
30
35
40
45
50
between 27 and 36 and between 37 and 40
between 32 and 36
оооо
between 32 and 37
O between 27 and 32 and between 37 and 40
Answer:
Between 32 and 37
Step-by-step explanation:
Here, we simply want to get the data portion represented by the box alone
we can see that the box starts from 32
It ends at the number 37
Note;
between each individual number on the plot, we have 5 small lines indicating an extra point
X: A)127
B)78
C)130
D)110
Y: A)50
B)98
C)60
D)102
Answer:
a,
Step-by-step explanation:
SOMEBODY PLEASE HELP
logo y = x means: log base b of y equals x.
True
False
If you meant to write [tex]\log_{b}(y) = x[/tex] then the statement is true.
As a more concrete example, something like [tex]\log_3(81) = 4[/tex] would be read out as "log base 3 of 81 is equal to 4".
In the diagram, the figures are similar. Use proportions to find x.
Answer:
x~11
Step-by-step explanation:
22:17=14:x
22/17=14/x
22x=17*14
22x=238
22x/22=238/22
x=238/22
x=10.818181818181818
x~11
How do I Simplify V5(8+3V6) ???
Answer:
[tex]8\sqrt{5}+3\sqrt{30}[/tex]
Step-by-step explanation:
When we have any quantity being multiplied to an expression, we can use the distributive property. The distributive property says that [tex]a(b+c)=ab+ac[/tex]. In other words, we can distribute the outer number inside the parentheses.
Using the distributive property, we can then simplify the given equation as follows:
[tex]\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}[/tex]
Finally, you should recall that when multiplying square roots, you can simply bring all the numbers inside of one root. For instance, [tex]\sqrt{2}*\sqrt{3}=\sqrt{2*3}=\sqrt{6}[/tex] (note, this does not work for addition or subtraction, only multiplication or division). Therefore, we can simplify [tex]\sqrt{6}\sqrt{5}=\sqrt{6*5}=\sqrt{30}[/tex].
Finally, we can combine our answer into [tex]\sqrt{5}(8+3\sqrt{6})=8\sqrt{5}+3\sqrt{6}\sqrt{5}=8\sqrt{5}+3\sqrt{30}[/tex]
Question 5 of 27
What is the measure of ZC in the parallelogram shown?
Answer:
C.35⁰
Step-by-step explanation:
C= 180⁰-145⁰= 35⁰
A square fits exactly inside a circle with each of the vertices being on the circumference of the circle. The square has sides length of X cm. The area of the circle is 56cm^2. Work out the value of x. Give your answer correct to 3sf
Answer: The value of x is 5.970.
Step-by-step explanation:
Given: The square has sides length of X cm.
Let r be the radius of the circle.
The square fits exactly inside a circle with each of the vertices being on the circumference of the circle.
Then diagonal of square = diameter of circle
i.e. [tex]\sqrt{2}x= 2r[/tex] [Diagonal of square = [tex]\sqrt{2}[/tex](side)]
i.e. [tex]r=\dfrac{x}{\sqrt{2}}[/tex]
area of circle =[tex]\pi r^2[/tex]
i.e. [tex]56=\frac{22}{7}(\frac{x}{\sqrt{2}})^2[/tex]
[tex]56=\frac{22}{7}\times\frac{x^2}{2}\\\\\Rightarrow\ x^2= \dfrac{7}{11}\times56\\\\\Rightarrow\ x^2=35.636\\\\\Rightarrow\ x=\sqrt{35.636}\approx5.970[/tex]
Hence, the value of x is 5.970.
the difference between 8 times a number and 3 is equal to -19 what's the number
Answer:
-2
Step-by-step explanation:
x = the number
difference refers to subtraction
(8*x) - 3 = -19
8x - 3 = -19
+ 3 + 3
8x = -16
/ 8 /8
x = -2
Hope that helps!
Answer:
- 2
Step-by-step explanation:
let the number be n , then
8n - 3 = - 19 ( add 3 to both sides )
8n = - 16 ( divide both sides by 8 )
n = - 2
The number is - 2
Figure ABCD is a rhombus.
Rhombus A B C D is shown. Angle A is (5 x + 25) degrees and angle D is (7 x minus 1) degrees.
What is the value of x?
13
14
26
28
The value of x is 13 in the rhombus ABCD
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners
In figure ABCD is a rhombus
Given as Angle ∠ A = (5x + 25)
Angle ∠ D = (7x - 1)
Since adjacent angles of a rhombus add up to 180°
(5x + 25) + (7x - 1) = 180 and both equal
So, 5x + 25 = 7x - 1
Rearrange the terms in the equation,
7x - 5x = 1 +25
2x = 26
x = 13
Hence, the value of x is 13 in given figure.
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9. Select all expressions that are
equivalent to 18a – 12.
2(9a - 6)
6(3a – 2)
-3(6a + 4)
3(6a + 4)
0 (
— 3(4 – 6а)
Answer:
Step-by-step explanation:
2(9a - 6) = 2*9a - 2*6 = 18a - 12
Yes, it is equivalent.
6*(3a-2) = 6*3a - 6*2 = 18a - 12
Yes, it is equivalent.
-3(6a+4)= -3*6a + 4*(-3) = -18a - 12
No, not equivalent
3(6a+4) = 3*6a + 3*4 = 18a + 12
No, not equivalent
-3(4-6a) = -3*4 - 6a*(-3 ) = -12 + 18a = 18a - 12
Yes, it is equivalent.
Answer:
2(9a - 6), 6(3a – 2) and -3(4 – 6а)Step-by-step explanation:
2(9a - 6) = 2 × 9a + 2 × (-6)
= 18a - 12
6(3a - 2) = 6 × 3a + 6 × (-2)
= 18a - 12
- 3( 4 - 6a ) = - 3 × 4 + (-3) × (- 6a)
= - 12 + 18a = 18a - 12
Parallel maze puzzle
Answers:
d) verticalc) alternate interiorf) supplementarye) alternate exteriorg) correspondinge) alternate exteriorf) supplementaryc) alternate interiore) alternate exteriorLetters 'a', b, and h are never used.
Letters c and f show up twice each; e shows up 3 times.
=====================================================
Explanations:
Angles 1 and 2 are vertical angles because they are opposite one another in this X configuration. Vertical angles are always congruent.These angles are alternate interior angles because they are inside the parallel lines (hence the "interior") and they are on alternating sides of the transversal cut.The two angles shown here form a straight line, so that's what makes them supplementary. Supplementary angles add to 180 degrees.Angle 4 and angle 5 are on alternating sides of the transversal, but this time they are outside the parallel lines. So that's why we go for alternate exterior this time. Angles 5 and 6 are in the same southwest corner of each four-corner configuration, which makes them corresponding angles.It's the same idea as problem 4Same idea as problem 3.Same idea as problem 2.Same idea as problems 4 and 6.---------------
None of the angle pairs mentioned are consecutive interior angles. These types of angles are on the same side of the transversal, and inside the parallel lines. So we never use option 'a'. We cross off option h as well for pretty much identical reasoning. Options 'a' and h are the same thing, just slightly different wording.
We cross off option b as well because none of the angles add up to 90 degrees.
Please help :(((((((((((((
3. Find the perimeter of AABC.
Answer:
34 units
Step-by-step explanation:
Perimeter of ∆ABC is,
2(6+4+7)
= 2×(17)
= 34
Answered by GAUTHMATH
Troy spends $9.75 on chicken feed
each week. He has 48 chickens and
each chicken lays one egg a day. At
the end of the week, Troy keeps one
dozen eggs for himself and sells the
rest at the farmer's market for $4.00 a
dozen. What is Troy's weekly profit?
A $98.25
B $102.25
© $112
D $192
Answer:
A
Step-by-step explanation:
Total eggs in lay in one week = 48 * 7 = 336
total eggs sold = 336 - 12 = 324
Total dozen = 324 : 12 = 27
Total profit = 27 * 4 = $108
Profit without chicken feed = 108 - 9.75 = $98.25
prove that: sin8A/1-cos8A=cot4A
Step-by-step explanation:
Recall the identity
[tex]\tan \frac{A}{2}= \dfrac{1 - \cos A}{\sin A}[/tex]
We can see that
[tex]\dfrac{\sin 8A}{1 - \cos 8A} = \dfrac{1}{\tan 4A}= \cot 4A[/tex]