Answer: C) [tex](-\dfrac{1}{2},\dfrac{3}{2})[/tex]
Step-by-step explanation:
The given system of equations :
[tex]2(y-x) = 5+2x\ \ ...(i)\\\\ 2(y+x)=5-2y\ \ ..(ii)[/tex]
Simplify left side, we get
[tex]2y-2x=5+2x\Rightarrow\ 2y-4x=5\ \ ...(iii)\\\\ 2y+2x=5-2y\Rightarrow\ 4y+2x=5\ \ ...(iv)[/tex]
Multiplying 2 on equation (iii), we get
[tex]4y-8x=10\ \ ...(v)[/tex]
Subtracting (v) from (iv) , we get
[tex]2x-(-8x)=5-10\\\\\Rightarrow\ 2x+8x=-5\\\\\Rightarrow\ 10x=-5\\\\\Rightarrow\ x=-\dfrac{5}{10}=-\dfrac{1}{2}[/tex]
Put value of [tex]x=-\dfrac{1}{2}[/tex] in (v), we get
[tex]4y-8(-\dfrac{1}{2})=10\\\\\Rightarrow \ 4y+4=10\\\\\Rightarrow\ 4y=10-4=6\\\\\Rightarrow\ y=\dfrac{6}{4}=\dfrac{3}{2}[/tex]
hence, the solution to the system is [tex](x,y)=(-\dfrac{1}{2},\dfrac{3}{2})[/tex]
BC is tangent to circle A. Determine the length of AC . ANSWERS: 1) 3 2) 4 3) 5 4) 6
A circle is a curve sketched out by a point moving in a plane. The length of AC in the given figure is 5 units. The correct option is
3.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
In a circle, the angle between the radius and tangent is always equal to 90°. Therefore, we can write that in the given figure ΔABC, the triangle is a right angle triangle with ∠B as the right angle.
Now, for the triangle using the Pythagoras theorem we can write,
AC² = AB² + BC²
AC² = 3² + 4²
AC² = 9 + 16
AC = √25
AC = 5
Hence, the length of AC in the given figure is 5 units.
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Plz help me 3(x+1)=5+x
Answer:
x=1
Step-by-step explanation:
3x+3=5+x
3x-x+3=5
2x=2
x=1
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 1
▹ Step-by-Step Explanation
3(x + 1) = 5 + x
Distribute
3x + 3 = 5 + x
Move the variable to the left and change the sign
3x - x + 3 = 5
Collect like terms
2x = 5 - 3
Calculate
2x = 2
Final Answer
x = 1
Hope this helps!
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Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Consider functions f and g below. [tex]g(x) = -x^2 + 2x + 4[/tex] Which of the following statements is true? A. As x approaches infinity, the values of f(x) and g(x) both approach infinity. B. As x approaches infinity, the values of f(x) and g(x) both approach negative infinity. C. As x approaches infinity, the value of f(x) approaches infinity and the value of g(x) approaches negative infinity. D. As x approaches infinity, the value of f(x) approaches negative infinity and the value of g(x) approaches infinity.
Answer:
Step-by-step explanation:
Where is f(x)? My answers pertains only to g(x) = -x^2 + 2x + 4.
Part of B is true: As x approaches infinity in either direction, g(x) approaches negative infinity. The graph of g(x) is an inverted parabola.
Trying to find the missing segment to the triangle in the attached image. Any help would be appreciated. Thanks.
Answer:
24 unit
Step-by-step explanation:
This question can be solved using concept of basic proportionality theorem,
according to this theorem, if a line is drawn parallel to one side of the triangle and intersect the other two sides then the two sides are divided in the same ratio.
Example:
let there be a triangle ABC
if DE is drawn parallel to BC such that D is a point on line AB and E is other point on AC, then
AD/DB = AE/EC (basic proportionality theorem)
_____________________________________
Similarly in this problem
15/5 = ?/8
3= ?/8
? = 8*3 = 24
Thus. missing segment value is 24 unit.
Given that 0≤β<2π, find all the solutions to the equation 2sin^2β=7sinβ+4.
Answer:
Step-by-step explanation:
2sin²β-7sinβ-4=0
2sin²β-8sin β+1 sin β-4=0
2 sin β(sin β-4)+1(sin β-4)=0
(sin β-4)(2sin β+1)=0
either sin β-4=0
sin β=4 (rejected,as |sin β|≤1)
or
2 sin β+1=0
sin β=-1/2=-sin (π/6)=sin (π+π/6),sin (2π-π/6)
β=7π/6,11π/6
10. The sum of four consecutive integers is at least 18. What's the smallest consecutive integer to make this statement true?
O A.3
O B.4
O C.5
O D.8
Answer:
A. 3
Step-by-step explanation:
Let the integers be
x
(x+1)
(x+2)
(x+3)
Sum the integers
We have,
x+(x+1)+(x+2)+(x+3)=18
x+x+1+x+2+x+3=18
4x+6=18
Subtract 6 from both sides
4x-6=18-6
4x=12
Divide both sides by 4
4x/4=12/4
x=3
The smallest integer which is x is equal to 3
Check:
3+4+5+6=18
-1 2/3 divided by (-2 1/5)
Answer:
25/33
Step-by-step explanation:
-1 2/3 ÷ ( -2 1/5)
Change from mixed number to improper fraction
- ( 3*1 + 2) /3 ÷ - ( 5*2+1) /5
-5/3 ÷ -11/5
Copy dot flip
-5/3 * -5/11
25/33
PLLLLLLLLLLZZZZZZZZZ
Answer: 4m + 3
Step-by-step explanation:
4m references the 4 bags of marbles and the m marbles in each bag. + 3 references the extra 3 marbles.
MULTIPLE CHOICE
What is 14+2(3x +9) - 5 when simplified?
A
20x +4
B
6x+27
С
X+27
Answer:
B: 6x+27
Step-by-step explanation:
14+2(3x+9)-5
14+6x+18-5
14+6x+13
6x+27 is the final answer
The Answer is: B
Step-by-step explanation:
Find the area of ΔDEF to the nearest tenth. ANSWERS: A) 127.8 square units B) 46.5 square units C) 63.9 square units D) 23.3 square units
Answer:
C) 63.9 square units
Step-by-step explanation:
From the above diagram, we can see that the triangle has 2 sides and and angle
The formula for the area of a triangle that has 2 sides and an angle = 1/2absinθ
θ = 70°
a = DE = 8 units
b = EF = 17 units
Area of ΔDEF = 1/2 × 8 × 17 × sin 70°
Area of ΔDEF = 63.9 square units.
Answer:
63.9 square units
Step-by-step explanation:I took the test
pllllllllzzzzzzz answer this!!!♥️♥️
9514 1404 393
Answer:
a) 7:24 pm
b) later than 7:24 pm
Step-by-step explanation:
The relationship between time, speed, and distance can be written as ...
time = distance/speed
So, Faris's travel time to London is predicted to be ...
time = (195 mi)/(50 mi/h) = 3.9 h = 3:54 hours
__
a) Faris's expected arrival time at a speed of 50 mph is ...
3:30 pm +3:54 = 6:84 pm = 7:24 pm
__
b) Time is inversely proportional to speed, so a lower speed will result in a longer time.
Faris's arrival time will be later than 7:24 pm.
Which is the graph of the linear inequality 2x – 3y < 12?
B
Answer:
C.
Step-by-step explanation:
Given
2x - 3y < 12
Required
Find the graph it represents
we start by solving for the x and y intercepts;
Let x = 0
2x - 3y < 12 becomes
2(0) - 3y < 12
0 - 3y < 12
-3y < 12
Divide both sides by -3
-3y/3 < 12/-3
y > -4
Let y = 0
2x - 3y < 12 becomes
2x - 3(0) < 12
2x - 0 < 12
2x < 12
Divide both sides by 2
2x/2 < 12/2
x < 6
So, we have
x < 6 and y > -4
This implies that the graph is bound by the region where the values of x is less than 6 and the values of y is greater than -4
From the list of given options,only option C answers this question. The dotted lines actually represent inequalities
pls help i give brainliest
Answer: B no
Step-by-step explanation:
Plot in the x and y coordinates into the equation to solve it.
The x coordinate is 4 and the y coordinate is 1
-4(4) +3(1)= 2
-16 + 3 = 2
-13 ≠2
-13 does not equal 2 so (4,1) is not a solution.
Answer: NO
Step-by-step explanation:
[tex]Substitute \\\\-4(4)+3(1)=2\\\\Multiply\\\\-16+3=2\\\\Combine \\like \\terms\\-13=2[/tex]
-13 does NOT equal 2, so it is not a solution
Hope it helps <3
You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost? Include a let statement in your answer.
Answer:
5$??.
Step-by-step explanation:
If a magazine was 5$, 25-5= 20. So then, 20÷4= 5. There fore an eraser costs 5$.
Answer:
5 dollars
Step-by-step explanation:
Let x be the price of each eraser
We bought a magazine and 4 erasers with 25 dollars
so : 5+4x = 25⇒ 4x= 20⇒x= 20/4⇒ x=5
The eraser costs 5 dollars
-125>-135 divide each side by -5 what is the resulting true inequality
Answer: 25<27
Step-by-step explanation:
-125/-5=25
-135/-5=27
25<27
Answer:
[tex]\boxed{25<27}[/tex]
Step-by-step explanation:
[tex]-125 > -135[/tex]
Dividing both sides by -5
=> [tex]\frac{-125}{-5} < \frac{-135}{-5}[/tex]
=> [tex]25 < 27[/tex]
!!!! PLEASE HELP ME !!!!Find each measure. m<1 m<2 m< 3
Answer:
m angle 1= 45
m angle 2= 76
m angle 3= 80
Step-by-step explanation:
I NEED HELP CAN SOMEONE PLEASE ANSWER THIS ASAP PLEASE!!!
Answer:
y = 5x - 3
Step-by-step explanation:
ok so perpendicular just means the opposite reciprocal of the slope of the normal equation. It just means that they form a 90 degree angel when they intersect.
12/ y + 8 = 4/9 Thats the question. Im dyin for help. :)
Answer:
-1 10/17
Step-by-step explanation:
Answer:
y = 1 10/17
Step-by-step explanation:
The LCD is 9y. Multiply all three terms by 9y:
(9y)(12) (9y)(4)
----------- + 8(9y) = -----------
y 9
This reduces to 108 + 72y = 4y, or 108 = -68y
Dividing both sides by 68, we get y = 1 10/17
f(x) = x2. What is g(x)?
Answer:
g (x-2) = x
Step-by-step explanation:
Set up the composite result function g (f(x))
Then Evaluate g (f(x)) by substituting in the value of F into G: g (x-2) = (x-2) + 2
finally Combine the opposite terms in (x-2) + 2: add -2 and 2: g(x-2) = x+0: add x and 0: g(x-2) = x
−7∘C denotes a temperature of 7∘C below 0∘C, what does 5∘C mean?
PLLLLLLLLLLZZZZZZZZZ
Answer:
Hey there!
Donald would have 20x+10 dollars.
20 dollars (number of 20 dollars) + 10 dollars
Answer: 20x + 10
Step-by-step explanation:
20x in this expression means 20 * the number of dollar bills he owns. Each bill is worth twenty dollars. + 10 is simply 10 * 1(the number of 10 dollar bills he owns)
Hope it helps <3
Question 5 (1 point)
(06.02 LC)
Which statement best describes the expression 3y = 8? (1 point)
O 1) 8 divided by 3 times y
O2) 8 times y divided by 3
03) 3 divided by 8 times y
O4) 3 times y divided by 8
Answer:
Step-by-step explanation:
None of these choices is correct.
3y = 8 is an equation, not an expression. It states that "y is 8 divided by 3," which again is an equation.
Answer:
3 times y divided by 8
Step-by-step explanation:
9. Annie works as a school tutor and a baker. As a tutor, she earns $18 per hour. Last
week she worked x hours as a tutor and her friend paid her $25 to bake a cake.
Write an expression to represent the total amount Annie earned last week.
Type your answer below:
The total amount Annie earned last week 18x+25.
What is work in math ?In conclusion, when a force acts on an object to induce a displacement, labor is done.To determine the amount of work, three quantities must be known. The force, the displacement, and the angle between the force and the displacement are the three variables.Annie earns $18 per hour. and she worked x hours .
So, total work = 18 * x = 18x
but she earned some extra cash = 25$
now Annie's total amount with extra cash = 18x + 25
Therefore, The total amount Annie earned last week 18x+25.
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A geometric sequence of positive integers is formed for which the first term is 2 and the fifth term is 162. What is the sixth term of the sequence?
Answer:486
Step-by-step explanation:
(Multiply by 3 each time ;))
Hope this helped!
<!> Brainliest is appreciated! <!>
Answer:
multipl each 3 times
Step-by-step explanation:
Which of the following is equivalent to: -5 - 4?*
Answer:
-9
Step-by-step explanation:
-5 - 4 = -5 + (4)
You are adding two negative numbers, so add the absolute values of the numbers, and the sign of the answer is negative.
-5 - 4 = -(|-5| + |4|) = -(5 + 4) = -9
If abc=dec b=2x+31 and e=7x-24 x=?
Answer:
x = 11
Step-by-step explanation:
As it is stated the the both the triangle ABC and DEC are congruent, it means that all the angles forms in these triangles are also congruent. We can states that
<A = <D
<C = <C
<B = <E
As both angles B and E are equal to each other, we can equate them
<B = <E
Where <B = 2x+31 and <E= 7x-24, substitute both values in above expression:
2x + 31 = 7x - 24
Solve for x:
7x - 2x = 31 +24
5x = 55
x = 11
Answer:
11
Step-by-step explanation:
The two cylinders are similar. Find the surface area of the smaller cylinder. Round your answer to the nearest hundredth.
A. 942.48 cm²
B. 376.99 cm²
C. 565.49 cm²
D. 226.19 cm²
Answer:
D
Step-by-step explanation:
To first tackle this question, use similarity ratio, where the missing diameter is d. 10/15 = d/9 which can be simplified into d = 6. Then use the surface formula
2πrh + 2πr². Then, since the radius is 0.5d, the radius or r is 3. Then, plus in values and simplify to get 226.19cm².
Solve for x 4 ( x + 3 ) < 3 ( x + 5 )
Answer: x < 3
Step-by-step explanation:
4(x + 3) < 3(x + 5)
4x + 12 < 3x + 15 Distributed
x + 12 < 15 Subtracted 3x from both sides
x < 3 Subtracted 12 from both sides
Answer:
4x^2+9x-15<0
Step-by-step explanation:
x.4(x+3)<3(x+5)
(4x)(x+3)<3x+3x5
(4x)(x+3)<3x+15
4xx+4x.3<3x+15
4x^1+1+4x3x<3x+15
4x^2+12x<3x+15
(4x^2+12x)+(-3x-15)<(3x+15)+(-3x-15x)
4x^2+9x-15<3x-3x+15-15
4x^2+9x-15<0
Please answer asap! What is the range of the function y = -|x|? y ≤ 0 x ≤ 0 all real numbers
Answer:
[tex]\huge \boxed{y\leq 0}[/tex]
Step-by-step explanation:
The range of a function are all possible values for y.
[tex]y = -|x|[/tex]
The domain is all real numbers. The value of x can be all real numbers.
The absolute value of a number will always be positive.
The negative sign gets distributed to the absolute value, the output or end result will always be a negative number or zero, the range is less than or equal to 0.
The range of the function is [tex]y\leq 0[/tex]
A car begins to depreciate at a rate of 24.9% annually as soon as it is driven off the lot. If a car was purchased for 26,500; how much is it worth after the second year? The equation you used is? What is the value of the car after two years?
Answer:
13197
Step-by-step explanation:
You have to do 24.9*2 and then find that percent of 26500