Answers
Answer:
[tex]y\leq \frac{1}{2} x+3[/tex]
Step-by-step explanation:
slope intercept form is [tex]y=mx+b[/tex] where [tex]m[/tex] is the gradient and [tex]b[/tex] is the y-intercept (the number at which it crosses the y axis)
firstly find the equation for this line:
the gradient can be found with the formula [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
so the gradient is [tex]\frac{4-3}{2-0}=\frac{1}{2} =0.5[/tex]
the y intercept is where it crosses the y axis so it is simply 3
our equation for the line is now [tex]y=\frac{1}{2} x+3[/tex] but the question is asking for an equality where the shaded area is BELOW the line.
so the inequality is [tex]y\leq \frac{1}{2} x+3[/tex]
Answer:
y ≤ [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
the equation of the line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-6)}[/tex] = [tex]\frac{3}{0+6}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = [tex]\frac{1}{2}[/tex] x + 3 ← is the equation of the line
the solution lies below the line and on the line.
as line is solid use ≤
y ≤ [tex]\frac{1}{2}[/tex] x + 3
Related Questions
Please do your thing smart people.
HELP ME PLEASE
Answers
Answer:
C. Natural Numbers
Step-by-step explanation:
Before we determine what groups [tex]\sqrt{100}[/tex] fits into, we must simplify it. We get the number 10, which is much easier to categorize. Out of the four options, the natural numbers are the smallest group, containing only the numbers we use to count (i.e. 1, 2, 3, 4 ...). We know that 10 fits into this category because 10 is a non-zero whole number. Since the natural numbers contain 10 and are the smallest subset, the answer is C.
As a note: 10 will also fit into the whole numbers and rational numbers since all natural numbers are parts of these two groups as well. These groups contain more numbers, however, making them larger than the natural number set so we can eliminate them. 10 is also not an irrational number since we can accurately define it with a fraction.
Please solve this question.
Answers
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π → A + B = π - C
A + C = π - B
B + C = π - A
Cofunction Identities: sin [(π/2) - A] = cos A
cos [(π/2) - A] = sin A
Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]
Pythagorean Identity: cos²A + sin²A = 1 → cos²A = 1 - sin²A
Even/Odd Identity: cos (-A) = -cos(A)
Double Angle Identity: cos (2A) = 2 cos²A - 1
Proof LHS → RHS:
LHS: cos [(B + C) - A] - cos [(A + C) - B] + cos [(A + B) + C]
Given: cos [(π - A) - A] - cos [(π - B) - B] + cos [(π - C) - C]
= cos (π -2A) - cos (π -2B) + cos (π -2C)
Cofunction: cos (-2A) - cos (-2B) + cos (-2C)
Even/Odd: -cos (2A) + cos (2B) - cos (2C)
Double Angle: -(2cos²A - 1) + cos (2B) - cos (2C)
= 1 - 2cos²A + cos (2B) - cos (2C)
Sum to Product: 1 - 2cos²A - 2sin(B+C) · sin (B-C)
Given: 1 - 2cos²A - 2sin (π - A) · sin (B - C)
Cofunction: 1 - 2cos²A - 2sin A · sin (B - C)
Pythagorean: 1 - 2(1 - sin²A) - 2sin A · sin (B - C)
= 1 - 2 + 2sin²A - 2sin A · sin (B - C)
= -1 + 2sin²A - 2sin A · sin (B - C)
Factor: -1 + 2sin A (sin A - sin (B - C))
Given: -1 + 2sin A [sin (π - (B + C)) - sin (B - C)]
Cofunction: -1 + 2sin A [sin (B + C) - sin (B - C)]
Sum to Product: -1 + 2sin A [2 cos B · sin C]
= -1 + 4sin A · cos B · sin C
LHS = RHS [tex]\checkmark[/tex]
So far, Ricardo has scores of 13, 17, 19 and 21 points for the first four rounds of a dice game. What does he need the total score to be for the next two rounds combined in order to achieve an average score of 20 points per round for all six rounds?
Answers
Answer:
40 points
Step-by-step explanation:
The score for the first four rounds of the game is 13, 17, 19, and 21 points.
Let [tex]S_5[/tex] and [tex]S_6[/tex] be the scores of the fifth and sixth games respectively in order to achieve an average score of 20 points per round for all six rounds.
[tex]\text{Average score} = \frac{\text{Sum of the scores of all the rounds}}{\text{Total number of the rounds}}[/tex]
[tex]\Rightarrow 20=\frac{13+17+19+21+S_5+S_6}{6}[/tex]
[tex]\Rightarrow 20\times6=80+S_5+S_6[/tex]
[tex]\Rightarrow S_5+S_6=120-80=40.[/tex]
Hence, the combined score of the fifth and sixth rounds are 40 points.
Find the Area of the Trapezoid
Answers
Area:-
1/2(Sum of parallel sides) (Height)1/2(2+5)(3)1/2(21)10.5units°2Answer:
[tex]A=\boxed{10.5}\; \;\rm sq. \; un.[/tex]
Step-by-step explanation:
Area of a Trapezoid
[tex]\boxed{A=\dfrac{1}{2}(a+b)h}[/tex]
where:
a and b are the bases of the trapezoid (the parallel sides).h is the height of the trapezoid (perpendicular to the bases).From inspection of the given diagram:
a = SK = 2 unitsb = OC = 5 unitsh = OS = 3 unitsSubstitute the found values into the formula and solve for A:
[tex]\implies A=\dfrac{1}{2}(2+5)(3)[/tex]
[tex]\implies A=\dfrac{1}{2}(7)(3)[/tex]
[tex]\implies A=\dfrac{7}{2}(3)[/tex]
[tex]\implies A=\dfrac{21}{2}[/tex]
[tex]\implies A=10.5\; \;\rm sq. \; un.[/tex]
In the given figure, O is Center of circle. If AC//DB and angle ABC=50 , find angle ACD
Answers
Answer:
Step-by-step explanation:
m∠ACB = m∠CBD = 90° ⇒ m∠CAB = 90° - 50° = 40° = m∠ABD ( Alternate interior angles )
m∠CBD = 90°
m∠CDB = 50 °
Check the picture below, notice the tickmarks, both sides are equal and they make twin angles on the "base" side of the isosceles triangle.
A cone with volume 1350 m³ is dilated by a scale factor of 13. What is the volume of the resulting cone? Enter your answer in the box. M³.
Answers
The volume of the resulting cone is equal to 50 [tex]m^3[/tex].
Given the following data:
Volume of cone = 1350 [tex]m^3[/tex].Dilation factor = [tex]\frac{1}{3}[/tex].How to calculate the volume.Mathematically, the volume of a cone is given by this formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where:
h is the height.r is the radius.Applying the dilation factor, we have:
[tex]V =(\frac{1}{3} )^3 \times 1350\\\\V=0.037037037 \times 1350[/tex]
V = 50 [tex]m^3[/tex].
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Find three consecutive integers such that the sum of the first and twice the second is 86 minus three times the third.
Answers
what is -6.5 x (-.4)
Answers
Answer:
2.6x
Step-by-step explanation:
Answer:
2.6
Step-by-step explanation:
Write an equation of the line passing through the points (4, 15) and (-2, -21).
Answers
Step-by-step explanation:
(y2-y1)/(x2-x1)=(y-y1)/(x-x1)
(-21-15)/(-2-4)=( y-15)/(x-4)
6(x-4)=y-15
6x-y-9=0
18+(-22.45) what does this equal?
Answers
Answer:
Today: Monday, 12 October 2020
Hour: 20.25 WIB (in Indonesian)
________________________
18 + (-22.45) = -4,45
-22.45
18
_____+
-4.45
A farm grew 19.8 tons of wheat in 2013. The farm’s wheat output increased by 9.8% from 2013 to 2014 and by 5.1% from 2014 to 2015. Which expression represents a for estimating the total output of wheat in tons, in 2015?
A. 20+10+5
B. 20(10)(5)
C. 20+1.1+1.05
D. 20(1.1)(1.05)
Please show ur work or at least explain!!
Tysm!
Answers
Answer:
B
Step-by-step explanation:
Because you are multiplying the 20 by the 10 and 5 to get the percentage that wheat increased. all the other options are either just adding number together of multiplying the wrong numbers.
If f(x) = 3^x and g(x) = 2x + 5, at which value of x is f(x) < g(x)?
A. -1
B. 2
C. -3
D. -4
Answers
Answer:
A) x = -1
Step-by-step explanation:
[tex]f(-1)=3^{-1}=\dfrac13\\\\g(-1)=2(-1)+5=3\\\\\implies f(x) < g(x)[/tex]
[tex]f(2)=3^{2}=9\\\\g(2)=2(2)+5=9\\\\\implies f(x)=g(x)[/tex]
[tex]f(-3)=3^{-3}=\dfrac{1}{27}\\\\g(-3)=2(-3)+5=-1\\\\\implies f(x) > g(x)[/tex]
[tex]f(-4)=3^{-4}=\dfrac{1}{81}\\\\g(-4)=2(-4)+5=-3\\\\\implies f(x) > g(x)[/tex]
6. If AB = CD, then CD = AB.
what is the postulate, or theorem
Answers
Answer:. Then either A = C and B = D, or A = D and B = C.
Step-by-step explanation:
please help its A Math Problem Please and Thank you .Consider the translation that is defined by the coordinate translation (x,y)à (x+12, y -7). What is the preimage of C’(-2,1)?
Question 5 options:
C(14, 5)
C(-10+5)
C ( 10,9)
C(-14,8)
Answers
Step-by-step explanation:
Since you added 12 to the x coordinate and subtracted 7 from the y coordinate, to undo that translation, you need to subtract 12 from the x coordinate of the image and add 7 to the y coordinate of the image.
This gives you that C=(-2-12, 1+7)=(-14, 8)
Solve for y.
2v+3y=10
Simplify your answer as much as possible.
V
D
Answers
Answer:
y = [tex]\frac{10-2v}{3}[/tex]
Step-by-step explanation:
Given
2v + 3y = 10 ( subtract 2v from both sides )
3y = 10 - 2v ( divide both sides by 3 )
y = [tex]\frac{10-2v}{3}[/tex]
Which equation can you create with the given information? m = 6, b = -2
a
y=6x-2
y=6x+2
y=2x+6
y=-2x-6
Answers
Answer:
y = 6x - 2
Step-by-step explanation:
y = mx + b
y = 6x + (-2)
If PQRS is a parallelogram and PQ=9x+1 and RS=13x-11, solve for x.
Answers
Applying the definition of a parallelogram, the value of x in the length of the sides of the given parallelogram is: x = 3.
What is a Parallelogram?A parallelogram is a quadrilateral that has two pairs of opposite sides that are congruent to each other.
Given the following:
PQ = 9x + 1RS = 13x - 11Find x by creating an equation:
PQ = RS (congruent sides)
Substitute
9x + 1 = 13x - 11
Combine like terms
9x - 13x = -1 - 11
-4x = - 12
x = 3
Therefore, applying the definition of a parallelogram, the value of x in the length of the sides of the given parallelogram is: x = 3.
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QUESTION NUMBER 1 I NEED HELP WITH
Answers
Answer:
330
Step-by-step explanation:
heart = 110, and the problem is asking the value of 3 hearts. 3 x 110 = 330
Answer:
d: 330
Step-by-step explanation:
spade = heart*2
spade-heart = 110
substitute spade into spade:
2*heart-heart = 110
heart = 110
So,
heart = 110
and,
spade = 2*heart = 2*110 = 220
so spade+heart = 220 + 110 = 330
also, please mark me as brainliest.
much appriciated if helping
Answers
4 quarters are equal in value to 10 dimes.
1. How many dimes equal the value of 6 quarters?
2. How many dimes equal the value of 14 quarters?
3. What value belongs next to the 1 in the table?
What does it mean in this context?
Answers
Answer:
Step-by-step explanation:
Helpp pls I need an answer
Answers
Answer:
It would be 6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
5x + 2 - 7x = -10
Combine the two x's:
-2x + 2 = -10
Subtract 2 from both sides:
-2x = -12
Divide both sides by -2:
x = 6
Find side x. Round to the nearest tenth.
Answers
180-162= 18
Round to the nearest tenth = 20
Answer=20
HURRY WILL NAME BRAINLIEST Which pairs of rational numbers are equivalent? Select all that apply.
-0.5 and Negative one-half
0.ModifyingAbove 7 with barand StartFraction 7 over 10 EndFraction
StartFraction 11 over 20 EndFractionand 0.55
StartFraction negative 1 over 50 EndFractionand -0.02
0.15 and 0.1ModifyingAbove 5 with bar
Answers
The 3 equivalent pairs are:
-0.5 and -1/211/20 and 0.55-1/50 and -0.02Which pairs of rational numbers are equivalent?
Remember that two numbers A and B are equivalent if:
A = B
The first pair given is:
-0.5 and (-1/2).
We know that 1/2 = 0.5, then (-1/2) = -0.5
So we conclude that
-0.5 and (-1/2) are equivalent.
Another equivalent pair is:
11/20 and 0.55
To check this, you can just solve the fraction in your calculator, you will see that:
11/20 = 0.55
Then 11/20 and 0.55 are equivalent.
The final equivalent pair is:
-1/50 and -0.02
Because:
-(1/50) = -(0.02) = -0.02
Then -1/50 and -0.02 are equivalent.
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Answer:
A B
Step-by-step explanation:
Which statement could be used in step 2 when proving x =
30?
Statements
1. mZORP - 80°; mZORN-(3x+10)°
Reasons
1. given
no
- N در دل
O ZORP and ZORN are a linear pair
O ZORP and ZORN are vertical angles
O 80 = 3x +10
O x = 30
Answers
(a) ∠ORP and ∠ORN are a linear pair .
Let us prove that option a , is the correct option by finding the value of x .
Angle ORP and angle ORN are a linear , which means their sum will be equal to 180° .
So :-
[tex]80 + 3x + 10 = 180[/tex]
[tex]3x + 80 + 10 = 180[/tex]
[tex]3x + 90 = 180[/tex]
[tex]3x = 180 - 90[/tex]
[tex]3x = 90[/tex]
[tex]x = \frac{90}{3} [/tex]
[tex]x = 30°[/tex]
As we were able to find put the value of x only after we cam to know that ∠ORP and ∠ORN are a linear pair , we say that option a is the correct statement .
Therefore , the correct answer is :-
(a) ∠ORP and ∠ORN are a linear pair .
The value of x is equal to 30°. Hence, proved.
What are angles at a point on a straight line?Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. Angles on a straight line add to 180°.
Given that, m∠ORP=80° and m∠ORN=(3x+10)°.
Here, m∠ORP+m∠ORN=180° (Angles on straight line adds upto 180°)
80°+(3x+10)°=180°
90°+3x=180°
3x=90°
x=90°/3
x=30°
Hence, proved.
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May I please have help. This is 7th-8th grade math.
30 POINTS
Answers
Answer:
See attached
Step-by-step explanation:
Refer to attachment
ΔA'B'C' is the image of ΔABC
Which set of ordered pairs represents a function?
a
{(1, 8), (8, 1), (1, 5), (5, 1)}
b
{(2, 1), (3, 1) (4, 3), (5, 3)}
c
{(5, 1), (3, 8), (3, 7), (7, 3)}
d
{(5, 1), (5, 6), (1, 3), (9, 7)}
Answers
Answer:
b. {(2, 1), (3, 1) (4, 3), (5, 3)}
what is the area of this circle
Answers
Answer:
4,500
Step-by-step explanation:
The surface area of a cylinder is approximately 640.56 square meters. The radius of the cylinder is 5 meters less than the height of the cylinder. To the nearest whole meter, what are the radius and height of the cylinder?
Answers
the radius is approximately 6 meters,
height is approximately 11 meters
The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
What is cylinder?A cylinder is a "three-dimensional object with two round flat bases and one curved side. It has a curved surface in the middle. The base and the top surface are identical".
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2(3.14)(x-5)(x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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There are 900 students
at Acute Middle
School. The ratio of
boys to girls is 2 to 3.
What percent of the
students are girls?
I need work to be shown.
Answers
Sort the following numbers in order from least (bottom) to greatest (top)
Answers
Answer:
bdacStep-by-step explanation:
the least value is negative 9 x 10-³
the greatest value is positive 7 x 10-⁵
Answer:
2,4,1,3
Step-by-step explanation:
So, I labeled each one, 1,2,3, and 4 respectively.
1, when expanded is 0.000005
2 is equal to -0.009
3 is simple 0.00007
and 4 is -0.0000002
Obviously the one of the negative numbers is the smallest. The bigger number with the negative sign is more negative because it is farther away from one on the number line. Therefore 2 is the smallest. That makes 4 the second smallest. 3 is larger than 1 because there are less zeros to the first non-zero digit. That places the order from least to greatest as:
2,4,1,3