A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. On a coordinate plane, points are at (negative 5, negative 7) and (3, 1). What is the solution to the system of equations? (–6, –4) (0, –1) (0, –2) (2, 0)
Answer:
The solution of the system of equations is (x,y) = (2,0)
Step-by-step explanation:
The equation of a line through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is equal to:
[tex]y-y_1=m(x-x_1)[/tex]
Where [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So, the equation of the line through the points (3, 1) and (–5, –7) is:
[tex]m=\frac{-7-1}{-5-3}=1[/tex]
[tex]y-1=1(x-3)\\y=x-3+1\\y=x-2[/tex]
Then, we have two equations, y=x-2 and y=0.5x -1 , so solving for x, we get:
x - 2 = 0.5 x - 1
x - 0.5x = 2 - 1
x = 2
Replacing x=2 in the equation y=x-2, we get:
y =2 - 2 = 0
Finally, the solution of the system of equations is (x,y) = (2,0)
Answer:The solution of the system of equations is (x,y) = (2,0)
Step-by-step explanation:
Please help me!!!!!! I do not understand...
Answer:
the second one........the shape of the conic section os circle
Find the measure of AEC and BED
Answer:
30°
Step-by-step explanation:
well AEB is a straight line which is 180° and we were already given the angles that made up the straight line ,so all u had to do was subtract 60° from 90°
BED =30°
Answer:
AEC=30
BED=30
Step-by-step explanation:
We know that AEC is 30 degrees because it is on line AB, along with a right angle and 60 degrees, add 90 to 60 to get 150, and subtract it from 180 to get your answer, 30
As for BED, AEC and BED are verticle angles so they are equivalent.
If you found this helpful, please consider giving me brainliest, it will help me a lot
Have a good day! :)
Can someone please help me with this and show work
Answer:
29/6-16/2549/30Rationalize(1.63333333333)1*(19/30)20 POINTS AND WILL GIVE THE BRAINLIEST!!! Jack's favorite sports drink comes in a 20-ounce bottle. The manufacturer of the sports drink requires a tolerance of 0.4 ounce. This means that as long as the bottle is within 0.4 ounce of 20 ounces, the bottle can be sent to stores to be sold.
sold. Write an absolute value inequality describes the acceptable weight, w, of a 20-ounce bottle of sports drink
Answer:
[tex]|w-20|\leq 0.4[/tex]
Step-by-step explanation:
The manufacturer requires that the weight differs from 20 oz in at most 0.4 oz, therefore we can write this difference (which can be either above or below 20 oz, to be smaller than or equal to 0.4 oz.
The weight can be:
1) smaller than or equal to 20 oz + 0.4 oz: [tex]w\leq 20+0.4[/tex] then [tex]w-20\leq 0.4[/tex]
2) larger than or equal to 20 oz - 0.4 oz: [tex]20-0.4\leq w[/tex] then [tex]-0.4\leq w-20[/tex]
and which combined, can be written as a double inequality;
[tex]-0.4 \leq w-20\leq 0.4[/tex]
This double condition can also be written using the absolute value symbol as: [tex]|w-20|\leq 0.4[/tex]
Find the equation of the circle whose center and radius are given. Center:(-2,-5) Radius=1
Answer:
( x+2)^2 + (y+5)^2 = 1
Step-by-step explanation:
The equation of a circle can be written in the form
( x-h)^2 + (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
( x- -2)^2 + (y- -5)^2 = 1^2
( x+2)^2 + (y+5)^2 = 1
Answer:
[tex](x + 2)^{2} + (y + 5)^{2} = 1[/tex]
Step-by-step explanation:
The guy above is correct! I just finished the quiz and checked the answer key.
Enter a range of values for x.
85°
25
5x - 10
[ ? ]
Enter
==================================================
Explanation:
We'll use the hinge theorem here. This says (more or less) that the larger an angle is, the side opposite of that will be longer.
Imagine that the segments with the single tickmarks represent a door swinging open/shut. The more open a door is, the further the distance it is from the handle to the frame. In terms of these triangles, the segment 25 is larger than 5x-10 because the angle 90 (opposite the 25) is larger than the angle 85 degrees (opposite the 5x-10)
In symbols we say
5x - 10 < 25
We also say 5x - 10 > 0 or 0 < 5x - 10 to ensure that the segment of length 5x-10 is not 0 or negative.
Put the two inequalities together and we get 0 < 5x - 10 < 25
------------
Solve for x
0 < 5x - 10 < 25
0+10 < 5x - 10 < 25 + 10 .... adding 10 to all sides
10 < 5x < 35
10/5 < 5x/5 < 35/5 ... dividing all sides by 5
2 < x < 7
We have x between 2 and 7, and not equal to either endpoint.
Middle school help???? fast
Answer:
8.4 ft
Step-by-step explanation:
Perimeter = side x 4
(Re-arrange)
Side = Perimeter / 4
34/4 = 8.4 ft
Answer:
8.5 feet
Step-by-step explanation:
Divide 34 by 4. A square has 4 sides which are all the same.
How many solutions are there to |x|=-8
Answer:No solution
Step-by-step explanation:An absolute value equation cannot equal a negative number
-5a-9+a=15 Explain please
Answer:
a = -6
Step-by-step explanation:
-5a-9+a=15
Combine like terms
-5a+a -9 = 15
-4a -9 = 15
Add 9 to each side
-4a -9+9 = 15+9
-4a = 24
Divide by -4
-4a/-4 = 24/-4
a = -6
Answer:
a = -6
Step-by-step explanation:
1. Combine like terms: -4a – 9 = 15
2. Use the additive property of equality to add 9 to both sides: -4a = 24
3. Use division property of equality to divide -4 on both sides: a = -6
If the perimeters of each shape are equal, which equation can be used to find the value of x? A triangle with base x + 2, height x, and side length x + 4. A triangle with length of x + 3 and width of one-half x. (x + 4) + x + (x + 2) = one-half x + (x + 3) (x + 2) + x + (x + 4) = 2 (one-half x) + 2 (x + 3) 2 (x) + 2 (x + 2) = 2 (one-half x) + 2 (x + 3) x + (x + 2) + (x + 4) = 2 (x + 3 and one-half)
Correct question :
If the perimeters of each shape are equal, which equation can be used to find the value of x? A triangle with base x + 2, height x, and side length x + 4. A rectangle with length of x + 3 and width of one-half x. (x + 4) + x + (x + 2) = one-half x + (x + 3) (x + 2) + x + (x + 4) = 2 (one-half x) + 2 (x + 3) 2 (x) + 2 (x + 2) = 2 (one-half x) + 2 (x + 3) x + (x + 2) + (x + 4) = 2 (x + 3 and one-half)
Answer: (x + 2) + x + (x + 4) = 2 (one-half x) + 2 (x + 3)
Step-by-step explanation:
Given the following :
A triangle with base x + 2, height x, and side length x + 4 - - - -
b = x + 2 ; a = x ; c = x + 4
Perimeter (P) of a triangle :
P = a + b + c
P =( x + 2) + x + (x + 4) - - - (1)
A rectangle with length of x + 3 and width of one-half x
l = x + 3 ; w = 1/2 x
Perimeter of a rectangle (P) = 2(l+w)
P = 2(x+3) + 2(1/2x)
If perimeter of each same are the same ; then;
(1) = (2)
(x + 2) + x + (x + 4) = 2(x+3) + 2(1/2x)
Answer:
B
Step-by-step explanation:
True or False: In a uniform probability distribution, any random variable is just as likely as any other random variable to occur, provided the random variables belong to the distribution.'
Answer:
True
Step-by-step explanation:
trust me, i remember this question
Clinical Trial When XELJANZ (tofacitinib) was administered as part of a clinical trial for this rheumatoid arthritis treatment, 1336 subjects were given 5 mg doses of the drug, and here are the numbers of adverse reactions: 57 had headaches, 21 had hypertension, 60 had upper respiratory tract infections, 51 had nasopharyngitis, and 53 had diarrhea. Does any one of these adverse reactions appear to be much more common than the others? (Hint: Find the relative frequencies using only the adverse reactions, not the total number of treated subjects.)
Answer:
Relative frequencies:
Headaches = 23.55 %
Hypertension = 8.68%
Upper respiratory tract infections =24.79%
Nasopharyngitis = 21.07
Diarrhea = 21.09%
None of these adverse reactions appear to be much more common than the others.
Step-by-step explanation:
Compute frequency:
The number of adverse reactions categories:
Headaches
Hypertension
Upper respiratory tract infections
Nasopharyngitis
Diarrhea
Frequency of each adverse reaction:
Adverse reaction Frequency
Headaches 57
Hypertension 21
Upper respiratory tract infections 60
Nasopharyngitis 51
Diarrhea 53
Compute total frequency
Total frequency is compute dby taking sum of all frequencies;
Sum of frequencies = 57 + 21 + 60 + 51 + 53
= 242
Compute relative frequency:
In order to find if any one of these adverse reactions appear to be much more common than the others, we have to compute relative frequency using these adverse reactions.
By calculating relative frequency we are looking at the number of times a specific adverse reaction appears to be more common, compared to the others.
To calculate relative frequency, divide the frequency of each adverse reaction by the total frequency i.e. 242.
Relative frequency for Headache = 57 / 242
= 0.2355
= 23.55 %
Relative frequency for Hypertension = 21 / 242
= 0.0868
= 8.68 %
Relative frequency for Upper respiratory tract infections = 60 / 242
= 0.2497
= 24.97 %
Relative frequency for Nasopharyngitis = 51 / 242
= 0.2107
= 21.07 %
Relative frequency for Diarrhea = 53 / 242
= 0.2190
= 21.90 %
If you observe the relative frequencies of all the adverse reactions, none of them appear to be much more common than the others. Relative frequencies of headaches, upper respiratory tract infections, nasopharyngitis and diarrhea are almost equally common however, relative of hypertension appears to be very less than the other three.
If approximately 10% of people are left-handed, how many lefties would you expect in a high school graduating class of 424
Answer:
42
Step-by-step explanation:
P(left) = 0.10
Expected number of lefties among high school grads of 424
= 424 * 0.10
= 42 (to the nearest person)
Answer:
you do 20% of 424
1 0% of 424 =42.4
you could round it to 42
Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2)
A. y + 2 = 2(x - 2)
B. y 4 20 + 1)
c. y + 1 = 2(3-4)
D. y 2 233 - 2)
Answer:
The answer is option BStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find an equation of a line given two points first find the slope / gradient
Slope of the line using points (-1,4) and (-2,2) is
[tex]m = \frac{2 - 4}{ - 2 + 1} = \frac{ - 2}{ - 1} = 2[/tex]
So the equation of the line using point (-1,4) is
y - 4 = 2( x + 1)Hope this helps you
HELP!!
According to the graph, what is the value of the constant in the equation below?
Answer:
The answer is option BStep-by-step explanation:
To find the constant in the equation pick any values of x and y and substitute it into the equation
First make constant the subject
constant = height × width
From the question
Using
height = 30
width = 2
We have
constant = 30 × 2 = 60
Again
Using
height = 12
width = 5
constant = 12 × 5 = 60
Since the constant is the same for any values used
constant = 60Hope this helps you
What the answer now now
Answer:
The area of the triangle is [tex]346.0\ mm^2[/tex]
Step-by-step explanation:
Given
Triangle VWU
Required
Determine the Area of the Triangle
First, we'll solve for the third angle
Angles in a triangle when added equals 180; So
[tex]36 + 24 + <V = 180[/tex]
[tex]60 + <V = 180[/tex]
[tex]<V = 180 - 60[/tex]
[tex]<V = 120[/tex]
Next is to determine the length of VW using Sine Law which goes thus
[tex]\frac{VW}{Sin24} = \frac{34}{Sin36}[/tex] (Because 24 degrees is the angle opposite side VW)
Multiply both sides by Sin24
[tex]SIn24 * \frac{VW}{Sin24} = \frac{34}{Sin36} * Sin24[/tex]
[tex]VW = \frac{34}{Sin36} * Sin24[/tex]
[tex]VW = \frac{34}{0.5878} * 0.4067[/tex]
[tex]VW = 23.5 mm[/tex] (Approximated)
At this stage, we have two known sides and two known angles;
The Area can be calculated as the 1/2 * the products of two sides * Sin of the angle between the two sides
Considering VW and VU
VW = 23.5 (Calculated);
VU = 34 (Given)
The angle between these two sides is 120 (Calculated);
Hence;
[tex]Area = \frac{1}{2} * 23.5 * 34 * Sin120[/tex]
[tex]Area = \frac{1}{2} * 23.5 * 34 * 0.8660[/tex]
[tex]Area = \frac{1}{2} * 691.934[/tex]
[tex]Area = 346.0 mm^2[/tex]
Hence, the area of the triangle is [tex]346.0\ mm^2[/tex]
Write the equation of the circumference that meets the condition: Center on the line: x -4y = 1 And it passes through the points A (3,7) and B (5,5)
Answer:
(x + 3)² + (y + 1)² = 100
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center of the circle and r is the radius.
The center is on the line x − 4y = 1, so:
h − 4k = 1
h = 1 + 4k
(x − 1 − 4k)² + (y − k)² = r²
Two points on the line are (3, 7) and (5, 5), so:
(3 − 1 − 4k)² + (7 − k)² = r²
(5 − 1 − 4k)² + (5 − k)² = r²
Set the equations equal:
(3 − 1 − 4k)² + (7 − k)² = (5 − 1 − 4k)² + (5 − k)²
(2 − 4k)² + (7 − k)² = (4 − 4k)² + (5 − k)²
4 − 16k + 16k² + 49 − 14k + k² = 16 − 32k + 16k² + 25 − 10k + k²
4 − 16k + 49 − 14k = 16 − 32k + 25 − 10k
53 − 30k = 41 − 42k
12k = -12
k = -1
h = 1 + 4k
h = -3
(3 − 1 − 4k)² + (7 − k)² = r²
(3 − 1 + 4)² + (7 + 1)² = r²
6² + 8² = r²
r = 10
Therefore, the equation of the circle is:
(x + 3)² + (y + 1)² = 10²
Can someone please help me Just the answer no need to explain it.
Answer:
C
Step-by-step explanation:
When you use pemdas, it gives the value of 1/32
Hurry I need it now !
(04.01 MC)
Which characteristics will prove that ΔDEF is a right, scalene triangle?
Answer:
A right scalene triangle would have a 90 degree angle and 3 non congruent sides
Step-by-step explanation:
4 men can make 4 Cupboards in 4 days ; how many cupboards can 14 men make in 14 days?
Answer:
49 cupboards
Step-by-step explanation:
See the steps below, it is self-explanatory:
4 men ⇒ 4 days ⇒ 4 cupboards4 men ⇒ 1 day ⇒ 1 cupboard1 man ⇒ 1 day ⇒ 1/4 cupboard14 men ⇒ 1 day ⇒ 14/4 cupboards14 men ⇒ 14 days ⇒ 14*14/4 cupboardsAs 14*14/4= 49, the answer is 49 cupboards
Find the value of x in the triangle shown below.
Answer: x=25
Step-by-step explanation: There are 180 degrees in a triangle. Two of the angles (56 and 99) add up to 155. The last angle, which is x, is 180-155. Therefore, x is 25.
hope this helped you:)
Answer:
The answer is 25°.
Step-by-step explanation:
simply,
here, a triangle of measure 99° and 56° is given.
now, we have;
99°+56+ x= 180° ( sum of an interior angle of a triangle is 180°)
or, 155°+x= 180°
or, x= 180°-155°
therefore, the value of x is 25°.
hope it helps..
Solve the answer -4(8+Y)= 90
[tex]-4(8+y)=90\implies8+y=-22.5\implies y=-30.5[/tex].
Hope this helps.
Answer:
-30.5.
Step-by-step explanation:
-4(8 + Y) = 90
-32 - 4Y = 90
-4Y = 122
Y = -30.5.
Hope this helps!
in a quiz bhaskar scored -60,20and0and tamanna scored 20,0and60 in three successive rounds.who socred more
Answer:
Tamanna scored more.
Step-by-step explanation:
Bhaskar scored -60, 20 and 0. His total score is therefore:
-60 + 20 + 0 = -40
Tamanna scored 20, 0, 60. His total score is therefore:
20 + 0 + 60 = 80
Therefore, Tamanna scored more.
Use pi=3.14. Round to the nearest hundredth
Answer:
9.42
pi x radius x radius x (height / 3) = volume
1 x 1 = 1 and 9/3 = 3
pi x 1 x 3 = volume
pi x 3 = volume
3.14 x 3 = 9.42
Hope this helps
Step-by-step explanation:
Which is a diagonal through the interior of the cube? Side A H Side B E Side C H Side F G
Answer:
Option (A)
Step-by-step explanation:
Every cube has 8 vertices and 6 faces.
Cube shown in the picture attached,
Diagonal through interior of the given cube will be the segments joining the vertices A-H, G-B, C-F and D-E.
Therefore, from the given options diagonal of the interior of the cube will be Side AH.
Option A will be the answer.
Answer:
the awnser is A
Step-by-step explanation:
i took a quiz
Brahmagupta’s solution to a quadratic equation of the form ax2 + bx = c involved only one solution. Which solution would he have found for the equation 3x2 + 4x = 6?
Answer:
0.897
Step-by-step explanation:
Brahmagupta formula for quadratic equation [tex]ax^2+bx=c[/tex] is
[tex]x=\dfrac{\sqrt{4ac+b^2}-b}{2a}[/tex]
It involved only one solution.
The given equation is
[tex]3x^2+4x=6[/tex]
Here, a=3, b=4 and c=6. Put these values in the above formula.
[tex]x=\dfrac{\sqrt{4(3)(6)+(4)^2}-4}{2(3)}[/tex]
[tex]x=\dfrac{\sqrt{4(3)(6)+(4)^2}-4}{2(3)}[/tex]
[tex]x=\dfrac{\sqrt{72+16}-4}{6}[/tex]
[tex]x=\dfrac{\sqrt{88}-4}{6}[/tex]
[tex]x\approx \dfrac{5.38}{6}[/tex]
[tex]x\approx 0.897[/tex]
Therefore, the required solution is 0.897.
What is the equation of the line of best fit for the following data? Round the
slope and yintercept of the line to three decimal places.
Need help ASAP!!
Answer:
The second choice should be the best fit line.
Please answer this question now
Answer:
<S = 62 degrees
Step-by-step explanation:
For this problem, you need to understand two things. A line tangent to a circle's radius creates a 90-degree angle, and the sum of the interior angles of a triangle is 180 degrees. With that said, let's continue.
<S + <P + <Q = 180
<S + 90 + 28 = 180
<S + 118 = 180
<S = 62
Hence, <S = 62 degrees.
Cheers.
Use the drawing tool(s) to form the correct answer on the provided number line. Consider the functions below. Represent the interval where both functions are increasing on the number line provided.
In order to solve this problem, we will need a little more information, for example, we need to know what the functions are. Let's say the problem looks like this:
Use the drawing tool(s) to form the correct answer on the provided number line. Consider the functions below.
[tex]f(x)=|3x|-3[/tex]
and
[tex]g(x)=-x^{2}+8x-5[/tex]
Represent the interval where both functions are increasing on the number line provided.
Answer:
See attached picture
Step-by-step explanation:
Since this problem is posted on the algebra section of Brainly, I assume we will need to make use of an algebraic approach to solve this. Basically, the idea is to graph the functions and find the x-values for which both functions increas. In order to graph the functions, we will need to build a table with points for each of the functions. In order to graph the functions you need to pick the x-values you wish and evaluate them in the given functions. (See attached pictures)
Once you got the desired points, you can plot them in the coordinate axis and find the x-values for which both graphs will be increasing. If we take a close look at the graphs we can see the f(x) graph increases in the interval:
(0,∞)
and the g(x) graph increases in the interval:
(-∞,4)
so the interval in which both graphs are increasing will be the region where both intervals cross each other, which will be (0,4)
so that's the interval we draw on our number line. (see attached picture.
Answer:
see photos
Step-by-step explanation:
Plato/Edmentum