The distance between the two lines,-2x + y = 6 and x = 1/2x - 4, is approximately 4.5 units
Calculating the distance between two linesTo find the distance between two lines, we can use the formula:
Distance = |(Ax + By + C)| / sqrt(A^2 + B^2)
Where A, B, and C are the coefficients of the standard form equation of the first line
and x and y are the coordinates of a point on the second line.
Let's first convert the equations of the lines into the standard form (Ax + By + C = 0):
-2x + y - 6 = 0 --> 2x - y + 6 = 0 (Line 1)
x - 2x/2 - 4 = 0 --> -x + 4 = 0 --> x - 4 = 0 (Line 2)
Now, we can use the formula to find the distance between the two lines:
distance = |(Ax + By + C)| / sqrt(A^2 + B^2)
Let's take a point on Line 2, for example, (4,0). Then:
Distance = |(24 - 10 + 6)| / sqrt(2^2 + (-1)^2)
Distance = |10| / sqrt(4 + 1)
Distance = 10 / sqrt(5)
Distance = 4.472
Distance ≈ 4.5
Hence, the distance is approximately 4.5 units
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the y intercept, to the nearest hundredth, of the line -9y=7x+8
Answer:
(0, -0.89) or -0.89
Step-by-step explanation:
Step 1: Solve for y by dividing both sides by -9
-9y = 7x + 8
-9y / -9 = (7x + 8) / -9
y = -7/9x - 8/9
Step 2: Identify the y-intercept
y = mx + b
m is slope
b is y-int
y = -7/9x - 8/9
Answer = (0, -0.89) or -0.89
Answer:
-0.89
Step-by-step explanation:
(see attached graphic for reference)
recall that the slope-intercept form of a line looks something likeL
y = mx + b
where m is the slope and b is the y-intercept.
Hence all we need to do is to rearrange our equation so that it looks like the one above.
-9y=7x+8 (divide both sides by -9)
-9y / (-9) = (7x+8) / (-9)
y = (7x+8) / (-9) (use distributive property )
y = [ 7x / (-9) ] + [ 8/(-9) ]
y = (-7/9)x + (-8/9)
comparing this equation with the general equation above,
we can see that the
y-intercept , b
= -8/9
= -0.88888..............
= -0.89 (nearest hundredth)
(−2x−3) as a fraction
Answer:
6 or 6/1
Step-by-step explanation:
Multiple: -2 * (-3) = 6
Can someone please help me???!!!
Answer:
A.)
Step-by-step explanation:
The point (x, y) is the top of a polygon. Which point would it map to if the polygon were reflected over the x-axis and then translated 5 units down?
A) (x, y+5)
B) (x,-y-5)
C) (-x+5, -y)
D) (-x, -y+5)
Answer:
it´s b for sure
Step-by-step explanation:
The coordinates of the transformed point is (x,-y-5), the correct option is B.
What is Reflection of an object?The reflection of an object refers to creating a mirror image of the object, similar in shape and size, just the coordinates are switched.
When a point is reflected over an axis, the coordinate of the other axis changes to its additive inverse.
The coordinates (x,y) when reflected over x axis change to (x,-y)
The polygon is reflected over x axis
then the coordinate ( x,y) will become (x,-y)
After translation, 5 units down, the coordinate change to
( x, -y-5)
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what positive number raised to the second power is equal to 64
Answer: 8
Step-by-step explanation: 8 times 8 is 64.
Answer:
8
Step-by-step explanation:
[tex]8^{2} = 64[/tex]
Last year, Jess saw x dramas and y comedies at the movie theater. If she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?
x + y < 8
x + y > 8
x + y ≤ 8
x + y ≥ 8
Answer:
[tex]x + y \leqslant 8[/tex]
Step-by-step explanation:
The key idea here is to identify how to translate the statement, no more than, into inequality.
No more than 8 means less or equal to 8.
If Jess saw x dramas and y comedies at the movie theater, and she went to the theater no more than 8 times,then the inequality that best describes the situation is:
[tex]x + y \leqslant 8[/tex]
The third choice is correct
Solve by elimination.. SHOW YOUR WORK. -3x + 2y = 18
-9x - 5y=21
Answer:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Point Form:
( − 4 , 3 )
Equation Form:
x = − 4 , y = 3
Step-by-step explanation:
Answer:
x = —4, y = 3
Step-by-step explanation:
-3x + 2y = 18 (1)
-9x - 5y =21 (2)
To solve by eliminating, the coefficients of either x or y must be the same in both equation.
Now let us make the coefficient of x in both equation to be the same. To do this, multiply equation (1) by the coefficient of x in equation (2) ie —9, and multiply equation (2) by the coefficient of x in equation (1) ie —3 this is illustrated below :
—9 ( —3x + 2y = 18)
27x — 18y = — 162 (3)
—3 ( —9x — 5y = 21)
27x + 15y = —63 (4)
Now, subtract equation 4 from equation 3
27x — 18y = — 162
— (27x + 15y = —63)
—33y = —99
Divide both side by —33
y = —99/—33
y = 3
Now we substitute the value of y into any of the equation to obtain x. In this case, let use equation 4
27x + 15y = —63
27x + 15(3) = —63
27x + 45 = —63
Collect like terms
27x = —63 —45
27x = —108
Divide both side by 27
x = —108/27
x = —4
Therefore, x = —4, y = 3
What fraction of a pound is 35 pence
Step-by-step explanation:
It is: 35/100 = 7/20 simplified
Answer:
Step-by-step explanation:
7/20
Write the decimal equivalent of each fraction 1/2
Answer:
(1/2) = 0.50.
Answer: 0.5
Step-by-step explanation: the answer is 0.5 because 1/2 i half of something 0.5 is half of 1 making 1/2 equivalent to 0.5
(12+4) divided by (11-7)
pemdas order of operations
Answer:
4
Step-by-step explanation:
[tex]\frac{12+4}{11-7} =\frac{16}{4} =4[/tex]
Write the formula of the function y whose graph is shown. A. Y equals 1 divided by x minus 4. B. Y equals 4 divided by the quantity x minus 4 end of quantity. C. Y equals 4 divided by the quantity x plus 4 end of quantity. D. Y equals 4 divided by x.
Answer:
Option D. Y equals 4 divided by x.
Step-by-step explanation:
The picture of the question in the attached figure
we know that
Looking a t the graph
For x=1, y=4
For x=4, y=1
For x=-1, y=-4
For x=-4, y=-1
therefore
The equation that satisfy these values is
[tex]y=\frac{4}{x}[/tex]
Sara got 88, 90, 75, 78, 100, 54, 90, 100, 45, and 60 on her English tests
What is the mean of Sarah’s English tests
Answer: 78
Step-by-step explanation:
88+90+75+78+100+54+90+100+45+60 = 780
Divide this number by the total number of factors,in this case 10:
780/10 = 78
Prove that pi is irrational
Answer:
Since pi cannot be expressed as a fraction, it is counted as an irrational number. Numbers that are irrational are: 1/3, e, 5/6
What is 2x(6-7)+(8x2)
Answer:
30
Step-by-step explanation:
Answer:
-2x+16
Step-by-step explanation:
So, we would first distribute.
2x·6=12x
2x·-7=-14x
12x-14x+(8·2)
Simplify:
12x-14x+16
12x-14x=-2x
-2x+16
Use the graph to find the coordinates of each vertex in
triangle ABC
is the coordinate of Point A.
is the coordinate of Point B.
is the coordinate of Point C
(0, -1)
Intro
Done
please make brainiest.
is the coordinate of point bJay earns $2,500 a month. He pays
$850 a month to rent an apartment
What percent of Jay's income does
he pay for rent?
Answer: 34%
Step-by-step explanation: 2,500 - 34% = 850 the remaining 76% equals 1,650
What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Select three options
Answer:
The phrase that best describes the the line representing the relationship between the number of balloons remaining and the number of hats created is: Negative slope. Constant slope.
Step-by-step explanation:
Answer: Negative slope
constant slope
decreasing function
for edge
What are two other forms to write the numbers 0.253 and 7.632?
Answer:
See below
Step-by-step explanation:
0.253 can be written as 253/1000
7.632 can be written as 7 632/1000 or 7 79/125 simplified
The hypotenuse of a 45°-45°-90° triangle measures 22 StartRoot 2 EndRoot units.
A right triangle is shown. The length of the hypotenuse is 22 StartRoot 2 EndRoot 2 units. The lengths of the other 2 sides are congruent.
What is the length of one leg of the triangle?
11 units
11 StartRoot 2 EndRoot units
22 units
22 StartRoot 2 EndRoot units
Length of the other leg is 22 units
Step-by-step explanation:
Step 1: The length of the other legs can be found using Pythagoras Theorem given hypotenuse = 22√2. Let the sides be x.Hypotenuse² = x² + x²
(22√2)² = 2x²
⇒ x² = 22 × 22 × 2/2 = 22 × 22
∴ x = 22 units
Answer:
C
Step-by-step explanation:
please help me again
Answer:
65 degrees
Step-by-step explanation:
Step 1: Find what the measure of JLK is
JLM + JLK = 180
140 + JLK - 140 = 180 - 140
JLK = 40
Step 2: Find what the measure of KJL is
KJL + JLK + JKL = 180
KJL + 40 + 75 = 180
KJL + 115 - 115 = 180 - 115
KJL = 65
Answer: 65 degrees
92
9
u
2
v
and which term are like terms?
Find the derivative of F(x)=-x^4+4x^3+ 70 for 0<=x<=3
Answer:
-4x^3 +12x^2 for 0 < x < 3
Step-by-step explanation:
The power rule is appropriate:
(d/dx)x^n = n·x^(n-1)
This is applied to each of the terms.
F'(x) = -(4·x^3) +4(3x^2) +0
F'(x) = -4x^3 +12x^2 . . . . for 0 < x < 3
__
The derivative is not defined at the endpoints of the interval, so F'(x) is only defined on (0, 3), not [0, 3].
a baker uses 84 cups of flour for 36 batches of cookies how many cups of flour are needed for one batch of the cookies
Answer:
I think 2.333333333
Step-by-step explanation:
Answer:
D. 2 + 1/3 Cups of Flour
Step-by-step explanation:
84 Cups of Flour / 36 Batches of Cookies
=
x Cups of Flour / 1 Batch of Cookies
x = 7/3 Cups of Flour
D. 2 + 1/3 Cups of Flour
Which shows one way to determine the factors of x^3+5x^2-6x-30 by grouping?
[tex]\left(x^{2}-6\right)(x+5)[/tex] are the factors of the expression by grouping
Step-by-step explanation:
[tex]x^{3}+5 x^{2}-6 x-30[/tex]
We have to group the terms as,
[tex]\left(x^{3}+5 x^{2}\right)-(6 x-30)[/tex]
We can take the common factors as,
= [tex]x^{2}(x+5)-6(x+5)[/tex]
So it can be written as,
= [tex]\left(x^{2}-6\right)(x+5)[/tex]
So it was factorized by grouping.
HELP WILL GIVE BRAINLIEST! RATE AND SAY THANKS!!
What is the density of a 50-gram pyramid with rectangular base 4 x 8 cm and height 10 cm?
The density of the pyramid is calculated by first finding the volume using the formula for a pyramid's volume, and then dividing the mass by this volume, resulting in a density of approximately 0.469 g/cm³.
Explanation:To find the density of a pyramid with a rectangular base, we first need to calculate its volume. The formula for the volume of a pyramid is V = (1/3)Bh where B is the area of the base and h is the height. In this case, the base has dimensions of 4 cm by 8 cm, so its area is 4 cm * 8 cm = 32 cm². The height of the pyramid is given as 10 cm, so the volume can be calculated as V = (1/3)*32 cm²*10 cm = 106.67 cm³.
With the mass of the pyramid given as 50 grams, the density (ρ) can be calculated using the formula ρ = mass/volume. Thus, the density is 50 grams / 106.67 cm³ = 0.469 g/cm³. Therefore, the density of the pyramid is approximately 0.469 g/cm³.
A segment has a midpoint at (2,-7) and an endpoint at (8,-5). What are the coordinates of the other endpoint?
Answer:
(-4,-9)
Step-by-step explanation:
Given a segment AB with endpoints with coordinates
A: [tex](x_A,y_A)[/tex]
B: [tex](x_B,y_B)[/tex]
The coordinates of the midpoint M of the segment AB are given by:
[tex]x_M = x_A + \frac{x_B-x_A}{2}\\y_M = y_A + \frac{y_B-y_A}{2}[/tex] (1)
In this problem, we know that:
- The midpoint of the segment AB has coordinates
[tex]x_M=2\\y_M=-7[/tex]
- One of the endpoint of the segment has coordinates
[tex]x_B=8\\y_B=-5[/tex]
So we can find the coordinates of the other endpoint A by re-arranging eq.(1) above:
[tex]x_A=2x_M-x_B\\y_A=2y_M-y_B[/tex]
And substituting, we find:
[tex]x_A=2(2)-8=-4\\y_A=2(-7)-(-5)=-9[/tex]
So, the coordinates of the other endpoint are (-4,-9).
To find the coordinates of the other endpoint, use the midpoint formula to average the x-coordinates and the y-coordinates of the given point and the midpoint.
Explanation:To find the coordinates of the other endpoint, we can use the midpoint formula. The midpoint formula states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates of the endpoints. So, we can calculate the x-coordinate of the other endpoint by averaging the x-coordinates of the given point and the midpoint: (8 + 2) / 2 = 5. Similarly, we can calculate the y-coordinate of the other endpoint by averaging the y-coordinates: (-5 + (-7)) / 2 = -6.
Therefore, the coordinates of the other endpoint are (5, -6).
Please help I appreciate it
Answer:
A
Step-by-step explanation:
g(x) got smaller
A - makes it thinner
B & C - move it to the left or right
D- makes it wider
Answer:
Step-by-step explanation:
#1 I
#2 D
#3 K
The first two steps in determining the solution set of the system of equations, y = x2 – 6x + 12 and y = 2x – 4, algebraically are shown in the table.Which represents the solution(s) of this system of equations? (4, 4) (–4, –12) (4, 4) and (–4, 12) (–4, 4) and (4, 12)
The solution to the system of equations is [tex]\( (4, 4) \)[/tex]. Therefore the correct option is a.
Given equations:
1. [tex]\( y = x^2 - 6x + 12 \)[/tex]
2. [tex]\( y = 2x - 4 \)[/tex]
To find the solution to the system, we'll set the two equations equal to each other because they both equal [tex]\( y \)[/tex]. So:
Step 1:
[tex]\[ x^2 - 6x + 12 = 2x - 4 \][/tex]
Now we will move all terms to one side to set the equation to zero.
Step 2:
[tex]\[ x^2 - 6x + 12 - 2x + 4 = 0 \][/tex]
[tex]\[ x^2 - 8x + 16 = 0 \][/tex]
This is a quadratic equation. To solve for [tex]\( x \)[/tex], we can either factor the quadratic, use the quadratic formula, or complete the square. The equation in Step 2 seems to be a perfect square trinomial.
Step 3:
The equation [tex]\( x^2 - 8x + 16 \)[/tex] factors to [tex]\( (x - 4)^2 = 0 \)[/tex].
Step 4:
Now, we solve for [tex]\( x \)[/tex] by taking the square root of both sides.
[tex]\[ (x - 4)^2 = 0 \][/tex]
[tex]\[ x - 4 = 0 \][/tex]
[tex]\[ x = 4 \][/tex]
Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into either of the original equations to solve for [tex]\( y \)[/tex]. We can use the simpler equation [tex]\( y = 2x - 4 \)[/tex].
Step 5:
[tex]\[ y = 2(4) - 4 \][/tex]
[tex]\[ y = 8 - 4 \][/tex]
[tex]\[ y = 4 \][/tex]
So the solution to the system of equations is [tex]\( (4, 4) \)[/tex]. There is only one solution because the quadratic equation had a repeated root, meaning the lines intersect at exactly one point.
The complete question is given below:
PLEASE HELP me I am struggling.
Answer:
ab - b^2
Step-by-step explanation:
The area of the large rectangle is
A = a*b
The area of the unshaded region is
A = b*b
The area of the shaded region is the large rectangle minus the unshaded region
ab - b*b
or
ab - b^2
A small welding shop employs four welders and one secretary. A workers' compensation insurance policy charges a premium of $ 10.57 per $100 of gross wages for the welders and $ 1.31 per $100 of gross wages for the secretary. If each welder earns $ 37 comma 000 per year, and the secretary earns $ 24 comma 000 per year, what is the total annual premium for this insurance?
Final answer:
To calculate the total annual premium for the welding shop, the premiums for the four welders and the secretary are calculated separately based on their wages and rates, and then added together, resulting in a total annual premium of $15,958.
Explanation:
The question is asking us to calculate the total annual premium for workers' compensation insurance for a small welding shop with four welders and one secretary, based on their respective wages and insurance premium rates.
First, we will calculate the premium for the welders. Since there are four welders each earning $37,000 per year, the total wages for welders is:
$37,000 x 4 = $148,000
The insurance premium per welder is $10.57 per $100 of gross wages. To find the total premium for all welders, we do:
($10.57/$100) x $148,000 = $15,643.60
Next, we'll calculate the premium for the secretary. The secretary earns $24,000 per year, and the insurance premium is $1.31 per $100 of gross wages, which gives us:
($1.31/$100) x $24,000 = $314.40
Adding the premiums for the welders and the secretary gives us the total annual premium:
$15,643.60 + $314.40 = $15,958
So, the total annual premium for the workers' compensation insurance for the welding shop is $15,958.
The total annual premium for the workers' compensation insurance is $15,958.00.
1. Calculate the premium for each welder:
- Each welder earns $37,000 per year.
- Premium rate for welders: $10.57 per $100 of gross wages.
- Annual premium for one welder:
[tex]\[ \text{Premium for one welder} = \left( \frac{37,000}{100} \right) \times 10.57 = 370 \times 10.57 = 3,910.90 \text{ dollars} \][/tex]
- Since there are four welders:
[tex]\[ \text{Total premium for welders} = 3,910.90 \times 4 = 15,643.60 \text{ dollars} \][/tex]
2. **Calculate the premium for the secretary:
- The secretary earns $24,000 per year.
- Premium rate for the secretary: $1.31 per $100 of gross wages.
- Annual premium for the secretary:
[tex]\[ \text{Premium for secretary} = \left( \frac{24,000}{100} \right) \times 1.31 = 240 \times 1.31 = 314.40 \text{ dollars} \][/tex]
3. Calculate the total annual premium:
[tex]\[ \text{Total annual premium} = 15,643.60 + 314.40 = 15,958.00 \text{ dollars} \][/tex]