Given:
A line passes through (1,-2) and is perpendicular to [tex]-4x+7y=21[/tex].
To find:
The equation of that line.
Solution:
We have, equation of perpendicular line.
[tex]-4x+7y=21[/tex]
Slope of this line is
[tex]m_1=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}[/tex]
[tex]m_1=-\dfrac{-4}{7}[/tex]
[tex]m_1=\dfrac{4}{7}[/tex]
Product of slope of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]\dfrac{4}{7}\times m_2=-1[/tex]
[tex]m_2=-\dfrac{7}{4}[/tex]
Now, slope of required line is [tex]-\dfrac{7}{4}[/tex] and it passes through (1,-2). So, the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope.
[tex]y-(-2)=-\dfrac{7}{4}(x-1)[/tex]
[tex]4(y+2)=-7(x-1)[/tex]
[tex]4y+8=-7x+7[/tex]
[tex]4y+7x=7-8[/tex]
[tex]7x+4y=-1[/tex]
Therefore, the equation of required line is [tex]7x+4y=-1[/tex].
will gibe brainlest and 5 stars and thanks
Answer:
2160 cm
Step-by-step explanation:
9x5x4x12=2160 :)
Answer:
42
Step-by-step explanation:
Divide the shape into a square and a triangle.
The area of the square would be 4×9 which is 36.
The area of the triangle will be 3*4/2=6
Add them to get 42
Please give me the correct answer
Answer:
YES
Step-by-step explanation:
Area of the largest square = Sum of area of the smaller squares
13² = 12² + 5²
169 = 144 + 25
169 = 169
TRUE
This proves the Pythagoras theorem in a right angle triangle.
(Hypotenuse)² = (leg 1)² + (leg 2)²
Therefore, answer is YES.
please help will give brainliest
Answer:
53 mph
Step-by-step explanation:
424 / 8 = 53
PLEASE HELP ME WITH MY DELTA MATH PLEASEEEE
Answer:
The range of the graph is {y: y ∈ R, -6 ≤ y ≤ 8}
Step-by-step explanation:
The domain is the set of values of the input (x)
The range is the set of values of the output (y)
In the given figure
∵ x is the input
∴ The set of the values of x is the domain
∵ Y is the output
∴ The set of the values of y is the range
∵ The smallest value of y is -6
∵ The greatest value of y is 8
→ That means values of y of the graph are from -6 to 8
∴ -6 ≤ y ≤ 8
∴ The range = {y : y ∈ R, -6 ≤ y ≤ 8}
∴ The range of the graph is {y: y ∈ R, -6 ≤ y ≤ 8}
Write the quadratic in standard form please!
-4x+6x^2=-4+3x^2
-4x +6x²=-4+3x²
6x²-3x²-4x+4=0
3x²-3x+4=0
5ft is what percent of 37 1/2 ft? I also need 37 1/2 is what percent of 5? Thank you!
Answer:
13.33333333
Step-by-step explanation:
Answer:
13.33333
Step-by-step explanation:
Use the Zero Product Property to find the x-intercepts (x+5)(−2x+3)=y
Answer:
Here you go, hope my handwriting is clear :D
X can either equal -5 or 3/2
This is my last question can someone help me with my homework.
9514 1404 393
Answer:
C, A, A
Step-by-step explanation:
In general, you ...
identify the coefficients of one of the variablesswap them, and negate one of themmultiply the corresponding equations by the "adjusted" coefficients.__
In problem 1, the x-coefficients are 8 and 2. A common factor of 2 can be removed so that we're dealing with the numbers 4 and 1. Assuming we want to multiply one of the equations by 1, leaving it unchanged, the value we want to multiply by will be -4. After we swap the coefficients, that multiplier is associated with equation 2:
multiply equation 2 by -4 . . . (eliminates x)
Likewise, the y-coefficients in problem 1 are -1 and 3. Again, if we want to multiply one of the equations by 1, leaving it unchanged, the coefficient we will change the sign of is -1 (becomes 1). After we swap the coefficients, the multiplier 3 is associated with equation 1:
multiply equation 1 by 3 . . . (eliminates y)
These two choices are B and A, respectively, so the one that does NOT work for problem 1 is choice C, as indicated below.
__
The other problems are worked in a similar fashion.
independent practice: tangents of circles
Find the value of x in each of the following:
(see picture)
Answer:
Step-by-step explanation:
9). "Tangent is perpendicular to the radius of a circle"
By applying Pythagoras theorem in the given triangle,
x² = 15² + 20²
x = √625 = 25
10). By applying Pythagoras theorem in the given triangle,
(r + x)² = r² + 15²
(8 + x)² = 8² + 225
8² + x² + 16x = 8² + 225
x² + 16x = 225
x² + 16x - 225 = 0
x² + 25x - 9x - 225 = 0
x(x + 25) - 9(x + 25) = 0
(x + 25)(x - 9) = 0
x = -25, 9
But x > 0
Therefore, x = 9 is the answer.
11). By the property of the tangents drawn to the circle from a point,
"Tangents drawn from a point lying outside the circle are equal in measure"
AC = BC
3x + 4 = 40
3x = 36
x = 12
12). By the same property used in question (11)
DE = DC = 4 units
BA = BC = 3 units
x = 4 + 3 = 7 units
Hilda adds 5 to a number, then multiplies the sum by negative 2. The result is 6. Write and solve an equation to find the number, x.
What is the number?
Answer:
I think answer is 3.
Step-by-step explanation:
2+3=52*3=6Answer:
I think it will be like that:
(X+5)×-2=6
-2x-10=6
-2X=16
X=-8
can anyone help me create the equation of the given parabola . is it x^2-x-3?
Answer:
The function of this parabola is is equal to [tex]f(x) = (x-1)^{2} - 4[/tex]
Step-by-step explanation:
If we look at this picture we cans see that the most bottom point of this parabola is located 4 units below and 1 unit tot he right of the origin point. From here we know tha tthe function will lokk something like this....
[tex]f(x) = (x^-1)^{2} + bx - 4[/tex]
But in our case b is equal to zero and so we get that the following parabola is represented by the following function....
[tex]f(x) = (x-1)^{2} - 4\\[/tex]
(If you don't believe me you can check this function on a graphing site called Desmos)
If solved will give brainless
1 . What is the relationship of angles 1 and 2 ?
2. What is the measure of angles 1 and 2?
3. What is the measure of angle 3
4. Each of these triangles would classify by angle to be :
Answer:
1.) Vertical angles. 2.) 76 degrees. 3.) 36 degrees.
the cost per month of making n number of wooden toys is 3n + 30. the income from selling n toys is 6n. how many toys must the company make to make a profit
Answer:
3×6=18+30=48. so company needs to make 48 toys
Answer:
n > 10, or n = 11. Not sure which answer fits your hw better.
Step-by-step explanation:
6n > 3n + 30
6n-3n > 30
(3n > 30)/3
n > 10
So, you need to sell 10 toys in order to break even, which means you need to make and sell 11 toys at least to make a profit.
Check time!
6(11) > 3(11) +30
66 > 63
OQ and RT are parallel lines.
Which angles are alternate exterior angles?
Options:
a) <OPN and <OPS
b) <OPN and <TSU
c) <OPN and <QPS
d) <OPN and <QPN
Answer: b) angle OPN and angle TSU
=========================================================
Explanation:
Each answer choice involves angle OPN, so the other angle must be based off this. The other angle is TSU because these two angles are on alternating sides of the transversal line UN.
Angle OPN and angle TSU are also exterior angles because they are on the outside region of the parallel lines OQ and RT.
So combine the two concepts and we can say that angles OPN and TSU are alternate exterior angles. The other alternate exterior angle pair is angle USR and angle NPQ.
Due to the parallel lines, the alternate exterior angles are congruent.
A kite is flying 100 m high from the ground level. If it starts descending 10 m/min, how much time will the kite take to touch ground level?
Answer:
10 minutes
Step-by-step explanation:
100 meters/10 meters per min. Cancel out the meters, and you're left with 10 minutes.
Hal is downloading a file from the internet. So far he has downloaded 25% of the file.
If 10 minutes have passed since he started, how long will it take to download the rest of the file?
Answer:
30 minutes
Step-by-step explanation:
If it takes 10 minutes to download 25%, and there is 75% left to reach 100%.
25% + 25% +25% = 75% there are 3 25% left thus,
10min + 10min + 10min = 30 minutes left to complete download.
The amount of time in minutes it will take to download the rest of the file
is 30 minutes.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Let, 'x' be the number of minutes required to download the complete movie.
Therefore,
25% of 'x' is 10 minutes, This can be numerically expressed as,
(25/100)×x = 10.
0.25x = 10.
x = 10/0.25.
x = 40 minutes.
So, it would take 40 10 = 30 minutes.
learn more about percentages here :
https://brainly.com/question/24159063
#SPJ2
During the 2009/2010 school year, Detroit students missed an average of 9 weeks of school. Let's say that the school year is 39 weeks long. If this is true, what percentage of school time did the average student miss that year in Detroit
Answer:
The percentage of school time missed by the average student during 2009/2010 school year in Detroit is 23.08%.
Step-by-step explanation:
The percentage of school time missed by the average student during 2009/2010 school year in Detroit can be calculated as follows:
Percentage of school time missed = (Average number weeks of school missed / Total number of weeks in a school year) * 100 ................... (1)
Where;
Average number weeks of school missed = 9
Total number of weeks in a school year = 39
Substituting the values into equation (1), we have:
Percentage of school time missed = (9 / 39) * 100
Percentage of school time missed = 0.230769230769231 * 100
Percentage of school time missed = 23.0769230769231%
Rounding to 2 decimal places, we have:
Percentage of school time missed = 23.08%
Therefore, the percentage of school time missed by the average student during 2009/2010 school year in Detroit is 23.08%.
What is the value of −4(9 + 6)?
Answer:
-60
Step-by-step explanation:
1. Add 9 and 6
9+6=15
2. Multiply by -4
-4 times 15
-60
2 3/4 divided by 5 1/2
Answer: 0.5
Step-by-step explanation:
Answer:
.5
Step-by-step explanation:
2.75/5.5=.5
math
pls help dudndjrjdjr
Answer:
it is not possible
Step-by-step explanation:
6+4=10
10+8=18
so it is not possible
Please give me the correct answer
Answer:
[tex] \sqrt{149} [/tex]
Step-by-step explanation:
leg 1 squared plus leg 2 squared = 3rd leg squared
Answer: [tex]c = \sqrt{149}[/tex]
Step-by-step explanation:
[tex]a =7 \\b=10\\a^{2} +b^{2}=c^{2}\\7^{2} + 10^{2} =c^{2}\\49 + 100 = c^{2}\\c^{2} = 49 + 100\\c^{2}=149\\\sqrt{c^{2}} =\sqrt{149}\\c = \sqrt{149}[/tex]
Question 15(Multiple Choice Worth 1 points)
(03.03 LC)
PLS HELP
PLS HELP
Given the exponential function f(x) = 16(0.75)*, classify the function as exponential growth or decay and determine the percent rate of growth or decay.
parallel lines l and m are intersected by transversal t as shown below which of the following angles are alternate interior angles
a. 1 and 5
b. 4 and 6
c. 2 and 7
d. 3 and 6
Answer:
c 2and7
Step-by-step explanation:
1 to 2 to 3 to 4 the789
a ball is launched upward from the ground with an initial velocity of 20 ft/s. The height of the ball at time t is represented by the function h(t). h(t)=-16t^2+20t, where t is measured in seconds and h(t) is measured in feet. drag the values to the lines to complete each sentence.
1. The ball reaches its maximum height when t is ____ seconds.
2. The maximum height of the ball is ____ feet.
3. The balls hits the ground when t is ____ seconds.
OPTIONS: 0.4 0.625 0.8 1.25 5.44 6.25 12.5 25
Answer:
1.-t₁ = 0,625 s
2.-h(max) = 6,25 f
3.-t = 1,25 s
Step-by-step explanation:
V₀ = 20 f/s
h(t) = - 16*t² + 20*t
h(max) = ??
h´(t) = - 32*t + 20
h(max) will occurs when V = 0 dh/dt = 0 then
- 32*t + 20 = 0
- 32*t = -20
t = 20/32
t₁ = 0,625 s
h(max) = h(0,625) = - 16*(0,625)² + 20*0,625
h(max) = - 6,25 + 12,5
h(max) = 6,25 f
c) The ball will hit the ground
t = 2*t₁
t = 2*0,625
t = 1,25 s
I WILL AWARD BRAINLIEST TO RIGHT ANSWER
an airplane 30,000 feet above the ground begins descending at a rate of 2000 feet per minute write a linear model to represent the model
Answer:
y = -2000x+30000
Step-by-step explanation:
Hi. So, you are just setting up a linear equation using slope intercept data. The slope being -2000 (because it is descending) and the intercept being 30,000 at t=0.
y = -2000x+30000
For f(x) = x
2 − 5, find f(0).
Answer:
f(0)=0
Step-by-step explanation:
If f(x) is x you don't have to do anything to it.
I'm assuming 2 - 5 is like the problem # or something but just in case... that is -3 lol
Which of the following statements is not true
Answer:
A: The slope of AB is
different than the
slope of BC.
.
What is the equation in standard form of the line that passes through the point (4, −8) and has a slope of 1/4?
A) x − 4y = 36
B) x − 4y = −28
C) x − 4y = −36
D) x − 4y = 28
Answer:
Option A is correct.
Step-by-step explanation:
Given
The point (4, -8)Slope m = 1/4To determine
What is the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line(x₁, y₁) is the pointsubstituting the values m = 1/4 and the point (4, -8)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-8\right)=\frac{1}{4}\left(x-4\right)[/tex]
[tex]y+8=\frac{1}{4}\left(x-4\right)[/tex]
Subtract 8 from both sides
[tex]y+8-8=\frac{1}{4}\left(x-4\right)-8[/tex]
[tex]y=\frac{1}{4}x-1-8[/tex]
[tex]y=\frac{1}{4}x-9[/tex]
Writing the equation in the standard form
As we know that the equation in the standard form is
Ax+By=C
where x and y are variables and A, B and C are constants
so
[tex]y=\frac{1}{4}x-9[/tex]
[tex]x=4y+36[/tex]
[tex]x - 4y = 36[/tex]
Therefore, the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4 will be:
[tex]x - 4y = 36[/tex]
Hence, option A is correct.
1 person can cut a large area of grass in 5 hours. How long would it take 2 people to cut the grass
Answer:
Well going with the answer mathematically, it would take 2.5 hours for 2 people to cut the grass.
How do you solve: 5In3-2In9
Answer: uhm is this a SAT
Step-by-step explanation: i'm sorry i didn't asnwer but i can't not subtract that is it 53 In - 29 In?