Answer:
y=-4x+4
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=-4(x-2)
y+4=-4(x-2)
y=-4x+8-4
y=-4x+4
A slope of a line is the change in y coordinate with respect to the change in x coordinate. The equation of the line in slope intercept form which is passing through (2,-4) is -4x +7.
What is the slope of a line?A slope of a line is the change in y coordinate with respect to the change in x coordinate. The equation of a line in slope intercept form is given by
y = mx + c.
Given the slope of the line, m=-4. Also, the point through which the line is passing,
(x₁ ,y₁) =(2,-4)
Since the equation of the line in the slope-intercept form of the line is given by
y = mx +c
Since, the above line is passing through (2, -4) and the slope is -4.
Therefore,-4 = -4(2) + c⇒ -4 = -8 + c⇒ -1 +8 = c⇒ c = 7
Substitute the value of m and c in the equation
y = mx + c
⇒ y = mx + c
⇒ y = -4x +7
Therefore, the equation of line in slope intercept form which is passing through (2, -4) is y = -4x +7.
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what is x in the equation 3x+4=2x+6?
Answer:
x= 2
Step-by-step explanation:
Answer:
3x + 4 = 2x + 6
3x +4 - 2x - 6 =0
x - 2 = 0
x = 2
3(2) +4 = 2(2) + 6
6 + 4 = 4 + 6
10 = 10
3x+2=2x+6
subtracting 2 from both sides
3x+2-2=2x+6-2
3x=2x+4
subtracting 2x from both sides
3x-2x=2x-2x+4
x=4
The book wants me to use the Pythagorean Theorem (a^2+b^2=c^2) to get the correct answer. I never learned how to use the theorem when finding distance and have only used Distance Formula. I tried using the Distance Formula to get the correct answer and got a negative outcome. Can someone please explain how Pythagorean Theorem works or maybe tell me how to fix the Distance Formula so it doesn't give me a negative outcome.
Answer:
C) [tex]\sqrt{106}[/tex] units
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where [tex]a[/tex] and [tex]b[/tex] are side lengths of a right triangle and [tex]c[/tex] is the hypotenuse, the longest side of the right triangle.
The distance formula is similar to that of the Pythagorean Theorem which is [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points that you wish to find the distance between them in an (x,y) coordinate plane.
Here, we are given that [tex](x_1,y_1)[/tex] is [tex]P(-4,-6)[/tex] and [tex](x_2,y_2)[/tex] is [tex]Q(1,3)[/tex]. So, we can use the distance formula as described previously to find the positive distance between the two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(1-(-4))^2+(3-(-6))^2}[/tex]
[tex]d=\sqrt{(1+4)^2+(3+6)^2}[/tex]
[tex]d=\sqrt{(5)^2+(9)^2}[/tex]
[tex]d=\sqrt{25+81}[/tex]
[tex]d=\sqrt{106}[/tex]
[tex]d \approx 10.295630141[/tex]
Since all of the given answer choices are in radical form, then C is the correct answer. The distance between the two points is [tex]\sqrt{106}[/tex] units.
If line ab is tangent to circle c , find AC?
Can anyone help?
Answer:
Step-by-step explanation:
If AB is tangent to the circle, the AB makes a right angle with the radius BC. That means that triangle ABC is a right triangle and we need Pythagorean's Theorem to find the missing side which is the hypotenuse.
[tex]AC^2=AB^2+BC^2[/tex] and filling in:
[tex]AC^2=14^2+9^2[/tex] and
[tex]AC^2=196+81[/tex] and
[tex]AC^2=277[/tex] so
[tex]AC=\sqrt{277}[/tex] ≈ 16.64
AC = 16.64
The Tangent theorem
"It states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency."
From given diagram,
tangent AB = 14 units
radius BC = 9 units
Using tangent theorem,
AB is perpendicular to BC.
This means ΔABC is right triangle with ∠B = 90°
Using Pythagoras theorem,
[tex]AC^2=AB^2+BC^2[/tex]
⇒ [tex]AC^2=14^{2}+9^{2}[/tex]
⇒ [tex]AC^2=196+81[/tex]
⇒ [tex]AC^2=277[/tex]
⇒ [tex]AC=\sqrt{277}[/tex]
⇒ [tex]AC=16.64[/tex]
Therefore, AC = 16.64
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What is the slope of the graph of 3x - 7y = 10 *
3/7
O-37
O 3
O -7
Answer:
Step-by-step explanation:
Solve this for y to determine the slope. Solving for y gets our line into the slope-intercept form, y = mx + b, where the number value of m will be the slope.
-7y = -3x + 10 and
[tex]y=\frac{-3}{-7}x+\frac{10}{-7}[/tex] which simplifies down to
[tex]y=\frac{3}{7}x-\frac{10}{7}[/tex]
The value for m is 3/7 so that is the slope, the first choice given.
answer please need belp ???
Point F is reflected over the yaxis to create F. Use an ordered pair to name the location of F, and determine the
distance between Fand F.
Answer:
Reflection about the y-axis is according to the rule
(x,y)->(-x,y)
Therefore F(x,y) -> F'(-x,y)
The distance between F' and F is (-x,y)-(x,y)=-2x, or the positive distance is 2x.
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Which is the best explanation for why − √ 10 is irrational?
Step-by-step explanation:
- square root of 10 is irrational because it is less than zero. - square root of 10 is irrational because it is not a whole number.
Upon prime factorizing 10 i.e. 21 × 51, 2 is in odd power. Therefore, the square root of 10 is irrational.
How can you apply the concept of area and perimeter in your everyday life?
Plz help what is the perimeter of the rectangle
Answer:
18 units
Step-by-step explanation:
The base is 7-4 = 3 units
The height is 8 - 2 = 6 units
P = 2(b+h)
P = 2( 3+6)
P = 2(9)
P = 18
Go step by step to reduce the radical. 112
Answer:
4 sqrt(7)
Step-by-step explanation:
sqrt(112)
We know sqrt(a*b) = sqrt(a) sqrt(b)
Look for perfect squares
sqrt(16*7)
sqrt(16)sqrt(7)
4 sqrt(7)
Answer:
4√7
Step-by-step explanation:
√112
we know that ( a × b) = √a √ b
[tex] \small \sf \: \sqrt{16 \times 7} [/tex]
√16 × √7
4√7
PLEASE HELP SHOULD BE EASY!! WILL GIVE BRAINLIEST
.........................
Answer:
I believe the answer will be 6. Here's why.:
Step-by-step explanation:
The total volume of the rectangle is 24 inches. 4in x 6in= 24 in. Then there is a half semi-circle. So 24/2=12. The circle is called a circumference and since there is a half, that is called a diameter. I am not sure if my reasoing is correct, but I gave it try.
if a 30 foot wire is attached to the top of a 12 foot pole and stretched to the ground, find the angle the wire makes with the ground
Answer:
52 degrees
Step-by-step explanation:
Answer:
52 degrees sorry if that's wrong
I don't understand math...i probably never will
Answer:
1/2 9/8
17/12 23/30
81/70 2/3
Step-by-step explanation:
I ordered it the way it appears in the image.
Convert r=53sinθ−cosθ to rectangular form.
Enter your answer in slope-intercept form by filling in the boxes. Enter values so that fractions are simplified.
Answer:
[tex]y = \frac{1}{3} x + \frac{5}{3}[/tex]
Step-by-step explanation:
r = 5/(3sinθ-cosθ)
multiply both sides by (3sinθ-cosθ):
r(3sinθ-cosθ) = 5
expand:
3rsinθ-rcosθ = 5
replace rsinθ with y and rcosθ with x:
3y-x = 5
add x to both sides:
3y = x + 5
divide both sides by 3:
y = 1/3x + 5/3
: )
plz help asap. i beg
The answer is -15.
Because others are rational numbers but not integers.
-15 is the only rational number and integer.
Which is the rationalized form of the expression. A, B , C, or D?
Answer:
C
Step-by-step explanation:
Multiply the top and bottom, both by sqrtx-sqrt5. This is in order to rationalize the denominators.
You get answer C.
Aimee says Bella is lying. Bella says Marc is lying. Marc says Bella is lying. Terry says Aimee is lying. How
many of the four children are lying?
a) 0 b)1 c)2 d)3 e)4
Your score on a game show is -150. You answer the final question correctly, so you get 400 points. what is your final score?
Answer:
250
Step-by-step explanation:
-150 + 400 = 250
Final Score= -150 + 400
= 250 --- (Answer)
Hey! can someone help me find the value of x please??!
Answer:
I think it´s 2.
Step-by-step explanation:
7(2) = 14
14+5=19
Pretty simple math for me, not sure about you though.
Answer:
x=2
Step-by-step explanation:
since the two angles are equivalent to each other, we also know that the legs of triangle are equal... so we set the legs equal to each other and solve for x...
7x+5=19
subtract five from both sides
7x=14
divide 7 from both sides
x=2
Given the box plot, will the mean or the median provide a better description of the center
Solve the expression for a=12 , b=6 and c=3
Answer:
50
Step-by-step explanation:
Substitute.
Answer:
320
Step-by-step explanation:
(6 x 3)² - 2(12) ÷ 6
324 - 24 ÷ 6
324 - 4
= 320
When the square of a number is increased by 24, the result is eleven times the original. Number find the number
Answer:
the number can be either 8 or 3.
Step-by-step explanation:
Let's define N as the "number"
We know that when the square of this number is increased by 24:
N^2 + 24
we got eleven times the original number, then:
N^2 + 24 = 11*N
We just need to solve this for N
To do it, we first move all the terms to one side of the equation:
N^2 - 11*N + 24 = 0
Now we can use the Bhaskara's formula for the zeros of a quadratic equation:
for a general quadratic equation:
a*x^2 + b*x + c = 0
the roots or zeros are given by:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
We get then:
[tex]N = \frac{-(-11) \pm \sqrt{(-11)^2 - 4*1*24} }{2*1} = \frac{11 \pm 5}{2}[/tex]
So we have two solutions:
N = (11 + 5)/2 = 16/2 = 8
N = (11 - 5)/2 = 6/2 = 3
So the number can be either 8 or 3.
Someone please help it’s the last question of my final.
Answer: $46,619
»» 288.44 / 0.7%
»› 41,205
»» 45 x 120.33
»» 5,414
A=41,205
A=5,414
A=46,619
[tex]\color{yellow}{}[/tex]
Answer:
The answer would be $46,619
Step-by-step explanation:
Someone already explained it pretty well, goodluck! :)
A vehicle was purchased for $64,000 when exponential depreciation is appeals at the rate of 18% per year, how much will the vehicle be worth 54 month after the purchased date?
Answer:
Step-by-step explanation:
The standard form of an exponential function is
[tex]y=a(b)^x[/tex] where y is the value of the car after x years have gone by, a is the initial value of the car and b is the rate of depreciation. For us, that looks like this:
[tex]y=64000(.18)^{4.5[/tex] where 64000 is the initial value of the car, .18 is the depreciation rate, and 4.5 is 54 months in years. Doing the math on that gives us that the value of the car will be $51,840 4.5 years after it's purchased new.
Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth
A. 5
B. 5.8
C. 17.3
D. 8.7
Answer:
B) 5.8
Step-by-step explanation:
Calculate cos0 to two decimal places. 7 8 Xà A. 0.69 B. -0.14 C. -0.42 OD. -0.07
Correct answer: -0.07
Answer:
D. -0.07 to nearest hundredth.
Step-by-step explanation:
Applying the Cosine Rule:
11^2 = 7^2 + 8^2 - 2*7*8 cos O
cos O = (11^2 - 7^2 - 8^2) / (-2*7*8)
= 8/-112
= -0.07143.
Is this polynomial positive or negative?
Answer:
The polynomial is positive.
Diane must choose a number between 61 and 107 that is a multiple of 4,7, and 14 . Write all the numbers that she could choose.
Answer:
84
Step-by-step explanation:
only three number are a multiple of 14
14 * 5 = 70
14 * 6 = 84
14 * 7 = 98
neither 70 nor 98 is a multiple of 4
only 84 is a multiple of 4, 7 and 14
squareroot of
[tex]12 \frac14[/tex]
Answer:
7/2
Step-by-step explanation:
12 1/4 is equivalent to the improper fraction 49/4.
The square root of 49/4 is 7/2.
The squareroot of [tex]12 \frac14[/tex] is [tex]3 \frac{1}{2} [/tex].
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \sqrt{12 \frac{1}{4} } \\ \\ = \sqrt{ \frac{49}{4} } \\ \\ = \sqrt{ \frac{7 \times 7}{2 \times 2} } \\ \\ = \sqrt{ \frac{( {7})^{2} }{( {2})^{2} } } \\ \\= \frac{7}{2} \\ \\ = 3 \frac{1}{2} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
Which is a solution for the following system of inequalities?pls help :3
(0,5)
(0,-2)
(1,-1)
(0,0)