An equation of the line through the point (-4, -2) parallel to y = 14x - 3 is 14x - y = 54.
To find an equation of a line through the point (-4, -2) that is parallel to the line y = 14x - 3, we can use the fact that parallel lines have the same slope.
The given line y = 14x - 3 is in slope-intercept form, y = mx + b,
where m represents the slope.
In this case, the slope is 14.
Since the desired line is parallel to the given line, it will also have a slope of 14.
Therefore, the equation of the line can be written as:
y - y1 = m(x - x1),
where (x1, y1) represents the coordinates of the given point (-4, -2), and m represents the slope.
Substituting the values into the equation, we have:
y - (-2) = 14(x - (-4)).
Simplifying this equation gives:
y + 2 = 14(x + 4).
Expanding the right side of the equation:
y + 2 = 14x + 56.
Finally, rearranging the equation to the standard form, we have:
14x - y = 54.
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What is the completely factored form of this polynomial?
x^4- 8x^2 + 16
A. (X+2)^2(x-2)^2
B. (x^2-4)^2
C. (x^2+4)(x+2)(x-2)
D. (x+2)(x-2)
Answer:
A. (x + 2)²(x - 2)²
Step-by-step explanation:
x⁴ - 8x² + 16 =
(x² - 4)(x² - 4) =
(x - 2)(x + 2)(x - 2)(x + 2) =
(x - 2)²(x + 2)²
In the triangles, GK PN and HG 2MP.
Which statement correctly compares the angles?
H
M
Angle G is congruent to angle P.
O Angle G is smaller than angle P.
O Angle G is larger than angle P.
O Angle G is congruent to angle N.
32 cm
40 cm
G
K
P
N
Answer:
G is smaller than P. Visually comparing G to P you are doing a rough comparison to a 90° (or right) angle. Angle G is a little bit tilted to the right making it just under 90°
The statement which correctly compares the angles is Angle G is smaller than angle P.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given are two triangles.
Given that,
GK is congruent to PN.
HG is congruent to MP.
Also, given that,
HK = 32 cm and MN = 40 cm
Angle G is opposite to the side HK.
Angle P is opposite to the side MN.
Angles opposite to the greater side will be greater.
So angle P is greater than angle G
Or, angle G is smaller than angle P.
Hence, Angle G is smaller than angle P.
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Juan works at a retail store. He earns $6 an hour plus 1 $5 bonus each time he gets someone to sign up for the stores credit card.
Write a formula that will help Juan determine how much he will earn in one week.
a= total amount earned
h= hours worked in one week
b= number of cards sold in one week
Answer:
6h + 5b = a
Step-by-step explanation:
Please help meeeee ASAP
What’s the equation of the blue line?
Answer:
Step-by-step explanation:
The equation of blue line A is x = 1.
That of blue line B is y = 4.
Please helppppppppp meeeeeee
Answer:
m∠B = 94º
Step-by-step explanation:
Supplementary angles total 180
(8x + 6) + ( 7x + 24) = 180
Combine like terms
15x + 30 = 180
15x = 150
x = 10
m∠B = 7x + 24
m∠B = 7(10) + 24
m∠B = 94º
Joe and Becky are buying fish for their new aquarium. The expression 3g + 4a represents the cost in dollars of buying fish
where 'g' is the number of guppies purchased and 'a' is the number of angel fish purchased. Find the cost of fish if they buy 12 guppies and 4 angel fish. Explain your work.
Answer:
$52
Step-by-step explanation:
Find the cost by plugging in 12 as g and 4 as a into the expression:
3g + 4a
3(12) + 4(4)
36 + 16
= 52
So, the cost will be $52
Hi can anyone pls help me with this problem I would really appreciate it !
Answer:
A
Step-by-step explanation:
The scale factor k is the ratio of corresponding sides, image to original.
k = [tex]\frac{CP'}{CP}[/tex] = [tex]\frac{15}{75}[/tex] = 0.2
Since k < 1 this represents a reduction.
Which of the following is NOT true about mathematical induction?
A.The first possible case is always n = 1.
B.Mathematical induction depends on a recursive process.
C.It can be used to prove that 1 + 2 + 3+...+n =
n(n+2)
2
D. Since Sn is valid for n = 1, it is valid for n = 2. Since it is valid for n = 2, it is valid for n = 3, and so on, indefinitely.
Answer:
A. the first possible case is always n = 1
Step-by-step explanation:
Mathematical induction is a technique used to provide proof for a statement such that the statement holds for all natural numbers which are the non-negative integers
Therefore, given that the natural numbers are 0, 1, 2..., we have that mathematical induction can start from n = 0
Therefore, the statement which is not true is that the first possible case is always n = 1
?...............................
Answer:
-2 ≤ n < 8
Step-by-step explanation:
_________________
Solve for w. Show your work! 5w + 16 - 9 - 8w = 19
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El perímetro de un rectángulo es 58 y su base excede en 10 a su ancho, ¿Cuánto mide la base? AYUDAAAA
Answer:
The base is 19.5.
Step-by-step explanation:
The given question is, "The perimeter of a rectangle is 58 and its base exceeds its width by 10, how long is the base?"
Perimeter = 58
Base, l = 10+b
The perimeter of a rectangle is :
P = 2(l+b)
58 = 2(10+b+b)
29 = (10+2b)
29-10 = 2b
19 = 2b
b = 9.5
Base, l = 10 + 9.5
= 19.5
Hence, the base is 19.5.
Solve the equation below :
7/8 = q + 1/2
A : q = 3/8
B : q = 1 3/8
C : q = 7/16
D q = 1 3/4
Answer:
q = -3/8
Step-by-step explanation:
Clearing out the fractions first simplifies this problem. The LCD here is 8, so we multiply all three terms of 7/8 = q + 1/2 by 8 and simplify the result:
7 + 8q = 4.
Combining the constants, we get: 8q = 4 - 7, or 8q = -3.
Finally, solve for q:
q = -3/8
P is in the shape of a circle. Q is in the shape of a quarter circle of radius 20 cm. P Q 20 cm The area of Q is 4 times the area of P. Work out the radius of P. You must show all your working.
What is the area of the circle in terms of pi?
Answer:
[tex]4.2025\pi\:\mathrm{m^2}[/tex]
Step-by-step explanation:
The area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]. In the figure, we're given a diameter of 4.1. All diameters of a circle are exactly 2 times the length of all radii of the circle. Therefore, the radius of the circle is [tex]4.1\cdot \frac{1}{2}=2.05[/tex].
Thus, the area of the circle is [tex]2.05^2\pi=\boxed{4.2025\pi\:\mathrm{m^2}}[/tex]
Find the value of x in the triangle shown below
Answer:
x = 48°
Step-by-step explanation:
Two sides of the triangle are equal, both 7, Then the 2 base angles are congruent, both 66°
The sum of the 3 angles in the triangle sum to 180° , so
x = 180° - (66 + 66) = 180° - 132° = 48°
Answer:
[tex]{ \tt{x + 66 + 66 = 180}} \\ x = 48 \degree \\ \\ { \boxed{ \bf{or : }}} \\ { \bf{ from \:lamis \: theorem : }} \\ { \tt{ \frac{5.7}{ \sin(x) } = \frac{7}{ \sin(66 \degree) } }} \\ \\ { \tt{x = { \sin }^{ - 1}( \frac{5.7 \times \sin(66 \degree) }{7} ) }} \\ x = 48 \degree[/tex]
Which tiles should be added to the model below to make zero?
- - - - - -
O 6 negative tiles
O 6 positive tiles
O 3 negative tiles and 3 positive tiles
O 6 negative tiles and 6 positive tiles
Answer:
3 positive tiles hope.helps
Lanu draws a rectangle that is 10 inches wide and 20 inches long. Which rectangle described down below has the same area
Answer:
b. 8 inches wide and 25 inches long
Step-by-step explanation:
Here are the options
5 inches wide and 25 inches long
b. 8 inches wide and 25 inches long
c. 15 inches wide and 15 inches long
d 15 inches wide and 25 inches long
Area of a rectangle = length x width
10 x 20 = 200
first option
5 x 25 = 125 does not have the same area as the one lanu drew
second option
8 x 25 = 200 has the same area as the one lanu drew
third option
15 x 15 = 225 does not have the same area as the one lanu drew
fourth option
15 x 25 = 375 does not have the same area as the one lanu drew
Solve 36 = byx for y.
y=-
Step-by-step explanation:
Simplifying
36 = byx
Solving
36 = bxy
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-1bxy' to each side of the equation.
36 + -1bxy = bxy + -1bxy
Combine like terms: bxy + -1bxy = 0
36 + -1bxy = 0
Add '-36' to each side of the equation.
36 + -36 + -1bxy = 0 + -36
Combine like terms: 36 + -36 = 0
0 + -1bxy = 0 + -36
-1bxy = 0 + -36
Combine like terms: 0 + -36 = -36
-1bxy = -36
Divide each side by '-1xy'.
b = 36x-1y-1
Simplifying
b = 36x-1y-1
Answer:
y = [tex]\frac{36}{bx}[/tex]
Step-by-step explanation:
Given
36 = byx ( isolate y by dividing both sides by bx )
[tex]\frac{36}{bx}[/tex] = y
f(x)=15x³+22x²-15x+2
Write f(x) as a product of linear factors.
Answer:
[tex](5x - 1)(3x - 1)(x + 2)[/tex]
Step-by-step explanation:
[tex](15 {x}^{3} + 22 {x}^{2} - 15x + 2)[/tex]
Apply Rational Root Theorem, our possible roots will be
plus or minus( 2/15, 2/5,2/3,2, 1/15,1/5,1/3,1).
I
I tried root -2 and it work so
If we apply synthetic dividon, we would be left with
[tex]15 {x}^{2} - 8x + 1[/tex]
We can factor this regularly.
Apply AC method that a number
AC will multiply to 15 but add to -8.
The answer are -5 and -3 so we write this as
[tex]15 {x}^{2} - 5x - 3x + 1[/tex]
Factor by grouping
[tex](15x {}^{2} - 5x) - (3x + 1)[/tex]
[tex]5x(3x - 1) - 1(3x - 1)[/tex]
So our factor are
[tex](5x - 1)(3x - 1)(x + 2)[/tex]
A country's population in 1994 was 21 million.
In 2001 it was 22 million. Estimate
the population in 2011 using the exponential
growth formula. Round your answer to the
nearest million.
P= Aekt
Enter the correct answer.
DONE
DOO
+1?
Answer:
Step-by-step explanation:
22 = 21 [tex]e^{7k\\}[/tex]
(22/21) = [tex]e^{7k}[/tex]
ln(22/21) = 7k ln(e)
ln(22/21) = 7k
0.046520016 = 7k
k=0.006645717
~~~~~~~~~~~~~~~~
P = 21 [tex]e^{0.006645717*17\\}[/tex]
P = 23.51
All swimming equipment is on sale with a 30% discount. A snorkeling set regularly sells
for $50. Find the discount.
Answer:
15
Step-by-step explanation:
50 * .30=15
Surface area is the sum of the areas of all the surfaces of a three-dimensional object.
(True or false)
Answer: True
Think of a 3D box. It has 6 faces and the surface area is the total of all six individual rectangular faces. This idea applies to any polyhedron.
SOMEBODY PLEASE HELP I DON’T HAVE MUCH TIME
Find the volume of this sphere.
Use 3 for TT.
V
V [?]cm
V = 713
12cm
Answer:
904.78
Step-by-step explanation:
I hope this is correct, if it isn't please feel free to let me know and I can fix it. I'm sorry in advance if it is incorrect.
f(2) if f(x) = (x + 1)2.
Answer:
6
Step-by-step explanation:
f(2) = (2 + 1)2
(3)2
6
Answer:
6
Step-by-step explanation:
f(2) = (2+1)*2, f(2) = 3*2 = 6
f(4) =
If g(x) = 2, x =
<
Is Mercury is a gas giant, and because it is hot, it is named after the mercury in a thermometer.
Please give real answers with explaination. I will follow + I will give brainliest. No Docs/No Files/No Links only answer with explaination.
Mercury is the smallest and fastest planet in the solar system. It is also the closest planet to the sun. It is named after the Roman messenger god Mercury, the fastest Roman god.
In the given figure alongside,prove that
Triangle ABC is simalar to Triangle SRT
Find the length of AC
Answer:
let's use Pythagoras theorem,
h²=b²+l²
so,
ad²=ac²+dc²
6²=ac²+3²
36-9=ac²=27
√27 can be written as 3√3,
hence ac= 3√3
Please solve with explanation
Step-by-step explanation:
total wood= 45½=22.5 units
cut wood= 8⅞= 7 units
wasted wood= 1/16=0.06
now wood left is,
total wood -cut wood-wasted wood
22.5-7-0.06
15.44 units
What is an equation of the line that is perpendicular to 3z +y=-5 and passes through the point (3, – 7)?
Enter your equation in the box