Answer:
y = −14x + 3
Step-by-step explanation:
Parallel lines have the same slope
The equation y = −14x + 7 is put in slope intercept form ( y = mx + b )
Where m = slope
-14 takes "m's" place meaning that the slope = -14
If parallel lines have the same slope than the equation of a line parallel to y = −14x + 7 must have a slope of -14
The only equation that has a slope of -14 is D
At the baseball stadium there are 548 seats that are divided into 14 rows how many seats are in each row
Answer:
There are 39 seats I think.
Step-by-step explanation:
548 divided by 14 is a decimal but rounded it to the nearest full number.
the theater sells two types of tickets: adult tickets for $6 and child tickets for 5$. last night, the theatre sold a total of 375 tickets for a total of $2153. How many adult tickets did the theatre sell
Hello,
Imagine Algebra does not exist .
Let's suppose all tickets are children's tickets
The sum should be 5$*375=1875$
Not enough, we must have $2153: 2153-1875=278 ($) must be found.
Let's replace a children ticket with an adult one,
we get one dollar more.
We must thus exchange 278 tickets
There are 278 adult tickets and 375-278=97 children tickets
Proof: 278*6+97*5=2153
solve for x. Round to the nearest tenth, if necessary.
Answer:
7.1
Step-by-step explanation:
We used SOHCAHTOA because it's a right angle triangle
So because we have an angle with an adjacent of 6.3 and hypotenuse of x
We will use
Cos=adjacent /hypotenuse
The current population of Fun City is 21000 people. If the population of the city will double every 51 years then the population after 171 years would be
Answer:
The population of Fun City after 171 years would be 214563.
Step-by-step explanation:
The statement depicts a case of exponential growth, whose model is described below:
[tex]p(t) = p_{o}\cdot r^{\frac{t}{T} }[/tex] (1)
Where:
[tex]p_{o}[/tex] - Initial population, no unit.
[tex]p(t)[/tex] - Current population, no unit.
[tex]r[/tex] - Growth rate, no unit.
[tex]t[/tex] - Time, in years.
[tex]T[/tex] - Growth period, in years.
If we know that [tex]p_{o} = 21000[/tex], [tex]r = 2[/tex], [tex]t = 171\,yr[/tex] and [tex]T = 51\,yr[/tex], then the population of the city after 171 years is:
[tex]p(t) = 21000\cdot 2^{\frac{171}{51} }[/tex]
[tex]p(t) = 214563[/tex]
The population of Fun City after 171 years would be 214563.
Can someone help me with this math homework please!
Answer:
[tex]j = - 0.45[/tex]
Step-by-step explanation:
Combine like terms and apply the rules of algebra.
[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1[/tex]
[tex] - 5.5 - 9.5j = 0.5j - 1[/tex]
[tex] - 9.5j = 0.5j + 4.5[/tex]
[tex] - 10 j= 4.5[/tex]
[tex]j = - 0.45[/tex]
Answer: j = -0.45
Step-by-step explanation:
Step 1: Combine like terms
2.25 - 11j - 7.75 + 1.5j = 0.5j - 1
-5.5 - 9.5j = 0.5j - 1
Step 2: isolate your variable
-5.5 - 9.5j = 0.5j - 1
Subtract 0.5j from both sides
-5.5 - 10j = -1
Add 5.5 to both sides
-10j = 4.5
Divide both sides by -10
j = -0.45
x = 4y + 3, 2x + y = -3
System of Equations
Answer:
x = -1, y = -1
Step-by-step explanation:
x = 4y + 3
2x + y = -3
We have the value of x in terms of y, so we substitute that in 2x + y = -3:
2(4y+3)+y = -3
8y+6+y = -3
9y = -9
y = -1
Now we substitute the value of y in x = 4y + 3:
x = 4(-1)+3
x = -1
Answer:
y = -1 & x = -1
Step-by-step explanation:
x = 4y + 3 .... ( 1)
2x + y = -3 ........(2)
substitute the 4y + 3 as x in the second equation
2( 4y + 3) + y = -3
simplify and solve for y
8y + 24 + y = -3
9 y + 24 = -3
9y = -3 -24
9y = -27
y = -27 / 9
y = -1
Now, substitute the value of y -1 in first equation
x = 4y + 3
solve for x
x = 4 ( - 1 ) + 3
x = -4 + 3
x = -1
find k so that x-1 is a factor of x^3 - 3x^2 + kx - 1
Answer:
[tex]{ \bf {factor : { \tt{x - 1}}}} \\ x - 1 = 0 \\ x = 1 \\ { \tt{f(x) = {x}^{3} - {3x}^{2} + kx - 1}} \\ { \tt{f(1) : {(1)}^{3} - 3 {(1)}^{2} + k(1) - 1 = 0}} \\ { \tt{k - 3 = 0}} \\ { \tt{k = 3}}[/tex]
Answer:
k = 3
Step-by-step explanation:
If x-1 is a factor of x³ - 3x² + kx - 1 then value of x is 1.
f (x ) = x³ - 3x² + Kx - 1 , then
plug 1 as x in the expression.
f ( 1) = ( 1)³ - 3 ( 1)² + k (1) - 1 = 0expand exponents
1 - 3 + k - 1 = 0combine like terms
-3 + k = 0Add 3 to both side
k = 3Solve the inequality.
k + 4 – 2(k – 12) > 0
k > 28
k > –20
k < –20
k < 28
k<28
Step 1: Simplify both sides of the inequality.
−k+28>0
Step 2: Subtract 28 from both sides.
−k+28−28>0−28
−k>−28
Step 3: Divide both sides by -1.
−k /−1 > −28 /−1
k<28
Answer:
k < 28
Step-by-step explanation:
Given inequality :-
k + 4 - 2( k - 12 ) > 0 k + 4 - 2k + 24 > 0-k + 28 > 0 28 > k k < 28Last Option is correct .
Evaluate the expression.
32 + 6 x 22-42 - 23
Answer:
25
Step-by-step explanation:
You need to simplify
.
.
.
.
................... :)
Answer:
D
Step-by-step explanation:
9+24-16+8= 25
The figure Jhows the graph of h(x) = px - 3+2 a translation of the parent function
g(x) = v. How is the graph of the parent function translated?
A) Right 3 units and up 2 units
OB) Right 2 units and up 3 units
C) Right 3 units and down 2 units
D) Left 3 units and up 2 units
Please helped timed question. Solve for a, b, and A. Round to the nearest tenth.
Answer:
[tex]\angle A=90-72[/tex]
[tex]\angle A=18[/tex]
---------------
[tex]sin~72=\frac{b}{11}[/tex]
[tex]11\times sin~72=6[/tex]
[tex]b=10.5[/tex]
----------------
[tex]11\times cos~72=a[/tex]
[tex]a=3.4[/tex]
----------------
ANSWER:
a=3.4
b=10.5
∠A=18
-----------------------
hope it helps...
have a great day!!
can someone help me state domain and range
Answer:
The domain and range is (as inequalities):
[tex]x\leq 3\text{ and } -\infty < y < \infty[/tex]
Or in interval notation:
[tex]D=(-\infty, 3]\text{ and } R=(-\infty, \infty)[/tex]
Step-by-step explanation:
Recall that the domain is simply the set of all x-values of the function.
From the graph, we can see that the function is defined for all x-values less than or equal to 3.
Therefore, the domain is:
[tex]x\leq 3[/tex]
The range is the set of all y-values of the function.
From the graph, we can see that the range will extend infinitely in both directions.
Therefore, the range is all real numbers. As an inequality:
[tex]-\infty < y < \infty[/tex]
Or in interval notation, the domain is:
[tex](-\infty, 3][/tex]
And the range is:
[tex](-\infty, \infty)[/tex]
Solve the qn in attachment .
Answer:
[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]
Step-by-step explanation:
The given expression to us is ,
[tex]\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}[/tex]
Now take the LCM as ( x - 1 ) and Simplify , we have ,
[tex]\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}[/tex]
Simplifying further , we get ,
[tex]\implies \dfrac{ -4x+7}{2(x-2) }[/tex]
Hence the second option is correct .
Answer:
[tex] \frac{ \frac{3}{x - 1} - 4 }{2 - \frac{2}{x - 1} } \\ = \frac{ \frac{3 - 4(x - 1)}{x - 1} }{ \frac{2(x - 1) - 2}{x - 1} } \\ = \frac{3 - 4x + 4}{2x - 2 - 2 } \\ \frac{7 - 4x}{2(x - 2)} \\ option \: b \: is \: your \: answer \\ thank \: you[/tex]
Which equation is correct?
x – 17 = 4
x – 4 = 17
x + 4 = 17
x + 17 = 4
Answer:
1 and 2.....then 3 is a different question
Please help me!!
I just don’t understand it!!
Answer:
(12, 2 )
Step-by-step explanation:
Given (x, y ) on the graph of f(x) , then on the inverse function
(x, y ) → (y, x ), then
(2, 12 ) → (12, 2 ) ← point on g(x) the inverse function
Which point is a solution to the inequality shown in this graph
Answer: C. (0, -3)
Step-by-step explanation:
You don't even need to find the function, just mentally graph every point in the options on the graph.
If it land in the white area, it's not a solution.If it land in the blue area or on the line, it's a solution.The line is not dotted, showing that the inequality is probably either ≥ or ≤, so points on the line do count as solution.
Let x=−1−5i and y=5−i. Find x+y
Answer:
[tex]4-6i[/tex]
Step-by-step explanation:
Substitute the value of the variable into the expression and simplify.
Every floor of a 20 storey building is 5m in high. If a lift moves 2m every second, how long will it take to move from 3rd floor to 15th floor?
Answer:
30 seconds
Step-by-step explanation:
→ Work out how many floors it's going to travel
15 - 3 = 12 floors
→ Work out how many meters 12 floors is
12 × 5 = 60 meters
→ Work out how long that will take
60 ÷ 2 = 30 seconds
What is the center of the circle:What is the center of the circle: (x+1)^2+(y-12)^2=25
1. 25
2. (1, -12)
3. 5
4. (-1, 12)
Answer:
option 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + 1)² + (y - 12)² = 25 ← is in standard form
with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5
What is the answer for y?
the answer is in the picture
Determine whether the lines are parallel, perpendicular, or neither.
9x + 3y = 12
24x + 8y = 35
Answer:
parallel
Step-by-step explanation:
Let's rewrite each equation into the slope-intercept form so that we can easily identify the slope of each line.
slope-intercept form: y= mx +c, where m is the gradient and c is the y-intercept.
9x +3y= 12
3x +y= 4 (÷3 throughout)
y= -3x +4 -----(1)
24x +8y= 35
8y= -24x +35 (-24x on both sides)
[tex]y = - 3x+ 4 \frac{3}{8} [/tex] -----(2)
Thus, the slopes of the lines are both -3. Since both lines have the same gradient, they are parallel to each other.
Notes:
• parallel lines have the same gradient
• the product of the gradients of two perpendicular lines is -1
• gradient and slope has the same meaning and can thus be used interchangeably
Write functions for each of the following transformations using function notation. Choose a different letter to represent each function. For example, you can use R to represent rotations. Assume that a positive rotation occurs in the counterclockwise direction.
• translation of a units to the right and b units up reflection across the y-axis
• reflection across the x-axis rotation of 90 degrees counterclockwise about the origin, point o
• rotation of 180 degrees counterclockwise about the origin, point o
• rotation of 270 degrees counterclockwise about the origin, point o
Answer:
1) [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
Coordinate change
(x, y) → (x + a, y + b)
2) RFy(x, y) = f(-x)
Coordinate change
(x, y) → (-x, y)
3) RFx(x, y) = -f(x)
Coordinate change
(x, y) → (-y, x)
4) RCCW90(x, y) = f⁻¹(-x)
Coordinate change
(x, y) → (-y, x)
5) RCCW180(x, y) = -(f(-x))
Coordinate change
(x, y) → (-x, -y)
6) A 270 degrees counterclockwise rotation gives;
RCCW270(x, y) = -(f⁻¹(x))
Coordinate change
(x, y) → (y, -x)
Step-by-step explanation:
1) Horizontal translation a units right = f(x - a)
The vertical translation b units up = f(x) + b
Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
The coordinate change
(x, y) → (x + a, y + b)
2) A reflection across the y-axis = RFy(x, y) = f(-x)
The coordinate change
(x, y) → (-x, y)
3) A reflection across the x-axis gives RFx(x, y) → (x, -y)
Therefore, in function notation, we get;
RFx(x, y) = -f(x)
4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)
In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)
5) A 180 degrees counterclockwise rotation about the origin gives;
(x, y) → (-x, -y)
Therefore, we get;
In function notation RotCCW180(x, y) = -(f(-x))
6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)
In function notation RotCCW270(x, y) = -(f⁻¹(x))
WRITE THE FUNCTION FOR THE GIVEN TABLE PLS
Answer:
y=X²-4x+5
Step-by-step explanation:
substitute all the left side values to get the outputs..
y=(5)²-4(5)+5 =10
Answer:
A
Step-by-step explanation:
In fact, if we try to substitute, we have:
10 = 5^2 -4(5) +5
10 = 25 - 20 + 5
10 = 10 (ok)
17 = -2^2 - 4(-2) + 5
17 = 4 + 8 + 5
17 = 17 (ok)
and so on
What is the scale factor from abc to xyz?
Answer:
C
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C
The scale factor will be equal to 1 / 5. the correct option is C.
What is a scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,
Scale factor = Original size / dilated size
Scale factor = XY / AB
Scale factor = 9 / 45
Scale factor = 1 / 5
Therefore, the scale factor will be equal to 1 / 5. the correct option is C.
To know more about scale factors follow
https://brainly.com/question/25722260
#SPJ2
What form do we place a quadratic in to find the Vertex, or "extrema” of a quadratic function?
Answer:
The vertex form of the quadratic function, f(x) = a·(x - h)² + k
Step-by-step explanation:
The general form of a quadratic function is given as follows;
f(x) = a·x² + b·x + c
The vertex form of the quadratic function is f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex of the parabola
h = -b/2·a, k = f(h)
What is the total value of digit 7 in the number 32.8794
STREAM WALLS BY LOUIS TOMLINSON
Answer:
OMG I LOVE LOUIS SO MUCH HE IS SO PERFECT
Step-by-step explanation:
Find (4/5+3/6-5/12) ÷ 2/3
Answer:
1/2 + 2/3 + 5/4 = 29/ 12 = 2 5/ 12 ≅ 2.4166667
Step-by-step explanation:
Add: 1/ 2 + 2/ 3 = 1 · 3/ 2 · 3 + 2 · 2/ 3 · 2 = 3/ 6 + 4/ 6 = 3 + 4/ 6 = 7/ 6
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - one half plus two thirds = seven sixths.
Add: the result of step No. 1 + 5/ 4 = 7/ 6 + 5/ 4 = 7 · 2/ 6 · 2 + 5 · 3/ 4 · 3 = 14/ 12 + 15/ 12 = 14 + 15/ 12 = 29/ 12
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 4 = 24. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - seven sixths plus five quarters = twenty-nine twelfths.
hope it helps...
correct me if I'm wrong...
© Find the quotient of 3/8 and ,4/9
Give your answer as a fraction in its simplest form.
[tex] \frac{3}{8} \div \frac{4}{9} \\ = \frac{3}{8} \times \frac{9}{4} \\ = \frac{27}{32} [/tex]
Hope it helps!!!
Thanks!!!
Select the correct product. (x^2+4)(x^2-4)
1. X^4-16
2. X^4+16
3. X^2+8x+16
4. X^2-8x-16
Answer:
[tex] ({x}^{2} + 4 )( {x}^{2} - 4) \\ 1)( {x}^{2} - 16) \\ = (x - 4)(x + 4) \\ 2)( {x}^{2} + 16) \\ = (x - 4)(x + 4) \\ 3) {x}^{2} + 8x + 16 \\ {x}^{2} + (4 + 4)x + 16 \\ {x}^{2} + 4x + 4x + 16 \\ x(x + 4) + 4(x + 4) \\ (x + 4)(x + 4) \\ 4) {x}^{2} - 8x - 16 \\ {x}^{2} - (4 + 4)x - 16 \\ {x}^{2} - 4x + 4x - 16 \\ x(x - 4) + 4(x - 4) \\ (x - 4)(x + 4)[/tex]