Answer:
x=2 x=-3
Step-by-step explanation:
4x2+3x=24-x
Subtract 24 from each side
4x^2 +3x -24 = 24-24 -x
4x^2 +3x -24 = -x
Add x to each side
4x^2 +3x+x -24 = -x+x
4x^2 +4x -24 = 0
Factor out a 4
4(x^2 +x -6) = 0
Divide by 4
x^2 +x -6 =0
Factor
What 2 numbers multiply to -6 and add to 1
-2*3 = -6
-2+3 =1
(x-2) (x+3) =0
Using the zero product property
x-2 =0 x+3 =0
x-2+2=0+2 x+3-3=0-3
x=2 x=-3
Answer:x=-3 , x = 2
Step-by-step explanation:
First move the expression ( 24-x) to the left.
This gives us 4x^2+3x+24-x.
Collect the like terms which gives us 4x^2+4x+24
4x^2+4x-24 = 0. Divide both sides by 4.
x^2 + x-6 = 0
Factorise the expression so you get (x+3)(x-2)=0
Solve the equations x+3 = 0 and x-2=0
The final solutions are x=-3 and x=2.
Write the first five terms of the arithmetic sequence whose first term is 5 and whose common difference is 6.
Answer:
5, 11,17,23,29
Step-by-step explanation:
To obtain the term in the sequence add the common difference to the previous term, that is
a(1) = 5
a(2) = 5 + 6 = 11
a(3) = 11 + 6 = 17
a(4) = 17 + 6 = 23
a(5) = 23 + 6 = 29
The first five terms of an arithmetic sequence starting with 5 and a common difference of 6 are 5, 11, 17, 23, and 29.
The first five terms of the arithmetic sequence with the first term 5 and a common difference of 6 can be found by successively adding the common difference to the previous term.
Third term (a3) = a2 + 6 = 11 + 6 = 17
Fifth term (a5) = a4 + 6 = 23 + 6 = 29
Therefore, the first five terms of the arithmetic sequence are 5, 11, 17, 23, and 29.
which of the following is the best approximation to a solution of the equation e^x=4x+1
Triangle QRS is dilated according to the rule DO,2 (x,y).
What is true about the image △Q'R'S'? Check all that apply.
DO,2 (x,y) = (2x, 2y)
Side Q'S' lies on a line with a slope of -1.
QR is longer than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image.
The distance from Q' to the origin is twice the distance from Q to the origin.
Answer:
True options:
[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]
Side Q'S' lies on a line with a slope of -1.
The distance from Q' to the origin is twice the distance from Q to the origin.
Step-by-step explanation:
Triangle QRS is dilated according to the rule [tex]D_{O,2} (x,y).[/tex] This dilation has the rule
[tex](x,y)\rightarrow (2x,2y)[/tex]
So,
[tex]S(-1,1)\rightarrow S'(-2,2)\\ \\Q(-3,3)\rightarrow Q'(-6,6)\\ \\R(2,4)\rightarrow R'(4,8)[/tex]
True options:
[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]
Side Q'S' lies on a line with a slope of -1.
The distance from Q' to the origin is twice the distance from Q to the origin.
False options:
QR is longer than Q'R', because QR is twice shorter than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image, because the vertices of the per-image are closer to the origin than those of the image (see attached diagram).
Answer:
1, 2, 5 on Ed
Step-by-step explanation:
simplify the expression below. 4^5 x 4^3
Answer:
4^8
Step-by-step explanation:
Because both expressions have the same base, we can add the exponents to simplify the expression:
[tex]4^5*4^3 = 4^{5+3} = 4^8[/tex]
Answer: 4^8 or 65,536
Step-by-step explanation:
The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents.
X+3y=28 find the value of y when x equals 28
Answer:
y = 0Step-by-step explanation:
x + 3y = 28
Put x = 28 and solve for y:
28 + 3y = 28 subtract 28 from both sides
28 - 28 + 3y = 28 - 28
3y = 0 divide both sides by 3
3y : 3 = 0 : 3
y = 0
Describe the symmetry of the plane figure shown below.
A.horizontal line symmetry
B.vertical line symmetry
C.rotational symmetry
D.diagonal line symmetry
Answer:B. vertical line symmetry
Step-by-step explanation:
Answer:
D. diagonal line symmetry
Step-by-step explanation:
Please Help I Will Offer 30!!!!
Answer:
Step-by-step explanation:
Compare y = (1/2)x - 3 and y = (-1/2)x - 3.
They have different slopes but the same y-intercept (0, -3). Eliminate the first answer choice.
They have different slopes. Eliminate the second answer choice.
Their graphs intersect, so they have a solution. Eliminate the third choice.
They have different slopes but the same intercept, so they have one solution. The fourth answer choice is the correct one.
Answer:
the fourth one is the corect one
Step-by-step explanation:
the fourth one is the corect one because i did the mathand i checked it twice and its right and also i asked my friend and he said it the fourth one
hope that helps you
What are the slope and the y-intercept of the linear function that is represented by the table?
Answer:
slope rise 3 run 2 1/2
Step-by-step explanation:
if you start from the bottom and if you start from the top it's -3 and -2 1/2
Answer: The slope is 3 and the y-intercept is 3/2
Step-by-step explanation:
The slope of a linear function can be calculated as:
s = (y2 - y1)/(x2 - x1)
Where y2 = f(x2) and y1 = f(x1) and f(x) is the linear function.
So here we can use any two pairs of the set of data, for example, the first two.
(-1 , -3/2) and (-1/2,0)
s = (0 -(-3/2))/(-1/2 - (-1)) = (3/2)/(1/2) =(3/2)*(2/1) = 3
So the slope is equal to 3.
the y-intercept is the value of y when x = 0, in the table we can see that when x = 0. the value of y = 3/2
So the function is: y = 3*x + 3/2
and the correct option is the fourth one.
A teacher wanted to buy a chair, a bookshelf, two tables and a desk. She spent $900 for all five items and the chair and the desk combined 70% of her total. If the bookshelf cost $50, how much did each of the tables cost?
Find the cost of the chair and desk by multiplying the total amount pent by the 70%
Chair and desk = 900 x 0.70 = $60
Subtract that cost from the total spent:
900 - 630 = $270 was spent on the other three items.
Subtract the cost of the bookshelf:
270 - 50 = 220
The two tables cost 220.
For the price of one table divide that cost by 2:
220/2 = 110
One table cost $110.
The cost of each table is $110.
Given that
There are five items i.e. chair, bookshelf, 2 tables, and a desk.
The total amount incurred for these 5 items should be $900.
And, the chair + desk = 70% of total.
The cost of the bookshelf is $50.
Since 70% of total = chair + desk
That means
Chair + desk = 0.70 of $900 = $630
So the other items cost should be
= $900 - $630
= $270
And, the cost of bookshelf is $50
So, the two tables cost should be
= $270 - $50
= $220
So for one it should be
= $220 ÷ 2
= $110
Therefore we can conclude that the cost of each table is $110.
Learn more about the cost here: brainly.com/question/5282141
Which is the point-slope form of an equation for the line that passes through (0, –5) with slope 2?
Question 3 options:
a)
y = 2x – 5
b)
y – 5 = x – 2
c)
y + 5 = 2x
d)
y = 2(x + 5)
Answer:
c) y + 5 = 2x
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are.
What is .5x5 equal???
Answer:
The answer is 25
Step-by-step explanation:
what the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
Answer: ≈ 1.414
Step-by-step explanation:
You can use the pythagorean theorem, a^2 + b^2 = c^2
a^2 and b^2 are the legs and c^2 is the hypotenuse.
1^2 + 1^2 = c^2
1 + 1 = c^2
2 = c^2
√ 2 = √ c^2
c = ≈ 1.414
A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus.
What is the value of x?
50
55
125
145
Answer:
The value of x is 55 ⇒ 2nd answer
Step-by-step explanation:
* Lets revise the properties of the rhombus
- It has 4 equal sides
- Every two opposite sides are parallel
- Every two opposite angles are equal
- Every two adjacent angles are supplementary (their sum is 180°)
* Now lets solve the problem
- A square divided into two rectangles
- Each rectangle contains a shaded rhombus
- The shaded rhombus has two adjacent angles their measures are
(2x + 20)° and 50°
∵ Every two adjacent angles in the rhombus are supplementary
∵ The sum of the supplementary angles = 180°
∴ The sum of the measures of the angles (2x + 20)° and 50° is 180°
- lets put the equation and solve it to find x
∴ (2x + 20)° + 50° = 180° ⇒ add the like terms
∴ 2x + 70° = 180° ⇒ subtract 70° from both sides
∴ 2x = 110° ⇒ divide both sides by 2
∴ x = 55°
* The value of x is 55
If f(x) = 5x^3 and g(x) = x+1, find (f•g)(x).
A. 5x^4+1
B. 5x^3+1
C. 5x^4+5x^3
D. 6x^3
If f(x) = 5x^3 and g(x) = x+1, find (f•g)(x).
Note: (f•g)(x) means f(x) times g(x).
(f•g)(x) = (5x^3)(x + 1)
(f•g)(x) = 5x^4 + 5x^3
Answer: Choice C
Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
Answer:
y+3 = -7/5(x+2)
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (4--3)/(-7--2)
= (4+3)/(-7+2)
=7/-5
= -7/5
The point slope form is y-y1 = m(x-x1)
y--3 = -7/5(x--2)
y+3 = -7/5(x+2)
We could use the second set of points
y-4 = -7/5(x--7)
y-4 =-7/5(x+7)
What is the rate of change of y with respect to x for this function?
bearing in mind that the average rate of change = slope, and for that we can simply use two points off the table.
[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -2&12\\ 0&3\\ 3&-10.5\\ 7&-28.5\\ \cline{1-2} \end{array}\qquad \qquad \begin{array}{llll} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-10.5}) \\\\\\ slope \implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-10.5-12}{3-(-2)} \\\\\\ \cfrac{-10.5-12}{3+2}\implies \cfrac{-22.5}{5}\implies -\cfrac{4.5}{1}\implies -4.5 \end{array}[/tex]
The rate of change of y with respect to x for the given function with coordinates expressed in the table is; dy/dx = -9/2
The rate of change of y with respect to x for a given linear function is simply the slope expressed as;
dy/dx = (y2 - y1)/(x2 - x1)
Let us take the first 2 coordinates which are;
(-2, 12) and (0, 3)
Thus;
dy/dx = (3 - 12)/(0 - (-2))
dy/dx = -9/2
Or dy/dx = -4.5
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ASAP help
The length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches. What is the width? If w = the width of the rectangle, which of the following expressions represents the length of the rectangle?
A. 2w + 3
B. 2(w + 3)
C. 3(2w)
Answer:
2W+3 I am really sorry if that's wrong, I don't think it is though GOODLUCK
Step-by-step explanation:
Answer:
The correct answer is option A. 2w + 3
w = 5 inches
Step-by-step explanation:
It is given that, the length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches.
To find the correct option
If 'w' is the width of rectangle, then length = 3 inches more than the twice the width
length = 2w + 3
The correct answer is option A. 2w + 3
To find the width
We have area = 65 square inches
Length * Width = 65
(2w + 3) * W = 65
2w² + 3w - 65 = 0
Solving we get ,
w = 5 and -6.5
Therefore w = 5 inches
Which expressions are equivalent to the given expression? Check all that apply.
(–2.4a – 1.8b) – (–3.8a – 4.4b) + (2.0a + 3.0b)
A. 3.4b – 3.2a
B. 3.4a – 3.2b
C. 5.6b + 3.4a
D. 3.2b + 3.4a
E. 3.4a
Answer:
5.6b + 3.4a
Step-by-step explanation:
Simply evaluate be match each term with its corresponding variable, and watch out for where you have to distribute negatives, meaning that you have a couple of double negatives in there.
Double Negative = Positive
Answer:
it’s C and E
Step-by-step explanation:
Which of the following is the equation of a line parallel to the line y = 3x + 2,
passing through the point (10.1)?
A. -3x - y = 29
B. 3x - y = 29
C -3x + y = 29
D. 3x + y = 29
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 is in this form with slope m = 3
• Parallel lines have equal slopes, hence
y = 3x + c ← is the partial equation of the parallel line
To find c substitute (10, 1) into the partial equation
1 = 30 + c ⇒ c = 1 - 30 = - 29
y = 3x - 29 ← in slope- intercept form
Subtract y from both sides
0 = 3x - y - 29 ( add 29 to both sides )
29 = 3x - y, thus
3x - y = 29 ← in standard form → B
Answer:
B
Step-by-step explanation:
Determine the end behavior for function f(x)=-x^4+5x^3-3
Answer:
Step-by-step explanation:
The dominant term of this function is x^4. The graph of x^4 starts in Quadrant II and continues in Quadrant I.
If we have y = -x^4, the graph starts in Quadrant III and continues in Quadrant IV. This is the end behavior for f(x)=-x^4+5x^3-3.
A walking path across a park is represented by the equation y=-2x+5. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-2,9). Identify the equation that represents the new path.
A. y= {x+10
B. y= -2x - 5
C. y= 2x+13
D. y -- 1x+8
Answer:
[tex]y = \frac{1}{2}x+10[/tex]
Step-by-step explanation:
The given path is:
y = -2x+5
Comparing with the standard form of equation:
y = mx+b
So,
m = -2
We know that product of slopes of two perpendicular lines is -1
Let m1 be the slope of the perpendicular line
m*m1=-1
-2*m1 = -1
m1 = -1/-2
m1 = 1/2
So the slope of perpendicular path is 1/2.
Since the new path passes through (-2,9)
[tex]9 = \frac{1}{2}(-2) +b\\9 = -1 +b\\b = 10[/tex]
Putting the values of m and b in standard form
[tex]y = \frac{1}{2}x+10[/tex]
Hence the equation of new path is:
[tex]y = \frac{1}{2}x+10[/tex] ..
Which angles form a linear pair?
Answer:
Step-by-step explanation:
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Answer:
Adjacent angles formed by two intersecting lines form a linear pair.
Step-by-step explanation:
A linear pair of angles is formed when two lines intersect. A linear pair of angles must add up to 180 degrees.
If two angles are adjacent angles that are formed by two intersecting lines, then they are called linear.
PLZZZZ GEOMETRY HELP solve for HI
Answer:
2 units
Step-by-step explanation:
ok, so, the line below says HJ is (x+1) units long. therefore:
2x-16+8 = x+1
now, let's isolate the variable.
2x-x = 1+16-8
x = 9
since we now defined variable x, we can add it to the equation that determines the length of HI.
2x-16
2(9)-16
18-16
2
the length of line segment HI is 2 units
hope this helped!
HI + IJ = HJ
With this knowledge you can from an equation like so...
2x - 16 + 8 = x + 1
Now combine like terms and solve for x
2x + (- 8 + 8) = x + 1 + 8
2x = x + 9
2x - x = x - x + 9
x = 9
To find HI plug 9 in for x and simplify
2(9) - 16
18 - 16
2
The length of HI is 2!!!
Hope this helped!
~Just a girl in love with Shawn Mendes
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
A. Q(1, 11)
B. R(2, 4)
C. S(4,-4)
D. T(9,-2)
Answer:
The correct answer is R(2, 4)
Step-by-step explanation:
an equation in slope-intersept form the lines that passes thought (-8,1) and is perpindicular to the y=2x-17.
Answer:
y = (-1/2)x -3
Step-by-step explanation:
We are given
y = 2x-17
which is in slope-intercept form: y = mx +b
Where m is the slope. so, m= 2
But this is perpendicular, When a line is perpendicular then the slope become -1/m so in our case the slope m will be = -1/2
Using the point(-8,1) we can find the b i.e the y intercept
We have x = -8, y =1 and m=-1/2
y = mx + b
1 = (-1/2)(-8) + b
1 = 4 + b
=> b = 1-4
b = -3
The equation of slope intercept form will be
y = mx + b
Putting value of m= -1/2 and b = -3
y = (-1/2)x -3
Use the properties of exponents to rewrite the expression.
(-5uv)(-5uv)(-5uv)(-5uv)
The expression can be simplified to [tex]625 \times (uv)^4.[/tex]
To rewrite the expression (-5uv)(-5uv)(-5uv)(-5uv) using the properties of exponents, you can consolidate it using the exponent rule that states when you multiply numbers with the same base, you add the exponents. In this case, the base is -5uv, and you are multiplying it four times, so the exponent is 4:
[tex](-5uv)(-5uv)(-5uv)(-5uv) = (-5uv)^4[/tex]
Now, you can simplify further by applying the rule for raising a power to a power, which states that when you raise an exponentiated term to another exponent, you multiply the exponents:
[tex](-5uv)^4 = -5^4 \times (uv)^4[/tex]
-5^4 means -5 multiplied by itself four times:
[tex]-5^4 = -5 \times -5 \times -5 \times -5 = 625[/tex]
So, the expression can be simplified to:
[tex]625 \times (uv)^4[/tex]
This is the expression rewritten using the properties of exponents.
for such more question on expression
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Which are possible first steps in solving the equation 4x + 3 = 18?
Answer:
C D and E
Step-by-step explanation:
The only one you probably can never do is B. It get's you no where. The way A is written, it is not much help to write 18 in base 2. So A and B both won't work. The common logs and the natural logs will both work
Log(4^(x + 3)) = Log(18)
(x + 3) Log(4) = log (18)
(x + 3) * 0.6021 = 1.2553
x + 3 = 1.2553/0.6021
x + 3 = 2.08496
Now all you need do is subtract 3 from both sides. The natural logs will give you the same answer.
You could take base-4 logs of both sides and it is a possible first step, but d and e are much more efficient. You have to change both sides to base 4 before you can proceed. This one is kind of iffy. It does say possible first steps.
Answer:
C.Take the base-4 logarithm of each side.
D.Take the natural logarithm of each side.
E. Take the common logarithm of each side.
Step-by-step explanation:
Points that lie on the same line are sold to be
collinear
Horizontal
ordered
Answer: b,c,e or 2,3,5
Step-by-step explanation:
Aaron bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow him to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on? (SHOW WORK)
Answer:
The scale factor is equal to 1/2
The dimensions of each channel when splits the screen is 46 in x 38 in
Step-by-step explanation:
we know that
The dimensions of the new television is 92 in x 76 in
Remember that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
A1 -----> the area of the new television
A2 ----> the area of each channel when splits the screen
z-----> the scale factor
[tex]z^{2} =\frac{A2}{A1}[/tex]
we have that
The area of the new television is 4 times the area of each channel
[tex]A1=4A2[/tex]
[tex](A2/A1)=1/4[/tex]
[tex]z^{2} =\frac{1}{4}[/tex]
[tex]z=\frac{1}{2}[/tex] -----> the scale factor
so
When splits the screen, the dimension of each channel is equal to
92/2 in x 76/2 in
so
46 in x 38 in
Remember, if two figures are similar then the scale factor is equal to the ratio of their corresponding sides
Verify the value of the scale factor
92/46=1/2
or
76/38=1/2
At which value of x does the graph of the function F(x) have a vertical asymptote?
Answer:
x = -8 & x = 3
Step-by-step explanation:
Vertical asymptote occur when denominator is 0.
So to find the x-values, we need to middle term factor the denominator. Shown below:
[tex]x^2+5x-24\\=(x+8)(x-3)\\x=3, -8[/tex]
Thus, at x = 3 and at x = -8 -- there is vertical asymptote.