Expand -2(5x+8), simplify, isolate x by moving terms, and solve to get x = -15/8.
To solve the equation -2(5x + 8) = 14 + 6x step by step, here's what was done:
Step 1: Expand the left side of the equation by distributing -2 across the terms inside the parentheses:
-2(5x + 8) = -2 * 5x - 2 * 8 = -10x - 16
So, the equation becomes: -10x - 16 = 14 + 6x
Step 2: Group like terms together. Subtract 6x from both sides to get all the x terms on one side of the equation:
-10x - 6x = 14 + 16
This simplifies to: -16x = 30
Step 3: Now, isolate the variable by dividing both sides by -16:
(-16x)/(-16) = 30/(-16)
This simplifies to: x = -30/16 or x = -15/8
So, the solution for x is x = -15/8.
The complete question is here:
-2(5x+8)=14+6x The equation was solved using the following steps Step 1: -10z-16=14+6z Step 2: -16x-16=14 Step 3: -16x=30 Step 4: z= 21/-16 Step 5: z=- 15/8 Complete the statements below with the process used to achieve steps 1-4 Stop 12 to 5x and 8. Step 26x Step 3 : 16. Step 4: 16.
the function f(x)= sqrt x is translated left 5 units and up 3 units to create the function g(x). what is the domain of g(x)?
Answer:
x ≥ -5
Step-by-step explanation:
If we have a translation to left c units, we write " x + c " in the function, and
If we have a translation to right c units, we write " x - c" in the function
If we have vertical translation up b units, we "add b to the function", and
If we have vertical translation down b units, we "subtract b to the function"
The parent function is [tex]f(x)=\sqrt{x}[/tex]
Since translation left 5 units and up 3 units, we can write:
[tex]f(x)=\sqrt{x+5} + 3[/tex]
The domain is affected by the square root sign and we know the number under the square root CANNOT be negative, so we can say:
x + 5 ≥ 0
x ≥ -5
This is the domain.
The domain of the function g(x), which is the translated version of f(x) = √x, is all x ≥ -5 after being shifted left 5 units and up 3 units.
Explanation:The function g(x) resulting from translating f(x) = √x left 5 units and up 3 units is expressed as g(x) = √(x+5) + 3. Because we cannot take the square root of a negative number in the set of real numbers, the domain of f(x) is all x ≥ 0. After the translation, the domain of g(x) will also be shifted 5 units to the left. Therefore, the domain of g(x) is all x ≥ -5, as this is the new point where the function starts to produce real number outputs.
what is the slope of the line y=-2x+3
Answer: The slope is -2
Step-by-step explanation:
It is important to remember that the equation of the line in Slope-Intercept form is the following:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
In this case you can observe that the given equation of the line [tex]y=-2x+3[/tex] is written in Slope-Intercept form.
Therefore, you can identify that the slope "m" is:
[tex]m=-2[/tex]
And the y-intercept "b" is:
[tex]b=3[/tex]
What is the exact volume of a cylinder whose radius is 13 meters and whose height is 20 meters?
Enter your answer, in terms of π in the box.
in the box.
____ m³
PLEASE HELP 25 POINTS !!
The exact volume of the cylinder is [tex]\( 3380\pi \)[/tex] cubic meters.
To find the exact volume V of a cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159,
- r is the radius of the cylinder, and
- h is the height of the cylinder.
Given:
- Radius (r=13) meters, and
- Height (h=20) meters.
Substitute these values into the formula:
[tex]\[ V = \pi \times (13)^2 \times 20 \]\[ V = \pi \times 169 \times 20 \][/tex]
[tex]\[ V = 3380\pi \][/tex]
The exact volume of the cylinder is 10,613.2 cubic meters.
To find the volume of a cylinder, we use the formula: Volume = πr²h, where π (pi) is approximately 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
Given:
Radius (r) = 13 meters
Height (h) = 20 meters
Calculate the area of the base (circle) using the formula A = πr².
A = 3.14 × (13)²
A = 3.14 × 169
A = 530.66 square meters
Multiply the area of the base by the height of the cylinder.
Volume = 530.66 × 20
Volume = 10,613.2 cubic meters
So, the exact volume of the cylinder is 10,613.2 cubic meters.
There were 425 tickets sold for the annual everglades middle school talent show. If this is 85% of the tickets available, how many tickets went unsold? A. 15. B. 75. C. 55. D. 35.
Answer:
425/85*100 = 500 thus: 500-425 =75 Tickets.
Step-by-step explanation:
Answer:
75
Step-by-step explanation:
One file clerk can file 10 folders per minute. A second file clerk can file 11 folders per minute. How many minutes would the two clerks together take to file 672 folders?
Answer:
32 Minutes
Step-by-step explanation:
Together the two clerks can file 21 files per minute (10+11=21).
Therefore to file 672 folders would take 32 minutes (672/21=32)
the perimeter of a rectangle swimming pool is 486 feet. The width of the pool is 35 feet less than the length. Find the length and the width
Answer:
Length: 139 feet
Width: 104 feet
Step-by-step explanation:
The formula for the perimeter of a rectangle can be given by [tex]P = 2l + 2w[/tex]. We are given the perimeter of the pool along with the width.
[tex]P = 486[/tex]
[tex]w = l - 35[/tex]
From here, all we have to do is plug back into the original formula:
[tex]486 = 2l + 2(l - 35)[/tex]
Which can be further simplified as:
[tex]486 = 2l + 2l - 70[/tex]
[tex]486 = 4l - 70[/tex]
From here, all we have to do is add 70 to both sides of the equation and divide by four:
[tex]556 = 4l[/tex]
[tex]139 = l[/tex]
To make sure that this answer is accurate, we can find that the width of the rectangle should then be 104 (given by 139 - 35). All we have to do is plug back into the original equation:
[tex]P = 2l + 2w[/tex]
[tex]P = 2(139) + 2(104)[/tex]
[tex]P = 278 + 208[/tex]
[tex]P = 486[/tex]
And the substitution works, so the length of the rectangle would be 139 feet and the width would be 104 feet.
Answer:
Length = 139 and Width = 104 .
Step-by-step explanation:
Given: The perimeter of a rectangle swimming pool is 486 feet. The width of the pool is 35 feet less than the length.
To find: Find the length and the width .
Solution: We have given that
Let the length = x
According to question
The width of the pool is 35 feet less than the length.
width = x-35
perimeter = 2(length + width)
plugging the values
486 = 2(x + x-35)
486 = 2x + 2x - 70
486 = 4x - 70
On adding by 70 both side
486 +70 = 4x-70 +70
556 = 4x
On dividing by 4 both side
139 = x
so, length = 139 .
width = x -35 = 139- 35 = 104
Therefore, length = 139 and width = 104.
Find the image of (-2, 1) obtained by
translating 3 units down, followed by a
reflection over the y-axis.
Please help it is urgent!!!
The y-axis runs vertically, so changing the y-coordinate moves a figure up or down. Adding a number to the y-coordinate shifts the image up, while subtracting a number shifts the figure down.
So to translate 3 units down, we just subtract 3 from the y-coordinate.
Instead of (-2, 1) it's now (-2, -2) since 1 - 3 (units) = -2
Now, another way to say "reflect across the y-axis" is to say "reflect across the line x=0" since the line created by graphing x=0 is the same as the y-axis.
An image that is a reflection across the y-axis, or across the line x=0, will have opposite x-coordinates from the pre-image but identical y-coordinates.
Therefore, the rule for reflecting an image across the y-axis can be described as (x, y) → (−x, y).
So using our translated point (-2, -2) it now becomes (2, -2).
You didn't provide an image, however, all you need to find is the translated and reflected point that lies on (2, -2).
Answer:
( 2 , 1 )
Step-by-step explanation:
literally have no idea how the other person got -2 as the second answer lol
its 1 not -2 , ik cause i had this problem on my acellus and had to guess until i got it
If 2x+y = 6 and x−6=y, what is the value of x?
(A) 0 (B) 2 (C) 3 (D) 4 (E) 6
Answer:
x = 4
Step-by-step explanation:
2x + y = 6 ... (i)
x - 6 = y ... (ii)
y = 6 - 2x ... (i)
y = x - 6 ... (ii)
So,
6 - 2x = x - 6
x + 2x = 6 + 6
3x = 12
x = 12/3 = 4
The graph of relation r is shown. Which of the following graphs represents the relation and it’s inverse
Answer:
To easily solve this question, we must realize that the graph of the relation is very similar to that of the expression
y = √(x-a) , where a>0
If we take a look at the image attached, we have plotted the graph of
y = √(x-1) , and its correspondent inverse function.
This means that the answer is the first option
Three families went to the movies together. The Smiths ordered two tubs of popcorn, one plate of nachos, and three drinks. They spent $65. The Langes ordered three tubs of popcorn, two plates of nachos, and five drinks. They spent $85. The Radfords ordered one tub of popcorn, one plate of nachos, and two drinks. They spent $40. Which system of equations matches their night at the movies?
Answer:
2t + n + 3d = 65
3t + 2n + 5d = 85
t + n + td = 40
Step-by-step explanation:
tubs of popcorn = t
plates of nachos = n
drinks = d
The Smiths: 2t + n + 3d = 65
The Langes: 3t + 2n + 5d = 85
The Radfords: t + n + td = 40
So, the correct answer would be the one including all 3 of these equations. :)
Answer:
The system of equations are:
[tex]2t + n + 3d = 65[/tex]
[tex]3t + 2n + 5d = 85[/tex]
[tex]t + n + 2d = 40[/tex]
Step-by-step explanation:
Consider the provided information.
let "t" represents tubes of popcorn, "n" represents nachos and "d" represents drink.
The Smiths ordered two tubs of popcorn, one plate of nachos, and three drinks. They spent $65. Which can be represents as:
[tex]2t + n + 3d = 65[/tex]
Langes ordered three tubs of popcorn, two plates of nachos, and five drinks. They spent $85. Which can be represents as:
[tex]3t + 2n + 5d = 85[/tex]
The Radfords ordered one tub of popcorn, one plate of nachos, and two drinks. They spent $40. Which can be represents as:
[tex]t + n + 2d = 40[/tex]
Thus, the system of equations are:
[tex]2t + n + 3d = 65[/tex]
[tex]3t + 2n + 5d = 85[/tex]
[tex]t + n + 2d = 40[/tex]
Hamid has gained weight. He now weighs 88kg, which is 10% higher than his normal weight. What is his normal weight?
Please help, this question is on reverse percentage.
Answer:
79.2kg
Step-by-step explanation:
So first step is to find 10% of 88, which is 8.8. And 88kg is higher than his normal weight, so his original weight would be lower than 88kg. So you subtract. 88-8.8=79.2. His normal weight is 79.2kg.
what is the answer?? need help now!
Answer:
x = 16 and z = 84
Step-by-step explanation:
The 2 given angles are vertical and congruent, hence
7x - 16 = 6x ( subtract 6x from both sides )
x - 16 = 0 ( add 16 to both sides )
x = 16
Hence 6x = 6 × 16 = 96°
z and 6x form a straight angle and are supplementary, hence
z + 6x = 180
z + 96 = 180 ( subtract 96 from both sides )
z = 84
f(4) = 1 :
If g(x) = 2, x=
Answer:
f(4) = -11, g(x) = 2 → x = 0Step-by-step explanation:
Look at the picture.
Answer:
2g{4} hahah sike
Step-by-step explanation:
Shelly biked 21 miles in 4 hours.
What is Shelly's average speed in miles per hour?
Answer: 5.25 miles per hour.
Step-by-step explanation:
21/4 = 5.25
Hello There!
WHAT WE KNOW Shelly biked 21 miles in 4 hours. We know that Shelly's average speed = 5.25 miles / hour because "21 divided by 4 equals 5.25"
What is the slope of the graph? Leave your answer as a reduced fraction.
Slope =
Identify the y-intercept. Write as a coordinate.
y-intercept =
Write an equation in slope-intercept form for the graph above.
y=
Answer:
slope = -2
y-intercept = (0,2)
y = -2x + 2
Step-by-step explanation:
In order to find the slope, we must use the formula y2-y1/x2 - x1. But in order to do so, we will have to find two perfect points.
perfect point #1: (-2,6)
perfect point #2: (2, -2)
Now, we simply input the corresponding points into our formula.
-2 - 6 = -8
2 - (-2) = 4
-8/4 = -2
So, the slope of the graph is -2
In order to find the y-intercept we must look at where the line intersects in the y axis. Looking back at our graph, we can determine that the line intersects at (0,2)
The slope-intercept form is y = mx + b, m represents the slope and b represents the y intercept. Therefore after inputting the slope and y-intercept we should get y = -2x + 2
Evaluate 4(x - 3) + 5x - x2 for x = 2.
Answer:
The value of the expression for x=2 is 2.
Step-by-step explanation:
Consider the provided expression.
[tex]4(x - 3) + 5x - x^2 [/tex]
We need to find the value of expression for x=2.
Substitute the value of x=2 in provided expression and simplify as shown.
[tex]4(2 - 3) + 5(2) - 2^2 [/tex]
[tex]4(-1) + 10 - 4 [/tex]
[tex]-4 + 6 [/tex]
[tex]2 [/tex]
Hence, the value of the expression for x=2 is 2.
The numerical value of the expression 4(x - 3) + 5x - x² when x = 2 is 2.
What is the value of the expression when x = 2?Given the expression in the question:
4(x - 3) + 5x - x²
x = 2
To evaluate the expression 4(x - 3) + 5x - x² for x = 2, repalce all the occurences of x in the expression with 2 and simplify:
4(x - 3) + 5x - x²
Plug in x = 2:
4(2 - 3) + 5(2) - (2)²
Subtract 3 from 2:
4(-1) + 5(2) - (2)²
Take the square of 2:
4(-1) + 5(2) - 4
Multiply 4 and -1:
-4 + 5(2) - 4
Multiply 5 and 2:
-4 + 10 - 4
Add the 3 numbers:
2
Therefore, the value of the expression is 2.
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Simplify 3(2x - 5).for me please
Answer:
6x-15
Step-by-step explanation:
3*2x= 6x
3*5=15
6x-15
Answer:
6x - 15
Step-by-step explanation:
3(2x - 5)
Distributive property
= 3(2x) + (3)(-5)
= 6x - 15
Add.
3x2 - 5x+1
2x2 +9x-6
+
Answer:
The sum of the two expressions is 5x^2 + 4x - 5
Step-by-step explanation:
Rewrite
3x2 - 5x+1
2x2 +9x-6
as
3x^2 - 5x+1
2x^2 +9x-6 " ^ " indicates exponentiation
-----------------
5x^2 + 4x - 5
Answer:
[tex]5x^2+4x-5[/tex]
Step-by-step explanation:
[tex]3x^2-5x+1 \ and \ 2x^2 + 9x -6[/tex]
Add both the polynomials
To add both the polynomials we combine like terms
[tex]3x^2-5x+1 +2x^2 + 9x -6[/tex]
3x^2 and 2x^2 are like terms . it becomes 5x^2
-5x and 9x are like terms . it becomes 4x
[tex]3x^2-5x+1 +2x^2 + 9x -6[/tex]
[tex]5x^2+4x-5/tex]
What is the answer to this question?
Answer:
(0,2/3)
Step-by-step explanation:
I would go for elimination on this one.
This will require we manipulate at least one equation.
I'm going to multiply bottom equation by -2: -2x-12y=-8
So we have
2x+3y=2
-2x-12y=-8
---------------add the two equations
0 -9y=-6
-9y=-6
y=6/9=2/3
2x+3y=2
2x+3(2/3)=2
2x+2=2
2x=0
x=0
(0,2/3)
Answer: The Answer is A X=0 Y=2/3
Step-by-step explanation:
2x+3y=2
X+6y=4
step one: substitute in the value of x into the equation
2x +3y = 2
x= 4-6y
Step two: Solve with the X substitution
2(4-6y) +3y = 2
You get Y= 2/3
Step three: plug in 2/3 for X
X= 4-6(2/3)
You get 0
therefore: X = 0 and Y=2/3
What is the measure of angle 3?
A. 120 degrees
B. 90 degrees
C. 45 degrees
D. 30 degrees
Answer:
c.45 degrees
Step-by-step explanation:
90 -180= 90
90÷2=45
For this case, we have by definition, that the four internal angles of a square measure 90 degrees. If we draw the diagonals of the square we have that the angles are divided between 2, that is, they go to measure 45 degrees.
So, according to this definition we have to:
[tex]Angle\ 3 = \frac {90} {2}\\Angle\ 3 = 45[/tex]
Answer:
The angle 3 is 45 degrees
Option C
An objects motion is described by the equation d= 4sin (pi t) what will the height of the object be at 1.75 seconds?
Answer:
-2√2, or ≈-2.83
Step-by-step explanation:
Well, when t = 1.75, our equation should be [tex]d=4\sin{(\pi \cdot1.75)}[/tex].
Note that [tex]\pi\cdot1.75=\frac{7\pi}{4}[/tex]. Using the unit circle (attached), we can find that the value of sine at [tex]\frac{7\pi}{4}[/tex] radians is exactly [tex]-\frac{\sqrt2}{2}[/tex]. Plugging that value back into our equation gives us
[tex]d=4\cdot\left(-\frac{\sqrt2}{2} \right)=-\frac{4\sqrt2}{2}=-2\sqrt2[/tex]
So our answer is [tex]d=-2\sqrt2[/tex], in whatever units we're using to measure height.
Answer: 0.38 Meters
Step-by-step explanation:
plug 1.75 in for t and solve, do not convert into units as you need the height so meters is accurate.
d=0.38
What is the surface area?
Answer:
Surface Area of Cone = 200π cm^2
Surface Area of Right Prism = 17.5 ft^2
Step-by-step explanation:
32. We are given a figure of a cone and we are to find its surface area.
We know that the formula for the S.A. of cone is given by:
Surface Area of cone = [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex]
Substituting the given values in the above formula.
Surface Area of cone = [tex]\pi \times 8(8+\sqrt{15^2+8^2} )[/tex] = 200π cm^2
25. We are to find the surface area of a right prism.
Surface Area of Right Prism = Base Perimeter × height + 2(Base Area)
Base Perimeter = 2(4 + 1.5) = 11 ft
Height = 0.5 ft
Base Area = 4 × 1.5 = 6 ft
Substituting these values in the above formula.
Surface Area of Right Prism = 11 × 0.5 + 2(6) = 17.5 ft^2
Answer:
Surface area of cone = 200π cm
Surface area of prism = 17.5 ft²
Step-by-step explanation:
To find the slant height of cone
slant height l = √(r² + h²)
= √(8² + 15²) = 17
To find the surface area of cone
Surface are = πr² + πrl
= π*8² + π*8*17
= 64π + 136π
= 200π cm²
To find the surface area of prism
l = 4 ft
b = 1.5 ft and h = 0.5 ft
Surface area = 2(lb + lh + bh)
= 2[(4* 1.5) + (4*0.5) + (1.5*.5)
= 2(6 + 2 +0.7.5)
= 17.5 ft²
Which is an equation of the line that passes through (–1, –5) and (–3, –7)?
Question 8 options:
a)
y = x – 4
b)
y = –2x + 4
c)
y = 2x + 4
d)
y = –x – 4
a) y = x - 4
First, to find the rate of change [slope], do rise\run: -y₁ + y₂\-x₁ + x₂. Doing this will result in the slope being 1, and the ONLY answer that has a slope of 1, is the top choice.
Slope-Intercept Formula: y = mx + b [m represents slope].
I am joyous to assist you.
rectangle q has an area of 2 square units thea drew scaled version and labled it rectangle r what scale factor did thea use to go from q to r
Pre-Image < Image, then the scale factor is k >1.
Pre-Image > Image, then the Scale factor will be lies between,
0 < k < 1.
Scale factor of a rectangleIt exists given that Rectangle Q has an area of 2 square units.
Thea Drew a scaled version of Rectangle Q and labeled it as R.
As you must keep in mind If we draw a scaled copy of the pre-image, then the two images.
Therefore, Pre-image and Image are similar.
Consider the Scale factor of transformation = k
Rectangle Q = Pre - image,
Rectangle R= Image
If, Pre-Image < Image, then the scale factor is k >1.
But If, Pre-Image > Image, then the Scale factor will be lies between,
0 < k < 1.
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A taxi driver charges a $5 flat fee to enter the car and $0.50 per mile .what is the total cost of a taxi ride ?
The total cost of a taxi ride includes a $5 flat fee plus $0.50 for every mile traveled. The total cost can be calculated using the formula: Total cost = $5 flat fee + ($0.50 × number of miles). For instance, a 10-mile trip would cost $10.
Explanation:The total cost of a taxi ride is dependent on the distance traveled in miles. The taxi driver charges a $5 flat fee to enter the car and $0.50 per mile. To find the total cost, you can use the equation:
Total cost = Flat fee + (Cost per mile × Number of miles traveled)
For example, if you traveled 10 miles, the total cost would be:
Total cost = $5 + ($0.50 × 10) = $5 + $5 = $10
This formula will give you the total expense for any number of miles traveled in the taxi.
The plane that contains points C and T can also be named plane .
Answer:
False
Step-by-step explanation:
You need 3 points to name a plane. 2 points is required to name a line
Answer:
It would be CUB
Step-by-step explanation:
On the coordinate plane shown below, points H and I have coordinates (-2,-3) and (3,2), respectively.
on
Use the Pythagorean theorem to determine the distance between points Hand I on the coordinate plane.
Answer:
[tex]5\sqrt{2}[/tex]
Step-by-step explanation:
Here we are given two coordinates and we are required to fin d the distance between them not by using the distance formula but by using Pythagoras theorem.
Let us see how we do that.
We will take the help of graph in this. We draw a line parallel to x axis passing through H (-2,-3) and a vertical line passing through I(3,2)
Let us assume that these two lines intersect at point J whose coordinates will be (-3,-3)
Now using scale of the graph we can see that Distance HJ = 5 units and IJ= 5 units and ΔHIJ makes and Right angle triangle where ∠IJH = 90°
Hence we can apply Pythagoras theorem in this.
[tex]HJ^{2}+JI^{2}=HI^{2}[/tex]
[tex]5^2+5^2=HI^{2}[/tex]
[tex]HI^{2}=25+25[/tex]
[tex]HI^{2}=50\\HI=\sqrt{50}\\HI=\sqrt{25*2}\\HI=5\sqrt{2}\\[/tex]
Please refer to graph in attachment for further clarification.
What is the value of p in the equation y^ = -4x?
ANSWER
p=-1
EXPLANATION
The given equation is
[tex] {y}^{2} = - 4x[/tex]
We compare with the general equation of the parabola with vertex at the origin.
[tex]{y}^{2} =4px[/tex]
Comparing the right hand side we have,
[tex]4px = - 4x[/tex]
Divide both sides by 4x
[tex] \frac{4px}{4x} = \frac{ - 4x}{4x} [/tex]
This implies that,
[tex]p = - 1[/tex]
One fourth of all telephones at the office have built in speaker phones. One -half the phones with the built-in speaker phones have conference-call capability,how many of the phones in the office have both a speaker phone and a conference-call capability?
Answer:
[tex]\frac{1}{8}[/tex] of the phones in office has both a speaker phone and a conference-call capability
Step-by-step explanation:
Since total number of phones in the office is not given, the answer will be "in that terms".
let it be x
So built in speaker phones is (1/4)x
Hence conference call phones would be (1/2)(1/4x) = (1/8)x
Hence "1/8th of the phones in office has both a speaker phone and a conference-call capability"
Answer:
(1/8)x phones have both speaker phone and a conference call capability
Step-by-step explanation:
Let the total phones be x
It is given that one forth of the phones have in built speaker = (1/4)x
It is also given that one half of the phone having built in speaker also have conference call capability = (1/2) of (1/4)x
= (1/8)x
Therefore, (1/4)x - (1/8)x
= (1/8)x
(1/8)x phones have both speaker phone and a conference call capability.
Which function is negative for the interval (–1, 1]?
⇒The Interval in which we have to find the function is Negative is (-1,1].
→(-1,1]=Semi closed or Semi Open Interval, Point -1, is not included in the set, but 1 is included in the set.
⇒ The meaning of negative here is,that either for positive or negative value of x , the value of f(x), that is y Should be negative.
⇒y is negative in third and fourth Quadrant.
Graph -(2), is the function , in which the function is negative for the interval (–1, 1].