Answer:
5x+3
Step-by-step explanation:
Three more than means we add 3
The product of 5 and a number means some number multiplied by 5 call it 5x
so three more than 5x is 5x+3.
Bell Ringer -- Find the distance of each side of the triangle: A(-10, 6) B(-6, 9) C(-6, 6)
Answer:
It is c) (-6, 6)
the top of the hill rises 67 feet above checkpoint 4, which is -211. What is the altitude of the top of the hill?
Answer:
-144 feet
Step-by-step explanation:
-211 plus the added 67 feet it is above equals an altitude of -144ft
I need help on answering 3. (d) I have two choices it can be which is false and sometimes true.
Question:
Solution:
If x represents a positive integer, then the point x is a natural number, that is, x is greater than zero, in particular, if x is a number greater than zero it can be a number greater than any number after zero. For example, it can be greater than 1.
Then the question d is ALWAYS TRUE.
Use the table to write an equation that relates the cost of lunch Y and the number of students X
In order to determine what is the equation which describes the values of the table, consider that the general form of the equation is:
y = mx
where m is the constant of proportionality between both variables x and y.
To calculate m you calculate the quotient between any pair of data from the table.
If you for example use the following values:
Students = 8.00
Lunch cost = 2
the constant of proportionality is:
m = 8.00/2 = 4.00
Next, you replace the value of m in the equation y=mx:
y = $4.00x
all i need is for question 14 to be answered please help
Given
The path of particle 1 is,
[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]And, the path of second particle is,
[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]To model the path of the two particles in cartesian form and to find whether, the two particles collide.
Explanation:
It is given that,
The path of the first particle is,
[tex]x(t)=3t-6,\text{ }y(t)=t^2-2t[/tex]That implies,
[tex]x=2t-6,\text{ }y=t^2-2t[/tex]Consider,
[tex]\begin{gathered} x=2t-6 \\ 2t=x+6 \\ t=\frac{x+6}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=(\frac{x+6}{2})^2-2(\frac{x+6}{2}) \\ y=\frac{x^2+12x+36}{4}-\frac{2x+12}{2} \\ y=\frac{x^2+12x+36-2(2x+12)}{4} \\ y=\frac{x^2+12x+36-4x-24}{4} \\ y=\frac{x^2+8x+12}{4}\text{ \_\_\_\_\_\_\_\_\_\_\lparen1\rparen} \end{gathered}[/tex]Also, the path of second particle is,
[tex]x(t)=\sqrt{t+6},\text{ }y(t)=-3+2t[/tex]That implies,
[tex]x=\sqrt{t+6},\text{ }y=-3+2t[/tex]Consider,
[tex]\begin{gathered} y=-3+2t \\ 2t=y+3 \\ t=\frac{y+3}{2} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x=\sqrt{t+6} \\ \Rightarrow x^2=(t+6) \\ \Rightarrow x^2=(\frac{y+3}{2})+6 \\ \Rightarrow x^2=\frac{y+3+12}{2} \\ \Rightarrow2x^2=y+15 \\ \Rightarrow y=2x^2-15\text{ \_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]Hence, y=(x^2+8x+12)/4, y=2x^2-15 are the paths of the two particles respectively.
The graph of the path of the two particles are,
From, this it is clear that the particle collide at the points (-2.686, -0.568) and (3.829, 14.324).
Frank makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
The equation will be
P = 8h
here, P = total pay
h= working hours.
A particular lawn requires 6 bags of fertilizer. A lawn next door requires 4 bags of fertilizer. How big is the lawn next door?A. 10 feet square feetB. 24 feet square feetC. 50 feet square feetD. Not enough information is given
Answer:
D. Not enough information is given
Explanation:
To know the size of the lawn next door, we would need a relation between the square feet and the number of bags of fertilizer.
Since all we know is the bags of fertilizer for the particular lawn and the lawn next door, we can say that we didn't have enough information to answer the question.
Therefore, the answer is:
D. Not enough information is given
How to fill out an income summary
Answer: Pick a Reporting Period. ...
Generate a Trial Balance Report. ...
Calculate Your Revenue. ...
Determine the Cost of Goods Sold. ...
Calculate the Gross Margin. ...
Include Operating Expenses. ...
Calculate Your Income. ...
Include Income Taxes.
Find the equation of a line that is parallel to the line x = 10 and contains the point (-8,1)the equation of the line is =
The given line is x = 10, which is a vertical line. All vertical lines have the form x = k, where k is a real number.
So, a parallel line passing through (-8,1) would be x = -8.
Hence, the answer is x = -8.Use substitution to solve the system of equations. y = x + 2 4x - 5y = 14 A. (-22,-24) C. (-4,-2)B. (-24, -22) D. (-14, -12)
Solve by substitution;
[tex]\begin{gathered} y=x+2---(1) \\ 4x-5y=14---(2) \\ \text{Substitute for the value of y into equation (2)} \\ 4x-5(x+2)=14 \\ 4x-5x-10=14 \\ \text{Collect like terms} \\ 4x-5x=14+10 \\ -x=24 \\ \text{Divide both sides by -1} \\ x=-24 \\ \text{Substitute for the value of x into equation (1)} \\ y=x+2 \\ y=-24+2 \\ y=-22 \end{gathered}[/tex]The pyramid has a square base with side
length 2 cm and height 3 cm. What is the
volume of the chocolate to the nearest
tenth?
A 12 cm
B 6 cm3
C 4 cm
D 2 cm
E 1.3 cm3
The radius of cylinder is r = 3 in.
The height of cylinder is h = 10 in.
The formula for the volume of cylinder is,
[tex]V=\pi\cdot(r)^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cylinder.
[tex]\begin{gathered} V=\pi\cdot(3)^2\cdot10 \\ =282.743 \\ \approx282.7 \end{gathered}[/tex]So volume of cylinder is 282.7 in^3.
Option H is correct.
Kindly assist in answering these questions
The point of origin on the graph is (0,0) and the constant of proportionality is equal to 3.
Equation of LineThe equation of a straight line is y=mx + c. y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line.
In the given question, we are asked to find several values relating to the graph attached.
5) The point of origin on the graph is at (0,0) because the graph passes through the center along the straight line.
6) The constant of proportionality (k) is the value before the variable x.
The equation of the line is y = 3x.
The constant of proportionality of the equation is equal to 3.
7) The value of the ratio k is given as y/x
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I only need part bb) A foam protector is covered with PVC material to make it waterproof. Find the total surface area of a protector which is covered by PVCmaterial.
Assuming all the parts are covered, inluding the internal part, we have to find the surface area of the whole protector.
So, let's list which areas we need:
- We need the lateral areas of the external parts, which are 4 rectangles.
- We need the top and bottom areas, which are both area of squares minus the area of the cicle of the hole.
- We need the interior aread, which is the same as the lateral area of a cylinder.
For the external part, we only need the dimensions of each rectangle. since they have the same length and the other sides are the sides of the squares, they are all the same.
The area of each of them is:
[tex]A_{\text{rectangle}}=300mm\cdot1.8m=0.3m\cdot1.8m=0.54m^2[/tex]Since we have 4, the total exterior lateral area is:
[tex]A_{\text{lateral}}=4\cdot0.54m^2=2.16m^2[/tex]For the top and bottom, both are the same, a square of 300 mm x 300 mm with a hole of 150 mm diameter.
First, let's get all to meters: 0.3 m x 0.3 m and 0.15 m diameter. The radius of the circle is half the diameter, so:
[tex]r=\frac{0.15m}{2}=0.075m[/tex]The area of a circle given its radius is:
[tex]A=\pi r^2[/tex]So, the area of both the top and bottom is the area of the square minus the area of the circle and double all of this:
[tex]\begin{gathered} A_{\text{top/ottom}}=2((0.3m)^2-\pi(0.075m)^2) \\ A_{\text{top/ottom}}=2(0.09m^2-0.005625\pi m^2) \\ A_{\text{top/ottom}}=2(0.09-0.005625\pi)m^2 \end{gathered}[/tex]We deal with π later on.
For the lateral area of the cylinder, we can remember that it is the same as the area of a rectangle with on dimension being the length of the cylinder and the other being the circumference of the top/bottom.
the circumference of a circle is:
[tex]C=2\pi r[/tex]The radius is the same as the hole, and the length is 1.8m, so the lateral area of the cylinder is:
[tex]\begin{gathered} A_{\text{cylinder}}=1.8m\cdot2\pi(0.075m) \\ A_{\text{cylinder}}=(1.8\cdot0.15\pi)m^2 \\ A_{\text{cylinder}}=(0.27\pi)m^2 \end{gathered}[/tex]So, the total surface area is the sum of all of these:
[tex]A=2.16m^2+2(0.09-0.005625\pi)m^2+(0.27\pi)m^2[/tex]Now, we just need to evaluate:
[tex]\begin{gathered} A=2.16m^2+2\cdot0.072328\ldots m^2+0.848230\ldots m^2 \\ A=2.16m^2+0.144657\ldots m^2+0.848230\ldots m^2 \\ A=3.152887\ldots m^2 \\ A\approx3.15m^2 \end{gathered}[/tex]So, the lateral area is approximately 3.15 m².
Sofia got a raise from her annual salary of $43,000 to $44,505. whay percent was her raise?
how do you solve 4 1/4 + 7/8
The given expression is,
[tex]4\frac{1}{4}+\frac{7}{8}[/tex]So, this can be solved as,
[tex]\begin{gathered} \frac{4\times4+1}{4}+\frac{7}{8}=\frac{17}{4}+\frac{7}{8} \\ \rightarrow\frac{8\times17+4\times7}{8\times4}=\frac{164}{32}=\frac{41}{8} \end{gathered}[/tex]Explanations:
To solve the mixed fraction,
[tex]4\frac{1}{4}\rightarrow\frac{(4\times4)+1}{4}=\frac{17}{4}[/tex]So, now we are adding the terms, as given in the expression,
[tex]\frac{17}{4}+\frac{7}{8}=\frac{(8\times17)+(7\times4)}{4\times8}[/tex]Here we are employing the rule,
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+cb}{bd}[/tex]Who am I? I am a quadrilateral with opposite sidescongruent and parallel, all of my angles are 90° andmy diagonals are congruent.d
Let's list all information we have:
- quadrilateral (4 sides)
- opposite sides congruent and parallel.
- all angles are 90°
- diagonal are congruent.
So, if we have a quadrilateral, we have something like this:
However, it is given that all anlges are 90°, which limits our possible drawing. So, something like this:
Let's see, this is a rectangle, it has opposite side congruent (equal length), the opposite sides are parallel, all the angles are 90° and the Diagonals have equal lengths, because they form congruent triangles.
It could also be a square:
Beucase it has all of the characteristics given.
determin wether true or false. (2 points) True False The functions f(x) = x – 5 and g(x) = -3x + 15 intersect at x = 5. The functions f (x) = 3 and g(x) = 11 – 2. intersect at x = 3. O The functions f (x) = x + 3 and g(x) = -x + 7 intersect at x = 2. The functions f (x) = {x – 3 and g(x) = -2x + 2 intersect at x = -2.
To find the intersection point between f(x) and g(x) we will equate their right sides
[tex]\begin{gathered} f(x)=x-5 \\ g(x)=-3x+15 \end{gathered}[/tex]Equate x - 5 by -3x + 15 to find x
[tex]x-5=-3x+15[/tex]add 3x to both sides
[tex]\begin{gathered} x+3x-5=-3x+3x+15 \\ 4x-5=15 \end{gathered}[/tex]Add 5 to both sides
[tex]\begin{gathered} 4x-5+5=15+5 \\ 4x=20 \end{gathered}[/tex]Divide both sides by 4 to get x
[tex]\begin{gathered} \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Then the first one is TRUE
For the 2nd one
f(x) = 3, and g(x) = 11 - 2x
If x = 3, then substitute x by 3 in g(x)
[tex]\begin{gathered} g(3)=11-2(3) \\ g(3)=11-6 \\ g(3)=5 \end{gathered}[/tex]Since f(3) = 3 because it is a constant function and g(x) = 5 at x = 3
That means they do not intersect at x = 3 because f(3), not equal g(3)
[tex]f(3)\ne g(3)[/tex]Then the second one is FALSE
For the third one
f(x) = x + 3
at x = 2
[tex]\begin{gathered} f(2)=2+3 \\ f(2)=5 \end{gathered}[/tex]g(x) = -x + 7
at x = 2
[tex]\begin{gathered} g(2)=-2+7 \\ g(2)=5 \end{gathered}[/tex]Since f(2) = g(2), then
f(x) intersects g(x) at x = 2
The third one is TRUE
For the fourth one
[tex]f(x)=\frac{1}{2}x-3[/tex]At x = -2
[tex]\begin{gathered} f(-2)=\frac{1}{2}(-2)-3 \\ f(-2)=-1-3 \\ f(-2)=-4 \end{gathered}[/tex]g(x) = -2x + 2
At x = -2
[tex]\begin{gathered} g(-2)=-2(-2)+2 \\ g(-2)=4+2 \\ g(-2)=6 \end{gathered}[/tex]Hence f(-2) do not equal g(-2), then
[tex]f(-2)\ne g(-2)[/tex]f(x) does not intersect g(x) at x = -2
The fourth one is FALSE
Suppose you open a bank account and deposit $50. Then, every month you deposit $20. Write anequation that relates the total number of dollars deposited, T, and the month, m.Which equation below relates the total number of dollars deposited, T, and the month, m?
Let:
T = Total number of dollars deposited
m = Number of months
b = Initial deposit
So:
[tex]\begin{gathered} T(m)=20m+b \\ where \\ b=50 \\ so\colon \\ T(m)=20m+50 \end{gathered}[/tex](x - 5) (4x - 5) = 0 there are two answers
The solutions are the values of x that makes the expression equal to zero:
x-5 =0
Add 5 to both sides
x=5
4x-5=0
Add five to both sides
4x=5
Divide both sides by 4
x= 5/4
x=1.25
A hot chocolate recipe calls for 2.5 gallons of milk. How many quarts of milk are needed for the recipe
Answer: 10
Step-by-step explanation: a gallon has 4 quarts, 4x2.5=10
10 quarts is 2.5 gallons.
how many apples are in 4 dozen
There are 48 apples in 4 dozen
Explanations:1 dozen = 12
This means that:
1 dozen of apples = 12 apples
4 dozen = 12 x 4
4 dozen = 48 apples
The dimensions of a rectangular prism are measured in centimeters. What unit will the volume of the prism be measured in?centimeterssquare centimeterscubic centimetersmeters
Given:
The dimensions of a rectangular prism are measured in centimetres.
Required:
What unit will the volume of the prism be measured in?
Explanation:
The volume of the prism will be measured in square centimetres
Final Answer:
Square centimeters
5. SOLVE THe linear equation : 13x – 5 + 171 = x
Answer:
x = -83/6 = -13.833
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
13*x-5+171-(x)=0
1.1 Pull out like factors :
12x + 166 = 2 • (6x + 83)
2.2 Solve : 6x+83 = 0
Subtract 83 from both sides of the equation :
6x = -83
Divide both sides of the equation by 6:
x = -83/6 = -13.833
Hello! I need help with this:Calculation of the confidence interval Statistics.The confidence interval should be calculated for the percentage of people who chose the answer spruce:Sample: 313Answers:Spruce - 272Pine - 41Confidence level - 0.9
We have to calculate a 90% confidence interval for the proportion that chose the answer "Spruce".
The sample proportion is p = 0.869:
[tex]p=\frac{X}{n}=\frac{272}{313}\approx0.869[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_p=\sqrt{\frac{p(1-p)}{n}} \\ \\ \sigma_p=\sqrt{\frac{0.869\cdot0.131}{313}} \\ \\ \sigma_p\approx\sqrt{0.0003637} \\ \sigma_p\approx0.019 \end{gathered}[/tex]The critical z-value for a 90% confidence interval is z = 1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot\sigma_p=1.645\cdot0.019\approx0.031[/tex]Then, the lower and upper bounds of the confidence interval are:
[tex]\begin{gathered} LL=p-z\sigma_p=0.869-0.031=0.838 \\ UL=p+z\sigma_p=0.869+0.031=0.900 \end{gathered}[/tex]Answer: The 90% confidence interval for the population proportion is (0.838, 0.900).
Multiply.-4u? ( – 5u?)Simplify your answer as much as possible.X $
SOLUTION:
Simplify;
[tex]-4u^2(-5u^3)[/tex]Using product rule;
[tex](-\times-)(4\times5)(u^2\times u^3)[/tex]From Indices law;
[tex]a^b\times a^c=a^{b+c}[/tex]Thus;
[tex]\begin{gathered} (-\operatorname{\times}-)(4\times5)(u^2\times u^3)=(+)(20)(u^{2+3}) \\ =20u^5 \end{gathered}[/tex]FINAL ANSWER:
[tex]\begin{equation*} 20u^5 \end{equation*}[/tex]Is ⅓ greater that 3/9?
1/3 and 3/9
Simplify 3/9 by 3
(3/3) / (9/3 ) = 1 /3
So, both fractions are equal
1/3 is not greater than 3/9
Find f(-4) and f(3) for the following funxripnf(x)=3x
Given the function:
[tex]f(x)=3x[/tex]• You need to substitute this value of "x" into the function:
[tex]x=-4[/tex]And then evaluate, in order to find:
[tex]f(-4)[/tex]You get:
[tex]f(-4)=3(-4)[/tex][tex]f(-4)=-12[/tex]Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]• Substitute this value of "x" into the function:
[tex]x=3[/tex]Then:
[tex]f(3)=3(3)[/tex]Evaluate, in order to find:
[tex]f(3)[/tex]You get:
[tex]f(3)=9[/tex]Hence, the answer is:
[tex]\begin{gathered} f(-4)=-12 \\ f(3)=9 \end{gathered}[/tex]A model rocket is launched with an initial upward velocity of 156 ft/s. The rocket's height h (In feet) after t seconds is given by the following.
h=156t-16t²
Find all values of t for which the rocket's height is 60 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Explanation
Check
ground
t = 0 seconds
☐or D
X
5
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I need help
The quadratic equation that gives the height of the rocket, h = 156·t - 16·t² is evaluated at h = 60 feet to give the two times the rocket's height is 60 feet as 0.40 seconds and 9.35 seconds.
What is a quadratic equation?A quadratic equation is an equation of the second degree that can be expressed in the form; a·x² + b·x + c = 0, where the letters, a, and b represents the coefficients of x and c is a constant.
The initial velocity of the rocket = 156 ft./s upwards
The given equation of the rocket is: h = 156·t - 16·t²
The times when the rocket height is 60 feet are found by plugging in the value h = 60, in the equation of the vertical height of the rocket as follows:
h = 60 = 156·t - 16·t²
156·t - 16·t² - 60 = 0
4·(39·t - 4·t² - 15) = 0
Therefore: [tex]39\cdot t - 4\cdot t^2 - 15 = \dfrac{0}{4} =0[/tex]
39·t - 4·t² - 15 = 0
-4·t² + 39·t - 15 = 0
From the quadratic formula which is used to solve the quadratic equation of the form; f(x) = a·x² + b·x + c, is presented as follows;
[tex]x = \dfrac{-b\pm\sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}[/tex]
The solution of the equation, -4·t² + 39·t - 15 = 0, is therefore:
[tex]t = \dfrac{-39\pm\sqrt{(39)^2-4\times (-4) \times (-15)} }{2\times (-4)}= \dfrac{-39\pm\sqrt{1281} }{-8}[/tex]
Therefore, when the height of the rocket is 60 feet, the times are: [tex]t = \dfrac{-39-\sqrt{1281} }{-8}\approx 9.35[/tex] and [tex]t = \dfrac{-39+\sqrt{1281} }{-8}\approx 0.40[/tex]
The times when the height of the rocket is 60 feet, the times are:
t ≈ 9.35 s, and t ≈ 0.40 s
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Find the values of x and y
Since the "x" values are vertical angles, and so are the "y" values, you must make them equal. If this is confusing, look at steps below (The order of solving the "x" or "y" values don't matter. I will write both ways down (in point form --> [tex](x,y)[/tex] and as just "x=..." "y=..."
First step is to make the "y" values equal each other
[tex]5y = 7y-34\\-2y = -34\\2y = 34\\\\y=17[/tex]
Next to solve make the "x" values equal each other
[tex]8x+7 = 9x-4\\-x = -11\\x = 11[/tex]
Final Answer:
[tex](11,17)[/tex]
x = 11; y = 17
Hope this helps :)
A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annual interest is $590
If a total of $6000 is invested, part at 5% and remainder at 10%, then the amount invested on 10% interest is $5800 and the amount invested on 5% interest is $200
The total amount = $6000
Consider the amount invested on 10% interest as x
The amount invest on 5% interest = (6000-x)
The the equation will be
x×(10/100) + (6000-x)(5/100) = 590
0.1x + 0.05(6000-x) = 590
0.1x + 300 - 0.05x = 590
0.05x +300 = 590
0.05x = 590-300
0.05x = 290
x = 290/0.05
x = $5800
The amount invested on 10% interest = $5800
The amount invested on 5% interest = 6000-5800
= $200
Hence, if a total of $6000 is invested, part at 5% and remainder at 10%, then the amount invested on 10% interest is $5800 and the amount invested on 5% interest is $200
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