Answer:
How many miles does he ride his bike there and back?
6 miles.
What information is extra?
The hour at which he leaves his house.
Step-by-step explanation:
We know that he rides 3 miles each way.
Then he rides 3 miles from his house to his friend's house, and another 3 miles from his friend's house to his house.
So he rides 3 miles both times, if we add that, we get:
3 miles + 3 miles = 6 miles
So:
How many miles does he ride his bike there and back?
6 miles.
And to answer the other question, we need to look at the given information that we did not use in this calculation. In this case, is the hour at which he leaves his house.
Notice that we never did use the fact that he leaves his house at 4 p.m.
Then:
What information is extra?
The hour at which he leaves his house.
Select the graph that best represents the inequality above.
Answer: B
Step-by-step explanation: Since x is less than 7, the graph would be all real numbers that are less than 7, so the arrow would be on the left.
Also, since x is not 7 itself (not less than or equal to), the dot cannot be a full dot. Thus, the dot must be open (or curved in some textbooks) to indicate x is not apart of 7 but less than 7.
Hope this helped!
n this equation, one-fourth is added to the variable y.
y+14=34
What is the value of y?
The value of y is = -------------
Answer:
I think its 19.75
Find two positive numbers whose difference is 5 and the
sum whose squares is 557.
Answer: 19 and 14
Step-by-step explanation:
19^2+14^2= 557
What I did to start it is I tried 20 and 15 because I know the square roots of those and once I added them I saw that their sum was too big, so then I tried 19 and 14 because 19-14 is 5. It was really just guess and check :)
what’s the equation for g(x)?
Answer:
Step-by-step explanation:
hello :
g(x) = (x+5)²
Find the equation of the line
Answer:
Step-by-step explanation:
hello :
Solut i on :
1) A line that passes through A(0, -6 ) andB (8 ,- -8)
Hello : let A(0,-6) B(8,-8)
the slope is : (YB - YA)/(XB -XA)
(-8+6)/(8-0) = -2/8=-1/4
an equation is : y=ax+b a is a slope
y = (-1/4)x +b
the line through point A (0;-6) : -6 = (-1/4)(0)+b
b = -6 the equation is : y =(-1/)4x-6
solve the inequality
x-2>15
Answer:
Inequality Form: x > 17
Interval Notation: (17, ∞)
WILL GIVE BRAINLIEST!!! If [tex]\frac{a}{b} =2[/tex] what is the value of [tex]\frac{a}{a-b}[/tex]?
Could the answer be D) or is it C)?
A) -2
B) 1
C) 2
D) It cannot be determined from the given information
Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:
C) 2
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion between a and b is given by:
a/b = 2.
Then:
a = 2b.
The expression is:
[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]
Hence option C is correct.
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Which of the following polynomials has an even degree and a negative leading coefficient?
Polynomial going down from the left and passing through the point negative 6 comma 0 and going to a local minimum and then going up through the point negative 2 comma 0 to a local maximum and then going down through the point 3 comma 0 to a local minimum and then going up to the right through the point 5 comma 0
Polynomial going up from the left and passing through the point negative 6 comma 0 and going to a local maximum and then going down through the point negative 1 comma 0 to a local minimum and then up through the point 2 comma 0 to a local maximum and then down to the right through the point 4 comma 0
Polynomial going up from the left and passing through the point negative 6 comma 0 and going to a local maximum and then going down through the point negative 2 comma 0 and 0 comma negative 6 to a local minimum and then up to the right through the point 5 comma 0
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0
Using limits, the polynomial that has an even degree and a negative leading coefficient is:
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.
What is a limit?A limit is given by the value of function f(x) as x tends to a value.
In this problem, to find the polynomial, we have to find the limits as x goes to infinity, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = [tex]\lim_{x \rightarrow -\infty} -a x^n[/tex]
Since n is even, we have that:
[tex]\lim_{x \rightarrow -\infty} -a (-\infty)^n = -a \times \infty = -\infty[/tex][tex]\lim_{x \rightarrow \infty} -a (\infty)^n = -a \times \infty = -\infty[/tex]Since it goes down to the left and down to the right, hence the function is:
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.
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Given: f(x) = x - 7 and h(x) = 2x + 3
Write the rule for f(h(x)).
f(h(x)) = 2x - 7
f(h(x)) = 2x - 4
f(h(x)) = 3x - 4
f(h(x)) = 3x - 7
Answer:
2nd option
Step-by-step explanation:
to find f(h(x)) substitute x = h(x) into f(x) , that is
f(h(x))
= f(2x + 3)
= 2x + 3 - 7
= 2x - 4
Which of these numbers is in the solution set of x-15=5?
Answer:
x=20
Step-by-step explanation:
x-15=5
x=5+15
x=20
If you invested $4,500 for 8 months at an interest rate of 2.75%, how much interest would you earn?
Given the money invested and the interest rate, the value of the interest earned after 8 months is $82.50.
What is the value of the Interest?
From the equation of simple interest; I = PRT
Given that;
Principal P = $4,500Interest rate R = 2.75% = 2.75/100 = 0.0275Time T = 8 months = 8/12 yearsInterest I = ?I = PRT
I = $4,500 × 0.0275 × 8/12
I = $82.50
Given the money invested and the interest rate, the value of the interest earned after 8 months is $82.50.
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What is the card balance
Answer:
A card balance is the total amount of money that you currently owe on your credit card. The balance increases when purchases are made and decreases when payments are made. Purchases, balance transfers, foreign exchange, fees, and interest all factor into your credit card balance.
please brainlest and like
Write equation for horizontal line and vertical lines passing through the point of 0 and 7
Answer:
Step-by-step explanation:
for horizontal line slope m=0
eq. of horizontal line at (0,7) with slope 0 is
y-7=0(x-0)
y-7=0
or
y=7
slope of vertical line=∝
eq of vertical line through (0,7) is
y-7=∝(x-0)
or
x-0=0(y-7)
x-0=0
or
x=0
1. Solve x² +5x+3=0
Give your solutions correct to 2 decimal places.
Answer:
Step-by-step explanation:
hello :
x² +5x+3=0
delta = b²-4ac when : a =1 and b=5 c=3
delta =5²-4(1)(3) =13
X1 =(-b-sqrt(delta))/2a
X2 =(-b+sqrt(delta))/2a
continu.....
Given the volume is 105 inches³ for an 8 pound bowling ball, find the radius of the bowling ball,
to the nearest hundredth of an inch.
Answer:
2.92
Step-by-step explanation:
[tex]V=\frac{4}{3}\pi r^3 \\ \\ 105=\frac{4}{3}\pi r^3 \\ \\ r^3=\frac{105}{\frac{4}{3}\pi} \\ \\ r=\sqrt[3]{\frac{105}{\frac{4}{3}\pi}} \\ \\ r \approx 2.92[/tex]
Mr. Carson washes his car every 8 days, checks the oil every 7
days, and checks the tire pressure every 9 days. He washed it Monday July 18,
2022, checked the oil on Wednesday and checked the tire pressure on Thursday
of that same week. When is the first day after that Monday on which he will
do all these activities on the same day? Find the number of days counted from
that Monday July 18, 2022.
The first day when he would do these activities on the same day is December 7, 2023.
When would he do these activities on the same day?In order to determine which day Mr. Carson would wash his car, check his oils and check the tire pressure, the multiple of 8, 7, and 9 have to be determined.
A multiple of a number is the product of an integer and that number. A common multiple is a number that is common to all three numbers. The lowest common multiple of 8, 7 and 9 is 504. So, in 504 days he would do all three activities on the same day.
In order to convert 504 days, take note of the following:
365 days = 1 year
12 month = 1 year
1 month = 4 weeks
30 days = 1 month
504 / 365 = 1 year 139 days
139 days / 30 days = 4 months 19 days
504 days = 1 year, 4 months and 19 days
1 year, 4 months and 19 days + July 18, 2022 = December 7, 2023
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Two angles in a triangle have measures of 42 and 82. (Degrees)
What is the measure of the third angle?
Answer:
angles of the triangle are equal 180
so 42+82=124
180-124=56
so the answer is 56
Step-by-step explanation:
Which graph best represents the solution to the system of equations shown below? y = -2x + 14 y = 2x + 2 A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 8, 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 8, negative 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, 8.
The graph whuch best represents the solution to the system of equations is; A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.
What is the graphical solution of the system big equations?As an alternative, solving the system of equations algebraically, we have;
-2x +14 = 2x +2
x = 3 and by substitution;
y = 8.
On this note, the point (3,8) is a solution of the graph and hence, the answer choice with two lines intersecting at (3,8) is correct.
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if the graph of f(x)=x^2 how will the graph be affected if the coefficient of x^2 is change to 1/3
The graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed
How to determine the change?The function is given as:
f(x) = x^2
When the coefficient of x^2 changes to 1/3, we have:
f(x) = 1/3x^2
The above represents a stretch of the function
This means that the graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed
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Solve the system of equations.
y = 2x+ 3
y=x^2+3x+3
Answer:
(0,3)
(-1,1)
Step-by-step explanation:
Hello!
Since both equations are equal to y, we can set the right-hand side of the equations equal to each other.
[tex]y = 2x + 3\\y = x^2 + 3x + 3[/tex][tex]y = y[/tex][tex]2x + 3 = x^2 + 3x + 3[/tex]Solve for x[tex]2x + 3 = x^2 + 3x + 3[/tex][tex]0 = x^2 + x[/tex][tex]0 = x(x + 1)[/tex][tex]x = 0, x =-1[/tex]X can either be 0 or -1. Remember, a solution to a system is not complete without a y-value. Plug in 0 and -1 for x in the first equation, and find the corresponding y-values.
[tex]y = 2(0) + 3\\y = 3[/tex]
And
[tex]y = 2(-1) + 3\\y = -2 + 3\\y = 1[/tex]
So the solutions to the system are (0,3) and (-1,1)
Write an equation for a line perpendicular to y=5x+1 and passing through the points (5,-2)
__________________________________________________________
[tex]\text{\textbf{Hello!} In this question, we are trying to find the equation of a line}\\\text{that is \underline{perpendicular} to our given equation}[/tex]
__________________________________________________________
[tex]\textbf{Explanation:}\\\\\text{To help us answer our question, we need to note some of our given info:}\\\\\text{Equation: y = 5x + 1}\\\\\text{Point passed through: (5, -2)}\\\\\text{We can use the above information to help us find our perpendicular equation.}\\\\\text{We will be using the slope-intercept form equation to help get us our answer:}\\\\\text{y = mx + b}[/tex]
[tex]\text{When a line is perpendicular to an equation, it means that its slope is }\\\text{\textbf{opposite} which results in the lines to meet at a \underline{90-degree} angle.}[/tex]
__________________________________________________________
[tex]\textbf{Solve:}\\\\\text{To get our perpendicular slope, we will use the formula:}\\\\\text{m1 = }-\frac{1}{m2}\\\\\text{m1 will be our given slope (5) and m2 will be our already provided slope. }\\\\\text{This is also known as a \underline{negative reciprocal}. }\\\\\text{Therefore: m1 = }-\frac{1}{5}\\\\\text{Since we now know our slope, we can plug it into our "m" variable in the}\\\text{slope intercept equation:}\\\\\text{y = }-\frac{1}{5}x+b\\[/tex]
[tex]\text{To find where the point is on the y-intercept, we will plug in our point}\\\text{(5, -2) to it's corresponding spots in our new equation above.}\\\\\text{Plug "5" to x and "-2" to y and solve:}\\\\\text{-2 = }-\frac{1}{5}(5)+b\\\\\text{-2 = }-1+b\\\\\text{Add 1 to both sides.}\\\\\text{-1 = }b\\\\\text{Therefore, our y-intercept is -1.}[/tex]
[tex]\text{When we plug -1 into our new equation, we get:}\\\\\text{y = }-\frac{1}{5}x-1\\\\\text{Therefore, our perpendicular equation is: }\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________
[tex]\textbf{Answer:}\\\\\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________
[tex]\textbf{Additional Info:}\\\\\text{You can learn more about \textbf{slope-intercept form} below:}[/tex]
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__________________________________________________________
HELP ME WOTH THIS QUESTIONNN!!
Answer:
C
Step-by-step explanation:
For lines l and m and the transversal line that creates angles 6 and 18, angles 6 and 18 are corresponding angles of lines l and m. If they are congruent, lines l and m are parallel.
Answer: Choice C
Party trays which cost $14 to make not including labor are sold for $35 if two people work eight hour shifts making the tray at seven dollars per hour how many trays must be sold to cover the cost including the labor?
Approximately 5 number of trays must be sold to cover all costs including labor.
How to find the work proportion?The profit on each tray that was sold excluding labor cost is;
Profit = $35-$14
Profit = $21
Total labor cost for making party tray for a day is;
Total Labor Cost = Total labor hours * wages per hour * No. of labors
Total Labor cost = $7 * $8*2
Total Labor Cost = $112
Number of trays that must be sold to cover cost is;
Total labor cost/ Profit per tray
Number of trays = $112/$21
= 5.33
Approximately 5 trays must be sold to cover all costs including labor.
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Point One = (0, -2)
Point Two = (-3,-5)
Slope-Intercept Form
Answer:
y = x - 2
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this formula, "m" represents the slope and "b" represents the y-intercept. Before writing our equation in this form, we first need to find the slope. The slope can be found using the point-slope formula:
y₁ - y₂ = m(x₁ - x₂)
In this formula, "m" represents the slope, "x₁" and "y₁" represent the values from Point One, and "x₂" and "y₂" represent the values from Point Two. You can find the slope by plugging the values from the points into the equation and then simplifying.
x₁ = 0 x₂ = -3
y₁ = -2 y₂ = -5
y₁ - y₂ = m(x₁ - x₂)
(-5 - (-2)) = m(-3 - 0)
-3 = m(-3)
1 = m
Now that we have a value for the slope, we can use the values from either one of the points to solve for the y-intercept (from the slope-intercept form equation).
m = 1
x = 0
y = -2
y = mx + b
-2 = (1)(0) + b
-2 = 0 + b
-2 = b
Therefore, the equation of the line in slope-intercept form is:
y = x - 2
Evaluate function expressions
Answer:
24
Step-by-step explanation:
1) according to the additional (see the attached picture) f(6)= -6 and g(5)= -5. Then
2) the given experssion can be written:
f(6)-6*g(5)=-6-6*(-5)=-6+30=24.
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
A. What is the area of the pool cover?
B. What is the length of the rope?
For the circular cover we have:
A) The area is 379.94 ft²
B) The length of the rope must be 68.2 ft
How to get the area of the cover?Remember that the area of a circle of radius R is given by the formula:
[tex]A = pi*R^2[/tex]
Where pi = 3.14
In this case, the diameter of the pool is 20ft, then the radius is:
R = 20ft/2 = 10ft
And it must extend 12 inches beyond, then the radius of the cover must be:
R = 10ft + 12in
Now, we know that 1ft = 12 in, then we can rewrite the radius as:
R = 10ft +1ft = 11ft
Then the area of the cover is:
[tex]A = 3.14*(11ft)^2 = 379.94 ft^2[/tex]
B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.
Remember that the circumference of a circle of radius R is:
[tex]C = 2*pi*R[/tex]
Then the length of the rope will be:
[tex]C = 2*3.14*11ft = 68.2ft[/tex]
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> Function g can be thought of as a translated (shifted) version of Y f(x) = x².
Using translation concepts, function g(x) is given as follows:
g(x) = x² - 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, g(x) is a shift down of 3 units of f(x) = x², hence:
g(x) = x² - 3.
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look at the picture
[tex]\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{9(|x-8|)}{9} < \frac{36}{9} \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}[/tex]
[tex]\underline{\boldsymbol{\sf{Answer}}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \ correct \ option}} \ \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}[/tex]
The graphs of f(x) = 5* and its translation, g(x), are
shown on the graph.
30 1x
30 25 20 15 10 f
goxx)
40
f(x)
-6-5-4-3-2-15-
(1,5)
(0
(2,25)
(2, 15)
2 3 4 5
(1.-5)
-10-0.9)
-15-
-20
-25
30
X
What is the equation of g(x)?
Og(x) = 5x-9
Og(x) = 5x-10
Og(x) = 5-9
Og(x) = 5-10
g(x) is just a translation of 10 units downwards, this means that the equation for g(x) is:
[tex]g(x) = f(x) - 10 = 5^x - 10[/tex]
Which is the equation of the translation?Here we know that:
[tex]f(x) = 5^x[/tex]
And we want to find the equation for g(x), which is a translation of f(x).
If you look at the graph of f(x), you can see that it passes through:
(0, 1), (1, 5), (2, 25), etc.
And the graph of g(x) passes through:
(0, -9), (1, -5), (2, 15)
So in each point, the y-component is 10 units smaller than the correspondent for f(x).
Then g(x) is just a translation of 10 units downwards, this means that the equation for g(x) is:
[tex]g(x) = f(x) - 10 = 5^x - 10[/tex]
So the correct option is the last one.
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If f(x) =2ײ+2 and g(x) =x² -1, find (f-g) (x)
Answer:
[tex]\boxed {(f-g)(x) = x^{2}+3}[/tex]
Step-by-step explanation:
Given :
f(x) = 2x² + 2g(x) = x² - 1Now, this problem can be used using a simple formula.
[tex]\fbox {(f - g)(x) = f(x) - g(x)}[/tex]
Let's solve.
(f - g)(x) = 2x² + 2 - (x² - 1)(f - g)(x) = 2x² - x² + 2 + 1(f - g)(x) = x² + 3∴ The answer will be x² + 3.