On a graph of g(x) = -3x + 9 the x - intercept is identified to be
What is x - intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
It is x - intercept where the line crosses the x axis and y intercept where the line crosses the y axis
How to identify the intercept from the graphOn the graph, the point where the line crosses the x axis is noted and written in ordered pair in the for (a, b)
Where a represents values in the x direction and y are values in the y direction
From the graph, a = 3 and b = 0
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Answer:
The answer is C. (3, 0)
x2 can be combined with X?
Answer:
Your first instinct might be to go ahead and add the x terms together, BUT this would be a bad thing to do! You cannot combine the x2 and 2x, because the first term has an exponent (2) and the second one does not have an exponent; therefore, you cannot add them together!
Step-by-step explanation:
Answer:
Not sure if you mean multiplying or adding by "combine". But generally the rule of thumb with exponents is when you are adding and they are not like terms, you cannot combine the two terms together. So in other words, they would be left as x²+x. However, when you are multiplying you can add the exponents together. So, it will be like this: x²·x = x³
Which disjunction is always true for any real number x? A number, x, is less than 0 or greater than 1. A number, x, is less than 0 or greater than 0. A number, x, is greater than 5 or less than 10. A number, x, is greater than 5 or less than 1.
Answer:C, a number, x, is greater than 5 or less than 10.
The disjunction from the above that is always true is:
A number, x, is greater than 5 or less than 10. (Option C)
What is a disjunction?In mathematics, a disjunction occurs when the connector between two or more statements is given as "or".
A disjunction is also formed when there is a compound mathematical statement that is formed using the word "or".
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(a^-7 x b^-2)^-9 =?
Select the equivalent expression.
The equivalent expression to the expression (a⁻⁷ × b⁻²)⁻⁹ is (a⁷ × b²)⁹.
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
The given expression is (a⁻⁷ × b⁻²)⁻⁹.
= a⁻⁷ˣ⁻⁹ × b⁻²ˣ⁻⁹.
= a⁶³ × b¹⁸.
= (a⁷ × b²)⁹.
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Help! Look at the figure. If mzJ = 55, find m
90
35
70
55
The value of the required missing angle is;
m<JKM = 35°
How to find the missing angle of the triangle?We know from geometry that the sum of angles in a triangle sums up to 180 degrees.
Now, we are trying told that in the given Triangle that the angle m<J = 55 degrees.
We also see that the angle <KMJ is equal to 90 degrees becasue it is a right angle.
Thus to find the angle m<JKM, we can write the name expression as;
m<JKM = 180 - (90 + 55)
m<JKM = 35°
Thus that's the value of the required missing angle.
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An antique has a price tag of $467. The sales tax rate for the county is 9
%
. How much sales tax will be due?
Write answer to the nearest cent.
If antique has a price tag of $467 and sales tax rate be 9% then the sales tax due will be $42.03.
Given that antique has a price tag of $467 and sales tax rate be 9%.
We are required to find the amount of sales that will be due.
A sales tax is basically a tax paid to a governing body for the sales of certain goods and services.
Sales=$467
Sales tax rate=9%
Sales tax=467*9/100
=4203/100
=$42.03
Hence if antique has a price tag of $467 and sales tax rate be 9% then the sales tax due will be $42.03.
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Nobody knows it somebody hel
The required value of x = 12 and the side length of the triangle is 12 units. which is determined by Pythagoras's theorem.
What is Pythagoras's theorem?
Pythagoras's theorem states that in a right-angled triangle, the square of one angle is equal to the sum of the squares of the other two sides.
The given triangle is a right-angled triangle.
As per Pythagoras's theorem,
⇒ a² + b² = c²
Here a = 16, b = x and c = 20
Substitute the values in the formula,
⇒ 16² + x² =20²
⇒ 256 + x² = 400
⇒ x² = 400 - 256
Apply the subtraction operation,
⇒ x² = 144
⇒ x = √144
⇒ x = 12
Therefore, the required value of x is 12 units.
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Let f (x) = log₃(x) + 3 and g(x) = log₃(x³) – 1.
Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form.
Part B: Determine the solution to the system of nonlinear equations of f(x) and g(x).
Answer:
See below
Step-by-step explanation:
\(\textbf{Part A: } \text{ If }h(x) = f (x) + g(x) \text{, solve for } h(x) \text{ in simplest form.}\)
We have
\( f (x) = \log_3(x) + 3 \)
and
\(g(x) = \log_3(x^3) - 1\)
Thus
\(h(x) = f (x) + g(x) = (\log_3(x) + 3) + ( \log_3(x^3) - 1) = \log_3(x) + 3 + \log_3(x^3) - 1\)
\(= \log_3(x) + \log_3(x^3) + 2\)
Recall the property of logarithms:
\(\boxed{\log_b(n\cdot m) = \log_b(n) + \log_b(m)}\)
then,
\(\log_3(x) + \log_3(x^3) + 2 = \log_3(x\cdot x^3) +2 = \boxed{\log _3(x^4)+2}\)
================================================================
\(\textbf{Part B: } \text{Determine the solution to the system of nonlinear equations of } f(x) \text{ and } g(x).\)
I am assuming that the system of equations is
\($\left \{ {{ f (x) = \log_3(x) + 3 } \atop {g(x) = \log_3(x^3) - 1}} \right$\)
and you probably want the solution when \(f(x)=g(x)\) I will name it \(y\), thus
\($\left \{ {{ f (x) = \log_3(x) + 3 } \atop {g(x) = \log_3(x^3) - 1}} \right \implies \left \{ {{y= \log_3(x) + 3 } \atop {y = \log_3(x^3) - 1}} \right$ \)
We should just solve
\(\log_3(x) + 3 = \log_3(x^3) - 1 \)
\(\log_3(x) - \log_3(x^3) = - 4\)
\(\log_3 \left(\dfrac{x}{x^3} \right) = - 4\)
\(\log_3 \left(\dfrac{1}{x^2} \right) = - 4\)
\(\log_3 (x^{-2}) = - 4\)
\(-2\log_3 (x) = - 4\)
\(\log_3 (x) = 2 \iff 3^2 = x \implies \boxed{x= 9} \)
7/5-6/5+3/2=17/10=1 7/10
Question:
Solution:
Let us denote by x the blank space in the given equation. Then, we get:
\(\frac{7}{5}-x+\frac{3}{2}=\frac{6}{5}\)this is equivalent to:
\(\frac{7}{5}+\frac{3}{2}-x=\frac{6}{5}\)this is equivalent to:
\(\frac{14+15}{10}-x=\frac{6}{5}\)that is:
\(\frac{29}{10}-x=\frac{6}{5}\)solving for x, we obtain:
\(\frac{29}{10}-\frac{6}{5}=x\)that is:
\(x=\frac{29}{10}-\frac{6}{5}=\frac{29-12}{10}=\frac{17}{10}\)so that, the blank space would be:
\(\frac{17}{10}\)and the complete expression would be:
\(\frac{7}{5}-\frac{17}{10}+\frac{3}{2}=\frac{6}{5}\)15 POINTS!!! ANSWERS NEEDED ASAP!!!!
what is the y intercept when the coordinate is -3,-3 and the slope is -1
The y-intercept is -6, when the coordinate is -3,-3 and the slope is -1
Describe Slope?More specifically, it is defined as the ratio of the change in the y-coordinate (vertical) to the change in the x-coordinate (horizontal) between any two points on the line or surface.
The slope of a line is often denoted by the letter "m" and can be calculated using the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
A positive slope indicates that the line is rising from left to right, while a negative slope indicates that the line is falling from left to right. A slope of zero indicates that the line is horizontal.
The slope of a surface can be calculated using partial derivatives. The slope of a surface at a point is the slope of the tangent plane at that point.
Slope is an important concept in mathematics, physics, and engineering, and is used to calculate rates of change, velocities, and accelerations, and to model relationships between variables. It is also used in a variety of practical applications, such as in construction and surveying, where it is necessary to determine the slope of the land.
To find the equation of the line when the coordinate is (-3, -3) and the slope is -1, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is the given point. Plugging in the values, we get:
y - (-3) = -1(x - (-3))
y + 3 = -x - 3
y = -x - 6
The y-intercept is the point where the line intersects the y-axis, which occurs when x = 0. Plugging in x = 0 into the equation, we get:
y = -0 - 6
y = -6
Therefore, the y-intercept is -6.
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A line has a slope of 1 and passes through the point (-8, -7). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer: y = x + 1
Step-by-step explanation:
y = 1x + c
-7 = 1(-8) + c
-7 = -8 + c
-7 + 8 = c
1 = c
y = 1x + 1 or
y = x + 1
Answer:
y+8=m(x+7)
hope this helps:
I used this formula y-y1=m(x-x1)
A leaking pipe loses 1.5 cups of water per hour. How many quarts of water does it lose in a week? PLEASE HELP
The water loss in a week is 63 Quarts.
What is unit conversion?The same property is expressed in a different unit of measurement through a unit conversion. For instance, distance can be converted from miles to kilometers, feet, or any other length measurement, and time can be expressed in minutes rather than hours. Measurements are frequently given in one set of units, like feet, but they are needed in other units, like chains. A numerical expression known as a conversion factor makes it possible to exchange feet for chains in an equitable manner.
Given pipe losses 1.5 cup of water per hour
loss in 24 hours or 1 day = 1.5 x 24 = 36 cup
water loss in 1 week or 7 days = 36 x 7 = 252 cup
and 1 cup = 0.25 quarts
252 cup = 0.25 x 252 Quarts
252 cup = 63 Quarts
Hence 63 Quarts water loss in 1 week.
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what is the slope intercept form of 4x+y=-3
Answer:
Step-by-step explanation:
-4x-3=y
order these numbes from least to greatest: -2, 0, -6, 4, 8
Step-by-step explanation:
-6,-2,0,4,8
this is the answer
Find all zeros? One zero has been given.
The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,
x = -1 and x = 1/2 respectively
What is the zeros of a function?The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
In the given problem, the zero of the function;
f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are
f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0
f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0
f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0
f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0
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Help??? Please? I need to pass.
Answer:
(x-8.5)2=81.25
find the slope of the line with y=7x+2/3
Answer:
slope is 7
Step-by-step explanation:
Please Solve, Thank you!
Answer:
1711
Step-by-step explanation:
\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)
Make sure to follow order of operations!
Solve the equation. Please help
\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)
Which equation is true?
107 = 10,000,000
106 = 10,000 × 10
105 = 10 × 1,000
104 = 1,000
The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?
Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.
Step-by-step explanation:
To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.
Answer:
the afternoon is the right one
Find the equation of the line that passes through point (-2,5) and is parallel to y=-3x+7 also write in slope-intercept form without any spaces
ANSWER
y = - 3x - 1
EXPLANATION
Recall: Parallel lines have the same slope.
The slope-intercept form is given as: y = mx + c
where m is the slope and c is the y-intercept.
From the given equation y = -3x + 7,
slope (m) = - 3
Now, the equation of the new line is:
y = -3x + c
Insert the point (-2, 5) as (x, y) to determine the 'c'
5 = -3(-2) + c
5 = 6 + c
subtract 6 from both sides
5 - 6 = 6 + c - 6
c = - 1
Hence, the equation of the line that passes through point (-2,5) and is parallel to y=-3x+7 is y = - 3x - 1.
TIME REMAINING
44:54
The table below shows the number of cars sold each month for 5 months at two dealerships.
Cars Sold
Month
Admiral Autos
Countywide Cars
Jan
4
9
Feb
19
17
Mar
15
14
Apr
10
10
May
17
15
Which statements are supported by the data in the table? Check all that apply.
The mean number of cars sold in a month is the same at both dealerships.
The median number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The range of the number of cars sold is the same for both dealerships.
The data for Admiral Autos shows greater variability.
The statements supported by the data in the table are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
To determine which statements are supported by the data in the table, let's analyze the given information:
The mean number of cars sold in a month is the same at both dealerships.
To calculate the mean, we need to find the average number of cars sold each month at each dealership.
For Admiral Autos:
(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13
For Countywide Cars:
(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13
Since both dealerships have an average of 13 cars sold per month, the statement is supported.
The median number of cars sold in a month is the same at both dealerships.
To find the median, we arrange the numbers in ascending order and select the middle value.
For Admiral Autos: 4, 10, 15, 17, 19
Median = 15
For Countywide Cars: 9, 10, 14, 15, 17
Median = 14
Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.
The total number of cars sold is the same at both dealerships.
To find the total number of cars sold, we sum up the values for each dealership.
For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65
For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65
Since both dealerships sold a total of 65 cars, the statement is supported.
The range of the number of cars sold is the same for both dealerships.
The range is determined by subtracting the lowest value from the highest value.
For Admiral Autos: 19 - 4 = 15
For Countywide Cars: 17 - 9 = 8
Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.
The data for Admiral Autos shows greater variability.
To determine the variability, we can look at the range or consider the differences between each data point and the mean.
As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.
Based on the analysis, the statements supported by the data are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
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what is 25+25458752452+5454466125+545454885422574212=
Answer:
5.4545492e+17
Step-by-step explanation:
aka a really big number
A 16-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
Answer:
Step-by-step explanation:
oi gooot
The rear windshield wiper of a car rotated 120 degrees,as shown. Find the area cleared by the wiper. 25inch,120 degrees, 14inch
The rear windshield wiper of a car rotated 120 degrees, as shown in the figure. The area cleared by the wiper blade is approximately 205.875 square inches.
The problem states that a car’s rear windshield wiper rotates 120 degrees, as shown in the figure. Our aim is to find the area cleared by the wiper.
The wiper's arm is represented by a line segment and has a length of 14 inches.
The wiper's blade is perpendicular to the arm and has a length of 25 inches.
Angular degree measure indicates how far around a central point an object has traveled, relative to a complete circle. A full circle is 360 degrees, and 120 degrees is a third of that.
As a result, the area cleared by the wiper blade is the sector of a circle with radius 25 inches and central angle 120 degrees.
The formula for calculating the area of a sector of a circle is: A = (θ/360)πr², where A is the area of the sector, θ is the central angle of the sector, π is the mathematical constant pi (3.14), and r is the radius of the circle.
In this situation, the sector's central angle θ is 120 degrees, the radius r is 25 inches, and π is a constant of 3.14.A = (120/360) x 3.14 x 25²= 0.33 x 3.14 x 625= 205.875 square inches, rounded to the nearest thousandth.
Therefore, the area cleared by the wiper blade is approximately 205.875 square inches.
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Two times the sum of a number and 8 is negative 48 what is the number?
Answer:
-32
Step-by-step explanation:
Let the number be x.
\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)
NEED HELP ASAP a bag contains four green marbles,six white marbles, and ten red marbles. One marble is picked at random from the bag. What is the probability of picking a white marble?
Answer:
3/10
Step-by-step explanation:
add all the marbles together4+6+10
=20
probability of picking a white marble is6/20
=3/10
5:30PM
You run to the store on your way home from school. You want to buy some Doritos. Should you buy
the regular size bag or the party size bag? Calculate the unit price for each size and determine which
one is the better buy.
15 oz. Party Size Doritos $3.98
9.75 oz. Doritos $2.98
The Unit Price is just a Ratio with a denominator of 1. Your textbook has information about ratios on
pgs. 305-307
Answer:
The regular size bag of doritos is a better deal, I believe. Hope this helps!
Step-by-step explanation:
Paxton invests $4850 at 7.6%/a simple interest. If she wants the money to increase to $8000, how long will she need to invest her money?
Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.
To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (initial investment)
r = Interest rate per year (expressed as a decimal)
t = Time (in years)
Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:
4850 * 0.076 * t = 8000
Simplifying the equation:
369.8t = 8000
To find t, we divide both sides of the equation by 369.8:
t ≈ 8000 / 369.8 ≈ 21.62 years
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Claudia records the hours is been studying and a test scores for five test
The correlation coefficient when Claudia records the hours she spent studying and her test scores for 5 tests is 0.85. This is a strong positive correlation.
How to explain the correlationAny statistical association between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.
Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. Theoretically, the same external forces can affect both of these separate variables because they travel in the same direction.
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Claudia records the hours she spent studying and her test scores for 5 tests.
What is the correlation coefficient?
-0.85-0.840.840.85
What is the strength of the model?