The average rate of change of the equation g(x) =−x²+2x−4 from x = 2 to x = 5 is -15 .
The average of change of the function f(x) from x=a to x=b is given by the formula
Average rate of change = (f(b)-f(a))/(b-a)
In the question ,
it is given that
the function is g(x) =−x²+2x−4
we need to find g(2) and g(5) .
g(2) = −(2)²+2(2)−4
= -4 + 4 -4
= -4
g(5) = −(5)²+2(5)−4
= -25 +10 -4
= -15 -4
= -19
So , Average rate of change = (g(5) - g(2))/(5-2)
Substituting the values , we get
Average rate of change = (-19 - (-4))/3
= (-19+4)/3
= -15/3
= -5
Therefore , the average rate of change of the equation g(x) =−x²+2x−4 from x = 2 to x = 5 is -15 .
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Helpppppppssssss hehe
Answer:
Step-by-step explanation:
a. From 4 to 7 is 3 units. 7-10 is another 3 units and so on. The constant 3 units is the common difference.
The formula for a arithmetic sequence is
[tex]a_{n}=a_{1}+d(n-1)[/tex]
Where d is the common difference and a_1 is the first term.
[tex]a_{1}=4[/tex] and [tex]d=3[/tex]. Thus the equation of the nth term is
[tex]a_{n}=4+3(n-1)[/tex]
Topic: Nonlinear Systems of EquationsCreate a system of equations that includes one linear equation and one quadratic equation.Show all work in solving your system of equations algebraically.
Answer:
• Equations
[tex]y=x+2[/tex][tex]y=x^2[/tex]• Solutions (2, 4) and (–1, 1)
Explanation
System of equations
• Linear equation
[tex]y=x+2[/tex]• Quadratic equation
[tex]y=x^2[/tex]We have to set both equations to 0 and equalize them:
• 1. Setting them to 0:
[tex]0=x+2[/tex][tex]0=x^2[/tex]• 2. Equalizing them:
[tex]x+2=x^2[/tex]To solve the system using the General Quadratic Formula, we have to set the equation in the form ax² + bx+ c = 0:
[tex]x^2-x-2=0[/tex]Thus, in this case a = 1, b = -1 and c = -2. Using the formula:
[tex]x_{1,2}=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-2)}}{2(1)}[/tex][tex]x_{1,2}=\frac{1\pm\sqrt{1+8}}{2}[/tex][tex]x_{1,2}=\frac{1\pm\sqrt{9}}{2}[/tex]Finding both solutions:
[tex]x_1=\frac{1+3}{2}=\frac{4}{2}=2[/tex][tex]x_2=\frac{1-3}{2}=\frac{-2}{2}=-1[/tex]Finally, replacing these values in the linear equation to find y:
[tex]y_1=2+2=4[/tex][tex]y_2=-1+2=1[/tex]Therefore, the solutions are (2, 4) and (–1, 1).
Kamryn’s doctor recommended that she drink 64 fluid ounces of water every day. There are about 30 milliliters in 1 fluid ounce. Which measurement represents the number of milliliters in 64 fluid ounces?
help my teacher wants the answer in 15 minutes please help!!!
The 64 fluid ounces of water, as suggested by Kamryn's doctor to drink everyday, will be equal to 1920 millilitres.
Writing the equation as per the relation between millilitres and fluid ounces -
1 fluid ounce = 30 millilitres
Now, we will perform multiplication to find the number of milliliters in 64 fluid ounces. Writing the expression representing relation between millilitres and fluid ounces
Number of milliliters = 30×64
Performing multiplication between the numbers 30 and 64
Number of milliliters = 1920
Therefore, on drinking 64 fluid ounces by Kamryn on her doctor's recommendation will drink 1920 millilitres of water everyday.
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4. Which statement is NOT true about the diagram below?
O AD = DC
O m<CDB =92
O m<ADB =88
O DB is a perpendicular of AC
Answer:
DB is a perpendicular of AC
I DONT KNOW PLS HELPP
The price of an item yesterday was $140. Today, the price rose to $357. Find the percentage increase.
Answer: 70% is percentage increase
Step-by-step explanation:
230-140/140 x 100 =90/140 x100 =0.7 x 100=70
Aldo has 61 miles remaining after 48 minutes of driving. How many miles will
be remaining after 60 minutes of driving?
Answer:
76.25
Step-by-step explanation:
61:48 = x:60
48x=3660
3660/48 = 76.25
So the answer is 76.25 miles are left.
 The measures of the angles of a triangle are shown in the figure below. Solve for x.
46°
34°
x°
Answer:
x = 100
Step-by-step explanation:
180 = 46 + 34 + x
180 = 80 + x
100 = x
u/3 = -51 solve for u simplify your answer as much as possible
Answer:
u = -153
Step-by-step explanation:
u/3 = -51
multiply both sides by 3:
3(u/3) = 3(-51)
u = -153
Please help me im getting stressed with solution
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-8, -5); y= -3x + 5
Step-by-step explanation:
a parallel line must have the same slope (otherwise it cannot be parallel).
a slope-intercept form looks like
y = ax + b
"a" (the factor of x) is always the slope, "b" is the y-intercept (the y-value when x = 0).
so, we know from y = -3x + 5 that the slope of the new line is also -3.
to get b we use the coordinates of the given point :
-5 = -3×-8 + b = 24 + b
-29 = b
that means the line equation is
y = -3x - 29
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
PLS HELP ME
The following table shows the distance from the bus stop as a function of time:
Time (in minutes) Distance (in meters)
(x) f(x)
0 45
3 40
6 35
9 30
12 25
Find and interpret the meaning of the x-intercept in this scenario. (4 points)
(45, 0); the distance away from the bus stop
(27, 0); the time it takes to reach the bus stop
(45, 0); the time it takes to reach the bus stop
(27, 0); the distance away from the bus stop
The x-intercept is (27,0). The time it takes to reach the bus stop
We first find the equation between time and distance as a linear function by finding the slope and y-intercept from the table values.
If we write the Time as x-values and Distance as y-values, we get the points,
(0,45), (3,40), (6,35), (9,30), (12,25)
We can find the slope from these points considering two points (0,45) and (3,40)
Slope = 45-40/0-3 = -5/3
The y-intercept of the function is the value of f(x) at x = 0.
Here, from the table, when x = 0, y = 45.
So y-intercept = 45
Then the equation of distance in terms of time is,
y = -(5/3)x+45
The x-intercept is the x-value when y = 0.
So when y = 0,
0 = -(5/3)x+45
⇒ (5/3)x=45
⇒ x = 45x 3/5
⇒ x = 27
Therefore, x-intercept = (27,0).
It is the time (in minutes) when distance = 0 meters.
So x-intercept is the time it takes to reach the bus stop.
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Answer:
B) (27,0); the time it takes to reach the bus stop
The question is clearly in the pic
A) The slope represents the probability of winning for each rank.
B) The y-intercept means the probability of winning for an unranked school.
C) The probability of winning for a school ranked number 4 is; 78%
How to Interpret Linear Equation Graphs?The formula representing the general form of an equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
A) From the given graph, we see that the y-axis represents the probability of winning for each rank while the x-axis represents the ranks of the schools. Thus;
Slope unit = Probability of winning/Rank
B) The y-intercept is the point at which the graph crosses the y-axis. In this case, it means no ranked school and that is the probability of winning for an unranked school.
C) The linear equation is given by the formula;
y = -6.4x + 103.8
Thus, for a rank of 4, we have;
y = -6.4(4) + 103.8
y = 78.2 ≈ 78%
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Divide.
2/7÷1/3
Responses
6/7
2/14
1/4
2/21
Answer:
6/7
Step-by-step explanation:
2Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/3 is 3/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - two sevenths divided by one third is six sevenths.
an office ceiling is 9 feet high file boxes are each 3/4 feet tall. what is the greatest number of these file boxes that can be stacked in the office? Show how you know.
Answer:
12
Step-by-step explanation:
Equation:
[tex]9 /\frac{3}{4}[/tex] [tex]=x[/tex]
[tex]12=x[/tex]
Check!
[tex]12(\frac{3}{4} )=9[/tex]
Therefore, the greatest number of file boxes that can be stacked is 12.
Daniel walks at a speed of 4 miles per hour. Daniel leaves his house at 1:00 p.m. and walks toward a playground that is exactly 2 miles away.
How long does it take Daniel to walk 1 mile?
Answer: 30 minutes to get to the playground
Step-by-step explanation:
What is the
Range??
Help me out plsss
Answer:
1 ≤ y ≤ 4
Step-by-step explanation:
Range is all possible y values
a point is written as (x, y)
The line starts at point (0, 1) and ends at (3, 4)
so the range of the y values is 1 to 4
Find an equivalent statement for the following absolute value equation |x - 5] = 1x +6
ANSWER:
STEP-BY-STEP EXPLANATION:
Which number line shows the points −125 and –2.8?
A. Alternative Text
B. Alternative Text
C. Alternative Text
D. Alternative Text
The number line having -2.4 and -2.8 is attached below
What is number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. We refer to these as closed number lines. Number lines may alternatively be left empty or blank. A number ladder is a vertical number line.
Given number: −12/5 and –2.8
As, we can write -12/5 in decimal form= -2.4
Now, we have to put the number on the number line
As, -2.4 lies between -2 and -3 on the left side of zero.
and, -2.4 lies between -2.5 and -3.0 on the left side of zero.
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3y+2x=-1 solve for x
Answer:
Answer down below!
Step-by-step explanation:
Your answer would be -3/2y + (-1/2)
If you need the steps, refer to the image below!
PLEASE HELP BRO WILL GIVE BRAINLI
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠n + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
Step 2; it should be m∠o − m∠p = 90 degrees (complementary angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 3; it should be m∠m + m∠n + m∠o = m∠o + m∠p
Answer:
Step 3; it should be angle m + angle n + angle o = angle o + angle p
Step-by-step explanation:
yes, the sum of the inner angles of the triangle, m, n, o must be 180°.
yes, the sum of supplementary angles (which the pair of inner and outer angles always is) p and o must be 180°.
so, step 3 wants to show that the sum of the 3 inner angles is the same as the sum of the inner/outer angle pair. m + n + o = o + p = 180.
but instead of o the student suddenly wrote n in the right side of the equation. and that is wrong. n + p can't be 180°, as both are inner angles, and that would make the third inner angle 0°, which is not really possible.
so, once n is replaced by o on the right side of the equating in step 3, all is correct again.
and step 4 is correct anyway (it fixed the mistake in step 3 of the original proof by another mistake, coming to the right conclusion just by coincidence), now that step 3 is corrected.
The personal assets and liabilities of a plumber are listed below.
What is the total value of the plumber's liabilities?
$149,367
$167,925
$241,231
$273,881
The total value of the plumber's liabilities = $441,806
How to calculate the total of something?One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
It is one of the fundamental mathematical operations we employ on a daily basis. We employ number addition in a variety of contexts. When we work with time or money, such as when adding up invoices and receipts, adding numbers is one of the most frequently used operations in daily life.
The total value of the plumber's liabilities :
is to simply add all the values and we will get
$441,806
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Answer:
Option B.) $167,925
Step-by-step explanation:
Liability is money you owe to another person or institution, including a credit card balance, mortgage and so on.
So the plumber's liabilities
= 149,367 + 6,283 + 12,275
= $167,925
Find the derivative of the function with solutions.y = In( e^(3 - x^2 ) + 9 ))
Answer:
[tex]\frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9}[/tex]Explanation:
We were given the function:
[tex]y=\ln\left(e^{3-x^2}+9\right)[/tex]We are to find the derivative of this function, we have it shown below:
[tex]\begin{gathered} y=\operatorname{\ln}(e^{3-x^{2}}+9) \\ If:y=ln(u) \\ Then:y^{\prime}=\frac{u^{\prime}}{u} \\ y^{\prime}=\frac{dy}{dy} \\ u=e^{3-x^2}+9 \\ u^{\prime}=-2xe^{3-x^2} \\ y^{\prime}=\frac{u^{\prime}}{u} \\ \Rightarrow y^{\prime}=\frac{-2xe^{3-x^2}}{e^{3-x^2}+9} \\ But:y^{\prime}=\frac{dy}{dx} \\ \frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9} \\ \\ \therefore\frac{dy}{dx}=-\frac{2xe^{3-x^2}}{e^{3-x^2}+9} \end{gathered}[/tex]13-14 question gemetri 10 grade
The angle measures formed by the parallel lines are:
9. m∠10 = 69°
10. m∠6 = 115°
11. m∠7 = 118°
12. m∠11 = 108°
13. m∠14 = 66°
14. m∠12 = 86°
How to Find the Angle Measures Formed by Parallel Lines?The angle measures can be determined by using the special angle relationship between the angles involved when a transversal crosses two lines that are parallel.
9. x and y are parallel lines
m∠5 = 69°
m∠10 = m∠5 [alternate interior angles theorem]
m∠10 = 69° [substitution]
10. x and y are parallel lines
m∠9 = 115°
m∠6 = m∠9 [alternate interior angles theorem]
m∠6 = 115° [substitution]
11. x and y are parallel lines
m∠12 = 118°
m∠7 = m∠12 [alternate interior angles theorem]
m∠7 = 118° [substitution]
12. x and y are parallel lines
m∠4 + m∠11 = 180 [supplementary angles]
72 + m∠11 = 180 [substitution]
m∠11 = 180 - 72
m∠11 = 108°
13. m∠4 + m∠14 = 180 [supplementary angles]
114 + m∠14 = 180 [substitution]
m∠14 = 180 - 114
m∠14 = 66°
14. m∠5 = 86° [given]
m∠12 = m∠5 [congruent angles]
m∠12 = 86°
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suppose arya stark draws a sample of 10 observations with a mean of 50 and a population standard deviation of 4. she would like to establish a 95% confidence interval. which formula would you tell her to use?
The formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.
What is termed as the confidence interval?A confidence interval shows the likelihood that a parameter would then fall between two values near the mean.The amount of uncertainty as well as certainty inside a sampling method is measured by confidence intervals.They are also used to test hypotheses and perform regression analysis.For the given question, the data is-
Mean μ = 50Standard deviation σ = 4Confidence interval 95%Sample size n = 10.Sample mean = xThe formula for finding the 95% confidence interval is normal approximation of the distribution.
z = (x - μ)/s
Where, s = σ/√n
The corresponding value of z for 96% is taken from the z score table.
Thus, formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.
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Write the equation of the line that goes between the two points (6, -5) and (2, 3).
The equation of the line that passes through points (6, -5) and (2, 3) is y = -2x + 7.
How to determine the equation of line from two points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point 1 ( 6, -5 )
x₁ = 6y₁ = -5Point 2 ( 2,3 )
x₂ = 2y₂ = 3First, we determine the slope of the line.
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = ( 3 - (-5) ) / ( 2 - 6 )
Slope m = ( 3 + 5 ) / ( 2 - 6 )
Slope m = ( 8 ) / ( -4 )
Slope m = -2
Now that the value of slope is known, we determine the y-intercept 'b' by plugging the slope and one point into equation of line formula.
y = mx + b
-5 = (-2)(6) + b
-5 = -12 + b
b = -5 + 12
b = 7
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-2)x + 7
y = -2x + 7
Therefore, the equation of the line is y = -2x + 7.
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100 POINTS + BRAINLEIST IF CORRECT!
[tex]\huge\boxed{\sf 16}\\\\ \sf The\ two\ right\ triangles\ are\ a\ reflection\ of\ each\ other.\\ Both\ sides\ are\ equal\ in\ size. \\\\ 5x+1=4x+4\\5x-4x=4-1\\1x=3\\\\ Plug\ the\ value\ of\ x\ back\ into\ any\ of\ the\ two\ equations.\\\\ 5(3)+1 =15+1=16[/tex]
If F(n) = -n Then F(-6)= ?
Answer: 6
Step-by-step explanation:
-n plug -6 in so -(-6)=6
Answer:
boo ba loob
Step-by-step explanation:
sweating in saucy bbq sauce
-3(v + 2) - 2v simplify and use distributive property
Answer: -5v-6
Step-by-step explanation: