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▹ Answer
1 - 9/7n
▹ Step-by-Step Explanation
1/7 - 3(3/7n - 2/7)
Remove the parentheses (Distribute -3 among the parentheses):
1/7 - 9/7n + 6/7
Calculate:
1 - 9/7n
Hope this helps!
CloutAnswers ❁
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Answer:
1-9/7n
Step-by-step explanation:
[tex]\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7} ) \\=\frac{1}{7}-\frac{9}{7}n +\frac{6}{7} \\=\frac{1-9n+6}{7} \\=\frac{7-9n}{7}\\=1-\frac{9}{7}n[/tex]
How do you compress this?
[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=2x\\b=3\\r+1=4\Rightarrow r=3\\n=5\\T_4=\binom{5}{3}\cdot (2x)^{5-3}\cdot3^3\\T_4=\dfrac{5!}{3!2!}\cdot 4x^2\cdot27\\T_4=\dfrac{4\cdot5}{2}\cdot 4x^2\cdot27\\\\T_4=1080x^2[/tex]
What is the approximate value of x in –2 ln (x + 1) − 3 = 7?
Answer:
x = 1/e^-5 - 1
Step-by-step explanation:
–2 ln (x + 1) − 3 = 7
–2 ln (x + 1) = 10
ln (x + 1) = –5
x + 1 = e^-5
x = e^-5 - 1
x = 1/e^-5 - 1
the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:
1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.
2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.
3. Simplify: -2 ln(x + 1) = 10.
4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.
5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.
6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.
7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.
8. Simplify: x ≈ -0.9933.
Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
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{4.OA.A.3} There are 1,492 chairs in the auditorium. Ms. Jones wants to put them into 10 rows. If she splits the chairs evenly into 10 rows, how many chairs will Ms. Jones have left over?
Answer:
2 chairs will be left over.
Step-by-step explanation:
Given that
There are a total of 1492 chairs.
which are to divided in 10 rows evenly.
To find:
Number of chairs left ?
Solution:
Let the number of chairs in each row = [tex]x[/tex]
There are 10 rows so number of chairs in rows = 10[tex]x[/tex]
Let the number of chairs left = [tex]y[/tex]
Total number of chairs =10[tex]x[/tex] + [tex]y[/tex] = 1492
The above equation is like:
Divisor [tex]\times[/tex] Quotient + Remainder = Dividend
So, we have to find the remainder in this question where we are given Divisor and Dividend.
10 [tex]\times[/tex] 149 + 2 = 1492
So, dividing 1492 with 10, we get remainder as 2.
Hence, 2 chairs will be left.
20 liters of mixture contain milk nad water in the ratio 5:3 of 4 liters of the mixture are replaced by 4 liters of milk find the new ratio of milk to water
Answer:
7:3
Step-by-step explanation:
5 + 3 = 8
The ratio is
5 milk : 3 water : 8 total
Milk is 5/8 of the total.
Water is 3/8 of the total.
The 20-liter mixture contains:
5/8 * 20 = 12.5 liters of milk, and
3/8 * 20 = 7.5 liters of water
4 liters of the mixture contain:
5/8 * 4 = 2.5 liters of milk, and
3/8 * 4 = 1.5 liter of water
When you remove 4 liters of the mixture from 20 liters of the mixture, you end up with
12.5 L - 2.5 L = 10 L milk, and
7.5 L - 1.5 L = 6 L water
Now you add 4 liters of milk. Now you have
10 L + 4 L = 14 L milk
6 L water
The new ratio of milk to water is 14:6 = 7:3
Answer
Step-by-step explanation:
sum of ratio=5+3=8
evaluate the expression for -c-12=
Answer:
-10
Step-by-step explanation:
We can substitute c into the equation as -2.
[tex]-(-2) - 12[/tex]
Two negatives make a positive:
[tex]2-12[/tex]
And [tex]2 - 12 = -10[/tex].
Hope this helped!
I need help with this question.
Answer:
Complement = 15 Degrees
Supplement = 105 Degrees
Step-by-step explanation:
The complement of an angle refers to the measure that will make the angle 90 degrees. So, the complement of 75 would be 15, since 90 - 75 = 15.
The supplement of an angle refers to the measure that will make the angle 180 degrees. So, the supplement of 75 would be 105, since 180-75 = 105.
Cheers.
Write an equation perpendicular to the line y=3/2x-2 that goes through (-4,3)
Answer: y=-2/3x-2/3
Step-by-step explanation:
concept to know: two lines that are perpendicular has opposite reciprocal slopes.
y=-2/3x+b
in order to find b or the y-intercept, we need to plug in a point
3=-2/3(-4)+b
3=8/3+b
b=-2/3
y=-2/3x-2/3
Hope this helps!! :)
The circumference of the circle shown below is 75 inches. Which expression
gives the length in inches of DE?
D
A.
. 75
72
O B.
360
75
O C.
361
. 75
O D.
360
75%
Answer:
B. 360 .75
Step-by-step explanation:
The circumference of the circle is represented by π * diameter of the circle. The circumference of the circle is its perimeter. The circumference is arc length of the circle. The perimeter is curve length around the figure of the circle. The circumference of the circle of 75 inches is represented by 75/360.
Answer: 72/360 multiply by 75
Step-by-step explanation:
i just did this question
F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23
Answer:
∠ H ≈ 23°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus
∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )
Consider the distribution of exam scores graded 0 from 100, for 79 students. When 37 students got an A, 24 students got a B and 18 students got a C. How many peaks would you expect for distribution?
Answer:
Three
Step-by-step explanation:
Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores
I need help with the following question
Answer:
a. 2
b. x²+10x+26
c. x²+2x+2
Step-by-step explanation:
To find each value, you plug in the x value into the function and solve.
a. 2
f(2)=(2)²-2(2)+2 [combine like terms]
f(2)=4-4+2
f(2)=2
---------------------------------------------------------------------------------------------------------
b. x²+10x+26
f(x+6)=(x+6)²-2(x+6)+2 [use FOIL method and distributive property]
f(x+6)=x²+12x+36-2x-12+2 [combine like terms]
f(x+6)=x²+10x+26
---------------------------------------------------------------------------------------------------------
c. x²+2x+2
f(-x)=(-x)²-2(-x)+2 [combine like terms]
f(-x)=x²+2x+2
Do phone surveys provide adequate coverage of households with respect to one particular parameter? The parameter is the proportion of households without children. If telephone surveys provide adequate coverage of households, then p , the proportion of households without children in the set of all future samples reached by phone, must be equal to the proportion of households without children in the population of all households. Suppose that Thomas, a market analyst, contacts a simple random sample of 300 households as part of a national telephone survey. Of the households contacted, 129 households, or 43 %, have no children and 57 % have at least one child. The most recent census indicates that 48 % of all households have no children and 52 % have at least one child.
Complete Question
The complete question is shown on the first uploaded image
Answer:
Based on the result of his test , Thomas should fail to reject null hypothesis at a significance level of 0.01. Thomas sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.
Step-by-step explanation:
From the question we see that the p-value is greater than the level of significance (0.01 )so we fail to reject the null hypothesis.
This means that Thomas has sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.
Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 8$, $BC = 4$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp \overline{AB}$, and $PB = 17$, then what is the volume of $PABCD$?
Answer:
181.33Step-by-step explanation:
Since the base of the pyramid PABCD is a rectangle, the shape in question is a rectangular based pyramid. Volume of a rectangular based pyramid is expressed as V = 1/3 * Base Area * Height of the pyramid.
Given a rectangle ABCD with AB = 8 and BC = 4, the area of the rectangle will be equivalent to the base area of the pyramid.
Base Area = Length * Breadth
Base Area = AB * BC
Base Area = 8*4 = 32
If [tex]\overline{PA}\perp \overline{AD}\ and \ \overline{PA}\perp \overline{AB}[/tex], and PB = 17, then the height of the pyramid is PB = 17.
Volume of the pyramid = 1/3 * 32 * 17
Volume of the pyramid = 1/3 * 544
Volume of the rectangular based pyramid = 181.33
a shopping center form 300000 square feet to an excess of 1 million square feer that consists mostly of large national chain stores is called a
Answer: Honeymoon2871
Step-by-step explanation:
square root of 49/64 answered as a fraction
Answer:
Hey there!
That would be 7/8
Let me know if this helps :)
1. Hypothesis Test. Gender bias researchers compared the promotion rate of 412 women in manufacturing management positions to the national average which was known to be 75 months for a mostly male population. They measured the number of months each woman worked in middle management. Given a 0.01 level of significance, the correct statistical conclusion is to reject the null.
A. True
B. False
2. Hypothesis Test. Gender bias researchers compared the promotion rate of 412 women in manufacturing management positions to the national average which was known to be 75 months for a mostly male population. They measured the number of months each woman worked in middle management before being promoted to senior management, and found an average 79 months (s.d. = 19). Researchers want to know if women are promoted more slowly (i.e. after a larger number of months). What is the correct research conclusion?
A. Evidence suggests there is no difference in promotion rates.
B. Evidence suggests a small difference in promotion rates favoring males.
C. Evidence suggests a large difference in promotion rates favoring males.
D. No way to tell.
Answer:
1. B. False
2. B. Evidence suggests a small difference in promotion rates favoring males.
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
The time it takes to install a certain hardware is random. A technician installs this hardware on 64 computers with the average installation time being 42 minutes and the standard deviation of the times being 5 minutes. What is a 90% confidence interval for the popu
Answer:
[tex]40.97<\mu<43.03[/tex]
Step-by-step explanation:
Th formula for calculating the confidence interval of a population is expressed as shown;
CI = xbar ± Z*S/√n where;
xbar is the mean or average sample
Z is the z-score at 90% confidence
S is the standard deviation
n is the sample size
Given parameters
xbar = 42
Z at 90% CI = 1.645
S = 5
n = 64
Substituting the values into the formula will give;
CI = 42±(1.645*5/√64)
CI = 42±(1.645*5/8)
CI = 42±(1.645*0.625)
CI = 42±1.028125
CI = (42-1.028125, 42+1.028125)
CI = (40.971875, 43.028125)
Hence the 90% confidence interval for the population is approximately (40.97, 43.03) i.e [tex]40.97<\mu<43.03[/tex]
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
a) What is the cost of a chicken shawarma wrap?
$10.99
b) What is the cost of one order of spiced potatoes?
$4.99
c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
Step-by-step explanation:
Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,
Cost of a chicken sharwarma wrap = x
Cost of an order of spiced potatoes = y
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
Hence, the Equations needed to solve the question is:
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
We use Elimination method to solve for this.
Multiply Equation 1 by coefficient of x in Equation 2
Equation 2 by coefficient of x in Equation 1
3x + 2y = $42.95 .............Equation 1 × 5
5x + 4y = $74.91 ................Equation 2 × 3
15x + 10y = 214.75..............Equation 3
15x + 12y = 224.73..............Equation 4
Subtract Equation 3 from Equation 4
2y = 9.98
y = 9.98/2
y = 4.99
Therefore, y = Cost of an order of spiced potatoes = $4.99
Subtitute 4.99 for y in Equation 1
3x + 2y = $42.95 .............Equation 1
3x +2(4.99) = 42.95
3x + 9.98 = 42.95
3x = 42.95 - 9.98
3x = 32.97
x = 32.97/3
x = 10.99
x = Cost of a chicken sharwarma wrap = $10.99
Therefore,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
Allison bought jelly beans to share with her friends. She bought pounds of blueberry jelly beans and pounds of lemon jelly beans. If she gave pounds of jelly beans away to her friends, how many pounds of jelly beans does Allison have left?
Answer: [tex]1\dfrac{11}{12}\text{ pounds}[/tex]
Step-by-step explanation:
The complete question is provided in the attachment.
Given, Amount blueberry jelly beans= [tex]1\dfrac{1}{4}[/tex] pounds
[tex]=\dfrac{5}{4}[/tex] pounds.
Amount lemon jelly beans = [tex]2\dfrac{1}{3}[/tex]pounds
[tex]=\dfrac{7}{2}[/tex] pounds
Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans
[tex]=(\dfrac{5}{4}+\dfrac{7}{3})[/tex] pounds
[tex]=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}[/tex]
Amount of jelly beans she gave away = [tex]1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}[/tex]
Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away
=[tex]\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}[/tex]
She has left [tex]1\dfrac{11}{12}\text{ pounds}[/tex] of jelly beans.
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
Answer:the mean is greater than the median
Step-by-step explanation:
The mean is less than the median. Then the correct option is A.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
Half the students scored 87.
The next highest score is 71.
Then the median will be
(71+ 87) / 2 = 79
A few students scored 52, so the mean is slightly lower than the mean of 71 and 87.
Thus, the mean is less than the median.
Then the correct option is A.
The missing options are given below.
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
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Help me please thank you
Answer:
x = 7
Step-by-step explanation:
The angles are alternate interior angles, so for the lines to be parallel, the angle measures must be equal.
7x - 7 = 4x + 14
3x = 21
x = 7
The first side of a triangle measures 3 in. less than the second side, the third side is 2 in. more than the first side, and the perimeter is 20 in. Set up an equation that relates the sides of the triangles in terms of the perimeter of the triangle.
Answer:
P = 3x - 4
Step-by-step explanation:
Side 1 = x - 3
Side 2 = x
Side 3 = 2 + (Side 1) = 2 + x - 3 = x - 1
Perimeter = 20 in
Perimeter = Side 1 + Side 2 + Side 3
Perimeter = (x - 3) + (x) + (x - 1)
Perimeter = x - 3 + x + x - 1
Perimeter = 3x - 3 - 1
Perimeter = 3x - 3 - 1
Perimeter = 3x - 4
P = 3x - 4
How much work is done in lifting a 1.4-kg book off the floor to put it on a desk that is 0.7 m high?
Use the fact that the acceleration due to gravity is g = 9.8 m/s^2. How much work is done in lifting a 21-lb weight 6 ft off the ground?
Answer:
Step-by-step explanation:
Work is said to be done when a force applied to an object cause the body to move in a specified direction.
Work-done = Force * Distance
Since Force = mass * acceleration due to gravity
Work-done = mass * acceleration due to gravity * distance
Given mass = 1.4kg, distance = 0.7m and g = 9.8m/s²
Workdone in lifting the book off the floor = 1.4*0.7*9.8
Workdone = 9.604Joules
- Similarly, work done in lifting a 21-lb weight book 6 ft off the ground is expressed using the same formula as above;
Given mass = 21-lb, g = 32ft/s² and distance = 6ft
Workdone = 21 * 32 * 6
Workdone = 4,032 lb-ft²/s²
Hence, work-done in lifting a 21-lb weight book 6 ft off the ground is 4,032 lb-ft²/s²
convert 407 in base 8 to decimal
[tex]4\cdot8^2+0\cdot8^1+7\cdot8^0=256+7=263[/tex]
[tex]407_8=263_{10}[/tex]
Answer the question :)
Answer:
A. -11
Step-by-step explanation:
In the function, replace x with -2
R(x) = x^2 - 3x - 1 ➡ R(-2) = (-2)^2 - 3 × 2 -1 = -11
Which statement best describes what Rutherford concluded from the motion of the particles?
Answer:
some particle traveled through empty spaces between atoms and some particles were deflected by electrons
Step-by-step explanation:
The motion of particles will be
some particle traveled through empty spaces between atoms and some particles were deflected by electrons.
What was Rutherford Experiment?The vast majority of the alpha particles simply passed through the gold foil.Some of the alpha particles had a slight angle of deflection.Only a tiny fraction of the alpha particles rebounded.So, the observation made the stamement
He came to the conclusion that the majority of space in an atom was unoccupied since there was very little alpha particle deflection.The fact that very few particles were diverted from their course led him to the further conclusion that positive charge takes up very little space in an atom.Then, motion of particles will be
some particle traveled through empty spaces between atoms and some particles were deflected by electrons.
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A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 307 persons, the following data was compiled. Can we conclude that brand perception is dependent on age?
Age Favorable Unfavorable Neutral Total
18-30 67 24 20 111
30-45 50 14 16 80
Over 45 69 41 26 116
Total 186 59 62 307
Find the value of the test statistic.
Answer:
The value for the Chi -square test statistics = 1.149
Step-by-step explanation:
The observed value Table can be shown better as:
Observed Value
Age Favorable Unfavorable Neutral Total
18-30 67 24 20 111
30-45 50 14 16 80
Over 45 69 21 26 116
Total 186 59 62 307
NOTE: when computing the question, in the third row and the second column, there is a mistake , the value is supposed to be 21 and not 41 because :
69 +21+ 26 will eventually give = 116
69 + 41 + 26 = 136
With that error being fix , let's get started.
Expected Value
The expected value can be determined by using the formula:
[tex]Expected \ Value = \dfrac{ row \ total \times column \ total }{grand \ total }[/tex]
For 67; (111 * 186)/307 = 67.251
For 24 : (111 * 59)/307 = 21.332
For 20 : (111 * 62)/307 = 22.417
For 50 :(80*186)/307 = 48.469
For 14 : (80* 59)/307 = 15.375
For 16 : ( 0 * 62)/307 = 16.156
For 69 : (116 * 186)/307 = 70.280
For 21 : (116* 59)/307 = 22.293
For 26 : (116*62)/307 = 23.427
Expected Value :
Age Favorable Unfavorable Neutral Total
18-30 67.251 21.332 22.417 111
30-45 48.469 15.375 16.156 80
Over 45 70.280 22.293 23.427 116
Total 186 59 62 307
The Chi - square test statistics = [tex]\dfrac{(observed \ value - Expected \ value)^2}{Expected \ value}[/tex]
For 67.251 : ( 67 - 67.251)²/67.251 = 0.0009
For 21.332 : ( 24 - 21.332)²/21.332 = 0.3337
For 22.417 : ( 20 - 22.417)²/ 22.417 = 0.2606
For 48.469 : ( 50 - 48.469)²/ 48.469 = 0.0484
For 15.375 : ( 14 - 15.375)²/ 15.375 = 0.1230
For 16.156 : ( 16 - 16.156)²/ 16.156 = 0.0015
For 70.280 : ( 69 - 70.280)²/ 70.280 = 0.0233
For 22.293 : ( 21 - 22.293)²/ 22.293 = 0.0750
For 23.427 : ( 26 - 23.427)²/ 23.427 = 0.2826
The chi square table is as follows:
Age Favorable Unfavorable Neutral Total
18-30 0.0009 0.3337 0.2606 0.5952
30-45 0.0484 0.1230 0.0015 0.1729
Over 45 0.0233 0.0750 0.2826 0.3809
Total 0.0726 0.5317 0.5447 1.149
The value for the Chi -square test statistics = 1.149
Solve the following equations
x-1=6/x
[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]
Answer 9 and 11 with explanation on how you solved it.
Answer:
(9). Range; {8, 5, 2, -1, -4}
(10). Range; {-15, -7, 1, 9, 17}
Step-by-step explanation:
Domain of a function is (x-values) determined by the input values and Range of a function is determined by the (y-values) output values of the function.
(9). For the given function,
f(x) = -3x + 2
If the Domain of this function is a set of values,
{-2, -1, 0, 1, 2}
For Range,
x -2 -1 0 1 2
f(x) 8 5 2 -1 -4
Therefore, Range of the function 'f' will be; {8, 5, 2, -1, -4}
(11). f(x) = 4x + 1
Domain is {-4, -2, 0, 2, 4}
Table for input-output values will be,
x -4 -2 0 2 4
f(x) -15 -7 1 9 17
Therefore, Range of the function will be {-15, -7, 1, 9, 17}
in the diagram, find the values of a and b.
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
