Exterior Angle Inequality Theorem
\( \normalsize\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}\)
Direction:
Use the Exterior Angle Inequality Theorem to find the measure of each angle below.
Answer:
\( \huge \underline{\boxed{\sf \red{ \angle C = 27^{\circ} }}}\)
\( \huge \underline{\boxed{\sf \red{ \angle D = 153^{\circ} }}}\)
Solution:
Add the ∠A and ∠B and minus it to 180° to know the measure of ∠C. To find the ∠D add only the ∠A and ∠B.
Finding ∠C
\(\large\tt{{180}^{\circ} = \angle A + \angle B + \angle C}\)
\(\large\tt{{180}^{\circ} = {35}^{\circ} + {118}^{\circ} + \angle C }\)
\(\large\tt{{180}^{\circ} = {153}^{\circ} + \angle C }\)
\(\large\tt{{180}^{\circ} - {153}^{\circ} = \angle C }\)
\(\large\tt{{27}^{\circ} = \angle C }\)
\(\large{\boxed{\tt{\angle C = {27}^{\circ}}} }\)
Finding ∠D or ∠ACD
\(\large\tt{ \angle A + \angle B = \angle ACD }\)
\(\large\tt{ {35}^{\circ} + {118}^{\circ} = \angle ACD }\)
\(\large\tt{ {153}^{\circ} = \angle ACD }\)
\(\large{\boxed{\tt{\angle ACD = {153}^{\circ} }}}\)
\( \normalsize\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}\)
\( \\ \)
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An investment portfolio is shown below.
Investment Amount Invested ROR
Money Market Account $3,200 2.1%
Government Bond $1,750 4.4%
Preferred Stock $1,235 −7.8%
Common Stock $2,300 10.5%
Using technology, calculate the difference between the arithmetic average ROR and the weighted average ROR. Round to the nearest tenth of a percent.
0.5%
1.1%
2.3%
3.5%
Using technology, the difference between the arithmetic average ROR and the weighted average ROR is 0.52%
What is arithmetic mean?The Arithmetic Mean will be called the Simple Arithmetic Mean when it is calculated as the quotient between the sum of all the different related values and the number of observations involved in this sum.
Given An investment portfolio
Since arithmetic average ROR:
The average arithmetic average ROR is the sum of the rate of returns divided by the number of investments arithmetic average:
ROR = (2.1%+ 4.4%+ 7.8% + 0.5%)/4
arithmetic average ROR=6.20%
total amount invested=$3200+$1750+$1235+$2,300
total amount invested=$8,485
weighted average:
ROR = (3200/8485 * 2.1%+ 1750/8485 * 4.4%+ 1235/8485 *7.8% + 2300/8485 *0.5%)
weighted average:
ROR=5.68%
difference=6.20%-5.68%
difference=0.52%
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Answer: it’s 1.1%
Step-by-step explanation: just got it right on the test
Find the domain of the rational expression: 6-x/4x+20
The domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.
To find the domain of a rational expression, we need to identify any values of x that would result in division by zero. Division by zero is undefined in mathematics
In this case, we need to set the denominator, 4x+20, equal to zero and solve for x:
4x + 20 = 0
Subtract 20 from both sides:
4x = -20
Divide both sides by 4:
x = -5
Therefore, the value x = -5 makes the denominator zero.
Now, we need to consider the values of x for which the denominator is not zero. Since the denominator is a linear expression (a polynomial of degree 1), it is defined for all real numbers except x = -5.
So, the domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.
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Select the correct answer.
Which statement correctly compares the graph of function g with the graph of function ??
FE) = e²-
g(x) = ² - 4
O A.
OB.
O C.
O D.
The graph of function g is a horizontal shift of the graph of function to the right.
The graph of function g is a vertical stretch of the graph of function f.
The graph of function g is a vertical compression of the graph of function f.
The graph of function g is a horizontal shift of the graph of function f to the left.
Reset
Next
A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.
Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.
When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;
g(x) = kf(x)
g(x) = 1/2f(x)
\(g(x) = \frac{1}{2} e^x -4\)
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A bank manager wants to encourage new customers to open accounts with principals of at least $3500. He decides to make a poster advertising a simple interest rate of 3%. What must the principal be if the bank manager also wants to advertise that one can earn $10 the first month?
The principal if the bank manager also wants to advertise that one can earn $10 the first month is $4000.
How to calculate the principal?From the information, the simple interest is $10 and the rate is illustrated as 3%.
The formula for the simple interest in a month is illustrated as:
S = (p × r × t/12 / 100)
r = rate
t = time
S = interest
Place the values in the formula:
10 = p × 3 × 1 / 100 × 12
10 = 3p/1200
Cross multiply
3p = 12000
Divide
p = 12000/3
p = 4000
The principal is $4000.
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The temperature T(d) in degrees Fahrenheit in terms of the Celsius temperature d is given by T(d) = 9/5 * d + 32
The temperature C(v) degrees Celsius in terms of the Kelvin temperature by C(v) = v - 273
Write a formula for the temperature F(v) in degrees Fahrenheit in terms of the Kelvin temperature
It is not necessary to simplify
Answer:
\(\displaystyle F(v) = \frac{9}{5}(v-273)+32\)
Step-by-step explanation:
The temperature T(d) in degrees Fahrenheit in terms of Celsius d is given by:
\(\displaystyle T(d)=\frac{9}{5}d+32\)
And the temperature C(v) in degrees Celsius in terms of Kelvin v is given by:
\(C(v)=v-273\)
We want the formula for the temperature F(v) in degrees Fahrenheit in terms of the Kelvin temperature.
So, we can use a composition of functions. Since T(d) outputs the temperature in Fahrenheit and C(v) inputs the temperature in Kelvin, T(C(v)) will be the temperature in Fahrenheit given the temperature in Kelvin. So:
\(\displaystyle T(C(v))=\frac{9}{5}(C(v)))+32\)
Substitute:
\(\displaystyle T(C(v)) = F(v) = \frac{9}{5}(v-273)+32\)
Therefore:
\(\displaystyle F(v) = \frac{9}{5}(v-273)+32\)
Which angle is an adjacent interior angle?
Los puntos A(13, a) y B (4,b) pertenecen a una parábola de vértice V (h, 1) Además el eje focal es paralelo al eje de las abscisas ,su parámetro es p y A, B están
contenidos en la recta 2x - y - 13 = 0. Hallar a" + bP.
The points on a parabola with the focal axis parallel to the abscissa axis, of parameter p and A, B is -12.
How to calculate parameters?Since A and B are points on the parabola, write two equations using the general form of the parabolic equation:
(x - h)² = 4p(y - 1)
The focal axis is parallel to the x-axis, so the distance from the vertex to the focus is equal to p. Therefore, use the distance formula to write an equation for the distance between the vertex and point A:
√((13 - h)² + (a - 1)²) = p
Similarly, write an equation for the distance between the vertex and point B:
√((4 - h)² + (b - 1)²) = p
A and B lie on the line 2x - y - 13 = 0, so substitute the x and y coordinates of A and B into this equation and solve for a and b:
2(13) - a - 13 = 0
2(4) - b - 13 = 0
Solving these equations gives us a = 3 and b = -5.
Now three equations and three unknowns (a, b, and h):
√((13 - h)² + 4) = p + 1
√((4 - h)² + 36) = p + 1
2h - 3 - 13 = 0
The third equation simplifies to 2h = 16, or h = 8.
Substituting this value of h into the first two equations and squaring both sides:
(13 - 8)² + 4 = (p + 1)²
(4 - 8)² + 36 = (p + 1)²
Simplifying these equations and solving for p gives us p = 3.
Finally, find a" + bP by substituting the values found for a, b, and p:
a" + bP = 3 + (-5)(3) = -12
Therefore, the solution is a" + bP = -12.
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i need help with this
3:7 = ___: 49
Answer:
3 : 7 = 21 : 49
Step-by-step explanation:
i need help with this
3:7 = ___: 49
3 : 7 = x : 49
x = 3 × 49 ÷ 7
x = 147 ÷ 7
x = 21
3 : 7 = 21 : 49 (your answer)
which would be the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! where: if n
The base case in a recursive solution to the problem of finding the factorial of a number is n = 0 .
Given :
the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! .
Base case :
The base case is the condition to stop the recursion. The recursive case is the part where the function calls on itself .
we know that ,
def func ( n ) :
if n == 0 :
return 1
Here the base case is clearly n = 0
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Considering only the factors of the form x - k, what is the relationship between the k values and the zeros?
Given:
Considering only the factors of the form x - k.
To find:
The relationship between the k values and the zeros?
Solution:
We know that, if (x-c) is a factor of a function f(x), then x=c is a zero of function f(x), i.e., f(c)=0, where, c is a constant.
It is given that, only the factors of the form x - k. Then by using the above theorem we can say that, k values are the zeros of the function.
The relationship between the k values and the zeros is defined as
k values = Zeros of the function
Therefore, the k values are to zeros of the function.
dont answer.m.........
Answer:
why not. I JUST GOT 41 POINTSSSSS
Step-by-step explanation:
Answer:
crusty
Step-by-step explanation:
Question 1-2
What is the value of a³ + b (6 + c), when a = 2, b = 3, and c = 4?
Answer:
\(\huge\boxed{\sf 38}\)
Step-by-step explanation:
Given expression:= a³ + b (6 + c)
Put a = 2, b = 3 and c = 4
= (2)³ + 3 (6 + 4)
= 8 + 3(10)
= 8 + 30
= 38\(\rule[225]{225}{2}\)
Answer:
Step-by-step explanation:
the requied answer is 38.
according to the question the value of a=2,b=3,c=4.
here,
to find the value of a³ + b (6 + c)we have to do it in steps:
step 1: solve the bracket (6+4) =10.
step 2: solve the value of a³ =8.
now put these values ,
=8+3(10)
=38.
Zayn and Attia are thinking of a number each. What is Attia's number? My number is greater than 2. 12 and 20 are multiples of my number. My number is the 11th multiple of Zayn's number.
Answer:
Me: 60
Zayn and Attia: 6
Step-by-step explanation:
12 = 2 × 2 × 3
20 = 2 × 2 × 5
LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60
My number is 60.
Zayn's and Attia's numbers are 6.
Find the mystery number from the following clues
It is a 2-digit number
It is a factor of 48
It is a multiple of 6
The sum of the digits is 3
Based on the given clues, the mystery number is 12.
Let's analyze the clues given to find the mystery number:
It is a 2-digit number: This means the number is greater than or equal to 10 and less than 100.
It is a factor of 48: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
It is a multiple of 6: The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, and so on.
The sum of the digits is 3: From the clues, we know that the mystery number is a 2-digit number, so let's consider the possible numbers where the sum of the digits is 3:
12 (1 + 2 = 3)
21 (2 + 1 = 3)
Now let's check which of these numbers satisfy the first three clues:
12: This number is a factor of 48 (48 ÷ 12 = 4) and it is a multiple of 6 (12 ÷ 6 = 2). The sum of the digits is 3. Therefore, 12 satisfies all the clues.
21: This number is not a factor of 48 (48 ÷ 21 ≈ 2.29), so it doesn't satisfy the second clue.
Based on the given clues, the mystery number is 12.
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Rick Rich owns a Mercedes dealership. Mercedes has 5 models, 4 standard options packages, and 5 colors. If Rick wants to immediately be able to deliver any car (model, option package, color), how many cars must Rick have on hand?
Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).
To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.
With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.
Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.
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Write an equation for the function graphed below
The rational function graphed in this problem is defined as follows:
y = -2(x - 1)/(x² - x - 2).
How to define the rational function?The vertical asymptotes of the rational function for this problem are given as follows:
x = -1 and x = 2.
Hence the denominator of the function is given as follows:
(x + 1)(x - 2) = x² - x - 2.
The intercept of the function is given as follows:
x = 1.
Hence the numerator of the function is given as follows:
a(x - 1)
In which a is the leading coefficient.
Hence:
y = a(x - 1)/(x² - x - 2).
When x = 0, y = -1, hence the leading coefficient a is obtained as follows:
-1 = a/2
a = -2.
Thus the function is given as follows:
y = -2(x - 1)/(x² - x - 2).
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*I need this done badly* George has a box of marbles. Each marble weighs the same amount. When George places 37 marbles on a scale, the total weight is 148 grams. Which equation models the weight (In grams) ,w, of m marbles? -- A. W = 0.25m B. W = 0.75m C. W = 4m D. W = 4.5m
Answer:
w = 4m
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
C because 148/37= 4. This means 1 marble weighs 4 grams.
W = 4m
Hope This Helped!
We have the number of emergency room admissions to SWTRHA hospital on 6 different Friday the 13ths along with the number of admissions to the same hospital on the previous Friday the 6th. Is there any difference between admissions on the 6th and the 13th. Conduct a depedent samples t-test to find out. What is the value of your t Stat
Answer:
Test statistic = - 2.71
Step-by-step explanation:
Table of the sample data is attached below :
Using a dependent sample t test :
H0 : μd = 0
H0 : μd ≠ 0
The difference in the 6th and 13th date data is :
Difference, d = -4, -6, -3, -1, 1, -7
The sample size, n = 6
The mean of d ; μd = Σd/ n = - 3.667
Standard deviation of difference, Sd = 3.011
The test statistic : μd/(Sd/√n)
Test statistic = - 3.33 / (3.011/√6)
Test statistic = - 3.33 / 1.2292356
Test statistic = - 2.709
Test statistic = - 2.71
Find the value of x. Round your answer to two decimal places
The value of the side x is equal to 64.77 the to two decimal place using the trigonometric ratios of tangent.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
tan 63° = x/33 {opposite/adjacent}
x = 33 × tan 63° {cross multiplication}
x = 64.7661
Therefore, the value of the side x is equal to 64.77 the to two decimal place using the trigonometric ratios of tangent.
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I need help with this practice, read below then read the picture Amy found 6 species in her backyard, she wrote down the names of the species and how many she found for each;Ruby throated hummingbird / 9 individuals Blue jay / 6 individuals Dandelions / 43 individuals Chipmunk / 3 individuals Cooper’s hawk / 3 individuals Red bellied woodpecker / 2 individuals
ANSWER
Biodiversity index = 0.091
EXPLANATION
Given a total number of 6 species with their individual numbers
Biodiversity index is:
\(\text{ }\frac{Total\text{ number of species }}{Total\text{ number of individual in the area}}\)i.e:
\(\begin{gathered} Biodiversity\text{ index = }\frac{6}{9+6+43+3+3+2} \\ \text{ = }\frac{6}{66} \\ \text{ = 0.09090} \end{gathered}\)Hence, the Biodiversity index of Amy's backyard is 0.091. This indicates a low biodiversity since it's closer to 0.
Rewrite 1.18 as a fraction in lowest terms
A. 1 18/100
B. 1 5/9
C. 1 10/18
D. 1 9/50
D) 1 9/50
Step-by-step explanation:Hi !
1.18 = 118/100 = 1 18⁽²/100 = 1 9/50
Good luck !
1.18 can be rewritten as a fraction in lowest terms as
D. 1 9/50
How to rewrite 1.18 as a fraction in lowest term?1. Write the number as a fraction with a denominator of 100:
1.18 = 118/100
2. Simplify the fraction by dividing the numerator and denominator by the greatest common factor:
The greatest common factor of 118 and 100 is 2.
3. Dividing both the numerator and denominator by 2 gives:
118/100 = 59/50
4. Write 59/50 as improper fraction:
118/100 = 59/50 = 1 9/50
Therefore, 1.18 can be rewritten as 1 9/50 in lowest terms.
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A teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!
Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.
What is the highest common factor?The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.
We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.
We can see that the highest common factor is 18.
When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2. When you divide 72 by 18, the result is 4.
The number of lined paper = 54 pieces
The number of grid paper = 36 pieces
The number of dividers = 72 dividers
The common factors of 54, 36, and 72 are 2, 9, and 18.
The highest common factor of 54, 36, and 72 is 18.
Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.
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find the slope and y-intercept.
The slope and the y-intercept of the line y = 4x + 5 are given as follows:
Slope of 4.y-intercept of 4.How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.The function for this problem is given as follows:
y = 4x + 5.
Hence the slope and the intercept are given as follows:
m = 4.b = 5.Missing InformationThe problem asks for the slope and the intercept of y = 4x + 5.
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AL'S hat shop bought a hat for $95. Al wants to markup the hat by 55% of the selling price. What should the selling price of the hat be?
Answer:
$147.25
Step-by-step explanation:
The hat shop wants to markup the hat that they bought for $95 by 55%.
This means that they want to increase the price by 1.55 of 95.
Multiply 95 by 1.55 to calculate the 55% increase of the hat.
$95 * 1.55 = $147.25The selling price of the hat should be $147.25.
f(1)=0
f(n)=f(n−1)+2
Answer: f(n) = 2n - 2
Therefore, we can use this formula to find the value of f(n) for any positive integer n.
Step-by-step explanation: Using the given recursive formula:
f(1) = 0
f(n) = f(n-1) + 2
We can find the values of f(n) for different values of n:
f(1) = 0
f(2) = f(1) + 2 = 0 + 2 = 2
f(3) = f(2) + 2 = 2 + 2 = 4
f(4) = f(3) + 2 = 4 + 2 = 6
f(5) = f(4) + 2 = 6 + 2 = 8
And so on.
We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:
f(n) = 2n - 2
Therefore, we can use this formula to find the value of f(n) for any positive integer n.
Question 2: Sarah is fencing a vegetable garden to keep rabbits out. The hardware store sells
fencing for $25.50/m. Her family has $165 to spend. What dimensions should Sarah use to build a
garden with the greatest area? Round all answers to 2 decimal places.
Answer:
circle with circumference of 6.47m
Step-by-step explanation:
1. $165/$25.50=6.47058823529m
2. she should use a circle because they have the greatest area, the circle should have a circumference of 6.47m.
Yoga Common Core Performance Assessment_ Regina takes yoga classes 2 days a week at the community center. The cost for the classes is $72, and Regina pays an additional one-time fee of $12 to rent the yoga equipment used in class. The classes run for 6 weeks. The local gym offers the same yoga program, including equipment, for $8 a class. Is Regina paying more or less than what the local gym charges for yoga classes?
On solving the provided question, we can say that - by the help of unitary method the value of 9 units will be
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
cost for the 12 classes = $72
cost of 1 unit = $6
cost of 9 units = $54
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[Probability / Statistics) Twenty families were surveyed. How many have boys only?
Answer:
5
Step-by-step explanation:
We start by seeing how many families we have in total, which is 20. We then must subtract the number of families with girls only, the number of families with both boys and girls, and the number of families with no children. 20 - 7 is 13, then 13 - 8 is 5, and 5 - 0 is 5.
Give the slope between the points
(-2,4) (-8, 13)
Answer
Answer:
9/-6
Step-by-step explanation:
when you subtract (x2-x1) and (y2-y1) this is the answer you get.
\(-\frac{3}{2}\)
Step-by-step explanation:Use the point slope formula
\(Slope = m = \frac{y_2-y_1}{x_2-x_1} = \frac{13-4}{-2-(-8)} = \frac{9}{6} = \frac{9}{6} = \frac{3}{2}\)
This is the difference between two points with the rise (change in y) over the run (change in x)
Sorry it took so long for so little my girlfriend was distracting me
Hope this helps :)
please help in this grade 7 percentage question im desperate
Answer:
See below
Step-by-step explanation:
320 x .1 = 32
320 + 32 = 352
352 x .5 = 176
352 + 176 = 528
320 x .65 = 208
320 + 208 = 528