One angle of an isosceles trapezoid has measure 57. What are the measures of the other angles?

Answers

Answer 1

Answer: $\alpha =57^o\n \n The \ interior \ angle \ at \ the \ shortest \ base \ is \ equal \ to :\n \n \beta = 180^o - 57^o = 123^o$

Answer 2

Answer: In an isosceles trapezoid the two adj angles are equal
& the two opposite angles are equal & the
sum of the interior angles =360
so 57 + 57 = 114
360-114 = 246
the other angles are 246/2 = 123
the measure of the other angles are 57,123 & 123

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Ji and Layla played a game in which they scored 10 points for a correct answer and lost 20 points for an incorrect answer. Ji answered 7 questions correctly and 3 questions incorrectly. Layla answered 5 questions correctly and 1 question incorrectly. Who had the higher score? By how many points?

Answers

Layla had the higher score by 20 points.

Step-by-step explanation:

Given,

Points for correct answer = 10 points

Points for incorrect answer = 20 points

Loss means subtraction;

Therefore,

Total points of Ji = Correct answers*10 - Incorrect answers*20

Total points of Ji = 7*10 - 3*20

Total points of Ji = 70 - 60

Total points of Ji = 10 points

Total points of Layla = Correct answers*10 - Incorrect answers*20

Total points of Layla = 5*10 - 1*20

Total points of Layla = 50 - 20

Total points of Layla = 30 points

Difference = Points of Layla - Points of Ji

Difference = 30 - 10 = 20 points

Layla had the higher score by 20 points.

Keywords: multiplication, subtraction

Learn more about subtraction at:

#LearnwithBrainly

Simplify the following: a) ((w^-5)/(w^-9))^1/2
b) (m^6)^-2/3
c) (3x^-4y^5)/((2x^3y^-7))^-2

Answers

a. $((w^(-5))/(w^(-9) ))^{ (1)/(2) } \n ( (w^(9) )/(w^(5) ))^{ (1)/(2) } \n (w^(9-5))^{ (1)/(2) } \n (w^(4))^{ (1)/(2) } \n \sqrt{w^(4) } \n w^(2)$
b. $(m^(6))^{ (-2)/(3) } \n ((1)/(m^(6) ))^{(2)/(3) } \n \frac{ \sqrt[3]{1^(2) } }{ \sqrt[3]{m^(6) }^(2) } \n \frac{ \sqrt[3]{1} }{m^(2*2) } \n (1)/(m^(4) )$
Hope this helps!

Problem A
$((w^(-5))/(w^(-9)))^{{(1)/(2)}$ = $((w^(9))/(w^(5)))^{{(1)/(2)}$ = $(w^(4))^{{(1)/(2)}$ = $\sqrt[2]{w^(4)}$ = $w^(2)$

Problem B
$(m^(6))^{-(2)/(3)}$ = $\frac{1}{(m^(6))^{(2)/(3)}}$ = $\frac{1}{\sqrt[3]{(m^(6))^(2)}}$ = $\frac{1}{\sqrt[3]{m^(12)}}$ = $(1)/(m^(4))$

Problem C
$((3x^(-4)y^(5))/(2x^(3)y^(-7)))^(-2)$ = $((3y^(12))/(2x^(7)))^(-2)$ = $((3y^(12))^(-2))/((2x^(7))^(-2))$ = $((2x^(7))^(2))/((3y^(12))^(2-))$ = $(4x^(14))/(9y^(24))$

On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?

Answers

Answer:

89.84375

Step-by-step explanation:

Given that on a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93.

To find weighted mean.

Here weights can be considered as number of majors in each subject

$Marks x 90 85 93\nWeights 15 7 10\nProduct 1350 595 930\n$

Weighted total = 1350+595+930 = 2875

Weighted mean = weighted total/total students

$=(2875)/(32) =89.84375$

6. What type of triangle has all acute angles?

Answers

Answer:

equilateral triangle is always all acute nothing else

Answer:

Acute triangles or also called as acute-angled triangles

Solve for x under the assumption that x<0.
x-5/x<4

Answers

If you would like to solve the inequality x - 5/x < 4, you can do this using the following steps:

x - 5/x < 4
x^2 - 5 < 4x
x^2 - 4x - 5 < 0
(x - 5) * (x + 1) < 0
x < 0
1. x = 5
2. x = -1

The correct result would be x = -1.

Is the sequence geometric? If so, identify the common ratio. 6, 12, 24, 48,

Answers

Answer: Yes, the given sequence is geometric with common ration 2.

Step-by-step explanation: The given sequence is:

6, 12, 24, 48, . . ..

We are to check whether the above sequence is geometric or not. If it is geometric, we are to find the common ratio.

Geometric sequence - a sequence of numbers where each term is found by multiplying by a constant to the preceding term. This constant is called the common ratio, r.

The consecutive terms of the given sequence can be written as:

$a_1=6,\n\na_2=12,\n\na_3=24,\n\na_4=48,\n\netc.$

We can see that

$(12)/(6)=(24)/(12)=(48)/(24)=~.~.~.~=2,\n\n\Rightarrow (a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)=~.~.~.~=2,\n\n\Rightarrow a_2=2* a_1,~~a_3=2* a_2,~~a_4=2* a_3,~.~.~.etc.$

Therefore, each term is formed by multiplying 2 to the preceding term.

Thus, the given sequence is a geometric sequence with common ratio 2.

Yes
common ratio= r2/r1 or r3/r2 or r4/r3 if it is all the same then it is a geometric sequence, so the common ratio is 2 because 12/6=2, 24/12=2 and 48/24=2

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