Mathematics High School

can anyone help me answer this?!?!

Answers

Answer 1

Answer:

if ∠PQR ≅ ∠STU, then ∠STU ≅ ∠PQR

We conclude that 'Symmetric Property of Angle Congruence' illustrates this statement.

Step-by-step explanation:

We know that the Symmetric Property of Angle Congruence can be defined as

For any angles X and Y, if ∠X≅∠Y , then ∠Y≅∠X

For example, Let suppose

m∠X = 20m∠Y = 20

As ∠X≅∠Y i.e. 20 ≅ 20

then

∠Y≅∠X i.e. 20 ≅ 20

Given

if ∠PQR ≅ ∠STU, then ∠STU ≅ ∠PQR

Thus, we conclude from the above discussion that 'Symmetric Property of Angle Congruence' illustrates this statement.

Related Questions

Prove that: (Sec A- cosec A)(1+ tan A+cot A) = tan A× sec A - cot A × cosec A

Answers

Answer:

Step-by-step explanation:

[tex](sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA[/tex]

we take the LHS so here goes,

[tex](sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA\\(\frac{1}{cosA} -\frac{1}{sinA})(1+\frac{sinA}{cosA}+\frac{cosA}{sinA})\\\\(\frac{sinA-cosA}{sinAcosA})(\frac{sinAcosA+sin^2A+cos^2A}{sinAcosA})\\[/tex]

since , [tex]sin^2A+cos^2A=1[/tex]

the identity becomes,

[tex](\frac{sinA-cosA}{sinAcosA})(\frac{1+sinAcosA}{sinAcosA})\\\\(\frac{sinA+sin^2AcosA-cosA-cos^2AsinA}{sin^2Acos^2A})\\\\[/tex]

now, we know,

[tex]sin^2A=1-cos^2A[/tex] and [tex]cos^2A=1-sin^2A[/tex]

the identity becomes,

[tex](\frac{sinA+(1-cos^2A)cosA-cosA-(1-sin^2A)sinA}{sin^2Acos^2A} )\\\\[/tex]

[tex](\frac{sinA+cosA-cos^3A-cosA-sinA+sin^3A}{sin^2Acos^2A})[/tex]

sin A and cos A cancel out it becomes zero

[tex]\frac{sin^3A-cos^3A}{sin^2Acos^2A} \\\\[/tex]

Splitting the denominator the identity becomes

[tex]\frac{sin^3A}{sin^2Acos^2A}-\frac{cos^3A}{sin^2Acos^2A} \\\\\frac{sinA}{cos^2A} - \frac{cosA}{sin^2A} \\\\\frac{sinA}{cosA}(\frac{1}{cosA})-\frac{cosA}{sinA}(\frac{1}{sinA})\\\\[/tex]

Hence,

[tex]tanAsecA-cotAcosecA[/tex]

Help me please I'm so stuck lol 15 pts.!!

Answers

Answer:

r = 0.1

Step-by-step explanation:

Constant proportionality or slope(rate of change) is found by Y divided by X.

1.4(y) ÷ 14(x) = 0.1(slope)

1.6(y) ÷ 16(x) = 0.1(slope)

2.1(y) ÷ 21(x) = 0.1(slope)

Check Work:

14 x 0.1 = 1.4

16 x 0.1 = 1.6

21 x 0.1 = 2.1

Answer:

1/10.

Step-by-step explanation:

The proportionality equation is given to you: [tex]y = rx[/tex]

Next, plug in the given [tex]x[/tex] and [tex]y[/tex] variables into the equation:

When: [tex]x = 14[/tex] & [tex]y = 1.4[/tex]

[tex]1.4 = r(14)\\1.4 = 14r\\(1.4)/14 = (14r)/14\\1.4/14 = r\\r = 0.1[/tex]

When: [tex]x = 16[/tex] & [tex]y = 1.6[/tex]

[tex]1.6 = r(16)\\1.6 = 16r\\(1.6)/16 = (16r)/16\\r = 1.6/16\\r = 0.1[/tex]

When: [tex]x = 21[/tex] & [tex]y = 2.1[/tex]

[tex]2.1 = r(21)\\[/tex]

[tex]21r = 2.1\\(21r)/21 = (2.1)/21\\r = 2.1/21\\r = 0.1[/tex]

r = 0.1 in all of the given, ∴ 0.1 is your answer. Change the decimal into a fraction:

0.1 = 1/10

1/10 is your answer.

(-2/10)^4 power

HELP MEE PLS

Answers

Answer:

1/625

Step-by-step explanation:

simply

(-1/5)^4

1/625

Answer:

The answer is 1/625

Step-by-step explanation:

hope this helps

here are two receipts from a meal in a restaurant one persons subtotal is $24.95 if the tax rate at the restaurant is 9.5% how much will their sale tax be?

Answers

Answer:

$24.95X.095=$2.37

Answer:

Step-by-step explanation: 3.27

A model house has a scale of 3 cm : 6 m.
If the model house is 9 cm wide, then how
wide is the real house?

Answers

It is going to be 18 because 9/18 is going to equal 3/6. Or both of them will equal 1/2

*BRAINIEST & 25 POINTS*

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

*irrelevant answers will be reported*

Answers

Answer:

63 degrees

Step-by-step explanation:

All angles add up to 180

(5x+6) + (4x-6) + (5x-2) = 180

put like terms together

5x+4x+5x + 6-6-2 = 180

14x -2 = 180

add 2 to both sides

14x = 182

divide both sides by 14

x=13

angle G is 5x-2, so if x=13, angle G is 5(13) -2

= 65 -2 = 63 degrees

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and crown if right

Tomika heard that the diagonals of a rhombus are perpendicular to each other. Help her test her conjecture. Graph quadrilateral ABCD on a coordinate grid with A(1, 4), B(6, 6), C(4, 1), and D(–1, –1).

a. A rhombus has 4 sides that are equal length. Is ABCD a rhombus? Show how you know.

b. Write the equations of the lines on which the diagonals lie. That is, write the equations of lines AC and BD.

c. Compare the slopes of lines AC and BD. What do you notice?

Answers

Answer:

a. The four sides of the quadrilateral ABCD are equal, therefore, ABCD is a rhombus

b. The equation of the diagonal line AC is y = 5 - x

The equation of the diagonal line BD is y = 5 - x

c. The diagonal lines AC and BD of the quadrilateral ABCD are perpendicular to each other

Step-by-step explanation:

The vertices of the given quadrilateral are;

A(1, 4), B(6, 6), C(4, 1) and D(-1, -1)

a. The length, l, of the sides of the given quadrilateral are given as follows;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

The length of side AB, with A = (1, 4) and B = (6, 6) gives;

[tex]l_{AB} = \sqrt{\left (6-4 \right )^{2}+\left (6-1 \right )^{2}} = \sqrt{29}[/tex]

The length of side BC, with B = (6, 6) and C = (4, 1) gives;

[tex]l_{BC} = \sqrt{\left (1-6 \right )^{2}+\left (4-6 \right )^{2}} = \sqrt{29}[/tex]

The length of side CD, with C = (4, 1) and D = (-1, -1) gives;

[tex]l_{CD} = \sqrt{\left (-1-1 \right )^{2}+\left (-1-4 \right )^{2}} = \sqrt{29}[/tex]

The length of side DA, with D = (-1, -1) and A = (1,4) gives;

[tex]l_{DA} = \sqrt{\left (4-(-1) \right )^{2}+\left (1-(-1) \right )^{2}} = \sqrt{29}[/tex]

Therefore, each of the lengths of the sides of the quadrilateral ABCD are equal to √(29), and the quadrilateral ABCD is a rhombus

b. The diagonals are AC and BD

The slope, m, of AC is given by the formula for the slope of a straight line as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Therefore;

[tex]Slope, \, m_{AC} =\dfrac{1-4}{4-1} = -1[/tex]

The equation of the diagonal AC in point and slope form is given as follows;

y - 4 = -1×(x - 1)

y = -x + 1 + 4

The equation of the diagonal AC is y = 5 - x

[tex]Slope, \, m_{BD} =\dfrac{-1-6}{-1-6} = 1[/tex]

The equation of the diagonal BD in point and slope form is given as follows;

y - 6 = 1×(x - 6)

y = x - 6 + 6 = x

The equation of the diagonal BD is y = x

c. Comparing the lines AC and BD with equations, y = 5 - x and y = x, which are straight line equations of the form y = m·x + c, where m = the slope and c = the x intercept, we have;

The slope m for the diagonal AC = -1 and the slope m for the diagonal BD = 1, therefore, the slopes are opposite signs

The point of intersection of the two diagonals is given as follows;

5 - x = x

∴ x = 5/2 = 2.5

y = x = 2.5

The lines intersect at (2.5, 2.5), given that the slopes, m₁ = -1 and m₂ = 1 of the diagonals lines satisfy the condition for perpendicular lines m₁ = -1/m₂, therefore, the diagonals are perpendicular.

Please help me ASAP!

Answers

Answer:

=x⁴-196x³+9204x²+32200x+40000

x⁴-196x³+9204x²+32200x+40000

A drama club made $3,200 from a school play. Seventy-five percent of that amount came from ticket sales. Identify the values of the variables in the model. Then use the model to find the amount of ticket sales.

a =
b =
The amount of ticket sales is $
.

Answers

Answer: $2400

Step-by-step explanation:

Based on the question above, a will be the percentage of tickets that were sold while b will be tickwt sales. Therefore,

a = 75%

b = 75% × $3,200

= 0.75 × $3200.

= $2400

Based on the information above, the amount of tickets sales is $2400

5) The sides of a quadrilateral are in the ratio 1:2:3:6. The perimeter is 138 cm.

Answers

Answer:

The first side is 11.5cm, the second is 11.5cm×2 = 23cm, the third is 11.5cm × 3 = 34.5cm,

and the fourth side is 11.5cm × 6 = 69cm.

Step-by-step explanation:

A quadrilateral is a 4 sided shape, while perimeter is the addition of all the sides of the quadrilateral. Since the sides of the quadrilateral is not stade, assume the sides of the quadrilateral is x, therefore 1:2:3:6 = x:2x:3x:6x. The total ratio is x+2x+3x+6x=12x, therefore 12x= 138 , x = 11.5cm, Therefore the first side is 11.5cm, the second is 11.5cm×2 = 23cm, the third is 11.5cm × 3 = 34.5cm, and the fourth is 11.5cm × 6 = 69cm.

Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription she sells. If Erica made $42.80 on Monday, $64.20 on Tuesday and $74.90 on Wednesday, how many subscriptions did she sell in the three days

Answers

to find the number of subscribtion sold we divide the money she made by the price of subscription

monday:

42.80/5.35=8 subscriptions sold

tuesday:

64.20/5.35=12 subscriptions sold

wednesday:

74.90/5.35=14 subscriptions sold

8+12+14=34 subscriptions sold in 3 days

Answer:

34 subscriptions she sold

Justin and Elena each launched a toy rocket into the air. The height of Justin's rocket is modeled by the equation h = –16t2 + 60t + 2. Elena launched his rocket from the same position, but with an initial velocity double that of Justin's. Which equation best models the height of Elena's rocket? h(t) = at2 + vt + h0

Answers

Mode is the highest frequency number while the median is the middle value of a data set after writing either increasing or decreasing manner.

For example;

Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.

Given the data set,

7,5, 12, 8, 2,9,4

If we write it in increasing order then,

2, 4, 5, 7, 8, 9, 12

Now median is middle value so here 7 is in between 3 - 3 from left and right.

Hence "The median of the given data set 7,5, 12, 8, 2,9,4 is 7".

To learn more about mode and median,

https://brainly.com/question/300591

#SPJ2

Help me with this please

Answers

Answer:

15 cans or D

Step-by-step explanation:

so it’s a pattern every 5 days add 3 cans

so Now do a table

5 = 3

10 = 6

15 = 9

20 = 12

25 = 15

Answer:

15 cans

Step-by-step explanation:

Set up a proportion.

3 cans / 5 days = x cans / 25 days

Note: both sides contain the same units on top and the same units on the bottom of each fraction.

3/5 = x / 25 Cross multiply

5x = 3*25

5x = 75

x = 75 / 5

x = 15

A store sells a 1/1/4 pound package of turkey for $9 whats the unit price of the turkey in the package

Answers

Answer:

$7.20

Step-by-step explanation:

The first step is to convert 1 1/4 to decimal form. 1/4=0.25, which when added to the 1 gives a total weight of 1.25 pounds. Dividing this by the price to find the unit price, you get 9/1.25=$7.20 per pound of turkey. Hope this helps!

Evaluate the expression yz when x= 3, y=6 and z=12.

Answers

Answer: 72

Answer:

$300.30

Step-by-step explanation:

100% - 30% = 70%

429 * 0.70 = 300.30

Therefore the sale price of the ipad is $300.30!

Please mark brainliest and have a nice day!

find the selling price: original price of a radio: 53.50 discount: 30

Answers

Answer:

48.69

Step-by-step explanation:

30% off $53.50

= 70% of $53.50

= $53.50 * (70/100) = $37.45.

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