Write an equation that represents the line.
Use exact numbers.

The measure of m∠ABD in the figure shown is 19°.

Given:

∠BCD = 71°

In the figure, ΔABC is an isosceles triangle where AB = BC.

According to the Isosceles Triangle Theorem, an isosceles triangle has equal angles on either side of its equal sides.

So, ∠BAD = ∠BCD = 71°

The sum of angles in a triangle sums to 180°.

∠ABC + ∠BAD + ∠BCD = 180°

∠ABC + 71° + 71° = 180°

∠ABC + 142° = 180°

∠ABC = 180° - 142° = 38°

DB is the angle bisector of ∠ABC.

Now, ∠ABD = ∠CBD = 38°/2 = 19°

The measure of ∠ABD is 19°.

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AE and BE are congruent lines or we can say lines with same length.

What are congruent lines?

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent.

As given in the question,

AC = BD, and

EC = ED

We can see in the figure that:

AC - EC = AE ___(1)

BD - ED = BE ___(2)

Substituting the value of AC and EC in equation (1):

AE = BD - ED ___(3)

From equations (2) and (3), we can conclude that,

AE = BC

Therefore, AE and BE are congruent lines.

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Answer:

5

Step-by-step explanation:

Since 7 into 42 is six we know the answer can't be 7 because it's too high. We can also rule out 6 because 6 times 7.94 is more than 41. The first answer choice is wrong because if you take away the .94, 7 times 4 is 28 which is pretty far from 41. If you multiply 5 and 7, it comes out to 35. That's significantly closer than four.

Hope this helps! :)

On subtracting 20 from twice a number we get 50, then the number is 35 in this context.

This is referred to as a type of mathematical operation in which one number is taken or deducted from the other and the sign is ( - ). this expression is used in every facet of life for their daily activities.

We were told that 20 was subtracted from twice a number to give 50 which means that twice the number is 70. The exact number will therefore be 70/2 which will then result in 35 and is therefore the most appropriate choice.

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Answer: 6400kg=6.4*10⁶ g

Step-by-step explanation:

6400 kg=

6.4*10³ kg=

6.4*10³*10³ g=

6.4*10³⁺³ g=

6,4*10⁶ g

Answer - 6.4 × 10^6

Step by step Explaination-

6400 kg=

6.4*10³ kg=

6.4*10³*10³ g=

6.4*10³⁺³ g=

6,4*10⁶ g

Firstly, we'll discuss the units of digits -

1. We'll convert 6400 kilograms into grams. Multiply the value in kilograms by the factor '1000'.

2.  Standard form may be a means of writing variety thus it's easier to browse. it's typically used for terribly large or small numbers.

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Answer:

[tex]\sf y =\dfrac{-3}{4}x+16[/tex]

Step-by-step explanation:

Where m is the slope and b is the y-intercept.

   3x + 4y = 64

Subtract 3x from both sides,

           4y = -3x + 64

Now, divide both sides by 4,

      [tex]\sf \dfrac{4y}{4}=\dfrac{-3x}{4}+\dfrac{64}{4}\\\\y = \dfrac{-3}{4}x + 16[/tex]

By using the properties of the 30-60-90 right triangles, the lengths of the long leg and the hypotenuse are √3 · L and 2 · L, respectively.

Right triangles are triangles where one of its internal angles is a right angle, that is, has a measure of 90°. 30-60-90 triangles are right triangles whose internal angles have measures of 30°, 60° and 90°, respectively.

This kind of right triangles have the following features:

If we know that the short leg has a length of L, then the lengths of the long leg and the hypotenuse are √3 · L and 2 · L, respectively.

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Answer:

First question mark is 4, second question mark is 64

Step-by-step explanation:

For the first question mark, 7 is half of 14, and half of 8 is 4, so they would be the same ratio, and then for the second, 12 to 24 is just one half, meaning you would need to find double 32, which is just 64

Standard deviation of population mean is 0.33.

Why is there a standard deviation?

it is shown that 5% values are over 2.1 pounds and 5% are under 1.9 pounds

so stastically that means

P( X > 2.1,  μ; σ) = 0.05 and P( X 1.9; μ; σ) = 0.05

where  μ is mean of the sample and σis the standard deviation of the sample.

so mean can be calculated easily μ = (2.1 + 1.9)/2 = 2.0

and as we can interpret P(1.9 <x < 2.1; 2.0; σ) = 0.90 by normal distribution the Z value for 90% confidence interval is 1.65

so σ = (2.1 -2) /1.65 = 0.06

standard deviation of the sample mean= 0.06

and by that standard deviation of population mean = 0.06 * (30) 0.5  = 0.33

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The complete question is -

A production process is checked periodically by a quality control inspector. the inspector selects simple random samples of 30 finished products and computes the sample mean product weight. If test results over a long period of time show that 5% of the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process? What is the population mean? (to 1 decimal) What is the population standard deviation (to 2 decimals)?

Answer: 7 units

Step-by-step explanation:

Answer:

(i) 7 + 4√2  cm^2.

(ii) 50 - 8√2  cm^2.

Step-by-step explanation:

(i)

Area = (3 + √8)(5 - 4/√2)

= 3(5 - 4/√2) + √8(5 - 4/√2)

= 15 - 12/√2 + 5√8 - 4√4

= 15 - 8 -( 12√2)/2 + 5*(2√2)

= 7 - 6√2 + 10√2

= 7 + 4√2.

(ii)

Area of the square

= AC^2

= (3 + √8)^2 + (5 - 4/√2)^2            (By Pythagoras)

= 9 + 6√8 + 8 + 25 - 40/√2 + 16/2

= 9 + 8 + 8 + 25 + 12√2 - 20√2

= 50 - 8√2.

Answer:

what is the symbol between the 2 fractions?

Answer:

x = 147

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 7 , then

sum = 180° × 5 = 900°

sum the interior angles and equate to 900

x + 141 + 112 + 129 + 106 + 139 + 126 = 900

x + 753 = 900 ( subtract 753 from both sides )

x = 147

The largest number of rods that the pole can be cut into is 86.

Given:

Length of Metal Pole = 500 cm

The pole is cut into rods.

Length of each rod = 5.8 cm

To determine the number of rods we can divide the total length of the pole by the length of each rod.

Number of rods that the pole can be cut into = (Length of Metal Pole) ÷ (Length of each rod )

⇒ Number of rods = 500 ÷ 5.8 = 86.2 ≈ 86

Therefore, the largest number of rods that the pole can be cut into is 86.

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Answer:

its the 3rd option

Step-by-step explanation:

you solve parenthesis then multiply then had to minus which gave you the total

Based on the given, the variable p from the expression 4.45p represent pounds of tomatoes sold.

Algebra is a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

The cost of the tomatoes for a number of packages = 4.45p

If the store sold 2 1/4 pounds of tomatoes

The cost of the tomatoes for a number of packages = 4.45p

= 4.45(2 1/4)

= 4.45(9/4)

= 4.45(2.25)

= $10.0125

In conclusion, the variable p represent pounds of tomatoes sold in the store.

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Answer: irelating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten:

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

AB + BC = AC

4x -6 + 4 = 2x + 10  Combine like terms

4x -2 = 2x + 10  Subtract 2s from both sides of the equation

2x -2 = 10  Add 2 to both sides

2x = 12  Divide both sides by 2

x = 6

Plug in 6 for x in AC

2x + 10

2(6) + 10

12 + 10

22

The surface area and the volume of solid prism are 432in² and 576in³ respectively.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles

The surface area of a rectangular prism is expressed as;

A = 2( wl + hl + hw )

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given the data in the question;

The surface area of the solid is;

A = 2( wl + hl + hw )

A = 2( (8in × 12in) + (6in × 12in) + (6in × 8in) )

A = 2( 96in² + 72in² + 48in² )

A = 2( 216in² )

A = 432in²

Therefore, surface area of the rectangular prism is 432in²

The volume of the solid is;

V = w × h × l

V = 8in × 6in × 12in

V = 576in³

Therefore, volume of the rectangular prism is 576in³

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c.(4x+8y)=60

it is equivalent

Answer:

A and C

Step-by-step explanation:

Substitute 4x + 8y = 12

A:

12+3=15

15=15 ✓

B:

12=10 ×

C:

5(12)=60

60=60 ✓

D:

Multiply 4 to x+2y=6 to make it 4x+8y=12

x+2y=6

4x+8y=24

12=24 ×

answer-x=π/7+y/7

Step-by-step explanation:

yes

Answer:

A

Step-by-step explanation:

using the sine ratio and the exact values

sin30° = [tex]\frac{1}{2}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

calculate the height of the wall below x , call it h

the hypotenuse is the length of the ladder

using the sine ratio in the lower right triangle.

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{18}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2h = 18 ( divide both sides by 2 )

h = 9

lower part of the wall is 9 meters

using the sine ratio in the right triangle on the right

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9+x}{18}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2(9 + x) = 18[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

9 + x = 9[tex]\sqrt{3}[/tex] ( subtract 9 from both sides )

x = 9[tex]\sqrt{3}[/tex] - 9 = 9([tex]\sqrt{3}[/tex] - 1)

Answer:

[tex]\textsf{A)} \quad x=9(\sqrt{3}-1)[/tex]

Step-by-step explanation:

Interior angles of a triangle sum to 180°.  Therefore, if the ladder makes an angle of 30° with the ground, the angle it makes with the wall is 60°.

Therefore, the two triangles are congruent as their corresponding angles are the same and the length of their longest side (hypotenuse) is the same.

30-60-90 Triangle Theorem

A 30-60-90 triangle is a special right triangle where the measures of its angles are in the ratio 1 : 2 : 3 and the measure of its sides are in the ratio 1 : √3 : 2.

The formula for the sides is  b : b√3 : 2b  where:

Therefore, as the length of the hypotenuse is 18:

[tex]\implies 2b=18[/tex]

[tex]\implies b=9[/tex]

[tex]\implies b\sqrt{3}=9\sqrt{3}[/tex]

To find x, subtract the length of the shortest leg of the right triangle from the length of the other leg of the right triangle:

[tex]\implies x=9\sqrt{3}-9[/tex]

[tex]\implies x=9(\sqrt{3}-1)[/tex]

Answer:

15

Step-by-step explanation:

40/100×25

=10

25-10=15

There will  be no interval of time when Josue has more in savings than Arianna, they have same savings is after 4 weeks

Step one:

For Josue

initial savings balance= $70

weekly savings = $9

Let J represent amount of money Josue has saved and  t the number of weeks after the beginning of the year

The total amount in the savings after t weeks is

J=9t+70-------1

For Arianna

initial savings balance= $30

weekly savings = $19

Let A represent the amount of money Arianna has saved and  t the number of weeks after the beginning of the year

The total amount in the savings after t weeks is

J=19t+30---------2

Step two

equation 1 and 2 to find t

9t+70=19t+30

9t-19t=30-70

-10t=-40

divide both sides by 10

t=4

t=4 weeks

so after 4 weeks Josue and Arianna will have the same amount of money

For Josue t=4

J=9(4)+70-------1

J=36+70

J=$106

For Arianna t=4

A=19(4)+30---------2

A=76+30

A=$106

The two equations above shows that after 5 weeks their savings will be $106.

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Answer:

x-0.5,1,2,3,4,5,6

y-12,6,3,2,1.5,1

Step-by-step explanation:

Substitute the x value inside the formula. E.g. y=6 over 0.5, then solve.

Plot the points on the graph and join the up.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

246 degrees

Answer:61.5

Step-by-step explanation:

123/2=61.5

61.5+57=118.5

180-118.5=61.5

Step-by-step explanation:

divide volume by product of length and width

54cm³= 3cm x 2cm

54/6= 9cm