Fill in the blanks so that the following statement is true

Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

Answer:

20

Step-by-step explanation:

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

10/7÷1/14

Applying the fractions formula for division,

=10×14/ 7×1

=140/7

Simplifying 140/7, the answer is

=20

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x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

Answer:

real

Step-by-step explanation:

-169  is a negative integer and integers are real numbers

Answer:

real

Step-by-step explanation:

The rectangular equation will be (y-1)(y-2) = x²/8

To convert from polar coordinates (r, θ) to rectangular coordinates (x, y), we use the following equations,

x = r Cos θ

y = r Sin θ

x² + y² = r²

So,

r(1 + 3 Sin θ) = 4

r + 3r Sin θ = 4

r = 4 - 3r Sin θ

√x²+y² = 4 - 3y

Squaring both sides,

x² + y² = 16 + 9y² - 24y

x² = 8y²-24y+16

(y-1)(y-2) = x²/8

Hence the rectangular equation will be (y-1)(y-2) = x²/8

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Answer:

3√41

Step-by-step explanation:

The diagonal can be gotten using the pythagoras theorem

d² = l²+w²

d² = 12²+15²

d² = 144 + 225

d² = 369

d = √9*41

d = 3√41

Hence the diagonal is 3√41

Answer:

10.44

Step-by-step explanation:

Answer:

3x + y = 9.5

Step-by-step explanation:

1) The equation of a line is in the form of y = mx + c, where m is the gradient and c is the y-intercept. Write the given values in that form.

y = -3x + c

2) Find the value of k by using the following formula: m = y2 - y1 / x2 - x1. We already know m.

-3 = 8 - k / k - 3

-3(k - 3) = 8 - k

-3k + 9 = 8 - k

-3k + k = 8 - 9

-2k = -1

k = -1/-2

k = 1/2

3) Therefore, a line with gradient of - 3 passes through the points (3, 1/2) and (1/2, 8). We can find the y-intercept (c). To do so, choose one of the coordinates and substitute.

y = -3x + c

1/2 = -3(3) + c

1/2 = -9 + c

1/2 + 9 = c

9.5 = c

Completed equation of the line: y = -3x + 9.5

4) Write it in the form of ax + by = c.

3x + y = 9.5

The slope of the line between these two points is $.06 / lb which is defined as the ratio of vertical extrade among points, the rise, to the horizontal extrade.

The slope is described because the ratio of the vertical extrade among points, the rise, to the horizontal extrade among the equal  points, the run. . A slope with a extra absolute price shows a steeper line. The course of a line is both increasing, decreasing, horizontal or vertical. If a line is horizontal the slope is zero.

Let X1 = 2.1 pounds, Y1 = $3.4 and

X2 = 70 pounds, Y2 = $7.5

ΔX = 70 - 2.1 = 67.9

ΔY = 7.5 - 3.4 = 4.1

Slope (m) = ΔY / ΔX

= 4.1 / 67.9

= 0.060382916053019

= 0.06 (Rounded)

Therefore, answer is Option $.06 / lb.

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Answer:

1080 for the bottom

650 for the top add them together

= 1730

Answer:

Shade 6

Step-by-step explanation:

There are 20 squares in the grid. Multiply 0.30 (percentages are written as decimals) by 20. There's your answer.

Answer:

Except me. The Alpha leaders don't fit in.

The answer would be 3 hours.

Using multiplication, the total length of all the sunflowers in the garden is 1,260 inches.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication operation involves the multiplicand, the multiplier, and the product.

The total number of sunflowers in the garden = 210

The length of each sunflower = 6 inches

The total length of all the sunflowers = 1,260 inches (210 x 6)

Thus, based on multiplication operation, the total length of the sunflowers in the garden can be stated to be 1,260 inches.

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Assume that each sunflower measures 6 inches in length and there are 210 sunflowers in the garden.

The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.

Given, A 6000-seat theater has tickets for sale at $24 and $40.

How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?

first, assign variables:

X = # of $24 tickets,  Y = # or $40 tickets

write equations based on the data presented:

"6000 seat theater..."

   X + Y = 6000 ...equation 1

"total revenue of 168,000"

The revenue from each type of ticket is the cost times the number sold, so:

  24X + 40Y = 168,000 .....equation 2

from equation 1:

   X = 6000 - Y

substitute this into equation 2:   (replace X with 6000-Y)

   24 (6000 - Y) + 40Y = 168,000

expand:

144,000 -24Y + 40Y = 168,000

rearrange and simplify:

    16Y = 168,000 - 144,000

    y = 24000/16

     Y = 1500

from equation 1:

     X = 6000 - 1500

     X = 4500

hence the number of tickets for sale at $24 should be 4500.

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Answer:

It would hold .5 liters because 1000ml is equal to 1 liter

Step-by-step explanation:

Answer: g it is 2x+21 ansd h is 3x+24

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

-3.4 - 1.6 = -5

Answer:

21894

Step-by-step explanation:

So, since we want to use the distrubutive property, we ant to simplify 3,649

3000+600+40+9

now, multiply 6 to each one of those numbers:

18000+3600+240+54

add them together to get one number

21894

And that's how I think it's done.

Answer:

Step-by-step explanation:

sry ion no 11

A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?

Applying proportion

28/1=x/8

solve for x

x=(28)*8

x=224 miles

Answer:

Step-by-step explanation:

uhh

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

Step-by-step explanation:

8x - 8 = 7x + 8

x - 8 = 8

x = 16

8(16) - 8= 128 - 8 = 120

7(8) + 8 = 56+8 = 64

Answer:

B.

Step-by-step explanation:

No matter what a square is a regular polygon

Answer:

6+3+11/4\(\neq\)5

Step-by-step explanation:

Answer:

The answer to the question is 0

Answer:

length= 17.5

width=11.5

( I worked this out myself but I don't know if its right tho)

The volume of the log will be 30,70,760 m³.

Mathematically, we can write Archimedes principle as -

F{buoyant} = - fluid density {ρ} x acceleration due to gravity {g} x volume {v}

Given is that a 3080 kg log of wood with a diameter of 1 m and 10 m long, it floats in the water.

Since the log floats on water, the density of both the log and water is same.

So, we can write volume as -

Volume = 3080 x 997 Volume = 30,70,760 m³

Therefore, the volume of the log will be 30,70,760 m³.

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{QUESTION IN ENGLISH -urgent A 3,080 kg log of wood with a diameter of 1 m and 10 m long, it floats in the water. What is the volume of the trunk above the surface of the water?}

The equivalent form of the function showing the remainder as a fraction is: h(x) = (x - 6) + 4 / (x - 4)

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The given function is:

h(x) = (x^2 - 2x - 4) / (x - 4)

To rewrite this function in an equivalent form showing the remainder as a fraction, we can use polynomial division.

Let's divide x^2 - 2x - 4 by x - 4:

           x - 6

   --------------------

x - 4 | x^2 - 2x - 4

      - (x^2 - 4x)

      -------------

            2x - 4

            - (2x - 8)

            ---------

                   4

Therefore, we can write:

h(x) = (x^2 - 2x - 4) / (x - 4) = (x - 6) + 4 / (x - 4)

Therefore,  the equivalent form of the function showing the remainder as a fraction is: h(x) = (x - 6) + 4 / (x - 4)

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Answer:

x=−8

y=6=

Step-by-step explanation:

3x+4y=0

5x−3y=−58

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

3x+4y=0,5x−3y=−58

To make 3x and 5x equal, multiply all terms on each side of the first equation by 5 and all terms on each side of the second by 3.

5×3x+5×4y=0,3×5x+3(−3)y=3(−58)

Simplify.

15x+20y=0,15x−9y=−174

Subtract 15x−9y=−174 from 15x+20y=0 by subtracting like terms on each side of the equal sign.

15x−15x+20y+9y=174

Add 15x to −15x. Terms 15x and −15x cancel out, leaving an equation with only one variable that can be solved.

20y+9y=174

Add 20y to 9y.

29y=174

Divide both sides by 29.

y=6

Substitute 6 for y in 5x−3y=−58. Because the resulting equation contains only one variable, you can solve for x directly.

5x−3×6=−58

Multiply −3 times 6.

5x−18=−58

Add 18 to both sides of the equation.

5x=−40

Divide both sides by 5.

x=−8

The system is now solved.

x=−8,y=6

Coordinates are: (-8,6)

Graph: