Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 10
and DC = 4, what is the length of AD?

Answer:

u will multiply -x by the big bracket and rhen start cancelling and factor it by common numbers

Answer:

(x + 3)(- x² - 3x + 1)

Step-by-step explanation:

Given

(x + 3) - x(x² + 6x + 9) ← factor is a perfect square

= (x + 3) - x(x + 3)² ← factor out (x + 3) from each term

= (x + 3)(1 - x(x + 3))

= (x + 3)(1 - x² - 3x)

= (x + 3)(- x² - 3x + 1)

Answer:

(-1) & 4/3

Step-by-step explanation:

           3x² - x - 4

Sum = -1

Product = 3*(-4) = -12

Factors = -4 and 3       { (-4)*3 = -12 & (-4) + 3 = -1}

3x² - x - 4 = 3x² + 3x - 4x -4 {Rewrite the middle term using the factors}

               = 3x(x + 1) -4(x + 1)

               =(x + 1)(3x - 4)

x + 1 = 0   ;  3x - 4 = 0

     x = -1  ;          3x = 4

                            x = 4/3

[tex]\sf Zeroes \ of \ the \ polynomial \ are \ (-1) \ and \ \dfrac{4}{3}[/tex]

Verification:

         [tex]\sf 3x^2 - x - 4 = 0\\\\Divide \ the \ entire \ equation \ by \ 3\\\\\\\dfrac{3x^2}{3}-\dfrac{x}{3}-\dfrac{4}{3}=0\\x^2 - \dfrac{x}{3}-\dfrac{4}{3}=0[/tex]

       Coefficient of x = sum of the zeroes

                                  [tex]\sf = -1 + \dfrac{4}{3}\\\\=\dfrac{-3}{3}+\dfrac{4}{3}\\\\=\dfrac{1}{3}\\\\[/tex]

Constant = product of the zeroes

               [tex]\sf = (-1)*\dfrac{4}{3}\\\\=\dfrac{-4}{3}[/tex]

Thus verified.

The value of 8(x + 7) is 8x + 56.

The value of 6(11 + x) is 66 + 6x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The distributive property of  multiplication over addition states that,

a x (b + c) = a x b + a x c

Now,

8 x (x + 7)

= 8 x (x) + 8 x 7

= 8x + 56

6 (11 + x)

= 6 x 11 + 6 x (x)

= 66 + 6x

Thus,

The value is 8x + 56 and 66 + 6x.

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So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.

In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers

the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).

Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.

Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.

So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.

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Answer:

the answer is B

Step-by-step explanation:

Answer:

18.2%

Step-by-step explanation:

Given data

Principal=  $2500

Final amount= $3600

Time = 2 years

Rate=???

The expression for the rate is given as

r= ln(A/P)/t

substitute

r= ln(2500/3600)/2

r= ln(0.6944)/2

r= -0.364/2

r= 0.182

Hence the rate is 18.2%

The two companies will be equal in cost when 21.428 miles are driven.

How do you calculate the cost of rent?

The weekly rental amount is divided by 7 to determine the daily rental rate, then multiplied by 365 (days per year) to determine the yearly rate, and finally divided by 12 to determine the monthly rental amount. For example, a property is advertised as $200 per week, ($200 divided by 7) is $28.57 for the daily rate.

We can set up an equation to represent the cost of renting a car from each company in terms of the number of miles driven, and then solve for the number of miles at which the cost is the same for both companies.

Let x be the number of miles driven.

The cost of renting from Sunshine Rental Company is given by:

Cost1 = 17 + 0.5x

The cost of renting from Rent Me company is given by:

Cost2 = 20 + 0.36x

We can set the two equations equal to each other, and solve for x:

17 + 0.5x = 20 + 0.36x

0.14x = 3

x = 21.428 miles

Hence, the two companies will be equal in cost when 21.428 miles are driven.

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The angle of elevation of the ramp is 28.6 degrees.

Tan = (Change in Height) / (Length of Ramp)

Therefore, using the given information, the angle of elevation of the 23-foot ramp is:

Tan = (6 feet) / (23 feet)

Tan = 0.26

= 14.5° (to the nearest tenth of a degree)

Therefore, the angle of elevation of the 23-foot ramp is 14.5°.

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On solving the provided question, we can say that the spherical balloon's initial radius is 7 cm.; the final radius is 14 cm. ratio =  (7/14) ^2 = 1:4

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

The spherical balloon's initial radius is 7 cm.

The final radius is 14 cm.

ratio =

(7/14) ^2 = 1:4

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Answer:

X= 18

Step-by-step explanation:

24/4=6 x 3= 18

Answer:

x=18

Step-by-step explanation:

3/4=x/24

3×24=4×x

72=4x

x=72/4

x=18

Answer:

ye

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

A perfect square is a number from a number system that can be shown as the square of the number in the given number system. 4 can be written as 2 x 2 Making 4 a perfect square. In other words, if a number can be multiplied by its self and equal the number you are trying to square, then it is a perfect square.

Answer:

46

Step-by-step explanation

11 x 22 and 9 x 18 then add them then do 450 - 404

Answer:

y = 5/2x - 11

Step-by-step explanation:

y = 5/2x + b

9 = 5/2 (8) + b

9 = 20 + b

-11 = b

y = 5/2x - 11

Answer:

Pick the yellow one. It's hard to read what's written but the yellow is the closest to what I would have written myself.

Answer:

Statement 1) Corresponding angles

Statement 2) Congruent

Statement 3) 150 degrees

Statement 4) Vertical Angles

Statement 5) Congruent

Statement 6) 150 degrees

Statement 7) Alternate exterior angles

Statement 8) Congruent

Statement 9) Alternate Interior angles are congruent

Step-by-step explanation:

Explanation:

1) I've learned this before

2) Not all Corresponding angles are obtuse

3) Corresponding angles have the same measure

4) I've learned this before

5) Vertical Angles are congruent

6) Same reason as before

7) I've learned this before

8) Alternate Interior angles are congruent

9) I've learned this before

Please mark me the brainliest! Thank you!

The values for figure is  x = 2, y = 9,

GH = 8, GJ = 7,

FE = 3, GE = 7​.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

The Latin words quadra, which means four, and latus, which means sides, are combined to form the English word quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides.

Given figure shows

GH parallel to EG

GH = EG

GH = 3y - 19

EG = 8

3y - 19 = 8

3y = 27

y = 9

GH = 3y - 19 = 3(9) - 19 = 8

and GJ parallel  to JE

GJ = JE

GJ = 3x + 1

JE = 5x - 3

3x + 1 = 5x - 3

5x - 3x = 1 + 3

2x = 4

x = 2

values are,

GJ = 3x + 1 = 3(2) + 1 = 7

JE = 5x - 3 = 5(2) - 3 = 7

FE = 6x - y

substitute values,

x = 2, y = 9

FE = 6x - y = 6(2) - 9 = 12 - 9 = 3

Hence x = 2, y = 9

GH = 8, GJ = 7,

FE = 3, GE = 7​.

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IM pretty sure its B.

Answer:

Q1 is Seth will have 10 more cards than Matt

Q2 is Chart B

Step-by-step explanation:

First let's find the equation of the lines and chart so we can extend the graph.

Seth's chart has the equation y = x × 4

Matt's graph has the equation y = x × 2 + 20

The extended graphs can be seen below in an attachment. If you want to make these graphs yourself, I suggest Desmos

So on week 15, Seth has 60 and Matt has 50

Find the difference by subtracting

60 - 50 = 10

The final answer is Seth will have 10 more cards than Matt

                                                        Question 2

A linear relationship is a statistical term used to describe a straight-line relationship between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.

Now we need to find the equations of the lines and graph them.

I have found the equations of the line and graphed them which can be seen in an attachment below.

We need to find the that follows the correct equation y = mx + b.

This would be answer B.

Hope this helps!!

Answer:

A.

[tex] SA= \frac{2}{3} \pi rl+16 \pi r^2[/tex]

Step-by-step explanation:

Surface area of the original cone

[tex] SA= \pi r l + \pi r^2... (1)[/tex]

When, radius is quadrupled and slant height is reduced to one sixth

[tex] i. e. \: \:r = 4r\: \: \&\:\: l= \frac{1}{6}l[/tex]

Plug the above values of r and [tex] l[/tex] in equation (1), new surface area becomes:

[tex] SA= \pi (4r)\times \frac{1}{6} l+ \pi (4r)^2[/tex]

[tex] SA= \frac{4}{6} \pi rl+16 \pi r^2[/tex]

[tex]\huge \purple {\boxed {SA= \frac{2}{3} \pi rl+16 \pi r^2}} [/tex]

Answer:

D) I’m 100% sure it’s correct!

Step-by-step explanation:

Answer:

slope = (3/2)

Step-by-step explanation:

point 1: (-1, 1); Point 2: (1, 4)

            (x₁, y₁)              (x₂, y₂)

y₂ - y₁         4 - 1            3            3

----------- = ------------ = --------- = -------

x₂ - x₁          1 - (-1)       1 + 1          2

I hope this helps!

A statement which correctly describes the solution set of the given inequality include the following: C. all rational-number values of n that are at least 0.5.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 12, 0.5, √16, etc.

Next, we would translate the word problem into algebraic inequality and then solve for the value of n as follows;

5n + 1.5 ≥ 4

Subtracting 1.5 from both sides of the algebraic inequality, we have:

5n + 1.5 - 1.5 ≥ 4 - 1.5

5n ≥ 2.5

Dividing both sides of the algebraic inequality y 5, we have:

n ≥ 2.5/5

n ≥ 0.5

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Answer: To find the length of an object in a scale drawing, you need to use the scale to convert the length on the drawing (measured in inches) to the actual length (measured in feet).

The scale of the drawing is given as 0.5 inches = 10 feet, which means that 1 inch on the drawing represents 10 feet in reality.

So, if the length of the object on the scale drawing is L inches, then the actual length of the object in feet would be:

Length (ft) = (Length (in) * 10 ft/0.5 in) = (L*20)

To find the actual length of the object in feet, you need to know the length of the object in inches from the scale drawing.

Once you have that measurement, you could then simply multiply it by 20.

Step-by-step explanation:

Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.

Two or more expressions with an Equal sign is called as Equation.

The billing cycle for the month = 28 days

Current beginning balance = x

Annual percentage rate (APR) = 24%

Monthly percentage rate (MPR) = 2% (24% ÷ 12)

Purchase on the last day = $1,400

Total finance charge for the month = $51

Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)

Finance charge for the beginning balance = $50 ($51 - $1)

The current beginning balance, x = $2,500 ($50 ÷ 2%)

Equation for current beginning balance, x = 51 - 1 ÷ 0.02

Total finance charge for the last-day purchase = $28 ($1,400 x 2%)

Savings in finance charge by purchasing on the last day = $27 ($28 - $1)

Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.

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first expression = 1×2, 1×1, 1×3, 1×4, 1×5, 1×6, 1×7, 1×8, 1×9, 2×2, 2×3, 2×4, 3×2, 3×3, 4×2 and second expression = 1×9

In mathematics, an expression is a statement that represent the method of mathematical operation in a symbolic form. An expression is developed based on numerical terms or both numerical and variable terms along with operator or signs.

it is stated that one factor is a two-digit number between one and ten.

the multiplication expression can be 1×2 , 1×1, 1×3, 1×4, 1×5, 1×6, 1×7, 1×8, 1×9, 2×2, 2×3, 2×4, 3×2, 3×3, 4×2

In the next, the multiplication expression for 2nd statement:

one factor is a two-digit number between one and ten and their product is greater than 8 and less than 10

1×9

the above is greater than 8 and less than 10.

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Answer:

n = - 1 , n = 3

Step-by-step explanation:

n² - 2n - 3 = 0 ( add 3 to both sides )

n² - 2n = 3

to complete the square

add ( half the coefficient of the x- term)² to bpth sides

n² + 2(- 1)n + 1 = 3 + 1

(n - 1)² = 4 ( take square root of both sides )

n - 1 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 1 to both sides )

n = 1 ± 2

Then

n = 1 - 2 = - 1

n = 1 + 2 = 3

Answer:

A and C or 2-6 and 4-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

from the graph we konw the ∠ABD=∠DBC, because ∠DBC=20, so ∠ABD=20

The height of the tree is closest to 40 feet.

We can use the proportion of similar triangles to determine the height of the tree.

Let h be the height of the tree and s be the length of the shadow cast by the tree.

We know that the height of the building is 60 feet and the length of its shadow is 21.5 feet. So:

(h/s) = (60/21.5)

We also know that the length of the shadow cast by the tree is 18 feet.

So we can substitute that into the proportion and solve for h:

h = (60/21.5) * 18

h = (60*18)/21.5

h ≈ 40

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