can 7, 6, 17 make a triangle

Answer:

answer

Step-by-step explanation:

step by step explanation

Similarity is the mathematical property of triangles. Two triangles are called similar if they fulfil wither of the properties: Angle Angle, wherein two angles should be congruent; Side Angle Side, wherein two sides are similar to each other and the angles congruent to each other; and Side Side Side, wherein three sides are similar to each other in ratio.

The triangle ABC and triangle EDF are similar.

The first property is angle,

∠BAC = ∠EDF = 65°

The second property is also angle.

∠ABC = ∠DEF = 48° (∠DEF = 180 - 65 - 67)

Thus, the three angles are same or congruent.

The AA property of similarity makes the two triangles ABC and DEF similar. The option 1 is correct.

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Answer:

Step-by-step explanation:

is a rhombus formed by 4 right triangles, let's consider the small / large couple

the triangle at the top and the triangle at the bottom are rectangles

we can solve with the Pythagorean theorem.

c² = 10² - 8²

c² = 100 - 64

c² = 36

c = √36

c = 6 cm

c² = 17² - 8²

c² = 289 - 64

c² = 225

c = √225

c = 15 cm

6 + 15 =  

21cm

Answer:

21 cm

Step-by-step explanation:

Let M be the point of intersection of the diagonals AD and BC.

\(\implies x=\sf AD=AM+MD\)

As ΔAMD and ΔBMD are right triangles, use Pythagoras Theorem to work out the lengths of AM and MD.

Pythagoras Theorem

  \(a^2+b^2=c^2\)

where:

\(\begin{aligned}\implies \sf BM^2+AM^2 & =\sf AB^2\\\sf 8^2+AM^2 & = \sf 10^2\\\sf 64+AM^2 & = \sf 100\\\sf AM^2 & = \sf 100-64\\\sf AM^2 & = \sf 36\\\sf AM & = \sf \sqrt{36}\\\sf AM & = \sf 6\:\: cm\end{aligned}\)

\(\begin{aligned}\implies \sf BM^2+MD^2 & =\sf BD^2\\\sf 8^2+MD^2 & = \sf 17^2\\\sf 64+MD^2 & = \sf 289\\\sf MD^2 & = \sf 289-64\\\sf MD^2 & = \sf 225\\\sf MD& = \sf \sqrt{225}\\\sf MD& = \sf 15\:\: cm\end{aligned}\)

Therefore:

\(\begin{aligned}\implies x & =\sf AM+MD\\x & = \sf 6+15\\x & = \sf 21\:\:cm\end{aligned}\)

So the value of \(x\) from the given figure is 21 cm.

ANSWER

994 main floor tickets, 707 balcony tickets, 139 mezzanine tickets

EXPLANATION

The local theater has three types of seats:

Main floor = $45

Balcony tickets = $36

Mezzanine tickets = $32

Let the number main floor seats sold be x.

Let the number of Balcony tickets be y.

Let the number of Mezzanine tickets be z.

One night, all sales totalled $74,630.

This means that:

45 * x + 36 * y + 32 * z = 74,630

=> 45x + 36y + 32z = 74630 ______(1)

There were 148 more main floor tickets than balcony and mezzanine tickets combined, that is:

x = 148 + y + z _____(2)

The number of balcony tickets sold is 429 more than 2 times the number of mezzznine tickets sold. That is:

y = 429 + 2 * z

y = 429 + 2z _______(3)

Now, we have a system of three equations:

45x + 36y + 32z = 74630 _____(1)

x = 148 + y + z _____________(2)

y = 429 + 2z _______________(3)

Put (2) in (1):

45(148 + y + z) + 36y + 32z = 74630

6660 + 45y + 45z + 36y + 32z = 74630

Collect like terms:

45y + 36y + 45z + 32z = 74630 - 6660

81y + 77z = 67970_______(4)

Now, put (3) in (4):

81(429 + 2z) + 77z = 67970

34749 + 162z + 77z = 67970

Collect like terms:

239z = 67970 - 34749

239z = 33221

z = 33221 / 239

z = 139 tickets

Put the value of z in (3):

y = 429 + 2(139)

y = 278 + 429

y = 707 tickets

Put the values of y and z in (2):

x = 148 + 707 + 139

x = 994 tickets

Therefore, 994 main floor tickets, 707 balcony tickets, 139 mezzanine tickets were sold that night.

Answer:

490000

Step-by-step explanation:

Substituting \(x=40\),

\(I=-425(40)^2 + 45500(40) - 650000=490000\)

Answer:

\(x^2 + 10x -24 = 0 \: \\ is \: equivalent \: to \: ( x + 2) {}^{2} + 10x - 36=0\)

Step-by-step explanation:

\(x^2 + 10x -24 = 0 \\ x^2 + 12x - 2x -24 = 0 \\x(x + 12) - 2(x + 12) = 0 \\ (x - 2)(x + 12) = 0\)

The expressions are illustrated below.

3x = 12

x = 12/3

x = 4

x + 4 = 17

x = 17 - 4

x = 13

9y + 3 = 21

9y = 21 - 3

9y = 18

y = 18/9

y = 2

x ÷ 2 = 4

x = 4 × 2

x = 8

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Hello!

First, we have to solve this system, then we can classify it.

Let's solve:

Let's isolate y in the second equation:

Now, let's replace it in the first equation:

As we can see, this linear system has no solution.

Now, let's classify it:

As this does not admit any solution, we can say that it is inconsistent.

The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x - y = (6 - 5)(y - x) → False

(x - y) (6 - 5) = 1 → False

x- y = (1)(x - y) → True

x - y = 1 + (x - y) → No solution, False

x - y = (6 - 5)(x - y)  → True

The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

The graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.

If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.

In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

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Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

Answer:

Step-by-step explanation:

1 pound of potato salad costs 2.96

0.75 pounds of potato salad costs x

1/0.75 = 2.96/x            Cross multiply

x = 0.75 * 2.96

x = 2.22  

0.75 pounds of potato salad costs 2.22 dollars.

Answer:   mean is 16.22

Step-by-step explanation:

Answer:Hehhe

Step-by-step explanation:

Jehehehbehe

The part of the budget went towards buying young adult novels is \(\frac{5}{16}\)

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

A fraction represents a part of a whole or, more generally, any number of equal parts.

Given,

Fraction of budget used to buy new books = \(\frac{5}{8}\)

Fraction of book money to buy young adult novels = \(\frac{1}{2}\)

Part of budget used to buy young adult novels = \((\frac{5}{8}).(\frac{1}{2}) =\frac{5}{16}\)

Hence, the part of the budget went towards buying young adult novels is \(\frac{5}{16}\)

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Answer:

18 T-shirts

Step-by-step explanation:

1gram = 1000milligrams

1gram × 156000milligrams ÷ 1000milligrams

The milligrams unit cancel out each other thus grams remains as the main unit.

=156grams

1 T-shirt = 156grams

1 T-shirt × 2808grams ÷156grams

The grams unit cancel out each other thus T-shirt remains as the main unit.

=18 T-shirts

Answer:

18

Step-by-step explanation:

The distinguishing feature between a square and a rectangle is that all sides of a square are equal in length.

Yes, a square is a special type of rectangle because it possesses all the properties of a rectangle.

The distinguishing feature of a rhombus is that all sides are equal in length, while a parallelogram can have unequal side lengths.

Yes, a rhombus is a special type of parallelogram because it possesses the properties of a parallelogram and has all sides equal in length.

The three features used to describe 3-dimensional objects are faces, edges, and vertices.

The common properties between a square and a rectangle are that both have four sides, four right angles (90 degrees), and opposite sides that are parallel. The distinguishing feature is that all sides of a square are equal in length, while a rectangle can have unequal side lengths.

Yes, a square is a special type of rectangle. A rectangle is defined as a quadrilateral with four right angles, while a square is a specific type of rectangle where all sides are equal in length. Since a square possesses all the properties of a rectangle, including four right angles, it can be considered a special case of a rectangle.

The common properties between a rhombus and a parallelogram are that both have four sides and opposite sides that are parallel. The distinguishing feature of a rhombus is that all sides are equal in length, while in a parallelogram, the opposite sides are equal in length.

Yes, a rhombus is a special type of parallelogram. A parallelogram is defined as a quadrilateral with opposite sides that are parallel. A rhombus possesses this property, but it also has the additional feature of having all sides equal in length. Therefore, a rhombus can be considered a special case of a parallelogram.

The three features used to describe 3-dimensional objects are:

Faces: The flat surfaces that make up the object.

Edges: The lines where two faces intersect.

Vertices: The points where multiple edges meet.

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Answer: 8 is the anwser

Step-by-step explanation:

14/50 to its simplest form is 7/25

Answer:

\(\frac{7}{25}\)

Step-by-step explanation:

Find the common factor for both the numerator and the denominator, which is 2:

\(\frac{14}{50} =\frac{7}{25}\)

Answer:

use cosine rule

15²=14²+11²-2×14×11cosC

225-196-121=-308cosC

-92/-308=cosC

cosC=23/77

C=cos-¹(23/77)=72.62° is your answer

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

Answer:

yup your answer is correct

Step-by-step explanation:

xhfdgkdhkchkdgjdgkfkyfgkfhg

Answer:

it's correct and i'm 13

if u add the whole numbers first which is 3+6 which equals 9 and then u add 1/7 + 4/7 which will give you 5/7. So the whole answer will be what you said 9 5/7

All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

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Answer:

This should be a permutation

Step-by-step explanation:

P (n, r) = n!/(n-r)!

P (12,5) = 12!/(12-5)!

P (12,5) = 12!/7!

P(12,5) = 95040

Answer:

the amount of Basil Yamey's capital is £16,480.

Step-by-step explanation:

To calculate Basil Yamey's capital, we need to add up the value of his assets and subtract his liabilities.

The value of his assets is:

Van: £9,000

Market stall: £1,800

Computer: £280

Inventory of goods: £11,200

Cash in hand: £900

Money in the bank: £6,300

Total value of assets = £9,000 + £1,800 + £280 + £11,200 + £900 + £6,300 = £29,480

His liabilities are:

Amount still owed for inventory of goods: £5,000

Amount borrowed from Luca Pacioli: £8,000

Total liabilities = £5,000 + £8,000 = £13,000

Therefore, Basil Yamey's capital is:

Capital = Total value of assets - Total liabilities

Capital = £29,480 - £13,000 = £16,480

So the amount of Basil Yamey's capital is £16,480.

Answer:

Basil Yamey's capital is the total amount of money that he has invested in his business. This can be calculated as the sum of the cost of the assets that he has purchased, minus any outstanding debts, plus any cash or cash equivalents he has on hand.

The cost of the assets that Basil has purchased is:

£9,000 (van) + £1,800 (market stall) + £280 (computer) + £11,200 (inventory) = £21,280

He still owes £5,000 for the inventory, so the total cost of the assets minus the outstanding debt is:

£21,280 - £5,000 = £16,280

He borrowed £8,000, so the total amount of his capital is:

£16,280 + £8,000 = £24,280

He also has cash on hand and in the bank:

£900 (cash) + £6,300 (bank balance) = £7,200

So, Basil Yamey's total capital is £24,280 + £7,200 = £31,480.

Answer:

D

Step-by-step explanation:

When you look for (f+g)(x), we are in essence say that we're looking for f(x)+g(x)

=(2x+1)+(x^2-7).        (substitute for f(x) and g(x))

=2x+1+x^2-7.            (remove the brackets by substituting positive 1 into g(x))

=2x+x^2-6                (add like terms- in this case 1-7=6)

=x^2+2x-6                 (rearrange the equation)