Finish the congruence statement for the triangles in question #4 by filling in the blank:

BCD = ???

Answer:

x = 3 1/2

Step-by-step explanation:

8/14 = 2/x

Using cross products

8*x = 14*2

8x = 28

Divide by 8

8x/8 = 28/8

x = 7/2

x = 3 1/2

The length of the leg is 9.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

From the triangle,

S = length of the leg.

Now,

Applying the Pythagorean theorem.

√18² = 3² + s²

18 = 9 + s²

s² = 18 - 9

s² = 9

s = 9

Thus,

The length of the leg is 9.

Learn more about the Pythagorean theorem here:

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Answer:

583

Step-by-step explanation:

The mean of a data set is the average of the data set. It can be found by adding up all of the values and then dividing by the total number of values added. In this case, one is given the mean, and one needs to find a missing value. Since there is a missing element, add one to the total number of values in the data set. The missing element is represented by the parameter (x). Set up an equation and solve:

Simplify,

Inverse operations,

Answer:

[tex]RS~\times~RT=RQ^2[/tex]

[tex]x(x+40)=45^2[/tex]

[tex]x^2+40x-45^2=0[/tex]

[tex]x=\frac{-40+-\sqrt{(40)^2+4\times45^2} }{2}[/tex]

[tex]=\frac{-40+-\sqrt{9700} }{2}[/tex]

[tex]x=29.2[/tex]

---------------------------

hope it helps..

have a great day!!

Answer:

[tex]p > s[/tex]

Step-by-step explanation:

Given

[tex]p \to poncho[/tex]

[tex]s \to scarf[/tex]

Required

The inequality

From the question, we understand that;

the number of p used is more than the number of s

more than means greater than.

So, the inequality is:

[tex]p > s[/tex]

To represent this on a number line.

First, we identify the position of s (i.e. scarf)

[tex]p > s[/tex] implies that p is any point to the right of s

Answer:

Durante el frente frío mencionado en el ejercicio, la temperatura de Canadá bajó:

Step-by-step explanation:

Para obtener la cantidad de grados que bajó la temperatura en el caso mencionado, debes primero identificar la disminución en los grados positivos, es decir, cuando los grados Celsius llegaron a 0°C:

En la operación matemática, solo restante la cantidad de grados necesarios a la temperatura inicial (7°C) para que la temperatura quedara en 0°C, donde obtenemos una diferencia de 7°C, ahora identificas la cantidad de grados que se necesitan para que la temperatura pase de 0°C a -5°C:

Recuerda que como ya estamos hablando de diferencia, no necesitas señalar si los grados son negativos, solo identificamos el número de grados Celsius entre esas temperaturas mencionadas, por lo tanto, al final sumas las dos diferencias halladas y esa será la diferencia total entre las dos temperaturas dadas:

Por lo tanto, durante el frente frío mencionado, la temperatura en Canadá bajó 12°C.

Answer:

Step-by-step explanation:

20 houses

Answer:

20

Step-by-step explanation:

You would set it up as 8:5=32:x. Since you are multiplying the number of cars by 4, you should do the same with houses. This gives 32:20, meaning there are 20 houses on the block.

**You may want to revise multiplying and dividing with ratios. I'm always happy to help!

Answer:

Step-by-step explanation:

angle 1 and angle 2 add to 180 degree because they are supplementary angel and in supplementary angle sum of two angles is 180 degree

angle 1 and angle 3 is equal as they are vetically opposite angles and vertically opposite angles are always equal.

angle 3 and 4 add to 180 degree because they are supplementary angle and in supplementary angle sum of two angles id 180 degree.

angle 2 and angle 4 are equal because they are vertically opposite angles and vertically opposite angles are always equal.

3x -17

4   -5 =0

3(x-4)=2

4          5

Answer:

Let x be one of the numbers

then since they differ by 3... Let (x-3) be the 2nd Number

Their product is 88

(x-3)x = 88

x²-3x =88

x² - 3x - 88=0

Solving The quadratic eqn

x=11 or x = -8.

To check this answer

since the Numbers are x and x-3

x= 11

x-3 = 11 - 3 = 8

(x-3)x = 8x11 = 88.

Or When x=-8

(x-3) = -8 - 3 = -11

x= -8

(x-3)x = -8 x - 11 = 88.

Have a great day!

Answer:

First Set: [11, 8], Second Set: [-8, -11]

Step-by-step explanation:

The first number will be x. The second number is x-3. So now make an equation: x(x-3)=88 because their product equals 88. So now solve.

Solving:

[tex](x)(x-3)=88[/tex]

[tex]x^{2}-3x-88=0[/tex]

Now you can factor:

[tex](x-11)(x+8)=0[/tex]

[tex]x=11, x=-8[/tex]

Now plug in each number for x for the following equation:

[tex](x)(x-3)=88[/tex]

[tex](11)(11-3)=88[/tex]

[tex]88=88[/tex]

This is true.

[tex](-8)(-8-3)=88[/tex]

[tex]88=88[/tex]

This is true.

Both are true. So now you have two sets of answers.

Your welcome!

Step-by-step explanation:

Decide on the number of classes.

Determine the range, i.e., the difference between the highest and lowest observations in the data.

Divide range by the number of classes to estimate approximate size of the interval

hope it helps.

Answer:

false

Step-by-step explanation:

false

Answer:

it is false it'll be (-infinity,infinity )

Step-by-step explanation:

Hope this helps!! <3

Answer: 14

Step-by-step explanation: I am guessing that you wrote the "c" incorrectly and that meant to be an "e". All you really need to do is replace the letters with the numbers that equal the letters, which would be:

(15) - 1/2(2)

1/2 * 2 = 1

15 - 1 = 14

Answer:

opposite of each other

Hope this helps!

Answer:

0.76

or

-0.76

hope this helps

Answer:

x<4

Step-by-step explanation:

To solve for x in the inequality equation, the terms should be rearranged such that x is on one side and integers are on the other side.

First, expand 4(x-3).

This will obtain:

[tex]4x - 12 < 2x - 4[/tex]

Now, shift x terms and integers on each side.

[tex]4x - 2x < - 4 + 12[/tex]

After simplifying, it will get:

[tex]2x < 8[/tex]

Finally, we can solve for x.

[tex]x < 4[/tex]

We can also draw the respective graph (please don't mind my drawings), where the area shaded in green is the range.

Answer:

FGE = 44 degrees

CD = 72 degrees

Step-by-step explanation:

Let's solve for FGE first;

We know that CGD and FGE are verticals angles and therefore congruent, so if;

CGD = FGE

44 = FGE

Now let's solve for CD;

Therefore we can say;

FED = FBE + ED

180 = 72 + ED

180 - 72 = ED

108 = ED

So;

FC also = 108

Now we know that the measure of a whole circle is 360 and here we are given 4 arcs that make up a full circle;

FBE + ED + DC + CF = 360

72 + 108 + DC + 108 = 360

288 + DC = 360

DC = 360 - 288

DC = 72

Hope this helps!

Answer:

104.6

just use the cone formula and add the two together.

Answer:

[tex]2.95\cdot 10^3\:\mathrm{km}[/tex]

Step-by-step explanation:

Distance is given by [tex]D=st[/tex], where [tex]s[/tex] represents speed or rate and [tex]t[/tex] represents time.

What we're given:

Thus, the distance covered by the airplane is:

[tex]d=885\cdot 3.\overline{3}=2,950\:\mathrm{km}[/tex]

In scientific notation:

[tex]2,950\:\mathrm{km}\implies\boxed{2.95\cdot 10^3\:\mathrm{km}}[/tex]

Answer:

Distance = speed * time

The distance is:

Answer: anser is the last one y-2=1/2(x-(7))

Step-by-step explanation:

The additional piece of information is ∠S ≅ ∠J, which satisfy the given condition.

If any two angles and side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

You need at least one pair of congruent corresponding sides to prove two triangles are congruent. If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

Here, We can get

ΔTBJ ≅ Δ DPS

Existing conditions, JB = PS

 and ∠B = ∠P

Prove by ASA,  ∠S ≅ ∠J

Thus, additional piece of information is ∠S ≅ ∠J, which satisfy the given condition.

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Answer:

9.1

Step-by-step explanation:

Answer:9.1

Step-by-step explanation: simply remove the 2 digits after 1 as the tenth place is always one digit after the point

Answer: 9

Step-by-step explanation:

Given

The function is [tex]x^2-6x+c[/tex]

To make it a perfect square, compare it with [tex](a-b)^2=a^2+b^2-2ab[/tex]

Here,

[tex]x=a,\\-6x=-2ab\\\\\therefore b=3[/tex]

So, c must be square of b i.e. 9

[tex]x^2-6x+c\Rightarrow x^2-6x+9\\\Rightarrow (x-3)^2[/tex]

Therefore, value of c is 9.

Answer:

A) A = 275 + 125x

B) 1850 - 100x

C) 7 months

D) 13 months

Step-by-step explanation:

He has $275 saved.

He plans to save $125 each month.

We are told that the computer is currently $1,850

And the price drops $100 each month.

Thus;

A) If x represents the number of months, then equation of the amount he will save is;

A = 275 + 125x

B) If x represents the number of months, then equation to represent the total cost is;

1850 - 100x

C) To find the Number of months he will need to save, we will equate gotten in question A to the equation gotten in question B. Thus;

275 + 125x = 1850 - 100x

Rearranging;

125x + 100x = 1850 - 275

225x = 1575

x = 1575/225

x = 7 months

D) If the price doesn't drop like he is anticipating, then the cost will still be $1850. Thus;

275 + 125x = 1850

125x = 1850 - 275

125x = 1575

x = 1575/125

x = 12.6 months

Approximating to the nearest whole number gives 13 months

Answer: 100 = 10d + 5

Step-by-step explanation:

Dolls are sold for $10 each so when checking the total amount made from the sale of d dolls you will multiply d by the price of each doll:

= 10 * d

= 10d

There is a $5 charge for shipping but this is one time so it is added to the total price of d dolls:

= 10d + 5

The total made was $100 so the equation above should equal $100:

100 = 10d + 5

Answer:

1) 187.5ms^2

1) 187.5ms^22) 307.5m

Step-by-step explanation:

1) You can use the formula:

Force = Mass x Acceleration

750 = 4 x a

750 = 4a

750/4 = a

187.5ms^2

2)

For every one second it travels 12.3 meters therefore you can just do 12.3x25 = 307.5m

Answer:

The absolute change in the height of the water is 9.5 inches

Step-by-step explanation:

Given

[tex]l =24in[/tex] --- length

[tex]w = 15in[/tex] --- width

[tex]h =12in[/tex] --- height

[tex]V_1 = 900in^3[/tex] --- the volume removed

Required

The absolute change in the height of the water

First, calculate the base area (b):

[tex]b = l * w[/tex]

[tex]b =24in * 15in[/tex]

[tex]b =360in^2[/tex]

The height of the water that was removed is:

[tex]H = \frac{V_1}{b}[/tex] i.e. the volume of the water removed divided by the base area

[tex]H = \frac{900in^3}{360in^2}[/tex]

[tex]H = \frac{900in}{360}[/tex]

[tex]H = 2.5in[/tex]

The absolute change in height is:

[tex]\triangle H = |h - H|[/tex]

[tex]\triangle H = |12in - 2.5in|[/tex]

[tex]\triangle H = |9.5in|[/tex]

[tex]\triangle H = 9.5in[/tex]

Answer:

True

Step-by-step explanation:

This is an Isosceles triangle because it has two equal sides.