in the diagram, triangle ABC is similar to triangle EDC. a. is line AB parallel to line DE? b. show that triangle ACD is similar to triangle ECB. c. find the measure of angle CAD. d find line ED. e. find line AD explain your reasoning

Answer:

Step-by-step explanation:

Here we will show you step-by-step how to get the solution to: "What is 5/14 rounded to the nearest whole number?"

First, we convert the fraction to a decimal number by dividing the numerator by the denominator:

5 / 14 = 0.3

Then, we round to the nearest whole number using the following rules:

If the number to the right of the decimal point is .5 or higher, then add 1 to the left of the decimal point.

If the number to the right of the decimal point is less than .5, then leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.

.4 is less than .5. Thus, we leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.

5/14 rounded to the nearest whole number is therefore:

0

Answer:

each teammate contributed 1.43 sorry but i do not know how many members they have because my head hurts

The approximate number of bacteria after 16 hours is 60 bacteria ,Option C is the right answer.

A function is a Mathematical statement which connects a dependent variable and an independent variable.

The graph shows the  the growth rate of a certain bacteria in a lab

the number of bacteria is on the y axis and

the number of hours is on the x axis

The function is continuous ,

From the graph the approximate number of bacteria after 16 hours is

60 bacteria

Therefore Option C is the right answer.

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Answer:

Step-by-step explanation:

a=-110

d=-102-(-110)=-102+110=8

let n be the number of terms.

74=-110+(n-1)×8

74=-110+8n-8

74+118=8n

192=8n

n=192/8=24

[tex]s=\frac{n}{2} [2a+(n-1)d]\\s=\frac{24}{2} [2(-110)+(24-1)\times8]\\=12[-220+184]\\=12(-36)\\=-432[/tex]

I thank the answer is B

Step-by-step explanation:

10

Answer:

60 points

100 - 5x

Step-by-step explanation:

If she got 8 questions wrong she missed (8 * 5) points or 40 points. This means she only got 60 points

This can be further generalized by simply subtracting the amount of questions someone got wrong by 5 from the total available points of 100

100 - 5x

Answer:

a

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (6, 4 ) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = [tex]\frac{1}{3}[/tex] x + 2 ← equation of line

Answer:

8 soccer balls

Step-by-step explanation:

Since the ratio of players to soccer balls is 5:2, we can conclude that:

The question asks to find how many soccer balls are needed for 20 players.

Multiply both players and soccer balls by 4, this will get:

Henceforth, 8 soccer balls are needed for 20 players.

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]~~~~~x = \dfrac{1}{2 - \dfrac 1{2-\dfrac{1}{2-x}}}\\\\\\\implies x = \dfrac{1}{2 - \dfrac 1{\dfrac{4-2x-1}{2-x}}}\\\\\\\implies x= \dfrac{1}{2 - \dfrac{2-x}{3-2x}}\\\\\\\implies x = \dfrac{1}{\dfrac{6-4x-2+x}{3-2x}}\\\\\\\implies x = \dfrac{3-2x}{4-3x}\\\\\\\implies 4x -3x^2 = 3-2x\\\\\\\implies 3x^2 -4x +3-2x = 0\\\\\\\implies 3x^2 -6x +3 = 0\\\\\\\implies 3(x^2 -2x +1) =0\\\\\\\implies x^2 -2x +1 = 0\\\\\\\implies (x-1)^2 = 0\\\\\\\implies x -1 = 0\\\\\\\implies x = 1[/tex]

Answer:

[tex]x = \frac{4y + 1}{3} [/tex]

The goal is to isolate the X value. So the first step would be to add 1 to both sides, making the equation 4y + 1 = 3x.

Then you divide both sides by 3, making the equation (4y + 1)/3 = x

If you have a Y value then you'd plug it in for Y and solve for x but since there isn't one provided you're done.

Step-by-step explanation:

i think b is right answer

Answer:

see photo for detailed analysis

Step-by-step explanation:

please mark me as brainlest

Answer:

A, C, D, E, F

Answer:

Amount in Blank total = $160

Amount of money Daniel’s agent made = $40

Amount of money Daniel and the agent made

from the show  = $160

Step-by-step explanation:

this question is based on the calculation of percentages

so,

it is is given in the question that -

Daniel is a singer, and he promises his agent that he will give him a 25% commission based on what he makes from a show.

After paying the agent, Daniel takes home =  $120

so,

let 'x' is the total amount of money that Daniel earned form the show

it is also given that Daniel promised to give 25 % to his agent from what he earned from the show

so, percentage of money left to the Daniel is

100-25 = 75%

therefore according to the question,

75percent of the x = $120

75/100×(x)   =  120

  3/4×(x)   =  120

     3x   =   120×4

     3x  =  480

       x  =  $160

so the total amount of money Daniel earned from the show is $160

Now we know that Daniel’s agent made 25% of the total amount of money earned from the show

therefore

25percent of 160 = Daniel’s agent made

     25/100 ×160  = Daniel’s agent made

             $40 =  Daniel’s agent made

so the amount of money earned by Daniel’s agent made is $40

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Answer: Daniel’s agent made

✔ $40

Daniel and the agent made a total of

✔ $160

from the show.

.

Step-by-step explanation:

The only increasing function is the last option:

[tex]f(x) = 5^x[/tex]

Here we only need to see that, is as x increases also do f(x). Then the function will be increasing.

The cases for exponential functions is actually more trivial than that.

In the given options there is only one function with a base larger than 1, which is the last option:

[tex]f(x) = 5^x[/tex]

That is the correct option.

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Answer:

[tex] \sqrt[4]{ {80}^{x} } [/tex]

Step-by-step explanation:

Hope it helps

Answer:

C- Yes, because it pases the vertical line test.

Step-by-step explanation:

It passes through one point exactly.

An isosceles triangle is one with two equal-length sides. The ΔBCD is an isosceles triangle.

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.

Given ΔABC is an isosceles triangle with side AB = AC. Therefore, as per the base angle theorem,

∠A = ∠C = 36°

Also, in ΔABC, the sum of the angles can be written as,

∠ABC + ∠BAC + ∠BCA = 180°

∠ABC + 36° + 36° = 180°

∠ABC = 108°

For ∠ABC we can write,

∠ABC = ∠ABD + ∠CBD

108° = 72° + ∠CBD

∠CBD = 36°

Now, in ΔBCD, the measure of ∠CBD and ∠DCB both equals to 36°. Therefore, we can write, that the ΔBCD is an isosceles triangle.

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Answer:

[tex]-\frac{1}{2} \vec {c}[/tex]

Step-by-step explanation:

Look at the component form of each vector.

Note that vector c is <4,4> and vector d is <-2,-2>

If one imagined the line that contained each vector, the line for both would have a slope of 1, because [tex]\frac{4}{4}=1=\frac{-2}{-2}[/tex]

Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).

If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector.  This means that there is some number "k", such that [tex]k \vec{c} = \vec {d}[/tex], or equivalently, [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex].

If [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex], we just need to substitute known values and solve for k:

[tex]kc_x=d_x\\k(4)=(-2)\\k=\dfrac{-2}{4}\\k=-\frac{1}{2}[/tex]

Double checking that k works for the y-coordinates as well:

[tex]kc_y=d_y[/tex]

[tex](-\frac{1}{2}) (4)[/tex]    ?    [tex](-2)[/tex]

[tex]-2=-2 \text{ } \checkmark[/tex]

So, [tex]-\frac{1}{2} \vec {c} = \vec {d}[/tex]

Answer:

Step-by-step explanation:

Look at the component form of each vector.

Note that vector c is <4,4> and vector d is <-2,-2>

If one imagined the line that contained each vector, the line for both would have a slope of 1, because

Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).

If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector.  This means that there is some number "k", such that , or equivalently,  and .

If  and , we just need to substitute known values and solve for k:

Double checking that k works for the y-coordinates as well:

   ?    

So,

Answer:

2,4,8,16

Step-by-step explanation:

2,4,8,16

difference is multiplied by 2

Answer:

[tex]\rightarrow \fbox {Yes} \leftarrow[/tex]

Step-by-step explanation:

ΔABC is a right triangle as it possesses a right angle (90°).

Triangle ABC is a right angled triangle since it holds Pythagoras theorem.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

For a right angled, triangle, there is a theorem called Pythagoras Theorem which relates the three sides of the triangle.

Pythagoras theorem states that,

Hypotenuse² = Base² + Altitude²

Here AC is the hypotenuse, BC is the base and AB is the altitude.

Base² + Altitude² = (BC)² + (AB)²

                             = 5² + 12²

                             = 25 + 144

                             = 169

                             = 13²

                             = AC²

                             = Hypotenuse²

Pythagoras theorem holds for the given triangle.

Hence the given triangle ABC is a right angled triangle.

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The graph that accurately shows the velocity of the park or at any time is as shown in the attached image.

Velocity is defined as the rate of change of position of object with respect to time. Velocity is also defined as the speed of an object moving in a definite direction.

Velocity is a vector quantity and so it has both magnitude and direction. Its' SI unit is in meters per second.

The velocity of a particle is modeled by the function;

v(t) = ¹/₁₀(3t - 8)³ + 2

The given velocity function is cubic function and as such the attached graph shows the velocity of the particle at any time.

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Answer:

x° = 75

(x + 30)° = 105°

Step-by-step explanation:

supplementary angle is two angles that sum is 180°

x° + (x + 30)° = 180°

2x + 30 = 180°

2x + 30 - 30 = 180 - 30

2x = 150

2x / 2 = 150 / 2

x° = 75

plug in 75,

75 + 30 = 105

check: 75 + 105 = 180

Answer: 75 degrees

Step-by-step explanation:

Do you see how both sides of the angle come together to form the straight line seen at the bottom? This means that these are supplementary angles.

Supplementary Angles: Both sides have to add up to a total of 180 degrees.

With this, form an equation: x+(x+30)= 180

Get rid of the parenthesis:

x+x+30= 180

Combine like terms.

2x+30= 180

2x= 180-30

2x= 150

x= 150÷2

x= 75

Checks:

x+x+30= 180

75+75+30= 180

You can also check using the equation in its simplified form: 2x+30= 180.

2x+30=180

2(75)+30=180

150+30=180

Hence x=75

Answer:

B. 66.0

Step-by-step explanation:

The formula for circumference is 2*π*r where r is the radius. MS and MR are both radii, so we can plug in 10.5 to the formula to get 2* π*10.5, which would be about 65.97, which rounds to 66.0. Hope this helps!

Answer:

============================

[tex]\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}[/tex]

Bring both fractions into common denominator:

[tex]\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}[/tex]

Simplify:

[tex]\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]

[tex]\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]

[tex]\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]

[tex]\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =[/tex]

[tex]\dfrac{4\sqrt{14} }{7-4} =[/tex]

[tex]\dfrac{4}{3} \sqrt{14} }[/tex]

Compare the result with given expression to get:

Answer:

Please see attachment.

The first one is a quadrilateral that is not a parallelogram.

The second one is a triangle with a right angle.

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

The area  of Vivian’s garage door is 62.5 square feet

The Vivian garage is made up of a trapezoid and a rectangle. The area of the door is expressed as;

Area = Area of rectangle + area of trapezoid

Area = (5 * 8) + 0.5(7 + 8)*3
Area= 40 +22.5
Area = 62.5 square feet

Hence the area  of Vivian’s garage door is 62.5 square feet

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