In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . If m∠ADE is with 34° smaller than m∠CAB, find the measures of the angles of ΔADE.

[tex]\theta=\dfrac{3\pi}{4}=\pi-\dfrac{\pi}{4}\\\\y=\tan\theta x\\\\y=\left(\tan\dfrac{3\pi}{4}\right)x\\\\y=\left(\tan\left(\pi-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(\tan\left(-\dfrac{\pi}{4}\right)\right)x\\\\y=\left(-\tan\dfrac{\pi}{4}\right)x\\\\y=-1x\\\\\boxed{y=-x}\to\boxed{D.}[/tex]

Answer:

If you are doing it on edge it is x+y=0

Step-by-step explanation:

x+y=0 when you solve for y it equals -x( y=-x)

Answer: y=54

Step-by-step explanation: so 24/4 is 6 soooo 9*6=54 ez

Answer:

y =54

Step-by-step explanation:

We can use the equation y =kx

If we know y and x we can solve fork

24 = k*4

24/4 = k

6 =k

y = 6x

Substitute in 9

y =6*9

y =54

Answer:

9

Step-by-step explanation:

Otf the 15 that have a view of the river, 6 have both selections.

The remaining 9 only have a view of the river.

x³y⁴

The Lowest Common Denominator of fractions is the Least Common Multiple of their denominators. That is, you want to find the LCM of ...

Find the highest power of each of the factors, and multiply those together.

The highest power of x is x³. The highest power of y is y⁴. So, the LCM of these expressions is ...

... x³y⁴

_____

Then the two fractions are ...

... 3y³/(x³y⁴) . . . and . . . 7x²/(x³y⁴)

Answer:

About 2614 years.

Step-by-step explanation:

We are given k, and the information that N/N0 = 0.77, so the C-14 function becomes:

[tex]N=N_0\cdot e^{-kt} \\0.77N_0 = N_0\cdot e^{-kt}\\0.77 = e^{-0.0001 t}[/tex]

and we can solve for t:

[tex]0.77 = e^{-0.0001 t}\\\ln0.77 = \ln e^{-0.0001 t}\\\ln 0.77 = -0.0001 t\implies\\t = -\frac{\ln0.77}{0.0001}=2613.65\approx 2614\,\,\,\mbox{years}[/tex]

The estimated age of the bird skeleton is 2614 years.

The mode is the number in the set that appears the most.

In the given data set, the number 45 is listed twice while all the other numbers are only listed once.

The mode is 45.

Answer:

45

Step-by-step explanation:

The value which appears most often or has the highest frequency in a data set is said to be the mode.

Here we are given the following data set:

{41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}

For this data set, we can see that the number / element 45 has occurred the most often which is twice. So the mode of this data set will be 45.

We can use a modified form of the Pythagorean Theorem to find the length of  x, also known as side b.

Pythagorean Theorem:

a^2 + b^2 = c^2

We can fill in the values of a^2 and c^2, and then solve for b.

14^2 + b^2 = 25^2

196 + b^2 = 625

Subtract 196 from both sides.

b^2 = 429

√ both sides.

b = 20.7

Answer:

3

Step-by-step explanation:

if the length and width is 3, 3 times 3 is 9

Answer:

BC = EF = 8

Step-by-step explanation:

Assuming you mean BC ≅ EF, then ...

... 3z +2 = z +6

... 2z = 4 . . . . . . . . add -2-z

... z = 2 . . . . . . . . . divide by 2

BC = EF = 2+6 = 8

The question is about finding the measures of given sides and angles in similar triangles. By setting up a proportion between the given sides BC and EF, we can solve for the variable 'z'. This 'z' can then be used to find the sides and angles of the triangles.

In the case of the problem, we're dealing with the concept of similar triangles in geometry. Since △ABC is similar to △DEF, this means that the corresponding sides are in proportion, and corresponding angles are equal.

Given that BC = 3z + 2 and EF = z + 6, we can write a proportion: BC/EF = 3z+2 / z+6, because the lengths of the corresponding sides of these two similar triangles should be in ratio.

Then you can solve this equation for the variable 'z', which will give us the values for sides BC and EF. If necessary,  you can also find the measure of the angles using the values of 'z'.

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Answer:

there are 49 passengers

Step-by-step explanation: 35%=0.35

0.35*140= 49

Answer:

102 ≤ heart rate ≤ 183.6

Step-by-step explanation:

... lower limit ≤ heart rate ≤ upper limit

Put 16 where "a" is and do the arithmetic.

... lower limit = 0.5(220 -16) = 102

... upper limit = 0.9(220 -16) = 183.6

Then the inequality is ...

... 102 ≤ heart rate ≤ 183.6

_____

Comment on the problem

There is nothing to "solve" here. One only needs to evaluate the limits.

In this Compound Inequality question, The recommended heart rate range for a 16 year old person, according to the provided formulas, is between 102 and 183.6 beats per minute.

Given that the age 'a' is represented by 16 years, we can simply substitute this value into the two given formulas to find the recommended heart rate range.

The lower limit of the heart rate is given by the formula 0.5 x (220 - a) and the upper limit is given by the formula 0.9 x (220 - a).

For the lower limit, substituting a = 16, we get 0.5 x (220 - 16) = 102 beats per minute. Similarly, for the upper limit, we get 0.9 x (220 - 16) = 183.6 beats per minute.

Therefore the range of the heart rate for a 16 year old person is 102 to 183.6 beats per minute.

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To choose unit vectors, one must understand that they have a magnitude of one and are directed along the axes in space. For any point P or S, the unit vectors are (i_p, j_p, k_p) or (i_s, j_s, k_s) respectively, each with a magnitude of one.

To determine which vectors are unit vectors, you must know that a unit vector has a magnitude (length) of one and indicates direction in space. The given information states that for a point P in space, the unit vectors are (î_p, â_p, k_p). Each of these vectors has a magnitude of one and points in the direction of increasing x, y, and z coordinates, respectively. Similarly, for point S, you have (i_s, j_s, k_s), also with a magnitude of one.

The special types of unit vectors such as î (i-hat), â (j-hat), and k (k-hat) are always of magnitude one and are parallel to the x, y, and z axes, respectively. The vector dê, represents a vector of length d pointing in the positive x-direction, implying dê is also a unit vector if d equals one.

Therefore, in the context provided, all options (a), (b), (c), and (d) are correct if their vectors have a magnitude of one and adhere to the rules to be considered unit vectors.

Answer:

February

Step-by-step explanation:

February is colder by 7°F

-9 - 7 = -16

~

Answer:February

Step-by-step explanation:

If you see the number line below -16 is more far than -9

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

' ' '

-16 -9 0

Answer:

35 x 10.6, 140 x 2.65 and 371 x 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the given expression represents the account balance, the initial amount (when x=0) is $500 in Account A, and $100 in Account B. (Less money was invested in account B.)

The growth rate of each account is $1.03 per year.* (The growth rate ($/year) is identical for each account.)

The total of the initial amounts invested is $500 +100 = $600.

_____

* Comment on growth rate

Since the account balance is shown as greater than or equal to the given expression, there appears to be the possibility that adjustments are made to the account balance by some means other than the growth predicted by this inequality. For example, if the balance in Account A is $900 at the end of 1 year, the inequality will still be true, but the extra $398.97 will be in addition to the $1.03 growth predicted by this expression.

This means we really cannot say what the growth rates of the accounts might be, except that it is a minimum of $1.03 per year in each account.

_____

Comment on the expressions

More usually, we would expect to see an account balance have the equation a = 400·1.03^x. That is, the interest rate would be 3% and it would be compounded annually. The expression 400 + 1.03x is very unusual in this situation.

See the attachment

The solid dot on the right-hand portion of the curve means the function is defined for x ≥ 2. Choices A and C have that condition.

The function is linear for x ≥ 2, so matches selection C, not A.

Answer:

2<x<∞

Step-by-step explanation:

The arrow has a filled in circle at around the 2.5 mark which allows us to deduce that the number 2 is not included in the inequality but almost all the numbers after 2 i.e. (2.1,2.2,2.3,2.4,2.4... etc ) are included. This gives us our lower bound.

The arrow goes to positive infinity. Which gives us our upper or left bound.

Answer:

r>(greater than or equal to)2.5

Step-by-step explanation:

Answer: that would be 3 months.

Step-by-step explanation:

feb

When the number of cars needed to be sold to meet fixed plus variable expenses is subtracted from the number of cars projected to be sold, the result is negative for all months listed except February. In that month, Barney covers is expenses.

We have computed ...

... (expected car sales) - (needed car sales)

where ...

... (needed car sales) = (variable expenses + fixed expenses)/(income per car sold)

For January, this calculation gives ...

... 32 - (2600 +3100)/175 = 32 -32.571 = -0.571

That is, Barney does not project he will sell enough cars to pay his January expenses.

In February, the result is 0, which means he will sell enough cars in February to pay all his monthly expenses.

To find a1, put 1 in the given equation and evaluate.

... a1 = -3·1 +1

... a1 = -2

Each time n increases by 1, an is 3 less than the previous value. So, you can write the recursion relation as ...

... a[n] = a[n-1] - 3

Final answer:

To find the value of x in a rectangle with a length of 4 inches, set up the equation 2(4 + x) = 4x and solve for x. The value of x is 4 inches.

Explanation:

To find the value of x, we need to set up an equation using the given information. The perimeter of a rectangle is equal to twice the length plus twice the width. The area of a rectangle is equal to the length times the width. So, we can set up the equation: 2(4 + x) = 4x. Next, solve the equation for x:

8 + 2x = 4x

8 = 4x - 2x

8 = 2x

4 = x

Therefore, the value of x is 4 inches.

Answer:

None, the answer will be the same

Step-by-step explanation:

(1, 1), (4, -25)

You can evaluate the function to see.

f(-1) = -3^(-1-1)+2 = -3^(-2)+2 = -1/9 +2 ≠ 2

f(1) = -3^(1-1) +2 = -1 +2 = 1

f(0) = -3^(0-1) +2 = -1/3 +2 ≠ 0

f(4) = -3^(4 -1) +2 = -27 +2 = -25

_____

Or, you can graph the points and the curve.

Answer:

(1, 1), (4, -25)

Step-by-step explanation:

Answer:

A is the right one

Step-by-step explanation:

it is right on edge

We find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

BCD is a right angle triangle

We have to find the angle B from the triangle

BD is the hypotenuse which is √89

DC is the opposite side of angle B

We can find angle B by using sine function.

Or we can find the length of BC by using pythagorean theorem

then find the tanB function

tanB=8/BC

Hence, we find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC

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Answer:

75 ft

Step-by-step explanation:

Here we are given a right angled triangle with a known angle of 20°, length of the hypotenuse to be 80 and we are to find the length of the base x.

For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.

[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]

So putting in the given values to get:

[tex]cos 20=\frac{x}{80} \\\\x= cos 20*80\\\\x=75.17[/tex]

Therefore, the value of x is the closest to 75 ft.

Answer:

as discriminant = 9, it has two real solutions.

Step-by-step explanation:

for eqn ax^2 + bx + c, discriminant = b^2 - 4ac

y = 4x^2 - 5x + 1

discriminant = (-5)^2 - 4(4)(1)

= 25 - 16

= 9

as discriminant > 0, it has two real solutions.

Answer:

Discriminant = 9 and the equation has two real solutions

Step-by-step explanation:

For a quadratic equation in the form of y = ax^2 + bx + c, its discriminant is equal to b^2 - 4ac.

If discriminant < 0, then the equation has two imaginary solutions. If it is 0, then the equation has 1 real solution and if it is > 0, 2 real solutions.

In this case, y = 4x^2 - 5x + 1.

So its discriminant = -5^2 - 4*4*1

= 9 so it has two real solutions.

Answer:

d  31 degrees

Step-by-step explanation:

We can use the formula

<C = 1/2 (arc AE - arc BD)

Let substitute in what we know

ARC AE = 120

ARC BD = 58

<C = 1/2 (120 - 58)

<c = 1/2(62)

<c = 31

Answer:

Step-by-step explanation:

The distance to the lookout is the sum of distances before and after the rest stop:

... "to" distance = 2 mi + 1 3/4 mi = 3 3/4 mi

The distance from the lookout is 1/2 mile shorter, so is ...

... "from" distance = 3 3/4 mi - 2/4 mi = 3 1/4 mi

Then the total hike is ...

... total distance = "to" distance + "from" distance

... = 3 3/4 mi + 3 1/4 mi = 6 4/4 mi

... total distance = 7 mi

The water each hiker will bring is ...

... (7 mi) × (1/4 gal/mi) = 7/4 gal = 1 3/4 gal

Each hiker will hike a total of 7 miles, and they will need to bring 1.75 gallons of water for the entire trip.

First, we need to determine the total distance each hiker will travel:

The return trail is described as 1/2 mile shorter than the trail to the lookout. Therefore:

Summing up the distances:

Calculating Total Water Needed:

Each hiker brings 1/4 gallon of water per mile:

Thus, each hiker will hike a total of 7 miles and will need to bring 1.75 gallons of water for the entire trip.

Answer:

C

Step-by-step explanation:

Triangle CGF and triangle CED are similar. Hence, the ratio of their corresponding sides are equal. Thus we can write:

[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}[/tex]

We can now cross multiply and solve for CD:

[tex]\frac{5x+4}{2x+3}=\frac{CD}{3x+0.8}\\(5x+4)(3x+0.8)=(2x+3)(CD)\\15x^2+4x+12x+3.2=(2x+3)(CD)\\15x^2+16x+3.2=(2x+3)(CD)\\CD=\frac{15x^2+16x+3.2}{2x+3}[/tex]

Since GF is a midsegment of CDE, CD is double of CF. So we can write:

[tex]CD=2CF\\\frac{15x^2+16x+3.2}{2x+3}=2(3x+0.8)\\\frac{15x^2+16x+3.2}{2x+3}=6x+1.6\\15x^2+16x+3.2=(6x+1.6)(2x+3)\\15x^2+16x+3.2=12x^2+18x+3.2x+4.8\\15x^2+16x+3.2=12x^2+21.2x+4.8\\3x^2-5.2x-1.6=0[/tex]

By using quadratic formula [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex] and with a=3, b= -5.2, and c= -1.6, we find the value of x to be:

[tex]\frac{5.2+-\sqrt{(-5.2)^2-4(3)(-1.6)} }{2(3)}=2[/tex]

Since the expression for CD is [tex]\frac{15x^2+16x+3.2}{2x+3}[/tex] , we plug in [tex]x=2[/tex] into this expression to find value of CD:

[tex]\frac{15(2)^2+16(2)+3.2}{2(2)+3}=13.6[/tex]

The correct answer is C

Answer:

C. 13.6

Step-by-step explanation:

We have been given that GF is a mid-segment of CDE.

Since we know that mid-segment of a triangle is half the length of its parallel side.

We can see that ED is parallel to GF , so measure of GF will be half the measure of ED. We can represent this information as:

[tex]GF=\frac{1}{2}ED[/tex]

Let us substitute given value of GF and ED to find our x.

[tex]2x+3=\frac{1}{2}(5x+4)[/tex]

Multiply both sides of equation by 2.

[tex]2*(2x+3)=2*\frac{1}{2}(5x+4)[/tex]

[tex]2*(2x+3)=5x+4[/tex]

[tex]4x+6=5x+4[/tex]

[tex]6=5x+4-4x[/tex]

[tex]6=x+4[/tex]

[tex]6-4=x[/tex]

[tex]2=x[/tex]

We can see that triangle CFG is similar to triangle CDE, so we will use proportions to find length of CD.

[tex]\frac{CF}{GF}=\frac{CD}{ED}[/tex]

Substitute given values.

[tex]\frac{3x+0.8}{2x+3}=\frac{CD}{5x+4}[/tex]

Upon substituting x=2 in our equation we will get,

[tex]\frac{3*2+0.8}{2*2+3}=\frac{CD}{5*2+4}[/tex]

Let us simplify our equation.

[tex]\frac{6+0.8}{4+3}=\frac{CD}{10+4}[/tex]

[tex]\frac{6.8}{7}=\frac{CD}{14}[/tex]

[tex]14*\frac{6.8}{7}=CD[/tex]

[tex]2*6.8=CD[/tex]

[tex]13.6=CD[/tex]

Therefore, CD equals 13.6 and option C is the correct choice.

The Diameter of Hydrogen Atom in Scientific Notation is :

✿  1.06 × 10⁻¹⁰ Meters

Answer:

Step-by-step explanation: I just solve it.