An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. Question 3 options: 11.1 cm, 4.9 cm 44.4 cm, 3.2 cm 44.4 cm, 11.1 cm 24 cm, 4.9 cm

Answers

Answer 1

You can solve this problem by applying the Angle Bisector Theorem. Let's call the lenghts we want to calculate: "x":

7.4/x=6/4

When we clear "x", we obtain:

6x=(7.4)(4)
x=(7.4)(4)/6
x=4.9 cm (This is the shortest possible length of the third side of the triangle)

Let's find the longest possible length:

4/6=7.4/x

When we clear the "x", we have:

4x=(7.4)(6)
x=(7.4)(6)/4
x=11.1 cm (This is the longest possible length of the third side of the triangle)

Answer 2

Answer:

11.1 cm, 4.9 cm

Related Questions

please help.
solve the inequality |6 - v| < 9

write the inequality as two inequalities with the absolute value and give a solution set.

Answers

-9 < 6 -v < 9 . . . . two inequalities
-15 < -v < 3 . . . . . subtract 6
-3 < v < 15 . . . . . . multiply by -1

The mean of 10,12,16,20,p,26 is 17.Find the value of p.

Answers

there are 6 numbers total

17 * 6 = 102

10 + 12 + 16 + 20 + 26 = 84

p = 102-84 = 18

p = 18

Answer: " p = 18 " .
__________________________________________________
Explanation:
__________________________________________________
The [arithmetic] mean =

{the sum of all the values in the data set}
divided by {the number of values in the number set} ;
__________________________________________________
→ 17 = (10 + 12 + 16 + 20 + 26 + p) / 6 ;

__________________________________________________
→ (10 + 12 + 16 + 20 + 26 + p) = 17 * 6 ;

→ (p + 84) = 102

Subtract "84" from each side of the equation;
to isolate "p" on one side of the equation; & to solve for "p" ;

→ p + 84 – 84 = 102 – 84 ;

→ p = 18 .
_________________________________________________

The answer is: " p = 18 " .
_________________________________________________

Which statements correctly use the properties of exponents to simplify? Check all that apply.

(xy2)2 = x2y4
x3x3 = x6
3y–2 =
2(x2)3 = 8x6
–x2(–x3) = –x6

Answers

the first one, second, and third

Answer:

1 2 and 3

Step-by-step explanation:

which are the solutions of the quadratic equation x^2=9x+6

Answers

You can use the quadratic equation to solve this once you have this set equal to zero. The answers would be roughly 9.6 and -0.6.

The solutions of the quadratic equation [tex]$x^2 = 9x + 6$[/tex]are:

[tex]\[x = \frac{9 + \sqrt{105}}{2}\][/tex] and [tex]\[x = \frac{9 - \sqrt{105}}{2}\][/tex]

To find the solutions of the quadratic equation [tex]$x^2 = 9x + 6$[/tex], we need to rewrite it in standard quadratic form [tex]$ax^2 + bx + c = 0$.[/tex]

Given:

[tex]\[x^2 = 9x + 6\][/tex]

Subtract [tex]$9x$ and $6$[/tex] from both sides to get it in standard form:

[tex]\[x^2 - 9x - 6 = 0\][/tex]

Now, to solve this quadratic equation, we can factor it or use the quadratic formula:

The quadratic formula is:

[tex]\[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\][/tex]

For our equation:

[tex]\[a = 1, b = -9, \text{ and } c = -6\][/tex]

Substituting these values into the quadratic formula:

[tex]\[x = \frac{-(-9) \pm \sqrt{(-9)^2-4(1)(-6)}}{2(1)}\]\[x = \frac{9 \pm \sqrt{81+24}}{2}\]\[x = \frac{9 \pm \sqrt{105}}{2}\][/tex]

So, the solutions of the quadratic equation [tex]$x^2 = 9x + 6$[/tex]are:

[tex]\[x = \frac{9 + \sqrt{105}}{2}\][/tex] and [tex]\[x = \frac{9 - \sqrt{105}}{2}\][/tex]

6.3% of 41 is?

a. 2.6
b. 6.5
c. 258.3
d. 650.8

Answers

(41/100)6.3= 2.583≈ 2.6
a✓

I think it's A 2.6 hope that helps

Find the lengths of x and y.

Answers

see the attached figure to better understand the problem

we know that

in the triangle ABD
applying the Pythagorean theorem
y²=3³+4²---------> y²=25------------> y=5 units
tan alfa=4/3-----------> equation 1

in the triangle BDC
tan alfa=DC/BD----------> tan alfa=(x-3)/4------------> equation 2

matching equations 1 and 2
4/3=(x-3)/4---------> 4*4=3*(x-3)--------> 16=3x-9---------> 3x=25----> x=25/3 units

the answer is
x=25/3 units
y=5 units

El lote de la familia lópez tiene un lote de 16m*10m y se desea construir una casa de base rectangular en el centro de el.¿que dimensiones debe tener el rectángulo del piso de la casa si tiene un área de 91m2?

Answers

The dimensions of the house should be 7 m by 13 m.

If the house is to be centered, we will take the same amount from the width as we do from the length of the lot for the dimensions. This gives us (10-x) and (16-x) as the dimensions.

The area of a rectangle is found by multiplying the length and width:
(10-x)(16-x) = 91

Multiplying the binomials we have:
10*16 - x*10 - x*16 -x*(-x) = 91
160 - 10x - 16x --x² = 91
160-10x-16x+x² =91

Combine like terms:
160-26x+x²=91

Rewrite this in standard form:
x²-26x+160=91

Subtract 91 from both sides:
x²-26x+160-91 = 91-91
x²-26x+69 = 0

Factoring this, we look for factors of 69 that sum to -26. -23*-3 = 69 and -23+-3 = -26, so:

(x-23)(x-3) = 0

Using the zero product property we know that either x-23=0 or x-3=0, so x=23 or x=3.

x was the amount we take off of the width and length of the lot; if we took 23m off of it, 10-23 gives us a negative amount, which is not realistic. This means both the width and length are subtracted by 3.

10-3 = 7 and 16-3 = 13.

These are the dimensions of the house.

30 POINTS + BRAINLIEST! SHOW YOUR WORK FOR BRAINLIEST PLEASE!

Answers

A four sided figure that figs inside a circle is called a cyclic quadrilateral. One of the properties of such a figure is that the opposite angles add up to 180o

2x + 3 + 4x + 3 = 180o
6x + 6 = 180
6x = 174
x = 174 / 6
x = 29

C = 2x + 1
C = 2*29 + 1
C = 59o

2x+3+4x+3= 180o 6x+6=180 6x=174 174/6 29

2x+1 (2)29+1 59o

Step-by-step explanation:

99pts WILL GIVE BRAINLIEST Use the diagram and given information to answer the questions and prove the statement. Given: X Z   Prove: [see image] Re-draw the diagram of the overlapping triangles so that the two triangles are separated.

What additional information would be necessary to prove that the two triangles, XBY and ZAY, are congruent?

What congruency theorem would be applied?

Prove using a list/flow chart proof.

Answers

I will base the figure from the one you attached in the other problem you posted. (Also attached here).

Statements [Reasons]
1. Angle X is congruent to Angle Z [Given]
2. Line XY is congruent to Line YZ [Given]
3. Angle Y is congruent to Angle Y [Congruence is reflexive]
4. Triangle XBY is congruent to Triangle ZAY [ASA]

ANSWER: The ASA (Angle Side Angle) Congruency Theorem could be applied.

ASAP Plz what is the value of x? Plz no joking around this is from quiz 4.09: Special Right Triangles 2

Answers

Ooh this is a good one!
Firstly, let's find RT so that we can solve the top triangle.
We could actually use 3 methods to find this side: 1) trig to find RT
2) trig to find ST, then Pythagorean Theorem to determine RT
3) use the special 30-60-90 right triangle rule ... hmm, I'm going with the last because it's easiest ;)

For 30-60-90 triangles, the sides are always as follows: smallest side (opposite the 30) is s, the middle side is sSR3, and the hypotenuse is 2×s
Thus, since we have the side opposite 60, it is = sSR3, so:
[tex]s \sqrt{3} = 2 \sqrt{3} \\ s \sqrt{3} \div \sqrt{3} = 2 \sqrt{3} \div \sqrt{3} \\ s = 2[/tex]
So now, the hypotenuse (RT) = 2s = 2(2) = 4

Secondly, we are looking at the other type of special right triangle, the 45-45-90:
The side opposite the 45s are s (remember side lengths are equal whose opposite angles are equal); and the hypotenuse is always
[tex]s \sqrt{2} [/tex]
we only need QR, which is s, which is also = RT
So the answer is:
QR = x = 4

x = 4 IS THE FINAL ANSWER!!!

[ i hope by my explanations you understand how better to do special right triangles in the future] :-D

Answer: The correct answer is 4

Step-by-step explanation:

Here is proof from the quiz

What is the term for a Wage and Tax statement and what is it’s purpose?

Answers

Most commonly referred to as a W-2. This form shows the amount of an individual's earnings and deductions.

△ABC is similar to △RST . In addition, m∠C=76° and m∠S=3(m∠A) . What is m∠A ? Enter your answer in the box.

Answers

∠A = 26, I took this test

Answer:

∠A = 26°

Explanation:

If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. In case of similar triangle, corresponding angles are congruent.

Angle ∠C = 76

So, ∠T = 76 because of corresponding angle.

Given that,

m∠S=3(m∠A)

We know that,

∠S ≅ ∠B

That means ∠B = 3 (∠A)

Sum of angles in a triangle = 180°

∠A + ∠B + ∠C = 180°

∠A + 3∠A + 76° = 180°

4∠A = 180° - 76°

4∠A = 104°

∠A = [tex] \frac{104}{4} [/tex]

∠A = 26°

Final answer.

What is the missing value in the following arithmetic sequence?

Answers

3.8 - 2 = 1.8

so
5.6 + 1.8 = 7.4

missing is 7.4

answer is C. 7.4

Answer:

Step-by-step explanation:

Alright, lets get started.

The first term is 2 and the second term is 3.8.

It means the common difference is [tex]3.8-2 = 1.8[/tex]

So, adding common difference :

First term = 2

Second term = 3.8

Third term = [tex]3.8+1.8=5.6[/tex]

Fourth term = [tex]5.6+1.8 = 7.4[/tex]

So the answer is 7.4 : answer

Hope it will help :)

If the function graphed is f(x), find f(1).
A) -4
B) -1/4

C) 0
D) 4

Answers

Answer: choice A) -4

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

Step 1) Draw a vertical line through 1 on the x axis

Step 2) Mark the point where the vertical line and the blue curve intersect (or cross each other)

Step 3) Draw a horizontal line through the point marked in step 2. Note how this horizontal line goes through -4 on the y axis.

So the point (1,-4) is on the blue curve. This means if x = 1 is the input then y = -4 is the output. Recall that y = f(x). So f(x) = -4 is the output as well when the input is x = 1.

In short, this is why f(1) = -4

Joes is 10 years older than james. in 8 years joe will be three times older than james. how old are they now

Answers

Joes is 16 and James is 6!!

Abby walked miles on Monday, miles on Tuesday, and miles on Wednesday. What is the total distance Abby walked in the three days?
a. miles
b. miles
c. miles
d. miles

Answers

Answer:WE Cant se the numbers

Step-by-step explanation:the ancwer would be 7 and 7/12

You buy 3 grapefruits for $1.50, a pound of apples for $.79, some grapes for $2.50, and some bananas for $1.21. Find the total cost of the fruit.

Answers

In all, the cost would be $6

6 dollars is the answer because 1.5 + .79+ 2.5+ 1.21= 6 in total.

Happy studying!

3. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35. To the nearest hundredth, find the search area. 2.08 mi²
2.97 mi²
1.49 mi²
1.04 mi²

Answers

Area = (1/2) x 2.75 x 1.32 x sin(35 deg) = 1.815 x (0.573576) = 1.04 sq. miles.

Answer:

2.08 mi²

Step-by-step explanation:

Since, the area of the triangle is,

[tex]A=s_1\times s_2\times sin \theta[/tex]

Where, [tex]s_1[/tex] and [tex]s_2[/tex] are adjacent sides and [tex]\theta[/tex] is the included angle of these sides,

Here, [tex]s_1[/tex] = 2.75 miles,

[tex]s_2[/tex] = 1.32 miles,

And, [tex]\theta[/tex] = 35°,

hence, the area of the given triangle is,

[tex]A=2.75\times 1.32\times sin 35^{\circ}[/tex]

[tex]= 3.63\times 0.57357643635[/tex]

[tex]= 2.08208246395\approx 2.08\text{ square miles}[/tex]

what is the sum of
2(5a-4a)+6a

Answers

The first step you would take is to combine all like terms in the parentheses.
5a - 4a = a
Then you would multiply 2 by a, which would equal 2a.
Finally, combine all like terms (all terms with a), to get 8a. (2a + 6a = 8a)
Hope this helps!

Hey there :)

We need to open the brackets and distribute the 2
However, we can see that both the terms within the parenthesis are like terms

5a - 4a = 1a or a

2(1a) + 6a

2a + 6a We can combine the like terms
= 8a

find the perimeter of the quadrilateral. if x = 2 the perimeter is ___ inched.

Answers

7(2) + 30 = 14+30 = 44
3(2^2) -5(2)+20 = 12 - 10 + 20 = 22
4(2^2) +8(2) = 16 + 16 = 32

P = 31 + 44 + 22 + 32 = 129

answer
129 inches

Answer:

Perimeter is 129 inches.

Step-by-step explanation:

We are given,

A quadrilateral with sides lengths [tex](4x^2+8x),(3x^2-5x+20),(7x+30),31[/tex] inches.

Now, the values of the side lengths when x = 2 are,

[tex](4x^2+8x)=(4\times 2^2+8\times 2)=(4\times 4+16)=16+16=32\ inch\\\\(3x^2-5x+20)=(3\times 2^2-5\times 2+20)=(3\times 4-10+20)=12+10=22\ inch\\\\(7x+30)=(7\times 2+30)=14+30=44\ inch[/tex]

Since, Perimeter of a quadrilateral = Sum of its sides.

Then, Perimeter of given quadrilateral = 32 + 22 + 44 + 31 = 129 inches.

Hence, the perimeter is 129 inches.

helppppppppppppppppppppp

Answers

Answer:
1.796

Explanation:
log base 6 of 25 can be rewritten as:
log base 6 of (5^2) = 2 * log base 6 of 5
= 2 *0.8982
= 1.7965

Hope this helps :)

12 ticket sellers, 25 cleaning persons, and 15 ushers employees will be paid $10, $7.50, 8.50 per hour for 50 hours per month what is the monthly salary

Answers

----------------------------------------------------------
Ticket Sellers
----------------------------------------------------------
1 ticket seller = $10 x 50
1 ticket seller = $500

12 ticket sellers = $500 x 12
12 ticket sellers = $6000

----------------------------------------------------------
Cleaning person
----------------------------------------------------------
1 cleaning person = $7.50 x 50
1 cleaning person = $ 375

25 cleaning person = $375 x 25
25 cleaning person = $9375

----------------------------------------------------------
Ushers
----------------------------------------------------------
1 usher = $8.50 x 50
1 usher = $425

15 ushers = $425 x 15
15 ushers = $6375

----------------------------------------------------------
Total
----------------------------------------------------------
$6000 + $9375 + $6375 = $21750

----------------------------------------------------------
Answer: Total monthly salary per month = $21750
----------------------------------------------------------

The sales tax on a $250 computer is 17.50. find the sales tax rate.

Answers

if we take 250 to be the 100%, what is 17.50 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 250&100\\ 17.50&t \end{array}\implies \cfrac{250}{17.50}=\cfrac{100}{t}\implies t=\cfrac{17.50\cdot 100}{250}[/tex]

Maria plans to fill pots in her garden with soil and plant food. Maria has 8 1/2 quarts of soil as 1 1/2 quarts of plant food. Each pot requires 3/4 quart of soil. For how many pots does Maria have enough soil?

Answers

1. You have the following information:

- Maria has 8 1/2 quarts of soil.
- Each pot requires 3/4 quart of soil.

2. Keeping this on mind, you can convert the mixed number 8 1/2 and the fracion 3/4 to decimals, as below:

8 1/2=8.5 quarts
3/4=0.75 quarts

3. Therefore, you have:

1 pot-----0.75 quarts
x-----8.5 quarts

x=(8.5x1)/0.75
x=11 pots

For how many pots does Maria have enough soil?

The answer is: 11 pots

2, 4, 6, 8, 10
I know this diverges but what is the limit?

Also, is there a limit with numbers that repeat? (ie: -1,1,-1,1...(-1)^n)

Answers

1. You are right, this sequence diverges (or converges to infinity) so

[tex]$\lim_{n\to\infty}\,2n=\infty[/tex]

2. In this case limit does not exist.

PLZ HELP ME ON THIS

PLZ EXPLAIN IT TO ME

Answers

I think it might be the first one 400(1.04) it can't be the last cause 80(1.04) + 5 is basically like the third one 85(1.04).
80 * 5 = 400
Hope it helps

someone please help :(

Answers

The answer would be answer choice a.

Because 5/4 = 1.25
tan (51) = 1.235
tan (45) = 1
tan (60) = 1.732
tan (57) = 1.5399

The closest to 1.25 is tan (51)

Hope this helps :)

Find the product of (x + 5)(x − 5). (1 point)

x2 − 10x + 25

x2 + 10x + 25

x2 − 25

x2 + 25

Answers

FOIL (first outside inside last)

x^2-5x+5x-25 = x^2-25

The answer is x2- 25 hope this helps!

a building in san francisco is shaped like a square pyramid it has a slant height og 856.1 feet and each side of its base is 145 feel long find the lateral area of the building

Answers

we know that

for a Square Pyramid
[lateral area]=4*[a*s/2]--------> 2aS

where
a is the length side of the square base
S is the slant height
a=145 ft
S=856.1 ft

[lateral area]=2*145*856.1---------> 248269 ft²

the answer is 248269 ft²

If the clock has a radius of 15 inches, how many inches of ribbon will terry need to use to surround the clock?

Answers

the circumference is C=2*3.14*r
r=15 inches
C=2*3.14*15=94.20 inches of ribbon

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The public health and environmental movements are sometimes at odds with each other. why is this the case? what might be done to improve the situation? The underlying themes in Dsires Baby are _____.loyalty and filial dutyfamily and domesticityracism and the role of womentrue love and class differences List one genetic technology that scientist have developed? What is one advantage and one disadvantage of using this technology? Is calcium disodium ionic or covalent? HELP!! Adding and subtracting radicals tickets to a play cost $11 each. There is also a service charge of $4 per order. Write ab equation for the relationship that gives the total cost y in dollars for an order of x tickets. When a trait has more than two alleles how is that trait inherited? given that oxygen has an atomic number of eight determine how many protons and neutrons are in the isotope 16O or oxygen -168 protons and 9 neutrons 8 protons and 8 neutrons8 protons and 7 neutrons 16 protons and 0 neutrons Metallurgy is the study of _____. What city was the cultural center of europe during most of the classical period? A conical hat has a radius of 7 inches and a height of 14. Whats the slant height Classify the responses in the given situations as part of innate immune response or adaptive immune response. Which of the following best describes magnetic fields? A. Magnetic fields need a conductor. B. Magnetic fields are always found in insulators. C. Magnetic fields have north and south magnetic poles. D. Magnetic fields must have only positive charges. The gas tank Ill be riding mower holds 5 L of gas how many 5 L gas tanks can you feel from a 20 L gas tank When you don't know the answer on a multiple-choice questions, it is generally best to:A.Go with your first guess.B.Answer only if you can eliminate one choice.C.Select the "A" or "E" options.D.Leave the question blank. 1. Which American author was most directly inspired by the ideals of Transcendentalism? (5 points)Herman MelvilleHenry David ThoreauHarriet Beecher StoweJames Fennimore Cooper2. Transcendentalism was centered on writers and thinkers from which region? (5 points)AppalachiaThe MidwestNew EnglandThe South3. Which of these values was central to the Transcendentalist writers? (5 points)Connection with natureConnection with urban lifePatriotism for the United StatesCharity for the poor4. Which of these Transcendentalist writings had the most direct influence on African American activists in the 1950s and 1960s? (5 points)"Ambition""Orphic Sayings""Woman in the Nineteenth Century""Two Rivers"5. During the mid-19th century, Transcendentalist writers had a strong influence over the formation of (5 points)labor unionsnew Protestant sectsutopian communitiesnativist organizationsmy answers are 1=b, 2=c, 3=a, 4=d, 5=c 30 points please help a girl out!A political action group that wants to overturn the Montreal Protocol monitors stratospheric ozone across the South Pole over a 10-year period. They compare changes in the ozone layer to increases in the average global temperature and find no correlation. Because of this, they claim that ozone layer depletion is a myth. What is the major flaw in their reasoning?a. Global warming is not observable at the South Pole.b. Only tropospheric ozone will correlate to global warming.c. The loss of stratospheric ozone is not connected to global warming.d. The effects of the Montreal Protocol will not be fully realized until 2050.e. Ten years is too short a time period for meaningful data to be acquired. A video game system that normally sells for $249 is on sale for 15% off Find the cardinal number for the following sets.A = {102, 103, 104, 105,..., 155} B = {102, 104, 106, ..., 252} WILL GIVE BRAINLEST Which is not a result of the Aral Sea shrinking by two-thirds in the last fifty years?decline of the fishing industryloss of aquatic biodiversityhealth issues from wind-carried saltdecline in fresh water resources