Which of the following equations has exactly one solution?



A. 5a + 4 = 9a + 3 – 4a
B. 3 + 5x – 12x = 2 – 7x
С. 9.2n + 3.1 = 5.2n – 4.9
D. 11 – 4s = -1/2(8s) + 1/2(22)

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Work Shown:

For now focus on triangle ABC. Since this is a right triangle, we can use the pythagorean theorem to find the hypotenuse BC.

a^2 + b^2 = c^2

(AC)^2 + (AB)^2 = (BC)^2

8^2 + 10^2 = (BC)^2

(BC)^2 = 164

BC = sqrt(164)

BC = 12.806248 approximately

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Move onto triangle ABD. Find the missing side BD through the pythagorean theorem

a^2 + b^2 = c^2

(AD)^2 + (AB)^2 = (BD)^2

5^2 + 10^2 = (BD)^2

125 = (BD)^2

(BD)^2 = 125

BD = sqrt(125)

BD = 11.1803399 which is approximate

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Move onto triangle ADC. We'll use the pythagorean theorem again

a^2 + b^2 = c^2

(AC)^2 + (AD)^2 = (CD)^2

8^2 + 5^2 = (CD)^2

89 = (CD)^2

(CD)^2 = 89

CD = sqrt(89)

CD = 9.433981 also approximate

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Focus on triangle BCD. We have the following side lengths

Let

Note the use of uppercase letters for angles and lowercase letters for side lengths.

We can then use the law of cosines to find the angle we're after

d^2 = b^2 + c^2 - 2*b*c*cos(D)

12.806248^2=9.433981^2+11.1803399^2-2*9.433981*11.1803399*cos(D)

163.999987837504=213.999997787893-210.950228380284*cos(D)

-210.950228380284*cos(D) = -50.000009950389

cos(D) = (-50.000009950389)/(-210.950228380284)

cos(D) = 0.237022781792173

cos(D) = arccos(0.237022781792173)

D = 76.2891111084541

D = 76.3

The size of the angle ∠BDC of the tetrahedron can be determined by

cosine rule.

The size of angle ∠BDC is approximately 71.1°

Reasons:

A tetrahedron is a pyramid with triangular faces.

By Pythagoras's theorem, we have;

[tex]\overline{DC}[/tex]² = [tex]\mathbf{\overline{AD}}[/tex]² + [tex]\mathbf{\overline{AC}}[/tex]²

∴ [tex]\overline{DC}[/tex]² = 8² + 5² = 89

[tex]\overline{DC}[/tex]² = 89

[tex]\overline{BC}[/tex]² = [tex]\overline{AB}[/tex]² + [tex]\overline{AC}[/tex]²

∴ [tex]\overline{BC}[/tex]² = 10² + 8² = 164

[tex]\overline{BC}[/tex]² = 164

[tex]\overline{DB}[/tex]² = [tex]\mathbf{\overline{AD}}[/tex]² + [tex]\mathbf{\overline{AB}}[/tex]²

[tex]\overline{DB}[/tex]² = 5² + 10² = 150

[tex]\overline{DB}[/tex]² = 150

By cosine rule, we have;

[tex]\overline{BC}[/tex]² = [tex]\overline{DB}[/tex]² + [tex]\overline{DC}[/tex]² - 2 ×  [tex]\mathbf{\overline{DB}}[/tex] × [tex]\mathbf{\overline{DC}}[/tex] × cos(∠BDC)

Therefore;

164 = 150 + 89 - 2 × √(150) × √(89) × cos(∠BDC)

2 × √(150) × √(89) × cos(∠BDC) = 150 + 89 - 164 = 75

[tex]cos( \angle BDC) = \mathbf{\dfrac{75}{2 \times \sqrt{150} \times \sqrt{89} }}[/tex]

[tex]\angle BDC = arccos \left(\dfrac{75}{2 \times \sqrt{150} \times \sqrt{89} } \right) \approx \mathbf{71.1 ^{\circ}}[/tex]

∠BDC ≈ 71.1°

Learn more here:

https://brainly.com/question/20839703

Answer: 31.42

Step-by-step explanation:

[tex]c = 2\pi \: r[/tex]

[tex]c = 2 \times 3.14 \times 5[/tex]

[tex]c = 31.4159[/tex]

Answer:

Lowest term

Step-by-step explanation:

you can write a ratio using a fraction form, a colon form, and a word form. The lowest term is just a part of an answer.

Answer:

It's 14% p.a simple interest

Step-by-step explanation:

Simple interst:

Answer:

I = $ 649.60

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 14%/100 = 0.14 per year,

then, solving our equation

I = 2320 × 0.14 × 2 = 649.6

I = $ 649.60

The simple interest accumulated

on a principal of $ 2,320.00

at a rate of 14% per year

for 2 years is $ 649.60.

Compound interest

Answer:

A = $2,945.78

A = P + I where

P (principal) = $2,320.00

I (interest) = $625.78

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 12/100

r = 0.12 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,320.00(1 + 0.12/12)(12)(2)

A = 2,320.00(1 + 0.01)(24)

A = $2,945.78

Summary:

Answer:

[tex] {p}^{2} - 13p - 30 \\ \\ {p}^{2} - 15p - 2p - 30 \\ \\ p(p - 15) + 2(p - 15) \\ \\ (p + 2)(p - 15)[/tex]

# Jerry Don is here#

Answer:

[tex]\displaystyle [p + 2][p - 15][/tex]

Explanation:

Find two quantities that when differed to 13, they also multiply to 30. Those will be 2 and 15. The TINIER quantity gets the plus sign because the B-value is −13, therefore 15 gets the minus sign, leaving 2 with the plus sign.

I am joyous to assist you at any time.

Answer:

well, they all give you answers as fractions,

A.=1/9

B.=1/64

C.=1/64

Step-by-step explanation:

The answer might be c. not 100% sure sorry

Answer:

Step-by-step explanation:

S+J+M=36

J=S-2 or J=x-2

M=S-16 or M=x-16

Answer:

Jake: x-2 and Matthew: x-16  (I think it is C on your sheet.)

Step-by-step explanation:

x = Sarah

x-2 = Jake

x-16 = Matthew

Step-by-step explanation:

what we trying to find the value of x and y

20x+6=y

x intercept,y=0

20x+6=0-6

20x/20=-6/20

×=-0.3

y intercept,x=0

20(0)+6=y

0+6=y

6=y

(-0.3,0)

19x+7=y

y intercept,x =0

19(0)+7=y

0+7=y

7=y

x intercept,y=0

19x+7=0-7

19x=-7

19x/19=-7/19

x=-0.37

Answer:

[tex]1848 ways[/tex]

Step-by-step explanation:

[tex]=(12nCr2)(8nCr2)=(66)(28)=1848[/tex]

Hope this helps

To solve algebraic equations, we must combine like terms and perform inverse operations on both sides of the equal sign to isolate the variable.

Inverse operations help us cancel values out.

[tex]- 4 a - 2 a = - 18[/tex]

⇒ First, combine like terms:

[tex]- 6a = - 18[/tex]

⇒ a is being multiplied by -6. To isolate a, divide both sides by -6:

[tex]\dfrac{- 6a}{-6} = \dfrac{- 18}{-6}\\\\a=3[/tex]

a = 3

Answer:

a=3

Step-by-step explanation:

-4a-2a=-18

-6a= -18

Divide both sides by -6

-6a/-6=-18/-6

a=3

Answer:

2.25 seconds, 86 feet.

Step-by-step explanation:

No idea where the r, second is, so I'm assuming that t is time in seconds.

Because this is a perfect parabola, we can find the zeroes (the places where the y value is 5, because that's where the teacher is launched from) and then get the middle of those 2 points.

First let's make the a term of this equation be positive so multiply everything by minus one.

16t^2-72t-5

After that, let's factor this (I won't go into details about this, you should already know how to do this if your asking this question)

we get t(t - 4.5) = 5

So the 2 x values are 0 and 4.5, and the whole flight time of the teacher is 4.5 seconds.

The half way between that is 2.25, and then we can plug that time back in to the equation to get a y value of 86.

Answer:

53.5

Step-by-step explanation:

Answer:

she drove b 53.5 mi

Step-by-step explanation:

214 divided by 4

Answer:

There are 364,000 people in the Air Force.

Step-by-step explanation:

Percentages

The N% of a number M is calculated by:

[tex]\displaystyle \frac{N*M}{100}[/tex]

For example, 15% of 280 is

[tex]\displaystyle \frac{15*280}{100}=42[/tex]

We know the total amount of people serving as of January is estimated to be 1,400,000 people and that 26% of them are serving in the Air Force.

Compute 26% of 1,400,000:

[tex]\displaystyle \frac{26*1,400,000}{100}=364,000[/tex]

There are 364,000 people in the Air Force.

Answer:

62

Step-by-step explanation:

Step-by-step explanation:

the answer is the last one, because if you plug in (5, -6) to both equations you would get equal answer.

Answer:

D

Step-by-step explanation:

5=x and -6=y so 5+-6 or 5-6=-1 so it makes the first equation true. Then plug it in to the second equation. (3)(5)--6 or (3)(5)+6 which = 15+6. 15+6=21. So both are true. Btw Im new to this hope this helps!

Answer:(-1,7)

Step-by-step explanation:

Answer:

4

The dot in the middle simply means multiplication. 4.4 is 16. 16/4 is 4

Step-by-step explanation:

Answer:

[tex]ML=27\\LN=27\\MN=54[/tex]

Step-by-step explanation:

Since L is the midpoint of MN, by the definition of midpoint:

[tex]ML=LN[/tex]

We can picture the following segment:

M----------L----------N

We know that [tex]ML=2x+7[/tex] and [tex]LN=3x-3[/tex]. Since the two segments are equivalent, we can set them equal to each other:

[tex]2x+7=3x-3[/tex]

Now, let's solve for x. Subtract -7 from both sides:

[tex]2x=3x-10[/tex]

Subtract 3x from both sides:

[tex]-x=-10[/tex]

Divide both sides by -1:

[tex]x=10[/tex]

So, the value of x is 10.

With this, we can find the remaining lengths.

We know that ML is [tex]2x+7[/tex].

Substitute 10 for x. So, the length of ML is:

[tex]ML=2(10)+7=20+7=27[/tex]

We know that LN is [tex]3x-3[/tex]. So, the length of LN is:

[tex]LN=3(10)-3=30-3=27[/tex]

Finally, MN will be the combined lengths of ML and LN. So:

[tex]MN=ML+LN=27+27=54[/tex]

And we're done!

Answer:

jdjssusaudisjdssdIes

Answer:

34°

Step-by-step explanation:

sum interior measure = (n-1)*180 ; n is the number of sides

of the polygon

(n-1)*180

(4-2)*180

2*180

360° ( sum interior measure )

The angles of the quadrilateral are ( 90 , 90 , w , 146 )

90+90+146+w = 360

326+w = 360

w = 360-326

w = 34°

Hope you get benefit from it

Answer:

The normal force is the force that a surface makes on an object that lies on that surface.

As the book rest flat in the table, the force acting on the book will be the gravitational force. This force pulls down the book against the table, then the normal force will be opposite to this, then the direction of this force is upwards. Being more exact, the normal force always acts on the normal direction to a given surface, to find the normal of a surface, you need to find the plane of the surface, then any perpendicular line to that surface will be "normal" to the surface (and the normal direction points away from the surface) then if the book is resting on top of the table, the direction of the normal will be upwards..

Then the force that acts on the book is normal to the surface of the table,

Answer:

2

Step by step explanation:

Given: The average mass of all the students in the class was 35.1 kg. After 1 student left the class, whose mass is 32.3kg, the average mass of the remaining students became 36.3kg, how many students were there in the class room now?

Find out: how many students were there in the class room after one student left

Solution: Let the total number of remaining student be= n

Let the total number of remaining student be= nAnd the sum of mass of all the students be = x kg

So,

[tex] \frac{x}{n + 1} = 35.1[/tex]

Make x the subject of formula

[tex]--› \: x = 35.1(n + 1)[/tex]

And

[tex]--› \: \frac{x - 32.3}{n} = 36.3[/tex]

[tex]--›x - 32.3= 36.3n[/tex]

[tex]--› \: 35.1(n + 1) - 32.3 = 36.3n[/tex]

[tex]--› \: 35.1n + 35.1 - 32.3 = 36.3n[/tex]

[tex]--› \: 2.8 = 1.2n[/tex]

divide both side by n

[tex]n = \frac{2.8}{1.2} [/tex]

N = 2.333

so total number of students remaining is 2

Answer:

(a) The unit rate for car B is greater because the slope is greater than the slope for car A.

Step-by-step explanation:

We have been given a graph that represents the distance cars A and B travel. We are asked to choose the correct option about our given graphs.

Since slope represents the change in y-value with respect to change in per unit x value, so slope is also unit rate of the graph.

Let us find the slope of car A using points (8,5) and (0,0).

Let us find the slope of car B using points (5,8) and (0,0).

We can see that slope of car B is greater than slope of car A, therefore, option A is the correct choice.

Step-by-step explanation:

Answer:

50,000 pounds

Step-by-step explanation:

1 ton = 2,000 pounds

Answer:

subtract 180 from the other two angles

Step-by-step explanation:

triangle involves 3 angles with x's in the equation, set the 3 angles = to 180 and solve

Answer:

100cm = 0.001km

Step-by-step explanation:

100 divided by 100,000=0.001

Answer:

1/100th part of the whole part.

Step-by-step explanation:

Hope this helps :)

Answer:

the <5 = 28

because if u add <1 and <5 it will be a 180°

so....if u 180 - 152 ( which is the angle of 1< )

and

same goes to 2< and <3 but its a 90°

so....<2 = 90° - 36°

= 54

u should get the <4 too....

hope u get it

please mark me brilliant

Step-by-step explanation:

I don't see all the options.

I only see the options under "angles", as it seems.

anyway, the way to prove this is :

the official definition of similar triangles is :

two triangles are said to be similar if their corresponding angles are congruent (and the corresponding sides are in proportion - but that is automatically true, when all 3 angles are matching).

so, if two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. we know this, because if two angle pairs are the same, then the third pair must also be equal (remember, the sum of all angles in a triangle is always 180°). When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

now, we look at the 2 triangles.

the angles QPR and STR are congruent (the same size).

we know also the angles QRP and SRT : they are both 90° and therefore congruent.

and that means that also the third angles PQR and RST are equal and therefore congruent (due to the 180° sum rule).

so, we have all 3 pairs of angles to be congruent, and the two triangles are therefore similar.

Answer:

- 9

Step-by-step explanation:

We require

- 15 , m₁, m₂, m₃, 9

The average of the end values gives m₂ , that is

m₂ = [tex]\frac{-15+9}{2}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

Similarly, the average of - 15 and m₂ gives m₁

m₁ = [tex]\frac{-15-3}{2}[/tex] = [tex]\frac{-18}{2}[/tex] = - 9

The first arithmetic mean m₁ = - 9

Answer:

441

Step-by-step explanation:

I think