Solve for x using the Quadratic Formula: x^2 + 2x+1=0
X=-b plus or minus b2-4ac squared all over 2a

[tex]\huge\bold{To\:find:}[/tex]

✎ The length of the hypotenuse.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\sf\purple{The\:length\:of\:the\:hypotenuse \:"c"\:is\:5.10\:km.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

Using Pythagoras theorem, we have

[tex]( {perpendicular})^{2} + ( {base})^{2} = ( {hypotenuse})^{2} \\ ⇢ ( {5 \: km})^{2} + ( {1 \: km})^{2} = ( {c})^{2} \\ ⇢ 25 \: {km}^{2} + 1 \: {km}^{2} = {c}^{2} \\ ⇢ 26 \: {km}^{2} = {c}^{2} \\ ⇢  \sqrt{26 \: {km}^{2} } = c \\ ⇢5.0990 \: km = c \\ ⇢5.10 \: km = c[/tex]

[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:hypotenuse\:is\:5.10\:km.}[/tex]

[tex]\huge\bold{To\:verify :}[/tex]

[tex]( {5 \: km})^{2} + ( {1 \: km})^{2} = ( {5.10 \: km})^{2} \\ ⇝25 \: {km}^{2} + 1 \: {km}^{2} = 26 \: {km}^{2} \\ ⇝26 \: {km}^{2} = 26\: {km}^{2} \\ ⇝L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Step-by-step explanation:

Therefore, 55+40+z=180

z=180-95

z=85

To get y,

z+y=180

85+y=180

y=95

Answ either

Step-by-step explanation:

Answer:

1.368

Step-by-step explanation: 1.14x1.2=1.368

Answer:

Mean Hypothesis is Mean values of the treatment and the control group is not equal

Step-by-step explanation:

The null hypothesis is mostly the problem statement.

Here the problem statement is

To check whether there is a difference in treatment result of two groups of patient; one which has received the treatment and the other is the control group.

Thus, the null hypothesis is

H0 - Mean values of the treatment and the control group is not equal

Answer:

$496800

Step-by-step explanation:

You need to find 3.5% of 480,000 and then add it to 480000:

You convert 3.5% to 0.035 (divided by 100).

Now you multiply 0.035 * $480,000 = $16800 (this is the amount of money to add to the value of the house)

Total value of the house: $480,000 + $16,800 = $496800

Answer:

Step-by-step explanation:

Answer:

D.

Step-by-step explanation: they can be different widths

Answer:

84

Step-by-step explanation:

0.5 · 7 · 24

0.5 · 168

84

Answer:

84

Step-by-step explanation:

Step 1: Convert number to a fraction

[tex]24=\frac{24}{1}[/tex]

[tex]\frac{1}{2}\times \frac{24}{1}\times \:7[/tex]

Step 2: Factor the number

[tex]\:24=2\times \:12[/tex]

[tex]\frac{2\times \:12}{2}\times \:7[/tex]

Step 3: Cancel the common factor

[tex]2[/tex]

Step 4: Multiply the remaining numbers

[tex]12\times \:7\\\\= 84[/tex]

Therefore, [tex]\frac{1}{2}\times 7\times 24\:=\:84[/tex]

Answer:

the third one ig

Step-by-step explanation:

Answer:

10.50

Step-by-step explanation:

Answer:

4 x 8.50

100

= 0.34

8.50 - 0.34 = 8.16

Step-by-step explanation:

a percentage is always over 100 so i 4 percent of 8.50 which gave me 0.34

Dont forget we are only focused on on the increase so we gotta subtract to make it normal from the original number which gives u 8.16...

Note dont forget it said an hour so multipy it by 1 hour since it said one hour which stills gives u the same answer

Answer:

B: 42°, 48°

Step-by-step explanation:

I took the test.

The pair of angles have congruent values for the sin x° and the cos y° is 42; 48.

Angles that are of the same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of the same measure,

then

[tex]m\angle A = m\angle B[/tex]

is the notation to say that they are of the same measurement, where the small m shows that its the measurement of the angles they're preceding.

We write the congruency between them as;

[tex]\angle A \cong \angle B[/tex]

Congruent angles can be defined as a type of angle that is known to have all sides in equal measure.

sin x  = cos (90-x)

therefore,  sin 42 = cos(90-42)

                             = cos 48

Hence, option B) 42°, 48° is correct

Learn more about congruent angles ;

brainly.com/question/2938476

#SPJ2

Answer:

x+x-20 = 180-90

2x-20 = 90

2x. =90+20

2x. =110

x. =55

y+55. =90

y. =90-55

y. =35

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

Explanation:

Since AB is smaller than AD, this must mean the angle ACB is smaller than angle ACD. Note how these angles are opposite the sides mentioned.

So 2x-10 < 48

At the same time, 2x-10 is also larger than 0.

Overall, we can say 0 < 2x-10 < 48

---------

Let's solve for x

0 < 2x-10 < 48

0+10 < 2x < 48+10 ...... add 10 to all sides

10 < 2x < 58

10/2 < x < 58/2 ..... divide all sides by 2

5 < x < 29

Answer:

[tex]\displaystyle \cos(A + B) =\frac{969}{1769}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}[/tex]

Where A and B are positive acute angles.

And we want to find cos(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:

[tex]o=\sqrt{29^2-20^2}=21[/tex]

Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:

[tex]h=\sqrt{11^2+60^2}=61[/tex]

In summary:

With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.

With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.

We can rewrite our expression as:

[tex]\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B[/tex]

Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:

[tex]\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)[/tex]

Simplify:

[tex]\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}[/tex]

Answer:

The 4th answer

Step-by-step explanation:

Answer:

D

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

All of these are done exactly the same way so I will work out one of them for you, and you can follow my example to get the answers to the rest of them. I will do #5. The formula for this is

7(7 + x) = 8(8 + 13) and then solve the equation to find x:

49 + 7x = 168 and

7x = 119 so

x = 17.

Follow that pattern for each of your problems and you should be fine.

Answer:

i believe the answer should be

Step-by-step explanation:

3x+14=65 which is telling you that 3 times a number which is unknown so we will call it x and add 14 equals 65. when you work it out you should get the total which is 65. so the way you work that out is you separate everything without an x to the right side of the equation which looks like 3x=65-14 then work it out subtract 14 from 65 and you get 3x=51 )which is total spent on 3 games. Then you divide 3x/3= 51/3 then the 3s cancel our so you have x=51/3 and when you work that out you get your answer x=17 which is the cost per game.

Answer:

x = 5

Step-by-step explanation:

Given

2x + 7 = 17 ( subtract 7 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Answer:

[tex]Area = 10[/tex]

Step-by-step explanation:

Given

[tex]A = (2,1)[/tex]

[tex]B =(4,7)[/tex]

[tex]C =(6,3)[/tex]

Required

The area of the park

The outline is a triangle and as such, the area is calculated using:

[tex]Area = \frac{1}{2}|(x_1y_2 - x_2y_1) + (x_2y_3 - x_3y_2) + (x_3y_1 - x_1y_3)|[/tex]

This gives:

[tex]Area = \frac{1}{2}|(2*7 - 4*1) + (4*3 - 6*7) + (6*1 - 2*3)|[/tex]

Using a calculator, we have:

[tex]Area = \frac{1}{2}|-20|[/tex]

Remove absolute bracket

[tex]Area = \frac{1}{2}*20[/tex]

[tex]Area = 10[/tex]

Answer:

Step-by-step explanation:

Answer:

exact: 48pi cm^2

approximate: 150.8 cm^2

Step-by-step explanation:

SA = 2 * (pi)r^2 + 2(pi)rh

SA = 2 * pi * (3 cm)^2 + 2(pi) * 3 cm * 5 cm

SA = pi(18 cm^2 + 30 cm^2)

SA = 48pi cm^2

SA = 150.8 cm^2

Answer:

I believe it would be B. SAS

Step-by-step explanation:

You have two sides and one angle that are congruent in both

Answer: I think the answer is 25 units squared

Step-by-step explanation:

A= l*w

A= 5*5

A=25^2

Answer: I think it's 80

Answer:

60 : 32

Step-by-step explanation:

Let x = Their present ages

Ritu : Nitu = 15x : 8x

After 10 years, their ages will be in the ratio 5:3

In 10 years

15x + 10 : 8x + 10 = 5 : 3

15x + 10 / 8x + 10 = 5/3

Cross product

15x + 10 * 3 = 8x + 10 * 5

45x + 30 = 40x + 50

45x - 40x = 50 - 30

5x = 20

x = 20/5

x = 4

Ritu : Nitu = 15x : 8x

Ritu : Nitu = 15 * 4 : 8 * 4

= 60 : 32

Ritu : Nitu = 60 : 32