In the diagram, the measure of angle 6 is 98°. what is the measure of angle 7?

Answer:

second option

Step-by-step explanation:

Given

[tex]x^{4}[/tex] + 6x² + 5 = 0

let u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Change u back into terms of x, that is

x² = - 1 ( take the square root of both sides )

x = ± [tex]\sqrt{-1}[/tex] = ± i ( noting that [tex]\sqrt{-1}[/tex] = i ), and

x² = - 5 ( take the square root of both sides )

x = ± [tex]\sqrt{-5}[/tex] = ± [tex]\sqrt{5(-1)}[/tex] = ± [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex] = ± i[tex]\sqrt{5}[/tex]

Solutions are x = ± i and x = ± i[tex]\sqrt{5}[/tex]

Answer:

  B.  False

Step-by-step explanation:

In order for segments to form a triangle, the sum of the lengths of the shorter two must be at least as much as the length of the longest one.

The sum of the shorter two is 6 + 5 = 11. This is not as great as 12, the length of the longest one, so no triangle can be formed.

Answer:

8x + 20 ≥ 25

Step-by-step explanation:

Well 8 times the sum of a number "x" plus 20,

So we can write the following,

8x + 20

and that should be greater than or equal to 25

8x + 20 ≥ 25

Thus,

as an inequality it is 8x + 20 ≥ 25.

Hope this helps :)

Answer:

x = 2

Step-by-step explanation:

x + 1/2 (6x - 4) = 6

Expand the brackets.

x + 3x - 2 = 6

Add like terms.

4x - 2 = 6

Add 2 on both sides.

4x = 6 + 2

4x = 8

Divide 4 into both sides.

x = 8/4

x = 2

Answer:

x=5/4

Step-by-step explanation:

Answer:

144π or 452.4

Step-by-step explanation:

Volume of a Sphere Formula: V = 4/3πr³

Step 1: Plug in 6 for r

V = 4/3π(6)³

V = 288π

Step 2: Divide by 2

V = 288π/2

V = 144π

Answer:

Step-by-step explanation:

6 and 7

Answer:

The answer is given below

Step-by-step explanation:

Let us assume the truck accelerates for 4 seconds.

Given that:

Initial velocity (u) = 0 (starts from rest),

acceleration (a) = 4 m/s²

time (t) = 4 s

Final velocity (v) = ?,

Distance (s) = ?

To calculate the final velocity, we use the formula:

v = u + at

Substituting values gives:

v = 0 + 4(4)

v = 0 + 16

v = 16 m/s

The final velocity is 16 m/s²

To calculate the distance traveled by the truck, we use the equation:

[tex]s=ut+\frac{1}{2}at^2\\ Substituting\ values\ into\ the\ equation:\\s=0(4)+\frac{1}{2}(4)(4)^2\\s=0+2(16)\\s=0+32\\s = 32\ meters[/tex]

The distance traveled by the truck during the time interval is 32 meters

Answer:

The answer is below

Step-by-step explanation:

A store carries four brands of DVD​ players, J,​ G, P and S. From past​ records, the manager found that the relative frequency of brand choice among customers varied. Using the given probability values for each of the four​ brands, find the probability that a random customer will choose brand J or brand P.

P(J)=0.22​, ​P(G)=0.18​, ​P(P)=0.35​, ​P(S)=0.25

Answer: Probability is the ration of possible outcomes to the total number of possible outcomes. The probability of mutually exclusive events i.e. events that cannot occur at the same time is the sum of their individual probabilities. If two events A and B are mutually exclusive events, then:

P(A or B) = P(A) + P(B)

Given that P(J)=0.22​, ​P(G)=0.18​, ​P(P)=0.35​, ​P(S)=0.25, the probability that a random customer will choose brand J or brand P is given by:

P(J or P) = P(J) + P(P) = 0.22 + 0.35 = 0.57

Answer:

x = 95°

Step-by-step explanation:

[tex]x = ?\\Sum -of- interior -angles=?\\Shape = pentagon\\No -of - sides= 5\\Sum- of- interior- angles = (n-2)180\°\\=(5-2)\times180\°\\3\times180\°\\Sum-of-interior-angles=540\°\\104\°+117\°+100\°+124\°+x\°=540\°\\445\°+x\° = 540\°\\x\° = 540\°-445\°\\x = 95\°[/tex]

Answer:

False

Step-by-step explanation:

A definition produces out of nothing a new mathematical entity. But a theorem utilizes some relation between previously defined mathematical entities.

Usually a theorem must be verified by a proof of its correctness on the basis of generally accepted statements or on the basis of previously established statements which might include other theorems.

Answer:

Step-by-step explanation:

Using the formula for calculating heat energy H = mcΔT

m = mass of the aluminum (in g/kg)

c = specific heat capacity of aluminum

ΔT = change in temperature = T - Ti (in °C)

T is the final temperature

Ti is the initial temperature

Given m = 100.0g,  c = 0.931096J/g °C, Ti = 20°C, H = 1100J T = ?

Substituting the given values into the formula;

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

The final temperature of the metal is 31.81°C

Answer:

31.81c

Step-by-step explanation:

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

Answer:  x=3

Step-by-step explanation:

5x+9 =24   subtract 9 from both sides

    -9    -9

5x = 15    Divide both sides by 5

x = 3

Answer:

[tex]5x = 24 - 9 \\ 5x = 15 \\ x = \frac{15}{5} \\ x = 3[/tex]

Answer:

6

Step-by-step explanation:

If 2 of the friends wants to stand beside each other, we can take these 2 friends like 1 option and calculated the number of ways, using the rule of multiplication as:

__ 3_____ * ____2_____ *____1____  =  6

1st place        2nd place        3rd place

Because we have 3 options (2 friends and the friends that are beside each other) for the first place of the picture, 2 options for the second and 1 option for the third.

Answer:

x2

Step-by-step explanation:

In 5x, 5 is a constant and therefore if we double x we will double 5 too.

Answer:2

Step-by-step explanation:

-5.4+8.2=14/5 and then opposite of -2 3/4 is 2.

Answer:

[tex]\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}[/tex]

Step-by-step explanation:

According to the given situation, as we know that the triangle which is ADE and triangle which is ABC are the same

. (as in the diagram)

So, the ratio of their corresponding sides are the same or an equal so that it can be reached at the truth which is here below:

[tex]\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}[/tex]

With the help of a diagram, we can better understand which has been attached.

The ratios  AD : DB  and  AE : EC  are equal.

Answer:

The population of the city was 25,000 in 1970 and 1983.

Step-by-step explanation:

In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.

[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]

Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.

Step-by-step explanation:

It's not cos x^2

[tex]\cos^2x\neq\cos x^2[/tex]

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

[tex]\cos x-\dfrac{\sin x\sin x}{\cos x}=\dfrac{\cos x\cos x}{\cos x}-\dfrac{\sin x\sin x}{\cos x}=\dfrac{\cos^2-\sin^2x}{\cos x}[/tex]

It's the same as

[tex]3-\dfrac{2}{3}=\dfrac{3\cdot3}{3}-\dfrac{2}{3}=\dfrac{3^2-2}{3}[/tex]

Answer:

53

Step-by-step explanation:

Explicit Formula: an = a1 + d(n - 1)

Simply plug in your known variables:

an = 8 + 3(n - 1)

Then plug in 16 for n:

a(16) = 8 + 3(16 - 1)

a(16) = 8 + 3(15)

a(16) = 8 + 45

a(16) = 53

Answer:

53

Step-by-step explanation:

an = dn + (a - d)

an = 3n + 8  - 3

an = 3n + 5

Put n as 16 and solve.

3(16) + 5

48 + 5

= 53

Answer:65.6

Step-by-step explanation:

So $0.25 per yard

16.4/$0.25=65.6

Answer:

ANSWER A

Step-by-step explanation:

Answer:

it has a horizontal asymptote at y=O

Step-by-step explanation:

answer is A.

because A linear parent function is the equation y = x or f(x) = x.

If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote.

Answer: 3π

I don't see 3π in your answer choices, but I'm assuming the "3x" is supposed to be 3π.

Step-by-step explanation:

To convert from degrees to radians, you multiply by π/180.

[tex]540*\frac{\pi }{180} =3\pi[/tex]

Answer:

D. 0.366

Step-by-step explanation:

Hello!

A stemplot is a way of arranging a data set.

In the stem you'll find the integer and first two decimal digits of the batting average, because these values are repeated several times.

In the leafs you'll find the third decimal digit.

So for the first value of the stem "0.32" there is only one observation:

0.329 ⇒  0.32 | 9

For the second value "0.33" correspond 14 observations: 0.330, 0.331, 0.331,0.333, 0.333, 0.333, 0.334, 0.334, 0.334, 0.336,  0.337, 0.338, 0.338, 0.338

0.33 | 0, 1, 1, 3, 3, 3, 4, 4, 4, 6, 7, 8, 8, 8

For the third value "0.34" correspond 12 observations: 0.340, 0.340, 0.341, 0.341, 0.342, 0.342, 0.342,  0.344, 0.344, 0.345, 0.346, 0.349

0.34 | 0, 0, 1, 1, 2, 2, 2, 4, 4, 5, 6, 9

For the fifth value "0.35" and the sixth value "0.36" there is only one observation, so, as happened with the first one, these values of the stem will only have one "leaf"

0.358 ⇒ 0.35 | 8

0.366 ⇒ 0.36 | 6

So the whole stem plot for this 30 observations is:

Stem | Leafs

0.32  | 9

0.33  | 0, 1, 1, 3, 3, 3, 4, 4, 4, 6, 7, 8, 8, 8

0.34  | 0, 0, 1, 1, 2, 2, 2, 4, 4, 5, 6, 9

0.35  | 8

0.36  | 6

Considering this, the correct option is D

I hope this helps!

Answer: 12 friends.

Step-by-step explanation:

the data we have is:

Mei Su had 80 coins.

She gave the coins to her friends, in such a way that every friend got a different number of coins, then we have that:

The maximum number of friends that could have coins is when:

friend 1 got 1 coin

friend 2 got 2 coins

friend 3 got 3 coins

friend N got N coins

in such a way that:

(1 + 2 + 3 + ... + N) ≥ 79

I use 79 because "she gave most of the coins", not all.

We want to find the maximum possible N.

Then let's calculate:

1 + 2 + 3 + 4 + 5 = 15

15 + 6 + 7 + 8 + 9 + 10 = 55

now we are close, lets add by one number:

55 + 11 = 66

66 + 12 = 78

now, we can not add more because we will have a number larger than 80.

Then we have N = 12

This means that the maximum number of friends is 12.

Answer:

12

Step-by-step explanation:

my

Answer:

Out of 8000 students, 10% take tuition in various subjects before the exam.

10% of 8000 is:

10/100 * 8000 = 800

Among the 800, 40% take tuition in English only and 20% take tuition in Math only.

80 students take tuition in other subjects, therefore, in percentage:

80/800 * 100 = 10%

Therefore, the percentage of students that take tuition in both Math and English is:

100% - (40% + 20% + 10%) = 100% - 70% = 30%

30% of the 800 students take tuition in both subjects. That is:

30/100 * 800 = 240 students

Therefore, among the 8000 students in the district, only 240 take tuition in both English and Math.

In percentage:

240/8000 * 100 = 3%

3% of students take tuition in both English and Math.

In Ratio:

3 : 100

3 out of 100 students take tuition in English and Math.

Answer:

1:15 pm

Step-by-step explanation:

It takes 6 hours to reach London from Minneapolis and she reached Minneapolis at 7:15pm so

7:15 - 6 = 1:15

Answer:

D:10

Step-by-step explanation:

find hyp. first

sin 45=opp/hyp.

√2/2=10/hyp.

hyp.=20/√2 0r 10√2

Pythagorean theorem: a²+b²=c²

now find x²=(10√2)²-10²

x²=200-100

x²=100

x=√100=10

Answer:

The rate of the water current is 4mph

Step-by-step explanation:

Let c= the rate of the current in mph

18+c= the rate of the boat going downstream in mph

18-c= the rate of the boat going upstream in mph

t = time in hrs for both upstream and downstream trips

Going downstream:

33=(18+c)*t (1)

Going upstream

21=(18-c)*t (2)

From (1)

33=(18+c)*t

t=33/1(8+c)

Substitute t=33/(18+c) into (2)

21=(18-c)*t

21=(18-c)*33/(18+c)

Cross product

21(18+c)=33(18-c)

378+21c=594-33c

21c+33c=594-378

54c=216

Divide both sides by 54

54c/54=216/54

c=4

Therefore,

The rate of the water current is 4mph

Complete Question :

In golf, a score below zero is “under par” and a score above zero is “over par.”

Tyrone played 18 holes of golf and had the same score on each of the first 14 holes. He then had the same score on each of the next four holes. His score on the first 14 holes was –42 and his final score was –34. Which describes Tyrone’s score on each hole?

A. He scored 3 under par on each of the first 14 holes and 2 over par on each of the next four holes.

B. He scored 3 under par on each of the first 14 holes and 2 under par on each of the next four holes.

C. He scored 3 under par on each of the first 14 holes and 4 over par on each of the next four holes.

D. He scored 3 under par on each of the first 14 holes and 4 under par on each of the next four holes.

Answer: A. He scored 3 under par on each of the first 14 holes and 2 over par on each of the next four holes.

Step-by-step explanation:

Given that :

a score below zero is “under par” and a score above zero is “over par.”

Same score on each of the first 14 holes

Total score on first 14 holes = - 42

Therefore, score on each hole = ( total score / number of holes)

= - 42/14 = - 3

Negative signifies that it is 'under par'

Score on each of the next four holes is also the same.

Therefore, total score on next four holes :

(final score - total score on first 14 holes)

(-34 - (-42))

(-34 + 42) = 8

Total score on next four holes = 8

Score on each hole = 8/4 = 2

Positive score means he scored over par

Answer:

a

Step-by-step explanation:

I did quiz