The x- intercepts of a parabola are (0,-6) and (0,4). The parabola crosses the y- axis at -120. Lucas said that an equation for the parabola is y=5x^2+10x-120 and that the coordinates of the vertex are (-1, -125). Do you agree or disagree? List why?

Answer:

see below

Step-by-step explanation:

point A(x,y) becomes A'(-x,-y).

So point E (-3,-5) becomes  E'( 3,5)

F (-1,-1) becomes F'(1,1)

and G (0,-5) becomes G'( 0,5)

___________________A

The function that represents the inequality of the given graph is;

Option A

From the given graph, the curve with the shaded dot shows less than or equal to because the dot indicates that the maximum input value of x is at that point.

Secondly, the curve without a shaded dot shows that the input function of x is only greater than 3.

Looking at the options, option A is right and we will prove it thus;

for y = x³ - 3

At x = 2, we see that;

y = 2³ - 3

y = 5

This corresponds with the given equation

For the second curve, for y = x² + 6;

At x = 2, we have;

y = 2² + 6

y = 4 + 6

y = 10

This corresponds with what is given and is thus correct.

Thus, option A is the correct answer

Read more about graphed inequalities at; https://brainly.com/question/11234618

Answer:

5/8 boxes

Step-by-step explanation:

1/3 ⋅ 1 7/8 = ?

1/3 ⋅ 15/8 = 15/24

15/24 = 5/8

5/8 boxes

[tex]we conclude that option B:[/tex]

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

[tex]Is the graphed function.[/tex]

On the graph we can see a parabola that opens downwards, so it has a negative leading coefficient.

We also can see that the vertex of the parabola is on the point (3, -5)

Then the equation of the parabola is something like:

y + 5 = a*(x - 3)^2

Where a is a negative real number.

The only option of this form is option B, so we conclude that option B:

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

Is the graphed function.

If you want to learn more about parabolas:

https://brainly.com/question/4061870

#SPJ1

Answer:

6

Answer:

a) 30

b)600pi

Step-by-step explanation:

For the first questions, since the arc is 240°, the area of the sector and circumference will be 240/360 or 2/3 of the total of the circles'. Therefore 125.6 x 3/2 is the circumference, which is 188.4. When we divide this by 6.28, we get 30

Now, since the area is pi r^2 where we know that r=30, we get 900pi as the area of the whole thing, however since the sector is 2/3 of the whole circle, 2/3 x 900pi = 600pi

Answer:

all of them are REAL numbers

1. is also RATIONAL

2. is also IRRATIONAL

3. is also IRRATIONAL

4. is also NATURAL, WHOLE, INTEGER and RATIONAL

5. is also INTEGER and RATIONAL

6. incorrect, because integer is just the whole numbers extended by their additive counterparts (the negative natural numbers). in other words, their absolute values are whole numbers. 5.5 as well as -5.5 are not fitting that criteria.

7. incorrect, because this pattern does not fit the definition of a radical number, where the number eventually begins to repeat the same finite sequence of digits over and over. in this example the pattern is not based on a finite sequence of digits.

Answer:

x=-3

Step-by-step explanation:

9514 1404 393

Answer:

  9.1 cm

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

  PQ/PR = AB/AC

  PQ/21.7 = 5.2/12.4 . . . . . . . . . . . . . . fill in the given values

  PQ = 21.7(5.2/12.4) . . . . . multiply by 21.7

  PQ = 9.1 . . . cm

Answer:

140

Step-by-step explanation:

Lowest common denominator 4 , 7 ,5 , 2  and 1

= 4 * 7 * 5

= 140

Answer:

1

Step-by-step explanation:

Since usually common denominator is usually used with fractions (in this case), we can find out it's one because of how no numbers (except for 2 and 4) go into each other without a remainder except for one, so one would be the correct answer

Answer:

D) y - 4 = -2 ( x - 1 )

Step-by-step explanation:

Point-slope form is y - y₁ = m ( x - x₁ )

so you just plug in your points, hope this helped

Answer:

common difference is 0.5

first term is 5

Step-by-step explanation:

use the formula for the nth term of an ap Tn=a+(n-1)d

T12=10.5

T18=13.5

therefore come up with two equations

T12=a+(12-1)d

10.5=a+11d(1st equation)

T18=a+(18-1)d

13.5=a+17d(2nd equation)

then solve both as a simultaneous equation

a+11d=10.5

a+17d=13.5

-6d/-6=-3/-6

d=0.5

use one of the equations to find the first term

a+11(0.5)=10.5

a+5.5=10.5

a=10.5-5.5

a=5

I hope this helps

please mark as brainliest

Answer:

The correct answer is - A.(112.86, 127.14)

Step-by-step explanation:

Given:

mean = $120

sd = $17.50

n = 40

Solution:

Confidence interval for a populationcan be express as mean +/- margin of error (E)

degree of freedom = n-1 = 40-1 = 39

confidence level (C) = 99% = 0.01

significance level = 1 - C = 1 - 0.01 = 0.99 = 99%

 by margin of error E = t×sd/√n = 2.58*17.50/√40

= 2.58*2.76

= 7.138 or 7.14

then the lower limit of mean = mean - E = 120 - 7.14 = $112.86

and, the upper limit of population mean = mean + E = 120 + 7.14 = $127.14

Answer:

The speed of balloon is 0.16 m/s.

Step-by-step explanation:

BC = 300 m

AD = x

AB = y

time, t = 3 min = 3 x 60 = 180 s

By the triangle, ADC,

[tex]tan 15 = \frac{AD}{BC}\\\\0.27 \times 300 = x \\\\x = 80.4 m[/tex]

By the triangle, BDC

[tex]tan 20 = \frac{BD}{BC}\\\\0.36 \times 300 = x + y \\\\x + y = 109.2 m[/tex]

So, y = 109.2 - 80.4 = 28.8 m

Speed of balloon = 28.8/180 = 0.16 m/s

Answer:

C.

0.5; 13.5; 1093.5

Step-by-step explanation:

Answer:

1350m

Step-by-step explanation:

Let the distance ran by Denise, Farah and Elaine be D, F and E meters respectively.

From the given information,

D= ⅔(E +F) -----(1)

E= ½(D +F) -----(2)

Let's get rid of the fraction so the equations are much easier to work with.

From (1):

3D= 2(E +F) (Multiply both sides by 3)

3D= 2E +2F -----(3) (Expand)

From (2):

2E= D +F -----(4)

Substitute (4) into (3):

3D= D +F +2F

3D -D= 3F

2D= 3F

Given that Farah ran 360m, F= 360.

2D= 3(360)

2D= 1080

D= 1080 ÷2

D= 540

2E= D +F

2E= 540 +360

2E= 900

E= 900 ÷2

E= 450

Total distance the 3 girls ran

= D +F +E

= 540 +360 +450

= 1350m

Alternatively, you could start by substituting F= 360 to equations (1) and (2).

Add the ratio: 3 + 5 = 8

Divide total students by that:

32/8 = 4

The ratio for girls is 3, multiply the 4 by 3:

4 x 3 = 12

There are 12 girls

Answer:

12

Step-by-step explanation:

If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:

[tex]\frac{3}{8}[/tex] of 32

= [tex]\frac{3}{8} * 32[/tex]

[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]

There are 12 girls.

after each year it's 83% of it's value from last year (100%-17%=83%)

the function in 19000 * (0.83) ^x

3 will be filled in for x

19000 * (0.83) ^3= 10863.953

$10863.95

Answer:

$10,863.95

Step-by-step explanation:

y = 19,000[tex](.83)^{t}[/tex]

y = 19,000[tex](.83)^{3}[/tex]

y =$10,863.95

I have to give 2 Ans form my question so sorry

Answer:

2,400,000,000,000

Step-by-step explanation:

2.4 x 10^12 means that the decimal point is moved 12 places to the right (hence the power of 12)

So by moving the decimal point 12 times you get this: 2,400,000,000,000

The reason why there are only 11 zeroes is because the 4 was a decimal place  to the right of 2, thus losing a zero.

Answer:

The orginal number is 26.

Step-by-step explanation:

So the units digit can be 3 6 or 9

The tens digit can be 1 2 or 3

So the original number can be 13

31 = 2*13+ (1+3) + 2

31 =? 26 + 4 + 2    

This doesn't work. The right side is 32

26

62 = 2*26 + 8 + 2

62 = 52 + 8 + 2

This is your answer.

3 and 9 won't work because 39 is odd and so is 93. The result has to be even.

Answer:

SR = 22 cm

Step-by-step explanation:

area = bh/2

(21 cm)(h)/2 = 231 cm^2

21h = 462 cm

h = 22 cm

SR = 22 cm

Answer:

[tex]\left(\dfrac{8}{7} , \ \dfrac{17}{35} \right)[/tex]

Step-by-step explanation:

The given system of equations is presented as follows;

[tex]\dfrac{s}{2} + 5 \cdot t = 3[/tex]

3·t - 6·s = 9

Making t the subject of both equations, gives;

In the first equation; t = (3 - s/2)/5

In the second equation; t = (9 + 6·s)/3

Equating both values of t to find the the values that satisfies both equations, gives;

(3 - s/2)/5 = (9 + 6·s)/3

3 × (3 - s/2) = 5 × (9 + 6·s)

9 - (3/2)·s = 45 + 30·s

45 - 9 = (30 + (3/2))·s

36 = (63/2)·s

s = 36/(63/2) = 8/7

t = (3 - s/2)/5

∴ t = (3 - (8/7)/2)/5 = 17/35

Therefore, the ordered pair is (8/7, 17/35)

Answer:

O Yes, because 1 kilogram = 1000 grams, and 1 liter = 100 centiliters.

Yes, because 1 gram per liter is the same as 1 kilogram per centiliter.

Step-by-step explanation:

Answer:

A. 272 cm^2

Step-by-step explanation:

The area of the rectangle is 17cm * 7cm = 119 cm^2

The area of the right triangle is (25-7) * 17cm * 1/2 = 153cm^2

Answer: 119+153 = 272 cm^2

Answer: 199 square yards

Step-by-step explanation:

If you break it down into 3 rectangles it’ll be easier to find the answer. Multiply it by H x W. First you do the 6 x 10. And then afterwards add the extra 5 to the 6 and it’ll make the

H = 11, and the W is 4. And then add the last 3 to H and it’ll make it 19 and the last W is 5

6 x 10 = 60

11 x 4 = 44

19 x 5 = 95

Total of 199

Hope this helps :)

Answer:

7+k=0

7-0=k

k=7

Step-by-step explanation:

7+k=0

7-0=k

k=0

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

Explanation:

Let x be the unknown angle we want to find. This angle is in degrees.

The diagram shows 19 is the opposite of this angle, and the side 35 is adjacent to the angle.

We use the tangent ratio to tie the two sides together

[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(x) = \frac{19}{35}\\\\x = \tan^{-1}\left(\frac{19}{35}\right)\\\\x \approx 28.4956386\\\\x \approx 28\\\\[/tex]

Note: The notation [tex]\tan^{-1}[/tex] refers to the inverse tangent, or arctangent.

Answer:

D

Step-by-step explanation:

The median goes from the vertex to the midpoint of the opposite side, so

LN = NM , that is

3x - 7 = 5 ( add 7 to both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Then

KL = 2x + 3 = 2(4) + 3 = 8 + 3 = 11 → D

Answer:

Step-by-step explanation:

There are 2 possibilities. Either you need to know the angles connect to the common side (that would give you ASA) or you need to know GF = UT. The latter would give you SAS