In science class, Victor started an experiment using a solution with a temperature of
–
5°C. During the experiment, the change in the solution's temperature was
–
4°C. What was the final temperature of Victor's solution?
To solve the problem, Antonio added
–
5+(
–
4) and came up with an answer of
–
9°C. Is Antonio correct? Why or why not?

Answer:

given function has 2 minimums - [tex]\frac{9}{4}[/tex]  and  [tex]\frac{9}{4}[/tex]  

Step-by-step explanation:

Step 1. g'(x) = 4x³ - 10x

Step 2. Find find the critical points:

4x³ - 10x = 2x(2x² - 5) = 0

[tex]x_{1}[/tex] = - [tex]\sqrt{\frac{5}{2} }[/tex] , [tex]x_{2}[/tex] = 0 , [tex]x_{3}[/tex] = [tex]\sqrt{\frac{5}{2} }[/tex]

Step 3. g'(x) > 0 :  - [tex]\sqrt{\frac{5}{2} }[/tex] < x < 0  or  x > [tex]\sqrt{\frac{5}{2} }[/tex]

g'(x) < 0 :   x < - [tex]\sqrt{\frac{5}{2} }[/tex]   or   0 < x < [tex]\sqrt{\frac{5}{2} }[/tex]

Step 4.

If x ∈ ( - ∞ , - [tex]\sqrt{\frac{5}{2} }[/tex] ) , g(x) is decreasing ;

If x = - [tex]\sqrt{\frac{5}{2} }[/tex] , g(x) has minimum value ;

If x ∈ ( - [tex]\sqrt{\frac{5}{2} }[/tex] , 0 ) , g(x) is increasing ;

If x = 0 , g(x) has maximum value ;

If x ∈ ( 0 , [tex]\sqrt{\frac{5}{2} }[/tex] ) , g(x) is decreasing ;

If x = [tex]\sqrt{\frac{5}{2} }[/tex] , g(x) has minimum value ;

If x ∈ ( [tex]\sqrt{\frac{5}{2} }[/tex] , ∞ ) , g(x) is increasing .

⇒ at ( - [tex]\sqrt{\frac{5}{2} }[/tex] , - [tex]\frac{9}{4}[/tex] ) and at ( [tex]\sqrt{\frac{5}{2} }[/tex] , [tex]\frac{9}{4}[/tex] ) , g(x) reaches its minimum

Answer:

Step-by-step explanation:

Comparing the triangles in the given questions, the following can be deduced:

5. The scale factor = [tex]\frac{15}{10}[/tex] = [tex]\frac{12}{8}[/tex] ≠ [tex]\frac{9}{7}[/tex]

So that;

QR is similar to UT, PR is similar to US, but PQ is NOT similar to TS.

Thus, the triangles are NOT similar.

6. Scale factor = [tex]\frac{15}{10}[/tex] = [tex]\frac{12}{8}[/tex] = [tex]\frac{9}{6}[/tex]

                         = 1.5

So that;

QR is similar to UT, PR is similar to US, but PQ is similar to TS.

Thus, the triangles are similar by Side-Side-Side (SSS).

7. Here, an exact scale factor can not be determined. Thus, the triangles are NOT similar.

Answer:

16 direct

17 indirect

Step-by-step explanation:

16.

If it is a direct variation

y/x = constant

4/-2  -2

-8/4 = -2

-12/6 = -2

This is a direct variation

17.

y/x = -1/2 /-2 = 1/4

y/x = -1/-1 = 1

This is not a direct variation

If it is an indirect variation then

yx = constant

-1/2 * -2 = 1

-1*-1 =1

3 * 1/3 =1

This is an indirect variation

Answer:

25

Step-by-step explanation:

The median of a trapezoid equals one half of the sum of the bases

AC is a median and EB and DF are the bases.

hence AC = 1/2(EB + DF)

We are given that EB = 13 and that AC = 19. And we need to find DF

To do so we plug in what we are given and solve for DF

AC = 1/2(EB + DF)

AC = 19, EB = 13

19 = 1/2(13 + DF)

Now solve for DF

* Multiply both sides by 2*

19 * 2 = 38

1/2(13 + DF) * 2 ( the 1/2 and 2 cancel out and we're left with 13 + DF )

We then have 38 = 13 + DF

* Subtract 13 from both sides *

38 - 13 = 13 - 13 + DF

We get that DF = 25

Answer:

pls use calculater

Step-by-step explanation:

because i also dont know now what shall i do so its a good suggestion for you i hope

Answer:

D. it is the point where the three angle bisectors of the triangle intersect.

Step-by-step explanation:

Because in geometry the incenter of a triangle is deliberated as the center of a triangle.

Answer:

7.2

Step-by-step explanation:

5y = 5 *7.2 = 36

36 ÷ 6 = 6

So, y = 7.2

Answer:

x = 8

x = -10

Step-by-step explanation:

Answer:

=51.63 m^2

Step-by-step explanation:

First find the area of the triangle

A = 1/2 bh = 1/2(3) * 5 = 7.5

Then find the area of the rectangle

A = l*w = 5*6 = 30

Then find the area of the semi circle, which is 1/2 the area of the circle

The diameter is 6 so the radius is 3

A = 1/2  pi r^2 = 1/2 (3.14) (3) ^2 = 14.13

Add the areas together for the total area

7.5+30+14.13

=51.63

Answer:

1050 people

Step-by-step explanation:

if there are x people at a conference

then 40% of x = 420

40% can be written as 40/100 --> 4/10 --> 2/5

2/5 * x = 420

x = 420 * 5/2

x = 1050

Answer:

104m, 0.096km, 2100cm

Step-by-step explanation:

0.096 kilometres = 9600

2100 cm

104m = 10400 cm

10400, 9600, 2100

104m, 0.096km, 2100cm

Answered by Gauthmath

Answer:

104m, 0.096km, 2100cm

Step-by-step explanation:

0.096 kilometres = 9600cm

2100cm

104m = 10400cm

10400, 9600, 2100

104m, 0.096km, 2100cm

Answer:

1 meter

Step-by-step explanation:

Previous spot of the eagle = 9 meters below him

Present spot of the eagle = 8 meters below him

What is the difference from earlier to now?

Diffetence in the spotting = Earlier position - present position

= 9 meters - 8 meters

= 1 meter

Answer:

one

Step-by-step explanation:

If two lines are not parallel, they will intersect one time as shown by the graph given.

Where the two graphs intersect is the solution to the system.

Answer:

EX = 51

Step-by-step explanation:

The 3 intersecting lines in the triangle are medians.

The distance from the vertex to the centroid is twice the distance from the centroid to the midpoint, that is

EJ = 2 JX = 2 × 17 = 34 , then

EX = EJ + JX = 34 + 17 = 51

Answer:

6, 5, 4

Step-by-step explanation:

Midpoint is exactly half so it would be half the value of triangle ABC's value

12/2=6

10/2=5

8/2=4

Answer:

3) 16π cm²

4) 240.625 cm²

Step-by-step explanation:

3. For this problem I'm going to use the formula Area = π × r²

To start off, I'm going to input our value of radius which is 4cm.

π × 4²

Finally, I'm going to square our value "4"

16π cm²

(I'm going to "leave my answer in terms of π" as the problem states but if you need the complete answer it would be about 50.24 cm²

4. For this problem I'm going to use the formula Area = π × (d/2)²

To begin, I will divide our diameter by 2 to find the radius.

17.5/2 = 8.75

Next, we are going to square our now, radius.

8.75² = 76.5625

Now, we have to multiply our squared radius by π (in this problem it states to use 22/7, so that's what we'll do :)

76.5625 × 22/7 = 240.625 cm²

So! This is our final answer!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

Congruent

Vertical

Step-by-step explanation:

E and G are vertical angles and vertical angles are equal

They are congruent because they are vertical

Answer:

No, P(high school | GPA above 3.0) ≠ P(high school)

Step-by-step explanation:

Given

See attachment for table

Required

Determine if High school and GPA above 3.0 are independent

Let

[tex]H \to[/tex] High school

[tex]G \to[/tex] GPA above 3.0

For both events to be independent, the following must be true

[tex]P(H\ |\ G) = P(H)[/tex]

From the table:

[tex]P(H) = \frac{H}{Total}[/tex]

[tex]P(H) = \frac{60}{100} = 0.60[/tex]

[tex]P(H | G) = \frac{H\ n\ G}{G}[/tex]

[tex]P(H | G) = \frac{14}{40} = 0.35[/tex]

The test for independence is as follows:

[tex]P(H\ |\ G) = P(H)[/tex]

By comparison

[tex]P(H\ |\ G) \ne P(H)[/tex]

i.e.

[tex]0.35 \ne 0.60[/tex]

Hence, both events are not independent

Answer:

y = 4x-1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 4x+b

Substitute the point in and solve for b

3 = 4(1)+b

3 = 4+b

3-4 = b

-1 =b

y = 4x-1

Answer:

y = 4x - 1

Step-by-step explanation:

y = mx + b

y = 4x + b

3 = 4(1) + b

3 = 4 + b

b = -1

y = 4x - 1

1) 8

2) 6(5x+2y) factor out greatest common factor

3) 10.8 just move over decimal two places to the left.

4) 30t=150? Then t=5kg Im not sure what the last one is asking, but I’m assuming it’s to solve for t.

Answer:

You can buy 40 tacos

You have enough money

Step-by-step explanation:

Given

[tex]Amount = \$20[/tex]

[tex]Taco = 20[/tex]

[tex]Unit\ Cost = \$0.50[/tex] --- missing from the question

Required

Determine if you have enough amount

The number of Tacos that $20 can afford is calculated as:

[tex]Tacos = \frac{Amount}{Unit\ Cost}[/tex]

So, we have:

[tex]Tacos = \frac{20}{0.50}[/tex]

[tex]Tacos = 40[/tex]

[tex]40 > 37[/tex] -- i.e. the number of Tacos will go round the 37 students

Hence, you have enough money

Answer:

Option D

Step-by-step explanation:

Alternate Interior angles are angles that are on the opposite sides of the transversal line (which is the line that cuts across the two parallel lines) and are on the inside of the two parallel lines which in this case is Option D.

Answer:

True

Step-by-step explanation:

Two angles form a pair of complementary angles

Answer:

The mistake was minus sign before the 15 and putting 15x² instead of 15x³.

The correct answer is:

[tex]-5x^{2} (3x-4)\\ = -15x^{3} + 20x^{2}[/tex]

Answer:

You can manipulate both equations into y = mx + b format and end up with the same result of y = 1.2x + 1.4

Step-by-step explanation:

y + 1 = 1.2(x + 2)

y = 1.2x + 2.4 - 1

y = 1.2x + 1.4

y - 5 = 1.2(x - 3)

y = 1.2x - 3.6 + 5

y = 1.2x + 1.4

So essentially, they're the same equation but in different forms.

Answer:

[tex]g(x)=x^2+6[/tex]

Step-by-step explanation:

Hi there!

We're given [tex]f(x)=x^2[/tex], and that [tex]g(x)[/tex] is a translation of [tex]f(x)[/tex] 6 units up.

This means that [tex]g(x)=f(x)+6[/tex].

[tex]g(x)=f(x)+6[/tex]

Rewrite the equation

[tex]g(x)=x^2+6[/tex]

This would be our final equation. It does not look like the form [tex]a(x-h)^2+k[/tex], However, when rewritten as [tex]g(x)=1(x-0)^2+6[/tex], we can tell clearly that it is.

I hope this helps!

Answer:

a) 10 blue balls, b) 5/18

Step-by-step explanation:

a)

R=3, G=5, B=x (unknown)

probability of picking red = 1/6 and red = 3 so total = 3(6) = total is 18

3+5 = 8 so B=18-8 -> B=10

b) total is 18 and G=5 so green probability = 5/18