f(x)=-x^2+x-5
What are the coordinates of the vertex of the parabola of the function ?

Answer:

The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.

Step-by-step explanation:

To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.

Convert the magnitudes to intensities and write them in exponential form.

R=logI

2011 earthquake:

9.1I=logI=109.1

2003 earthquake:

8.3I=logI=108.3

Form a ratio of the intensities.

intensity for 2011intensity for 2003

Substitute in the values and divide by subtracting the exponents to find

109.1108.3100.8≈6.

The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.

Your answer:

The intensity of the 2011 earthquake was about 15 times the intensity of the 2003 earthquake.

The intensities of the two earthquakes will be 6.3095.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

In 2011, Japan encountered a serious quake with an extent of 9.1 on the Richter scale. In 2003, Japan encountered another extraordinary seismic tremor that deliberate 8.3 on the Richter scale.

The intensity of the earthquake is given as,

㏒ (I₁ / I₂) = M₁ - M₂

㏒ (I₁ / I₂) = 9.1 - 8.3

Simplify the equation, then we have

㏒ (I₁ / I₂) = 9.1 - 8.3

㏒ (I₁ / I₂) = 0.8

Take anti log, then we have

(I₁ / I₂) = 6.3095

The intensities of the two earthquakes will be 6.3095.

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The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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1

Step-by-step explanation:

She has 3 carrots and 4 cucumbers that's a week done and 6 apples so she needs 1 more

dentify the percentage of change and increase or decrease 75 people to 25 people increase or decrease find the percent of change round to the nearest tenth of a percent ​

we have that

75 people represent the 100 % so

Applying proportion, find out how much percentage represent the difference (75-25=50)

so

100/75=x/50

solve for x

x=(100/75)*50

x=66.7 %

therefore

Answer:

m= -5/9

Step-by-step explanation:

m= y2-y1/ x2-x1

m= -3-2/ 5-(-4)

m= -3-2/ 5+4

m= -5/9

y= mx + b

(-4,2)

2= -5/9(-4) + b

2= 2.2+ b

-2.2 +2= b

-0.2= b

Solution :

From the given graph the x-intercept is 2 and y-intercept is -1 .

So, equation of line in intercept form is :

\(\dfrac{x}{2} + \dfrac{y}{-1} = 1\\\\x - 2y = 2\)

\(y = \dfrac{x-2}{2}\)

Now, putting x = 4 in above equation, we get :

\(y = \dfrac{4-2}{2}\\\\y = 1\)

Therefore, the value of function at x =4 is 1 .

12.985 rounded to 2 decimal places is 12.99

Answer:

Step-by-step explanation:

Step 1:

Identify the digit in the hundredths place, as it is the 2nd decimal place.  The 8 is the digit in the hundredths place.

Step 2:  

Look at the digit in the thousandths place and its value is 5 thousandths, so increase the digit in the hundredth's place to 9.

Step 3:

The new number is 12.99 rounded to the 2nd decimal place.

Answer:

1,208.92613

Step-by-step explanation:

this is the answer

Answer:

I believe the answer may be 31.5cm.

Step-by-step explanation:

I first found the area of the total region which was 70cm. From there I found the area of the triangle to the left of the region by doing 6x7 which is 42, and multiplied by 1/2 because it is a triangle. I did the same to the triangle on the right, doing 5x7 which is 35, and multiplied by 1/2 since this is also a triangle. Finally, I subtracted both totals of 21, and 17.5 from the 70, getting a grand total of 31.5cm.

Answer:

31.5 cm²

Step-by-step explanation:

To find the area of the crossed region, subtract the areas of the two triangles from the area of the rectangle.

Formulae:

Area of the rectangle

⇒ A = (4 + 6) × 7

⇒ A = 10 × 7

⇒ A = 70 cm²

Area of triangle 1

⇒ A = ¹/₂ × 6 × 7

⇒ A = 3 × 7

⇒ A = 21 cm²

Area of triangle 2

⇒ A = ¹/₂ × 5 × 7

⇒ A = 2.5 × 7

⇒ A = 17.5 cm²

Area of the crossed region

⇒ A = 70 - 21 - 17.5

⇒ A = 49 - 17.5

⇒ A = 31.5 cm²

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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Answer:

\(r=\frac{-a+p}{a+p}\)

Step-by-step explanation:

\(-pr+p=ar+a\)

\(-ar-pr+p=a\)

\(-ar-pr=a-p\)

\(r(-a-p)=a-p\)

\(r=\frac{-a+p}{a+p}\)

Answer:

\(r = \frac{p - a}{(p + a)} \)

Step-by-step explanation:

\(p = \frac{a(1 + r)}{(1 - r)} \\ p(1 - r) = a(1 + r) \\ p - pr = a + ar \\ p - a = pr + ar \\ p - a = r(p + a) \\ \frac{p - a}{(p + a)} = \frac{r(p + a)}{(p + a)} \\ \frac{p - a}{(p + a)} = r\)

hope this helps

brainliest appreciated

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Each scenario can be used to simulate probability, and there are 3 correct scenarios and 2 incorrect scenarios in the list of options

From the question, we have the following parameters:

This means that the probability of hit is:

P(Hit) = 20/30

Simplify

P(Hit) = 2/3

Using the complement rule,

P(Miss) = 1/3

The above means that the simulation that represents the situation must have the following parameters:

Using the above highlights, the correct scenarios are:

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Apply the fraction rule:

\(\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}\)

Answer:

\(\longrightarrow\boxed{\bold{\frac{\text{fx}}{\text{g}}}}\)

Answer:

Step-by-step explanation

The bottle had 20 ounces that before and 8 ounces after

8+x=20

20-x=8

20-8=x

20-8=12

Answer:

4 is your answer

Step-by-step explanation:

The given angles are:

M arc CB=64°,M<AOC= 116° ,M arc AD=26°,M arc DFB=154°,M<CDB=32°.

First, we use the property that the measure of a central angle is equal to the measure of the intercepted arc.

Given that <COB = 64°, we know that the measure of arc CB is also 64°.

Next, we use the fact that the measure of an angle made on the circumference is half the measure of the angle made at the center.

We know that the measure of intercepted arc AD is 26°, and since the angle made at the center, <ABD, is 13°, we can calculate that the measure of arc AD is 2 x 13° = 26°.

Using the fact that a semicircle has a measure of 180°, we know that the measure of arc DFB is 180° - 26° = 154°.

Finally, we can use the angle CDB to find the missing angle.

We know that <CDB is an angle made on the circumference and that the measure of arc CB is 64°.

Thus, we can calculate that <CDB = 64°/2 = 32°.

Therefore, the missing angle is 32°.

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It can be noted that the true statements about the relations include:

A. The equality relation on the real numbers is an equivalence relation.

C. A relation from a set with n elements to itself can have up to elements.

E. A function is a special relation.

G. The equality relation on the real numbers is anti-symmetric.

H. If is a reflexive relation on a set S, then any two - related elements of S must also be related.

I. The less than or equal relation on the real numbers fails to be an equivalence relation because it is reflexive and transitive but not symmetric.

It should be noted that a relation simply means the relationship between the set of values.

The information given about the relations above are true in these cases.

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Answer:

a] 24.5; b] 2.8; c] 39.59.

Step-by-step explanation:

a. after t=1sec:

h(1)=-4.9*1²+27*1+2.4; ⇔h(1)=24.5 [m];

b. more than 30 [m] heigh:

-4.9t²+27t+2.4≥30; ⇔ 4.9t²-27t+27.6≤0; ⇔(t-1.35)(t-4.15)≤0;

Δt≈4.15-1.35=2.8 [sec];

c. maximum height:

h'(t)=-9.7t+27; ⇒ h'(t)=0, ⇒ -9.7(t-2.78)=0; ⇒ t=2.78 [sec], then

\(h_{max}=h(2.78)=-4.9*2.78^2+27*2.78+2.4=39.59[m].\)

Answer:

6

Step-by-step explanation:

-3 | 6 - 2| + 1

-3 + 6 + 2 + 1

-3 + 9 = 6

SOLUTION

We want to get the intervals for which the function graphed is decreasing

The intervals are the x-values

Looking at the graph (notice the arrow heads, it means the graph is continuous), the function is decreasing (sloping downwards) between x-values of negative infinity to 1, And later again between x-values of 3 to 4.

So the intervals where the function is decreasing written as interval notation is

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

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

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Answer:

The answer is A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

I would help but I can't see the numbers correctly so I can not help.

Answer:

B {-6, -3, 3, 11}

Step-by-step explanation:

Answer:

(-10,0)

Step-by-step explanation:

2a =[2(-2) , 2(-3)] = (-4 -6) <--- add them

-3b = [-3(1) . -3(-1)] = (-3 +3) <--- add them

2a - 3b =  

[(-4  -6), (-3  +3)] =

(-10,0)

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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Answer: 3

Step-by-step explanation: