Find the vertex of the following. f(x) = x2 - 12x + 35

Answer/Step-by-step explanation:

The two triangles we have in the diagram shar the same vertex. They are both similar triangles. Therefore, their side lengths would be proportional.

This means:

[tex] \frac{9.8}{4.3} = \frac{r}{5.1} = \frac{n}{2.7} [/tex]

Solve for variable r and n respectively.

Thus:

[tex] \frac{9.8}{4.3} = \frac{r}{5.1} [/tex]

Multiply both besides by 5.1

[tex] \frac{9.8}{4.3} \times 5.1 = \frac{r}{5.1} \times 5.1 [/tex]

[tex] \frac{9.8 \times 5.1}{4.3} = r [/tex]

11.6 = r (nearest tenth)

Also,

[tex] \frac{9.8}{4.3} = \frac{n}{2.7} [/tex]

Multiply both besides by 2.7

[tex] \frac{9.8}{4.3} \times 2.7 = \frac{n}{5.1} \times 2.7 [/tex]

[tex] \frac{9.8 \times 2.7}{4.3} = r [/tex]

6.2 = n (nearest tenth)

Answer:

35

Step-by-step explanation:

Answer:

155.384615385

Step-by-step explanation:

Answer: z>0.6

Step-by-step explanation:

You isolate the variable by dividing each side by factors that don’t contain the variable.

The answer is verified it came from Math-way .

Answer:

z≥0.6

Step-by-step explanation:

Answer:

have

Step-by-step explanation:

Have is used alongside plural nouns , And has is used alongside singular nouns. So books and supplies are plural so you use have

Answer:

Sorry, you didn't send the picture with it. But, I have the picture that you forgot to send, here is the picture.

Step-by-step explanation:

That is the image down there! Thanks. Sorry, I can't answer though.

Answer:

1/3

Step-by-step explanation:

First you have to do this step to find your slope: y2-y1/x2-x1

So your first point is (0,-4) (3,-3)

I got 1/3

You can also do rise over run as well

Answer:

a. The following will be needed to make 6 dozen cakes:

Number of grams of butter needed = 600g

Number of grams of sugar needed = 2,000g

Number of grams of currants needed = 400g

b. The number whole that cakes could be made with 1kg of butter is still 18 whole cakes.

Step-by-step explanation:

a. how many of each ingredient will be needed to make 6 dozen cakes

This can be calculated as follows:

One dozen = 12

Number of small cakes in 6 dozen cakes = 6 * 12 = 72 small cakes

Number of 18 small cakes that can be obtained from 72 small cakes = 72 / 18 = 4

Therefore, we multiply each ingredient by 4 to obtain the number oof each ingredient that will be needed to make 6 dozen cakes as follows:

Number of grams of butter needed = 150 * 4 = 600g

Number of grams of sugar needed = 500 * 4 = 2,000g

Number of grams of currants needed = 100 * 4 = 400g

b. how many whole cakes could be made with 1kg of butter

Ordinary in terms of measurement, we have:

1kg = 1,000g

Since it is not indicated in the question that additional grams of other ingredients are made available, only 150g butter will be used out of the 1,000g butter made available together with already available 500g sugar and 100g currants to make just 18 cakes. This implies that no additional whole cakes will be made to add to the current 18 small cakes that is being made. Additional whole cakes would only be made when additional grants of sugar and currants are made available.

Therefore, the number whole that cakes could be made with 1kg of butter is still 18 small cakes.

9514 1404 393

Answer:

  4421 cubic feet

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr²h

where r is the radius (half the diameter), and h is the height.

Using your numbers, the cylinder volume is ...

  V = (3.14)(8 ft)²(22 ft) ≈ 4421.12 ft³

The maximum amount of water the tank can hold is about 4421 cubic feet.

Answer:

$175

Step-by-step explanation:

Answer:

1/16

Step-by-step explanation:

The probability of getting heads with 1 coin toss is 1/2.

For 4 tosses, the probability is 1/2 * 1/2 * 1/2 * 1/2 = 1/16

Answer:

1.9

Step-by-step explanation:

1 3/5 is the same as 1.6. So, which ones bigger? 1.9.

Answer:

x²=5x

x=5... probably c

Answer:

i. R699. 2

ii. 26.4%

Step-by-step explanation:

Given the following data;

First discount (on original price) = 20%

Second discount (on reduced price) = 8%

Original price = R950.00

*To find how much Jay will pay*

First discount;

[tex] Discount = \frac {20}{100} * 950[/tex]

[tex] Discount = 0.2 * 950[/tex]

Discount = R190.00

Reduced price = 950 - 190

Reduced price = R760.00

Second discount;

[tex] Discount = \frac {8}{100} * 760[/tex]

[tex] Discount = 0.08 * 760[/tex]

Discount = R60.8

Selling price = 760 - 60.8

Selling price = R699.2

Therefore, Jay will pay R699.2 for the speaker.

ii. To find the final discount percentage;

[tex] Percent \; discount = \frac {original \;price - selling \; price}{original price} * 100[/tex]

Substituting into the equation, we have;

[tex] Percent \; discount = \frac {950 - 699.2}{950} * 100[/tex]

[tex] Percent \; discount = \frac {250.8}{950} * 100[/tex]

[tex] Percent \; discount = 0.264* 100[/tex]

Percent discount = 26.4%

Therefore, the final discount percentage Jay gets off the original price is 26.4%.

Answer:

16 males and 9 females.

Step-by-step explanation:

If you subtract 7 from 25 you get 18. If you split 18 in half you get 9. Which means if you add 7 to 9 you get the number of males, which leaves you with 9 students left so the rest are females.

Answer:

16 males and 9 females

Step-by-step explanation:

To solve this we can use a system of equations.

Let's start by naming the number of females x.

The number of males would then be y.

Using these variables, we can set up 2 equations using info provided:

A french class has a total of 25 students, -> x+y=25

The number of males is 7 more than the number of females -> x+7=y

Use substitution to solve.

From the second equation:

x+7=y

Subtract 7 from both sides.

x=y-7

Substitute that into the first equation.

x+y=25

y-7+y=25

Combine like terms.

2y-7=25

Add 7 to both sides.

2y=32

Divide both sides by 2.

y=16

Substitute y=16 into equation 2.

x+7=y

x+7=16

Subtract 7 from both sides.

x=9

Therefore, there are 16 males and 9 females in the french class.

Answer:

i dont speak or type spanish

Step-by-step explanation:

Answer: Sorry, i don't speak spanish dude

Step-by-step explanation: Would you like to translate it for me?

Answer:

x=2

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

The answer is 43 because when you multiply 6x6 you get 36 and if you add 6 more you get 42 which is one less that 43

Answer:

1/18

Step-by-step explanation:

5/6 of an estate is to be divided among relatives

Let the total estate = 1

Remaining estate = 1 - 5/6

= 6-5/6

= 1/6 of the estate

Of the remaining a state 1/3 goes to the American cancer society

what fraction of the estate goes to the American Cancer Society

= 1/3 × 1/6

= 1/18

The fraction of the estate that goes to the American Cancer Society = 1/18

Answer:

y = 2

Step-by-step explanation:

For the equation x - y = -1, if x = 1,

then we would plug that in to solve for the y value

1 - y = -1

Subtract 1 from both sides to find y

-y = - 2

Divide by -1 to find y

y = 2.

To double check our answer we would plug in our x-value and y-value into the equation

1 - 2 = -1

This is true, so our answer is y = 2

Answer:

y = 2

Step-by-step explanation:

x - y = -1

1 - y = -1

1 + 1 - y = 0

2 - y = 0

2 = y

y = 2

Answer:Its B

Step-by-step explanation:

Bc I just got it right

ARM for which interest will stay fixed for 8 years and then be adjusted every year after that = 8/1 ARM

The correct option is (B).

The term adjustable-rate mortgage (ARM) refers to a home loan with a variable interest rate. With an ARM, the initial interest rate is fixed for a period of time. After that, the interest rate applied on the outstanding balance resets periodically, at yearly or even monthly intervals.

Given statement

ARM for which Interest rate stay fixed for 8 years and then be adjusted every year after that.

Above information is typically expressed in two numbers. The first number indicates the length of time that the fixed rate is applied to the loan, while the second refers to the duration or adjustment frequency of the variable rate.

By the above method ARM for Interest rate stay fixed for 8 years and then adjusted every year after that can be expressed as 8/1 ARM.

Hence, for 8/1 ARM, interest rate will stay fixed for 8 years and then

be adjusted every year after that.

Learn more about ARM here:

https://brainly.com/question/13028045

#SPJ2

Your question: "Which equation represents the polar form of x – y = 0?"

Answer:

b. Theta = pi/4

We want to write an equation that represents the polar form of:

x - y = 0.

We will see that the correct option is b, the polar form is given by:

θ = pi*/4

First, polar form is a way to write equations using radius and angle as variables, instead of the known x and y that we usually use.

To change the variables we have the general rule:

R = √(x^2 + y^2)

θ = Atan(y/x)

So here we have:

x - y = 0.

Then we can write this as:

x = y.

Then the angle is given by:

θ = Atan(y/x) = Atan(x/x) = Atan(1) = 45°

Writing this in radians we get:

45° = 45°*(pi/180°) = pi*/4

Then we have:

θ = pi*/4

Then the equation that represents the polar form is:

θ = pi*/4

From this, we can see that the correct option is b.

If you want to learn more, you can read:

https://brainly.com/question/20864390

Answer:

a

   [tex]P(X = 5) = 0.2423 [/tex]

b

    [tex]P( X \ge  6 )=  0.4516 [/tex]

c

   [tex]P( X <  4 )=  0.12694[/tex]

Step-by-step explanation:

From the question we are told that

   The population proportion is   p = 0.53

    The sample size is  n = 10

Generally the distribution of the confidence of US adults in newspapers follows a binomial distribution  

i.e  

         [tex]X  \~ \ \ \  B(n , p)[/tex]

and the probability distribution function for binomial  distribution is  

      [tex]P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}[/tex]

Here C stands for combination hence we are going to be making use of the combination function in our calculators        

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is exactly​ five is mathematically represented as

     [tex]P(X = 5) =  ^{10}C_5 *  0.53^5 *  (1- 0.53)^{10-5}[/tex]

=>  [tex]P(X = 5) =  252 * 0.04182 *  0.023[/tex]

=>  [tex]P(X = 5) = 0.2423 [/tex]

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is  at least​ six is mathematically represented as

  [tex]P( X \ge 6 )= P( X = 6) + P( X = 7) + P( X = 8) + P( X = 9) + P( X = 10)[/tex]

=> [tex]P( X \ge  6 )=  [^{10}C_6 *  [0.53]^6 *  (1- 0.53)^{10-6}] +  [^{10}C_7 *  [0.53]^7 *  (1- 0.53)^{10-7}] +  [^{10}C_8 *  [0.53]^8 *  (1- 0.53)^{10-8}] +  [^{10}C_9 *  [0.53]^9 *  (1- 0.53)^{10-9}] + [^{10}C_{10} *  [0.53]^{10} *  (1- 0.53)^{10-10}][/tex]

=> [tex]P( X \ge  6 )=  [0.227] +  [0.1464] +  [0.0619] +  [0.0155] + [0.00082][/tex]

=> [tex]P( X \ge  6 )=  0.4516 [/tex]

Generally the probability that the number of U.S. adults who have very little confidence in newspapers is  less than four is mathematically represented as

    [tex]P( X < 4 )= P( X = 3) + P( X = 2) + P( X = 1) + P( X = 0)[/tex]

=>  [tex]P( X <  4 )=  [^{10}C_3 *  0.53^3 *  (1- 0.53)^{10-3}] +  [^{10}C_2 *  0.53^2 *  (1- 0.53)^{10-2}] +  [^{10}C_1 *  0.53^1 *  (1- 0.53)^{10-1}] +  [^{10}C_0 *  0.53^0 *  (1- 0.53)^{10-0}] [/tex]

=>  [tex]P( X <  4 )=  0.09051  +  0.03 +  0.0059 +  0.000526[/tex]

=>  [tex]P( X <  4 )=  0.12694[/tex]

Answer:

478miles

Step-by-step explanation:

32=1gallons 32×15 = 510miles

15g

510- 32= 478miles

Answer:

The value is  [tex]\sigma = 9.976[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is [tex]\mu = 61.6[/tex]

Given that 20% of the values are greater than 70, the z-score to  the right of the curve  corresponding to 20% (0.2) of the values is

     [tex]z-score = 0.842[/tex]  

Generally this z-score is mathematically represented as

       [tex]z-score = \frac{x - \mu }{\sigma }[/tex]

Here  x = 70  

So

     [tex]0.842 = \frac{70 - 61.6 }{\sigma }[/tex]

=>   [tex]\sigma = 9.976[/tex]

Answer:

680

Step-by-step explanation:

Answer:

680

Step-by-step explanation:

10 to the  2nd power is 10 times 10 which is 100.

Now, 6.8 times 100 is 680.

Hope this helps you!!

Answer:

34.12-9.8=24.32

Step-by-step explanation: