the vertex form of the equation of a parabola is y=(x-5)2+16. what is the standard form of the equation

Answer:

The sum is [tex]144,177[/tex]

Step-by-step explanation:

we know that

The formula of the sum in a geometric sequence is equal to

[tex]S=a1[\frac{1-r^{n}}{1-r}][/tex]

where

a1 is the first term

r is the common ratio

n is the number of terms

we have

a1=-11

r=-4

n=8

substitute the values

[tex]S=(-11)[\frac{1-(-4)^{8}}{1-(-4)}][/tex]

[tex]S=(-11)[\frac{1-(65.536)}{5}][/tex]

[tex]S=144,177[/tex]

Answer:

3

Step-by-step explanation:

Is means equals and of means multiply

15% * 20 = ?

Change to decimal form

.15 * 20 = ?

3 = ?

15% of 20 is 3

Answer:

C

Step-by-step explanation:

Using the rules of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

Hence

[tex]7^{-5/6-7/6}[/tex] = [tex]7^{-\frac{12}{6} }[/tex] = [tex]7^{-2}[/tex], then

[tex]7^{-2}[/tex] = [tex]\frac{1}{7^{2} }[/tex] = [tex]\frac{1}{49}[/tex] → C

ANSWER

C. 1/49

EXPLANATION

The given expression is

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } [/tex]

Recall that:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We apply this product rule of exponents to get:

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{5}{6} + - \frac{7}{6} } [/tex]

This implies that:

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{12}{6} } [/tex]

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - 2} [/tex]

Recall again that:

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

We apply this rule to get:

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{ {7}^{2} } [/tex]

This simplifies to:

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{49} [/tex]

We can sum two fractions if they have the same denominator, so we have to rewrite both fractions so that they'll have the same denominator.

We can generate equivalent fractions by multiplying both numerator and denominator by the same number.

So, we have

[tex]-\dfrac{7}{9} = -\dfrac{7\cdot 10}{9\cdot 10} = -\dfrac{70}{90}[/tex]

Similarly, we have

[tex]-\dfrac{5}{10} = -\dfrac{5\cdot 9}{10\cdot 9} = -\dfrac{45}{90}[/tex]

Now we can sum the fractions:

[tex]-\dfrac{7}{9}-\dfrac{5}{10} = -\dfrac{70}{90}-\dfrac{45}{90} = \dfrac{-70-45}{90} = -\dfrac{115}{90} = -\dfrac{23}{18}[/tex]

To simplify the expression -7/9 - 5/10, find a common denominator, which is 90, convert and add the fractions to get -115/90, which is the simplified form of the expression.

The question asks to simplify the expression -7/9 - 5/10. To do this, we need to find a common denominator to combine these fractions. The least common denominator (LCD) for 9 and 10 is 90.

First, convert both fractions:

Then, add the fractions:

-70/90 - 45/90 = -115/90

Finally, it is usually a good practice to simplify the fraction, but in this case, -115 and 90 do not have any common factors other than 1, so the simplified expression is -115/90.

Answer:The answe is D

Step-by-step explanation:

The correct next step is to keep the compass at the same width used at point B to draw an arc through points C and D, enabling the construction of a perpendicular line. Hence correct option D.

The best next step in the construction of a line that passes through point B and is perpendicular to line A is to keep the compass setting the same width as when it was placed at point B to draw the arc that passes through points C and D. This ensures that the arcs intersect the line A at points that are equidistant from B, which is essential in establishing a perpendicular line.

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\stackrel{\stackrel{k}{\downarrow }}{4.2}x~~\checkmark~\hfill[/tex]

Answer: its proportional,

bud

Step-by-step explanation:

Answer:

production cost f(x), in dollars, for x number of units produced by company 1:

f(x) = 0.05x^2 − 7x + 300

2) Table that represents the production cost g(x), in dollars, for x number of units produced by company 2:

x        g(x)

0.6     899.58

0.8     899.52

1        899.50

1.2     899.52

1.4     899.58

3) Comparison: do a table for f(x) with the same x-values of the table for g(x).

x            f(x) = 0.05x^2 − 7x + 300    g(x)

0.6         295.818                               899.58

0.8         294.432                               899.52

1            293.05                                 899.50

1.2         291.672                               899.52

1.4          290.298                              899.58

As you can see the values of f(x) are consistently lower than the values of g(x) for the same x-values.

The minimum production cost for company 2 is around 899.50 at x = 1, while the minimum production cost of company 1 is defintely lower (lower than 292.298 for sure, in fact if you find the vertex it is 55).

Answer: Based on the given information, the minimum production cost for company 2 is greater.

Step-by-step explanation:

The answer is A, Angles in an equilateral triangle are congruent.

Which fact would help you to solve for x in the diagram shown?

A) Angles in an equilateral triangle are congruent.  

y = -5x + 24

y = 4x - 21

Since both of these equations are equal to Y, theyre equal to each other.

So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.

-5x + 24 = 4x - 21

Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:

-5x + 24 - 24 = 4x - 21 - 24

-5x = 4x - 45

Now we subtract 4x from both sides so the 4x shift to the other side

-5x - 4x = 4x - 4x - 45

-9x = -45

Finally divide both sides by -9 so x is by itself

(-9)÷(-9x) = -(45)÷(-9)

x = 5

Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.

Now apply x = 5 to either of the initial equations to find the value of Y

y = -5x + 24 or y = 4x - 21

(I'll do both but u only need one)

y = -5(5) + 24

y = -25 + 24

y = -1

y = 4(5) - 21

y = 20 - 21

y = -1

Either way, X is 5 and Y is -1

Answer (5, -1)

Final answer:

The solution to the system of equations is (5, -1), matching option b. This is found by setting both equations equal to each other, combining like terms, solving for x, and then using that value to find y.

Explanation:

To solve the system of equations, set the two equations equal to each other since they both equal y:

y = -5x + 24
y = 4x - 21

Now equate them:

-5x + 24 = 4x - 21

Add 5x to both sides:

24 = 9x - 21

Add 21 to both sides:

45 = 9x

Now divide by 9 to solve for x:

x = 5

Substitute x back into either original equation to find y:

y = -5(5) + 24
y = -25 + 24
y = -1

The solution is (5, -1), which corresponds to option b.

To check the solution, we can substitute x = 5 into both of the original equations to verify that they are true. For the first equation:

-5(5) + 24 = -25 + 24 = -1

For the second equation:

4(5) - 21 = 20 - 21 = -1

Since both substitutions lead to an identity, the solution is correct. The final answer is (5, -1), or option b.

The expression '2 3/2' is a mixed number. Converting this to an improper fraction results in 7/2, which simplifies to 3.5. This does not match any of the provided options.

The expression '2 3/2' implies that we are dealing with mixed numbers, meaning you have a whole number and a fraction combined. When you see this, you should convert the mixed number into an improper fraction. The way to do this is to multiply the whole number by the denominator of the fraction and then add the numerator to this product. In this case that would be (2*2) + 3 which equals 7. Your new fraction would be 7/2 which equals 3.5 when simplified to a decimal. This does not correspond to any of the provided options (A, B, C, D), signifying that the original question may have been misinterpreted or contains a typographical error.

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2 3/2 is equal to 7/2 or D) Two times the square root of 16​.

When we have a whole number followed by a fraction, we can convert it to an improper fraction.

To do this, we multiply the whole number by the denominator of the fraction and add the numerator.

So in this case, 2 x 2 + 3 = 7.

Therefore, 2 3/2 is equal to 7/2 or D) Two times the square root of 16​.

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Answer:

Both Scott and Tara have responded correctly.

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

A=(1/2)[b1+b2]h

we have

b1=16 cm

b2=24 cm

h=8 cm -----> Note The height is 8 cm instead of 18 cm

substitute

A=(1/2)[16+24](8)

A=160 cm²

Verify Scott 's work

Note Scott wrote A = (1/2)(24 + 16)(8) instead of A = 2(24 + 16)(8)

Remember that the Commutative Property establishes "The order of the addends does not alter its result"

so

(24+16)=(16+24)

A = (1/2)(24 + 16)(8)=160 cm²

Verify Tara's work

Note Tara wrote A = (1/2)(16+24)(8) instead of A = (16 + 24)(8)

A = (1/2)(16+24)(8)=160 cm²

ANSWER

See below

EXPLANATION

The given point (-3,1) lies in the second quadrant.

In this quadrant only sine is positive.

The length of the hypotenuse formed by the right angle triangle is

[tex] {h}^{2} = {3}^{2} + {1}^{2} [/tex]

[tex] {h}^{2} = 9 + 1[/tex]

[tex]{h}^{2} = 10[/tex]

[tex]h = \sqrt{10} [/tex]

The side opposite to θ, is 1 units.

The adjacent side is 3 units.

[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]

[tex]\sin( \theta) = \frac{1}{ \sqrt{10} } = \frac{ \sqrt{10} }{10} [/tex]

[tex]\cos( \theta) = - \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos( \theta) = - \frac{3}{ \sqrt{10} } = - \frac{3 \sqrt{10} }{10} [/tex]

[tex] \tan( \theta) = - \frac{opposite}{adjacent} [/tex]

[tex]\tan( \theta) = - \frac{1}{3} [/tex]

The values of sine, cosine and tangent of θ are; 1/√10, -3/√10 and -1/3 respectively.

From the task content, it follows from Pythagoras theorem that;

On this note;

Read more on Trigonometric identities;

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Answer:

X= -13

Step-by-step explanation:

Your first goal is to get all the X’s to one side of the equation.

So:

3x - 5 = 9x + 8 - 5x

+5x +5x

8x - 5 = 9x + 8

-9x -9x

-1x - 5 = 8

Now that you have all the X variables simplified and on one side, you make sure all of you constant terms are on the other side.

-1x - 5 = 8

+5 +5

-1x = 13

Because you can’t have a negative X, you divide the entire equation by -1.

-1x = 13

-1

x = -13

Dividing by -1 will give you the inverse of the equation which is positive one x equals negative thirteen.

Answer:

7x-y=61

Step-by-step explanation:

The standard form is Ax+By=C.

Let's simplify the equation first.

1. Distribute: y+5=7x-56

2. Subtract 5: y=7x-61

3. Arrange into standard form: 7x-y=61

Answer

-7x+y=-61

Its the same as 7x-y=61, but in a different form

Answer:

66 ⅔ m

Step-by-step explanation:

2 ⅓ km can be written in improper form as 5/3 km.

There's 1000 m in 1 km, so we can convert this:

5/3 km × (1000 m / km) = 5000/3 m

The submarine rises at 800 m/h.  So after 2 hours:

distance = rate × time

d = 800 m/h × 2 h

d = 1600 m

So the new position is:

5000/3 m − 1600 m

5000/3 m − 4800/3 m

200/3 m

66 ⅔ m

Final answer:

After ascending at a rate of 800 meters per hour for 2 hours from a depth of 2 1/3 kilometers, the position of the submarine would be 733.3 meters below sea level.

Explanation:

The student has asked to find the position of a submarine after it ascends from a depth of 2 1/3 km below sea level at a rate of 800 m/h for 2 hours.

Firstly, we convert the depth of the submarine from kilometers to meters to match the ascent rate's unit. There are 1,000 meters in a kilometer, so 2 1/3 km is equivalent to 2,333.3 meters (since 2 km = 2000 m and 1/3 km = 333.3 m).

The submarine ascends at a rate of 800 meters per hour. After 2 hours, the total ascent will be 800 m/h * 2 h = 1,600 meters.

To find the new position, we subtract the ascent distance from the original depth: 2,333.3 m - 1,600 m = 733.3 meters below sea level.

Therefore, after 2 hours, the position of the submarine would be 733.3 meters below sea level.

Answer:

Step-by-step explanation:

You could use the 'brute force' method, which would be to simply write out all the possible subsets.  We could avoid repetition within the subsets.

{2} would be the first subset; it contains one even number.

Next would be {2, 4}, next {2, 4, 6} ... {2, 4, 6, ... 94, 96, 98, 100}.  Provided that we correctly understand what this problem is asking for, writing out and then counting all these subsets should answer the question.

Answer:

answer is Z

Step-by-step explanation:

Their are 34 females in the class.

If 42 is the total amount of French students; subtract the amount of males(8) from the whole class to receive how many females their are in the class. Which is 34.

Answer: [tex](y-4)=3(x-1)[/tex]

Step-by-step explanation:

We know that the point slope form of a line that has a slope m and passing through point (a,b) is given by :-

[tex](y-b)=m(x-a)[/tex]

Given: Slope of a line: m = 3

Point through which line is passing : (1, 4)

The point slope form of a line that has a slope 3 and passing through point (1, 4) is given by :-

[tex](y-4)=3(x-1)[/tex]

– 4 = 3[(x – (–1)]

Step-by-step explanation:

Answer: i say its A but i could be wrong

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Look at where the two functions intersect.

[tex](-3,-3)[/tex] and [tex](0,6)[/tex].

Those are the solutions.

Answer:

C.) n < 6

Step-by-step explanation:

Subtract 8:

n/-3 > -2

Multiply by -3. The negative multiplier requires the comparison be reversed:

n < 6

To solve the inequality n/-3 + 8 > 6, we first subtract 8 from both sides of the inequality and then multiply by -3. This reveals that n < 6, which corresponds to option C.

To solve the inequality n/-3 + 8 > 6, we first isolate the term containing n by subtracting 8 from both sides of the inequality:

n/-3 + 8 - 8 > 6 - 8

n/-3 > -2

Now, we can multiply both sides of the inequality by -3 to find the value of n. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:

n/-3 × -3 < -2 × -3

n < 6

Thus, the correct answer to the inequality n/-3 + 8 > 6 is n < 6, which corresponds to option C.

Answer:

20% of the number 40 is 8

20% x 40=800 divide 100 =8

The answer would be [tex]\frac{1}{4}[/tex] because half the chance of landing on an even number divided by 2 (2 times landing on the even number).

The probability that the spinner will land on an even number both times when spun twice is 1/4 or 25%.

To find the probability of two independent events occurring together, we multiply their individual probabilities. First, let's determine the probability of landing on an even number in a single spin. There are two even numbers (2 and 4) out of the four possible outcomes, so the probability of landing on an even number in one spin is 2/4 or 1/2.

Since we're spinning the spinner twice, the events are independent. This means that the outcome of the first spin does not affect the outcome of the second spin. Therefore, the probability of landing on an even number in both spins is the product of the individual probabilities. So, the probability of landing on an even number both times is:

Probability of landing on an even number in one spin = 1/2

Probability of landing on an even number twice = (1/2) * (1/2) = 1/4

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Answer:

There are no real number solutions to this question.

The statement which is true for the equation[tex]\sqrt{2x-1} =-1[/tex] is option C which is that x=1.

It is a relationship between variables and it can be in the form of one variable also.

We have been given [tex]\sqrt{2x-1} =-1[/tex]

squaring both sides we get

2x-1=1

2x=1+1

2x=2

x=1

Hence the solution of the equation is x=1.

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Answer:

154 adults 94kids

Step-by-step explanation:

14×3×3=126. So 126 is your answer.

Answer:

14*4*3         168

Step-by-step explanat

Answer:

The correct answer is third option

The sum of any number and its opposite is 0

Step-by-step explanation:

It is given an expression,

8.29 * (-5.62 + 5.62)/5.62

To find the correct reason

Here - 5.62 + 5.62 = 0

5.62 is opposite to - 5.62

because sum of a number and its opposite is 0.

Therefore the correct answer is third option.

The sum of any number and its opposite is 0

[tex]\bf \begin{array}{|lllllllll|ll} \cline{1-9} label&A&B&C&D&E&F&G&H\\ &&&&&&&&&\\ pennies&2^0&2^1&2^2&2^3&2^4&2^5&2^6&2^7\implies 128\\ \cline{1-9} \end{array}[/tex]

Answer: part 2: 2n-1

Step-by-step explanation:

You brought back 12.2

hope that helped