Where is the vertex of the equation?y = x2 – 18x + 80

Answer:

Try the suggested solution, shown on the picture attached

Step-by-step explanation:

Note, 'm(MNO)' means m(∠MNO), and for issues 2, 4 ,5 - the described angles are angles inside the declared triangle.

Answer:

67º

Step-by-step explanation:

Answer: Second option.

Step-by-step explanation:

Below are some transformations for a function  f(x) :

1. If [tex]f(x)+k[/tex], the function is shifted "k" units up.

2. If [tex]f(x)-k[/tex], the function is shifted "k" units down.

3. If [tex]f(x-k)[/tex], the function is shifted "k" units right.

4. If [tex]f(x+k)[/tex], the function is shifted "k" units left.

The Cube root parent function is:

[tex]f(x)=\sqrt[3]{x}[/tex]

By definition, the graph of this function passes through the origin, as you can observe in  the picture attached.

In this case, you need to analize the graph given in the exercise. You can see that the the graph of the function h(x) is like the parent function f(x), but shifted 2 units left.

Therefore, based on the transformations explained above, you can determine that the equation of the function h(x) is the following:

[tex]h(x)=f(x+2)\\\\h(x)=\sqrt[3]{x+2}[/tex]

Answer:

Option B: [tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex]

Step-by-step explanation:

When the focus (h, k) of a parabola and the equation of the directrix y = c are given, the equation of the parabola is given by:

                     [tex]$ \textbf{(x - h)}^{\textbf{2}} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{k}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{c}^{\textbf{2}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{2(k - c)y}} $[/tex]

Here, we are given the focus: (h, k) = (0, -2)

Directrix: y = c = -3.

We substitute in the formula to get the equation of the parabola.

[tex]$ (x - 0)^2 + (-2)^2 - (-3)^2 = 2(-2 - (-3))y $[/tex]

[tex]$ \implies x^2 + 4 - 9 = 2(- 2 + 3)y $[/tex]

[tex]$ \implies x^2 - 5 = 2(1) y$[/tex]

[tex]$ \implies 2y = x^2 - 5 $[/tex]

Dividing by 2, throughout we get:

[tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex] which is the required answer.

68 is the 22nd term of the following sequence.

Step-by-step explanation:

the twenty second (22) term of the sequence 5, 8, 11, ...... is: D. 68.

Given the following data:

To find the twenty second (22) term of the sequence:

Mathematically, the [tex]n^{th}[/tex] term of a sequence is calculated by using the following formula;

[tex]a_n = a + (n - 1)d[/tex]

Where:

First of all, we would determine the common difference.

[tex]d = 2^{nd} \; term - 1^{st}\;term\\\\d = 8 - 5 \\\\d = 3[/tex]

Substituting the given parameters into the formula, we have;

[tex]a_{22} = 5 + (22 - 1)3\\\\a_{22} = 5 + (21)3\\\\a_{22} = 5 + 63\\\\a_{22} = 68[/tex]

Therefore, the twenty second (22) term of the sequence is 68.

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Answer:

She earned $8.5 per hour.

Step-by-step explanation:

110.5/13=8.5

Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

Given:

Elena ate 2/8 of a pizza.

Dylan ate 1/5 of a pizza.

Question asked:

How much of the pizza did they eat ?

Solution:

By simply adding.

Elena ate of a pizza. = [tex]\frac{2}{8}[/tex]

Dylan ate of a pizza = [tex]\frac{1}{5}[/tex]

Total of a pizza they ate = [tex]\frac{2}{8}[/tex] + [tex]\frac{1}{5}[/tex]

By taking LCM of 8 and 5 ; 40

[tex]\frac{10 + 8}{40} = \frac{18}{40} = \frac{9}{20}[/tex]

Thus, [tex]\frac{9}{20}[/tex] f the pizza they eat.

Answer:

The number of jumps that the game piece took, was 40.

Step-by-step explanation:

Every jump a game piece makes measures [tex]\frac{8}{9} = 0.889[/tex].

Now, the piece starts at point A = 7 and jumps to the right.

So, the number of jumps required by the piece to jump over B = 24 will be

[tex]\frac{24 - 7}{0.889} = 19.122[/tex] jumps ≈ 20 jumps {As the piece crosses the point B}

Now, as soon as the piece jumps over B = 24, it switches direction and jumps to the left. And the piece then stops at point A.

Therefore, the number of jumps that the game piece took, was (20 × 2) = 40. (Answer)

Final answer:

Calculating the jumps based on the jump size of 8 / 9 units, the piece makes 20 jumps to go from point A past point B, and then 23 jumps to return to point A, for a total of 43 jumps.

Explanation:

To solve the question, we must calculate the total number of jumps the game piece takes from the starting point A at 7, over point B at 24, and back to A. Each jump measures 8 / 9 units. To calculate the number of jumps to reach just past point B (24 units), we can set up a division problem to find the number of jumps it would take to first reach or pass 24 starting from 7. The formula for this is (B - A) / jump size.

So, the calculation for jumps to point B is: (24 - 7) / 8 / 9 = 17 × 9 / 8 = 153 / 8 = 19.125. Since the game piece cannot make a partial jump, we must round up to 20 jumps to reach beyond 24 units.

After the piece switches direction, we perform a similar calculation to find how many jumps it takes to go back to point A (7 units).

Here, since the piece is already beyond 24, it only needs to jump back to the next integer value before 7 which is 6.

Now, the game piece is at (20 × 8 / 9) + 7 = approximately 24.222 + 7 = approximately 31.222 units along the path.

To calculate the jumps back to 6, we have (31.222 - 6) / 8 / 9 which is approximately 22.556 jumps, and rounding up gives us 23.

Therefore, the total number of jumps made is the sum of the jumps to point B and back to point A,

which is 20 + 23 = 43 jumps.

Option D

The trip lasts for [tex]6\frac{1}{4}\ hours[/tex]

Solution:

Mr Patel is planning to drive 325 miles

Average speed is 65 mph

He will stop one hour for lunch and take a 15 min rest break

Let us first find the time taken

[tex]Time = \frac{distance}{speed}[/tex]

[tex]Time = \frac{325}{65}\\\\Time = 5[/tex]

Thus he covers 325 miles in 5 hours

Also, given that, he will stop one hour for lunch and take a 15 min rest break

Therefore, total time taken for trip is:

Total time = 5 hours + 1 hour + 15 minutes

Total time = 6 hours 15 minutes

We know that,

1 hour = 60 minutes

Therefore,

[tex]6\ hours\ 15\ minutes\ = 6 + \frac{15}{60}\ hours = 6 + \frac{1}{4} = 6\frac{1}{4}\ hours[/tex]

Thus the trip lasts for [tex]6\frac{1}{4}\ hours[/tex]

Mr. Patel's trip will last a total of 6.25 hours, including his driving time, lunch break, and rest break. The calculation was done using the formula Time = Distance / Speed, and factoring in the break times.

First, we need to calculate how many hours Mr. Patel will spend driving. To do this, we use the formula Distance = Speed * Time. We rework this formula to find time, giving us Time = Distance / Speed. So, Mr. Patel’s total driving time is 325 miles divided by 65 mph (miles per hour), which equals 5 hours.

The next task is to factor in Mr. Patel’s lunch and rest breaks. He takes one hour for lunch and 15 minutes for a rest break. Note that 15 minutes is 0.25 of an hour. Add these two periods to our initial 5 hours of driving time, and we get a total of 6.25 hours. So, Mr. Patel's trip will last 6.25 hours, which corresponds to answer choice D).

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The given dilation is an isometry dilation.

Step-by-step explanation:

Step 1; First, we need to compare the dimensions of the two figures. We check to see if the side lengths are the same. If the parameters are the same, the dilation could be an enlargement or a reduction. Whereas if the parameters are the same, it could be an isometric dilation or just a reflection.

Step 2; The first shape has a side length of approximately 2.5 units. We compare this to the same side length as the second shape. The second shape has the same side length.

The first shapes side length of the  / same side length of the second shape = 2.5 / 2.5 = 1,

So the scale factor is 1. As the parameters do not change, it could either be a reflection or an isometric dilation.

Step 3; The base side in shape 1 is BC whereas the same base side in shape 2 is [tex]A^{1}[/tex][tex]B^{1}[/tex]. So shape ABCDE has rotated to form the shape  the dilation is isometric and not a reflection with a scale factor of 1.

Answer:

1: Isometry

Step-by-step explanation:

As both the shapes are having equal area hence the scale factor remains 1.

As scale factor remains 1this is neither enlargement or reduction.

It is the isometry that the distance between two pints remains the same.

Answer:

B. Square root of 25

Step-by-step explanation:

It is a whole number.

Thus, it is not an irrational number.

The square root of 25 is equal to 5

Therefore

An irrational number is a number that cannot be written as a ratio of two integers. It is a non-terminating and non-repeating decimal.

Answer:7 bags

Step-by-step explanation:

Divide 60 by 8 because she has a total of $60 and each bag costs $8. The answer would actually be 7.5 bags but since you can’t buy half a bag your answer would be 7 bags.

Step-by-step explanation:

Hdhcnkcube hxjdje8277ru288xhei8chne

Diicinrhcurnje8f77 8eun3if7 hh8

Answer:

I would say it is c but im not sure.

Step-by-step explanation:

Well you use distributive property to solve this to get a simplified answer.

[tex]b. \: 5d - 3 \\ \\ 1. \: 2d + 6 + 3(d - 3) \\ 2. \: 2d + 6 + 3d - 9 \\ 3. \: (2d + 3d) + (6 - 9) \\ 4. \: 5d - 3[/tex]

Answer:

if it as more

Step-by-step explanation:

no need to thank me just add me on snap wgilpenn

Answer:

it's 408,471

Step-by-step explanation:

[tex]400000 \\ + 8000 \\ \: + 400 \\ \: \: + 70 \\ \: \: \: + 1 \\ = 408471[/tex]

Answer:

Option C) 2=2 is the last step of Naomi and it is the correct answer

Step-by-step explanation:

Given that Naomi solves a system of equation by Substitution method :

The given system has infinite many solutions

Naomi's last step is 2=2

Then the system of equations has infinite many solutions

Therefore it must be 2=2

Hence option C) 2=2 is the last step and it is the correct answer

The correct last step in a solution with infinitely many solutions is option C, '2 = 2,' which shows that the system of equations is dependent and represents an identity.

When Naomi solves a system of equations using substitution and finds that the system has infinitely many solutions, this means that the two equations are essentially the same line. Therefore, the last step in her solution would demonstrate that the two expressions are identical. Option C, which states 2 = 2, would be the correct answer because it represents an identity, showing that the two sides of the equation are the same no matter what value is chosen for the variables. This is consistent with a situation where the system of equations is dependent, having an infinite number of solutions.

To determine how many pounds of blueberries are left in the container after using 1/5 for muffins, calculate 4/5 of the initial amount, as this represents the remaining 80%. The ability to work with fractions and percentages is crucial here.

The question involves understanding percentages and unit conversion. If 1/5 of the remaining blueberries is used to make muffins, that means 80% (or 4/5) of the blueberries are left in the container. To find out how many pounds of blueberries are left, we first need to know the total quantity before using any for muffins. Assuming we had a specific weight to begin with, we would calculate 4/5 of that weight to determine what remains.

For example, if there were 10 pounds of blueberries initially, 2 pounds (1/5) would be used for muffins, leaving 8 pounds (4/5) of blueberries in the container. It's essential to be comfortable with fractions and percentage calculations when dealing with such problems in mathematics.

a. Each bowl contains 1/12 of the total blueberries.

b. There were 72 ounces of blueberries in the full container.

c. There are 3 pounds of blueberries left in the container.

a. What fraction of the blueberries is in each bowl?

Initially, 1/6 of the blueberries are poured equally into two bowls. Therefore, each bowl receives 1/6 * 1/2 = 1/12 of the total blueberries.

b. If each bowl has 6 ounces of blueberries in it, how many ounces of blueberries were in the full container?

Since each bowl has 6 ounces of blueberries, and there are two bowls, the total amount of blueberries poured into the bowls is 6 * 2 = 12 ounces. Since this represents 1/6 of the total blueberries, we can set up the equation:

Total blueberries = 12 * 6 = 72 ounces

c. If 1/5 of the remaining blueberries are used to make muffins, how many pounds of blueberries are left in the container?

After pouring 1/6 of the blueberries into the bowls, 5/6 of the blueberries remain. Then, 1/5 of these remaining blueberries are used to make muffins. So, the fraction of blueberries remaining after making muffins is 5/6 * 4/5 = 20/30 = 2/3.

To convert the remaining blueberries to pounds, since 1 pound equals 16 ounces, we divide the total remaining ounces by 16:

Remaining blueberries in pounds = (72 ounces * 2/3) / 16 ounces/pound = (72 * 2) / (3 * 16) = 144 / 48 = 3 pounds

So, there are 3 pounds of blueberries left in the container.

The probable question maybe:

A container is filled with blueberries. 1/6 of the blueberries are poured equally into two bowls.

a. What fraction of the blueberries is in each bowl?

b. If each bowl has 6 ounces of blueberries in it, how many ounces of blueberries were in the full container?

c. If 1/5 of the remaining blueberries are used to make muffins, how many pounds of blueberries are left in the container?

Answer:

y=-2/7x+1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-1))/(21-7)

m=(-5+1)/14

m=-4/14

simplify

m=-2/7

y-y1=m(x-x1)

y-(-1)=-2/7(x-7)

y+1=-2/7(x-7)

y=-2/7x+2-1

y=-2/7x+1

The equation of the line in slope-intercept form is: [tex]\[ \boxed{y = -\frac{2}{7}x + 1} \][/tex]

To find the equation of the line in slope-intercept form  y = mx + b that passes through the points 7, -1 and 21, -5 we need to follow these steps:

1. Find the slope  m  of the line.

2. Use the slope and one of the points to find the y-intercept b

3. Write the equation in the form y = mx + b

Step 1: Find the slope m

The formula for the slope between two points [tex]\((x_1, y_1)\) and \((x_2, y_2)\) is:[/tex]

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

For the points 7, -1 and 21, -5

[tex]\[ x_1 = 7, y_1 = -1 \][/tex]

[tex]\[ x_2 = 21, y_2 = -5 \][/tex]

Substitute these values into the slope formula:

[tex]\[ m = \frac{-5 - (-1)}{21 - 7} = \frac{-5 + 1}{21 - 7} = \frac{-4}{14} = -\frac{2}{7} \][/tex]

Step 2: Find the y-intercept b

Use the slope[tex]\( m = -\frac{2}{7} \)[/tex] and one of the points

[tex]\[ -1 = -\frac{2}{7}(7) + b \][/tex]

b = 1

Step 3: Write the equation

Now that we have the slope [tex]\( m = -\frac{2}{7} \)[/tex] and the y-intercept  b = 1 we can write the equation in slope-intercept form:

[tex]\[ y = -\frac{2}{7}x + 1 \][/tex]

Thus, the equation of the line in slope-intercept form is:

[tex]\[ \boxed{y = -\frac{2}{7}x + 1} \][/tex]

Answer:

(This is in my own words)

ALL terms of the numerator must be subtracted out, not just the first term. -2 should be subtracted out to get a numerator of x+1-x+2. Thus, the difference of the numerator should be 3, and not –1. This is when simplified correctly.

On solving the expression correctly, we get -

3/(x - 2)(x + 1)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is the following equation -

1/(x - 2) - 1/(x + 1)

We have -

1/(x - 2) - 1/(x + 1)

[(x + 1) - (x - 2)]/(x - 2)(x + 1)

3/(x - 2)(x + 1)

Therefore, on solving the expression correctly, we get -

3/(x - 2)(x + 1)

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⁶⁾4/5 = ¹⁰⁾24/30 = 240/300

⁵⁾5/6 = ¹⁰⁾25/30 = 250/300

Rational numbers between 4/5 & 5/6​ :

241/300

242/300

243/300

.................

248/300

249/300

Yo sup??

There are infinite numbers possible but since we are asked to find only 2 we can say

4/5=0.8000

5/6=0.8334

Therefore the possible numbers are:

0.81=81/100

0.82=82/100=41/50

0.83=83/100

and so on

Hope this helps.

Answer:

B- 240 cm²

Step-by-step explanation:

Hope it can help you lovelots

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Answer: Since 3−5+2=0, then 2

is the additive inverse of 3−5 is 2

 Since 5−3−2=0, then −2is the additive inverse of 5−3. is -2

Step-by-step explanation: additive inverse

The additive inverse of any number

x

is the number that gives zero when added to

x

. Example: the additive inverse of

5 is −5.

Answer:

The value of x is 120°

Step-by-step explanation:

To solve for x, you need to introduce a third line that is parallel to the two parallel lines.

This line should divide the angle at x into two as shown in the attachment.

By the alternate interior angle property, m=70°

and

n=50°

This implies that, x=50+70=120°

Answer:

Step-by-step explanation:

Answer:

71 ducks

Step-by-step explanation:

1. 56 + 20 = 76

2. 76 - 5 = 71

See the graph below

First of all, let's rename those expressions as follows:

[tex]\left\{ \begin{array}{c}y=10+3x\\y=4x\end{array}\right[/tex]

So we we have two lines written in slope-intercept form. In order to graph those lines, let's find two points for each:

First line:

[tex]For \ x=0: \\ \\ y=10+3(0) \\ \\ y=10 \\ \\ \\ For \ x=-10/3: \\ \\ y=10+3(-10/3) \\ \\ y=10-10 \\ \\ y=0 \\ \\ \\ So \ the \ line \ passes \ through \ (0,10) \ and \ (-10/3,0)[/tex]

This line is the green one shown below.

Second line:

[tex]For \ x=0: \\ \\ y=4(0) \\ \\ y=0 \\ \\ \\ For \ x=1: \\ \\ y=4(1) \\ \\ y=4 \\ \\ \\ So \ the \ line \ passes \ through \ (0,0) \ and \ (1,4)[/tex]

This line is the red one shown below.

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Evaluating 3^3/2 gives us 5.196152423, so we can round this to 5.

Answer:

C

Step-by-step explanation:

product of 7 and 10 is 70

product of 10 and 12 is 120

a = 12

b =45

c =120

d =49

The​ number is 5 which sum of the square of a positive number and the square of 3 more than the number 89.

The quadratic function is defined as a function containing the highest power of a variable is two.

We have to determine the​ number which sum of the square of a positive number and the square of 3 more than the number 89.

Let the first number would be x

So second number = x + 3

According to the given condition,

⇒ x² + (x + 3)² = 89                    

⇒ x² + x² + 6x + 9 = 89                    

⇒ 2x² + 6x + 9 = 89

⇒ 2x² + 6x - 80 = 0

⇒ x² + 3x - 40 = 0

⇒ (x + 8)(x - 5) = 0

⇒ x + 8 = 0 or x - 5 = 0    

⇒ x = -8 or x = 5  

The answer is 5 because we are looking for a positive number.

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Final answer:

The positive number where the sum of its square and the square of 3 more than the number equals 89 is 5.

Explanation:

To determine the positive number where the sum of squares of the number and the square of 3 more than the number equals 89, we set up the following equation:

Let x be the positive number. Then:

x² + (x + 3)² = 89

Expanding the equation:

x² + x² + 6x + 9 = 89

Combining like terms, this becomes:

2x² + 6x + 9 = 89

Subtract 89 from both sides:

2x² + 6x - 80 = 0

We now have a quadratic equation. Dividing by 2 for simplicity:

x² + 3x - 40 = 0

Factor the quadratic equation:

(x + 8)(x - 5) = 0

Setting each factor equal to zero gives us two possible solutions for x:

Therefore, the positive number is 5.

Answer:

t = 40

Step-by-step explanation:

Start by breaking the equation down to a simpler form.  To do this you would need to divide 28 by 7.

28 / 7 = x

x = 4

Now we can create a new equation.

4x = t

T would represent the total number of students in the band.  X would be the any number from 1 to 10.  This is because 10 is the highest faction to make the fraction a whole.  Since we a looking for the total we would put ten in place for x.

4 x 10 = t

t = 40

There you go.

Hope this helped.

The answer is.

The Lamp post is 800cm

x = height of lamp post

160/90 = x/450

450 is the length from the base of the lamp post to the end of the shadow (360+90)

cross multiple

90x = 72000

x =800cm

Have a great day!

The lamp post is 800 cm high

From the diagram in the attachment below,

The height of the girl is /AG/ = 160cm

The length of her shadow is /SG/ = 90cm

The height of the lamp post is /LP/ = /LM/ + /MP/ = x + 160cm

To determine the height of the lamp post, we will calculate the value of x

Consider ΔASG

Determine <ASG = θ

From

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

Opposite = /AG/ = 160 cm

Adjacent = /SG/ = 90 cm

∴ [tex]tan\theta = \frac{160}{90}[/tex]

Also, Consider ΔLAM

[tex]tan\theta = \frac{/LM/}{/AM/}[/tex]

NOTE: <LAM = θ (Corresponding angles) since line AM is parallel to line SP

∴[tex]\frac{160}{90} = \frac{/LM/}{/AM/}[/tex]

But, /LM/ = x and /AM/ = 360 cm

∴[tex]\frac{160}{90} = \frac{x}{360}[/tex]

[tex]90x = 360 \times 160[/tex]

[tex]x = \frac{360 \times 160}{90}[/tex]

[tex]x = 4 \times 160 \\[/tex]

[tex]x = 640 cm[/tex]

x = 640 cm

Recall that, the height of the lamp post is /LP/ = /LM/ + /MP/ = x + 160cm

∴ The height of the lamp post is 640 cm + 160cm

The height of the lamp post is 800 cm

Hence, the lamp post is 800 cm high

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