The equation of a parabola is y=x^2-10x+27. Write the equation in vertex form

Answer:

1) C

Step-by-step explanation:

1) 2x + 4 < 5x + 3

3x > 1

x > ⅓

Answer:

Use compatible numbers that are close to the actual numbers

Choose 36 for 35 3/4 and 6 for 5 7/8 because the divide evenly.

Step-by-step explanation:

Compatible numbers are numbers that are close to the actual values of a particular number. They make estimating easier when yo udo the different operations.

We choose 36 for 35 3/4 because 36 is closer to its value that 34. Conveniently, 5 7/8 is closer to 6 than 5, and they divide evenly. So a best estimate for the number of rows Holly can make would be:

36/6 = 6 rows.

Volume of the cone is 100 in³

Step-by-step explanation:

Volume = 1/3 × 3.14 × 3² × 9

             = 84.78 in³ ≈ 100 in³ (rounding off to nearest hundredth)

Final answer:

The volume of a cone with a radius of 3 inches and a height of 9 inches is approximately 84.78 cubic inches.

Explanation:

To find the volume of a cone with a radius of 3 inches and a height of 9 inches, you can use the formula for the volume of a cone, which is:

[tex]V = (1/3)\pi r^2h[/tex]

Plugging the given values into the formula gives us:

[tex]V = (1/3) * 3.14 * (3 inches)^2 * 9 inches[/tex]

Now, calculate the square of the radius:

[tex]V = (1/3) * 3.14 * 9 * 9[/tex]

Next, multiply all the numbers together:

[tex]V = 3.14 * 27[/tex]

V = 84.78 cubic inches

Therefore, the volume of the cone is approximately 84.78 cubic inches, rounded to the nearest hundredth.

Step-by-step explanation:

[tex]10 \times 9 \sqrt{72} \\ = 90 \sqrt{36 \times 2} \\ = 90 \times 6 \sqrt{2} \\ = 540\sqrt{2} [/tex]

Final answer:

To find the product of 10 and 9√72, simplify √72 to 6√2, then multiply the outside coefficients (10 and 9) to get 90, and attach the simplified radical. The final answer is 90√2.

Explanation:

The question asks to find the product of 10 and 9√72 in simplest radical form. First, recognize that the square root of 72 can be simplified by factoring out perfect squares. The square root of 72 is equal to the square root of 36 times 2, which simplifies to 6√2. Now, multiply the outside coefficients (10 and 9) and then multiply the result by the simplified radical. The final simplification is 90√2, which is the product of 10 and 9√72 in simplest radical form.

Answer:

75 miles

Step-by-step explanation:

We can use cross products to solve

3 in                   5 in

--------------- = -------------------

45 mi               x miles

3 * x = 5 * 45

3x = 225

Divide each side by 3

3x/3 = 225/3

x =75 miles

To find the actual distance between two towns on a map, use the scale provided. Set up a proportion using the scale and the map distance to find the actual distance. In this case, the actual distance is 75 miles.

To find the actual distance between two towns on a map, you can use the scale provided. In this case, the scale is 3 in: 45 mi. This means that 3 inches on the map represents 45 miles in the real world. If the map distance between the two towns is 5 inches, you can set up a proportion to find the actual distance.

Using the scale, you can set up the equation:

3 inches / 45 miles = 5 inches / x miles

Cross-multiplying, you get:

3 * x = 5 * 45

Simplifying, you get:

x = (5 * 45) / 3

x = 75 miles

Therefore, the actual distance between the two towns is 75 miles.

Step-by-step explanation:

Sequence 1:

term1=26

term2=26-3=23

term3=23-3=20

term4=20-3=17

term5=17-3=14

sequence2:

term1=-3

term2=-3+10=7

term3=7+10=17

term4=17+10=27

term5=27+10=37

The first sequence starts at 26 and subtracts 3 to find the next terms: 26, 23, 20, 17. The second sequence starts at -3 and adds 10 to find the next terms: -3, 7, 17, 27.

The first term of the sequence is 26. To find the next term, subtract 3 from 26, which gives you 23. Continuing this pattern, the second term is 23. To find the third term, subtract 3 from 23, which gives you 20. The fourth term is 20. To find the fifth term, subtract 3 from 20, which gives you 17. The fifth term is 17.

The first term of the second sequence is -3. To find the next term, add 10 to -3, which gives you 7. Continuing this pattern, the second term is 7. To find the third term, add 10 to 7, which gives you 17. The fourth term is 17. To find the fifth term, add 10 to 17, which gives you 27. The fifth term is 27.

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Answer:

x= 33.8

Step-by-step explanation:

Please see attached picture for full solution.

The possible length for the third side of a triangle with two sides of length 5 must be greater than 0 and less than 10, as determined by the Triangle Inequality Theorem.

The student is asking about a possible third side of a triangle with two sides of length 5. To answer this, we will apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, any third side length must be less than 10 (5 + 5) but also greater than 0, because if it were 10 or more it wouldn't form a triangle but a straight line. However, since the smallest possible non-zero length a side can have is just above 0, we can say the third side must be greater than 0 and less than 10.

Answer:

No, 40(2x - 16y) is not equivalent to 42 - 56y

Step-by-step explanation:

40(2x -16y)

If we expand the above expression, we will have

80x - 16y which is not equivalent to 42 - 56y

Answer:

[tex]m\angle A=98^o[/tex]

Step-by-step explanation:

we know that

In a parallelogram opposite angles are congruent and consecutive angls are supplementary

In this problem

we have the parallelogram  ABCD

so

[tex]m\angle A=m\angle C[/tex] ----> by opposite angles

[tex]m\angle B=m\angle D[/tex] --> by opposite angles

and

[tex]m\angle A+m\angle B=180^o[/tex] ----> by consecutive angles

[tex]m\angle B+m\angle C=180^o[/tex] ----> by consecutive angles

we have

[tex]m\angle C=98^o[/tex]

therefore

[tex]m\angle A=98^o[/tex]

Answer:

Step-by-step explanation:

help me

Answer:

The three methods most commonly used to solve systems of equation are substitution, elimination and augmented matrices. Substitution and elimination are simple methods that can effectively solve most systems of two equations in a few straightforward steps.

Step-by-step explanation:

hope this helps

Answer:

x = -4

Step-by-step explanation:

1. Basically you do the cube root on both sides of the equation.

2. Giving you x = -4

Answer:

  14.02056

Step-by-step explanation:

Multiply the rate by the quantity:

  38,946 × 0.36/1000 = 14.02056

_____

Sometimes it is helpful to think of "per" as meaning "divided by."

Answer:

X=0.8 or x=4/5

Step-by-step explanation:

Answer:

x = 0.8

Step-by-step explanation:

Step 1:  Divide both sides by 5

4 / 5 = 5x / 5

0.8 = x

Answer:  x = 0.8

Answer:

x = 5 is incorrect

Step-by-step explanation:

12 1/2 should be -12 1/2

Answer:

For this question, x = 16

Step-by-step explanation:

x/20 = 4/5

if we cross multiply, we will have

x × 5 = 4 × 20

5x = 80

x = 80/5

x = 16

Answer: 16

Step-by-step explanation:

X/20 = 4/5

Cross multiply

(5×X) = (20×4)

5x = 80

x = 80/5

x = 16

Answer:

85/99

Step-by-step explanation:

[tex]\frac{171717}{200000}[/tex]

Answer:

B. 3 ÷ 1/4 = 12

This is the correct division problem because the result is 12 and we're calculating how many fourths are in 3 wholes.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Number of circles = 3

Number of divisions of every circle = 4

2. Which of the following division problems describes Melinda's work?

A. 4 ÷ 3 = 4/3

It's incorrect because the total number of fourths in 3 circles is 12.

B. 3 ÷ 1/4 = 12

This is the correct division problem because the result is 12 and we're calculating how many fourths are in 3 wholes.

C. 4 ÷ 1/3 = 12

It's incorrect because the question is to determine how many fourths are in 3 wholes, not how many thirds are in 4 wholes.

D. 3 ÷ 4 = 3/4

It's incorrect because the total number of fourths in 3 circles is 12.

Answer:

x = [tex]\sqrt{13}[/tex]

Step-by-step explanation:

The line from the vertex to the base is a perpendicular bisector and divides the triangle into 2 right triangles.

Consider the right triangle on the left with base 2

Using Pythagoras' identity

The square on the hypotenuse (x) is equal to the sum of the squares on the other 2 sides, that is

x² = 2² + 3² = 4 + 9 = 13 ( take the square root of both sides )

x = [tex]\sqrt{13}[/tex]

Answer:

Option 4

Step-by-step explanation:

sqrt(3² + 2²)

sqrt(9+4)

sqrt(13)

Answer: 94.3%

Step-by-step explanation:

Average daily attendance = total sum of attendance ÷ frequency

=754.4/8

= 94.3%

Answer:

160 beads

Step-by-step explanation:

let x be the number of beads to make a bracelet, then

It requires 5x beads to make a necklace and the sum is

x + 5x = 192, that is

6x = 192 ( divide both sides by 6 )

x = 32

Number of beads to make a necklace = 5x = 5 × 32 = 160

Answer:

160 beads

Step-by-step explanation:

Beads for bracelet: b

Beads for necklace: 5b

b + 5b = 192

6b = 192

b = 32

Beads for necklace: 5b = 5(32)

= 160

Answer: 75 boys

Step-by-step explanation: Our first step in this problem is to write down the unit ratio that is involved. In this case, it's boys/girls.

Next, we set up our proportion.

We know that there are 5 boys for every 6 girls.

So we have 5/6 and we're asked how many boys are at the dance if 90 girls are at the dance.

So we have [tex]\frac{5}{6} = \frac{x}{90}[/tex].

Notice that the 99 girls must go on the bottom of the second ratio because our unit ratio tells us that we put boys/girls.

Solving from here, we use the means-extremes property.

The product of the extremes,

(90)(5) equals the product of the means, (6)(x).

So we have (90)(5) or 450 equals (6)(x) or 6x.

So we have 450 = 6x and dividing both sides by 6, 75 = x.

So 75 boys are at the winter dance.

Answer:

ONE

Step-by-step explanation:

Only one.  Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.

Answer:  ONE

The required, an obtuse triangle is a triangle that has one angle measuring more than 90 degrees. By definition, an obtuse triangle has exactly one obtuse angle.

An obtuse triangle, by definition, contains one obtuse angle, which is an angle greater than 90 degrees but less than 180 degrees. The obtuse angle is the largest angle in an obtuse triangle, while the other two angles are acute angles (less than 90 degrees).

Since there is only one angle in an obtuse triangle that qualifies as an obtuse angle, we can conclude that there is exactly one obtuse angle in an obtuse triangle. The remaining two angles are acute angles.

It's important to note that the sum of the angles in any triangle is always 180 degrees. In the case of an obtuse triangle, the obtuse angle occupies a portion of that sum greater than 90 degrees, leaving the remaining acute angles to share the remaining portion of the 180-degree total.

Learn more about Angle here:

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Answer:

The scale factor is 1.25 and this represents an enlargement.

Step-by-step explanation:

As shown at the figure

The side length of the first hexagon = 5

The side length of the second hexagon  = 6.25

So, the scale factor = 6.25/5 = 1.25

and the second hexagon is larger than the first hexagon.

So,

The scale factor is 1.25 and this represents an enlargement.

Answer:

Step-by-step explanation:

Answer:

$65/hour

Step-by-step explanation:

Let C(h) represent the total amount payable to the plumber.  Then:

C(h) = $75 + (rate)(2 hr) = $205.  Solve for the "fixed hourly rate."

Subtracting $75 from both sides, we get:

(rate)(2 hr) = $130.

Dividing both sides by (2 hr) results in (rate) = $65/hour

The total bill of $205 is composed of a $75 fixed charge and $130 for the 2 hours worked. This implies that the plumber charges an hourly rate of $65. A representative tape diagram would show these components separately, with 2 equal blocks for the hourly rate totaling to the overall cost of $205.

The situation described is a basic arithmetic problem dealing with a fixed cost ($75) and a variable cost (hourly rate, represented as h). The equation that represents this problem is 75+2h=205, derived from the fixed cost plus two times the hourly rate (since the plumber worked for 2 hours). To solve for h (the hourly rate), we subtract 75 from both sides which leaves us with 2h=130, then divide by 2, giving us h=65. This means the hourly rate, h, the plumber charges is $65.

Without seeing the options A, B, C, and D, I can't explicitly say which tape diagram would best represent this situation. However, ideally, the tape diagram should illustrate $75 as a fixed cost and then two equal blocks (each equivalent to $65) to represent the cost of each hour worked. The total of all blocks combined should equal $205, the total cost.

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Solution:

Given that,

[tex]\text{ slope of line } =\frac{3}{4}[/tex]

A different line passes through the points (6, 3) & (-1, 5)

Find the slope of this line

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

From given,

[tex](x_1, y_1) = (6, 3)\\\\(x_2, y_2) = (-1, 5)[/tex]

Substituting we get,

[tex]m = \frac{5-3}{-1-6}\\\\m = \frac{2}{-7}[/tex]

For two lines are parallel, then their slopes must be equal

But here,

[tex]\frac{3}{4} \neq \frac{-2}{7}[/tex]

Therefore, They are not parallel because their slopes are not equal

Answer:

4 feet wide

Step-by-step explanation:

Area of the garden = 32 square feet

Length = 8 feet

Width = ?

The mimchi garden is rectangular in shape.

Area of a rectangle = L x W

32 = 8 x W

Divide both sides by 8

32/8 = 8/8 x W

4 = w

W = 4 feet wide

Answer:

4 ft.

Step-by-step explanation:

i did the quiz

Answer:

The height is 67 cm

Step-by-step explanation:

Remember that

[tex]1\ in=2.54\ cm[/tex]

we know that

The size of a TV is measured by its diagonal

Convert 60 inches to centimeters

[tex]60\ in=60(2.54)=152.4\ cm[/tex]

Applying the Pythagorean Theorem

[tex]D^2=H^2+W^2[/tex]

where

D is the diagonal

H is the height

W is the width

we have

[tex]D=152.4\ cm\\W=137\ cm[/tex]

substitute

[tex]152.4^2=H^2+137^2[/tex]

solve for H

[tex]H^2=152.4^2-137^2\\H^2=4,456.76\\H=67\ cm[/tex]

Hey there!

The distributive property is when you take one number and multiply by a quantity within parentheses and once multiplied and out of the parentheses it is the same value.

A is a simple addition problem.

C shows the associative property

D shows the commutative and associative property.

B shows that an expanded value is the same as something multiplied by something else in parentheses. Therefore, the answer is B.

I hope this helps!

Answer:

6.28 feet

Step-by-step explanation:

1.) Find the radius.

The area is given, and the formula for area of a circle is A = [tex]\pi r^{2}[/tex]  Let's substitute.

3.14 = [tex]\pi r^{2}[/tex]

Divide by pi on both sides

1 = [tex]r^{2}[/tex]

Find the square root of r

1 = r

The radius is 1.

2.) Find the circumference.

C = [tex]2\pi r[/tex]

C = [tex]2\pi (1)[/tex]

Multiply 2 and 1

C = [tex]2\pi[/tex]

C ≈ 6.28

The circumference is approximately 6.28 feet.

Final answer:

To find the circumference of a circular serving tray with an area of 3.14 square feet, one must first calculate the radius using the area formula and then apply the circumference formula 2πr, yielding a circumference of 6.28 feet when rounded to the nearest hundredth.

Explanation:

In order to find the circumference of Isaac's circular serving tray given its area, we need to apply the formula for the area of a circle, which is A =
^2. Since the area was provided as 3.14 square feet, and using 3.14 as an approximation for
, we can set up the equation as 3.14 = 3.14r^2. This allows us to solve for the radius(r).

First, divide both sides by 3.14 to isolate r^2: r^2 = 3.14 / 3.14 = 1. Then take the square root of both sides to get the radius: r =
1 = 1 foot. Now that we have the radius, we can calculate the circumference using the formula C = 2
, substituting 3.14 for
, and the radius we just found: C = 2 * 3.14 * 1 = 6.28 feet.

After following these steps, we determine that the circumference of the serving tray is 6.28 feet. Rounded to the nearest hundredth, the circumference is 6.28 feet.

Equation:

37.29 = 34.85 + 34.85(x)

Solving:

37.29 = 34.85 + 34.85x

2.44 = 34.85x

x = 0.07

The approximate sales tax rate is 7%.

Hope this helps!! :)

Answer:

im pretty sure its 0.07

Step-by-step explanation: