what is the vertex of the graph of the quadratic function f(x)= x^{2} + 6x + 10?

Answer:

Step-by-step explanation:

The direct distance there (without the island in the way) is found using the Pythagorean Theorem

c^2 = a^2 + b^2

a = 8.4

b = 11.5

c = ?

c^2 = 8.4^2 + 11.5^2              Square the length of the legs.

c^2 = 70.56 + 132.25            Combine  

c^2 = 202.81                          Take the square root.

c = 14.24

But the island is there. The distance travelled = 8.4 + 11.5 = 19.9 miles

So the additional distance = 19.9 - 14.24 = 5.66 miles.

Answer:

235

Step-by-step explanation:

325( Three digit number)

No zero

5-3=2

3+2+5=10

The house number if the house number is a three-digit number, it is a multiple of 5. There are no zeros in this number, is 235.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

A house number is a three-digit number.it is a multiple of 5,

The number in the hundreds place is two less than the number in the one's place,

The sum of the digits is 10,

Write the equation as shown below,

x + y + z = 10

Here x is in one place y is in the tens place and z is in the hundred places,

The number will be = 100z + 10y + x

y = x - 2

As we know if the number is a multiple of 5 then its one's place is either 0 or 5 here no zeroes in the number,

x = 5,

y = 5 - 2 = 3

z = 10 - 3 - 5

z = 2

Thus, the number will be,

Room number = 100 × 2 + 10 × 3 + 5

Room number = 200 + 30 + 5

Room number = 235

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Answer:

$5

Step-by-step explanation:

20/4 = 5

Answer:

(1,3), (2,1

Step-by-step explanation:

Answer:

1. m = -3

2. m = 4

Step-by-step explanation:

1. m = -3

2. m = 4

slope intecept form is y = mx + b

Solution:

To classify the system of equations as no solutions, the lines must be parallel (Not intersect).

First, let's identify the equation forming the line.

We also know that the slope of the equation must be -1.5.

A) 2x + 3y = 0

B) 2x + 3y = 6

C) 2x - 3y = 9

D) y = 3x + 2

Option B is correct.

Answer:

Step-by-step explanation:

Kamille is wrong, because:

or

She needs about 8 inches ribbon not 60 inches

Answer:

480 Boy

Step-by-step explanation:

The ratio of Boys =  4x

The ratio of  Girls =  5x

The Number of Boys in the School = 4x + 5x = 1080

=         9x = 1080

=        x  = 1080/9

=         x  = 120

The ratio of Boys = 4x  = 4 x 120 = 480

The ratio of  Girls =  5x = 5 x 120 = 600

Hence, Number of Boys = 480

Ratio Boys to Girls = 480:600

[RevyBreeze]

Answer:

  cos(45°) = (√2)/2

Step-by-step explanation:

The cosine of 45° is the x-coordinate of the point on the unit circle where the line y=x intersects it. That is, it is the positive solution to the equation ...

  x^2 +x^2 = 1

  x^2 = 1/2 = 2/4 . . . . . collect terms, divide by 2, express the fraction with a square denominator

  x = √(2/4) . . . . . . take the square root

  x = (√2)/2 . . . . . simplify

The cosine of 45° is (√2)/2.

Answer:

11.7 - 12y

Step-by-step explanation:

1. Open parenthesis

3 - 4y - 8y + 8.7

2. Combine like terms

11.7 - 12y

The answer is 11.7 - 12y

Hope this helps :)

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Answer:

B) [tex]-38[/tex]

Step-by-step explanation:

[tex]\frac{4}{(-1.6+3.6)}+\frac{0.8(9+11)}{-0.4}\\\\=\frac{4}{2}+\frac{0.8(20)}{-0.4}\\\\=2+-2(20)\\\\=2-40\\\\=-38[/tex]

[tex]\bold{\huge{\blue{\underline{ Solution }}}}[/tex]

The given figure is composed of two figures triangle and circle. In which triangle is enclosed in the circle.

We know that,

Area of triangle

[tex]\bold{\red{ = }}{\bold{\red{\dfrac{1}{2}}}}{\bold{\red{\times{ Base }}}}{\bold{\red{\times{ height }}}}[/tex]

Here,

Subsitute the required values,

Area of the given triangle

[tex]\sf{ = }{\sf{\dfrac{1}{2}}}{\sf{\times{ 10 }}}{\sf{\times{ 5 }}}[/tex]

[tex]\sf{ = 5 }{\sf{\times{ 5}}}[/tex]

[tex]\bold{ = 25\: units }[/tex]

Thus, The area of triangle is 25 units

We have to find the area of the circle

We know that,

Area of circle

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

Subsitute the required values,

[tex]\sf{ = }{\sf{\pi{(5)^{2}}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{ 25}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{550}{7}}}[/tex]

[tex]\bold{ = 78.57\: units }[/tex]

Thus, The area of circle is 78.57 units

Area of shaded region

= Area of circle - Area of triangle

Subsitute the required values,

[tex]\sf{ = 78.57 - 25 }[/tex]

[tex]\bold{\green { = 53.57 \: units }}[/tex]

Hence, The area of shaded region is 53.57 units.

The area of the shaded figure is 13.375 square units.

The shaded region is a circle with a triangle inside of it removed.

To get the area, we need to get the area of the circle and remove the area of the triangle.

Remember that for a circle of radius R, the area:

A = 3.14*R^2

In this case, we can see that the diameter of the circle measures 5 units, then the radius (half of the diameter) measures 2.5 units.

A = 3.14*(2.5)^2 = 19.625 square units.

And a triangle of base B and height H has an area:

A' = B*H/2

In this case, the base of the triangle is equal to the diameter of the circle, and the height is equal to the radius of the circle, so we have:

B = 5 units.

H = 2.5 units.

Then:

A' =5*2.5/2 = 6.25 square units.

Then the shaded area is:

shaded area =  19.625 square units -  6.25 square units.

                     = 13.375 square units.

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Answer:

Direct Variation:

Inverse Variation:

1. The bank balance is inversely proportional to expenditures.

2. The number of family members (which not work) are inversely proportional to amount of saving.

3.The working days required to complete the work are inversely proportional to number of labors.

4. The velocity of body is inversely proportional to time.

5. The acceleration is inversely proportional to time.

6.  The acceleration of body is inversely proportional to mass of body.

7. The number of student fail in the class is inversely proportional to number of qualify teachers and hardworking.

8. The battery power is inversely proportional to time for which it used.

9. The ability of do work hard is inversely proportional to age of man after youngness to onward.

10.  The number of mistake in work is inversely proportional to practice.

Explanation:

Direct Variation: A relationship where one quantity is a constant multiplied by another quantity is called direct variation.

Inverse Variation: Inverse variation is defiend as the relationship between two variables in which the resultant product is a constant. If a is inversely proportional to b, the form of equation is a = k/b, where k is constant. Inverse variation is known as the opposite of direct variation. If there an increas ein one variable, the other variable decreases in proportion so that the resultant product remains unchanged.

I think 100 grams per box

Answer:

you must be so stiupid that you have to use answers ff a website to cheat for school

Step-by-step explanation:

Answer:

The choice B. 5°

Step-by-step explanation:

The angle in the figure is 90°

[tex]36 + (11x - 1) = 90 \\ 36 + 11x - 1 = 90 \\ 11x + 35 = 90 \\ 11x = 90 - 35 \\ 11x = 55 \\ \\ x = \frac{55}{11} \\ \\ x = 5[/tex]

Answer:

115.5

Step-by-step explanation:

comparing side lengths of 49 and 28:

49 ÷ 28 = 1.75, so to get from 28 to 49 multiply by 1.75

this is the same thing for side lengths 38.5 and 22 as

22 × 1.75 = 38.5

the scale factor of the first triangle (GHI) to the second triangle (JKL) is 1.75 which means multiply each side of the first triangle by 1.75

so to work out x:

16 × 1.75 = 28

perimeter of JKL (second triangle) - add up lengths of the sides:

28 + 38.5 + 49 = 115.5

Answer:

Step-by-step explanation:

to find the mean is another way of saying to find the average. To do this we add all the listed values(45,52,17,63,57,42,54,58) then divide them by how many values we are given which in this case is 7. so the mean would be 49. now to find the median we must first put the values in numeric order(17,42,45,52,54,57,58,63) then see the number in the middle or in cases or even number of values we find the two values in the middle of the set then we add them together and divide by two. which would be 53. now to find the mode we simply find the most reoccurring number in the set and seeing as there are no repeated values in this set there is no mode.

Answer: 25

Step-by-step explanation:

Finding the product of complex numbers is not different to finding the product of real numbers

(-3i+4) * (3i+4) = -9i^2 + 12i - 12i + 16 = 25

Answer:

25

Step-by-step explanation:

An easy way to multiply binomials is the FOIL(first, outer, inner, last) method. Multiply the first terms of each binomial, -3i×3i=-9i^2. Then do the outer terms, -3i×4=-12i. Then do the inner terms 4×3i=12i. Then do the last terms, 4×4=16. Lastly combine like terms, the -12i and 12 cancel out, and you're left with -9i^2+16. i^2=1, so then you get -9(-1)+16. -9×-1=9. 9+16=25

Answer:

Center: (2/3, 0) Radius: 6

Step-by-step explanation:

I used desmos(.com) to graph the equation.

Answer:

  4. 11/6, 121/36

  5. 5/8, 25/64

  6. 4/7, 16/49

  7. 14/9, 196/81

Step-by-step explanation:

The ratio of perimeters is the same as the ratio of corresponding legs:

  perimeter ratio = red leg/blue leg

The area ratio is the square of that:

  area ratio = (perimeter ratio)²

__

perimeter ratio = 11/6

area ratio = (11/6)² = 121/36

__

perimeter ratio = 5/8

area ratio = (5/8)² = 25/64

__

perimeter ratio = 4/7

area ratio = (4/7)² = 16/49

__

perimeter ratio = 14/9

area ratio = (14/9)² = 196/81

Using the percentage concept, it is found that the percentage of 6- to 11-year-olds who were obese was about 17.76% more than the percentage of two- to five-year-olds who were obese.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

Researching on the internet, we find that:

Hence:

[tex]P = \frac{17.9}{15.2} \times 100\% = 117.76\%[/tex]

117.76% - 100% = 17.76%.

Hence the percentage of 6- to 11-year-olds who were obese was about 17.76% more than the percentage of two- to five-year-olds who were obese.

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Answer: 25°

Step-by-step explanation: Notice that in this figure, we are given two triangles and to find the value of x, we first need to find the missing angle measure in the big triangle.

Since all the interior angles of a triangle add up to 180 degrees, we know that the missing angle of the big triangle is 180° - 94° - 41° or 45°.

Now we know all the angles of the big triangle and we know two of the angles of the smaller triangle, so we can find the value of x.

The missing angle of the smaller triangle will be 180° - 110 - 45° or 25°

So we know that the missing angle is 25°.

Answer:

Step-by-step explanation:

m=26 when u as u go as down as {{6-2} -13

Answer:

2

Step-by-step explanation:

By definition, the slope or gradient of a line describes its steepness, incline, or grade.

m = y2 - y1 / x2 - x1

Where

m — slope

If the 2 Points are Known:

Slope (m) = ΔY/ΔX

= 7-(-1) / 3-(-1)

= 8/4

= 2/1

= 2

θ = arctan (ΔY/ΔX)

= tan¯¹(8/4)

= 63.434948822922°

ΔX = 3 – (-1) = 4

ΔY = 7 – (-1) = 8

Distance (d) = √ΔX2 + ΔY2 = √80

= 8.9442719099992

Equation of the line:

y = 2x + 1

When x=0, y = 1

When y=0, x = -0.5

Answer:

x = ± √11 i

Step-by-step explanation:

x^2 + 5 + 6 = 0

subtract 6 and 5 from both sides

x^2 = -11

find the square root of both sides

x = ± √-11

x = ± √11 √-1

x = ± √11 i

Answer:

118

Step-by-step explanation:

LCM = 12×10 = 120

HCF = 12-10 = 2

Difference = 120-2 = 118

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