Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then vertex is minimum

• If a < 0 then vertex is maximum

Given

y = x² + 6x + 10

(a)

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 6x

y = x² + 2(3)x + 9 - 9 + 10

y = (x + 3)² + 1 ← in vertex form

(b)

Since a = 1 > 0 then vertex is a minimum

(c)

(h, k ) = (- 3, 1 ) ← coordinates of vertex

The expression that correctly shows the amount remaining in the piggy bank will be; 22d + 7n + 15q - (8d + 3n) = $4.85

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels.

LEt consider

→ dimes = d

→ nickels = n

→ quarters = q

Now the expression will be;

22 dimes + 7 nickels + 15 quarters - 8 dimes - 3 nickels

22d + 7n + 15q - 8d - 3n = $4.85

22d + 7n + 15q - (8d + 3n) = $4.85

To know more about an expression follow;

brainly.com/question/19876186

#SPJ1

Answer:

It is

Step-by-step explanation:

Parralel Lines. Since they have the same opposite angles, they will never touch, being parallel

Answer:

  2.  mean: 53.75; median: 56.5; mode: 65; median is best

  4.  mean: 24.4; median: 20.45; no mode; median is best

Step-by-step explanation:

You want the mean, median, mode, and best representation of the data for data sets ...

  2. — 55,65,49,22,56,65,61,57

  4. — 20.1, 13.4, 9.8, 21.3, 20.8, 19.1, 68.1, 22.6

The mean of the data is the sum of the data values, divided by the number of data values.

The median data value is the middle of the sorted list, or the average of the two middle values. Here, there are an even number of data values in each list, so the median is the average of the middle two.

The mode of the data set is the value that is repeated most often. A data set may have multiple modes. Here, where one of the datasets has no repeated values, we describe it as having "no mode."

The first attachment shows the descriptive statistics are ...

The data is skewed to the left, with the value 22 being an outlier. This value reduces the mean. The mode is the maximum value in the data set, so it does not fairly represent the data, either.

The median best represents the data.

The second attachment shows the descriptive statistics are ...

The data is skewed to the right, with the value 68.1 being an outlier. This tends to raise the mean above what it would otherwise be. There is no mode.

The median is best represents the data.

<95141404393>

Answer:

He scored an average of 4.8 points per minute.

a) The flowchart for the congruency of triangles is given below.

b) The triangles are congruent as DQ ≅ XZ, PQ ≅ XY, and ∠PQD ≅ ∠ZXY.

What is congruency?

The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.

In the given diagram, it can be seen that -

Line segment DQ = Line segment XZ.

Similarly, Line segment PQ = Line segment XY.

Since, the two sides of the triangle are equal, hence the third side must also be equal.

Line segment PD = Line segment ZY.

Also, in the diagram it can be seen that ∠PQD ≅ ∠ZXY.

Therefore, the triangles PDQ and ZXY are equal and congruent.

The flowchart for the same is given below.

To learn more about congruency from the given link

https://brainly.com/question/2938476

#SPJ1

Answer:

-4.3

Step-by-step explanation:

It is asking for the temperature at midnight so to find out what it is. We simply subtract the starting temperature of 11.4f from 15.7 degrees

( 11.4 - 15.7 ). That would leave us with -4.3f at night.

Answer:the blue one

Step-by-step explanation:

Answer:

triangle isn't right angled

Step-by-step explanation:

For a right tangled triangle :

Length of the longest side, hypotenus is given by :

Hypotenus = √(opposite² + adjacent ²)

From.the question :

Hypotenus = 11

Opposite and adjacent = 5 units and 6 units

Let's test :

Hypotenus = √(5² + 6²)

Hypotenus = √(25 + 36)

Hypotenus = √61 units

Hypotenus = 7.8

Hypotenus for a right angled triangle = 7. 8 units and not 11.

Hence, triangle isn't right angled

Answer:

(0,5),(2,6) these are the coordinates of the line.

Step-by-step explanation:

I hope this helps.

Answer:

Option A

Step-by-step explanation:

Min: 72

Q1: 83

Median: 89

Q3: 92

maximum: 94

Therefore , the solution of the given problem of median comes out to be

a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.

Specify median.

The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.

Here,

Given : mean age is 36.

Standard deviation = 3.5

a) z - score = (34 - 28.3)/3.8 = 1.50

b) Interpretation:

An age of 34 is about 1.50 standard deviations above the mean.

c) Option B is correct.

Therefore , the solution of the given problem of median comes out to be

a)z-score = 1.50 b)age 34 has SD=1.5 and C. option B correct.

To know more about median , visit

brainly.com/question/28060453

#SPJ4

The unit rate of change of the proportional relationship is given as follows:

2.25.

The graph of the proportional relationship is given by the image presented at the end of the answer.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

The constant k, representing the unit rate, is obtained by the division of the output of the input from the table, hence:

k = 4.5/2 = 6.73/3 = 9/4 = 2.25.

Meaning that the function is defined as follows:

y = 2.25x.

The function is graphed for a domain of x ≥ 0, as the number of cups of sugar must be a countable, non-negative amount.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

they can ship out 271 boxes each day. 3,258/12 is 271.5 but the 0.5 doesn't matter bc that'd be half a box. a total of 2 crates can be filled fully with another crate that isn't completely full (in total 3 crates max)

Answer:

B i think I'm kinda sure tho

b

Answer:

9.06 units (3 s.f.)

Step-by-step explanation:

[tex]\boxed{distance \: between \: 2 \: points = \sqrt{(y1 - y2)^{2} + {(x1 - x2)}^{2} } }[/tex]

☆ (x₁, y₁) is the 1st coordinate and (x₂, y₂) is the 2nd coordinate.

Distance between (-1, -6) and (8, -7)

[tex] = \sqrt{[- 7 - ( - 6)]^{2} + [8 - ( - 1)]^{2} } [/tex]

[tex] = \sqrt{ {( - 7 + 6)}^{2} + (8 + 1) {}^{2} } [/tex]

[tex] = \sqrt{( - 1)^{2} + {9}^{2} } [/tex]

[tex] = \sqrt{1 + 81} [/tex]

[tex] = \sqrt{82} [/tex]

= 9.06 units (3 s.f.)

Answer:

No.

Step-by-step explanation:

No because the dot is not in the area where BOTH red AND blue cover. It is only in the red area, not in BOTH red AND blue.

If in a survey of 1,500 people who owned a certain type of​ car, 750 said they would buy that type of car again, the percent of people surveyed who were satisfied with the car is 50%.

To find the percent of people surveyed who were satisfied with the car, we can use the following formula:

percent satisfied = (number of satisfied people / total number of people surveyed) x 100

In this case, the number of satisfied people is 750 and the total number of people surveyed is 1,500. So we have:

percent satisfied = (750 / 1,500) x 100 = 0.5 x 100 = 50%

So, 50% of the people surveyed were satisfied with the car.

To know more on percentage

https://brainly.com/question/19968524

#SPJ4

Answer:

2 blocks would be the correct answer

Answer: C) The mean will increase more than the median, but both will increase.

Step-by-step explanation:

I got it right already! :)

The solution is, The mean will increase more than the median, but both will increase.

[third option listed]

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

here, we have,

the median of a data set is the number in the middle [when listed from lowest to highest in value]

1 2 3 4 5 6 7 8 9 10 11 12 13

is the current median

let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)

1 2 3 4 5 6 7 8 9 10 11 12 12 13

[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]

so, 7.5 is the current median

(this is an increase of 0.5)

the mean of a data set is what we commonly refer to as the "average"

[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]

1 2 3 4 5 6 7 8 9 10 11 12 13

mean of original data set:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]

_______________________________________

                                   13

[91 ÷ 13 = 7]

because our number is greater than our original mean [12 > 7], we know that the mean must increase:

[91 + 12 = 103]

[103 ÷ 14 ≈ 9.36]

[we had an increase of 2.36]

so, median increased by 0.5, mean increased by 2.36

so, both values increased, whilst the mean increased by more than the median [as to be expected]

so, we get,

"The mean will increase more than the median, but both will increase." [third option listed]

To learn more on median click:

brainly.com/question/20425811

#SPJ7

Step-by-step explanation:

0.40x = 35 ---> x = (35 /0.40) = 87.5

Answer:

what do you need there's no image or question

Answer:

answer is yes points thanks

Step-by-step explanation:

Answer:

Step-by-step explanation:

3n3

we have to combine like terms

n5-n2 is n3 (dividing exponents means subtracting)

this could be 1/3 n3 or 3 n3

Answer:

A.(-2,4) and (11,-7) ...

I hope I'm correct

Answer:

(x,y) = (7,2)

Step-by-step explanation:

Hope it helps

Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.

Here,

Given:

Mean = 2

Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.

We can determine that at least

100 (1-1k2)% = 100 (1-1/4)% = 75%

is within 2 standard deviations of the mean using Chebyshev's Rule with

k = 2.

The percentage times the sample size yields the equivalent number of households:

=> 75% x 40 = 30

Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

To know more about mean , visit

https://brainly.com/question/30112112

#SPJ1

The thickness of each cookie is 0.318 cm.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

We are given that;

Diameter=5cm

Volume= 100cm3

Now,

To find the thickness of each cookie, you need to follow these steps:

Plug in the values into the formula for volume and solve for height:

Volume = π × radius^2 × height

100 = π × 2.5^2 × height

100 = 19.635 × height

height = 100 / 19.635

height = 5.093 cm

Divide the height by the number of cookies to get the thickness of each cookie:

Thickness = height / number of cookies

Thickness = 5.093 / 16

Thickness = 0.318 cm

Therefore, by the volume of cylinder answer will be 0.318 cm.

Learn more about volume of cylinder here:

https://brainly.com/question/12763699

#SPJ2

Step-by-step explanation:

x= -1

y= 2

r = √(-1)²+2² =√1+4=√5

sin a = 2/√5

cos a = -1/√5

tan a = 2/-1= -2

sec a = √5/-1 =-√5

csc a = √5/2

cot a = -1/2

The amount he estimated (11 gallons). 11 - 8.16 = 0.21 gallons.

Estimation is the process of making an educated guess about the value of something, such as a quantity, cost, or other measurement, based on the available information. It's used in many fields, including mathematics, engineering, economics, business, and project management. Estimation is an important skill which can help people make decisions and solve problems quickly.

Mr. Langley was away from his estimation by 0.21 gallons of paint. This is calculated by subtracting the total amount of paint he actually used (7.5 + 0.66 = 8.16 gallons) from the amount he estimated (11 gallons). 11 - 8.16 = 0.21 gallons.

To learn more about estimation
https://brainly.com/question/28416295
#SPJ4