make a table of values then graph the following quadratic functions include 5 points

Answer:

x =  − 4  ±  √ 10,

Step-by-step explanation:

2(x + 4)² = 20

=> 2(x + 4)  (x + 4) = 20

=> 2x + 8 (x + 4) = 20

=> 2x² + 8x + 8x + 32 = 20

=> 2x² + 16x + 32 = 20

=> 2x² + 16x + 12 = 0

=> Now solve using the quadratic formula:

x =  − 4  ±  √ 10,

Radical form: − 4  ±  √ 10,

Decimal form: -0.84, -7.16

Hope this helps!

The value of the distance across the sea is 302 feet

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion.

Triangle PRE and triangle POC are similar triangles based on the angle - angle similarity. Hence:

PR / PO = RE/OC

substituting:

x/ (x + 135) = 185 / 335

335x = 185x + 45225

150x = 45225

x = 302 feet

The value of PR is 302 feet

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Answer:

Step-by-step explanation:

(-2 - 4)/(-1 + 3)= -6/2 = -3

y - 4 = -3(x + 3)

y - 4 = -3x - 9

y = -3x - 5

Option 1

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

The measure of other two sides of triangle is12cm and 17cm.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane. In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

If all of geometry is the Euclidean plane, then all triangles are enclosed in a single plane, however in higher-dimensional Euclidean spaces, this is no longer the case. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

here it is given in the question

the base of the triangle is 10cm.

then the value of other two side is 12cm and 17cm.

Hence, The measure of other two sides of triangle is12cm and 17cm.

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Answer: $46.08

Step-by-step explanation:

Find the surface Area of the box

the bases are 12*12= 144 times 2 bases 144*2= 288

The area of each side is 12*18=216 times 4 sides 216*4=864

add the totals together to find the total surface area 288+864=1152

total surface area is 1152 inches. Multiply by the cost per square inch

1152*.04= 46.08

Answer:

y = 2x

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Find slope m

2x - y = -4

-y = -2x - 4

y = 2x + 4

Since the 2 lines are parallel, they have the same slope.

Step 2: Define variables

Slope m = 2

Origin (x-int and y-int) (0, 0)

Step 3: Write parallel linear equation

y = 2x + 0

y = 2x

50000 tens

5000hundreds

How?

50000 tens:-

\(\\ \sf\longmapsto 50000(10)=500000\)

5000hundreds

\(\\ \sf\longmapsto 5000(100)=500000\)

The number 500,000 can be composed of in 50,000 tens and 5,000 hundred option (B) 50,000 tens and option (C) 5,000 hundreds are correct.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that a number that is:

= 500, 000

In the above number there is five zeroes

As we know,

Tens = 10 (one zero)

Hundreds = 100 (two zero)

We can write the above number as follows:

500,000 = 50,000x10 = 5,000 tens

500,000 = 5,000x100 = 5,000 tens

The number 500,000 can be composed of:

Where tens mean 10 and hundreds mean 100.

Thus, the number 500,000 can be composed of in 50,000 tens and 5,000 hundred option (B) 50,000 tens and option (C) 5,000 hundreds are correct.

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The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)

Divide both sides by 433.4:

\(e^{(0.032t)} = 1.836\)

Take the natural logarithm of both sides:

\(ln(e^{(0.032t)}) = ln(1.836)\)

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

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The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

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Answer:

700,000

Step-by-step explanation:

55,325 is closer to 100,000 than it is to 0, so the hundred-thousands place would round up.

Answer:

655,325

Step-by-step explanation:

Im pretty sure it would just stay the same because 3 is not enough to bring the 5 up to 6.

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

We know that, the standard form of equation of a circle is expressed as:

(x-a)^2 + (y-b)^2 = b=r^2

where;

(a, b) is the center of the circle

r is the radius of the circle

From given information,

diameter = 12 units

radius = 12/2

           = 6 units

It is given that, the center lies on the y-axis, the center will be at (0, 3)

Substituting above values in the formula,

(x-0)^2 + (y-3)^2 = 6^2

x²+ (y-3)² = 36

Therefore, an equation that represent circle that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y - 3)² = 36

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The distance David hiked can be determined as,

Thus, option (c) is the correct solution.

ln(2e/x)

ln2+ ln e -ln x

ln 2 + 1 - ln x

OPTION D is the correct answer

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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The order of the given fractions will be 5/3>3/2>5/6.

What exactly is a fraction?

A fraction is a mathematical term that represents a portion or part of a whole. It represents the equal parts of the whole. A fraction has two components: the numerator and the denominator. The top number is referred to as the numerator, while the bottom number is referred to as the denominator. The denominator describes the total number of equal parts in a whole, whereas the numerator defines the number of equal parts taken.

5/10, for example, is a fraction.

In this case, 5 is the numerator and 10 is the denominator.

Now,

Given fractions are 5/6 ,5/3,  3/2

lets make the denominator same

Divide and multiply fraction 2 and 3 by 2 and 3 respectively

then fractions are 5/6, 10/6, 9/6

so, the order will be 10/6>9/6>5/6 i.e. 5/3>3/2>5/6

hence,

           The order of the given  fractions will be 5/3>3/2>5/6.

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Answer: 8

Step-by-step explanation:

The time taken where there is 220 grams of the element remaining should be considered as the 5 minutes.

Since An element with a mass of 650 grams decays by 13.2% per minute.  and there is 220 grams of the element remaining.

So, the mass decays be

= 650 - 220

= 430

Now the total percentage be like

\(= 430 \div 650\)

= 66.15%

Now the time taken should be

= \(66.15\div 13.2\)

= 5 minutes

The time taken where there is 220 grams of the element remaining should be considered as the 5 minutes.

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Answer:

4

Step-by-step explanation:

First off, \(\frac{2}{3}\) can be changed to \(\frac{4}{6}\) and still be equal to \(\frac{2}{3}\).

Lastly, you can find out how many can fit,

4  \(\frac{1}{6}\) yard stripes can fit

An observation of a blue automobile occurs at 20.8% of the relative frequency.

The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency.

Divide each frequency by the overall sample size, in this example 20 students, to determine the relative frequencies.

Example: Out of a total of 12 games played, your team has won 9 of them, making its winning percentage 9 percent. 9/12, or 75%, is the relative frequency of winning.

So, we have:

RF(A) = f(A) / ∑f

Where f(A) is the frequency of event A and ∑f is the total frequency.

(Refer to the table attached below)

Total car = 251 + 198 + 195 + 293 = 937

The relative frequency of blue cars is as follows:

RF(blue) = 195 / 937 = 0.208 = 20.8%

Therefore, an observation of a blue automobile occurs at 20.8% of the relative frequency.

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Complete question:

Using the following table, what is the percent of the relative frequency of a Blue car being observed? Car Color Frequency Relative FrequencyBlack 251 0.251Red 198 0.198Blue 203 0.203Silver 293 0.293A. 20.3%B. 0.002%C. 23.625%D. 2.03%

Answer:

  y = 9

Step-by-step explanation:

Both points are on the same horizontal line:

  y = 9

_____

The first step in problem solving is to look at the information you are given. If you want to skip that step, and go straight to the procedure for finding the equation of a line through two point, here it is:

The slope is given by ...

  m = (y2 -y1)/(x2 -x1)

  m = (9 -9)/(7 -5) = 0/2 = 0 . . . . . . . tells you the line is horizontal

The y-intercept is given by ...

  b = y1 -m·x1

  b = 9 -0·5 = 9

Then the equation of the line is ...

  y = mx +b

  y = 0·x +9

Simplifying gives ...

  y = 9

__

Additional comment

The equation for a horizontal line is y = constant.

The equation for a vertical line is x = constant. A vertical line will not have a unique y-intercept. It will be the entire y-axis if it is x=0.

Answer:

9 hours.

Step-by-step explanation:

31 + 5.9*t < 84.10.

To solve it, collect the constant terms on the right side:

5.9*t < 84.10 - 31 = 53.10,

Hence, t < 53.10%2F5.9 = 9 hours.

SOLUTION

The given sequence is

From the sequence it follows

The formula for sum of an arithmetic sequence

Since the number of terms is not given then

Using the nth term formula

Substitute

Into the nth term formula

Therefore the sum is

Therefore the solution is:

The rate of change of the cost in dollars with respect to the number of t-shirts printed is $0.75 per shirt.

An equation is an expression that shows the relationship between two or more numbers and variables.

A linear function is in the form:

y = mx + b

Where m is the rate of  change and b is the initial value of y.

Given that the cost f(x) in dollars for printing x, t-shirts is given by:

f(x) = 100 + 0.75(x - 50)

f(x) = 0.75x + 62.5

Comparing with linear function, the rate of change is 0.75

The rate of change of the cost in dollars with respect to the number of t-shirts printed is $0.75 per shirt.

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Answer:

\(\frac{-4}{3}\)

Step-by-step explanation:

a rational number is expressed as

\(\frac{a}{b}\) where a and b are integers , then

- 1 \(\frac{1}{3}\) = \(\frac{-4}{3}\)

Answer:

the surface area S of the red solid is 90m^2

Step-by-step explanation:

The computation of the surface area of the red solid is shown below:

First find the scale factor i.e.

= 6 ÷ 4

= 1.5

Now the surface area of the red solid is

= 40 × 1.5 × 1.5

= 90m^2

Hence, the surface area S of the red solid is 90m^2

The same would be considered

Answer:

(-3,5)

Step-by-step explanation:

notice how nice the equation is set up,

its in vertex form

basically set up like this, a(x-h)+k,  where the vertex = (h,k) or in other words, the x value is the opposite value than the one inside the parenthesis () and the y value is the same as the value outside of the parenthesis

in this equation a =-1 h=-3 and k=5

just putting a negative sign instead of -1(x+3)^2 +5 is way nicer, so that's why the equation is built like that

lmk if u got ?s :>

Answer:

To find cosθ, use the formula for the area of a triangle i.e. AREA=1/2 x a x b x sinC.=> For this case: 15= 1/2 x 10 x 5 x sinC to find sinC.=> SinC = 3/5 thus, Arcsin(3/5)=+- 4/5 or +-0.8

To find the exact length of BC, use the cosine rule.=> c(sq)=a(sq)+b(sq)-2abCosC=> c(sq)=10(sq)+5(sq)-2(10)(5)(+-4/5)=> c(sq)= Square root of 205