Solve the following quadratic equation using the quadratic formula. Separate multiple answers with a comma if necessary.

y2+7y−2=0

6x8 is 48. You can't simplify 48/5, so that's your answer. If you wanted to create a mixed number, you could write 9 3/5

Answer:

See the explanation below

Answer:

im pretty sure it is 4/9

Step-by-step explanation:

From the question, we are to determine the probability of selecting two cards with D and D

From the formula for probability, we have that

P(D) = Number of favorable outcomes to D / Total number of possible outcomes

From the given information,

Number of favorable outcomes to D = 2

Number of possible outcomes = 3

Thus,

P(D) = 2/3

Then,

The probability of selecting two cards that have D and D with replacement is

P(D, D) = P(D) × P(D)

P(D, D) = 2/3 × 2/3

P(D, D) = 4/9

Hence, the probability is 4/9.

Answer:

Step-by-step explanation:

To find the total distance traveled by the hikers to get home, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the straight line distance) is equal to the sum of the squares of the lengths of the other two sides.

Since the hikers traveled 3 km north and 4 km east, we can consider this as the sides of a right-angled triangle, with the hypotenuse being the straight line distance traveled to get home. So, the square of the distance traveled to get home is equal to the sum of the squares of the sides, i.e., 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of 25 gives us 5 km, so the distance traveled by the hikers to get home is 5 km.

The required scale factor for the first rectangle is 5.

What is a scale factor?

In mathematics, a scale factor is a numerical factor that describes the relationship between two similar shapes. It is the ratio of the length of a side or the measure of any other corresponding linear dimension of one shape to the length or corresponding dimension of another similar shape.

Given that,

A rectangle with a short side of 2.5,

And an arrow points to a smaller rectangle with a short side of 0.5

We have to find,

The scale factor was applied to the first rectangle.

According to the question,

The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

Then,

Scale factor = Dimensions of the short side ÷ Dimensions of the small rectangle with the same side.

Scale factor = 2.5/0.5

Scale factor = 5

Hence, The required scale factor for the first rectangle is 5.

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The input is 8, the output of the function f(x) would be -5.

What is the function?

Function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet

To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:

f(x) = 8/x - 6

f(8) = 8/8 - 6

f(8) = 1 - 6

f(8) = -5

Hence, if the input is 8, the output of the function f(x) would be -5.

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The surface area of cube will be 600 square units.

What exactly is a cube?

A Cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges in geometry. It is also described as a regular hexahedron. You've probably seen the 3 3 Rubik's cube, which is the most prevalent example in real life and is useful for improving brain capacity. Similarly, you will come across several real-life instances, such as 6 sided dice, etc. Solid geometry is concerned with three-dimensional objects and figures with surface areas and volumes. Other solid forms include cuboid, cylinder, cone, and sphere.

Surface area of cube=6*side²

Volume of cube=side³

Now,

As Side of cube=10 units

and Surface area of cube=6*side²

=6*10*10

=600 square units.

Hence,

           The surface area of cube will be 600 square units.

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Answer:

  (4, 0)

Step-by-step explanation:

You want the image point coordinates of (1, 0) dilated by a factor of 4 centered at the origin.

When the dilation is centered at the origin, all coordinate values are multiplied by the scale factor.

  (1, 0) ⇒ 4(1, 0) = (4, 0)

The image of the point is (4, 0).

Answer:

4,233,000

Step-by-step explanation:

4,232,000                 4,4232,852                  4,233,000

4,4232,852 is between 4,232,000 and 4,233,000.  It is closer to 4,233,000.

The rule is to look a the digit in the hundreds' place.  That number is 8.  If the digit in the hundreds' place is 5 or larger, you round up.

Answer:

12th term = -61

Step-by-step explanation:

Given sequence,

→ 5, -1, -7, ...

Now we have to,

→ Find the 12th term of the sequence.

The common difference is,

→ d = a2 - a1

→ d = -1 - 5

→ [ d = -6 ]

Formula we use,

→ an = a1 + (n - 1)d

Then value of 12th term will be,

→ an = a1 + (n - 1)d

→ a12 = 5 + (12 - 1) × (-6)

→ a12 = 5 + 11 × (-6)

→ a12 = 5 - 66

→ [ a12 = -61 ]

Therefore, the 12th term is -61.

well, let's take a looksie at both

[tex]~~~~~~ \stackrel{\textit{\LARGE Henry}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (5000)(0.042)(4) \implies I = 840 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\LARGE Ingrid}}{\textit{Simple Interest Earned}}[/tex]

[tex]I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.039)(6) \implies I = 1170 \\\\[-0.35em] ~\dotfill\\\\ 1170~~ - ~~840\implies \text{\LARGE 330}[/tex]

The graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and  a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x). Where it equals zero is where the quadratic equation finds its solutions. They are also known as the equation's roots.

Assuming the question is to graph the quadratic function y = 6x².

The x-intercept can be found by substituting y = 0

0 = 6x²

x = 0

x-intercept = (0,0)

y-intercept can be found by substituting x=0

y = 6 * 0

y = 0

y-intercept = (0,0)

The given quadratic equation is the equation of an upward parabola with the vertex as (0,0).

The axis of symmetry is x = 0 i.e y-axis.

Hence the graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

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The proof of congruence by SAS, then 2 corresponding sides and the corresponding included angles of both triangles are equal.

Angles who are of same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of same measure, then

[tex]m\angle A = m\angle B[/tex]is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

The SAS postulate , Two sides and the included angle of one triangle are identical to the corresponding two sides and the included angle of another triangle.

In the triangle, the angles mCAD and mACB are congruent.

m∠CAD ≅ m∠ACB

Since m∠CAD and m∠ACB are congruent, AD and BC must also be congruent.

As a result, the SAS Congruence postulate is proven.

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Mr. Kazoo needs to buy 6 boards to complete his fencing as he can not buy exactly 5.71 boards.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables.

We can form numerical expressions from statements.

Given, Mr. Kazoo is planning to build a fence.

The gate is 40 inches wide.

Therefore, He needs to buy (40/7) = 5.71 boards.

But, He can not buy a board 0.71 part of the whole part, So he needs to buy 6 boards to complete his fencing.

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Answer:

option

Step-by-step explanation:

f(x)=-3x²-4x+15

if (-3,-2) is substitute

x=-3 x=-2 is substitute in above given equation we get real zero.

Answer:

Step-by-step explanation:

18-5=13

18-9=9

Answer:

x = -5

Step-by-step explanation:

Since both horizontal lines are parallel, the marked angles are corresponding angles and are congruent. This, we can set them equal to each other:

47 = 10x + 97

Next, isolate “x” to find the value of “x”:

47 - 97 = 10x

-50 = 10x

-5 = x

Answer: a) Mean and standard deviation of the sampling distribution:

The mean of the sampling distribution, also known as the expected value or the population mean, is equal to the proportion of U.S. residents who receive a jury summons each year, which is 15%. So, the mean of the sampling distribution is:

µ = 0.15

The standard deviation of the sampling distribution, also known as the standard error, can be calculated using the formula:

σ = √(p(1 - p) / n)

where p is the population proportion of U.S. residents who receive a jury summons each year (0.15), and n is the sample size (500).

σ = √(0.15 * (1 - 0.15) / 500)

σ ≈ 0.03

So, the standard deviation of the sampling distribution is approximately equal to 0.03.

b) Interpretation of the standard deviation:

The standard deviation measures the spread of the sampling distribution, or how much the sample proportions deviate from the population proportion. A smaller standard deviation indicates that the sample proportions are more likely to be close to the population proportion, while a larger standard deviation indicates that the sample proportions are more likely to be further from the population proportion.

In this case, the standard deviation of 0.03 indicates that the sample proportions are expected to be within 0.03 of the population proportion (0.15) about 68% of the time.

c) Justification for the approximate normality of the sampling distribution:

According to the central limit theorem, the distribution of the sample proportions will be approximately normal as long as the sample size is large enough. In this case, with a sample size of 500, we can assume that the sampling distribution is approximately normal.

Step-by-step explanation:

The parameters that can help to raise the living standard are mentioned below.

Living standard is defined as the quality of housing, material comfort, and wealth experienced by an individual or group.

Given is that the standard of living is too low for many individuals in the united states.

The government can focus on the following factors -

Therefore, the parameters that can help to raise the living standard are mentioned above.

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The constant terms for the given expression are -7 and 2 and the variable terms for the given expression are  15 and 3a² respectively.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 15a-7+ 3a²+2.

a) A constant term of an expression is a term that does not change its value.

So the constant terms are -7 and 2 as their value never changes in the expression.

b) The value of x changes in the expression because its value can change over time. So the terms containing x are variable terms.

In the given expression, the variable terms are 15a and 3a².

Therefore the constant and variable terms are found for the given expression.

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Answer:

=58%

Step-by-step explanation:

If rate of 5.8% = 1 day

than ? = 10 days

therefore 10/1 × 5.8%

= 10 × 5.8

= 58%

To the nearest whole number

= 58%

Answer:

Step-by-step explanation:

To factorise the expression, we can use the factor theorem which states that if a polynomial p(x) has a factor (x - r), then p(r) = 0.

We can use this theorem to find the factors of the polynomial expression:

(a - 2b)^3 + (2a - b)^3

We can write (a - 2b)^3 as (a - 2b)(a^2 - 4ab + 4b^2). Using the factor theorem, we see that:

(a - 2b)(a^2 - 4ab + 4b^2) = 0 when a = 2b

Similarly, we can write (2a - b)^3 as (2a - b)(4a^2 - 4ab + b^2). Using the factor theorem, we see that:

(2a - b)(4a^2 - 4ab + b^2) = 0 when a = b/2

Now we have two equations: a = 2b and a = b/2, which we can use to solve for a and b in terms of each other. We see that:

a = 2b = b/2

Multiplying both sides by 2, we get:

2a = b

We can substitute this back into the original expression:

(a - 2b)^3 + (2a - b)^3 = (a - 2(2a))^3 + (2a - (2a))^3 = (-3a)^3 + (0)^3 = -27a^3

So the factorised form of the expression is:

(a - 2b)^3 + (2a - b)^3 = -27a^3.

Work Shown:

Use the sum of cubes factoring rule

x^3 + y^3 = (x+y)(x^2 - xy + y^2)

In this case,

So,

x^3 + y^3 = (x+y)(x^2 - xy + y^2)

(a-2b)^3 + (2a-b)^3 = (a-2b+2a-b)((a-2b)^2 - (a-2b)(2a-b) + (2a-b)^2)

(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-ab-4ab+2b^2) + (4a^2-4ab+b^2))

(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-5ab+2b^2) + (4a^2-4ab+b^2))

(a-2b)^3 + (2a-b)^3 = (3a-3b)(a^2-4ab+4b^2 - 2a^2+5ab-2b^2 + 4a^2-4ab+b^2)

(a-2b)^3 + (2a-b)^3 = (3a-3b)(3a^2-3ab+3b^2)

(a-2b)^3 + (2a-b)^3 = 3*3(a-b)(a^2-ab+b^2)

(a-2b)^3 + (2a-b)^3 = 9(a-b)(a^2-ab+b^2)

The answer has been fully confirmed with WolframAlpha.

Answer: x=35

Step-by-step explanation:

How to determine this

Using product rule,

[tex]\frac{d}{dx}[/tex](u.v) = du/dx.v + dv/dx.u

where u = x-5

v = x+7

Using the rule,

d/dx = 1(3x + 7) + 3(x - 5)

d/dx = 3x +7 +3x - 15

d/dx = 6x - 8

Using the expanding, then differentiating,

d/dx = (x - 5)(3x + 7)

open bracket,

d/dx = 3x^2 + 7x - 15x - 35

Differentiating it,

d/dx = 6x + 7 - 15

d/dx = 6x - 8

Therefore, using different rule,it has been verified that both methods gave the same results.

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Guido can choose his Jolly Rancher in 78,125 different ways over the course of a week.

Guido chooses one sweet per day from a selection of five options; there are a total of five possible selections for a single day. Since there are seven days in a week, the sum of the ways Guido can choose candy over the course of a week equals the sum of the methods for each day.

Using the multiplication principle of counting

Total number of ways = 5 x 5 x 5 x 5 x 5 x 5 x 5

Simplifying this expression gives:

Total number of ways = 5^7

Using a calculator or by hand, we can compute:

Total number of ways = 78,125

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The volume of the solid is -5.54 cubic units.

The region is bounded by the parabola x = 1 + (y-2)^2 and the line x = 2. To use the method of cylindrical shells, we imagine rotating this region around the x-axis, which gives us a solid shape.

The shell has thickness Δx and height y, and is located at a distance x from the y-axis. To find the volume of the solid, we'll add up the volumes of all the cylindrical shells.

The volume of a cylindrical shell is given by the formula V = 2πrhΔx, where r is the radius of the shell and h is its height. In this case, the radius of the shell is x - 2 (the distance from the y-axis to the edge of the region), and the height is y. So we have:

V = 2π(x - 2)yΔx

To find the total volume of the solid, we integrate this expression over the range of x values that corresponds to the region we're interested in. The region is bounded by x = 1 + (y-2)^2 and x = 2, so we integrate with respect to x from x = 1 + (y-2)^2 to x = 2:

V = ∫[1+(y-2)²]^2 2π(x - 2)y dx

To evaluate this integral, we can use the substitution u = y - 2, which gives us:

V = ∫1^0 2π(u^2 + 3) (1 + u)^2 du

This integral can be evaluated using the power rule and the substitution v = 1 + u:

V = 2π/5 [(1 + u)^5 - (1 + u)^3] from 1 to 0

V = 2π/5 [1 - 32/5]

V = 2π/5 ( -22/5)

V = - 8.8π/5

So the volume of the solid is approximately -5.54 cubic units. Note that the negative sign means that the solid is oriented in the opposite direction from what we might expect - in other words, it has a hole in it.

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a) Standard factored form is 2^4 × 3^2 × 5.

b) Standard factored form is 2^18 × 5^8.

c) There are 6 zeros at the end of (20!)^2

If n is an integer and n > 1, then  factorial of n is the product of n and every other positive integer that is less than n.

We have to find the standard factor form of 6!

6! = 6 × 5 × 4 × 3 × 2 × 1

Then, we can simplify by grouping the factors of 6! into pairs that multiply to 10:

6! = 2 × 3 × 2 × 2 × 5 × 1 × 3 × 2 × 1 = 2^4 × 3^2 × 5

Therefore, 6! in standard factored form is 2^4 × 3^2 × 5.

Part b

To write 20! in standard factored form, we start with 20 and multiply by every positive integer less than 20:

20! = 20 × 19 × 18 × ... × 3 × 2 × 1

To simplify this expression, we can group the factors into pairs that multiply to 10

20! = (2 × 10) × (2 × 9) × (2 × 8) × ... × (2 × 1) × (5 × 3) × (5 × 2) × 5

We can then combine the factors of 2 and the factors of 5:

20! = 2^18 × 5^8

Therefore, 20! in standard factored form is 2^18 × 5^8.

Part C

The number of zeros at the end of (20!)^2 in decimal form is equal to the number of factors of 10 in (20!)^2. Since 10 = 2 × 5, we need to count the number of factors of 2 and 5 in (20!)^2.

The number of factors of 2 in (20!)^2 is the number of even integers less than or equal to 20, which is 10.

The number of factors of 5 in (20!)^2 is the number of multiples of 5 less than or equal to 20, which is

5, 10, 15, and 20.

However, since we are squaring (20!), we also need to count the number of factors of 25, which is 2:

5^2 and 10^2.

There are 6 zeros at the end of (20!)^2 when it is written in decimal form.

Therefore, each part has been solved

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Answer:

------------------------------

Full surface area is the sum of areas of 4 triangles and the square base:

Find the height h of the pyramid, using slant height and the side of the base and Pythagorean:

Find the volume:

Answer: 753.98m³

Formula:V=πr2h3=π·62·203≈753.98224m³