if a quadratic in x is greater than zero for all values of x, then can it have real roots?

Answer:

21

Explanation:

To solve this problem, you substitute in the 5 for the x creating this equation: f(5)=6+3(5).

f(5)=15+6

f(5)=21

Based on observation, in this polyhedron, there are a total of six vertices, nine edges, and five faces.

In geometry, this refers to the point where two line meet. In this case, the vertices are A, B, C, D, E, F for a total of six vertices.

This term refers to line segments, for example the line between B and C is an edge. Based on this, there are nine edges in this shape.

This refers to flat surfaces; in this, case the total of flat surfaces are five.

Learn more about geometry in: https://brainly.com/question/16836055

Step-by-step explanation:

could not find the formula ?

the volume is a cylinder is

ground area × height

the ground area is a circle, so we get

pi×r²×h

where r is the radius, h is the height.

therefore

pi×4.5²×2.9 = 184.4900286... ft³ ≈ 184.5 ft³

Answer:

The smaller number is 24

The larger number is 45

Step-by-step explanation:

smaller number  = x

Larger: 2x - 3

Smaller + larger = 69

x + 2x - 3 = 69                        Combine left

3x - 3 = 69                              add 3 to both sides

3x - 3+3 = 69+ 3                     Combine

3x = 72                                    Divide by 3

3x/3 = 72/3                        

x = 24

Larger number = 2*24 - 3

Larger number = 45

Correlation measures the relationship between variables

The true statements are:

For a correlation coefficient to be valid, the following, must be true:

Using the above highlights, the true statements are: (b) (c) and (e)

Read more about correlation coefficients at:

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Answer:

2/7

Step-by-step explanation:

Total no. of chocolates in the box =14

No. of dark Chocolates=4

No. of white chocolates=5

No. of milk chocolates=5

Probability of getting a white chocolate

= No. of possible outcomes /Total No. of outcomes

=5/14

Probability of getting a dark chocolate =4/14=2/7

Part A

Part B

Answer:

See below ↓↓

Step-by-step explanation:

Part A

Part B

Using it's concept, it is found that the probability that the coin shows tails and he rolls a 5 is of [tex]\frac{1}{12}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the coin has two outcomes, one of which is tails, while the number cube has six outcomes, one of which is five. Since the coin and the number cube are independent, we just multiply the probabilities, hence:

[tex]p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]

The probability that the coin shows tails and he rolls a 5 is of [tex]\frac{1}{12}[/tex].

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

-12g+32

Simplify and combine like terms.

Answer:

270

Step-by-step explanation:

90, 180, 270, and 360 are standard position because they hold a part of a 90 angle

Answer:

Step-by-step explanation:

Standard position means that you will move clockwise about the origin to create the angle.

Answer:

B

Step-by-step explanation:

Cut vertical but off vertcal axis.

A will produce a square and C and D will produce triangles.

If Carly's bedroom is 15.3ft long and 8.7 ft long then it is necessary to multiply them because you need to find the area of the room so 15.3*8.7= 133.11. We have to do the same for Carter's room so we multiply 14.4 and 9.6 to find the area of the room which is 138.24.

Now that we have both the areas we can compare which room is bigger. Carly's room is 133.11 ft in total and Carter's room is 138.24 ft in total. So it is clear that Carter's room is going to be more expensive to cover with carpet since Carter's room is bigger than Carly's.

Carly:-

Area:-

#Carter

Area:-

Carter's room is expensive

Answer:

gradient:  1/4; y-intercept:  3

Step-by-step explanation:

In math, 'gradient' is another word for slope.

Here we have y = (1/4)x + 3.  The coefficient of x is the slope or gradient:  1/4.  The y - intercept is 3:  (0, 3).

Answer:

Step-by-step explanation:

The equation is in y = mx + b form.

Here, m is the slope or gradient and b is the y-intercept.

[tex]y =\dfrac{1}{4}x+3\\\\\\Gradient =\dfrac{1}{4}[/tex]

y-intercept = 3

Using proportions, it is found that the total cost of three bottles of detergent is of $11.55.

A proportion is a fraction of a total amount.

A certain brand of laundry detergent is manufactured for $4.40 and then marked up 25% by the local store before selling, hence the price of each bottle is given by:

P = 4.40 x 1.25 = $5.50.

The store offers a 30% discount with the purchase of three or more bottles of the detergent, hence the total cost is given by:

T = (3 x 5.50) x 0.7 = $11.55.

More can be learned about proportions at https://brainly.com/question/24372153

24

[tex]Convert\ the\ unit\ for\ \frac{12in}{1ft}:\\ \downarrow\\ 24[/tex]

I hope this helps you

:)

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20953.80\\ P=\textit{original amount deposited}\dotfill & \$18000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6 \end{cases} \\\\\\ 20953.80=18000[1+(\frac{r}{100})(6)]\implies \cfrac{20953.80}{18000}=1+\cfrac{6r}{100}[/tex]

[tex]\cfrac{20953.80}{18000}=\cfrac{100+6r}{100}\implies \cfrac{2095380}{18000}=100+6r\implies \cfrac{11641}{100}=100+6r \\\\\\ \cfrac{11641}{100}-100=6r\implies \cfrac{1641}{100}=6r\implies \cfrac{1641}{600}=r \\\\\\ \cfrac{547}{200}=r\implies \stackrel{\%}{2.735} = r[/tex]

Answer: 90 dergrees

Step-by-step explanation: 90 dergrees

Answer:

5[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Glass: [tex]\frac{2}{3}[/tex] × 10

Hours: 1[tex]\frac{1}{4}[/tex]

1) Find the real value. He drinks [tex]\frac{20}{3}[/tex] glasses of water in 1[tex]\frac{1}{4}[/tex] hours. 1[tex]\frac{1}{4}[/tex] × [tex]60[/tex] gives us the minutes because 1 hour is 60 minutes.

Glass : Minutes:

[tex]\frac{20}{3}[/tex]      :    [tex]75[/tex]

2) Use ratio to find the value of one. 60 ÷ 75 gives us 0.8. Multiply [tex]\frac{20}{3}[/tex] by 0.8 or [tex]\frac{8}{10}[/tex].

Glass : Minutes

  [tex]\frac{16}{3}[/tex]        :  60

3) Convert [tex]\frac{16}{3}[/tex] into a mixed number.

= 5[tex]\frac{1}{3}[/tex]

Answer:

6/7

Step-by-step explanation:

3x2/7 in the same as 3/1x2/7, which is 6/7

(simply multiply the denominator and numerator of the fraction)

Answer: hii <3

Exact Form:

6/7

Decimal Form:

0.857142

Step-by-step explanation:

Simplify the expression.

Hopefully this helps you

- Matthew

Check the picture below.

Answer:

Step-by-step explanation:

Find the zero's of f(x)

Answer:

[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]

(one real zero and 2 complex zeros)

Step-by-step explanation:

Given polynomial:

[tex]f(x)= 2x^3-12x^2+20x-16[/tex]

According to the Factor Theorem, if f(4) = 0 then (x - 4) is a factor of the given polynomial.

[tex]\implies f(x)=(x-4)(ax^2+bx+c)[/tex]

Expand the brackets:

[tex]\implies f(x)=ax^3+bx^2+cx-4ax^2-4bx-4c[/tex]

[tex]\implies f(x)=ax^3+(b-4a)x^2+(c-4b)x-4c[/tex]

Compare coefficients with the given polynomial:

[tex]\implies a=2[/tex]

[tex]\implies -4c=-16 \implies c=4[/tex]

[tex]\implies (b-4a)=-12 \implies b-8=-12 \implies b=-4[/tex]

Substitute the found values of a, b and c:

[tex]\implies f(x)=(x-4)(2x^2-4x+4)[/tex]

To find the zeros of f(x), set the function to zero and solve for x:

[tex]\implies (x-4)(2x^2-4x+4)=0[/tex]

[tex]\textsf{Therefore},\: (x - 4) = 0\: \textsf{ and }\: (2x^2-4x+4)=0[/tex]

[tex]\textsf{To solve}\: (2x^2-4x+4)=0\: \textsf{ use the quadratic formula}[/tex]

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]\implies x=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(2)(4)} }{2(2)}[/tex]

[tex]\implies x=\dfrac{4 \pm \sqrt{-16}}{4}[/tex]

[tex]\implies x=\dfrac{4 \pm \sqrt{16 \cdot -1}}{4}[/tex]

[tex]\implies x=\dfrac{4 \pm \sqrt{16}\sqrt{-1}}{4}[/tex]

[tex]\implies x=\dfrac{4 \pm 4i}{4}[/tex]

[tex]\implies x=1 \pm i[/tex]

Therefore, the zeros of the function are:

[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]

(one real zero and 2 complex zeros)

Answer:

Undefined.

Formula's used:

[tex]\longrightarrow \bold{sec(x) = \dfrac{1}{cos(x)} }[/tex]

[tex]\longrightarrow \bold{cosec(x) = \dfrac{1}{sin(x)} }[/tex]

[tex]\longrightarrow \bold{cot(x) = \dfrac{1}{tan(x)} }[/tex]

[tex]\longrightarrow \bold{tan(x) = \dfrac{sinx}{cos(x)} }[/tex]

[tex]\longrightarrow \bold{sin^2x + cos^2 x = 1 }[/tex]

[tex]\longrightarrow \sf \bold{Sum \ Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx}[/tex]

[tex]\longrightarrow \bold{ \int \:{sec^2(ax+b) = \dfrac{1}{a}tan(ax+b)+c }}[/tex]

[tex]\longrightarrow \bold{\int \:\dfrac{1}{ax+b} =\dfrac{1}{a} ln|ax+b|+c}[/tex]

Explanation:

[tex]\sf \Longrightarrow \int _{\pi }^{2\pi }\:\dfrac{sin^6(x)+cos^6(x)}{sin^3(x) \ * \ cos^3\left(x)}[/tex]

[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)} +\dfrac{cos^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)}[/tex]

[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^3\left(x\right)}{\:cos^3\left(x\right)} +\dfrac{cos^3\left(x\right)}{sin^3\left(x\right)}[/tex]

[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\ tan^3(x)+ cot^3(x)[/tex]

[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi } \tan ^3(x)dx+\int _{\pi }^{2\pi } \cot ^3 (x)dx[/tex]

[tex]\Longrightarrow \sf \bold{ [ }-\ln |\sec \left(x\right) |+\dfrac{\sec ^2(x)}{2}-\dfrac{\cot ^2 (x)}{2}-\ln |\sin(x)| \bold{ ] }^{2\pi }_\pi[/tex]

apply limits

[tex]\sf \Longrightarrow \sf -\ln \left|\sec \left(2\pi \right)\right|+\dfrac{\sec ^2\left(2\pi\right)}{2}-\dfrac{\cot ^2\left(2\pi\right)}{2}-\ln \left|\sin \left(2\pi\right)\right|-(-\ln \left|\sec \left(\pi \right)\right|+\dfrac{\sec ^2\left(\pi\right)}{2}-\dfrac{\cot ^2\left(\pi\right)}{2}-\ln \left|\sin \left(\pi\right)\right|)[/tex]

simplify using trigonometric basic functions

[tex]\Longrightarrow \sf -\ln \left|\dfrac{1}{\cos \left(2\pi \right)}\right|+\dfrac{\left(\dfrac{1}{\cos \left(2\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(2\pi \right)}{2}-\ln \left|\sin \left(2\pi \right)\right|- ( -\ln \left|\dfrac{1}{\cos \left(\pi \right)}\right|+\dfrac{\left(\frac{1}{\cos \left(\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(\pi \right)}{2}-\ln \left|\sin \left(\pi \right)\right|)[/tex]

⇒  Undefined

Answer:

[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \boxed{\text{un} \text{de} \text{f}}[/tex]

General Formulas and Concepts:
Calculus

Differentiation

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Methods: U-Substitution + U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Step 4: Integrate Pt. 3

Identify variables for u-solve.

1st Integral

2nd Integral

Step 5: Integrate Pt. 4

∴ we have found the value of the given integral.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

through lengthy mafs, your answer should be 307 mi (wrong somehow)

Step-by-step explanation:

if you want an explanation, please, dont be afraid to comment ;)

(to other people who look this up the answer is actually 318 i dont know, but i got it wrong

The area of the composite figure from the image attached is 112.5 units²

The area of a composite figure refers to the sum total of all the areas of the shapes in that composite figure. This can be done by first identifying the shapes in that composite figure, then finding each area, followed by the addition of all the areas to determine the area of the composite figure.

From the given figure; we can break it down into:

The area of a parallelogram = b × h

where;

The area of a parallelogram =  9 × 6

The area of a parallelogram = 54 units²

The area of a rectangle = Length × breadth

The area of a rectangle = (9 × 3) units²

The area of a rectangle = 27 units²

The area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times b \times h}[/tex]

where;

The area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times b \times h}[/tex]

The area of the triangle [tex]\mathbf{=\dfrac{1}{2}\times 9 \times 7}[/tex]

The area of the triangle [tex]\mathbf{= 31.5 units^2}[/tex]

Therefore, the area of the composite figure is:

= 54 + 27 + 31.5

= 112.5 units²

Learn more about composite figures here:

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Answer:

answer A

Step-by-step explanation:

Option C is correct, the Coriolis Effect shows us that when moving from the equator towards the poles, the air is moving at the same speed.

Speed is the time rate at which an object is moving along a path,

The Coriolis Effect causes moving objects, including air, to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

As air moves from the equator towards the poles, it experiences a change in latitude, which causes it to be deflected.

This deflection results in the formation of high-pressure and low pressure systems that move weather patterns around the globe.

The speed of the air is affected by a number of factors, including temperature, pressure, and the Coriolis Effect.

However, the Coriolis Effect does not directly affect the speed of the air as it moves from the equator towards the poles.

Therefore, the Coriolis Effect shows us that when moving from the equator towards the poles, the air is moving at the same speed.

To learn more on Speed click:

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#SPJ2

Answer: x = -.6

Step-by-step explanation:

2(3x+5) = 6x + 10

10 = -6x

x = -.6

Use the slope formula:-

[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]

[tex]\displaystyle\frac{1-4}{0-5}=\frac{-3}{-5} =\frac{3}{5}[/tex]

Second pair:-

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

If we multiply/divide a negative by a negative, we get a positive. :)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

24

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=24

Answer:

A.)

Step-by-step explanation:

Try each choice to see which one works.

A.)

a_n = 4n + 10

a_5 = 4(5) + 10 = 30

a_6 = 4(6) + 10 = 34

a_7 = 4(7) + 10 = 38

Answer: A.)