Determine the next term in the sequence. 4, -2, 1, -0.5, ...
-1.5
1.5
-0.25
0.25

The verbal statement 'three times a number increased by 8 is at most 40 more than the number' is expressed as the inequality 3x + 8 ≤ x + 40 in mathematical terms. This inequality simplifies to x ≤ 16, indicating that the original number must be 16 or less.

The question involves translating a verbal statement into a mathematical inequality. The phrase 'three times a number increased by 8 is at most 40 more than the number' can be represented algebraically. Begin by letting the variable 'x' represent the unknown number. The phrase 'three times a number' translates to '3x', 'increased by 8' means we add 8, and 'is at most' indicates that the expression is less than or equal to something. '40 more than the number' is translated to 'x + 40'. Combining these elements, we have the inequality 3x + 8 ≤ x + 40.

To solve this inequality, we would subtract 'x' from both sides to get 2x + 8 ≤ 40, and then subtract 8 from both sides to find 2x ≤ 32. Next, we would divide both sides by 2 to get x ≤ 16. This tells us that the original number must be 16 or any number less than 16 to satisfy the condition described in the question.

Understanding how to translate verbal statements into mathematical expressions and inequalities is a fundamental math skill. Knowing terms such as 'at most' is crucial for setting up the correct inequality. This situation is an application of basic algebra to interpret and solve problems.

Answer: v = 1

1v + 6v = 7             Combine like terms

7v = 7                    Divide both sides by 7

v = 1                       Answer!

Answer:

v=1

Step-by-step explanation:

You can add the similar variables (1v and 6v) to get 7v. now your equation should be 7v=7. divide each side by 7 so that the variable stands alone. 7/7 = 1, so v=1.

should be 20%

Hope this helps

Answer:it's 12.20

Step-by-step explanation:

Answer:

Maximum number of relative extremes contained in the graph of this function = 3.

Step-by-step explanation:

We have been given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Degree of the given function = 4.

Because degree is the highest power of variable.

Then relative number of extrema = degree - 1 = 4 - 1 = 3

Hence final answer is 3.

17 and 8

Step-by-step explanation:

8 is the shortest board so multiply 8 by 2 add the 1 foot more gives you 17

Answer:

70 times

Step-by-step explanation:

12 * 5 = 60

28 * 5 = 140

140/2 = 70

According to the question,

Friend clap,

then,

→ [tex]12\times 5 =60 \ times[/tex]

→ [tex]28\times 5 = 140 \ times[/tex]

In 0.5 minutes, he clap.

= [tex]\frac{140}{2}[/tex]

= [tex]70 \ times[/tex]

Thus the response above is appropriate.

Learn more about time here:

https://brainly.com/question/16611166

Answer:

Step-by-step explanation:

fv xcfvsvsvfber

Answer:

D

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A= [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 8 and h = 2, so

A= 0.5 × 8 × 2 = 8 units² → D

Answer: B

Step-by-step explanation: edge2022

is this the full question?

Answer:

c: no solution

Step-by-step explanation:

Final answer:

The function f(x) = 3x^2 + 2x + 4 has no real zeros because the discriminant (b^2 - 4ac) is negative, indicating that the roots of the quadratic equation are complex.

Explanation:

The question asks us to identify the real zeros of the function f(x) = 3x2 + 2x + 4. To find the real zeros, we look for values of x that make f(x) equal to zero. We can approach this by attempting to solve the quadratic equation 3x2 + 2x + 4 = 0 using the quadratic formula, which is x = [-b ± √(b2 - 4ac)]/(2a), where a = 3, b = 2, and c = 4.

Inserting these values into the formula, we get:

x = [-2 ± √((2)2 - 4*3*4)]/(2*3)

x = [-2 ± √(4 - 48)]/(6)

x = [-2 ± √(-44)]/(6)

Since the part under the square root (√(-44)) is negative, this indicates that the solutions for x are complex, not real. Therefore, the equation 3x2 + 2x + 4 has no real solutions.

To find the volume of a rectangular prism, multiply the 3 side lengths by each other.

Volume  = 7.9 x 6.3 x 12.4 = 617.148 cubic cm.

Rounded to the nearest tenth = 617.2 cubic cm.

Answer: [tex]617.1\text{ cm}^3[/tex]

Step-by-step explanation:

In the given picture, we have a rectangular prism.

Height : 7.9 cm

Length = 12.4 cm

Width = 6.3 cm

The volume of a rectangular prism is given by :-

[tex]V=l\times w\times h[/tex], where l is length, w is width and h is height of the prism.

Now, the volume of a rectangular prism will be :-

[tex]V=12.4\times 6.3\times 7.9\\\\\Rightarrow\ V=617.148\approx617.1\text{ cm}^3[/tex]

Hence, the  volume of a rectangular prism = [tex]617.1\text{ cm}^3[/tex]

Answer:

33 laps

Step-by-step explanation:

we know that

There are 6.6 laps in a mile

so

using proportion

Find how many laps will you have to make to run 5 miles

so

Let

x ----> the number of laps

[tex]\frac{6.6}{1}\frac{laps}{mile}=\frac{x}{5}\frac{laps}{mile} \\ \\x=6.6*5\\ \\ x=33\ laps[/tex]

Answer:

21. D

22. A

Step-by-step explanation:

R; all quadratic functions are going to have ranges and domains of *ALL REAL NUMBERS*.

Answer:

x=1 and y = 9

Step-by-step explanation:

Solving using elimination method:

In elimination method we solve equations such that one variable cancels out and we find the value of other variable.

x + 7y = 64

x + 3y = 28

Subtracting both equations:

x + 7y = 64

x + 3y = 28

-   -       -

___________

0 +4y = 36

y= 36/4

y=9

Putting value of y in one of the equation,

x+7y = 64

x + 7(9) = 64

x + 63 = 64

x = 64-63

x = 1

So, x=1 and y=9

Solving using substitution method:

In substitution method, we substitute value of one variable into other value

x + 7y = 64   (1)

x + 3y = 28   (2)

From 1

x = 64 -7y

Putting value of x in eq(2)

(64 -7y) + 3y = 28

64 -7y +3y =28

64 - 4y = 28

-4y = 28 -64

-4y = -36

y = -36/-4

y = 9

Putting value of y in eq (1)

x + 7y = 64

x + 7(9) = 64

x + 63 = 64

x = 64 - 63

x = 1

So, x=1 and y = 9.

Answer:

Step-by-step explanation:

1 option 2c

1. The equation of a circle with center (h,k) and radius r units is given by

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The given circle has center (5,-2) and a radius r=3 units.

We substitute these values into the formula to get:

[tex](x-5)^2+(y--2)^2=3^2[/tex]

This simplifies to:

[tex](x-5)^2+(y+2)^2=9[/tex]

The correct answer is A.

2.  The given circle has center (3,-5) and radius r=8 units.

We substitute the given values into the formula to obtain:

[tex](x-3)^2+(y--5)^2=8^2[/tex]

We simplify to get:

[tex](x-3)^2+(y+5)^2=64[/tex]

The correct answer is C

3. The given circle has equation:

[tex](x+8)^2+(y+9)^2=169[/tex]

We can rewrite this equation as:

[tex](x--8)^2+(y--9)^2=13^2[/tex]

Comparing this to

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The center is (-8,-9) and the radius is 13.

The correct answer is A.

4. The given circle has equation:

[tex](x-7)^2+y^2=225[/tex]

We can rewrite this equation as:

[tex](x-7)^2+(y-0)^2=15^2[/tex]

Comparing this to

[tex](x-h)^2+(y-k)^2=r^2[/tex]

The center is (7,0) and the radius is 15.

The correct answer is B.

5. The given circle has center (-2,6) and passes through (-2,10).

We can use the number line to find the radius.

[tex]r=|10-6|=4[/tex]

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We substitute the center and the radius into the formula to get:

[tex](x--2)^2+(y-6)^2=4^2[/tex]

This simplifies to:

[tex](x+2)^2+(y-6)^2=16[/tex]

The correct answer is A

6. The given circle has center (1,2) and passes through (0,6).

We can use the distance formula to find the radius.

[tex]r=\sqrt{(1-0)^2+(2-6)^2}=\sqrt{17}[/tex]

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We substitute the center and the radius into the formula to get:

[tex](x-1)^2+(y-2)^2=\sqrt{17}^2[/tex]

This simplifies to:

[tex](x-1)^2+(y-2)^2=17[/tex]

The correct answer is C

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=2,143.57 \end{cases}\implies 2143.57=\cfrac{4\pi r^3}{3}\implies 6430.71=4\pi r^3 \\\\\\ \cfrac{6430.71}{4\pi }=r^3\implies \sqrt[3]{\cfrac{6430.71}{4\pi }}=r\implies \stackrel{\pi =3.14}{7.9999956 \approx r}\implies \stackrel{\textit{rounded up}}{8=r}[/tex]

Answer

5000

Step-by-step explanation:

You convert the numbers into  standard #'s which gets you 7000 and 2000. Subtract 7000 - 2000 and you get 5000.

7x10^3 is 3-1/2 times the size of 2x10^3.

Well I guess I can do it tomorrow but I’m not sure if it’s a good

Answer:

Radius of the cone is 6 unit.

Step-by-step explanation:

Given:

Lateral Surface Area of Cone, LSA = 100π unit²

Total Surface Area of cone, TSA = 136π unit²

Let, r be the radius of cone.

According to the question,

Total Surface area = lateral surface area + Area of circle

136π = 100π + πr²

πr² = 36π

r² = 36

r = 6

Therefore, Radius of the cone is 6 unit.

The radius of the cone is 6 units.

To solve for the radius of the cone, we need to use two formulas: the lateral area (LA) and the total surface area (TSA) of a cone. The given values are:

We use the following formulas:

From the given values:

From the first equation, we can express l in terms of r:

l = 100 / r

Substitute l in the second equation:

136 = r² + r(100 / r)
=> 136 = r² + 100

Rearrange the equation to solve for r:

r² = 136 - 100
=> r² = 36
=> r = √36
=> r = 6.

Answer:

Yes

Step-by-step explanation:

The standard form for a quadratic equation in the US has the terms in decreasing order by power on the left of the equal sign, and the right side zero. Preferably, the leading coefficient is positive. This might also be called "general form." Elsewhere, the "standard form" may be different.

[tex]

f(x)=3x^2-24x+36 \\

0=3(x-2)(x-6) \\

0=(x-2)(x-6)

[/tex]

There will be 2 solutions.

[tex]

x-2=0\Longrightarrow\boxed{x_1=2} \\

x-6=0\Longrightarrow\boxed{x_2=6}

[/tex]

Hope this helps.

r3t40

The zeros of the function f(x) = 3x^2 - 24x + 36 are found using the quadratic formula to be x = 6 and x = 2.

The zeros of the function f(x) = 3x2 \- 24x + 36 are the values of x for which f(x) equals zero. To find the zeros, we set the quadratic equation equal to zero and solve for x. This can be done using the quadratic formula x = (-b \\pm (sqrt{b2 \(- 4ac})/(2a), where a = 3, b = -24, and c = 36. Applying the quadratic formula:

Therefore, the zeros of the function are x = 6 and x = 2.

Step-by-step explanation:

The highest point of a parabola is at the vertex.

x = -b / (2a)

x = -1 / (2×-0.0023)

x ≈ 217.4

y = (217.4) − 0.0023 (217.4)²

y ≈ 108.7

The horizontal distance can be found when the potato lands (y=0):

0 = x − 0.0023x²

0 = x (1 − 0.0023x)

x = 0, x ≈ 434.8

So the potato reaches a maximum height of 108.7 m and travels a horizontal distance of 434.8 m.

The height point of the trajectory is 217.39 meters and the horizontal distance the potato travels before hitting the ground is 434.78 meters.

To find the height point of the trajectory and the horizontal distance the potato travels before hitting the ground, we can use the equation y=x-0.0023x^2 to represent the trajectory. Since the trajectory is a parabola, the height point corresponds to the vertex of the parabola. To find the vertex, we can use the formula x = -b / (2a), where a = -0.0023 and b = 1. To find the horizontal distance the potato travels before hitting the ground, we need to find the x-intercepts of the parabola, which correspond to the points where y = 0.

First, let's find the height point:

Using the formula x = -b / (2a) and substituting the values, we get:

x = -1 / (2 * (-0.0023)) = 217.39 meters

Now, let's find the horizontal distance:

Setting y = 0 and solving for x, we get:

0 = x - 0.0023x^2

0 = x(1 - 0.0023x)

x = 0 or x = 434.78 meters

Therefore, the height point of the trajectory is 217.39 meters and the horizontal distance the potato travels before hitting the ground is 434.78 meters.

Answer:

55

Step-by-step explanation:

[tex]

s=\frac{\Delta{y}}{\Delta{x}}=\frac{9-7}{4+2}=\boxed{\frac{2}{6}=\frac{1}{3}}

[/tex]

Hope this helps.

r3t40

[tex]\bf \textit{volume of a right-circular cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=15 \end{cases}\implies V=\cfrac{\pi (12)^2(15)}{3}\implies V=720\pi[/tex]

Answer:

939,520

Step-by-step explanation:

You round up because you have a 5 in the tens place and as the saying goes: "Five or more up the score, four or less let it rest"

The number  939,515 rounded to the nearest tens is 939520.

We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, A number 939515 and we have to round it to the nearest ten.

To round this number to the nearest ten we'll look at the digit at the unit's place.

The digit at the unit place is 5 so we'll add 1 to the tens digit and make the unit digit zero.

Therefore the number 939515 rounded to the nearest tens place is

939520.

learn more about rounding of numbers here :

https://brainly.com/question/13391706

#SPJ2

The answer are:

1.D

2.C

3.A

Explanation is in above pictures.

Answer:

[tex]\large\boxed{6\times\dfrac{2}{3}=4}[/tex]

Step-by-step explanation:

[tex]6\times\dfrac{2}{3}=\dfrac{6^{:3}}{1}\times\dfrac{2}{3_{:3}}=\dfrac{2}{1}\times\dfrac{2}{1}=2\times2=4[/tex]

Answer:

option C

Step-by-step explanation: