97) If the average of 3a and 4b is less than 50 and a is twice b, what
is the largest integer value of a?
a) 8
b) 9
c)10
d)11​

Answers

Answer 1

The average of [tex]3a[/tex] and [tex]2b[/tex] satisfies

[tex]\dfrac{3a+4b}2<50[/tex]

Then

[tex]a=2b\implies\dfrac{3(2b)+4b}2=5b<50\implies b<10[/tex]

[tex]a=2b[/tex], so if [tex]a[/tex] must be an integer, then the largest integer value it can take on is 19 if [tex]b[/tex] can be a rational number (in which case [tex]b=9.5[/tex]) or 18 if [tex]b[/tex] must also be an integer.

Given that none of the provided answer choices lists 18 or 19, I'd bet there's a typo and you're supposed to find the maximum integer value of [tex]b[/tex], in which case the answer would be B as the largest integer value would be 9.


Related Questions

Which strategies can be used to solve this problem? Marcus bought books for his vacation. He bought a mystery book for $14, a fantasy novel for $25, and 3 biographies that cost $6 each. How much money did Marcus spend on the books altogether? Choose all answers that are correct. A. Translate into an equation. 14 + 25 + 6 = n B. Work backward. Start with $6 and add this amount to $25 and $14. Multiply the sum by 3 to get the amount Marcus spent. C. Use logical reasoning. Think that Marcus bought a total of 5 books. Multiply $6 by 3 to get the cost of the biographies. Add this amount to the cost of the two other books ($14 and $25) to get the total amount Marcus spent. D. Draw a diagram. Draw 5 rectangles to represent the 5 books Marcus bought. Put $14 in one rectangle and $25 in another rectangle. Write $6 in each of the remaining 3 rectangles. Add the 5 amounts together to get the total amount Marcus spent.

Answers

Answer: c is your answer

Step-by-step explanation:

what is the quotient when x^3 -5x^2 + 3x -8 is divided by x-3 ?

Answers

For this case we have that the parts of a division are:

Dividend, divisor, quotient and remainder.

To make the division of polynomials, we must build a quotient that when multiplied by the divisor (and when the sign is changed), eliminate the terms of the dividend until reaching the remainder of the division.

It must be fulfilled that:

[tex]Dividend = Quotient * Divider + Remainder[/tex]

Then, if we look at the attached figure, the quotient is:

[tex]x ^ 2-2x-3[/tex]

Answer:

[tex]x ^ 2-2x-3[/tex]

The ratio of 3 to 4 and the ratio of 4 to 3____ the same number. A)Are or B)are not

Answers

Answer: Option B

Step-by-step explanation:

By definition, the ratio is a comparison between two different things. It can be written in:

Odd notation

[tex]a:b[/tex]

Fractional notation

[tex]\frac{a}{b}[/tex]

Or in words:

[tex]a\ to\ b[/tex]

Given the ratio 3 to 4 and the ratio of 4 to 3, you can rewrite them the fractional form:

[tex]\frac{3}{4}\\\\\frac{4}{3}[/tex]

To know if these ratios are the same number, divide the numerator by the denominator of each one of them:

 [tex]\frac{3}{4}=0.75\\\\\frac{4}{3}=1.33[/tex]

Therefore, the ratio of 3 to 4 and the ratio of 4 to 3 ARE NOT the same number.

how many millimeters are in a centimeter

Answers

10 millimeters in 1 centimeter

Answer:

1 centimeter = 10 millimeters  

Step-by-step explanation:

we have to find about how many millimeters are in a centimeter.

We know that  1 centimeter = 10 millimeters

or 10 millimeters  = 1 centimeter

divide both sides by 10

or \frac{10}{10} millimeters  = \frac{1}{10} centimeter

or 1 millimeters  = 0.1 centimeter

But we need millimeters  in centimeters so we should write :

final answer as 1 centimeter = 10 millimeters.

A parabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis.

Which could be the equation of the parabola?

Answers

Answer:

[tex]\boxed{x^2=4py}[/tex]

Step-by-step explanation:

A parabola is the set of all points that lies on a plane and are equidistant from  a fixed line called the directrix and a fixed point called focus, that doesn't lies on the line. If the  vertex is at the origin and the directrix crosses the negative part of the y-axis, then the equation takes the following forms:

[tex]\boxed{x^2=4py}[/tex]

Where the focus lies on the axis [tex]p \units[/tex] (directed distance) from the vertex.

The representation of this problem is shown below. As you can see, the vertex lies on the origin while the directrix crosses the negative part of the y-axis.

Answer:

The actually answer is x(2) = 4y

what is the inverse of y=4x-16

Answers

Answer:

x=y/4 + 4

Step-by-step explanation:

y=4x-16

-need to isolate x

add 16 to both sides.

y+16=4x

divide by 4 on both sides.

y/4 + 4 = x

Assume that the lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x to the nearest tenth

Answers

X=3.6

See the attached photo

Final answer:

Without specific diagram or context, this answer is based on the relationship between tangent lines and circles. The angle between a tangent and a radius of a circle is always 90 degrees. Understanding this along with the Pythagorean theorem and trigonometric ratios will help solve for 'x'.

Explanation:

Based on the information provided, it seems the question is related to circular geometry, however, we need more specific information to solve your problem such as a diagram or more context. However, if we consider that we're dealing with a tangent and a radius of a circle, it's important to know that the angle between a tangent and a radius of a circle is always 90 degrees. So, if we have an angle opposite a 90-degree angle in a right triangle, we could use tangent properties, Pythagorean theorem, or trigonometric ratios to solve for 'x'

For example, in a right triangle, tangent of an angle is equal to the opposite side length divided by the adjacent side length (tan(θ) = opposite/adjacent). Also, the Pythagorean theorem tells us that the square of the hypotenuse (radius) is equal to the sum of the squares of the other two sides (c² = a² + b²).

Those concepts and formulas are key to understanding the intersection between lines and circles, and they should assist you in solving queries closely related to this problem.

Learn more about Circle Geometry here:

https://brainly.com/question/27802544

#SPJ3

An equation is written to represent the relationship between the temperature in Alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. A graph of the equation is created. Which quadrants of a coordinate grid should be used to display this data? Quadrant 1 only

Answers

Answer:

1 and 4

Step-by-step explanation:

What is the x-intercept of the equation y=-5x+1,450?​

Answers

Substitute the value for y as 450

450=-5x+1

Solve for x

450-1=-5x

449=-5x

89.8=-x

x=-89.8

Answer:

x = 290

Step-by-step explanation:

The x- intercept is the point on the x- axis where the line crosses.

substitute y = 0 into the equation and solve for x

- 5x + 1450 = 0 ( subtract 1450 from both sides )

- 5x = - 1450 ( divide both sides by - 5 )

x = 290 ← x- intercept

line crosses x- axis at (290, 0)

Find the rate of change of the function h(x)=2x^2 in the interval 2<_ x<_4

Answers

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ h(x)= 2x^2\qquad 2\leqslant x \leqslant 4 \qquad \begin{cases} x_1=2\\ x_2=4 \end{cases}\implies \cfrac{h(4)-h(2)}{4-2} \\\\\\ \cfrac{2(4)^2~~-~~2(2)^2}{2}\implies \cfrac{32-8}{2}\implies \cfrac{24}{2}\implies 12[/tex]

Can you please help me.​

Answers

Answer:

7)60

8)1/6

9)9

10)11.5

11)14.4

Step-by-step explanation:

Answer:divide

Step-by-step explanation:

Which statement is always true

Answers

Answer:

Step-by-step explanation:

The sine of any acute angle is equal to the cosine of its complement. The cosine of any acute angle is equal to the sine of its complement. of any acute angle equals its cofunction of the angle's complement. Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle.

hope this helps u

What is the absolute value of 1 -321?

Answers

it’s 321 because whether negative or positive it’s absolute value

1 minus 321 is -320. Since you’re finding the absolute value it’s 320

Can someone please help me

Answers

Answer:

Lines RQ and SP are perpendicular to SR

Step-by-step explanation:

SR are parallel to PQ so that means that RQ and SP are perpendicular to SR

10. Jaime is running a marathon, which is a 26 2/5 Mile Race. At 6 3/4 miles from the start, she passes Friends cheering on her. After she passes a water stop 9 1/2 miles farther along the route, How Far From The Finish Line is Jaime?

Answers

Answer:

A

Step-by-step explanation:

6 3/4 + 9 1/2 = 65/4

26 2/5 - 65/4 = 203/20 or 10 3/20

1 2/7 divide (-2 1/4)

Answers

The answer is -4/7 or in decimal it’s -0571429

A line passes through the origin and has a slope of -3 what is the equation of the line that is perpendicular to the first line and passes through the point (3,4)?

Answers

Answer: [tex]y=\frac{1}{3}x+3[/tex]

Step-by-step explanation:

The equation of the line is Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" the y-intercept.

The slopes of perpendicular lines are negative reciprocal.

Then, if the slope of the first line is -3, the slope of the other line must be:

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

Substitute the point (3,4) into the equation and solve for b:

[tex]4=\frac{1}{3}(3)+b\\ 4-1=b\\b=3[/tex]

Then the equation of this line is:

[tex]y=\frac{1}{3}x+3[/tex]

ANSWER

[tex]y= \frac{1}{3} x + 3[/tex]

EXPLANATION

We want to find the equation of a line which is perpendicular to another line with slope -3 and passes through (3,4).

Our line of interest is has a slope that is the negative reciprocal of -3

[tex]m = - \frac{1}{ - 3} = \frac{1}{3} [/tex]

The equation is given by

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the point and slope to get:

[tex]y-4= \frac{1}{3} (x-3)[/tex]

Expand

[tex]y-4= \frac{1}{3} x-1[/tex]

[tex]y= \frac{1}{3} x-1 + 4[/tex]

[tex]y= \frac{1}{3} x + 3[/tex]

If you can explain your answer that’d be great!! Thank you!

Answers

Answer:

[tex]A(t)=A_{0}e^{\frac{ln(\frac{1}{2})}{22}t}[/tex]

Step-by-step explanation:

This half life exponential decay equation goes by the formula:

[tex]A(t)=A_{0}e^{kt}[/tex]

Where

[tex]k=\frac{ln(\frac{1}{2})}{Half-Life}[/tex]

Since half life is given as 22, we plug that into "Half-Life" in the formula for k and then plug in the formula for k into the exponential decay formula:

So,

[tex]k=\frac{ln(\frac{1}{2})}{Half-Life}\\k=\frac{ln(\frac{1}{2})}{22}[/tex]

Now

[tex]A(t)=A_{0}e^{\frac{ln(\frac{1}{2})}{22}t}[/tex]

third choice is correct.

Find the value of x to the nearest tenth tan x =5

Answers

Answer:

x ≈ 78.7° (in degree)

x ≈ 1.4      (in radians)

Step-by-step explanation:

Given in the question an equation

tan(x) = 5

       x =  [tex]tan^{1}(5)[/tex]

       x = 78.69

       x ≈ 78.7°

In radian:

x ≈ 1.4

Answer:

The correct answer is x = 78.7°

Step-by-step explanation:

It is given that,

Tan x = 5

To find the value of x

If tan ∅ = x then ∅ = tan⁻¹ x =

Here  we have tan x = 5

x =  tan⁻¹ 5 = 78.69 ≈ 78.7°

Therefore the value of x = 78.7°

The correct answer is 78.7°

How do you solve for a side in right triangles?

Answers

Answer:

pythagorean theorem

Step-by-step explanation:

a²+b²=c²

Pythagorean theorem

What is the percent approximate percent decrease when a fish count goes down from 850 to 500

Answers

the answer is 40% hope this helps

Answer:

Aproximately 40% is the correct option)))

Find all solutions for a triangle with a=26, b=29, and A=58

Answers

Answer:

i think its C

Step-by-step explanation:

Final answer:

To solve the triangle with sides a=26, b=29, and angle A=58 degrees, apply the Law of Sines to find another angle, use the sum of angles to find the third angle, and then the Law of Cosines to find the remaining side, ensuring all conditions are satisfied for a valid triangle.

Explanation:

To find all solutions for a triangle given a=26, b=29, and A=58 degrees, we use the Law of Sines, which relates the lengths of sides to the sine of their opposite angles. Since sin A > sin a (opposite side to angle A) would result in no solution and considering the given values, we don't encounter this issue. Instead, we have:

sin B / b = sin A / a

Rearranging for B, we have:

B = sin⁻¹(sin A / a × b)

Plugging in our numbers:

B = sin⁻¹((sin 58°) / 26 × 29)

Once B is calculated, we can find angle C since the interior angles of a triangle sum to 180 degrees. Following that, we can use the Law of Cosines to find the third side, c. The process is:

Calculate B using the Law of Sines.Calculate C by subtracting A and B from 180 degrees.Calculate c using the Law of Cosines: c² = a² + b² - 2ab cos C.

After finding all angles and sides, verify the solution by checking if the interior angles sum to 180 degrees and the sides satisfy the Triangle Inequality Theorem.

30 POINTS! x + 1 = 2 ÷ x + 1

In the equation above, which choice is a possible value of x + 1?

A) 1 - √2

B) √2

C) 2

D) 4

Answers

For this case we have the following equation:

[tex]x + 1 = \frac {2} {x + 1}[/tex]

We must find the value of [tex]x + 1[/tex]:

Multiplying both sides of the equation by[tex]x + 1:[/tex]

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

Applying square root on both sides of the equation to eliminate the exponent:

[tex]x + 1 = \sqrt {2}[/tex]

Answer:

Option B

Answer: B

Step-by-step explanation:

Triangle ABC is similar to triangle WYZ. select all angles whose tangent equals 3/4

Answers

Answer:

∠B

∠Y

Step-by-step explanation:

we know that

In the right triangle ABC

[tex]tan(B)=\frac{AC}{BC}[/tex] ----> opposite side to angle B divided by the adjacent side to angle B

substitute the values

[tex]tan(B)=\frac{3}{4}[/tex]

Remember that

If two triangles are similar, then the corresponding sides are proportional and the corresponding angles are congruent

so

∠A=∠W

∠B=∠Y

∠C=∠Z

therefore

[tex]tan(B)=tan(Y)[/tex]

Base on the fact that the triangle ABC and WYZ are similar, the angles whose tangent equals 3 / 4 are ∠B and ∠Y

What are similar triangles?

Similar triangle are only different in sizes but are of the same shape.

Similar triangles, corresponding sides are always in the same ratio. Corresponding angles of similar triangles are always congruent. Therefore,

∠A = ∠W

∠B = ∠Y

∠C = ∠Z

Therefore, let's find all angles in the similar triangles whose tangent is equal to 3 / 4 .

tan ∅ = opposite / adjacent

Since,

tan B = 3 / 4

Then

tan Y = 3 / 4

Therefore,

The angles whose tangent equals 3 / 4 are ∠B and ∠Y

learn more on similar triangle here: https://brainly.com/question/11969453

how many points out of 416 do i need to get to get a 60% in class
Right now I have 153.

Answers

Answer: 249.6 so 250

Step-by-step explanation: Take 416 times it by 0.6 Have a nice day. Hope it helped!

You currently have a 36%.

You need 249-250% to get a 60% in your class.

Best of luck!

"Complete the square" to convert the equation of each circle to graphing form. Identify the center and the radius.

x² + 6x + y2 – 4y= -9

Answers

Answer:

The center is (-3,2) and the radius is r=2

Step-by-step explanation:

The general equation of the given circle is

[tex]x^2+6x+y^2-4y=-9[/tex]

Add the square of half the coefficient of the linear terms to both sides of the equation to obtain;

[tex]x^2+6x+3^2+y^2-4y+(-2)^2=-9+3^2+(-2)^2[/tex]

[tex]x^2+6x+9+y^2-4y+4=-9+9+4[/tex]

[tex]x^2+6x+9+y^2-4y+4=4[/tex]

The quadratic trinomials in x and y on the left side of the equations are perfect squares.

We factor to obtain;

[tex](x+3)^2+(y-2)^2=4[/tex]

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

Comparing to:

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

The center is (-3,2) and the radius is r=2

Final answer:

To complete the square and put the equation into graphing form, group x's and y's, add appropriate constants to each group, and rewrite. The circle's equation becomes (x + 3)² + (y - 2)² = 4, with the center at (-3, 2) and a radius of 2.

Explanation:

To complete the square for the equation x² + 6x + y² - 4y = -9 and convert it to graphing form, we need to group the x's and y's together and add the right constants to each group.

First, group the x terms and the y terms: (x² + 6x) + (y² - 4y).Next, for x terms, add and subtract (6/2)², which is 9, inside the parentheses: (x² + 6x + 9) - 9.For y terms, add and subtract (-4/2)², which is 4, inside the parentheses: (y² - 4y + 4) - 4.Combine the constant terms with -9, the constant on the right side of the equation: -9 - 9 - 4.The equation becomes (x + 3)² + (y - 2)² = 4.

Now, the equation is in the graphing form of a circle ((x-h)² + (y-k)² = r²), where (h, k) is the center and r is the radius. Hence, the circle's center is at (-3, 2) and its radius is 2.

Evaluate the following expression 2+(3-2x2)x1

Answers

Answer:

answer: 1

Step-by-step explanation:

using pemdas you would first go into the parenthesis and multiply 2 by 2 the subtract that from three giving you -1. then, you would multiply that by 1 and add that to 2.

find the 107 terms of sequence -9,-5,-1,3,7​

Answers

Answer:

415

Step-by-step explanation:

the nth term of the sequence is -13 + 4n

the sequence is an arithmetic progression with nth term a + (n - 1)d

a = -9, d = a5- a4 = 7 -3 =4

nth = -9 + (n -1) 4

       = -9 + 4n -4

       = -13 + 4n

hence the 107th term; -13 + 4*107

                                      -13 + 428 = 415

Water and orange squash is mixed in the ratio 7 : 4 Find how much water is needed to dilute 120 cl of orange squash.

Answers

Answer:

210

Step-by-step explanation:

Divide 120 by 4 and get 30 and multiply 7 by 30 and you get 210

Final answer:

To dilute 120 cl of orange squash with a ratio of 7:4 (water to squash), you need 210 cl of water. The total mixture will be 330 cl (7+4 parts), of which 120 cl is the squash and the remainder is water.

Explanation:

The student is asking how much water is needed to dilute 120 cl of orange squash if the mixture ratio of water to orange squash is 7:4. To solve this, you need to work with ratios.

First, add the parts of the ratio together: 7 (water) + 4 (orange squash) = 11 parts in total. Now, find out how many parts of the total mixture the 120 cl of orange squash represents. Since the ratio of orange squash is 4 parts, this means that 120 cl is 4 parts of the total mixture.

We can then set up the proportion: 4 parts / 11 parts total = 120 cl / total mixture in cl. Solving for the total mixture gives us: 11 parts * 120 cl / 4 parts = 330 cl.

Finally, to find out how much water is needed, subtract the volume of orange squash from the total mixture volume: 330 cl - 120 cl = 210 cl of water.

A solid piece of wood shaped as a cylinder with an 8-centimeter diameter is cut as shown.



What is the surface area of the figure? Express the answer in terms of π.

96 + 64π cm2
96 + 80π cm2
96 + 112π cm2
96 + 128π cm2

Answers

Answer:

The surface area of the figure is 96 + 64π ⇒ 1st answer

Step-by-step explanation:

* Lats revise how to find the surface area of the cylinder

- The surface area = lateral area + 2 × area of one base

- The lateral area = perimeter of the base × its height

* Lets solve the problem

- The figure is have cylinder

- Its diameter = 8 cm

∴ Its radius = 8 ÷ 2 = 4 cm

- Its height = 12 cm

∵ The perimeter of the semi-circle = πr

∴ The perimeter of the base = 4π cm

∵ The area of semi-circle = 1/2 πr²

∴ The area of the base = 1/2 × π × 4² = 8π cm²

* Now lets find the surface area of the half-cylinder

- SA = lateral area + 2 × area of one base + the rectangular face

∵ LA = perimeter of base × its height

∴ LA = 4π × 12 = 48π cm²

∵ The dimensions of the rectangular face are the diameter and the

   height of the cylinder

∴ The area of the rectangular face = 8 × 12 = 96 cm²

∵ The area of the two bases = 2 × 8π = 16π cm²

∴ SA = 48π + 16π + 96 = 64π + 96 cm²

* The surface area of the figure is 96 + 64π

Answer:

A

Step-by-step explanation:

edge 2021

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