Solve. 10x^2 = 6 + 9x10x 2 =6+9x10, x, start superscript, 2, end superscript, equals, 6, plus, 9, x Choose 1 answer: Choose 1 answer: (Choice A) A x =\dfrac{5 \pm \sqrt{65}}{-2}x= ?2 5± 65 ? ? x, equals, start fraction, 5, plus minus, square root of, 65, end square root, divided by, minus, 2, end fraction (Choice B) B x =\dfrac{9 \pm \sqrt{321}}{20}x= 20 9± 321 ? ? x, equals, start fraction, 9, plus minus, square root of, 321, end square root, divided by, 20, end fraction (Choice C) C x =\dfrac{4 \pm \sqrt{26}}{10}x= 10 4± 26 ? ? x, equals, start fraction, 4, plus minus, square root of, 26, end square root, divided by, 10, end fraction (Choice D) D x =\dfrac{-1 \pm \sqrt{109}}{18}x= 18 ?1± 109 ? ?

Answer:

negative 2 square root of 10 over 7

Step-by-step explanation:

Answer:

arc BG = 14°

Step-by-step explanation:

∠BMG = [tex]\frac{1}{2}[/tex] ( arc BG + arc JS) = 30

Multiply both sides by 2

arc BG + arc JS = 60, that is

arc BG + 46° = 60° ( subtract 46° from both sides )

arc BG = 14°

Answer:

arc BG= 14°

Step-by-step explanation:

It is given in the figure that  mJS = 46∘ and m∠BMG = 30∘.

If two chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs. So,  

m∠BMG = 12 (mJS +mBG)

Substitute the given values and solve for mBG.

30∘ = 12 (46∘ + mBG)

Multiply by 2.

60∘ = (46∘ + mBG)

Subtract 46∘.

14∘ = mBG

Therefore, mBG = 14∘.

ANSWER

[tex]3\le x\le6[/tex]

EXPLANATION

The given inequality is

[tex] {x}^{2} - 9x + 18 \leqslant 0[/tex]

This is the same as

[tex](x - 3)(x - 6) \leqslant 0[/tex]

The corresponding equation is

[tex](x - 3)(x - 6)= 0[/tex]

By the zero product principle,

[tex]x = 3 \: or \: x = 6[/tex]

We now plot the boundaries and test for the region that satisfies the inequality.

See attachment.

From the graph the solution is

[tex]3\le x\le6[/tex]

Answer:

The manufacturer will have no profit or loss when the selling price equals $200 or $100.

Step-by-step explanation:

The expression to model the monthly profit from sales of a new model of bicycle is

-x^2 + 300x -20,000

Let

f(x) -----> the monthly profit in dollars

x -----> s the selling price of one bicycle in dollars

[tex]f(x)= -x^{2}+300x-20,000[/tex]

we know that

The manufacturer will make no profit nor a loss when the profit is equal to zero

so

f(x)=0

[tex]-x^{2}+300x-20,000=0[/tex]

Multiply by -1 both sides

[tex]x^{2}-300x+20,000=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]a=1\\b=-300\\c=20,000[/tex]

substitute in the formula

[tex]x=\frac{300(+/-)\sqrt{-300^{2}-4(1)(20,000)}}{2(1)}[/tex]

[tex]x=\frac{300(+/-)\sqrt{10,000}}{2}[/tex]

[tex]x=\frac{300(+/-)100}{2}[/tex]

[tex]x=\frac{300(+)100}{2}=200[/tex]

[tex]x=\frac{300(-)100}{2}=100[/tex]

therefore

The manufacturer will have no profit or loss when the selling price equals $200 or $100.

To find the selling prices at which the manufacturer will make neither a profit nor a loss, set the profit expression equal to zero and solve for x, giving a selling price of $5.

To determine the selling prices at which the manufacturer will make neither a profit nor a loss, we set the profit expression equal to zero:

0 = 100x - (500 + 20x)

Solving for x, we get x = 5. This means the selling price for the bicycle to break even is $5.

86 which equals 90 and then you divide by two

Answer:

x = 53.1°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanx = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{8}{10}[/tex]

x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{10}[/tex] ) ≈ 53.1°

Answer:

Blue: 1/16 square units

Green: 1/64

yes

1/3

Step-by-step explanation:

The areas of these shaded triangles. Orange: 1/4 square units, Blue: 1/16 square units, Green: 1/64 square units

A fraction represents a part of a whole number of equal parts.

The area of the largest triangle is given as 1 square unit.

The area of the triangle is colored and follows a geometric sequence with the common ratio of 1/4.

The area of the non-shaded triangle is given by 1 square unit.

The area of the orange triangle

1 × 1/4 = 1/4 square units.

The area of the blue triangle

1/4 × 1/4 = 1/16 square units.

The area of the green triangle

1/16 × 1/4  = 1/64 square units.

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C.Government is the answer

Answer:A-Price

Step-by-step explanation:

Real Gross Domestic Product is adjusted for Price changes.

Unlike Nominal GDP Real GDP accounts for the change in prices and provides a better figure than nominal GDP. Real GDP differentiate GDP in different years more significant because it permits comparisons of the real volume of services and goods without taking inflation.

Answer:sd

D. [tex]f\left(x\right)=2x^2+3x-5[/tex]

Step-by-step explanation:

Given choices are:

[tex]f\left(x\right)=\frac{2}{x^2}[/tex]

[tex]f\left(x\right)=3\left(3-x\right)[/tex]

[tex]f\left(x\right)=7^2[/tex]

[tex]f\left(x\right)=2x^2+3x-5[/tex]

Now we need to find about which of them is the quadratic function.

We know that quadratic function is written in form of [tex]f\left(x\right)=ax^2+bx+c[/tex]

Last choice looks similar to that form.

Hence coorect choice is D. [tex]f\left(x\right)=2x^2+3x-5[/tex]

Answer:

D. f(x) = 2x^2 + 3x - 5

Step-by-step explanation:

Answer:

500 lb

Step-by-step explanation:

You have to make a proportion:

[tex]\frac{part}{whole} = \frac{percent}{100}[/tex]

77 lb is part of the whole weight ( which we don't know) so 77 will go on top

The problem tells us that 15.4% of the total weight is pecans so 15.4 will go over 100 (since % are out of 100)

[tex]\frac{77}{x} = \frac{15.4}{100}[/tex]

Then you cross multiply giving you: 7700 = 15.4x

then you divide 15.4 to both sides to isolate x which will give you 500

Final answer:

To find the total weight of a batch of mixed nuts where pecans make up 15.4% and weigh 77 pounds, we set up a proportion and solve for the total weight, resulting in 500 pounds for the whole batch.

Explanation:

The question asks how many pounds of mixed nuts are in a batch altogether if 77 pounds are pecans, which represent 15.4% of the mix. To find the total weight, we need to set up a proportion where 15.4% corresponds to 77 pounds, and we want to find 100% (the whole mix).

We can set up the equation like so: 15.4 / 100 = 77 / x, where x stands for the total weight of the mixed nuts. To find x, we solve for x using algebra: x = 77 / (15.4 / 100). When you perform the calculation, the result is x = 500 pounds. So, the batch of mixed nuts weighs 500 pounds in total.

Answer:

The function is continuous for all real numbers

Step-by-step explanation:

We have the following function

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

Note that the denominator of the function is:

[tex]x^2 +1[/tex]

This expression is different from zero for all real numbers, since for [tex]x^2 +1[/tex] then [tex]x^2 =-1[/tex], there is no number in the real numbers whose square root is equal to -1.

For this reason the function is defined for all real numbers and has no discontinuity.

This function is always positive, continuous and has horizontal asymptote

[tex]y = 1[/tex]

Observe the attached image

Answer:

1.=128     2.= 128      3.= 0      4.= 0

Step-by-step explanation:

Answer:

128 + 0 = 128

128 - 0 = 128

128 x 0 = 0

128 / 0 = 0

The answer is D because that’s the answer lol

1)

[tex]\bf \cfrac{cot(x)}{sin^2(x)}=\cfrac{csc^2(x)}{tan(x)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{cos(x)}{sin(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{cos(x)}{sin(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos(x)}{sin^3(x)}~\hfill \textit{doing the left-hand-side} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{1}{sin^2(x)}~~}{\frac{sin(x)}{cos(x)}}\implies \cfrac{1}{sin^2(x)}\cdot \cfrac{cos(x)}{sin(x)}\implies \cfrac{cos(x)}{sin^3(x)}~\hfill \textit{doing the right-hand-side}[/tex]

2)

[tex]\bf \cfrac{cos^2(x)+tan(x)}{sec(x)}=cos^3(x)+sin(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~cos^2(x)+\frac{sin(x)}{cos(x)}~~}{\frac{1}{cos(x)}}\implies \cfrac{~~\frac{cos^3(x)+sin(x)}{cos(x)}~~}{\frac{1}{cos(x)}}~\hfill \textit{doing the left-hand side} \\\\\\ \cfrac{cos^3(x)+sin(x)}{\underline{cos(x)}}\cdot \cfrac{\underline{cos(x)}}{1}\implies cos^3(x)+sin(x)[/tex]

The measure of angle K and angle L is 35 degrees and 105 degrees

In Triangle JKL the measure of angle J = 40 and the measure of angle L is 3 times the measure of angle K.

here we assume the angle K be x

So Angle L be 3x

Now

J + K + L = 180

40 + x + 3x = 180

40 + 4x = 180

4x = 180 - 40

4x = 140

x = 35 degrees

So, the angle K be 35 degrees

And, angle L should be 3(35) 105 degrees

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Answer:

B

Step-by-step explanation:

Make an equation.

[tex]\frac{x}{-5}=6[/tex]

[tex]x=-30[/tex]

Answer:

B, -30

Step-by-step explanation:

Answer:  The smallest possible area of the tabletop=[tex]113\text{ square inches}[/tex]

The largest possible area of the tabletop =[tex]1662\text{ square inches}[/tex]

Step-by-step explanation:

Given: The minimum radius of the tabletop = 6 inches

The maximum radius of the tabletop = 23 inches

We know that the area of circle is given by :-

[tex]A=\pi r^2[/tex], where r is the radius of the circle.

Now, the smallest possible area of the tabletop that will fit on Timothy’s table is given by :-

[tex]A_s=(3.14159265359) (6)^2=113.097335529\approx113\text{ square inches}[/tex]

The largest possible area of the tabletop that will fit on Timothy’s table is given by :-

[tex]A_s=(3.14159265359) (23)^2=1661.90251375\approx1662\text{ square inches}[/tex]

Answer:

113 square inches

1,662 square inches

Step-by-step explanation: Have a good day :)

Answer:

1.  does not occur

2. a sample

3. an independent

Step-by-step explanation:

The correct answer for this question would be Occurs, Sample and an independent variable.

A survey is a type of research that involves gathering data from a predetermined group of people in order to get knowledge and insights about a variety of issues.

1) In an observational study, randomization of subjects has to occur to get a lot of diverse information from all the participants.

2) In a survey, randomly a sample is chosen from the population and all the inferences about the population are made from studying this sample only.

3) In a survey a treatment is imposed on all the participants so as to neutralize all the qualities they have which are quite different from the others.

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Answer:

Step-by-step explanation:

The key here is that AB ║ EC. This makes arc AE have the same measure as arc BC. Since those have the same measure as AB and the three arcs together make a semicircle, each has measure 180°/3 = 60°.

Then the various arc measures are:

Then your answers are ...

a) AE = 60°

b) ∠ABD = (1/2)(DE +EA) = (1/2)(100° +60°) = 80°

c) ∠DFC = (1/2)(CD +EB) = (1/2)(80° + (60° +60°)) = 100°

d) ∠P = (1/2)(DA -AB) = (1/2)(100° +60° -60°) = 50°

e) ∠PAB = (1/2)(AB) = (1/2)(60°) = 30°

Answer:

20 bricks

Step-by-step explanation:

So if you multipy the dimentions given, you get 750 inches squred. You now take 15,000 and divide it by 750 to get 20. This is your answer.

A company makes 20 concrete bricks.

Given:

Find:

Solution:

A company makes concrete bricks shaped like rectangular prisms.

So, the volume of the brick = 15*10*5 = 750[tex]inches^{3}[/tex]

Now, to find how many bricks they make we have to divide 750[tex]inches^{3}[/tex] from 15000.

Number of brick = 15000/750 = 20

Hence, the number of bricks that the company makes is 20.

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Answer:

4.7%

Step-by-step explanation:

Kevin's commission was 4.7% of the price of the house.

Answer:

(−4, 12), (1, −3)

Step-by-step explanation:

y = −3x

x^2 −4 = y

so

x^2 −4 = −3x

x^2 + 3x - 4 = 0

(x + 4)(x - 1) = 0

x + 4 = 0; x = -4

x - 1 = 0; x = 1

when x = 1, y = -3(1) = -3

when x = -4, y = -3(-4) = 12

Answer

(-4 , 12), (1 , -3)

ANSWER

(−4,12), (1,−3)

EXPLANATION

The system has equations:

y=−3x

[tex] {x}^{2} - 4 = y[/tex]

We equate the two equations to get:

[tex] {x}^{2} - 4 = - 3x[/tex]

[tex]{x}^{2} + 3x - 4 = 0[/tex]

[tex]{x}^{2} + 4x - x - 4 = 0[/tex]

[tex]x(x + 4) - 1(x + 4) = 0[/tex]

[tex](x + 4)(x - 1) = 0[/tex]

[tex]x = - 4 \: or \: x = 1[/tex]

When x=1,

y=-3(1)=-3

when x=-4, y=-3(-4)=12

The solution is (1,-3) and (-4,12)

Answer:

13. 26

14. The answer is 71

$2,431 is the answer to this problem I think

Answer:

Step-by-step explanation: 6?

Answer:

It's the second choice ⁶√2.

Step-by-step explanation:

Convert to fractional exponents:

√2 = 2^1/2

∛2 = 2^1/3

√2 / ∛2

= 2^1/2 / 2^1/3 = 2^(1/2-1/3)

= 2^(1/6)

Now change back to radicals:

= ⁶√2.

Answer:

The fraction of the fans at the football game that wore both a team T-shirts and team hat is [tex]2\frac{1}{20}[/tex]

Step-by-step explanation:

Let

x----> total fans

we know that

[tex]8\frac{1}{5}x[/tex] ----> wore team T-shirts

Convert to an improper fraction

[tex]8\frac{1}{5}x=8\frac{8*5+1}{5}=\frac{41}{5}x[/tex]

Multiply by 1/4

[tex]\frac{41}{5}x*\frac{1}{4}=\frac{41}{20}x[/tex]

convert to mixed number

[tex]\frac{41}{20}x=\frac{40}{20}+\frac{1}{20}=2\frac{1}{20}x[/tex]

therefore

The fraction of the fans at the football game that wore both a team T-shirts and team hat is [tex]2\frac{1}{20}[/tex]

Final answer:

To solve the exponential equation 7^(3x-1) = 5^(x-1) using properties of common logarithms, we can take the natural logarithm (ln) of both sides. By expanding and isolating x, we can solve for x approximately as x ≈ 0.08.

Explanation:

To solve this exponential equation, you can take the natural logarithm of both sides. The natural logarithm (ln) cancels out the exponential function. So, taking the ln of both sides, we have:

ln(7^(3x-1)) = ln(5^(x-1))

Using the property of logarithms, we can bring down the exponents:

(3x-1)ln(7) = (x-1)ln(5)

Now, we can solve for x by isolating it. Let's expand the equation:

3xln(7) - ln(7) = xln(5) - ln(5)

Combining like terms:

3xln(7) - xln(5) = ln(7) - ln(5)

Factoring out x:

x(3ln(7) - ln(5)) = ln(7) - ln(5)

And finally, dividing:

x = (ln(7) - ln(5))/(3ln(7) - ln(5))

Using a calculator or a math software, we can approximate the value of x to the nearest hundredth to find:

x ≈ 0.08

Answer:

[tex]-x^{2}+4x[/tex]

Step-by-step explanation:

we have

[tex](x^{2}+x)-(2x^{2} -3x)[/tex]

step 1

Eliminate the parenthesis

[tex]x^{2}+x-2x^{2} +3x[/tex]

The symbol of the term 3x is incorrect, must be positive instead of negative

so

[tex]-(-3x)=+3x[/tex]

Group terms that contain the same variable

[tex](x^{2}-2x^{2})+(x+3x)[/tex]

Combine like terms

[tex]-x^{2}+4x[/tex]

Answer:

X x 26= 26x +840

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

Linear model:

E = 24x + 840   where E is the  enrolment .

If there are 900 students then

900 = 24x + 840

24x = 900-840 = 60

For  E < 900 we have the inequality

24x < 60

x < 2.5

As we are dealing in years our answer is

x <  3 years .

she ran 15 miles in the first month and 15 in the second but because it doubled in the third month she ran 30 miles. 15+15+30=60 miles total