If the equation below is solved by graphing, which statement is true?
log(6x+10) = log 1/2 x

a. the curves intersect at approx. x=0.46
b. the curves intersect at approx. x=0.75
c. the curves intersect at approx. x=1.11
d. the curves intersect at approx. x=3.07​

Answer:

First of all, let's find the area of the upper rectangle. We have side lengths 5 and 6, so its area is 30.

Now to find the bottom. If we add our ten, and the five on top, we get a length of 15. We multiply this by 6, giving us 90.

Now we add.

90+30=120

Therefore, our answer is A) 120 square units.

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Step-by-step explanation:

Answer:

r = 6

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportionality

To find k use the condition r = 4 when M = 160

k = [tex]\frac{M}{r^3}[/tex] = [tex]\frac{160}{64}[/tex] = 2.5, so

M = 2.5r³ ← equation of proportionality

When M = 540, then

540 = 2.5 r³ ( divide both sides by 2.5 )

216 = r³ ( take the cube root of both sides )

r = [tex]\sqrt[3]{216}[/tex] = 6

Answer:

B. 1.47*10^18

Step-by-step explanation:

Given

Distance of largest start from earth in light years = 250000

1 light year = 5880000000000 miles

So,

Distance of largest star from earth in miles = 250000 * 5880000000000

= 1470000000000000000 miles

In order to convert in scientific notation, point will be moved 18 places to the left, so the number will become:

1.47* 10^18 miles

So option B is correct..

Answer: OPTION B

Step-by-step explanation:

Scientific notation has the form:

[tex]a10^n[/tex]

Where "a" is a number between 1 and 10 but is not less than 10 and "n" is an integer.

If a light-year is about 5,880,000,000,000 miles and the large star is 250,000 light-years from Earth, then this distance in miles is:

[tex]d=(250,000)(5,880,000,000,000)\\d=1,470,000,000,000,000,000.0\ mi[/tex]

To express this distance in scientific notation, the decimal point must be after the first digit. You can observe that the decimal point must be moved 18 places, then:

[tex]a=1.47[/tex] and  [tex]n=18[/tex]

Therefore, you get that the distance of the large star from Earth in scientific notation is:

[tex]d=1.47*10^{18}\ mi[/tex]

Answer:

Step-by-step explanation:

[tex]\left(\dfrac{4}{7}\right)^r=\dfrac{s}{343}\\\\\dfrac{4^r}{7^r}=\dfrac{s}{7^3}\to r=3\ and\ 4^r=s\\\\4^r=4^3=64\to  s=64[/tex]

Answer:

i believe it would be 1/27 or 0.037 depending on the form you need it in

Step-by-step explanation:

[tex] \bf \underline{Solution-} \\ [/tex]

[tex]\textsf{Given}\\[/tex]

[tex] \sf{ {9}^{ \frac{3}{2} } } \\ [/tex]

[tex] \longrightarrow{ \: ( {3}^{2} {)}^{ \frac{3}{2} } } \\ [/tex]

[tex] \longrightarrow{ \: {3}^ { \cancel2 \times \frac{3}{ \cancel2} } } \\ [/tex]

[tex] \longrightarrow{ {3}^{3} } \\ [/tex]

[tex] \longrightarrow{ \: 3 \times 3 \times 3} \\ [/tex]

[tex] \sf \longrightarrow{ \: 27 \: ans.} \\ [/tex]

[tex]\textsf{Hope this helps!!}\\[/tex]

Answer:

the first one is 23

the second one is 70-79

the third one is 11

Step-by-step explanation:

this is because frequency refers to the amount of people who got the scores on the x-axis.

so for the first one you would count up how many people participated i.e. 2+9+7+5 = 23

the second one is asking for the mode test score and mode refers to the most common, so the most common test score is the 70-79 bar

the third one is asking for how many people scored below 80, which is 11 as 2 people scored 60-69 and 9 scored 70-79 on the test (2+9=11)

Hope this helps :)

the answer is 23

hope this helps

Answer:

∛4²

Step-by-step explanation:

A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.

To write an exponent in radical form , the denominator, or index goes in front of the radical, and the numerator goes inside of the radical. We raise the base to the power of the numerator

4 2/3

∛4².

The radical form of 4 2/3 is the cube root of 4 squared, denoted as √(4^2).

The radical form of the expression 4 2/3 means expressing the number as a radical, which refers to roots of numbers. In this case, the number 2/3 is the exponent in fractional form. To convert this into a radical, the numerator indicates the power and the denominator indicates the root. Therefore, 42/3 can be expressed as the cube root of 4 squared. The cube root is denoted by the radical symbol √ with a small three above or to the left of the radical. Thus, 42/3 = √(42).

Answer:

Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1). This latter form can be more useful for many problems that involve polynomials.

Step-by-step explanation:

The quotient in polynomial division refers to the result of dividing one polynomial by another. When a polynomial S is divided by a polynomial P, the result is a quotient Q of a degree less than P. The quotient Q represents a rational function when it is derived from the division of two polynomials.

In terms of algebra, let's consider a polynomial P of degree n, and we divide another polynomial S with a degree less than 2n by P. The result is a quotient Q and a remainder R, both of which are polynomials and Q has a degree less than n. If P(x) has a degree higher than Q(x), one can use the method of long division to find the quotient. This quotient, Q, alongside the remainder, R, conforms to the relation S(x) = P(x)\Q(x) + R, where Q and R are of lesser degrees than P.

When dealing with rational functions, we often find ourselves in positions of evaluating expressions formed by dividing polynomials. These functions are called rational functions, which are essentially the quotient of two polynomials. Applying the quotient rule can simplify differentiable polynomial functions and is useful when finding limits or derivatives in calculus.

Answer:

The probability is 1/15 or 6.67%

Step-by-step explanation:

step 1

Find the probability that when she shakes the piggy bank a half-dollar fall out

P=2/15

step 2

Find the probability that when she shakes the piggy bank a dime fall out

P=7/14

step 3

Find he probability that when she shakes the piggy bank a half-dollar and then a dime fall out

P=(2/15)(7/14)=1/15

Convert to percentage

(1/15)*100=6.67%

Answer:

[tex]x_1=-4\\\\x_2=\frac{1}{3}[/tex]

Step-by-step explanation:

Given the quadratic equation:

[tex]2x^2+14x-4=-x^2+3x[/tex]

You can follow these steps in order to solve it:

- Make the equation equal to 0:

[tex]2x^2+14x-4+x^2-3x=0[/tex]

- Now, add the like terms:

[tex]3x^2+11x-4=0[/tex]

- Finally, apply the Quadratic formula ([tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]):

In this case we know that:

[tex]a=3\\b=11\\c=-4[/tex]

Therefore, substituting values into the Quadratic formula and evaluating, we get:

[tex]x=\frac{-11\±\sqrt{11^2-4(3)(-4)} }{2(3)}\\\\x_1=-4\\\\x_2=\frac{1}{3}[/tex]

To find the solutions to the quadratic equation 2x^2+14x-4=-x^2+3x, we need to rearrange the equation and use the quadratic formula.

The quadratic equation is 2x^2+14x-4=-x^2+3x. To find the solutions, we need to rearrange the equation in the form ax^2 + bx + c = 0. Combining like terms, we get 3x^2 + 11x - 4 = 0. Now we can use the quadratic formula to find the solutions:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values a = 3, b = 11, and c = -4 into the formula, we can calculate the solutions.

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Answer:

Step-by-step explanation:

Just use the slope equation.

ANSWER

Option D

EXPLANATION

The parent radical function is

[tex]f(x) = \sqrt{x} [/tex]

The transformed function is

[tex]g(x) = 2 \sqrt{x - 3} [/tex]

This is a transformation of the form.

[tex]y = a \sqrt{x - k} [/tex]

which shifts the parent function horizontally by k units to the right and stretches the parent function vertically by a factor of 'a'.

In this case a=2 and k=3,

there is a horizontal shift of 3 units to the right and a vertical stretch by a factor of 2.

The last choice is correct.

This is the answer (I believe): 18 + x = 29

Answer:

11

Step-by-step explanation:

29-18 is 11

Answer:

77 inches

Step-by-step explanation:

Given

1 inch = 3 miles in map

We are also given the actual distance between City A and City B = 231 miles.

In order to get the distance in inches = Distance between City A and City B in miles/ 3

We are dividing the distance by 3 to get the distance in inches.

So,

Distance on map = 231/3

= 77 inches

Answer: 77 inches.

Step-by-step explanation:

You know that this map uses this scale:

[tex]1in=3mi[/tex]

This means that 1 inch in the map represents 3 miles.

In this case, you know that the actual distance between City A and City B is 231 miles, then, to find the distance between the cities on the map, you can set up de following proportion:

[tex]\frac{1in}{3mi}=\frac{x}{231mi}[/tex]

Now, you need to solve for "x":

[tex](231mi)(\frac{1in}{3mi})=x\\\\x=77in[/tex]

Answer:

c. 10

Step-by-step explanation:

First of all, the sum can be simplified.

[tex]\sum\limits^6_{n=1} {(x-3n)}=\sum\limits^6_{n=1} {x}-3\sum\limits^6_{n=1} {n}\\\\=6x-3\cdot\dfrac{6\cdot 7}{2} =6x-63[/tex]

This result can be used in the equation ...

6x -63 = -3

6x = 60 . . . . . add 63

x = 10 . . . . . . . divide by 6

_____

Comment on the ∑n

The sum of numbers 1 to n is n(n+1)/2. We have used that fact here. For this problem, the sum is short enough you can simply add it up: 1+2+3+4+5+6 = 21.

[tex]\bf \displaystyle\sum\limits_{n=1}^{6}~(x-3n)=-3\implies \sum\limits_{n=1}^{6}~x-\sum\limits_{n=1}^{6}~3n=-3\implies \sum\limits_{n=1}^{6}~x-3\sum\limits_{n=1}^{6}~n=-3 \\\\\\ 6(x)~~-~~3\left[ \cfrac{6(6+1)}{2} \right]=-3\implies 6x~~-~~3[3(7)]=-3\implies 6x - 63 = -3 \\\\\\ 6x=60\implies x=\cfrac{60}{6}\implies x=10[/tex]

Answer:

[tex]7.7n=112.42[/tex]

[tex]n=14.6[/tex]

Step-by-step explanation:

The product is the result obtained by multiplying two factors. Then, the sentence ""The product of a number n and 7.7 equals 112.42" can be expressed with the following equation:

[tex]7.7n=112.42[/tex]

To solve for the variable "n", you has two apply the Division property of equality and divide both sides of the equation by 7.7

Therefore, the value of "n" is:

[tex]\frac{7.7n}{7.7}=\frac{112.42}{7.7}\\\\n=14.6[/tex]

Answer:

m∠8 = 4x

Step-by-step explanation:

Angle 8 is the same angle measure of angle 1, which is m∠1 = 4x

A. f(-3) = -11

If the function is f(x) = 2x - 5, then just replace x with -3 to find f(-3).

f(-3) = 2(-3) - 5

Multiply 2 times -3.

f(-3) = -6 - 5

Subtract -6 minus 5.

f(-3) = 11

There’s the answer.

Answer:

-11

Step-by-step explanation:

If you substitute x with -3 in the equation then you will get -11. Have a good night/day!

=)

Answer:

637

Step-by-step explanation:

Ticket ending 00= £12 * 7 = £84  

Tickets ending 5 = £1.5 * 75 = £112.5  

£84+£112.5=£196.5  

Price money + Profit: £196.5+£163= 356

356/£0.5 = 719 total tickets sold

719- 82 (WINNING TICKETS) = 637 losing tickets sold

Tomas made £232.5 from the winning tickets. Subtracting his profit of £163, we see he made £69.5 from the losing tickets. At a price of £0.5 per ticket, that means he sold 139 losing tickets.

First, calculate the total amount Tomas made by selling all the winning tickets. There are ten tickets that end in '00' between 1 and 750, each valued at £12, i.e., £120. There are 75 tickets that end in '5' between 1 and 750, each valued at £1.50, i.e., total of £112.50. So, the total income from these tickets is £120 + £112.50 = £232.5.

Then, subtract Tomas's profit from the total income of the winning tickets to get the total revenue from the losing tickets. So, £232.5 - £163 = £69.5. Given each ticket costs 50p or £0.5, divide £69.5 by £0.5 to find the number of losing tickets sold. That is, £69.5/£0.5 = 139. Thus, Tomas sold 139 losing tickets.

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Answer: 4 + (-1)^10 = 4+ 1 = 5

The tenth term of the sequence is 5.

Given to us,

Sequence, [tex]\bold{a_n=4+(-1)^n}[/tex]

For tenth term,

n = 10,

Subsituting the value of n we get,

[tex]{a_n=4+(-1)^n}\\a_{10}=4+(-1)^{10}\\a_{10} = 4 + 1\\a_{10} = 5[/tex]

Hence, the tenth term of the sequence is 5.

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The value of the expression is 14.

Answer:

Part 1) The equation for the monthly charges for Runfast is [tex]y=8x+8[/tex] and for BA&D is [tex]y=4x+15[/tex]

Part 2) The solution of the system of equations is the point  (1.75.22)

Step-by-step explanation:

Let

x -----> the number of gig of data

y -----> the total monthly charges

we know that

Runfast Company

[tex]y=8x+8[/tex] -----> equation A

BA&D Company

[tex]y=4x+15[/tex] -----> equation B

Part 2) Use your mathematical skill to solve this system of equations using the substitution method

we have

[tex]y=8x+8[/tex] -----> equation A

[tex]y=4x+15[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]4x+15=8x+8[/tex]

[tex]8x-4x=15-8[/tex]

[tex]4x=7[/tex]

[tex]x=1.75\ Gb[/tex]

Find the value of y

[tex]y=8(1.75)+8=\$22[/tex]

so

The solution is the point (1.75.22)

That means

For the number of gig equal to 1.75 the monthly charge is equal to $22 in both company's

therefore

For a number of gigs less than 1.75 the company Runfast has the better pricing, while for a number of gigs greater than 1.75 the company BA&D has the better pricing

By buying 9 packs of 4 cartons and 2 single cartons, Lewis was able to spend the least amount of money to get the 38 cartons he needed. The total cost was £14.94.

The subject of this question is mathematics, specifically cost optimization and arithmetic. Lewis can buy single carton of juice for 45p or a pack of 4 cartons for £1.56. The goal is to minimize the cost. First, Lewis can start by buying packs of 4. The number of 4-carton packs he can buy is 38 divided by 4 which gives you 9 packs that include 36 cartons. He then needs to buy 2 more single cartons to reach 38. So, the total cost is 9 packs times £1.56/pack plus 2 single cartons times 45p/carton. Doing the arithmetic:

Convert 90p to pounds that is £0.90. Adding both gives £14.94. Therefore, Lewis spent a total of £14.94 on juice cartons.

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y = 4x - 10. The linear functions y = 4x - 10 represent the line given by the point-slope equation y - 2 = 4(x - 3).

In order to solve this problem, we have to take the point-slope equation y - 2 = 4(x - 3) and convert it to the linear function form y = mx + b as follow:

y - 2 = 4(x - 3)

y - 2 = 4(x) - (4)(3)

y - 2 = 4x - 12

y - 2 + 2 = 4x -12 +2

y = 4x - 10 (Linear function)

The answer is I. 8

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

Answer:

option A

f(x) = (x – 1)2 + 3

Step-by-step explanation:

Given in the question a function,

f(x) = 4 + x² – 2x

f(x) = 4 + x² – 2x

here a = 1

        b = -2

        c = 4

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

ANSWER

The vertex form is

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

EXPLANATION

The given function is

[tex]f(x) = 4 + {x}^{2} - 2x[/tex]

This is the same as:

[tex]f(x) = {x}^{2} - 2x + 4[/tex]

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} - 2x + {( -1 )}^{2} - {( -1 )}^{2} + 4[/tex]

[tex]f(x) = {x}^{2} - 2x + 1 - 1 + 4[/tex]

The first three term is a perfect square trinomial:

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

The vertex form is

[tex]f(x) = {(x - 1)}^{2} + 3[/tex]

Answer:

about 785.4

Step-by-step explanation:

The circumference of a circle is pi times the diameter:

C = πd

C = π·(250 ft) ≈ 785.4 ft

_____

Most scientific or graphing calculators have the value of π built in. If yours doesn't, a value good for at least 6 significant figures is the ratio 355/113.

The ferris wheel rotates approximately 785 feet in one complete turn. This was calculated using the circumference formula, 2πr, with the radius derived from the given diameter of 250 feet.

To solve this problem, we need to determine the circumference of the Ferris wheel as that would be equivalent to the distance the ferris wheel rotated in one complete turn. The formula to calculate the circumference of a circle (or ferris wheel in this case) is 2πr (2 times pi times the radius), where 'r' is the radius of the circle. However, since we're given the diameter of the Ferris wheel as 250 feet, we know that the radius 'r' would be half of the diameter. That would imply that the radius in this case is 250/2 = 125 feet. So, using the aforementioned formula, the circumference would therefore be 2 × π × 125, or approximately 785 feet. Therefore, with each complete turn, the Ferris wheel would rotate by about 785 feet.

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Answer:

Step-by-step explanation:

[tex]x^o\ \text{and}\ \left(\dfrac{2}{3}x\right)^o\ \text{are suplementary angles, therefore}\\\\x^2+\left(\dfrac{2}{3}x\right)^o=180^o\\\\x+\dfrac{2}{3}x=180\qquad\text{multiply both sides by 3}\\\\3x+2x=540\\\\5x=540\qquad\text{divide both sides by 5}\\\\x=108[/tex]

THE ANSWER ABOVE/ BELOW IS WRONG!!!

The correct answer is actually:

140

Answer:

140

Step-by-step explanation:

Answer:

Final answer is [tex]x=9[/tex].

Step-by-step explanation:

we know that if BD is angle bisector of angle B in triangle ABC then

[tex]\frac{AB}{BC}=\frac{AD}{DC}[/tex]

[tex]\frac{36}{28}=\frac{x}{DC}[/tex]

[tex]\frac{36}{28}=\frac{x}{16-x}[/tex]

[tex]\frac{9}{7}=\frac{x}{16-x}[/tex]

cross multiply

[tex]7x=9(16-x)[/tex]

[tex]7x=144-9x[/tex]

[tex]7x+9x=144[/tex]

[tex]16x=144[/tex]

[tex]x=\frac{144}{9}[/tex]

[tex]x=9[/tex]

Hence final answer is [tex]x=9[/tex].