Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. Select all that apply. f(x)=2(3)^x g(x)=10log(x+3)

Answer:

9.4 units

Step-by-step explanation:

To find the distance between two points D ( 1, 3 ) and H ( 9, 8 ), we can use the distance formula:

d = √(( x₂ - x₁ )² + ( y₂ - y₁ )² )

Substituting the coordinates, we have:

d = √( ( 9 - 1 )² + ( 8 - 3 )²)

Simplifying,

d = √( 8² + 5² )

d = √( 64 + 25 )

d = √89

d ≈ 9.4 units

The distance between point D and H to the nearest tenth is 9.4 units

The distance between two points is the length of the line segment joining them. Since the length of the line segment cannot be negative, the distance between two points is always positive.

The distance between two points is expressed as

S = √ X -x)² + (Y -y)²

= √ 9-1)² + 8-3)²

= √ 8² + 5²

= √ 64 +25

= √89

= 9.4 ( nearest tenth)

Therefore the distance between point D and H to the nearest tenth is 9.4 units

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To feed 58 people at the party there should be 10 cakes.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Desmond knows that 2 cakes will feed 11 people. If he is inviting 58 people to his parent's anniversary party.

The number of cakes for 58 people will be calculated as,

11 people = 2 cakes

1 person = 2 / 11

58 people = ( 58 x 2 ) / 11

58 people = 10 cakes

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Answer:

[tex]f(7)=\frac{-5}{3}[/tex] or [tex]f(7)=-1.67[/tex]

Step-by-step explanation:

We are given the following function of x and we are to find the value of [tex] f ( 7 ) [/tex]:

[tex] f ( x ) = \frac { 3 } { x + 2 } - \sqrt { x - 3 } [/tex]

Substituting the given value (7) in the above function to get:

[tex]f(x)=\frac{3}{x+2}-\sqrt{x-3}[/tex]

[tex] f ( 7 )= \ frac{3}{7+2}-\sqrt{7-3}[/tex]

[tex] f(7) = \frac { 3 } { 9 } - \sqrt { 4 } [/tex]

[tex]f(7)=\frac{1}{3}-2[/tex]

[tex]f(7)=\frac{1}{3}-\frac{6}{3}[/tex]

[tex]f(7)=\frac{-5}{3}[/tex] or [tex]f(7)=-1.67[/tex]

Answer:

s - 8

Step-by-step explanation:

TO find the function rule, substitute (s-2) in place of v. Then simplify.

h(v) = v - 6

h(s - 2) = (s - 2) - 6

h(s - 2) = s - 8

Answer: The graph is attached.

Step-by-step explanation:

The region is limited by two lines:

[tex]x+y=6[/tex] and [tex]x=4[/tex]

You can write the first inequlity [tex]x+y\leq6[/tex] in the following form:

[tex]y\leq-x+6[/tex]

This region are all the values for which the y-axis is less than the line f(x)=x+6 (all the values under the line).

The other inequality  x ≤ 4 are all the values for which the x-axis is less than the line x=4 (all the values to the left of the line).

Observe the graphs attached.

Answer:

its this one

Step-by-step explanation:

so the difference is 975 - 828.75 = 146.25.

now, if we take 975 to be the 100%, what is 146.25 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 975&100\\ 146.25&x \end{array}\implies \cfrac{975}{146.25}=\cfrac{100}{x}\implies 975x=14625 \\\\\\ x=\cfrac{14625}{975}\implies x=15[/tex]

4.0003 x 10^7 is already in scientific notation. If you mean in regular notation/as a regular number, it is 40003000. Since it is 10 to the power of positive 7, you move the decimal place 7 to the right.

Answer:

40,003,000

Step-by-step explanation:

The given number is :

[tex]4.0003\times 10^{7}[/tex]

As we can see that [tex]4.0003\times 10^{7}[/tex] is already in scientific notation.

Scientific notation means writing numbers in powers of 10.

Hence, we can write this notation in regular way as:

40,003,000

Answer:

Step-by-step explanation:

(a) In order to use the elimination method, multiply the second equation by 2.

It becomes 2x + 4y = 20.

Subtract that from the first equation: 3x + 4y = 12

3x + 4y - 2x - 4y = 12 - 20

x = -8

Put that back in the second equation: -8 + 2y = 10

2y = 18

y = 9

(b) In order to use the substitution method, subtract 2y from the second equation.

It becomes x + 2y - 2y = 10 - 2y

x = 10 - 2y

Substitute that into the first equation:

3(10 - 2y) + 4y = 12

30 - 6y + 4y = 12

30 - 2y = 12

2y = 18

y = 9

Put back into the equation for x:

x = 10 - 2(9)

= 10 - 18

= -8

Answer:

Step-by-step explanation:

(1) 3x + 4y = 12

(2) x + 2y = 10

(2)*3: 3x+6y=30

by elimination (2)*3 - (1)

6y-4y=30-12

2y=18

y=9

x+2(9)=10

x=-8

rearrange (2): x=10-2y

substitute in (1): 3(10-2y)+4y=12

30-6y+4y=12

2y=30-12

y=9

x=10-2(9)

=-8

same ans either way

Answer:

We shall use the method of splitting the middle term

To factorize

3x² - 10 x + 8

We need two numbers which add to give -10 and multiply to give 3 × 8 = 24

The numbers are -6 & -4

(-6)+(-4) = -10

(-6)(-4) = 24

So we shall split -10x as -6x - 4x

We get

3x² -10x + 8

= 3x² -6x -4x+8

Taking out 3x common from first two terms & -4 from the lest two terms we get

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

Taking out (x-2) common we get

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

So

3x² - 10x + 8 = (x-2)(3x-4)

Answer:

2 and 3

Step-by-step explanation:

on EDGE 2021

Answer:

THE THIRD ONE I THINK :D

Answer:

C

Step-by-step explanation:

To divide 3 by 3/5

Leave the 3, change division to multiplication and turn the fraction upside down, that is

3 ÷ [tex]\frac{3}{5}[/tex]

= 3 × [tex]\frac{5}{3}[/tex]

= [tex]\frac{3(5)}{3}[/tex] = [tex]\frac{15}{3}[/tex] = 5 → C

Answer:

first one

Step-by-step explanation:

first one

1^13 = 1

1^15 = 1

P.S.

1 to the exponent of any number is equal 1

Answer:

1¹³ and 1¹⁵

Step-by-step explanation:

The answer does not change however we add or reduce the exponents. This is the uniqueness of the integer 1. When the others are tried, 6¹=6 and 9¹=9

7⁸=5764801 and 8⁷=2097152

9²=81 and 4³=64

Therefore the integer 1 is the only number that is not affected by exponents.

Answer:

0.5amps

Step-by-step explanation:

I is inversely proportional to resistance

I = k/R

k = I/ R

k = 20/5

k = 4

This means that, I = 4/R

So, when R = 8ohms,

I = 4/8

 =0.5amps

Using Ohm's law, the inverse relationship between current and resistance in a simple circuit allows calculation of the new current as 12.5 amps when the resistance changes from 5 ohms to 8 ohms.

The student's question involves an application of Ohm's law, which is a fundamental principle in Physics that relates electric current (I), resistance (R), and voltage (V). According to Ohm's law, in a simple circuit, the current is inversely proportional to the resistance when the voltage is held constant. Given that the current is 20 amps when the resistance is 5 ohms, we can write the relationship as I1 * R1 = I2 * R2 where I1 and R1 are the initial current and resistance, and I2 and R2 are the final current and resistance we wish to find.

Plugging in the given values, we have:

20 amps * 5 ohms = current when resistance is 8 ohms * 8 ohms

Solving for the current when the resistance is 8 ohms:

20 amps * 5 ohms = I2 * 8 ohms

100 = I2 * 8

I2 = 100 / 8

I2 = 12.5 amps

Therefore, the current when the resistance is 8 ohms is 12.5 amps.

The answer is C. Hope this helps!

Answer:

B

Step-by-step explanation:

use the exponent rule of division: you just subtract the exponents if the base is the same, so 4-8=-4

The fraction with a numerator of 3.74 x 10⁻¹⁶ and a denominator of 10⁻³⁰ represented as a single exponential expression is 3.74 x 10¹⁴, obtained by dividing the digit terms and subtracting the exponents.

To represent the fraction as a single exponential expression, you follow the division of exponentials rule, which involves dividing the digit terms and subtracting the exponents of the exponential terms. Given the fraction with a numerator of 3.74 x 10-16 and a denominator of 10-30, you would divide 3.74 (the digit term of the numerator) by 1 (the implied digit term of the denominator) which is just 3.74, and subtract the exponents (-16 - (-30)) which equals 14. Therefore, the fraction as a single exponential expression is 3.74 x 1014.

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Answer:

y  = x+3;  y = -2x +5

Step-by-step explanation:

x + 3 = -2x + 5

Let   y = x + 3 = -2x + 5

If a = b = c then a=b and a=c

we can write the equation as

y = x + 3 and y = -2x + 5

Thus, this is the system of equations

y = x + 3

y = -2x + 5

Answer:

y = x + 3 and y = -2x + 5

Step-by-step explanation:

If we consider one set of equation as:

[tex] y = x + 3 [/tex]

and the other set of equation as:

[tex] y = - 2 x + 5 [/tex]

Since the left hand side for both these equations is same, therefore we can equate the right hand side and write it as:

[tex] x + 3 = - 2 x + 5 [/tex]

zoom out a little i cant see it that well

Answer:

The answer is (b) ⇒[tex]\frac{d^{5} }{2\sqrt{c} }[/tex]

Step-by-step explanation:

∵ [tex]\frac{\sqrt{c^{2}d^{6}}}{\sqrt{4c^{3}d^{-4}}}[/tex]

∵ √x² = x ⇒ that means to cancel the square root divide

  the power by 2

∴ [tex]\sqrt{c^{2}d^{6}}=cd^{3}[/tex]

∵ √4 = 2 ⇒ √2×2 = √2² = 2

∵ √c³  = [tex]c^{\frac{3}{2}}[/tex]

∴ [tex]\sqrt{4c^{3}d^{-4}}=2c^{\frac{3}{2}}d^{-2}[/tex]

∴ [tex]\frac{cd^{3}}{2c^{\frac{3}{2}}d^{-2}}[/tex]

∵ In the same base with multiplication we add the power,

  in same base with division we subtract the power

∴ [tex]\frac{1}{2}c^{1-\frac{3}{2}}d^{3-(-2)}=\frac{1}{2}c^{\frac{-1}{2}}d^{5}=[/tex]

  [tex]\frac{d^{5}}{2c^{\frac{1}{2}}}=\frac{d^{5}}{2\sqrt{c}}[/tex] ⇒  [tex]c^{\frac{1}{2}}=\sqrt{c}[/tex]

∴ The answer is (b) ⇒ [tex]\frac{d^{5}}{2\sqrt{c}}[/tex]

Answer:

b. [tex]\frac{d^{5}}{2\sqrt{c} }[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{\sqrt{c^2d^6} }{\sqrt{4c^3d^{-4}} }[/tex]

We simplify the radicand using the property;  [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

[tex]\frac{\sqrt{d^{6--4}} }{\sqrt{4c^{3-2}} }[/tex]

[tex]\frac{\sqrt{d^{10}} }{\sqrt{4c^{1}} }[/tex]

[tex]\frac{d^{5}}{2\sqrt{c} }[/tex]

Answer: [tex]8x+36[/tex]

Step-by-step explanation:

To simplify the expression you must apply the Distributive property.

Keep on mind that:

- According to the Distributive property, the product of the difference is equal to the difference of the products:

[tex]a(b-c)=ab-ac[/tex]

- Remember the multiplication of signs:

(-)(-)=+

(+)(+)=+

(-)(+)=-

Then, you obtain the following:

[tex](-2x-9)(-4)=8x+36[/tex]

Answer: The correct answer is 8x - 36.

Step-by-step explanation: I am 98% sure.

Answer:

The swimming pool lost 500,000 liters

Step-by-step explanation:

Now it only has .5 million liters now

Answer:

1. Count the total number of items. In this chart the total is

2. Divide the count (the frequency) by the total number.

3. Then, convert it to a percent.

Answer:

The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.

Step-by-step explanation:

The length of the chord AB is the same as the distance OC from the center to the cord. Let OC=2x, then CA=x. By the Pythagorean theorem, the radius r of the circle is

[tex]r^2=OC^2+AC^2,\\ \\r^2=(2x)^2+x^2=5x^2,\\ \\r=\sqrt{5}x.[/tex]

The length of the arc ED is 4x.

Consider right triangle EFO. In this triangle, EF=2x, EO=r, then the distance OF is

[tex]OF^2=OE^2-EF^2,\\ \\OF^2=5x^2-(2x)^2=x^2,\\ \\OF=x.[/tex]

The distance from the center of the circle to the longer chord is twice smaller than the distance from the center to the shorter chord.

The distance between the second chord from the center of the circle is 'a' (half the length of the first chord).

A circle chord is a straight line segment with both endpoints on a circular arc.

As the length of a chord is equal to its distance to the center of the circle, therefore, the length of the chord and the distance to the center of the circle is 2a. Thus, In ΔAOB the length of the third side of the triangle can be written as,

[tex]OA^2= OB^2+AB^2\\\\OA^2 =(2a)^2+a^2\\\\OA^2=5a^2\\\\OA = a\sqrt5[/tex]

Now, OA and OQ are the radii of the circle and the length of the radius of the circle is a√5 units.

Now, the length of the second chord in the same circle is twice as long as the first one, therefore, the length of the half chord is 2a. Therefore, in ΔAOB the length of the perpendicular side of the triangle can be written as,

[tex]OQ^2=OP^2+PQ^2\\\\(a\sqrt5)^2= OP^2+(2a)^2\\\\5a^2-4a^2=OP^2\\\\OP = a[/tex]

Hence, the distance between the second chord from the center of the circle is 'a' (half the length of the first chord).

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Answer:

g(x) = 4/5 x² - 4

Step-by-step explanation:

∵ f(x) = 2/5 x² - 2

∵ f(x) stretched vertically by scale factor 2

∴ g(x) = 2[f(x)]

∴ g(x) = 2[2/5 x² - 2] = 4/5 x² - 4

The resulting function is g(x) = [tex]\( \frac{4}{5} x^2 - 4 \).[/tex].

Given the function f(x) = [tex]\( \frac{2}{5}x^2 - 2 \)[/tex] and the function g(x) representing a vertical stretch of f(x) by a factor of 2, we need to find the equation of g(x).

A vertical stretch of a function f(x) by a factor of k means multiplying the function by k. Here the factor k is 2.

So, the equation of g(x) will be:

Substitute f(x) into the equation:

Distribute the 2:

Therefore, the equation for g(x) after a vertical stretch by a factor of 2 is g(x) = [tex]\( \frac{4}{5} x^2 - 4 \)[/tex].

Answer:

First Option

Step-by-step explanation:

The number of solutions is given by the values in which the equation of the circumference is equal to the equation of the line.

In other passwords the number of solutions is equal to the number of times the line intersects or touches the circumference.

Notice in the graph that the line does not touch the circumference.

Therefore for this case there are no solution

Answer:

The answer is A (no solution)

Step-by-step explanation:

Answer:

3^9

Step-by-step explanation:

We we multiply exponents with the same base, we can add the exponents

a^b * a*c = a^(b+c)

3^5 * 3^4

3^(5+4)

3^9

Answer:

The slope of Function A is greater than the slope of function B  while the y-intercept of Function  B is greater than the y-intercept of function A.

Step-by-step explanation:

Function A is f(x) = 5x + 2

The slope is 5 and the y-intercept is (0, 2).

Function B. The slope is  (5-2) / (0- -1) = 3.

also (8-5) / (1 - 0) = 3

The slope is 3.

The y-intercept is at (0, 5) because one point on the graph is (0, 5).

Answer:

Their slopes are equal but y-intercepts are not equal.

Step-by-step explanation:

Its simple arithmatics

Answer:1846.32

Step-by-step explanation:

3.14 times 7 squared times 12 equals 1846.32

The answer should be 1846.32 ft³

Answer:

59

Step-by-step explanation:

Substitute.

6 ^ 2 = 36

36 + 23 = 59

Answer:

$11.67

Step-by-step explanation:

14 (the price he sold it for) = x + 1/5(x) (how much he upped the price)

14 = 6/5x

x = 11.67

To check find 20% of 11.67 which is 2.33 and add them together, which equals  $14, so it checks out.

Answer:

Step-by-step explanation:

A motorcycle dealer paid a certain price for a motorcycle

certain price = x

And marked it up by 1/5 of the price he paid.

marked price = 6/5x

Because x + 1/5x = 6/5x

Later, he sold it for $14.

6/5x = 14

1/5x = 14/6

x = 14/6 * 5

14 * 5 = 70

70/6 = 35/3

x = 35/3

x = 35/3 = $11.666666667

Substitute this back in to check it's right.

11.666666667 * 6/5 = 14

To find out how much the grocer spent on marketing last year, we need to set up an equation with x as the original budget. By solving the equation, we find that the grocer spent approximately $1511.63 on marketing last year.

To find out how much the grocer spent on marketing last year, we first need to determine the original marketing budget. Since the grocer cut their marketing budget by 57%, this means they spent only 43% of their original budget this year. Let's represent the original budget as 'x'.

Therefore, the grocer spent approximately $1511.63 on marketing last year.