Please find the area of the shaded region.

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:

545454

Step-by-step explanation:

This is a ratio.  you take 666/333 = x/272727.  Basically tis says 666 cm to 333 m is equal to some number of centimeters to 272727 meters.  Then just solve for x.  272727(666/333) = 545454.

Another way of looking at it is what did we multiply 333 by to get 666.  Answe is 2, so we do the same  for 272727.  2*272727 = 545454

If you wanted to you could have also converted units so everything was in either centimeters of meters, but as long as you keep things in the right order this works.  

Answer: the number of centimetres is 54cm

Step-by-step explanation:

Given that 6 centimeters represents 3meters.

The number of centimeters on the blue print that will represent an actual distance of 27meters will be Y

6 : Y = 3 : 27

That is

6/Y = 3/27 = 1/9

Cross multiply

Y = 54 cm

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.

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: Madeline is 20 yrs old

Step-by-step explanation:

If Laura is 50 and she is 10 years older than Raena then Raena is 40 that would then make Madeline 20 years old.

Final answer:

To determine Madeline's age, we set up an equation based on the given relationship and solved it to find that Madeline is 20 years old.

Explanation:

To solve the question about Raeana, Madeline, and Laura's ages, we first define the variables. Let's denote Madeline's age as M. Since Raeana is twice as old as Madeline, Raeana's age would be 2M.

The problem states that Laura is 10 years older than Raeana, making Laura's age 2M + 10. Given that Laura is 50 years old, we can set up an equation: 2M + 10 = 50.

Now, we solve for M:
Subtract 10 from both sides of the equation to isolate the term with M on one side: 2M = 40.

Divide both sides by 2 to solve for M: M = 20.

Therefore, Madeline is 20 years old.

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:

The swimming pool lost 500,000 liters

Step-by-step explanation:

Now it only has .5 million liters now

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:

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

zoom out a little i cant see it that well

Answer:

A

Step-by-step explanation:

With this question, its actually way easier than you think. If you want to find corresponding angles, you have to find a way to make the shapes overlap to be exactly the same. If they cannot be exactly the same, there will not be corresponding angles. For this, if you rotate quadrilateral 90 degrees counter-clockwise, you will see that the shapes look the same. Then you can just match up the angles that have the same degree measure (or just look the same for simplicity) and you have your answer. The answer is actually in the question too. ABCD=JKLM, but each letter is actually in the right place. A=J B=K C=L D=M.

Hope this helped! ^-^

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 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: [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:

[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]

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:

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:

Stacy

Step-by-step explanation:

4.23 < 4.3

Stacy is 0.07 feet taller than Erik, as of the given conditions.

Given that,
Erik is 4.23 feet tall. Stacy is 4.3 feet tall.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Heights
Stacy = 4.3 feet
Erik = 4.23 feet
Difference = 4.3 - 4.23 = 0.07 feet

Thus, Stacy is 0.07 feet taller than Erik, as of the given conditions.

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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

Answer:

C

Step-by-step explanation:

Each of the tables is a linear relationship. Linear relationships increase or decrease steadily by adding or subtracting a constant. Table A increases by 5. Table B decreases by 2. Table C doesn't change. Table D increase by 4.

A "no change" means the y values never change. The constant is 0 and is a horizontal line. Table C is the solution.

Answer:

Option C.

Step-by-step explanation:

Linear relationship : If the relation between variables is represent by a non vertical straight line, then it is called a  linear relationship.

Horizontal line is a special case of linear relationship. It is know as no change linear relationship. It means the output value remains same for each input value.

In option C, the given table is  

x      y

14    12

20   12

26   12

32   12  

Only in option C, the y-values are constant. So, it represents no change linear relationship.

Therefore the correct option is C.

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:

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

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]

The function could be used to model this situation is D. y = 2ˣ.

The function that could be used to model the situation where the number of bacteria, y, in a certain area doubles every hour, x, is: D. y = 2ˣ

This function represents exponential growth, where the number of bacteria doubles every hour.

The variable x represents the number of hours, and 2^x represents the doubling of the bacteria population over time.

QUESTION 1

If f(x)=1-x² and g(x)=1-x,

Then,

(f-g)(x)=f(x)-g(x)

This implies that,

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

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

We simplify to get,

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

The correct choice is B.

QUESTION 2

Given:

f(x)=3+x

and

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

[tex](f\circ g)(x)=f(g(x))[/tex]

[tex](f\circ g)(x)=f( {x}^{2} + 1 )[/tex]

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

[tex](f\circ g)(x)= {x}^{2} +4[/tex]

Also,

[tex](g\circ f)(x)=g(f(x))[/tex]

[tex](g\circ f)(x)=g( 3+ x)[/tex]

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

[tex](g\circ f)(x)= 9 + 6x + {x}^{2} + 1[/tex]

[tex](g\circ f)(x)= {x}^{2} + 6x + 10[/tex]

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:

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:

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.

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:

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.