"I think of a number multiply if by itself and add 4 to the result"

Answer:

C) Both

Step-by-step explanation:

The given equation is:

[tex]0=(3x+2)(x-4)[/tex]

To solve the given equation, we can use the Zero Product Property according to which if the product A.B = 0, then either A = 0 OR B = 0.

Using this property:

[tex](3x+2) = 0 \Rightarrow \bold{x = -\frac{2}{3}}\\(x-4) = 0 \Rightarrow \bold{x = 4}[/tex]

So, Erik's solution strategy would work.

Now, let us discuss about Caleb's solution strategy:

Multiply [tex](3x+2)(x-4)[/tex] i.e. [tex]3x^2-12x+2x-8[/tex] = [tex]3x^2-10x-8[/tex]

So, the equation becomes:

[tex]0=3x^2-10x-8[/tex]

Comparing this equation to standard quadratic equation:

[tex]ax^2+bx+c=0[/tex]

a = 3, b = -10, c = -8

So, this can be solved using the quadratic formula.

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4\times3 \times (-8)}}{2\times 3}\\x=\dfrac{-(-10)\pm\sqrt{196}}{6}\\x=\dfrac{10\pm14}{6} \\\Rightarrow x= 4, -\dfrac{2}{3}[/tex]

The answer is same from both the approaches.

So, the correct answer is:

C) Both

Answer:

Both

Step-by-step explanation:

Answer:

[tex]AB \approx 70.7[/tex]

Step-by-step explanation:

This is a right triangle.

We have sides:

[tex]BC=52[/tex]

[tex]AC=48[/tex]

In order to find the other side, you can use the Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

as 'c' equal to the hypotenuse and, 'a' and 'b' are legs or cathetus.

For this triangle,

[tex]AC^2+BC^2=AB^2[/tex]

[tex]48^2+52^2=AB^2[/tex]

[tex]2304+2704=AB^2[/tex]

[tex]AB=\sqrt{5008}=4\sqrt{313}[/tex]

[tex]AB \approx 70.7[/tex]

Answer:

y = 2( x-3)^2 +5

Step-by-step explanation:

The vertex form of a parabolic functions is

y = a( x-h)^2 +k

where (h,k) is the vertex

y = a( x-3)^2 +5

Substituting the point into the equation

13 = a( 1-3)^2 +5

13 = a*( -2)^2 +5

13 = 4a +5

Subtract 5

8 = 4a

Divide by 4

8/4 =a

2=a

y = 2( x-3)^2 +5

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

Answer:2y

Step-by-step explanation:

!!!

Answer:

Answer: h(x) = 1/5x

Step-by-step explanation:

6x + y = 4x + 11y

    -y            -y  

6x       = 4x + 10y

-4x        -4x        

2x       =         10y

÷10               ÷10  

1/5x =     y

Since "y" represents h(x), then h(x) =

Answer:

y = -x + 10

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

Step 1: Find slope m

m = (11 - 9)/(-1 - 1)

m = 2/-2

m = -1

y = -x + b

Step 2: Find y-intercept b

9 = -(1) + b

9 = -1 + b

b = 10

Step 3: Rewrite linear equation

y = -x + 10

Answer:

$-48

Step-by-step explanation:

(-125 + -86 +54 +-35)/4 = -48

Add all the Profits/losses and divide by the number of weeks.

Answer:

145 feet.

Step-by-step explanation:

Given that:

An underwater canyon begins at depth = 40 ft

Depth of canyon = 105 ft

To find:

The elevation of the bottom of the canyon = ?

Solution:

Kindly refer to the image attached for the given dimensions.

A is the sea level.

B is the point at which the canyon starts and

C is the bottom of the canyon.

As per question statement, we are given that:

AB = 40 feet

BC = 105 feet

And we have to find the distance AC = ?

It is clearly observable that:

[tex]AC = AB + BC\\\Rightarrow AC = 40 + 105\\\Rightarrow \bold{AC = 145 ft}[/tex]

So, the elevation of the bottom of the canyon is 145 ft.

Answer:

The answer is A

Step-by-step explanation:

Step 1: Use Cosine to find ∅

Cos∅=[tex]\frac{4}{5}[/tex]

∅=Cos[tex]^{-1}[/tex]([tex]\frac{4}{5}[/tex])

Therefore the answer is A

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

Perimeter = 90 inches

The statement

The length of a rectangle is five inches more than four times it’s width is written as

l = 5 + 4w

Substitute this expression into the above formula and solve for the width

That's

90 = 2(5 + 4w) + 2w

90 = 10 + 8w + 2w

10w = 90 - 10

10w = 80

Divide both sides by 10

w = 8

Substitute this value into l = 5 + 4w

That's

l = 5 + 4(8)

l = 5 + 32

l = 37

Therefore we have

Hope this helps you

Answer:

[tex]3 \sqrt 5}[/tex]  and [tex]-3 \sqrt 5}[/tex]

Step-by-step explanation:

Given

[tex]x^2 = 45[/tex]

Required

Determine the values of x

[tex]x^2 = 45[/tex]

Take square root of both sides

[tex]\sqrt{x^2} = \±\sqrt{45}[/tex]

[tex]x = \±\sqrt{45}[/tex]

Expand 45 as 9 * 5

[tex]x = \±\sqrt{9 * 5}[/tex]

Split the square root

[tex]x = \±(\sqrt{9} *\sqrt 5}[/tex]

[tex]x = \±3 *\sqrt 5}[/tex]

[tex]x = \±3 \sqrt 5}[/tex]

This can be further split to:

[tex]x = 3 \sqrt 5}[/tex] or [tex]x = -3 \sqrt 5}[/tex]

Hence, the possible values of x are

[tex]3 \sqrt 5}[/tex]  and [tex]-3 \sqrt 5}[/tex]

Answer:

[tex]y=\frac{5}{3}x-5[/tex]

Step-by-step explanation:

Slope-intercept:

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

m is the slope and b is the y-intercept. We know that the line passes through the y-axis at -5, so this is the y-intercept (where x is equal to 0). Insert this into the equation:

[tex]y=mx-5[/tex]

With the given information, we can form two points:

[tex](3,0)(0,-5)[/tex]

The first one is the x-intercept and the second the y-intercept. Use these to find the slope:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert the appropriate values:

[tex](3_{x1},0_{y1})\\(0_{x2},-5_{y2})\\\\\frac{-5-0}{0-3}[/tex]

Solve:

[tex]\frac{-5-0}{0-3}=\frac{-5}{-3}[/tex]

Note that both the numerator and denominator are negatives. Two negatives make a positive, so:

[tex]\frac{5}{3}[/tex]

The slope is [tex]\frac{5}{3}[/tex]

Insert into the equation:

[tex]y=\frac{5}{3}x-5[/tex]

:Done

Answer:

  √8106

Step-by-step explanation:

8106 = 2·3·7·193

It has no square factors, so the radical cannot be simplified further.

Answer:

true

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

a) line marked a is tangent

b) line marked b is radius

c) line marked c is diameter

d) line marked d is chord

Answer:

A had 22 mangoes, B had 26 mangoes

Step-by-step explanation:

We can write the following system:

A + 10 = 2(B - 10) -- Equation 1

3(A - 10) = B + 10 -- Equation 2

A + 10 = 2B - 20 → A = 2B - 30 -- Equation 3 (Simplify Equation 1)

3(2B - 30 - 10) = B + 10 -- Equation 4 (Substitute 3 into 2)

3(2B - 40) = B + 10

6B - 120 = B + 10

5B = 130

B = 26 -- (Solve for B in Equation 4)

A = 2 * 26 - 30 = 22 -- (Substitute B = 26 into Equation 3)

Answer:

assosiative property

Answer

the second value is ten times higher then the refference one

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

Answer:

2 in 32000 is in the thousands place

2 in 26000 is in the ten thousands place

Step-by-step explanation:

Answer:

[tex]\huge \boxed{8\sqrt{3}}[/tex]

Step-by-step explanation:

[tex]2\sqrt{48}[/tex]

Simplify [tex]\sqrt{48}[/tex].

[tex]2\sqrt{16} \sqrt{3}[/tex]

[tex]\sqrt{16}=4[/tex]

[tex]2 \times 4\sqrt{3}[/tex]

Apply rule : [tex]a \times b\sqrt{c} =ab\sqrt{c}[/tex]

[tex]8\sqrt{3}[/tex]

Answer:

[tex]\dfrac{1}{9}[/tex]

Step-by-step explanation:

Given a spinner with 3 equally spaced colors Red, Blue, Yellow.

The colors are equally spaced, therefore probability of each color must be same.

i.e. Probability of occurrence of any one color in one spin is [tex]\frac{1}{3}[/tex].

To find:

Probability that spinner will stop one green in first spin and yellow in the second spin = ?

Solution:

As all the colors are equally likely to occur, so

Probability of green color in the first spin, P(G) = [tex]\frac{1}{3}[/tex]

Probability of yellow color in the second spin, P(Y) = [tex]\frac{1}{3}[/tex]

As we can observe that occurrence of any color in the second round of spin is not dependent on the color occurrence in the first spin, therefore these are the independent events.

P(G and Y) = P(G) [tex]\times[/tex] P(Y)

[tex]\Rightarrow P(G\ and\ Y) = \dfrac{1}{3} \times \dfrac{1}{3}\\\Rightarrow P(G\ and\ Y) = \bold{\dfrac{1}{9}}[/tex]

Therefore, the required probability is

[tex]\dfrac{1}{9}[/tex].

Answer:

Alphabet J

Step-by-step explanation:

Given

Alphabet: A - Z

Required

Determine which alphabet is at the 10 millionth position

Represent the number of alphabets with n

n = 26

To get the alphabet at the required position, we have to divide 10 million by 26 and note down the remainder

[tex]\frac{10000000}{26} = 384615\ R\ 10[/tex]

The division gives, 384615 remainder 10

This implies that, the alphabet at the 10th position is the same alphabet at the 10 millionth position;

And this alphabet is J

Answer:

11/5

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = (5 - -6)/(-4 - -9)

    = (5+6)/( -4+9)

   = 11/5

Let's find the slope using the graphing method.

First set up a coordinate system like I have done below.

Now, graph each ordered pair.

Let's call (-9, -6) point A and (-4, 5) point B.

Now remember that the slope or m is equal

to the rise over run from point A to point B.

To get from point A to point B, we rise 11 units and run 5 units.

So our slope is 11/5.

Answer: Hi!

The equation given is 5.29 * 10^4.

First, we need to solve the exponent.

10^4 = 10,000

Next, we multiply 10,000 by 5.29.

10,000 * 5.29 = 52,900

Therefore, your answer is a), 52,900.

Hope this helps!

Answer:

A.

Step-by-step explanation:

It is 5.29 x 10,000

= 52,900.

Answer:

Cups of water she needs to make the punch is 12.

Step-by-step explanation:

Amount of water Carson need to make fruit punch = 3 quarts

2 cups is 1 pint

2  pints is 1 quart

1 pint = 1/2 quarts

2 cups is 1 pint which is 1/2 quarts

So, 1 cup:

1 cup is 1/2 times 2 quarts

1 quart is 1 times 2 times 2 cups equals 4 cups

So, 3 quarts equals 3 times 4 cups which equals 12 cups.

So it is 12 cups.

Cups of water she needs to make the punch is 12.

A unit conversion expresses the same property as a different unit of measurement.

Given that, Carson needs 3 quarts of water to make fruit punch, but has only an l-cup measuring cup.

She knows there are 2 cups in 1 pint, and 2 pints in 1 quart.

Amount of water Carson need to make fruit punch = 3 quarts

2 cups is 1 pint

2  pints is 1 quart

1 pint = 1/2 quarts

2 cups is 1 pint which is 1/2 quarts

So, 1 cup:

1 cup is 1/2 times 2 quarts

1 quart is 1 times 2 times 2 cups equals 4 cups

So, 3 quarts equals 3 times 4 cups, which equals 12 cups.

Hence, she need 12 cups.

For more references on unit conversion, click;

https://brainly.com/question/19420601

#SPJ2

Answer:

The quantity of the first model is 150 and the second model is 100 that maximize the profit.

Step-by-step explanation:

Let the quantity of first model = x

Let the quantity of second model = y

The cost of the first model = $100

The cost of the second model = $150

Total number of models = 250 units

Total amount to spend on units = $30000

Now form the equations.

x  +  y  = 250

100x + 150y = 30000

Now solve for the x and y.

x = 250 – y

Now insert this value in the 100x + 150y = 30000.

100(250 –y) + 150y = 30000

25000 – 100y + 150y = 30000

50y = 30000 – 25000

50y = 5000

Y = 100

Now insert the Y in x + y = 250

x = 250 – y

x = 250 – 100

x = 150

Therefore, the first model is 150 units and the second model is 100 units that maximize the profit.

Answer: a constant

Step-by-step explanation:

A constant is a numerical expression like 2, 0,78 etc .

A variable is a alphabetical expression that vary like a,b,c,d,x,y,z.

An expression can consists of both numerical and alphabets and also any arithmetic expression like x, 2abc, 6a+2c etc

A term consist of either numbers and variables multiplied together or only numbers or variable like 2xy, x, 2ab etc.

X is all (a term, a variable , an expression) except a constant because a constant is a numerical expression.

Answer: D, a constant

Step-by-step explanation: A constant is an expression without variables.

Answer:

The government paid an interest of $41.9, which is 4.19%

Step-by-step explanation:

Given the 189-day, $1,000 U.S Treasury bill is purchased at a discount of 4.19%, this means that:

It was purchased at a discount of:

4.19% of $1000

= (4.19/100) × 1000

= $41.9

Purchase price = $1000 - $41.9 = $958.1

Because the treasure is sold for $1000 on maturity day, that means the government paid an interest of $41.9, which is 4.19%

Answer:

1

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = (5-8)/(-8 - -5)

    = -3/(-8+5)

    = -3/-3

   = 1

Answer:

-96+24= -72   or just -72

Step-by-step explanation:

4(-24+6)

-96+24= -  72

put the values of x,y and z

4(-24+6)

4(-18)

= -72