Lesson 4 practice problems.

The height of rectangle is 10 inch

Answer:

10 inches

Step-by-step explanation:

Answer:

Option B. [tex]x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i[/tex]

Step-by-step explanation:

we know that

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]14x^{2}+9x+10=0[/tex]

so

[tex]a=14\\b=9\\c=10[/tex]

substitute in the formula

[tex]x=\frac{-9(+/-)\sqrt{9^{2}-4(14)(10)}} {2(14)}[/tex]

[tex]x=\frac{-9(+/-)\sqrt{-479}} {28}[/tex]

Remember that

[tex]i=\sqrt{-1}[/tex]

substitute

[tex]x=\frac{-9(+/-)\sqrt{479}i} {28}[/tex]  

[tex]x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i[/tex]

[tex]

3i(-7+11i)=-28i+33i^2=\boxed{-33-28i}

[/tex]

Answer:

-33 - 21i

Step-by-step explanation:

3i (-7 + 11i)

= -21i + 33i^2                   (i^2 = -1)

= -21i + 33(-1)

= -33 - 21i

Answer:

Part A) The equation is [tex]t=3.50z+40[/tex]

Part B) Kristina did go to the gym 20 times

Step-by-step explanation:

Let

t-----> the total amount

z----> the number of times that Kristina go the health club

Part A) Write an equation

we know that

The linear equation that represent this situation is

[tex]t=3.50z+40[/tex]

Part B) For [tex]t=\$110.00[/tex]

Substitute the value of t in the linear equation and solve for z

[tex]110.00=3.50z+40[/tex]

[tex]3.50z=110.00-40[/tex]

[tex]3.50z=70.00[/tex]

[tex]z=70.00/3.50[/tex]

[tex]z=20\ times[/tex]

The surface of the ocean is 0 meters.

Because the fish is below the surface it would be a negative number. ( it is less than 0)

The elevation of the fish would be -12 meters.

Answer:

-12 meters

Step-by-step explanation:

Elevation is the height above a given level, most often the sea. Therefore, elevation is like a vertical numerical line. If the sea level is 0, and to the right of the 0 is positive numbers, then the left has to be negative.

Therefore, the fish is -12 meters below sea level.

Answer:

9,-5

Step-by-step explanation:

2x^2-8x-90

Factor by 2

2(x^2 -4x-45)

What two numbers multiply to -45 and add to -4

-9*5 = -45

-9+5 = -5

2(x-9) (x+5)

Set this equal to zero

2(x-9) (x+5) =0

Divide by 2

(x-9) (x+5) =0

Using the zero product property

x-9=0  x+5=0

x=9  x=-5

Answer:

Asin(wt + φ) = c2sinwt +c1coswt

Step-by-step explanation:

Proof:

wt here is periodic where as φ is constant

taking left hand side

Asin(wt + φ)

Using trigonometric identity sin(θ+φ) = sinθcosφ +sinφcosθ

Asin(wt +φ) = A[sinwtcosφ +sinφcoswt]

                  = Asinwtcosφ +Asinφcoswt

Now as we know φ is constant

so will Asinφ and Acosφ will also be constant

let     Asinφ= c1

and Acosφ=c2

Putting in above expression, we get

Asin(wt +φ) = c2sinwt +c1coswt !

Hello There!

Your answer would be “B”

Forget about the -5 and just do 5 multiplied by 3 and you get a product of 15.

Then, make it negative and it would be 4^-15

Answer:

A) 33

Explanation:

There are always chances so you never know where the samples could be from. The answer 33 makes the most logical sense.

A.33.sample population

let the width of the rectangle be x

area of rectangle is l*b

x * (x + 6) = 40^2

x^2 + 6x = 40^2

x^2 + 6x = 1600

x + 6x =√1600

x + 6x = 40

7x = 40

x = 5.7

Hope you found this useful

9. Area = 59.755[tex]cm^{2}[/tex] square cm. when the area to nearest tenth then, area = 60 square cm.

10. Area = 22.9813[tex]mi^{2}[/tex]. When the area to nearest tenth then, area = 20 square mi.

Area of the Triangle:

Area of the triangle is = half of (base x height)

=> (1/2) x (b x h)

Trigonometry:

sinθ = opposite side / hypotenuse

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The area of the triangles are 59.8 square cm and 23.0 square miles

From the question, we have the following parameters that can be used in our computation:

The triangle

The area of each triangle is calculated using the following sine equation

Area = 1/2absin(C)

Using the above as a guide, we have the following

Area of triangle 1 = 1/2 * 11 * 11 * sin(99 degrees)

Area of triangle 1 = 59.8 square cm

Area of triangle 2 = 1/2 * 5 * 12 * sin(50 degrees)

Area of triangle 2 = 23.0 square miles

Hence, the area of the triangles are 59.8 square cm and 23.0 square miles

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Answer:

120 votes

Step-by-step explanation:

So one way to solve this is by creating an equation to solve for x.

So we are given 4/7, that will be one side of the equation.  

And we are trying to figure out how many votes out of the 210 she received, so on the other side of the equation we will have x/210, since we are solving for x.  

So 4/7 = x/210

We want to get x alone, so we can multiply 4/7 by 210, which equals 120.

So x equals 120!

Isabel received 4/7 of the 210 votes for class treasurer, which equals 120 votes when the total is multiplied by the fraction.

The student is asking for help with a mathematics problem related to finding a fraction of a whole number. Isabel received 4/7 of the total votes cast for class treasurer, and the total number of votes cast was 210. To find how many votes Isabel received, we simply multiply 210 by 4/7:

Isabel's votes = (210) * (4/7)

Isabel's votes = 840 / 7

Isabel's votes = 120

Therefore, Isabel received 120 votes.

Answer:

72

Step-by-step explanation:

(24*6)/2 = 72

Answer:

[tex]144ft^2[/tex]

Step-by-step explanation:

For this problem, we can use the formula for the area of a kite.

[tex]A=\frac{pq}{2}[/tex]

Where p and q are the diagonals.

Since line AE starts at the edge of the kite and ends at the center, we can multiply its value by 2 to find the value of the p diagonal.

[tex]6*2=12[/tex]

So diagonal p is 12ft.

Now we can find the value of the q diagonal, which will be adding BE and DE.

[tex]9+15=24[/tex]

So diagonal q is 24ft.

Let's plug them into the area formula I mentioned earlier.

[tex]A=\frac{12*24}{2} \\ \\ A=\frac{288}{2} \\ \\ A=144[/tex]

Answer:

C

Step-by-step explanation:

It is all the points on a plane that are the same distance away from 1 fixed point.

That makes C the answer. There are definitions here for a parabola (B), an ellipse (A) and a Hyperbola (D).

Only C is correct for the circle.

Answer: C just did it

Answer:

A' = (5,7)

Step-by-step explanation:

So, we start with the original point A at (3,1), that means x = 3 and y = 1.

We move it 2 units to the right... so we're moving along the X-axis... and we're moving to the right.. so we're increasing the value of x.  That means starting with x = 3, we go 2 more units... we then get to x = 5.

In the same way, we move 6 units up... so we move along the Y-axis.  We go up, so we also increase the value of y.  Starting with y = 1, we move up by 6 units... so we are now at y = 7.

A' point is then at (5,7).

Answer:

11

Step-by-step explanation:

11*2=22, 22+14=36, quick maths

Answer:

11

Step-by-step explanation:

36-14 gives you the doubled-number you chose, 22.

Then since the number is doubled, divide it by 2. 22÷2=11

anwser is 5/12

dividing a fraction is the same as multiplying by a reciprocal

Answer:

length=10\ yd,  width=16\ yd

Answer:

Length of the playground is 10 yd and the Width of the playground is 16 yd .

Step-by-step explanation:

Formula

Area of a rectangle = Length × Width

As given

The area of a playground is 160 yd².

The width of the playground is 6 yd longer than its length.

Let us assume that the length be x .

Thus

Width = x + 6

Put all the values in the formula

160 = x × (x + 6)

160 = x² + 6x

x² + 6x - 160 = 0

x² + 16x - 10x - 160 = 0

x (x + 16)-10 (x + 16) = 0

(x -10)(x + 16) = 0

Thus

Either (x - 10) = 0 or (x + 16 ) = 0

x = 10 or x = -16

(Negative value is neglected because sides cannot be negative.)

Thus

x = 10

Length = 10 yd

Width = 10 + 6

             = 16 yd

Therefore the length of the playground is 10 yd and the width of the playground is 16 yd .

Answer:

x = 14; x = 0  

Step-by-step explanation:

(x)(6 + 8) = x²

(x)(14) = x²

14x = x²

14x - x² = 0

(x)(14 - x) = 0

x = 14; x = 0  

Answer:

Step-by-step explanation:

The way that this function looks when graphed could be similar to the seismic waves recorded when an earthquake hits.

A logarithmic measure known as the Richter scale is used to quantify the overall energy generated during an earthquake. Each number higher on the Richter scale denotes a ten-times-stronger intensity. For instance, a magnitude 5 earthquake is ten times more powerful than a magnitude 4 earthquake.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.

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A quantity is proportional to 18/3 if it simplifies to the same value, which is 6. The proportional quantities are 90/15, 36/6, 72/12, and 6/1, as they all simplify to 6. The quantity 36/12 is not proportional since it simplifies to 3.

To determine which quantities are proportional to 18/3, we need to find what 18 divided by 3 equals and then compare this to the given fractions to check for equivalence. Calculating 18/3 gives us 6. Now, let's examine each option:

90/15: This fraction reduces to 6, which is proportional to 18/3.

36/6: This fraction also equals 6 after simplification, so it is proportional to 18/3.

72/12: Simplifying 72/12 gives us 6, making it proportional to 18/3

6/1: 6 divided by 1 is just 6, so this too is proportional to 18/3.

36/12: Simplifying 36/12 results in 3, which is not equal to 6, so it is not proportional to 18/3.

Answer:

112 trucks

Step-by-step explanation:

so you take ratio:

1000-250

3584-x

x=896

and after you divide 896 by 8 hours and get 112

hope it helped you

Answer:

A) 35 cm2

Step-by-step:

Answer:

A- 35 cm2

Step-by-step explanation:

Answer: The population in Eric's survey is the high school seniors.

Answer:

all high school seniors at Eric’s school

Step-by-step explanation:

Answer:

The answer is 3/4.

Step-by-step explanation:

1 1/2 is equal to 1.5.

1.5 divided by 2 is 0.75.

0.75 is equal to 3/4.

Answer:

Step-by-step explanation:

first you gotta make 1 1/2 an improper fraction then you put 2 over one to make a fraction to divide then swich 1 and 2 and multiply and the answer would be 3/4

Answer:

x² + 23x + 49

Step-by-step explanation:

Area of the big rectangle

= (x + 10)(2x + 5)

= 2x² + 5x + 20x + 50

= 2x² + 25x + 50

Area of the small white rectangle

= (x + 1)(x + 1)

= x² + x + x + 1

= x² + 2x + 1

Area of the shaded area

= (2x² + 25x + 50) - (x² + 2x + 1)

= 2x² + 25x + 50 - x² - 2x - 1

= x² + 23x + 49

Answer: [tex]f(2)=25[/tex]

Step-by-step explanation:

You know that the given function is:

[tex]f(x)=4x^3-x^2-5x+7[/tex]

You know that you must evaluate this function for [tex]x=2[/tex].

Then, to evaluate the function for [tex]x=2[/tex], you need to substitute this value into the given function and simplify it.

Therefore, you get:

[tex]f(x)=4x^3-x^2-5x+7\\f(2)=4(2)^3-(2)^2-5(2)+7\\f(2)=4(8)-(4)-10+7\\f(2)=32-4-10+7\\f(2)=25[/tex]

So, the answer is: [tex]f(2)=25[/tex]

Answer:

coordinate of the other endpoint is (-9,-2)

Step-by-step explanation:

Given that a segment has endpoints at (1, -2). The midpoint is at (-4, -2).

Now we need to find about what are the coordinates of the other endpoint.

let the coordinates of other end points are (x,y)

Then mid point of (1,-2) and (x,y) is given by mid point formula:

[tex]\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]

[tex]\left(\frac{x+1}{2},\frac{y-2}{2}\right)=(-4,-2)[/tex]

[tex]\Rightarrow \frac{x+1}{2}=-4, \frac{y-2}{2}=-2[/tex]

[tex]\Rightarrow x+1=-8, y-2=-4[/tex]

[tex]\Rightarrow x=-9, y=-2[/tex]

hence coordinate of the other endpoint is (-9,-2)

Answer:

what the otherperson said

Step-by-step explanation:

just read what the other person said

i believe they would spend $36.12

Answer:

not a factor

Step-by-step explanation:

If (x - 3) is a factor then f(3) = 0

f(x) = 2x² - 4x + 30

f(3) = 2(3)² - 4(3) + 30 = 18 - 12 + 30 = 36 ≠ 0

Since f(3) ≠ 0 then (x - 3) is not a factor of f(x)