Question 9 - (3 marks available )
By rounding to 1 significant figure, estimate the answers to these questions:
a)
17 x 82
b)
54 * 671
c)
207 x 643​

Answer:

Step-by-step explanation:

The length of the base is 3 feet and the height of the triangle is 6 feet.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.

The dimensions of the triangle will be calculated as,

A = (1/2)  x b x h

A = (1/2) x b x ( b + 3 )

54 = ( 1 / 2 ) x ( b² + 3b )

108 =  ( b² + 3b )

( b² + 3b - 108) = 0

( b² + 12b -3b -108 ) = 0

(b - 3 ) ( b+ 12 ) = 0

b = 3 and b = -12 ignore negative value.

The height will be calculated as,

h = b + 3

h = 3 + 3

h = 6 feet

Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.

To know more about the area of a triangle follow

https://brainly.com/question/17335144

#SPJ2

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The general form of a quadratic equation with roots a and b is expressed as shown;

x²-(sum of root) x + (product of roots) = 0

x² - (a+b)x + ab = 0 ... 1

Given the sum of roots a+b = -7

Product of roots ab = -2

Substituting this values in equation 1 above wil give;

x²-(-7)x+(-2) = 0

x²+7x-2 = 0

The resulting quadratic polynomial is x²+7x-2 = 0

Answer:

5 people have pink cups

Step-by-step explanation:

10-5=5

:D

Answer:

5

Step-by-step explanation:

10-5=5

^--^

Answer:

The speed is still water is [tex]v = \frac{d}{h} - c[/tex].

Step-by-step explanation:

Dimentionally speaking, speed is distance divided by time. Since, the person is travelling downstream, absolute speed is equal to the sum of current speed and speed of the person regarding current. Both components are constant. That is:

[tex]c + v = \frac{d}{h}[/tex]

Where:

[tex]c[/tex] - Current speed, measured in miles per hour.

[tex]v[/tex] - Speed of the person regarding current, measured in miles per hour.

[tex]d[/tex] - Distance travelled downstream, measured in miles.

[tex]h[/tex] - Time spent on travelling, measured in hours.

Speed in still water occurs when current speed is zero. Then, such variable is obtained after subtracting current speed on both sides of the expression. Hence:

[tex]v = \frac{d}{h} - c[/tex]

The speed is still water is [tex]v = \frac{d}{h} - c[/tex].

Answer:

d.

Step-by-step explanation:

i looked at the graph!

Answer:

b)

Step-by-step explanation:

the easy way of doing this in my opinion is just to multiply the options by their corresponding values so in this case 3x10=30 and 5x14=70 then add those together and it equals 100 points with a total of 24 questions

Answer:

The correct option is;

B. -2

Step-by-step explanation:

From the graph, we have;

At x₁ = 300, y₁ = 800

At x₂ = 400, y₂ = 600

The formula for the slope, m, of a graph is given as follows;

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{600 - 800}{400 - 300}= \dfrac{-200}{100} = -2[/tex]

Therefore, a reasonable estimate of the rate of change for the interval 300 ≤ x ≤ 400 is -2 which is a negative slope as expected as the y-coordinate values, which is the value of the function, decreases while the x-coordinate values which is the independent variable increases as we go from 300 ≤ x ≤ 400.

Answer:

Step-by-step explanation:

Hello

(fog)(x)=f(g(x))=10(x-6)/10+6=x-6+6=x

(gof)(x)=(10x-6+6)/10=10x/10=x

So YES the functions are inverse

hope this helps

Answer:

y=x_1 is the solution of system

Answer:

5/2

Step-by-step explanation:

You slope is always mx

In point-slope form, your mx is just in factored form. All you need to do is distribute to find m.

Answer:

3/2

Step-by-step explanation:

45/30 can be simplified.

The highest common factor of 45 and 30 is 15.

45÷15/30÷15

Divide.

3/2

Answer:

6

Step-by-step explanation:

Let the number be x.

2x - 7 = 5

Add 7 to both sides.

2x = 5 + 7

2x = 12

Divide 2 into both sides.

x = 12/2

x = 6

The number is 6.

Answer:

6

Step-by-step explanation:

2x-7=5

2x=12

x=6

x=the varible that represents the number

Answer:

A

Step-by-Step Explanation:

We want to find the limit:

[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}[/tex]

Use direct substitution.

Hence:

[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}\cos(\frac{\pi}{2}})[/tex]

Recall the unit circle. cos(π/2) is simply 0. Hence:

[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}(0)=0[/tex]

Therefore:

[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}=0[/tex]

So, our answer is A.

Answer:

The magnitude of the boat's velocity is 5.66 m/s

Step-by-step explanation:

Given;

Radius of curvature of the circular path, r = 40 m

speed of the boat, v = 0.8 t m/s

The magnitude of the boat's velocity when it has traveled 20 m is ?

a = dv / dt,

v = 0.8 t (differentiate with respect to t)

dv / dt = 0.8 = a

thus, a = 0.8 m/s²

If the boat starts from rest, initial velocity, u = 0

Apply kinematic equation, to solve for the boat velocity at 20 m

v² = u² + 2as

v² = 0 + 2 x 0.8 x 20

v² = 0 + 32

v² = 32

v = √32

v = 5.66 m/s

Therefore, the magnitude of the boat's velocity when it has traveled 20 m is 5.66 m/s

Answer:

B. 116

Step-by-step explanation:

Answer:

D) 102

Step-by-step explanation:

Angle ABC is an inscribed angle.

Inscribed angle = 1/2 * Intercepted Arc

The intercepted arc is arc CD + arc DA, which would be 128 + 76 = 204

m<ABC = 1/2(204)

m<ABC = 102 degrees

You answer is D) 102

Answer:

Half;  twice

Step-by-step explanation:

In a circle, the radius is said to be the distance from the center of the circle to any point on the edge of the circle, it is denoted as "r". The radius is called a radii if it is more than one.. The radius of a circle is half the length of the diameter of a circle because the diameter of a circle is the distance of the line that passes through the center of a circle touching both edges of the circle. It is denoted as "d".

Thus,

2r = d

r = d/2

For example, if the radius of a circle is 10cm, the diameter of the circle will be calculated as: d = 2 * 10 = 20cm. Which means if the radius is 10cm, diameter will be 20cm.

Therefore, the radius of a circle is half the length of its diameter. the diameter of a circle is twice the length of its radius

Answer:

6.8 nearly 7

Step-by-step explanation:

beacuse mean is sum of all terms in a data/number of terms in the data

Answer: 7

Step-by-step explanation:

To find the mean of a set, you take the sum of the set and divide it by the number of numbers in the set.

[tex]\frac{2+6+7+9+9+9}{6} =\frac{42}{6} =7[/tex]

Answer:

(y-6)=-2/3(x+4)

Step-by-step explanation:

Answer:

The answers are below

Step-by-step explanation:

a)67.592

b)21.748

c)241.402

Answer:

New dimensions are; Width = 12m and Length = 12m

Step-by-step explanation:

Let length of rectangle be L

Let width be W

Area of rectangle has a formula;

Area = Length x Width = LW

We are given the area = 144 m²

So,

LW = 144 - - - (eq1)

Now, we are told that width is doubled and length is decreased by 12m but area remains the same.

Thus, we have;

Width as 2W and Length as L - 12.

Area = 2W(L - 12)

So,

2W(L - 12) = 144 - - - (eq2)

Equating eq 1 and 2,we have;

LW = 2W(L - 12)

W will cancel out to give;

L = 2(L - 12)

L = 2L - 24

2L - L = 24

L = 24m

From equation 1, LW = 144

Thus; W = 144/L = 144/24

W = 6m

So new design of rectangle now has a dimension of;

Width = 2W = 2 × 6 = 12m

Length = L - 12 = 24 - 12 = 12m

So, new dimensions are; Width = 12m and Length = 12m

Answer:

2 for both

Step-by-step explanation:

The distance between the points and the y-axis will be the value of the x coordinate, as x is the horizontal distance from 0 and the y-axis.

Answer:

Answer 4

Step-by-step explanation:

Answer:

12.7 years to the nearest tenth.

Step-by-step explanation:

The total of the ages for the 25 students = 10*25 = 250.

For the 30 students it is 15*30 = 450.

The average for the 2 classes = (250 + 450) / (25 + 30)

= 700 / 55

=  12.7 years to the nearest tenth.

Answer:

True

Step-by-step explanation:

The distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].

The given points are  (1, 2) and [tex](x_{1} , y_{1})[/tex] .

We to find the distance between the given points.

The formula to find the distance between points is [tex]\sqrt{(x_{1}-x_{2} )^{2}-(y_{1}-y_{2} )^{2} }[/tex].

Now, [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex]

Therefore, the distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].

To learn more about the distance between the points visit:

https://brainly.com/question/15958176.

#SPJ2

Answer:

x = 10000

Step-by-step explanation:

log x = 4

Raise each side to the base of 10

10^log x = 10 ^4

x = 10 ^4

x = 10000

Answer:

x = 10,000

Step-by-step explanation:

I got it right on the test.

Answer:

Positive correlation

Step-by-step explanation:

From the scatter plot shown in the graph above, we can observe that the data points that are clustered in a band run upwards from left of the graph to the right.

In simple terms, both variables move along the same direction, which means, as variable on one axis increases, the variable on the other axis increases as well.

This shows that the variables depicted on the scatter plot are positively correlated. It shows a positive correlation between the variables.

The relationship between the variables on the scatter plot it a positive correlation

From the graph, we have the following highlights

When the x and the y values increase or decrease in the same direction, then the correlation of the graph is positive.

Hence, the relationship between the variables on the scatter plot it a positive correlation

Read more about correlation at:

brainly.com/question/7289927

Answer:

C(6,-4)

Step-by-step explanation:

-8+-4=-12

-12÷2=-6

I hope this helps

Answer:

C

Step-by-step explanation:

(6,-4)

Answer:

third option

Step-by-step explanation:

When x is less than 3, f(x) is negative so the first statement is false. The second statement is also false because the entire function is not positive. The third statement is true because when x is less than 3 f(x) is negative. The fourth statement is false because the entire function is not negative.

Answer:

Step-by-step explanation:

When each of the dimensions is multiplied by 1/3, the result is a rectangle that is ...

   (12 mm)·(1/3) by (15 mm)·(1/3) = 4 mm by 5 mm

The result is ...

  a smaller rectangle with length 4 millimeters and width 5 millimeters

__

The perimeter of the smaller rectangle has the same ratio to the original that the side lengths do.

The new perimeter will be 1/3 times the perimeter of the original rectangle.

The change in perimeter of the new rectangle will be 3 times the perimeter of the original rectangle.

For a known length and width of a rectangle, the expression for calculating the perimeter of a rectangle is 2(L × w).

From the given information:

A rectangle's length = 12 mm, and width = 15 mm

Therefore, we can deduce that the change in perimeter of the new rectangle will be 3 times the perimeter of the original rectangle.

This is because by using the scale factor:

[tex]\mathbf{\dfrac{1}{3}(12) \times \dfrac{1}{3}(15)}[/tex]

We can get the value for the length and width of the new smaller rectangle as 4 mm and 5 mm respectively.

Learn more about the perimeter of a rectangle here:

https://brainly.com/question/19819849

#SPJ2

Answer:

B

Step-by-step explanation:

Volume of Sphere = 4/3 x 3.14 (pi) x r^2