Grade:
Subject: Ma
Stream: Advanced
Number of P
End of Term 1 Exam
Academic Year 2018/2019
Part 1
Circle the letter corresponding to the correct answer.
1) Write an algebraic expression for "3 times X squared minus 4 times X"
a) 3x - 4x?
c) 3x² - 4
b) 3x - 4x
d) 3x2 - 4x​

Answer:

y=2

Step-by-step explanation:

y = 26

If you substitute x for -3 in the equation y = 6x + 8, your equation becomes:

y = 6(-3) + 8 now you can simplify it and solve for y

6 x -3 = -18

18 + 8 = 26

y = 26

Answer:

y = -1/3x + 2

General Formulas and Concepts:

Pre-Algebra

Algebra I

Perpendicular lines have the negative reciprocal slope of the original.

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = 3x - 11

Point (-6, 4)

Step 2: Find slope m

Negative Reciprocal of 3 = -1/3

Step 3: Define

y = -1/3x + b

Step 4: Find y-intercept b

Step 5: Write perpendicular linear equation

y = -1/3x + 2

Answer:

There are no partial products to this equation. There is only one product! Okay first we will multiply 4 x 6 to get 4 in our ones place, carry the 2 over the zero put the 2 down 4 x 7 is 28 put the 8 down carry the 2, 4 x 3 is 12 + 2 is 14! So you're final product is 14,824!!!

The partial products of the given expression will be ( 3000 x 4 ) + ( 706 x 4 ).

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

The given product is 3706 x 4 and can be written as:-

3706 x 4 = [ 3000 x 4 + 706 x 4 ]

Therefore, the partial products of the given expression will be ( 3000 x 4 ) + ( 706 x 4 ).

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Answer

8

Step-by-step explanation:

16

Using the distance formular, the distance between the coordinate points given is 25

Recall the relation :

Distance = √[(28 - 4)² + (5 - 12)²]

Distance = √[(24)² + (-7)²]

Distance = √(576 + 49)

Distance = √625

Distance = 25

Hence, the distance between the points is 25

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Answer:

C) 93 r 3

Your Welcome! ^O^

   0 0 9 3

7 2 6 6 9 9

 − 0      

   6 6    

 −   0    

   6 6 9  

 − 6 4 8  

     2 1 9

   − 2 1 6

         3

Answer:

thats wrong the correct answer is 94 r 3

Step-by-step explanation:

Answer: a.

Step-by-step explanation:

If there is a negative mark next to the whole fraction, that means both of the numbers are negative.

I am not sure if this answer is accurate. Please inform me if I am incorrect. TY.

Let x be -b/2a

x = -193/2•(-16)

x = -193/-32

x = 6.03125

Now, plug this value of x into every x in the function and simplify. The max is the y value.

Can you finish?

The time at which the rocket will hit the ground to the nearest hundredth of seconds is 13 seconds.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

As per the given height of tower y in terms of time is seconds x

y = -16x² + 193x + 128

The height of the tower when the rocket hit the ground will be zero.

Thus, y = 0

0 = -16x² + 193x + 128

16x² - 193x - 128=0

By quadratic equation formula,

x = [-(-193) ± √((-193)²-4×16×(-128))]/ 2×16

x = [193 ± 213.168]/32

x = 12.69 and x = -0.63 since time can be never negative thus 12.69 seconds will be correct.

12.69 to the nearest hundred is 13.

Hence "The time at which the rocket will hit the ground to the nearest hundredth of seconds is 15 seconds".

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In 3 hours, one good worker can paint one fourth of your house. Three good workers can thus paint three fourths of your house in three hours, leaving one fourth to be done by bad workers.

One bad worker can paint one twelfth of your house in 3 hours. There are three twelfths in one fourth, so you will need to hire three bad workers to have your house painted on time.

Answer: 12.6

Step-by-step explanation: calculator  ._.

Answer:

Step-by-step explanation:

d + 2d - 8 = 46

3d - 8 = 46

3d = 54

d = 18

The first option is correct.

if we multiply the 34 and 12 so it comes 408

And according to first option, it we add 340 and 68 so it comes 408.

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Answer:

freeeeeeeeeeeeeee  pointtttttttttttt

Step-by-step explanation:

Answer:

1/3 times 1/3

Step-by-step explanation:

the answer is 1/3 * 1/3 because when you divide with fraction you make the 3 or 3/1 turned around which is 1/3, then you multiply 1/3 * 1/3

The distance between the points have been calculated.

The distance formula is used to calculate distance between two points on a coordinate system.

The formula is

[tex]\rm d = \sqrt { (x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates of ABCD is A(0,4), B(2,4), C(2,3), D(4,2), E(4,0)

The coordinates of FGHI is F(7,1), G(6,1), H(6,1.5), I(5,2), J(5,3)

AB² =  (2-0)²+(4-4)²      

AB =     2

FG² =  (6-7)²+(1-1)²

FG =1                  

BC² =  (2-2)²+(3-4)²=1          

BC = 1

GH² =  (6-6)²+(1.5-1)²=0.5        

GH = 0.5

DI² =  (5-4)²+(2-2)²

DI = 1

HI² =  (5-6)²+(2-1.5)² = 1.25

HI =  1.12

DE² =  (4-4)²+(0-2)²

DE =    2

IJ² =  (5-5)²+(3-2)²

IJ = 1

EA² =  (0-4)²+(4-0)²      

EA = 5.66

JK² =  (7-5)²+(1-3)²    

JK =    2.83

The missing data of the question is

The coordinates of ABCD is A(0,4), B(2,4), C(2,3), D(4,2), E(4,0)

The coordinates of FGHI is F(7,1), G(6,1), H(6,1.5), I(5,2), J(5,3)

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Answer:

It's C

Step-by-step explanation:

In step 2, he should have divided. Have a great day!

Answer:

C: In step 2 he should divide the equation on both sides by 5.

Step-by-step explanation:

Took the test, got it right.

Answer: 162

60466176/373248

Step-by-step explanation: 12^4*9^3*4= 60466176 and 6^3*8^2*27= 373248. If you divide these together you get 128.

Answer:

1000000000000000005

Answer:

1000000000000005

Step-by-step explanation:

Answer:

A little over 4 and a half

Step-by-step explanation:

8 divided by 2 (making it one half) is 4 and 7/8 is greater than 1/2

Answer:

Step-by-step explanation:

Given

[tex]Length = 450\ m[/tex]

[tex]Width = 1200\ m[/tex]

Required

Determine the number of hectares  in this dimension

First, we need to calculate the area of the land

[tex]Area = Length * Width[/tex]

[tex]Area = 450m * 1200dm[/tex]

Convert dm to m

[tex]Area = 450m * 120m[/tex]

[tex]Area = 54 000 m^2[/tex]

[tex]1 hectare = 0.0001m^2[/tex]

So, we have:

[tex]1\ hectare = 0.0001m^2[/tex]

Multiply by 54000

[tex]Hectare = 0.0001 * 54000[/tex]

[tex]Hectare = 5.4[/tex]

Hence, there are 5.4 hectares

Answer:

117.6 meter per min

Step-by-step explanation:

since the jogger wants to complete the trail in 30 minutes and the total length of the trail is 3528m you just need to divide the length of the trail (3528) by the total amount of time to get the answer

Answer:

117.6m per minute

Step-by-step explanation:

3528:30

588:5

30 divided by 6=5

3528 divided by 6=588

Then

5 divided by 5=1

588 divided by 5=117.6

117.6m:1

Answer:

ez pts tysm

Step-by-step explanation:

Answer:

Step-by-step explanation:

Leon visited Chicago, which is located on the shore of

Lake Michigan. The lake has a volume of about 4,920

km cubed. Chicago was a major gateway to the west in

1825 when the Erie Canal was completed. When built,

the Erie Canal was 680 long and only 100 or

10 deep. While in Chicago, Leon visited the Sear

Tower. One of the tallest buildings in the world, the

Sears Tower is 443 tall

during Leon's visit was about 7

If we can translate the statement "The ice rink costs $200 plus $4 per person to rent for a birthday celebration and the entire cost of the rental is $324" into an algebraic equation, we get 4x + 200 = 324, where x is the number of people at the birthday party. The solution of this equation i.e. the number of people at the birthday party is 31.

A statement of the equivalence of two expressions created by executing algebraic operations on a set of variables, such as addition, subtraction, multiplication, division, raising to a power, and root extraction, is known as an algebraic equation.

Let the number of people at the birthday party be x.

Given that the ice rink costs $200 plus $4 per person to rent for a birthday celebration. So, the rent is 4x + 200.

Also, given that the entire cost of the rental is $324.

We can write the corresponding algebraic equation as

4x + 200 = 324

Now we have to solve this equation.

So, 4x = 324 - 200 = 124

i.e. x = 124/4 = 31

Therefore the required algebraic equation is 4x + 200 = 324, where x is the number of people at the birthday party. Also, the solution of this equation i.e. the number of people at the birthday party is 31.

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Answer:

y = 8x + 13

Step-by-step explanation:

slope-intercept form: y = mx + b

Given equation: [tex]y = -\frac{1}{8}x -2[/tex]

Second equation: unknown

Slope: unknown

Given point: (-2, -3)

When two lines are perpendicular, their slopes are negative reciprocals. So, since the slope(m) of the given line is [tex]-\frac{1}{8}[/tex], the slope of the line perpendicular to it is 8.

Now we know the slope of the line. To find the y-intercept, input the values of the slope and the given point into the equation format and solve for b:

y = mx + b

-3 = 8(-2) + b

-3 = -16 + b

13 = b

The y-intercept is 13.

Now that we know the slope and the y-intercept, we can write the equation:

y = 8x + 13

Hope this helps :)

Answer:

Null hypothesis; H0: μ1 = μ2

Alternative hypothesis; Ha: μ1 > μ2

Step-by-step explanation:

We are told that the telraffic was experiencing an average of 20 accidents per week.

Thus, μ = 20

We are told that the council decided to try to reduce the number of accidents.

Thus defining the hypothesis, we have;

Null hypothesis; H0: μ1 = μ2

Alternative hypothesis; Ha: μ1 > μ2

Answer:

Can give you the example then you have to figure out.

Step-by-step explanation:

We are assuming the center of the tower is at the origin, so we can use the standard form of a horizontal hyperbola centered at the origin: \displaystyle \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1

​a

​2

​​  

​

​x

​2

​​  

​​ −

​b

​2

​​  

​

​y

​2

​​  

​​ =1, where the branches of the hyperbola form the sides of the cooling tower. We must find the values of \displaystyle {a}^{2}a

​2

​​  and \displaystyle {b}^{2}b

​2

​​  to complete the model.

First, we find \displaystyle {a}^{2}a

​2

​​ . Recall that the length of the transverse axis of a hyperbola is \displaystyle 2a2a. This length is represented by the distance where the sides are closest, which is given as \displaystyle \text{ }65.3\text{ } 65.3  meters. So, \displaystyle 2a=602a=60. Therefore, \displaystyle a=30a=30 and \displaystyle {a}^{2}=900a

​2

​​ =900.

To solve for \displaystyle {b}^{2}b

​2

​​ , we need to substitute for \displaystyle xx and \displaystyle yy in our equation using a known point. To do this, we can use the dimensions of the tower to find some point \displaystyle \left(x,y\right)(x,y) that lies on the hyperbola. We will use the top right corner of the tower to represent that point. Since the y-axis bisects the tower, our x-value can be represented by the radius of the top, or 36 meters. The y-value is represented by the distance from the origin to the top, which is given as 79.6 meters. Therefore,

x

2

a

2

−

y

2

b

2

=

1

Standard form of horizontal hyperbola

.

b

2

=

y

2

x

2

a

2

−

1

Isolate  

b

2

=

(

79.6

)

2

(

36

)

2

900

−

1

Substitute for  

a

2

,

x

,

and  

y

≈

14400.3636

Round to four decimal places

The sides of the tower can be modeled by the hyperbolic equation

\displaystyle \frac{{x}^{2}}{900}-\frac{{y}^{2}}{14400.3636 }=1,\text{or}\frac{{x}^{2}}{{30}^{2}}-\frac{{y}^{2}}{{120.0015}^{2} }=1

​900

​

​x

​2

​​  

​​ −

​14400.3636

​

​y

​2

​​  

​​ =1,or

​30

​2

​​  

​

​x

​2

​​  

​​ −

​120.0015

​2

​​  

​

​y

​2

​​  

​​ =1

The shape of hyperbolic cooling tower is a conic section that can be described with a formula equation.

a = 28.5, b ≈ 52.65

[tex]Equation \ of \ hyperbola;\ \dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]

Reasons:

The parameters of the hyperbolic cooling tower are;

Minimum diameter = 57 feet

The height at which the diameter occurs = 155 ft.

The diameter of the tower = 175 feet

Total height of the tower = 200 feet

Height at which the center of the hyperbola occurs = 155 feet

Solution:

The equation of a hyperbola is; [tex]\dfrac{(x - h)^2}{a^2} - \dfrac{(y- k)^2}{b^2} = 1[/tex]

The center of the hyperbola = (0, 155)

[tex]a = \dfrac{57}{2} = 28.5[/tex]

At y = 155,  

Therefore;

[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y -155)^2}{b^2} = 1[/tex]

At y = 200 feet [tex]x = \dfrac{75 \ feet}{2} = 37.5 \ feet[/tex]

Therefore;

[tex]\dfrac{37.5^2}{28.5^2} - \dfrac{(200 -155)^2}{b^2} = 1[/tex]

b² = 2769.0340909

b ≈ 52.62

The equation of the hyperbola is therefore;

[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]

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Answer:

Yes, that's right:  the cross section will be a rectangle (but also a parallelogram).

Step-by-step explanation: