Match the title of the parent functions with thedescription of the graph of the function.

Answer:

Step-by-step explanation:

Hello,

Let's develop both expressions and try to re factorise.

\(\forall (a,b,x,y) \in \mathbb{R}^4 \\ \\ (a^2+b^2)(x^2+y^2)=(ax+by)^2\\ \\<=>(ax)^2+(ay)^2+(bx)^2+(by)^2=(ax)^2+(by)^2+2(ax)(by)\\ \\<=> (ay)^2+(bx)^2-2(ay)(bx)=0\\ \\<=> (ay-bx)^2=0\\ \\<=> ay-bx=0\\ \\<=> \boxed{\sf \bf ay=bx}\)

Thanks

Answer: y = -2x

Step-by-step explanation:

For a line to be perpendicular to another, it must have the opposite reciprocal slope.  In this case, that means 1/2 becomes -2/1 or -2.  For the line to pass through 0,0 the y intercept must be 0.  Thus the line is y = -2x + 0, or y = -2x

Answer:

6 1/3

Step-by-step explanation:

You just have to see how many times it goes into it

The general form of a quadratic formula is

where a,b and c are constants. Also, note that a is a constant that helps to determine the shape of the function. As we want that the vertex is a minimum, we are in the following situation

so, this adds the restriction that a>0.

Now, we are given the points (-4,2) and (1,2). We can replace this values in our function. Let us do that with (-4,2). So we get

if we do that with the other point we get

so if we make this two equations equal, we have

so if we subtract c on both sides, we get

we can subtract a and b from both sides, so we get

so if we divide both sides by 5 we get

This means that we can give values to a and b freely. Recall that a must be positive. So let us choose a=1 and b=3. So our equation becomes

Now we need to give values for c. Note that if x = -4, we have that

so, we subtract c 4 from both sides and we get

So our equation becomes

Let us check that it passes through the other point. Note when x=1 we have

so this equation fulfills the task

Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:

p(x) = (x + 1) q(x)

for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:

p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0

So,

0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c

= -5 + 7 - 2 + 3 + c

= c = 3

So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.

The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.

Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:

(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)

This is the vector equation; getting the parametric form is just a matter of delineating

x(t) = 1 + t

y(t) = 3t

z(t) = 6 + t

The vector equation for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5 is v =(1+t)i + (3t)j + (6+t)k

The parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5

The parametric equation of a line through the point A(x, y, z) perpendicular to the plane ax+by+cz= d is expressed generally as:

A + vt where:

A = (x, y, z)

v = (a, b, c) (normal vector)

This can then be expressed as:

s = A + vt

s = (x, y, z) + (a, b, c)t

Given the point

(x, y, z) = (1,0,6)

(a, b, c) = (1, 3, 1)

Substitute the given coordinate into the equation above:

s = (1,0,6) + (1, 3, 1)t

s = (1+t) + (0+3t) + (6+t)

The parametric equations from the equation above are:

x(t) = 1+t

y(t) = 3t

z(t) = 6+t

The vector equation will be expressed as v = xi + yj + zk

v =(1+t)i + (3t)j + (6+t)k

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Answer:

V = a^7b^3

Step-by-step explanation:

Volume = length × width × height

Vol =

a^2 × a^4b^2 × ab

This is all multiplication, so we can rearrange.

a^7b^3

This is a to the seventh power times b to the 3rd power.

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Explanation:

Let's go through each of the answer choices to see which are true and which are false.

----------------

Choice A

The general slope intercept form is y = mx+b

m = slope and b = y intercept.

For y = 3x+1, the boundary line of the first inequality, the slope is 3.

For y = -x+2, the slope is -1.

None of the slopes are 2.

Choice A is false.

We'll use the concept of slope again in choice E.

----------------

Choice B

The "or equal to" part of the inequality sign is what directly determines the boundary line being solid. This is because we include points on the boundary.

Choice B is true.

----------------

Choice C

Plug x = 1 and y = 3 into the first inequality

\(y \le 3x+1\\\\3 \le 3(1)+1\\\\3 \le 3+1\\\\3 \le 4\\\\\)

The last inequality is true, so the first inequality is true when (x,y) = (1,3). This makes (1,3) a solution to \(y \le 3x+1\\\\\)

Repeat those steps for the other inequality given to us

\(y \ge -x+2\\\\3 \ge -1+2\\\\3 \ge 1\\\\\)

which is also true, so that makes (1,3) also a solution to \(y \ge -x+2\\\\\)

The point (1,3) is a solution to both inequalities at the same time, making it a solution to the system overall.

Choice C is true

----------------

Choice D

When y is fully isolated, the "less than" inequality indicates the shading is below the boundary. This is due to us considering points of y coordinates smaller than the boundary line. So we'll shade below the boundary for \(y \le 3x+1\\\\\)

We don't do the same for \(y \ge -x+2\\\\\). Instead, we'll shade above the solid boundary line.

Choice D is false.

----------------

Choice E

If two lines have equal slopes, but different y intercepts, then we have parallel lines. Parallel lines never intersect.

If on the other hand, the slopes are different values, then the two lines will intersect somewhere on the xy grid. There will only be exactly one point of intersection.

The given system has boundary lines of slopes 3 and -1, for the first and second inequality respectively. Refer back to choice A.  These differing slopes tell us that the boundary lines intersect somewhere.

Choice E is true

Let's go through all the options one at a time and look for the correct ones

Option 1: The slope of one boundary line is 2

We have 2 equations of lines, where the coefficients of are 3 and -1 respectively

because the coefficient of x denotes the slope of a line, we know that the lines have the slope 3 and -1, not 2

Hence, this option is Incorrect

Option 2: Both boundary lines are solid

In order for the boundary lines to be solid, the inequality must have an 'equal to', like ≤ (less than or equal to) or ≥ (greater than or equal to)

we can see that that's the case in our case and hence, this option is Correct

Option 3: A solution to the system is (1, 3)

To confirm this, we'll plug these coordinates into the given inequalities and see if it stands correct

y ≤ 3x + 1

3 ≤ 3(1) + 1

3 ≤ 4 which is correct because 3 is less than 4

Second equation:

y ≥ 2 - x

3 ≥ 2 - 1

3 ≥ 1

Which is also true because 3 is greater than 1

Now, we can say that (1 , 3) is a solution to the system because it satisfies both the equations and is Correct

Option 4: Both inequalities are shaded below the boundary lines

For an inequality to be shaded below the boundary line, it must have the ≤ inequality (in case of solid line) and < inequality (in case of dotted line)

because the second inequality listed includes the ≥ inequality, which was not mentioned above, it won't be shaded below

another way to think about it is that any 'greater than' inequality will shade everything above the line and the 'lesser than' inequality will shade below the line

which means that this option is Incorrect

Option 5: The boundary lines intersect

In order for the boundary lines to intersect, they must have have different slopes.

as we mentioned in the explanation of the first option, that the slopes of the lines is 3 and -1, which are different slopes

Therefore, this option is Correct

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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Answer:

HJ > KP

Step-by-step explanation:

Form the figure attached,

Two triangles PKL and JGH have been given with HG ≅ KL and PL ≅ GJ

m∠HGJ = 90°

m∠KLP = 85°

Since m∠HGJ > m∠PLK

Therefore, measure of opposite sides of these angles have the same relation.

HJ > KP

8 dollars

Step-by-step explanation:

without rounding it is $7.52 but you would round that to 8

Answer:

Positive 8 3/4

Step-by-step explanation:

My way:

-1 2/3 times -5 1/4

- 1 2/3 simplifies to -5/3

-5 1/4 simplifies to -21/4

-5/3 times -21/4 is 35/4

Simplify that which is 8 3/4

(negative times negative = positive)

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meow meow hahaha

The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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The vertex form of the parabola is y + 1 = - 4 · (x + 1)².

Graphically speaking, parabolae can be generated by quadratic equations, whose forms are described below: (Please notice that the parabola described by statement is parallel to y-axis since axis of symmetry is a vertical line)

Standard form

y = a · x² + b · x + c

Vertex form

y - k = C · (x - h)²

Where:

If we know that h = - 1, k = - 1 and (x, y) = (0, - 5), then the equation of the parabola in vertex form is:

C = (y - k) / (x - h)²

C = (- 5 + 1) / (0 + 1)²

C = - 4 / 1²

C = - 4

The equation of the parabola in vertex form is equal to y + 1 = - 4 · (x + 1)².

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Answer:

f(x) = (x+2)(x+4)

Step-by-step explanation:

4 + 2 = 6

4 * 2 = 8

f(x) = (x+2)(x+4)

Answer:

The price for one pound of cherries is $3.5

Step-by-step explanation:

$9.8/2.8= $3.5 for one pound of cherries

Answer:

$3.50

Step-by-step explanation:

Divide 9.80 by 2.8 and add a zero to get $3.50 per pound. Hope this helps.

Answer:

a

Step-by-step explanation:

The solution of the linear equation  is determined as x = -4.

The solution of the linear equation is calculated by applying the following method as follows;

The given linear equation;

2/x+3 - 1/x = -4/x² +3x

We can start by simplifying the equation and getting rid of the fractions.

Multiplying every term by x will help us achieve that:

2 + 3x - 1 = -4/x + 3x²

Simplifying further:

2 + 3x - 1 = (-4 + 3x²) / x

Combining like terms:

3x + 1 = (-4 + 3x²) / x

(x)(3x + 1) = -4 + 3x²

3x² + x = -4 + 3x²

We can subtract 3x² from both sides:

x = -4

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y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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The percentile for a redwood tree that is 375 feet tall would be 93rd percentile. This is because the z-score of 1.5 (375-360/10) corresponds to a percentile of 93.

Step 1: Find z-score

z-score = (375-360)/10 = 1.5

Step 2: Find percentile

Using a z-score table, the percentile corresponding to a z-score of 1.5 is 93.

Therefore, the percentile for a redwood tree that is 375 feet tall is 93rd percentile.

The percentile of a redwood tree that is 375 feet tall can be determined using a z-score table. The z-score of a data point is the difference between the data point and the mean, divided by the standard deviation. In this case, the z-score is (375-360)/10 = 1.5. This z-score corresponds to a percentile of 93 on a z-score table. Therefore, the percentile for a redwood tree that is 375 feet tall is 93rd percentile. This means that 93% of redwood trees are shorter than 375 feet tall. It also means that only 7% of redwood trees are taller than 375 feet tall. This information can be used to compare the size of a particular redwood tree to other redwood trees.

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The probability of rolling a sum from 2 to 12 on 2 dices is 100%

Given the data,

The two dice should be rolled.

Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).

The resultant 36 results are as follows:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6

2-1, 2-2, 2-3, 2-4, 2-5, 2-6

3-1, 3-2, 3-3, 3-4, 3-5, 3-6

4-1, 4-2, 4-3, 4-4, 4-5, 4-6

5-1, 5-2, 5-3, 5-4, 5-5, 5-6

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

When using two dice, there are a total of 36 possibilities that might occur.

As a result, the results' total ranges from 2 to 12.

Hence , the probability is 100 %

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Answer:

The answer is 2240m².

Step-by-step explanation:

Given that the formula of area of trapezium is A = 1/2×(a+b)×h where a and b represents the length and h is height :

\(area = \frac{1}{2} \times (a + b) \times h\)

\(let \: a = 50 \\ let \: b = 90 \\ let \: h = 32\)

\(area = \frac{1}{2} \times (50 + 90) \times 32\)

\(area = \frac{1}{2} \times 140 \times 32\)

\(area = 70 \times 32\)

\(area = 2240 \: {m}^{2} \)

Answer:

2,240 square meters

Step-by-step explanation:

The shape above is a trapezoid. Therefore, we can use the area formula for a trapezoid:

A=1/2(a+b) *h

where a is the short base, b is the long base is h is the height.

In this trapezoid, the short base is 50 meters , the long base is 90 meters and the height is 32 meters.

a= 50

b=90

h=32

A=1/2(50+90)*32

Add inside the parentheses first.

A=1/2(140)*32

Multiply 1/2 and 140, or divide 140 by 2.

A=70*32

Multiply 70 and 32

A=2240

Add appropriate units. In this case, the units are meters^2

A=2240 meters^2

The area of the playground is 2,240 meters^2

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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