If ON= 5x - 7, LM = 4x+ 4, NM = x -7, and OL =3y-4, find the values of c and y for which LMNO MUST BE a parallelogram.

Answer:

f(x) ⇒ Graph C

g(x) ⇒ Graph D

h(x) ⇒ Graph A

j(x) ⇒ Graph E

Step-by-step explanation:

* Lets revise the quadratic function and its inverse

- The quadratic function if f(x) = x², its vertex is the origin

- To find its inverse, switch x and y and solve for y

∵ y = x² ⇒ switch x and y

∴ x = y² ⇒ solve for y

∴ y = ± √x

- If y = √x , then the graph is up the x-axis

- If y = -√x , the graph is down the x-axis

∴ The inverse function is y = √x

* Now lets solve the problem

- All the figure are the inverses of the quadratic function y = x²

∵ f(x) = √(x - 1)

# x - 1 means the graph move to the right 1 unit

∴ Its vertex is (1 , 0)

* The graph of f(x) = √(x - 1) is graph C

∵ g(x) = -√x

# The sign (-) means the graph reflected about the x-axis

∴ Its vertex is (0 , 0) but the graph under the x-axis

* The graph of g(x) = -√x is graph D

∵ h(x) = √x

∴ Its vertex is (0 , 0)

- It is the inverse of y = x² , the graph up to the x-axis

* The graph of h(x) = √x is graph A

∵ j(x) = -√(x - 1)

# x - 1 means the graph move to the right 1 unit

# The sign (-) means the graph reflected about the x-axis

∴ Its vertex is (1 , 0) , the graph down the x-axis

* The graph of j(x) = -√(x - 1) is graph E

Answer: -x^2+12x+3

Step-by-step explanation:

3q - 2p; all you are doing is simplifying straight across. I think you got confused by the parentheses unwrapped around 6p - 9q. Well, it is STILL the same process.

Find the exact value of each one:

5^2 = 25

2^4 = 16

3^3 = 27

1^8 = 1

Now you can list them in order from smallest to largest:

1^8, 2^4, 5^2, 3^3

Answer:

Step-by-step explanation:

5²=25

2^4=16

3^3=27

1^8=1

1<16<25<27

so 1^8<2^4<5^2<3^3

Answer:

17) Ф = 57.99 ≅ 58°

18) Ф = 20.10 ≅ 21°

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problems

17) In Δ ACB

∵ m∠C = 90°

∵ BC = 16 units ⇒ opposite to angle Ф

∵ AC = 10 units ⇒ adjacent to angle Ф

∵ tanФ = opposite/adjacent

∴ tanФ = BC/AC

∴ tanФ = 16/10 = 8/5

- To find angle Ф find the inverse of tan (tan^-1)

∴ Ф = tan^-1 8/5 = 57.99 ≅ 58°

18) In Δ ACB

∵ m∠C = 90°

∵ BC = 5.6 units ⇒ opposite to angle Ф

∵ AC = 15.3 units ⇒ adjacent to angle Ф

∵ tanФ = opposite/adjacent

∴ tanФ = BC/AC

∴ tanФ = 5.6/15.3 = 56/153

- To find angle Ф find the inverse of tan (tan^-1)

∴ Ф = tan^-1 56/153 = 20.10 ≅ 21°

Answer:

17).  θ = 57.99°

18).  θ =20.10°

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

Question (17).

From the figure we can write,

Tan θ = Opposite side/Adjacent side

= BC/AC = 16/10 = 1.6

θ = Tan⁻¹ (1.6) = 57.99°

Question 18)

From the figure we can write,

Tan θ = Opposite side/Adjacent side

= BC/AC = 5.6/15.3 = 0.366

θ = Tan⁻¹ (0.366) = 20.10°

Answer:2 > -6 or -6 < 2

Step-by-step explanation:

Answer:  2>-6 is correct

Step-by-step explanation:

We know that 2 is a grater number than -6 so what we can do is put this > but make sure that its facing the 2 and there its simple  hope I helped! :p plz rate me

Answer:

First question

a = 1 , h = 0 , k = 6 ⇒ third answer

Second question

y = 2x² + 4 ⇒ second answer

Third question

No of the choices correct ⇒ fourth answer

Step-by-step explanation:

First question

∵ f(x) = x² + 6

- It is a quadratic function with general form ax² + bx + c

- Its vertex is (h , k), where h = -b/2a and k = f(h)

∵ a = 1 , b = 0 , c = 6

∴ h = 0/2(1) = 0

∴ f(0) = 0² + 6 = 6

∴ a = 1 , h = 0 , k = 6 ⇒ third answer

Second question

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

∵ y = 2x²

∵ y is shifted 4 units up

∴ k = 4

∴ y + 4 = 2x² + 4

∴ y = 2x² + 4 ⇒ second answer

Third question

∵ y = -2x² + 3

- It is a quadratic equation with general form ax² + bx + c

- It represented graphically by parabola

- If a is positive the parabola opens upward

- If a is negative the parabola opens downward

∵ a = -2

∴ The parabola opens downward

∴ No of the choices correct ⇒ fourth answer

Answer:

t+m=20--------> t=20-m

3t+11m=100

Substitute

3(20-m)+m=100

60m-3m+11m=100

Get rid of 60

-3m+11m=40

8m=40

Divide by 8

m=5

This tells us that there are 5 Multiple Choice questions. So the remaining 15 question on the test must be True/False questions.

If we got all 5 Multiple Choice questions correct we would score 11 points for each of the five questions and this would give us 55 points. Then if we got all 15 True/False questions correct at 3 points each, we would score 15 times 3 or 45 points. So the total number of points on the test would be 55 + 45 = 100.

Step-by-step explanation:

The answer is:

There are 15 true/false questions while there are 5 multiple choice questions.

To solve the problem, we need to write two equations using the given information.

We know that there are twenty (20) questions consisting of true/false and multiple choice questions, so, writing the first equation we have:

Let be the true/false questions "x" and the multichoice questions "y".

First equation,

[tex]x+y=20[/tex]

Also, we know that the true/false questions worth 3 points while the  multichoice questions worth 11 points making a total of 100 points for the total examen, so, writing the second equation, we have:

Second equation,

[tex]3x+11y=100[/tex]

Now, we have to isolate one of the variables in function of the other variable, so, from the first equation, we have:

[tex]x+y=20[/tex]

[tex]x=20-y[/tex]

Then, substituting "x" into the second equation, we have:

[tex]3x+11y=100[/tex]

[tex]3(20-y)+11y=100[/tex]

[tex]60-3y+11y=100[/tex]

[tex]60+8y=100[/tex]

[tex]8y=100-60=40[/tex]

[tex]y=\frac{40}{8}=5[/tex]

Then, substituting "y" into the first equation, we have:

[tex]x+y=20[/tex]

[tex]x+5=20[/tex]

[tex]x=20-5=15[/tex]

Hence, we have that there are 15 true/false questions while there are 5 multiple choice questions.

Let's prove that we are right by substituting the obtained answers into the both equations, if the equations are satisfied, the answers are ok.

Substituting into the first and the second equation, we have:

First equation,

[tex]x+y=20\\5questions+15questions=20questions\[/tex]

Second equation,

[tex]3x+11y=100points\\3*(15)+11*(5)=100points\\45points+55points=100points[/tex]

We can see that both equations are satisfied, so, the answers are ok.

Have a nice day!

Answer:

All real numbers

Step-by-step explanation:

This equation is well defined for all real values of x, hence

domain : x ∈ R

[tex]\text{Hey there!}[/tex]

[tex]\text{Both numbers are divisible to 4, so divide the numerator and denominator from 4}[/tex]

[tex]\frac{7,848\div4}{4\div4}[/tex]

[tex]\text{7,848}\div4=1,962[/tex]

[tex]\text{4}\div4=1[/tex]

[tex]\text{1,962}\div1=1,962[/tex]

[tex]\boxed{\boxed{\text{Answer: 1,962}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

2 pounds total!

3/6 * 4 cans = 2 pounds

Answer:

The weight of 4 cans of peaches will be 2 pounds if one can of peaches weigh 3/6 pound.

Step-by-step explanation:

We need to find the weight of 4 cans of peaches altogether.

Weight of 1 can of peaches = 3/6 pounds

Weight of 4 cans of peaches = 3/6 * 4

                                                = 12 / 6

                                                = 2 pounds.

So, The weight of 4 cans of peaches will be 2 pounds if one can of peaches weigh 3/6 pound.

The question is a binomial distribution problem in mathematics. You can use the binomial probability formula to calculate the probability that exactly 4 out of 8 treated dolphins are cured.

This mathematics problem involves understanding probability and the binomial distribution. The word 'exactly' is a clue that this is a binomial problem.

The general formula for a binomial probability is: P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where:

So, if we substitute the values into the formula, we have:

P(X = 4) = C(8, 4) * (0.94^4) * ((1-0.94)^(8-4))

Therefore, Use this formula to find the probability that exactly 4 out of 8 dolphins are cured.

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Hello There!

[tex]\frac{18}{20}[/tex] as a decimal is 0.9

You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 18 and 20 using 2.

18 ÷ 2 ≈ 9

20 ÷ 2 ≈ 10

We now have the fraction [tex]\frac{9}{10}[/tex]

Finally, we divide 9 by 10 and we get a quotient of 0.9

The equivalent value of the decimal is A = 18/20 = 0.9

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the numerator of the fraction be p

where the value of p = 18

Let the denominator of the fraction be q

where q = 20

Now , the fraction is A = p/q

On simplifying the expression , we get

So , the left hand side of the equation is equated to the right hand side by the value of p/q

A = 18/20

A = 9/10

On further simplification , we get

A = 0.9

So , the decimal number is A = 0.9

Therefore , the value of A = 0.9

Hence , the expression is A = 0.9

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Answer:

A=13+B

Step-by-step explanation:

Linda earns $13  each hour working part-time at a bookstore.

Linda earns $1 for each book she sells.

Let

A be the amount (in dollars) that Linda earns in an hour;

B be the number of books Linda sells in an hour.

So,

[tex]A=13+B\cdot 1\\ \\A=13+B[/tex]

The graph is shown in attached diagram

Answer:

Step-by-step explanation:

It's the parallelogram. The formula of an area of a parallelogram:

A = bh

b - base

h - height

We have b = 11 ft, h = 6.1 ft. Substitute:

A = (11)(6.1) = 67.1 ft²

Answer:

12

Step-by-step explanation:

we can see that the base's size is doubled, from that we can find that 6 will be doubled to twelve.

Answer: 12

Step-by-step explanation: The Answer is 12. This is because the numbers on the left are 2x less than on the right.

Answer:

Step-by-step explanation:

Surface area of a cylinder = 2 x 3.14 x rh + 2 x 3.14 x r^2

S.A. = (2 x 3.14 x 3 x 18.2) + (2 x 3.14 x 3^2)

S.A. = 399.4cm^2

Answer:

x = 2.

y =  6.

Step-by-step explanation:

Consider the triangle on the left.

Because there are 2 equal angles at the vertex on the bottom right:

3/9 = x/(8 - x)

1/3 = x / (8 - x)

3x = 8 - x

4x = 8

x = 2  (answer).

Similarly, for the second triangle:

3/y = 2/4

3/y = 1/2

y = 6

(answer).

The answer is C. Compass.

Compass isn't used in the geometric constructions.

Among pencil, protractor, compass, ruler protractor is not used in the geometric constructions.

Geometric construction refers to the process of drawing lines, angles and other geometric shapes and figures using only a compass and a ruler.

There are four things pencil, protractor, compass, ruler.

For any drawing we need a pencil, To draw straight lines we need a ruler and to draw circles we need to use compass.

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Answer:

(−1, –1.25), (5, –2.75)

Step-by-step explanation:

If "slope-intercept form" is mentioned, then we already know that the function rule is that of a straight line with slope m and y-intercept b.

As we go from (−1, –1.25) to (5, –2.75), x increases by 6 and y decreases by 1.50.  Thus, the slope, m, is m = rise / run = -1.50 / 6, or m = -0.25 or -1/4.

Choosing one of the given points at random:  (8, -3.5), we start with the slope-intercept form y = mx + b and substitute -1/4 for m, 8 for x and -3.5 for y:    y = mx + b  becomes  -3.5 = (-1/4)(8) + b.  Then -3.5 + 2 = b, or b = -1.5.

The desired equation is y = (-1/4)x - 3/2, or y = -0.25x - 1.5

To write a function rule in slope-intercept form for the given ordered pairs, we need to calculate the slope and find the y-intercept. The slope can be calculated using the formula (Y2 - Y1) / (X2 - X1), and the y-intercept can be found by using the point-slope form and substituting one of the ordered pairs. The function rule in slope-intercept form for the given ordered pairs is y = -0.25x - 1.5.

To write a function rule in slope-intercept form, we need to find the slope (m) and the y-intercept (b). Given the ordered pairs (–12, 1.5), (−1, –1.25), (5, –2.75), (8, −3.5), we can calculate the slope using the formula m = (Y2 - Y1) / (X2 - X1). Let's choose two ordered pairs to calculate the slope:

Using (–12, 1.5) and (−1, –1.25):

m = (-1.25 - 1.5) / (-1 - (-12)) = (-2.75) / (11) = -0.25

Now, we can use the point-slope form y - y1 = m(x - x1), where (x1, y1) is one of the ordered pairs and substitute the slope and one of the points to find the y-intercept:

Using the ordered pair (–12, 1.5):

y - 1.5 = -0.25(x - (-12))

y - 1.5 = -0.25(x + 12)

y - 1.5 = -0.25x - 3

y = -0.25x - 3 + 1.5

y = -0.25x - 1.5

Therefore, the function rule in slope-intercept form (fraction form) is y = -0.25x - 1.5.

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Basically, the question is asking for 18% of $23.

The answer is $4.14.

The tip was $4.14, because you take 18% of $23 and then you end up with $4.14

Hello There!

The "Inter-Quartile Range" is 9

Answer:

The interquartile range is 9

Step-by-step explanation:

Answer:

A = 90 - x

Step-by-step explanation:

The square on the lower right means the two line segments form a right angle.

If B = x

and C = 90

the A = 180 - x - 90    (Every triangle has 180 degrees -- no exceptions).

A = 90 - x

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given a number n then the multiplicative inverse is [tex]\frac{1}{n}[/tex]

The product of a number and it's multiplicative inverse = 1

Given 2, then multiplicative inverse is [tex]\frac{1}{2}[/tex]

Answer:

A)3,9

Step-by-step explanation:

lets take the length as "x"

since the width is 3 times the length we can use 3x to represent the width

formula for perimeter: 2(l)+2(w)

2(x)+2(3x)=24

2x+6x=24

8x=24

8x/8=24/8

x=3

if x is 3, the length is 3

if x is 3, the width, 3x is 9, (3*3)

The dimensions of the rectangle are a length of 9 inches and a width of 3 inches, with the width being one-third of the length. This corresponds to option D (9, 3) in the list of given choices.

The length and width of the rectangle when the perimeter is 24 inches and the length l is 3 times the width w, we can set up equations based on the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Given that l = 3w, we substitute this into the perimeter formula to get:
24 = 2(3w) + 2w24 = 6w + 2w24 = 8w
Dividing both sides by 8 to solve for w:
w = 3

Now that we know the width is 3 inches, we can find the length by multiplying the width by 3:
l = 3w = 3(3) = 9

So, the length is 9 inches, and the width is 3 inches, which corresponds to option D. Therefore, the dimensions of the rectangle are a length of 9 inches and a width of 3 inches.

Answer:

-480

Step-by-step explanation:

If f varies directly as g, and inversely as h, then we can write the variation equation:

[tex]f=\frac{kg}{h}[/tex], where k is the constant of variation.

If g=56 when h=-2 and f=-7, then we substitute these values into the formula to find the value of k.

[tex]-7=\frac{k(56)}{-2}[/tex]

[tex]-7\times -2=56k[/tex]

[tex]k=\frac{14}{56}=\frac{1}{4}[/tex]

The equation now becomes:

[tex]f=\frac{g}{4h}[/tex]

if f=10 and h=-12, then;

[tex]10=\frac{g}{-48}[/tex]

[tex]g=-48\times 10=-480[/tex]

The correct answer is B.

To find g when f = 10 and h = -12, use the formula for direct variation: f = kg. Substituting the given values, we can solve for g.

We are given that f varies directly as g, and f varies inversely as h. To find g when f = 10 and h = -12, we can use the formula for direct variation: f = kg, where k is the constant of variation. So, f/g = k. Substituting the given values, we have 10/g = k. To find k, we need to find g when f = -7 and h = -2. Using the same formula, we have -7/g = k. Since k is the same constant in both cases, we can equate the two equations: 10/g = -7/g. Solving for g, we get g = -70/10 = -7.

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13. y > 2

14. x - 13 < 9;; x < 22

15. x + 86 < 263;; at most 177 pounds

The volume of the gigantic fridge is 2.5 times grater than the volume of the regular fridge.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic m.

The volume is found as the product of the area and the length;

Volume  = Area ×length

V=A×L

Volume of the regular fridge;

V=  1 m²× 2 m

V=2 m³

Volume of the large fridge;

V=  2 m²× 5/2 m

V=5 m³

The ratio of the volume of the gigantic fridge as the volume of the regular fridge is;

[tex]\rm n = \frac{5}{2} \\\\ n= 2.5[/tex]

Hence, volume of the gigantic fridge is 2.5 times grater than the volume of the regular fridge

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Answer: x= 8

Step-by-step explanation:

x^2 = 64

sqrt{x^2} = sqrt64}

x = 8

it’s the last option

The  correct application of the quadratic formula is:

               [tex]x=\dfrac{9\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]

The quadratic equation is given by:

[tex]y=6x^2-9x+22[/tex]

We know that the solution of the quadratic equation:

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

is given by:

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

Here we have:

[tex]a=6[/tex]

[tex]b=-9[/tex]

and

[tex]c=22[/tex]

Hence, the quadratic formula is given by:

[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4\cdot (6)\cdot (22)}}{2\cdot (6)}[/tex]

i.e.

[tex]x=\dfrac{9\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]