Find the measure of XY

(-4, 0)

(-0.667, 0)

(0.5, 0)

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Equation of directrix is : y = 1, so we can say that it's a parabola of form : -

[tex]\qquad \sf  \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)[/tex]

and since the focus is above the directrix, it's a parabola with upward opening.

[tex]\qquad \sf  \dashrightarrow \: (x - ( - 4)) {}^{2} = 4(2)(y - 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (x + 4) {}^{2} = 8(y - 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 8x + 16 = 8y - 40[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8y = {x}^{2} + 8x + 56[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \cfrac{1}{8} {x}^{2} + x + 7[/tex]

Directrix

Focus

Focus lies in Q3 and above y=1

Then

Perpendicular distance

Find a for the equation

Now the equation is

[tex]\\ \rm\dashrightarrow 4a(y-k)=(x-h)^2[/tex]

[tex]\\ \rm\dashrightarrow 4(2)(y-5)=(x+4)^2[/tex]

[tex]\\ \rm\dashrightarrow 8(y-5)=x^2+8x+16[/tex]

[tex]\\ \rm\dashrightarrow 8y-40=x^2+8x+16[/tex]

[tex]\\ \rm\dashrightarrow 8y=x^2+8x+16+40[/tex]

[tex]\\ \rm\dashrightarrow 8y=x^2+8x+56[/tex]

[tex]\\ \rm\dashrightarrow y=\dfrac{x^2}{8}+x+7[/tex]

Answer: 10 tables in each room 14 kids at each table

The letter for the graphed function is y = √(x) - 5

The parent function is given as:

y = √x

From the graph, we can see that the function is shifted downwards by 5 unts

This is represented as:

y = √(x) - h

Where h = 5

Substitute the known values in the above equation

y = √(x) - 5

This means that the letter for the graphed function is y = √(x) - 5

Hence, the letter for the graphed function is y = √(x) - 5

So, the complete functions are

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The pounds of alloy that contains 26% copper that would be used is  23.42 pounds.

The pounds of alloy that contains 69% copper that would be used is 29.58 pounds.

0.26a + 0.69b = (53 x 0.5)

0.26a + 0.69b = 26.50 equation 1

a + b = 53 equation 2

Where:

Multiply equation 2 by 0.26

0.26a + 0.26b = 13.78 equation 3

Subtract equation 3 from equation 2

12.72 = 0.43b

b = 12.72 / 0.43

b = 29.58 pounds

a = 53 - 29.58 = 23.42 pounds

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Answer:

yes

Step-by-step explanation:

yes

Answer:

35

Step-by-step explanation:

Since the two sides are equal in a parallelogram angle B = y ,so we have angle to be equal to 145°

We sum both angles and divide from

360° - [145° +145°]

360° - 290° = 70

Since the left sides( X And Z) are equal then we divide what we got into 2

70 ÷ 2 = 35

therefore angle X equals 35

Answer:

4

Step-by-step explanation:

this is the same question as what number can divide

13-1 = 12, 17-1 = 16 and 21-1 = 20 and has 0 remainder ?

the greatest number that can do that is 4.

we can easily see that, but formally, let's do prime factorization :

12 ÷ 2 = 6

6 ÷ 2 = 3

3 ÷ 2 no

3 ÷ 3 = 1 finished

12 = 2×2×3

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1 finished

16 = 2×2×2×2

20 ÷ 2 = 10

10 ÷ 2 = 5

5 ÷ 2 no

5 ÷ 3 no

5 ÷ 5 = 1 finished

20 = 2×2×5

so, the largest common factor is the combination of the longest streaks per factor they have in common.

they only have 2s in common.

and the longest common streak is 2×2 = 4.

hence the answer

Answer:

  ∠a = 39°

  ∠b = 129°

Step-by-step explanation:

Vertical angles are congruent. An exterior angle of a triangle is equal to the sum of the remote interior angles.

Angle y and angle 'a' are vertical angles, so congruent.

  ∠a = ∠y = 39°

The angle marked 'b' is an exterior angle to the triangle. Its remote interior angles are 'a' and the one marked 90°.

  ∠b = ∠a +90° = 39° +90°

  ∠b = 129°

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

In the given figure, angles a and y are vertically opposite angles. The measure of vertical angles is equal, therefore :-

[tex]\small\longrightarrow\sf{m<a = m<y}[/tex]

[tex]\small\longrightarrow\sf{m<a= \: 39^\circ}[/tex]

Next, angles a and 90° are the opposite interior angles to the exterior angle b. By the triangle theorem below :-

[tex]\small\longrightarrow\sf{m<b=m<a+90^\circ}[/tex]

[tex]\small\longrightarrow\sf{39^\circ+90^\circ}[/tex]

• [tex]\small\longrightarrow\sf{m<b= 129^\circ}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

m<a= [tex]\large\sf{\boxed{\sf 39^\circ}}[/tex]

m<b = [tex]\large\sf{\boxed{\sf 129^\circ}}[/tex]

The theorem used and the angle measures are:

D. corresponding angles postulate

m∠1 = 150°, m∠2 = 150°

According to the corresponding angles postulate, if two angles lie on same relative corner along a transversal that cuts two parallel lines (corresponding angles), then their measures are equal.

Thus, ∠1 and ∠2 are corresponding angles, therefore:

m∠1 = m∠2 [corresponding angles postulate]

Given the following:

m∠1 = (50x − 50)∘,

m∠2 = (20x + 70)∘

Therefore, we would have:

50x − 50 = 20x + 70

Subtract 20x from both sides

50x − 50 - 20x = 20x + 70 - 20x

30x − 50 = 70

Add 50 to both sides of the equation

30x − 50 + 50 = 70 + 50

30x = 120

Divide both sides by 30

30x/30 = 120/30

x = 4

Plug in the value of x

m∠1 = (50x − 50) =  50(4) − 50 = 150°

m∠2 = (20x + 70)∘ = 20(4) + 70 = 150°

Thus, the answer is: D. corresponding angles postulate

m∠1 = 150°, m∠2 = 150°

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Answer:

Step-by-step explanation:

1 liter = 1000 milliliters

so

3 liters = 3000 milliliters

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

1 : 1000 = 3 : x

x = 3 * 1000 : 1

x = 3000

Answer: 3000 mL

Step-by-step explanation:

1 L = 1000 mL

3x1000 = 3000

The volume of the cone illustrated will be 117.2 unit³.

From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.

It should be noted that the volume of a cone is calculated as:

= 1/3 πr²h.

where,

π = 3.142

r = radius = 4cm

h = height = 7cm

In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:

= 1/3πr²h

= 1/3 × 3.14 × 4² × 7

= 117.2 unit³

Therefore, the volume of the shape is 117.2 unit³.

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Complete question:

A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.

Answer:

C. x > 5 or x < - 3

Step-by-step explanation:

Step 1:

x - 1 > 4

x > 4 + 1

x > 5

Step 2:

x - 1 < -4

x < -4 + 1

x < -3

HP: {x > 5 or x < -3} (c)

Answer:

Step-by-step explanation:x+y+z=100(let x ,y,z represent the first second and third numbers respectively)

Therefore,y=2z

z=x-8

y=2x-16

substituting the values of x,y and z into the question,we have

x+(2x-16)+(x-8)=100

Simplifying,we have

4x-24=100

adding 24 to both sides of the equation,

4x=100+24

4x=124

dividing both sides of the equation by the co-efficient of x,we have

4x/4=124/4

4.31=124

therefore,x=31.

The number of years it would take sales to reach $1,750,000 is 14.65 years.

The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:

Number of years : In (FV / PV) / r

Where:

Number of years : In ($1,750,000 / 850,000) / 0.04931998

Number of years : In (2.06) / 0.04931998

Number of years : 14.65 years

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Answer:

16 batches

Step-by-step explanation:

we can divide 12 by 3/4 or 0.75: 12/0.75 = 16

The factored form of the given quadratic expressions are

1. (x -1)(x +7)

2. (x -2)(x -3)

3. (x +1)(x -7)

4. (x -1)(x +6)

5. (x -3)(x +4)

6. (x +2)(x -4)

7. (x +1)(x -5)

8. (x -1)(x +3)

9. (x +4)(x -4)

10. (x +3)(x -4)

11. (x -3)(x -6)

12. (x +2)(x -7)

13. (x -2)(x -5)

14. (x -3)(x -8)

15. (x +5)(x -6)

From the question we are to factor the given quadratic expressions

1. x² + 6x - 7

x² +7x -x - 7

x(x +7) -1(x +7)

(x -1)(x +7)

2. x² -5x +6

x² -3x -2x +6

x(x -3) -2(x -3)

(x -2)(x -3)

3. x² -6x -7

x² -7x +x -7

x(x -7) +1(x -7)

(x +1)(x -7)

4. x² +5x -6

x² -x +6x -6

x(x -1) +6(x -1)

(x -1)(x +6)

5. x² + x - 12

x² +4x -3x -12

x(x +4) -3(x +4)

(x -3)(x +4)

6. x² -2x -8

x² -4x +2x -8

x(x -4) +2(x -4)

(x +2)(x -4)

7. x² -4x -5

x² -5x +x -5

x(x -5) +1(x -5)

(x +1)(x -5)

8. x² + 2x - 3

x² +3x -x -3

x(x +3) -1(x +3)

(x -1)(x +3)

9. x² - 16

(x +4)(x -4)

10. x² -x -12

x² -4x +3x -12

x(x -4) +3(x -4)

(x +3)(x -4)

11. x² -9x +18

x² -6x -3x +18

x(x -6) -3(x -6)

(x -3)(x -6)

12. x² -5x -14

x² -7x +2x -14

x(x -7) +2(x -7)

(x +2)(x -7)

13. x² -7x +10

x² -5x -2x +18

x(x -5) -2(x -9)

(x -2)(x -5)

14. x² -11x +24

x² -8x -3x +24

x(x -8) -3(x -8)

(x -3)(x -8)

12. x² -x -30

x² -6x +5x -30

x(x -6) +5(x -6)

(x +5)(x -6)

Hence, the factored form of the given quadratic expressions are

(x -1)(x +7)

(x -2)(x -3)

(x +1)(x -7)

(x -1)(x +6)

(x -3)(x +4)

(x +2)(x -4)

(x +1)(x -5)

(x -1)(x +3)

(x +4)(x -4)

(x +3)(x -4)

(x -3)(x -6)

(x +2)(x -7)

(x -2)(x -5)

(x -3)(x -8)

(x +5)(x -6)

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Step-by-step explanation:

let the younger person be x and older be y

4x + 9 = 24

4x = 15

x = 3.75

y = 24 - 3.75

y = 20.25

Answer:

The answer is 4900, because the next number is less than five, due to that we don't have to add a number (+1).

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I hope help you :)

Kind regards, Antonio.

[tex]{ \red{ \bold{cos \: y \: }}}[/tex]

Step-by-step explanation:

[tex]{ \green{ \tt{ \frac{1 \: + \: \cos \: y \: }{1 \: + \: \sec \: y \: }}}} \: → {eq}^{n} (1)[/tex]

But, as you know that

[tex]{ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{\frac{1}{ \ \cos \: y }}}} [/tex]

Then the equation (1) becomes

[tex]{ \green{ \tt{ \frac{1 \: + \: cos \: y }{1 \: + \: \frac{1}{cos \: y} }}}} \: [/tex]

Multiply Numerator and Denominator by [tex] \frac{cos \: y}{cos \: y} [/tex]

then,

[tex]{ \green{ \tt{( \frac{cos \: y}{cos \: y})}}} \: { \green{ \tt{ \frac{1 \: + \: cos \: y}{1 \: + \: \frac{1}{cos \: y}}}}} [/tex]

[tex] = { \green{ \tt{ \frac{cos \: y \: + \: {cos}^{2} \: y }{cos \: y \: + \: 1 }}}}[/tex]

take cos y as common, then

[tex]{ \green{ \tt{cos \: y}}} \: { \green{ \tt( \frac{1 \: + \: cos \: y}{cos \: y \: + \: 1} )}}[/tex]

Here, (1+cos y/cos y + 1) gets cancelled.

Then the remaining answer is cos y.

Answer:

standard form

hope this helps! <3

The transformation of the function is illustrated below

Parent function is: f(x) = 2x - 6

Transformations are:

shifts f(x) 4 units down

f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10

stretches f(x) by a factor of 4 away from the x-axis

f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24

shifts f(x) 4 units right

f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14

compresses f(x) by a factor of toward the y-axis (must be 4)

f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6

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By the fundamental theorem of calculus,

[tex]\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}[/tex]

In general,

[tex]\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}[/tex]

The integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2

We are given the functions as;

y = ¹/₂x - 2

y = ∛x

Now, from the graph the coordinate of the point where both curves intersect is at; (8, 2)

Thus, the x-coordinate here is x = 8

∛x - (¹/₂x - 2)

∛x - ¹/₂x + 2

Similarly, another point of intersection of both curves is at the coordinate (0, -2). Thus, the x-coordinate here is; x = 0

Thus, the integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2

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Answer: 320 mL

Step-by-step explanation:

Given information

The bottle is currently 3/8 full

Current Volume = 240 mL

Concept:

Imagine the water in the bottle being separated into 8 parts

Currently, 3 parts are being occupied

Determine the volume for 1 part

3 parts = 240 mL

1 part = 240 / 3 = 80 mL

Determine the volume for half-full (4 parts)

1 part = 80 mL

4 parts = 80 × 4 = [tex]\Large\boxed{320~mL}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

160

Step-by-step explanation:

22+18=40, and this was 25% of the cars.

So, 40(4)=160 cars were sold that week.

The number of cars Captain's Autos sold in total that week is 160.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Number of used car on monday= 22

Number of cars on tuesday= 18

Now,

Let's call the total number of cars sold during the week "x".

We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:

22 + 18 = 0.25x

Simplifying, we get:

40 = 0.25x

Dividing both sides by 0.25, we get:

x = 160

Therefore, by the unitary method the answer will be 160.

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Answer:

  76/165

Step-by-step explanation:

The difference of fractions can be found using the formula ...

  a/b -c/d = (ad -bc)/(bd)

Using the given values in the formula, we have ...

  [tex]\dfrac{8}{11}-\dfrac{4}{15}=\dfrac{8(15)-11(4)}{11\cdot15}=\dfrac{120-44}{165}=\boxed{\dfrac{76}{165}}[/tex]

Here, the difference fraction does not need to be reduced. Many calculators and spreadsheets can do this arithmetic for you.

The above formula can also be used for sums of fractions. In that case, the sign changes from minus to plus.

Answer:

Step-by-step explanation:

76/165 is the answer

The common ratio of the given sequence is -1/4. In a geometric sequence, the common ratio is the value that is in between each number in the sequence.

The ratio of the value of a term in the sequence to the value of the previous term in the sequence is said to be the common ratio. I.e.,

C.R = (nth term)/(n - 1)th term

The given sequence is 64, -16, 4, -1, ...

Taking the ratio of the second term to the first term, we get

-16/64 = -1/4

Similarly, the ratio of the third term to the second term,

4/16 = -1/4

Since the ratios are equal, then the common ratio of the sequence is -1/4.

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Answer:

The function would be odd

The answer is neither.

Let's take an odd number and substitute.

Now, let's take an even number.

Since both even and odd numbers are possible, it is neither.

Answer:

⇒  The given quadratic equation is x2−kx+9=0, comparing it with ax2+bx+c=0

∴  We get, a=1b=−k,c=9

⇒  It is given that roots are real and distinct.

∴  b2−4ac>0

⇒  (−k)2−4(1)(9)>0

⇒  k2−36>0

⇒  k2>36

⇒  k>6 or k<−6

∴  We can see values of k given in question are correct.