The measures of ∠1, ∠2, and ∠3 are 40%, 12.5%, and 25% of the sum of the angle measures of the quadrilateral. Find the value of x.

Answer:

lower case p

Step-by-step explanation:

The law of sines: [tex]\frac{sinA}{a} = \frac{sinB}{b}[/tex]

Therefor look for which sides and angles are accounted for. If we are given angle P, Angle R, and Side r, then Side p is the last term that fits into the law of sines equation.

Step-by-step explanation:

[tex] \frac{r}{32} = \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: \frac{r}{32} = \frac{5}{8} \\ \\ \therefore \: r = \frac{32 \times 5}{8} \\ \\\therefore \: r = 4 \times 5\\ \\ \huge \orange{ \boxed{\therefore \: r = 20}} \\ \\ \frac{5}{8} =\frac{30}{t} \\ \\ \therefore \: t = \frac{8 \times 30}{5} \\ \\ \therefore \: t = 8 \times 6 \\ \\ \huge \purple{ \boxed{ \therefore \: t = 48}}[/tex]

Answer:

Step-by-step explanation:

4.75 x [tex]10^{2}[/tex]

Answer:

Step-by-step explanation:

[tex]4.75 x 10^{2}[/tex]

Answer:

The average rate of change is = - 4

Step-by-step explanation:

If y = f(x) is a function then the average rate of change for f(x) between the interval a ≤ x ≤ b is given by

[tex]\frac{f(b) - f(a)}{b - a}[/tex].

Now, in this case the function is given by f(x) = - 4x + 40 and the interval is 1 ≤ x ≤ 3.

Therefore, f(1) = - 4(1) + 40 = 36 and f(3) = - 4(3) + 40 = 28

So, the average rate of change is = [tex]\frac{28 - 36}{3 - 1} = - \frac{8}{2} = - 4[/tex] (Answer)

Answer:

−30

Step-by-step explanation:

−30 is the average rate of change for ƒ(x) = −4x + 40 over the interval 1 ≤ x ≤ 3.

ƒ(b) − ƒ(a)

b − a

=  ƒ(3) − ƒ(1)

3 − 1

=  −24 − 36

2

=  −60

2

= −30

Answer:288

Step-by-step explanation:32 x 9 = 288

Answer: B

Step-by-step explanation: you multiply 25 x 13 + 150

Answer:

it is D. $9.50

Step-by-step explanation:

Answer: The answer is (D) $9.50/9.50 dollars

Answer:

9/2

Step-by-step explanation:

Slope of line=rise/run=

y2-y1/x2-x1

Where

x1=2

x2=0

y1=5

y2= -4

Slope =(-4-5)/(0-2)

Slope=-9/-2

Slope=9/2

Answer:

look at the picture shown

Answer:

Pie

Step-by-step explanation:

Answer:

pi

Step-by-step explanation:

Answer:

y = - 17

Step-by-step explanation:

[tex]y = 1 - 2x[/tex]

When x = 9

[tex]y = 1 - 2(9)[/tex]

[tex]y = 1 - 18[/tex]

[tex]y = - 17[/tex]

Therefore, given equation y = 1 - 2x; when x = 9, y = - 17

Answer:

Step-by-step explanation:

4 - 2b = 2

collect terms

4 - 2 = 2b

2 = 2b

divide both side by 2

2/2 = 2b/2

b = 1

Answer:

32.24 gallons

Step-by-step explanation:

From the question,Jed’s shower head releases

6.2 gallons = 1 minute

x gallon = 5 mins 12 secs

First convert 12 secs to minutes and add it to 5 mins .

1 minute = 60secs

x minute = 12 secs

x = 12/60

= 0.2 mins + 5 mins

= 5.2 mins

Therefore,

6.2 gallons = 1 minute

x gallons = 5.2 mins

Cross multiply

x = 6.2 x 5.2 /1

= 32.24/1

= 32.24 gallons

Degree of polynomials:

[tex]6x^2 = 2\\\\18x^3+5ab-6y = 3\\\\4x^3y +3x^2-xy-4 = 4\\[/tex]

Least to greatest based on degree:

[tex]6x^2[/tex]

[tex]18x^3+5ab-6y[/tex]

[tex]4x^3y +3x^2-xy-4[/tex]

Solution:

The degree of the polynomial is the highest degree of any of the terms

Know that the degree of a constant is zero

Option I

[tex]6x^2[/tex]

Here the highest degree is 2 ( x power 2)

In this case, degree of polynomial is 2

Option II

[tex]18x^3+5ab-6y[/tex]

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

[tex]Degree\ of\ 18x^3 = 3[/tex]

[tex]Degree\ of\ 5ab = 5a^1b^1 = 1+1 = 2[/tex]

[tex]Degree\ of\ 6y = 6y^1 = 1[/tex]

Thus the highest degree is 3

Option III

[tex]8a^{-5}[/tex]

This is not a polynomial

A polynomial does not contain variables raised to negative

Option IV

[tex]4x^3y +3x^2-xy-4[/tex]

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

[tex]Degree\ of\ 4x^3y = 4x^3y^1=3+1 = 4\\\\Degree\ of\ 3x^2 = 2\\\\Degree\ of\ xy = x^1y^1 = 1+1 = 2\\\\Degree\ of\ 4 = 0[/tex]

Thus highest degree is 4

Then organize the expressions from least to greatest based on their degree

Least to greatest based on degree:

[tex]6x^2[/tex]

[tex]18x^3+5ab-6y[/tex]

[tex]4x^3y +3x^2-xy-4[/tex]

The expression 3(4x+7)−4(12x−15) simplifies to -36x + 81. First distribute the constants to the terms inside the parentheses, then combine like terms.

In mathematics, to simplify an algebraic expression like 3(4x+7)−4(12x−15), you need to perform the operations in a certain order, respecting the laws of arithmetic. This is often referred to as simplifying the expression using the distributive property.

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y

=

−

(

x

−

2

)

2

+

16

is the vertex form

Explanation:

The vertex form of a quadratic function is given by

y

=

a

(

x

−

h

)

2

+

k

where (h, k) is the vertex of the parabola.

when written in vertex form

(h, k) is the vertex of the parabola and x = h is the axis of symmetry

the h represents a horizontal shift (how far left, or right the graph has shifted from x = 0)

the k represents a vertical shift (how far up, or down the graph has shifted from y = 0)

Now let convert this  

y

=

−

x

2

+

4

x

+

12

into vertex form

y

=

−

x

2

+

4

x

+

12

y

−

12

=

−

x

2

+

4

x

y

−

12

=

−

(

x

2

−

4

x

)

y

−

12

=

−

(

x

2

−

4

x

+

4

−

4

)

y

−

12

=

−

(

x

2

−

4

x

+

4

)

+

4

y

−

16

=

−

(

x

2

−

4

x

+

4

)

y

−

16

=

−

(

x

−

2

)

2

y

=

−

(

x

−

2

)

2

+

16

is the vertex form

show the vertex in the figure below

graph{-x^2+4x+12 [-10.06, 15.25, 6.58, 19.25]}   Hope iam right

The function f(x) = x² - 4x - 12 in vertex form is f(x) = (x - 2)² - 16, and the axis of symmetry is x = 2.

To rewrite the function f(x) = x² - 4x - 12 in vertex form and find the axis of symmetry, we need to complete the square. The general vertex form of a quadratic is f(x) = a(x - h)² + k, where (h, k) is the vertex, and the line x = h is the axis of symmetry.

The first step is to factor the coefficient of x², which is 1 in this case, so we can leave it as is. The next step is to rearrange the equation as x² - 4x and then add and subtract the square of half the coefficient of x, which is (4/2)² = 4. Adding and subtracting 4 inside the parentheses gives us:

f(x) = (x² - 4x + 4) - 4 - 12

Now we can rewrite this as:

f(x) = (x - 2)² - 16

This equation is in vertex form, with the vertex at (2, -16), and the axis of symmetry is the line x = 2.

Therefore, the correct option is f(x) = (x - 2)² - 16, with the axis of symmetry being x = 2.

Yo sup??

m3 and m6 for a supplementary pair therefore

m3+m6=180

122+m6=180

m6=58

Hope this helps

The required measure of the angle m∠6 is given as 58 degrees. Option B is correct.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For the bisection of parallel line by transversal line,
Corresponding angles always have an equal measure,
So, ∠2 = ∠6

Now,
∠2 + ∠3 = 180

∠6 + 122 = 180
∠6 = 58°

Thus, the required measure of the angle m∠6 is given as 58 degrees. Option B is correct.

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Answer:

In mathematics, compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally...For instance, if we have to add 493 and 549, we can make the numbers compatible by rounding them up to the nearest tens or hundreds.

SO YES! :)

First, we need to find out how many siblings the students have in total and how many siblings the teachers have in total.

The students: (1 x 4) = 4 + (2 x 7) = 18 + (3 x 5) = 33 + (4 x 2) = 41. The students have a total of 41 siblings.

The teachers: (1 x 3) = 3 + (2 x 2) = 7 + (3 x 4) = 19 + (4 x 5) = 39 + (5 x 3) = 54 + (6 x 1) = 60 + (8 x 1) = 68. The teachers have a total of 68 siblings.

Now that we have this information, we know that the answer is option 1, the students tend to have fewer siblings than the teachers. This is because the students had a total of 41 siblings and the teachers had a total of 68 siblings, and 41 is less than 68 so the students have fewer siblings than the teachers.

I really hope I could help! I put a lot of work into this answer! :D

Final answer:

To determine the number of charms for the bracelet to cost the same at both jewelry shops, we set up a system of equations and solved it using substitution. We found that Hana will need to add 2 charms, resulting in a total cost of $96 for the bracelet at either shop.

Explanation:

To determine the number of charms Hana can add to her bracelet such that the cost is the same at Dayton Fine Jewelry and Cain Jewelers, we need to set up a system of equations and solve using the substitution method.

System of Equations:

Let x represent the number of charms and y represent the total cost of the bracelet with charms.

Equation for Dayton Fine Jewelry: y = 17x + 62

Equation for Cain Jewelers: y = 18x + 60

Solution Using Substitution:

Hana will need to add 2 charms to her bracelet, and the total cost of the bracelet will be $96 at either jewelry shop.

Answer:

  use the Pythagorean theorem

Step-by-step explanation:

The slant height is the hypotenuse of a right triangle whose legs are the height of the pyramid and the distance from the edge of the base to the center of the pyramid (where the height segment reaches the base).

For h = pyramid height, b = base edge length, s = slant height, the Pythagorean theorem tells you ...

  h² + (b/2)² = s²

Solving for h gives ...

  h = √(s² -(b/2)²) . . . . . the height of the pyramid

8th term is 0.30

Step-by-step explanation:

⇒ r = a2/a1 = 216/648 = 1/3

⇒ 8th term =  648 × (1/3)^8-1 = 648 × (1/3)^7 = 648/2187 = 0.30

QT = 36

Step-by-step explanation:

Step 1 :

Lines RT and SV are the diagonals of the parallelogram RSTV.

Step 2 :

The diagonals of a parallelogram bisect each other . (Properties of a parallelogram)

Step 3 :

Given that the diagonals RT and SV intersect at Q, we have QT = RQ.

=> 5 x + 1 = 3 x + 15

=> 5 x - 3 x = 15 -1

=> 2 x = 14

= > x = 7

Step 4:

QT = 3 x + 15

=> QT = 3 * 7 + 15

=> QT =  21 + 15 = 36

Applying the properties of the diagonal of a parallelogram, the length of QT = 36 units.

Therefore,

RQ = QT

5x + 1 = 3x + 15

5x - 3x = -1 + 15

2x = 14

x = 7

QT = 3x + 15

QT = 3(7) + 15

QT = 36

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Answer:

Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))

Step-by-step explanation:

Solve for Q:

T = sqrt((P Q)/R) - Q R^2

T = sqrt((P Q)/R) - Q R^2 is equivalent to sqrt((P Q)/R) - Q R^2 = T:

sqrt((P Q)/R) - Q R^2 = T

Add Q R^2 to both sides:

sqrt((P Q)/R) = Q R^2 + T

Raise both sides to the power of two:

(P Q)/R = (Q R^2 + T)^2

Expand out terms of the right hand side:

(P Q)/R = Q^2 R^4 + 2 Q R^2 T + T^2

Subtract Q^2 R^4 + 2 Q R^2 T + T^2 from both sides:

(P Q)/R - Q^2 R^4 - 2 Q R^2 T - T^2 = 0

Collect in terms of Q:

-Q^2 R^4 - T^2 + Q (P/R - 2 R^2 T) = 0

Divide both sides by -R^4:

Q^2 + T^2/R^4 - (Q (P/R - 2 R^2 T))/R^4 = 0

Subtract T^2/R^4 from both sides:

Q^2 - (Q (P/R - 2 R^2 T))/R^4 = -T^2/R^4

Add (P/R - 2 R^2 T)^2/(4 R^8) to both sides:

Q^2 - (Q (P/R - 2 R^2 T))/R^4 + (P/R - 2 R^2 T)^2/(4 R^8) = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4

Write the left hand side as a square:

(Q - (P/R - 2 R^2 T)/(2 R^4))^2 = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4

Take the square root of both sides:

Q - (P/R - 2 R^2 T)/(2 R^4) = sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

Add (P/R - 2 R^2 T)/(2 R^4) to both sides:

Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:

Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt((P^2)/(4 R^10) - (P T)/(R^7)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

Add (P/R - 2 R^2 T)/(2 R^4) to both sides:

Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4))

(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:

Answer: Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))

Therefore the inequality is x≤11

and maximum I can withdraw 11 bills.

Step-by-step explanation:

Given ,

Current balance $320

Minimum balance $100

I could spent =$(320-100) = $220

Let the number of bills be x.

Total amount of x bills = $20x

According to the problem,

20x≤ 220

⇔x ≤ [tex]\frac{220}{20}[/tex]

⇔x≤11

Therefore the inequality is x≤11

and maximum I can withdraw 11 bills.

Answer: 18 months or a year and a half

Step-by-step explanation:

2.5 centimeters every 2 months, so...

1.25 centimeters every month.

22.5 ÷ 1.25 = 18

So it will take 18 months to grow 22.5 centimeters of hair

Answer:

The polynomial will be P(x) = - 5 (x + 2)²(x - 3)

Step-by-step explanation:

The degree of the polynomial P(x) is 3 and it has zeros at x = - 2 with multiplicity 2 and at x = 3 with multiplicity 1.

Therefore, (x + 2)² and (x - 3) are the factors of the equation.

Let the polynomial is

P(x) = a(x + 2)²(x - 3) ........... (1)

Now, the polynomial passes through the point (2,80).

So, from equation (1) we gat,

80 = a(4)²(-1)

⇒ a = - 5

Therefore, the polynomial will be P(x) = - 5 (x + 2)²(x - 3) (Answer)

The required polynomial is [tex]P(x) = - 5 (x + 2)^{2} (x - 3)[/tex]

Any polynomial have number of roots equal to its degree of polynomial.

Since, the degree of the polynomial P(x) is 3. it means that it has 3 roots.

it has zeros at x = - 2 with multiplicity 2, it means that factor (x - 2) have power 2 and at x = 3 with multiplicity 1 means that factor (x - 3) have power of 1 .

Thus, [tex](x + 2)^{2}[/tex] and (x - 3) are the factors of the equation.

Let us consider the polynomial is [tex]P(x) = k(x + 2)^{2} (x - 3) .[/tex]

Since,  the polynomial passes through the point (2,80).

So, substituting point (2, 80)  in above polynomial equation.

   We get,   [tex]80 = a(4)^{2} (-1)[/tex]

                      a = - 5

Therefore, the polynomial is [tex]P(x) = -5(x + 2)^{2} (x - 3) .[/tex]

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Answer:

368.94

Step-by-step explanation:

New value =

258 + Percentage increase =

258 + (43% × 258) =

258 + 43% × 258 =

(1 + 43%) × 258 =

(100% + 43%) × 258 =

143% × 258 =

143 ÷ 100 × 258 =

143 × 258 ÷ 100 =

36,894 ÷ 100 =

368.94

To increase 258 by 43% using the multiplier method, multiply 258 by 1.43. The result is 369.14.

To use the multiplier method to increase 258 by 43, you simply need to calculate 258 times the multiplier. The multiplier is 1 plus the rate of increase, which is 43% in this case. So, the multiplier is 1+0.43=1.43.

Here is the calculation:

258 * 1.43 = 369.14

So, 258 increased by 43% is approximately 369.14.

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Answer:

30

Step-by-step explanation:

a right angle is 90 degrees so if it split into two parts and one is 30 degrees and the other is x (an unknown) you could do 90-30 to get 60 but since it is 2x but has to equal 60 it is going to be 30 because 30 times 2 is 60

Answer:

The answer is 30

Step-by-step explanation:

hope this helps!

Answer:

42 miles

Step-by-step explanation

Distance = Speed * Time

X=12mph*3.5h

X=42 miles

Distance he can travel is 42 miles.

Step-by-step explanation:

⇒ Distance = 12 × 7/2 = 42 miles