b) Find the least number that must be subtracted from 2120 so that the result is a perfect square. ​

Answer:

45

Step-by-step explanation:

The three angles equal to x are: ∠x = ∠BAD = ∠BED = ∠BFD

It is proved that, ABHD ||AFED and  proved that AB BD = FD BH

Here, we have,

from the given figure, we get,

CD is a tangent to the circle ABDEF at D.

Chord AB is produced to C.

Chord BE cuts chord AD in H and chord FD in G.

ACFD and AB = EF.

we have,

AC || FD

FE = AB

i) The three angles equal to x are:

∠x = ∠BAD = ∠BED = ∠BFD

as the angles on the same chord.

ii) ∠DBH = ∠DFE [angle on same chord DE ]

∠BDH = ∠FDE [angle inscribed by equal chord]

∠BHD = ∠FED [ when two angles of a triangle are equal so the other will

                               also equal ]

so, we get, by AAA similarity ΔBHD ≡ Δ FDE

iii)  now, we have, from  ΔBHD ≡ Δ FDE

BD/BH = FD/FE

=> BD/BH = FD/AB

=> AB.BD = FD.BH [by cross multiplication]

Hence, Proved.        

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complete question:

CD is a tangent to circle ABDEF at D Chord AB IS produced to C Chord BE cuts chord AD in H and chord FD in G ACI/FD and FE = AB Let ZD4 = and ZD = y 1 2 3 Determine THREE other angles that are equal tox Prove that ABHD ||AFED Hence or otherwise, prove that AB BD = FD BH                      

Answer:

3/4

Step-by-step explanation:

The 0 <= theta <= pi/2 makes it so the angle must be in the first quadrant. From there, you can use the fact that sin = opposite / hypotenuse.

Thus the opposite side length would be 5, the hypotenuse would be 5, and the adjacent side length would be 3 (by Pythagorean theorem).

Recall that cot = cotangent = 1 / tan. And recall that tan is opposite of adjacent. So tan(theta) = 4/3, and cot (theta) = 3/4.

[tex]\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{nr^2}{2}\sin(\frac{360}{n}) ~~ \begin{cases} r=\stackrel{ circumcircle's }{radius}\\ n=sides\\[-0.5em] \hrulefill\\ n=10\\ r=13 \end{cases}\implies A=\cfrac{(10)(13)^2}{2}\sin(\frac{360}{10}) \\\\\\ A=845\sin(36^o)\implies A\approx 496.7[/tex]

Answer:

496.7 square units

Step-by-step explanation:

A regular polygon is a polygon with equal side lengths and equal interior angles, meaning all of its sides and angles are congruent.

The radius of a regular polygon is the distance from the center of the polygon to any of its vertices.

The given figure is a regular decagon (10-sided figure) with a radius of 13 units.

To find the area of a regular polygon given its radius, use the following formula:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=nr^2\sin \left(\dfrac{180^{\circ}}{n}\right)\cos\left(\dfrac{180^{\circ}}{n}\right)$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute n = 10 and r = 13 into the formula and solve for A:

[tex]A=10 \cdot 13^2 \cdot \sin\left(\dfrac{180^{\circ}}{10}\right)\cdot \cos\left(\dfrac{180^{\circ}}{10}\right)[/tex]

[tex]A=10 \cdot 169 \cdot \sin\left(18^{\circ}\right) \cdot \cos \left(18^{\circ}\right)[/tex]

[tex]A=496.678538...[/tex]

[tex]A=496.7\; \sf square \; units[/tex]

Therefore, the area of a regular decagon with a radius of 13 units is 496.7 square units (to the nearest tenth).

Answer:

2m - 72

Step-by-step explanation:

2x Malik's age = 2 × m, m represents his age because it is unknown

72 less means -72

Answer:

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

Direct variation equation in terms of given values:

10 cm³ of oil has a mass of 9 grams:

Substitute values of m and v and find the value of k:

Substitute the value of k back to initial equation:

The matching choice is B.

Answer:

[tex]m= \frac{9}{10}*v[/tex]

Step-by-step explanation:

Since the mass of cooking oil is directly proportional to the oil's volume, we can write the following equation:

m = kv

where k is the constant of proportionality.

We know that when v = 10, m = 9, so we can plug these values into the equation to solve for k:

9 = k * 10

k =[tex]\frac{9}{10}[/tex]

Now, we can plug k =[tex]\frac{9}{10}[/tex] into the original equation to get the following equation:

m =[tex]\frac{9}{10}[/tex] v

The reconciled balance is $600.13.

Pat's approximate monthly Payment would be $304.32 to repay all her loans after the deferment period.

The Pat's monthly payment, we need to consider the terms and interest rates of each loan. Let's break down the calculation step by step:

1. Federally subsidized student loans:

  - Pat receives four annual loans, each for $5400 at an interest rate of 6.5%.

  - Since the loans are annual, we need to calculate the interest for each year and add it to the principal amount.

  - The total principal amount for the four loans is $5400 * 4 = $21,600.

  - The interest for each year is $21,600 * 6.5% = $1,404.

  - Therefore, the total amount owed for the federally subsidized loans is $21,600 + ($1,404 * 4) = $27,816.

2. Private student loan:

  - Pat takes out a private student loan for $4100 at an interest rate of 7.5% for a term of 10 years.

  - The loan is capitalized, which means the interest is added to the principal amount.

  - The total principal amount for the private loan is $4100.

  - The interest for each year is $4100 * 7.5% = $307.50.

  - Since Pat capitalizes the interest for her last year of college, the loan will accrue interest for a total of 9 months.

  - Therefore, the total interest accrued for the private loan is ($307.50 * 9) = $2767.50.

  - The total amount owed for the private loan is $4100 + $2767.50 = $6867.50.

3. Total amount owed:

  - To find the total amount owed by Pat, we add the amounts from the federally subsidized loans and the private loan.

  - Total amount owed = $27,816 + $6867.50 = $34,683.50.

4. Monthly payment:

  - The monthly payment is calculated based on the total amount owed and the repayment term.

  - The term is 10 years for the private loan, but since payments are deferred until 6 months after graduation, the actual term is 10 years - 0.5 years = 9.5 years.

  - The number of monthly payments is 9.5 years * 12 months/year = 114 months.

  - Therefore, the monthly payment is $34,683.50 / 114 months ≈ $304.32.

So, Pat's approximate monthly payment would be $304.32 to repay all her loans after the deferment period.

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Answer:

-1 and -6

Step-by-step explanation:

If you multiply negative times negative or minus times minus it will turn to plus so

- x - = +

-1 x -6 = +6

If you add negative plus negative or minus plus minus it remain negative or minus

- + - = -

-1 + -6 = -7

The two numbers that multiply to 6 and add to -7 are -1 and -6.

We are given two conditions:

xy = 6

x + y = -7

We can rearrange equation 2 to express one variable in terms of the other.

x = -7 - y

Now we can substitute this expression for x in equation 1:

(-7 - y) y = 6

Expanding the equation:

-7y - y²= 6

Rearranging the equation to bring it to a quadratic form:

y² + 7y + 6 = 0

We can now solve this quadratic equation to find the values of y.

Factoring the quadratic equation:

(y + 6)(y + 1) = 0

Setting each factor equal to zero and solving for y:

y + 6 = 0 --> y = -6

y + 1 = 0 --> y = -1

So we have two possible values for y: -6 and -1.

Substituting these values back into equation 2 to find the corresponding values of x:

For y = -6:

x + (-6) = -7

x = -1

For y = -1:

x + (-1) = -7

x = -6

Therefore, the two numbers that multiply to 6 and add to -7 are -1 and -6.

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Answer:

50 people

Step-by-step explanation:

After removing the people who liked neither, we are left with,

320 - 72 = 248

now, out of these 248, 196 like cats

248 - 196 = 52 so 52 dont like cats

also, 102 like dogs so 248 - 102 = 146

so 146 dont like cats

these 146 cannot be included in liking both

similarly the 52 cannot be included in liking both

so we are left with 248 - 52 - 146 = 50

so 50 people like both cats and dogs

This symbol "  [tex]\phi = {u : u\neq u}[/tex]" given in set statement means that the set is empty and has no element in it.

[tex]\phi = {u : u\neq u}[/tex] is a set notation that represents the empty set. In set theory, the empty set, denoted by the symbol [tex]\phi[/tex] or {}.

An empty set is defined as a set that does not contain any elements and it is just empty or null.

For this question,  [tex]\phi = {u : u\neq u}[/tex] , the set is defined using a condition or property.

The condition given is u ≠ u, which is always false for any element. So we can say that it implies that there is no element that satisfies the condition u ≠ u, meaning there are no elements in the set.

Hence, the set is empty.

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This is the Law of Cosines, which relates the Lengths of the sides of a triangle to the cosine of one of its angles.CD² = AC² + (b - x)² - 2 * AC * (b - x) * (sin(ABD) / sin(ACD))

To derive the Law of Cosines, follow these steps:

Step 1: Consider the triangle AABD, where A and B are vertices and AB is the side opposite the angle ABD.

Apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:

AB² = AD² + BD²

Step 2: Now, consider the triangle ACBD, where C is another vertex and AC is the side opposite the angle ACD.

Apply the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all sides and angles in the triangle. In this case, we have:

AC / sin(ACD) = BD / sin(ABD)

Rearrange the equation to isolate AC:

AC = (BD / sin(ABD)) * sin(ACD)

Step 3: Notice that BD = b - x, where b is the length of AB and x is the length of CD.

Substitute this expression for BD in the equation from step 2:

AC = ((b - x) / sin(ABD)) * sin(ACD)

Step 4: Square both sides of the equation obtained in step 3:

AC² = ((b - x) / sin(ABD))² * sin²(ACD)

Step 5: Recall that sin²(ACD) = 1 - cos²(ACD). Substitute this expression in the equation from step 4:

AC² = ((b - x) / sin(ABD))² * (1 - cos²(ACD))

Step 6: Rearrange the equation to isolate cos²(ACD):

cos²(ACD) = 1 - (AC² / ((b - x) / sin(ABD))²)

Step 7: Simplify the equation:

cos²(ACD) = 1 - AC² / (b - x)² * (sin(ABD) / sin(ACD))²

Step 8: Finally, recall that cos²(ACD) = 1 - sin²(ACD) = 1 - (CD / AC)². Substitute this expression in the equation from step 7:

1 - (CD / AC)² = 1 - AC² / (b - x)² * (sin(ABD) / sin(ACD))²

Rearrange the equation to obtain the Law of Cosines:

CD² = AC² + (b - x)² - 2 * AC * (b - x) * (sin(ABD) / sin(ACD))

This is the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

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Maria's current age is 15 and Susy's current age is 5.

We have,

Let's denote Maria's current age as M and Susy's current age as S.

We can use the given information to set up a system of equations and solve for their ages.

According to the first statement, "When I have the age that you are, your age will be 2 times that I have," we can write the equation:

M + S = 2(M - S)

Expanding and simplifying:

M + S = 2M - 2S

S + 2S = 2M - M

3S = M

According to the second statement, "When I was 10 years old, you were the age that I am," we can write the equation:

M - 10 = S

Now we have a system of equations:

3S = M

M - 10 = S

To solve the system, we can substitute the value of M from the first equation into the second equation:

3S - 10 = S

Simplifying:

2S = 10

S = 5

Substituting the value of S back into the first equation:

3(5) = M

M = 15

Therefore,

Maria's current age is 15 and Susy's current age is 5.

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The complete question:

Maria tells Susy: "When I have the age that you are, your age will be 2 times that I have and you know that when I was 10 years old, you were the age that I am".

How much do the current ages of both?

a.i) The variable cost per haircut is $5.

a.ii) The monthly fixed costs are $2,800

b.i) The break-even point in units is approx. 467 haircuts.

b.ii) The break-even point in dollars is $5,137.

c) The net income, assuming 1,500 haircuts are given in a month, is $6,200.

We shall first break down the costs to estimate the variable cost per haircut and the total monthly fixed costs.

Then, we shall use the results to calculate the break-even point in units and dollars. Lastly, we compute the net income.

a.i) Variable cost per haircut (VC):

Total variable cost per haircut = Commission + Store rent + Barber supplies

Given:

Commission for each haircut per barber = $4

Rent for store per haircut = $0.60

Barber supplies per haircut = $0.40

Price of a haircut (P): $11

VC = $4 + $0.60 + $0.40

= $5

So, the variable cost per haircut is $5.

a.i)Total monthly fixed costs (TFC)

Total monthly fixed costs: Manager's salary + Depreciation on equipment + Utilities + Advertising

Given:

Manager's salary = $1,800

Depreciation on equipment = $500

Utilities =$300

Advertising = $200

TFC = $1,800 + $500 + $300 + $200

= $2,800

Therefore, the total monthly fixed costs are $2,800.

b) Break-even point:

The break-even point is the point: total revenue = total costs.

b.i) Break-even point in units = TFC divided by contribution margin per unit

contribution margin = price - VC

= $11 - $5

= $6

break-even point in units = $2,800 / $6

= 466.67

So, the break-even point in units is ≈ 467 haircuts.

b.ii) Break-even point in dollars:

Break-even point (in dollars) = break-even point (in units) * P

= 467 * $11

= $5,137

Thus, the break-even point in dollars is $5,137.

c) The net income:

Total costs(TC) - Total Revenue (TR):

TR = Number of haircuts * P

= 1,500 * $11

= $16,500

Total Cost (TC) = TVC + TFC

TC = (Variable cost per haircut * Number of haircuts) + Total fixed costs

= ($5 * 1,500) + $2,800

= $7,500 + $2,800

= $10,300

Net income = TR- TC

= $16,500 - $10,300

= $6,200

Hence, the net income, assuming 1,500 haircuts are given in a month, is $6,200.

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Answer:

The total volume is 1660 cubic feet.

Step-by-step explanation:

The volume of a room is:

Vol = l × w × h

We calculate the two rooms separately, then add them together for the final answer.



The large room is:

Vol = 14 × 9 × 10

= 1260

The smaller room is:

Vol = 8 × 5 × 10

= 400



The total volume is

1260 + 400

= 1660

The total volume of the two rooms is 1660 cubic feet.

Answer:

[tex]y=-\frac{4}{5}x-\frac{21}{5}[/tex]

Step-by-step explanation:

The fastest way is to use point-slope form with [tex]m=-\frac{4}{5}[/tex] and [tex](x_1,y_1)=(-4,-1)[/tex]:

[tex]y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}[/tex]

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

     |

     |

     |     *

     |    /

     |   /

     |  /

-----*--------

     |

     |

     |

     |

     |

The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

Answer:

The correct answer is 30 degrees.

Answer:

58° + x = 180°

x = y = 122°

z = j, so 122° + 2z = 180°

2z = 58°

z = j = 29°

The Constant of proportionality (r) in the equation x = ry is 1/11.

The constant of proportionality (r) in the equation x = ry, where x and y are proportional, we can use the given pairs of values for x and y and solve for r.

Let's consider the given pairs of values:

x = 3, y = 33

x = 30, y = 3030

x = 10, y = 1010

x = 100, y = 100100

x = 16, y = 1616

x = 160, y = 160160

We can select any pair of values and set up the equation x = ry. Let's choose the pair x = 3 and y = 33:

3 = r * 33

To find r, we divide both sides of the equation by 33:

r = 3 / 33 = 1 / 11

Therefore, the constant of proportionality (r) in the equation x = ry is 1/11.

We can verify this by substituting other pairs of values into the equation and checking if the equation holds true. For example, let's substitute x = 160 and y = 160160:

160 = (1/11) * 160160

160 = 14560

The equation holds true, confirming that the constant of proportionality is indeed 1/11.

Hence, the constant of proportionality (r) in the equation x = ry is 1/11.

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To find the property tax on the house, we need to calculate the assessed value and then multiply it by the property tax rate.

The property tax rate is $2.45 per $100 of assessed value, which can be written as 0.0245 (since $2.45 divided by $100 is 0.0245).

To calculate the assessed value, we need to find the assessed value as a percentage of the market value. Let's assume the assessed value is x.

x/100 * $250,000 = $a

We don't have the value of 'a,' so we can't directly calculate the assessed value.

Could you please provide the value of 'a' (the assessed value) so that we can calculate the property tax on the house?

~~~Harsha~~~

Answer:

$4,593.75

Step-by-step explanation:

To find the property tax on the house, we need to first determine the assessed value of the house.

If the market value of the house is $250,000, and the assessed value is a dollars, then we can set up the following equation:

a = 0.75 x 250,000

where 0.75 represents the assessment rate, which is typically a percentage of the market value used to determine the assessed value for tax purposes.

Simplifying the equation, we get:

a = 187,500

Therefore, the assessed value of the house is $187,500.

To find the property tax, we can use the given tax rate of $2.45 per $100 of assessed value.

First, we need to convert the assessed value from dollars to hundreds of dollars, which we can do by dividing by 100:

187,500 / 100 = 1,875

Next, we can multiply the assessed value in hundreds of dollars by the tax rate per hundred dollars:

1,875 x 2.45 = 4,593.75

Therefore, the property tax on the house is $4,593.75.

Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         [tex]\boxed{b= 1}[/tex]

    Equation of line in slope-intercept form:

                  [tex]\boxed{\bf y = x + 1}[/tex]      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

Slope is 1 so

[tex]\sf{y-y_1=1(x-x_1)}[/tex]

Simplify

[tex]\sf{y-y_1=x-x_1}[/tex]

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

[tex]\sf{y-(-2)=x-(-3)}[/tex]

Simplify

[tex]\sf{y+2=x+3}[/tex]

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

[tex]\sf{y=x+1}[/tex]

Answer:

Hi

Please mark brainliest ❣️

The simplified form of[tex]-6ru^2 -ur^2 - 22u^2r^2[/tex]is [tex]-u^2(7r + 22r^2)[/tex].

To simplify the expression[tex]-6ru^2 -ur^2 - 22u^2r^2[/tex], we can combine like terms and factor out common factors.

First, let's look at the variables r and u separately:

For r:

We have terms[tex]-6ru^2[/tex] and [tex]-ur^2.[/tex] We can factor out r from these terms:

[tex]r(-6u^2 - u^2)\\r(-7u^2)[/tex]

For u:

We have term[tex]-22u^2r^2[/tex]. We can factor out[tex]u^2[/tex]from this term:

[tex]u^2(-22r^2)[/tex]

Combining the simplified terms for r and u, we get:

[tex]r(-7u^2) + u^2(-22r^2)[/tex]

Now, we can factor out the common factor of[tex]-u^2[/tex]:

[tex]u^2(7r + 22r^2)[/tex]

Therefore, the simplified expression is[tex]-u^2(7r + 22r^2)[/tex] .

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Answer:The correct graph for the given system of equations is:

graph of two lines, one with a positive slope and one with a negative slope, that intersect at the point negative 1, 1 with text on graph that reads One Solution -1, 1.

Step-by-step explanation:

Answer:

A. z+50

Step-by-step explanation:

Friday => z visitors

Saterday => z+100 visitors

sunday => (z visitors + z+100 visitors) /2 = (z+z+100)/2 = (2z+100)/2 =
2z/2 + 100/2 = z+50  

To calculate the number of different CD-Rs that the computer user can create with 15 songs from the available 35 songs, we need to calculate the number of permutations.

The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items taken at a time.

In this case, the computer user has 35 songs available, and they want to create a CD-R with 15 songs.

Number of permutations = 35P15 = 35! / (35 - 15)!

Calculating this:

35! / (35 - 15)! = (35 * 34 * 33 * ... * 21) / 15!

However, the factorial calculation for 35! / 15! is extensive and can be challenging to compute directly. Instead, we can simplify the expression using cancelations:

35! / (35 - 15)! = (35 * 34 * 33 * ... * 21) / (15 * 14 * 13 * ... * 1)

Many terms will cancel out:

(35 * 34 * 33 * ... * 21) / (15 * 14 * 13 * ... * 1) = 35 * 34 * 33 * ... * 21

Now, we can calculate the simplified expression:

35 * 34 * 33 * ... * 21 ≈ 5.0477859e+19

Therefore, the computer user can create approximately 5.0477859e+19 different CD-Rs with 15 songs from the available 35 songs.

The Probabilities are:

1. 3/10, 0.3, 30%

2. 7/10, 0.7, 70%

3. 9/10, 0.9, 90%

4. 1/10, 0.1, 10%

From the data,

Total people = 20

Number of Female Candidate = 6

Number of Male Candidate = 6

1. Probability of Women could win

= 6/20

= 3/10

In decimal = 0.3

In Percentage = 30%

2. Probability of Men could win

= 14/20

= 7/10

In decimal = 0.7

In Percentage = 70%

3. Probability of Democrat win

= 18/20

= 9/10

In decimal = 0.9

In Percentage = 90%

4. Probability of Republican win

= 2/20

= 1/10

In decimal = 0.1

In Percentage = 10%

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The measure of angle BDA is 3

From the question, we have the following parameters that can be used in our computation:

ABC = 4x - 2

DBC = 3x - 3

The figure is a rhombus

This means that

ABC = 2 * DBC

So, we have

4x - 2 =2 * (3x - 3)

When evaluated, we have

4x - 2 = 6x - 6

When solved for x, we have

2x = 4

So, we have

x = 2

This also means that

BDA = DBC = 3x - 3

So, we have

BDA = 3(2) - 3

Evaluate

BDA = 3

Hence, the measure of angle BDA is 3

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Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

[tex]24+32p=8(3+4p)[/tex]

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)