Rhombus ABCD. Finf x

Answer:

A. 5x^2 − 2x − 24 = 0

Step-by-step explanation:

height = 5b-2

b =x

We can rewrite the height as

h = 5x-2

We know the formula for area of a triangle

A = 1/2 bh

A =1/2 x * (5x-2)

Distributing the x

A=    1/2 (5x^2 - 2x)

We know A =12

12 = 1/2 (5x^2 - 2x)

Multiply each side by 2

12*2 = 2*1/2 (5x^2 - 2x)

24 = 5x^2 - 2x

Subtract 24 from each side

24-24 = 5x^2 - 2x-24

0 = 5x^2 - 2x-24

Answer:

C.  5x^2 − 2x − 24 = 0

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Gross taxable Income = $ 1,166

Rate of Income tax = 30%

Amount of income tax = 30 % of 1,166

                                     = [tex]\frac{30*1166}{100}[/tex]

                                     =$339.6

                                      ≅$340

Answer:

$340

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

For a parallelogram m < A = m < C so:-

75 + 5x = 87 + 3x

2x = 12

x = 6  

and m< A = 75 + 30 = 105

and m < C = 87 + 18 = 105

Now if the other 2 angles are  = 75 degrees( that is the same side angles add up to 180 degrees) we have proved that it is a parallelogram.

m < B = m < D

111 - 6x = 39 + 6x

-12x = -72

x = 6

m < B = 111 - 36 = 75 and m < D = 39 + 36 = 75

So this has been proved.

To prove that quadrilateral ABCD is a parallelogram, solve for x to find the values that make the opposite angles congruent. Plug in the values of x to find the measures of the opposite angle pairs. None of the given answer choices are correct.

To prove that quadrilateral ABCD is a parallelogram, we need to show that both pairs of opposite angles are congruent. We are given the measures of the angles using variable expressions. We can set the expressions for opposite angles equal to each other and solve for x to find the values of x that make the opposite angles congruent. Finally, we plug in the values of x to find the measures of the opposite angle pairs.

Since the opposite angles are not congruent, we cannot conclude that quadrilateral ABCD is a parallelogram. Therefore, none of the given answer choices (A) 95°, 85°, (B) 105°, 75°, (C) 115°, 65°, or (D) 125°, 55°, are correct.

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Answer:

C.) 413 cm^2

Step-by-step explanation:

To figure out the area of a square, much like a rectangle we multiply length × width.  In this case because the length and width are the same (definition of a square) then it's simply [tex]s^2[/tex] and 8 inches is 20.32 cm (8x2.54):

[tex]s^2=20.32^2=412.90 \approx 413[/tex]

a.) 413 cm^2

Answer:

41 sq cm is the answer

Step-by-step explanation:

Answer: Probability of randomly selecting a member who likes to cook or likes to sew = 58%

Step-by-step explanation:

Since we have given that

Probability of a randomly selecting a member who likes to cook=P(C) = 42%

Probability of a randomly selecting a member who likes to sew =P(S)= 23%

Probability of a randomly selecting a member who likes to both cook and sew

[tex]P(C\cap S)=7\%[/tex]

As we know the "Probability rules " :

[tex]P(C\cup S)=P(C)+P(S)-P(S\cap C)\\\\P(C\cup S)=42+23-7\\\\P(C\cup S)=58[/tex]

So, Probability of randomly selecting a member who likes to cook or likes to sew = 58%

Answer:

58%

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

There is one root for each binomial factor.

... y = (x -2)(x +3)(x +3) . . . has 3 binomial factors

_____

The roots are the values of x that make the factors be zero.

... (x -2) = 0 when x = 2

... (x +3) = 0 when x = -3

... (x +3) = 0 when x = -3

The root at x = -3 is said to have multiplicity 2.

_____

Sometimes, we're concerned with the number of distinct roots. Since the three roots only have two different values, there are 2 distinct roots.

Step-by-step explanation:

1) Graph the function (if you don't know how you can use the website Desmos, it's an online graphing calculator.

2) Count the roots (roots are the number of times the line touches the x-axis)

Confirmed answer on ∧pe×

^just check that the equation is the exact same

Answer:

The number of wreaths Alaina sells is 9 .

Step-by-step explanation:

As given

Alaina is selling wreaths and poinsettias for her chorus fundraiser.

Wreaths cost $27 each poinsettia cost $20 each.

If she sold 15 poinsettias and made $543.

Let us assume that the number of wreaths Alaina sells = x

As the number of poinsettias  Alaina sells = 15

Than the equation becomes

27x + 15 × 20 = 543

27x + 300 = 543

27x  = 543 - 300

27x  = 243

[tex]x = \frac{243}{27}[/tex]

x = 9

Therefore the number of wreaths Alaina sells is 9 .

Alaina sold 9 wreaths. After calculating the revenue from poinsettias ($300), the remaining amount ($243) was divided by the cost of one wreath ($27) to find the number of wreaths sold.

To determine how many wreaths Alaina sold, we first need to calculate the total revenue from selling 15 poinsettias. Since each poinsettia costs $20, we multiply 15 by $20:

Now, subtract the total revenue from poinsettias from the total amount made:

This remaining amount must be from the sale of wreaths. Since each wreath costs $27, we divide $243 by the cost of one wreath:

Therefore, Alaina sold 9 wreaths.

Answer:

Step-by-step explanation:

[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-8,0)\qquad B(-3,5)\qquad \qquad \stackrel{\textit{ratio from 2 to 3}}{2:3} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-8,0)=2(-3,5)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf P=\left(\cfrac{(3\cdot -8)+(2\cdot -3)}{2+3}\quad ,\quad \cfrac{(3\cdot 0)+(2\cdot 5)}{2+3}\right) \\\\\\ P=\left(\cfrac{-24-6}{5}~,~\cfrac{0+10}{5} \right)\implies P=(-6~,~2)[/tex]

Answer:

Correct choice is D

Step-by-step explanation:

Let h represent the number of horses. If there are 2 more horses than cows in a field,  then (h-2) represent the number of cows. In total there are h+(h-2) animals. It is known that there are 16 animals in the field in all, then

h+h-2=16,

2h-2=16.

i will only be adding the answer  due to the fact that I have to leave soon and i have been helping people with this all day.

8916 AFTER 20 YEARS

Answer:

C = 15 + 20*p

Step-by-step explanation:

Cost for ordering = shipping and handling plus cost per part * number of parts

C = 15 + 20*p

The linear equation representing the cost of ordering machine parts from B&B Inc. is c = 15 + 20p. This accounts for a fixed shipping cost of $15 and a variable cost of $20 per part.

The subject of this question is linear equations in Mathematics. B&B Inc. is ordering machine parts and incurs a fixed shipping and handling cost of $15, plus a variable cost of $20 per part. The equation representing this situation can be developed with 'c' representing the total cost and 'p' representing the number of parts ordered. Considering the fixed and variable costs, the equation would be c = 15 + 20p where $15 is the fixed shipping and handling cost, and $20p represents the variable cost which depends on the number of parts ordered.

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Answer:

2A/h - b1 =  b2

Step-by-step explanation:

A = 1/2 h ( b1+b2)  

We want to solve for b2

Multiply each side by 2

2A = 2* 1/2 h ( b1+b2)  

2A =  h ( b1+b2)  

Divide each side by h

2A / h =  h/h ( b1+b2)  

2A / h =   b1+b2

Subtract b1 from each side

2A/h - b1 = b1 + b2 -b1

2A/h - b1 =  b2

Answer:

Option no C 600 minutes

Step-by-step explanation:

Given:

gallons of pool = 24000 gallon

Rate at which it is filled = 40 gallons per minute

To find :

Time taken to fill the pool=?

Solution:

We know that rate is the time in which a thing is being done at per minute or per hour or per second. In our question it is given that the rate is 40 gallons per minute which means that 40 gallons are filled in one minute

Now

In one minute = 40 gallons filled

Total pool size = 24000 gallons

Total time taken = [tex]\frac{Total pool size}{gallon filled in one minute}[/tex]

Putting in the values

Total time taken = [tex]\frac{24000}{40}[/tex]

Total time taken = 600 minutes

So the answer is option c which is 600 minutes

Answer:

(12,14)

Step-by-step explanation:

9x-3(3x-4)=14

9x-9x+12=14

12=14

To prove a rhombus you need to show that the sides are congruent and the diagonals are perpendicular.

Sides:

[tex]d_{RM}=\sqrt{(-4-1)^2+(5-4)^2}[/tex]

    [tex]=\sqrt{(-5)^2+(1)^2}[/tex]

    [tex]=\sqrt{25+1}[/tex]

    [tex]=\sqrt{26}[/tex]

[tex]d_{MB}=\sqrt{(1-2)^2+(4+1)^2}[/tex]

    [tex]=\sqrt{(-1)^2+(15)^2}[/tex]

    [tex]=\sqrt{1+25}[/tex]

    [tex]=\sqrt{26}[/tex]

[tex]d_{BS}=\sqrt{(2+3)^2+(-1-0)^2}[/tex]

    [tex]=\sqrt{(5)^2+(-1)^2}[/tex]

    [tex]=\sqrt{25+1}[/tex]

    [tex]=\sqrt{26}[/tex]

[tex]d_{SR}=\sqrt{(-3+4)^2+(0-5)^2}[/tex]

    [tex]=\sqrt{(1)^2+(-5)^2}[/tex]

    [tex]=\sqrt{1+25}[/tex]

    [tex]=\sqrt{26}[/tex]

[tex]\overline{RM}[/tex] ≅ [tex]\overline{MB}[/tex] ≅ [tex]\overline{BS}[/tex] ≅ [tex]\overline{SR}[/tex]

Diagonals:

Use the slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m_{RB}=\dfrac{5+1}{-4-2}[/tex]

       [tex]=\dfrac{6}{-6}[/tex]

       = -1

[tex]m_{MS}=\dfrac{4-0}{1+3}[/tex]

       [tex]=\dfrac{4}{4}[/tex]

       = 1

Slopes are opposite reciprocals so they are perpendicular.

***************************************************************************

All of the sides are congruent and the diagonals are perpendicular so RMBS is a rhombus.

Answer:

1) 11 quaters and 4 dimes

Step-by-step explanation:

1) 11 quaters = 2.75

   4 dimes = .40

   $2.75 + .40 = 3.15

Final answer:

Meesha has 4 dimes and 11 quarters. To make a 12oz 12% bleach solution, 1 ounce of pure bleach must be combined with a 4% solution.

Explanation:

Solving Coin and Bleach Solution Problems

Problem 1: Coin Combination

Meesha has dimes and quarters adding up to $3.15, with 7 more quarters than dimes. To solve this, let's denote the number of dimes as d and the number of quarters as q. We have two equations based on the problem statement:

0.10d + 0.25q = 3.15 (The total value in dollars.)

q = d + 7 (There are 7 more quarters than dimes.)

Substituting the second equation into the first gives:

0.10d + 0.25(d + 7) = 3.15

This simplifies to:

0.10d + 0.25d + 1.75 = 3.15

Combining like terms:

0.35d = 3.15 - 1.75

0.35d = 1.40

Dividing both sides by 0.35 gives:

d = 1.40 / 0.35 = 4

Therefore, there are 4 dimes and substituting back:

q = 4 + 7 = 11 quarters.

Problem 2: Mixing Bleach Solutions

To make a 12oz 12% bleach solution from a 4% solution, let's denote the amount of pure bleach needed as b ounces. The amount of 4% solution would then be 12 - b ounces. The equation representing the mixture is:

(12 - b) * 0.04 + b = 12 * 0.12

This simplifies to:

0.48 - 0.04b + b = 1.44

0.96b = 0.96

b = 0.96 / 0.96 = 1 ounce of pure bleach is needed.

Answer:

40

Step-by-step explanation:

x + 2x + x + 20 = 180

4x + 20 = 180

4x = 160

x = 40

Answer:

Step-by-step explanation:

x=40

Answer:

The sale price of the bicycle is $120.

Step-by-step explanation:

To find the amount, simply multiply the cost by the fraction of the cost that you are paying.

$270 * 4/9 = $120

This would be the cost of the bike.

Answer:

The equation would be y = -2x + 19

Step-by-step explanation:

To find this, we can use the point and the slope in point-slope form. The we solve for y.

y - y1 = m(x - x1)

y - 7 = -2(x - 6)

y - 7 = -2x + 12

y = -2x + 19

To write an equation in slope-intercept form, use the formula y = mx + b. In this case, substitute the given point and slope into the equation.

To write an equation in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept. In this case, we are given a point P(6,7) and a slope of -2. We can substitute these values into the equation to find the y-intercept.

Using the point-slope form of the equation: y - y1 = m(x - x1), we substitute x1 = 6, y1 = 7, and m = -2. This gives us the equation: y - 7 = -2(x - 6).

Distributing the -2 on the right side of the equation, we get: y - 7 = -2x + 12. Finally, we can rearrange the equation to slope-intercept form by isolating y on one side: y = -2x + 12 + 7, which simplifies to y = -2x + 19.

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Answer:

[tex] \dfrac{49}{4} = 12.25 [/tex]

Step-by-step explanation:

[tex] 4^{x-1} = [/tex]

[tex] = (2^2)^{x - 1} [/tex]

[tex] = 2^{2(x - 1)} [/tex]

[tex] = 2^{2x - 2} [/tex]

[tex] = 2^{x + x - 2} [/tex]

[tex] = 2^x \times 2^x \times 2^{-2} [/tex]

[tex] = 7 \times 7 \times \dfrac{1}{2^2} [/tex]

[tex] = \dfrac{49}{4} = 12.25 [/tex]

Answer:

The recursive formula to model Kendyl's progress is:

Fourth option: an=an-1 + 2, a1=8

Step-by-step explanation:

She currently has the first eight bars memorized: The first value is 8:

a1=8

She plans to memorize two more bars everyday until she has the whole piece memorized:

The number of bars memorized is two more than the last day:

an=an-1 + 2

Then, the recursive formula is:

an=an-1 + 2, a1=8

Answer:

D an=an-1 + 2, a1=8 hope that helps

Answer:

341..

Step-by-step explanation:

i would personally say 341 because 620 multiplied by 55% or .55, as written on a calculator, would be 341.

Answer: if you are looking to put it in a proportional relationship you get the same answer but I can show you how to do it.

Step-by-step explanation:

55/ 100 ✖️ n/620=

34100/100 equals 100n ➗ 100 equals 341= n

Answer:

the answer is C. 31 units

I just did the assignment

The length of segment AD be for the quadrilateral to be a parallelogram is 8 units. Therefore, option A is the correct answer.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

In quadrilateral ABCD, AD║BC.

Here, AD=BC

3x+7=5x-9

2x=16

x=8

Therefore, option A is the correct answer.

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Answer:

A' (0, -1)

B' (0, 1)

C' (4, 1)

D' (4, -1)

Step-by-step explanation:

We have the following points of a quadrilateral ABCD:

A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)

and the rule of the translation is given by:

(x, y) ---> (x + 2, y − 3)

which means that each point will move means  3 units to the left and 4 units upwards.

So the points after transformation will be:

A(−2, 2) ---> (-2+2, 2-3) ---> A' (0, -1)

B(−2, 4) ---> (-2+2, 4-3) ---> B' (0, 1)

C(2, 4) ---> (2+2, 4-3) ---> C' (4, 1)

D(2, 2) ---> (2+2, 2-3) ---> D' (4, -1)

If we plot these points on a graph and join the corresponding vertices with line segments, then we will see that all the the lines will be parallel to each other since they followed the same rule of transformation.

The new coordinates of the transformed vertices A', B', C', and D' are:

A' (0, -1)

B' (0, 1)

C' (4, 1)

D' (4, -1)

To find the new coordinates of the transformed vertices A', B', C', and D', you need to apply the transformation rule (x + 2, y - 3) to the original coordinates of A, B, C, and D.

A' = (x + 2, y - 3)

A' = (-2 + 2, 2 - 3)

A' = (0, -1)

B' = (x + 2, y - 3)

B' = (-2 + 2, 4 - 3)

B' = (0, 1)

C' = (x + 2, y - 3)

C' = (2 + 2, 4 - 3)

C' = (4, 1)

D' = (x + 2, y - 3)

D' = (2 + 2, 2 - 3)

D' = (4, -1)

So, the new coordinates of the transformed vertices A', B', C', and D' are:

A' (0, -1)

B' (0, 1)

C' (4, 1)

D' (4, -1)

Now, let's describe the characteristics of the quadrilateral ABCD and its image A'B'C'D' when the corresponding vertices are connected with line segments:

Quadrilateral ABCD:

A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2)

ABCD is a trapezoid with two parallel sides (AB and CD) and two non-parallel sides (BC and AD).

The trapezoid is located in the first quadrant.

Image A'B'C'D':

A'(0, -1), B'(0, 1), C'(4, 1), and D'(4, -1)

A'B'C'D' is also a trapezoid with two parallel sides (A'B' and C'D') and two non-parallel sides (B'C' and A'D').

A'B'C'D' is located in a different position due to the transformation. It has been shifted 2 units to the right and 3 units down.

The transformation (x + 2, y - 3) has effectively shifted the entire quadrilateral 2 units to the right and 3 units down in the coordinate plane. The basic shape and characteristics of the trapezoid are preserved, but its position in the plane has changed.

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Answer:

The kitchen requires 288 sq. ft. of tile

The master bathroom requires 180 sq. ft. of tile

In total, we will spend $1170

Step-by-step explanation:

The area of the kitchen is length * width:

Area of Kitchen = [tex]18*16=288[/tex] sq. ft.

The area of the master bathroom is length * width:

Area of Master Bathroom = [tex]12*15=180[/tex] sq. ft.

The kitchen requires 288 sq. ft. of tile

The master bathroom requires 180 sq. ft. of tile

In total, we require [tex]288+180=468[/tex] sq. ft. of tiles. If $2.50 is charged per square feet, in total we will spend:

[tex]468*2.5=1170[/tex] dollars

You'll need 288 square feet of tile for the kitchen, 180 square feet for the bathroom, and the total cost for the tile will be $1170.

To calculate the amount of tile needed for the kitchen and the master bathroom, you first need to determine the area of each room. Area is calculated by multiplying the length by the width of the room.

For the kitchen:

Length = 18 feet

Width = 16 feet

Area = Length x Width = 18 ft x 16 ft = 288 square feet

For the master bathroom:

Length = 15 feet

Width = 12 feet

Area = Length x Width = 15 ft x 12 ft = 180 square feet

To calculate the total cost of the tile:

Cost per square foot = $2.50

Total area = Area of kitchen + Area of bathroom = 288 sq ft + 180 sq ft = 468 square feet

Total cost = Total area x Cost per square foot = 468 sq ft x $2.50 = $1170

Answer:

10^14

Step-by-step explanation:

  Number of bacteria  For 10^2 hours =  10^13

  Number of bacteria for 1 hour =   10^13/10^2 =  10^11

 Number of bacteria for 10^3 hours = 10^11 x 10^3 =  10^ (11+3) = 10^14

Answer:

5/13

Step-by-step explanation:

sine W = sine 50 degrees = opposite /hypotenuse

= 10/26

= 5/13

Final answer:

The sine of angle W in the right triangle is the ratio of the side opposite to angle W (24 units) to the hypotenuse (26 units). Therefore, the sine of angle W is 12/13(option D).

Explanation:

The problem describes a right triangle with sides of length 26 units, 24 units, and 10 units, and it asks for the sine of angle W, which is known to be 50 degrees. In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the angle over the length of the hypotenuse. Thus, to find the sine of angle W, we need the opposite side to angle W, which is WD measuring 24 units, and the hypotenuse RW, measuring 26 units.

The sine of angle W is calculated by the formula

sine of angle W = WD\RW

24\26  

12\13