98 + 14 using distributive property

ABCD is forming a Cycling Quadrilateral

we know that, sum of opposite angle in Cycling Quadrilateral is 180°

=>B + D = 180°

=>5x+2 +68 = 180

=>5x + 70 = 180

=> 5x = 110

=> x = 22°

Angle B = 5×22+2 = 110+2 = 112°>

Answer:

£200

Step-by-step explanation:

To determine how many pounds Jenny got back, we first need to calculate the exchange rate between pounds (£) and dollars ($).

Jenny initially changed £480 into $744, so £480 = $744.

To find the exchange rate in terms of pounds (£) to dollars ($), divide both quantities by 480:

\(\dfrac{480}{480}=\dfrac{744}{480}\)

\(\£1=\$1.55\)

Therefore, the exchange rate was £1 = $1.55.  

This means that for every £1 Jenny exchanged, she received $1.55.

To convert the $310 Jenny had left back into pounds (£), divide the dollar amount by 1.55:

\(\dfrac{310}{1.55}=200\)

Therefore, if the exchange rate stayed the same, Jenny got back £200.

Answer:

100

Step-by-step explanation:

Answer:

100 times greater

Step-by-step explanation:

Because the number 55 moves to the right.

In linear equation, 3437.5  feet - lbs is the work done to haul the anchor .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Anchor  weighing = 100 lbs

   given 3  lb/ft

  the combined weight  = 3( 25 -y ) + 100

                                 = 175 - 3y

    the workdone on small solution is = (175 - 3y)Δy

                      w = ∫₀²⁵ (175 - 3y) dy

                        = 175[y]²⁵₀- 3/2[y²]²⁵₀

                       = 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]

                       = 3437.5  feet - lbs

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Answer:

x=3

x=−3

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

4x + 4x - 4x = 4x

24x ÷ 2 = 12x

3x • 4x = \(12x^2\)

15x - 3 = 15x - 3

Answer:

B. 24x/2

Step-by-step explanation:

12x

A. 4x + 4x - 4x = 8x - 4x = 4x

B. 24x/2  = 24/2 x = 12x

C. (3x)(4x) = 12 x^2

D. 15x - 3​ = 15x -3  ( no like terms

If the diagonals of a parallelogram PQRS intersect at z, then the correct statements are:

A. QZ ≅ SZ

D. ∠QRP ≅ ∠SPR

The diagonals of a parallelogram which is a quadrilateral are known to bisect each other. The diagonals of a parallelogram form an angle of 90 degrees with each other.

These diagonals are formed from congruent angles and can also separate into congruent angles. So, for the parallelogram above whose sides intersect at z, we can conclude that QZ is approximately equal to SZ  and angle QRP is approximately equal to angle SPR.

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Answer:

the answer is 6

Step-by-step explanation:

i took the test

Answer:

The answer is D 6

Step-by-step explanation:

Answer:

1kg/2.2lbs = 48kg/x

1kgx = 105.6

x = 105.6lbs

B

Answer:

136.74

Step-by-step explanation:

Answer: 5832

Step-by-step explanation:

18^3 = 324 * 18 = 5832

Answer:

5,832

Step-by-step explanation:

18^3 = (18)(18)(18) = 5,832

0.80 = (x + 8)(0.05) is the equation used to find x.

Given,

Darryl has a solution of bleach with the concentration of 10%.

10% bleach solution means in 100 ml solution amount of bleach is 10 gm

Here,

Darryl wants to change the concentration of this solution to 5%, means he wants to add water so that amount of liquid will change but amount of bleach in grams will remain the same.

Amount of bleach in 8 gallons of 10% solution of bleach will be = (Volume)×(concentration) = 8(.10) gm

Let Darryl adds x gallons of water in 10% solution of bleach to make it 5% solution of bleach.

Amount of bleach in 5% solution of bleach = (x + 8)(0.05) gm

Now in both the concentrations of bleach solution amount of bleach will remain same.

So, 0.8 = (x + 8)(0.05) will be the equation from which he can find the value of x.

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9514 1404 393

Answer:

  2x +y = -2

Step-by-step explanation:

The bisector must have a slope that is the negative reciprocal of the slope of the line between these points. It must pass through the midpoint of the segment.

The slope of the line through the given points is ...

  m = (y2 -y1)/(x2 -x1)

  = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2

The slope of the required bisector is then ...

  m = -1/(1/2) = -2

__

The midpoint of the given segment is ...

  ((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)

__

Then the point-slope form of the equation of the bisector is ...

  y -y1 = m(x -x1)

  y -2 = -2(x -(-2))

  y = -2x -4 +2

  y = -2x -2 . . . . . . . slope-intercept form equation

  2x +y = -2 . . . . . . . standard form equation

Answer:

$8

Step-by-step explanation:

It says P = per ball (which will be a number, n, for balls times the fixed price) plus a set entrance fee. So we find that the price per ball is $0.80, so 10 balls cost $8.

Answer:

$8

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

They are similar triangles.  Since 6 is 1.5 times the four, x has to be 1.5 times the 6.

6*1.5=9

80° is the value of angle in quadrilateral .

What is a quadrilateral in mathematics?

A rectangle is defined as a two-dimensional shape with four sides, four vertices, and four corners. There are two main types:

concave and convex.

                            There are also various subcategories of convex quadrilaterals such as trapezoids, parallelograms, rectangles, rhombuses and squares. 

In quadrilateral ,

X + 100 + 100 + 80 = 360°

 X + 280° = 360°

  X = 360° - 280°

  X =  80°

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The ERD for the described situation would include entities such as county jails, mental health facilities, shelters, hospitals, and a coordinating database. Relationships between these entities would allow for coordination and prediction of the type of assistance individuals may need to reduce their involvement in the justice system.

The ERD for the Miami-Dade County court system's database would include the following entities:

County Jails: Represents the jails within the county system where individuals may be incarcerated.

Mental Health Facilities: Represents the facilities that provide mental health services and support.

Shelters: Represents the shelters that offer temporary housing and assistance to those in need.

Hospitals: Represents the healthcare institutions where individuals receive medical treatment.

Coordinating Database: Represents the central database that coordinates activities and stores information from all the other entities.

The relationships between these entities would be established through appropriate connections:

County Jails to Coordinating Database: This relationship would allow for the exchange of information about individuals in the jail system, including their personal history and involvement in the justice system.

Mental Health Facilities to Coordinating Database: This relationship would facilitate the sharing of information regarding individuals' mental health needs and treatment plans.

Shelters to Coordinating Database: This relationship would enable the coordination of housing services and assistance programs for individuals in the justice system.

Hospitals to Coordinating Database: This relationship would allow for the integration of medical records and healthcare services for individuals involved in the justice system.

These relationships and the information stored in the coordinating database would serve as the foundation for algorithms to predict the type of help individuals might require to reduce their involvement in the justice system.

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The probability of the arrow landing on section a is 1/5 since there are 5 equal sections. The probability of the coin landing on heads is 1/2 since there are only 2 possible outcomes (heads or tails) for the coin.

To find the probability of both events happening, we need to multiply the probability of the arrow landing on section a by the probability of the coin landing on heads. This gives us (1/5) * (1/2) = 1/10. So the probability that the arrow will land on the section labeled a and the coin will land on heads is 1/10. In other words, there is a 1 in 10 chance of both events happening. It is important to note that each event is independent of each other, meaning the outcome of one does not affect the other. This is because the spinner and the coin are not connected or related in any way.

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Answer:

Please check the explanation.

Step-by-step explanation:

Given

ABC ↔ RQP

so

ΔABC ≅ ΔABC

It means the triangles are congruent.

Please check the attached diagram.

In the diagram,

Parts of ΔABC that correspond to

(i) PQ

\(PQ\) corresponds to \(CB\)

(ii) ∠Q

∠Q corresponds to ∠B

(iii) RP

\(RP\) corresponds to \(AC\)

The parametric equations for the line tangent to the curve of intersection of the surfaces at the point (1, 3, 3/2) are x = 2t + 1, y = 2t + 3,z = 3/2

To find the parametric equations for the line tangent to the curve of intersection of the surfaces at the given point, we need to find the direction vector of the tangent line.

First, let's find the curve of intersection of the surfaces by setting the two equations equal to each other:

x^2 + 2y + 2z = 10 ...(1)
y = 3 ...(2)

Substituting the value of y from equation (2) into equation (1), we have:

x^2 + 2(3) + 2z = 10
x^2 + 6 + 2z = 10
x^2 + 2z = 4

Now we have an equation that represents the curve of intersection in terms of x and z.

To find the direction vector of the tangent line at the given point (1, 3, 3/2), we need to find the partial derivatives of the equation with respect to x and z.

Taking the partial derivative with respect to x:

d/dx (x^2 + 2z) = 2x

Taking the partial derivative with respect to z:

d/dz (x^2 + 2z) = 2

Now, we have the direction vector of the tangent line as <2x, 2, 0>.

To obtain the parametric equations, we can use the point-slope form of a line:

x - x0 = t(2x)
y - y0 = t(2)
z - z0 = t(0)

Substituting the given point (1, 3, 3/2) as the initial point (x0, y0, z0), the parametric equations for the tangent line become:

x - 1 = t(2)
y - 3 = t(2)
z - 3/2 = t(0)

Simplifying, we have:

x = 2t + 1
y = 2t + 3
z = 3/2

Therefore, the parametric equations for the line tangent to the curve of intersection of the surfaces at the point (1, 3, 3/2) are:

x = 2t + 1
y = 2t + 3
z = 3/2

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Answer:

150 inches cubed

Step-by-step explanation:

108 triangles Congruent to triangle B would fit inside triangle A.

To determine how many triangles congruent to triangle B would fit inside triangle A, we need to consider the scale factor between the two triangles.

Given that triangle B is similar to triangle A with a scale factor of 1/6, it means that the corresponding sides of triangle B are 1/6 the length of the corresponding sides of triangle A.

Let's calculate the dimensions of triangle B:

Width of triangle B = 1/6 * width of triangle A

Height of triangle B = 1/6 * height of triangle A

Width of triangle B = 1/6 * 7 cm = 7/6 cm ≈ 1.17 cm

Height of triangle B = 1/6 * 20 cm = 20/6 cm ≈ 3.33 cm

Now, to find out how many triangles congruent to B would fit inside triangle A, we need to compare the areas of the two triangles.

Area of triangle A = (1/2) * base * height

Area of triangle B = (1/2) * base * height

Area of triangle A = (1/2) * 42 cm * 20 cm = 420 cm²

Area of triangle B = (1/2) * (7/6 cm) * (20/6 cm) ≈ 1.17 cm * 3.33 cm ≈ 3.89 cm²

To find the number of congruent triangles that can fit inside triangle A, we divide the area of triangle A by the area of triangle B:

Number of triangles congruent to B = Area of triangle A / Area of triangle B

Number of triangles congruent to B = 420 cm² / 3.89 cm² ≈ 108.01

Therefore, approximately 108 triangles congruent to triangle B would fit inside triangle A.

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The length of the diagonal of the rectangle is 6.4 meters

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

Length = 5 meters

Width = 4 meters

The length of the diagonal can be calculated as

diagonal = √(length² + width²)

substitute the known values in the above equation, so, we have the following representation

diagonal = √(5² + 4²)

Evaluate

diagonal = 6.4

Hence, the diagonal is 6.4 meters

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Answer:

First one, true

Second one, 23/45

Third one, 11/29

Step-by-step explanation:

There's thy answer for thy self t-t

Answer:

1.)true

2.) 23/45

3.)11/29

Step-by-step explanation:

Answer:

75.5x is the slope

453x+(-6y)=-45

-6y/-6y= y

-45/-6= 7.5

-453/-6= 75.5

y=7.5+ 75.5x

Answer:

divide by 2

Step-by-step explanation:

to find x you must divide 8 by 2.

Answer:

you divide 8 by 2

Step-by-step explanation:

To isolate the variable, x you need to divide by 2 on both sides so it cancels out the 2 on 2x and will divide 8 by 2=4

The fraction of the total vote he should expect to get is 23/75.

A fraction is a mathematical unit used to represent a portion of a whole or a ratio of two integers. They are shown as the top number, or numerator, and the bottom number, or denominator, separated by a line. The denominator is the total number of pieces that make up the whole, whereas the numerator is the number of shares or parts.

For instance, you may write 3/8 for the portion of pizza you consumed if there were 8 pieces and you only ate 3. This indicates that you consumed three of the pizza's eight equally sized portions.

From the given table we can determine the total number of votes are:

13 + 9 + 10 + 8 + 10 + 14 + 5 + 6 = 75.

Now, Jamal received 13 + 10 = 23 votes.

Thus, the fraction of the total vote he should expect to get is 23/75.

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the function could be a probability density function with C = (24/25).

The given function is f(x) = {C (2x - x^3) 0 < x < 5/2 0 otherwise. It is possible that this function is a probability density function. However, for it to be a probability density function, it must satisfy two conditions.

First, the function must be non-negative for all values of x.

Second, the area under the curve of the function must be equal to 1.

Since the function is non-negative for all values of x, the first condition is satisfied. To determine if the second condition is satisfied, we need to calculate the integral of the function from 0 to 5/2. We get:Integral from 0 to 5/2 of f(x)dx = Integral from 0 to 5/2 of C(2x - x^3)dx= C[ x^2 - (x^4/4) ] from 0 to 5/2= C [(5/2)^2 - ((5/2)^4/4)] - C[0 - 0]= (25C/4) - (125C/16)= (25C/16)Now, for the second condition to be satisfied, (25C/16) = 1Therefore, C = (16/25).Thus, the function could be a probability density function with C = (16/25). Now, let's repeat this process for the function f(x) = {C (2x - x^2) 0 < x < 5/2 0 otherwise. This function is non-negative for all values of x. To determine if the second condition is satisfied, we need to calculate the integral of the function from 0 to 5/2. We get:Integral from 0 to 5/2 of f(x)dx = Integral from 0 to 5/2 of C(2x - x^2)dx= C[x^2 - (x^3/3)] from 0 to 5/2= C [(25/4) - (125/24)] - C[0 - 0]= (25C/4) - (125C/24)= (25C/24)Now, for the second condition to be satisfied, (25C/24) = 1Therefore, C = (24/25)

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By the probability density function c= -64/225.

In probability theory, a probability density function (PDF) is refers the random variable’s probability coming within a  range of values, as opposed to taking on any one value. The function describes the probability density function of normal distribution and the process the mean and deviation exists.

The value of PDF is equals to 1.

Given function f(x) = {C (2x - x³) } 0

x = 5/2      

If it is a probability density function then

\(\int\limits^a_b {f(x)} \, dx =1\)

Here  f(x) = {C (2x - x³)} and a = 0 , b = 5/2

At first by integration we get,

 \(\int\limits {c(2x-x^{3}) } \, dx\)

=c ∫ 2x dx -c∫ x³dx      

= c(2×(x²/2) - x⁴/4)      

=c( x² - x⁴/4)

putting upper limit and lower limit that is x=0 and x= 5/2 we get,

c((5/2)² - (1/4)(5/2)⁴)

=c(5/2)²{ 1- (1/4)(5/2)² }

= c(25/4) { 1- (25/16)}

=  c(25/4) (-9/16)

= -225c/64

Now according to the probability density function the value is equals to 1

so

-225c/64 = 1  

Hence c = -64/225.

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the equation of each line using the given y- intercept and x- intercept

is \(y= -\frac{2}{3} x-2\)

Given :

given the y- intercept and x- intercept . y intercept ( 0, -2) and x intercept is (-3, 0)

We need to frame the equation of the line y=mx+b

where m is the slope and b is the y intercept

y intercept is (0,-2) so the value of b=-2

Now we find slope using two points (0,-2) and (-3,0)

Apply slope formula

\(slope m =\frac{y_2-y_1}{x_2-x_1} =\frac{0+2}{-3+0} =-\frac{2}{3}\)

We got the slope m and y intercept b =-2

Replace it in y=mx+b to get the equation of the line

\(y=mx+b\\y=-\frac{2}{3} x-2\)

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