D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is mZDEF?

Answer:  19/21

Step-by-step explanation:  Find the least common denominator of the two which is 21 the first fraction since 3 X 7=21

For the first fraction since 3X7=21, 1/3=1X7=7/3X7=7/21

For the second fraction since 7X3=21, 4/7=4X3/7X3=12/21

Add the two like fractions 7/21+12/21=7+12/21=19/21

The answer is 1/3+4/7=19/21

Line A:

1. The points are (4,5) and (2,3)

2. The slope is 1

3. Unit for slope is inch/week

Line B:

1. The points are (4,4) and (2,3)

2. The slope is 1/2

3. Unit for slope is inch/week

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Line A:

1. The points are (4,5) and (2,3) ( write in (x,y) form )

2. slope = (5-3)/(4-2) = 2/2 = 1

( slope= change in y values/  change in x values )

3 . mark the slope as 1 inch/week

Line B:

1. The points are (4,4) and (2,3)

2. slope = (4-3)/(4-2) = 1/2

3 . mark the slope as 1/2  inch/week

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The evaluation of the fraction (5/6 + 2/3) - (3/4 + 1/12) in its simplest form is 2/3

A fraction is a number which consists of a numerator and a denominator.

A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.

(5/6 + 2/3) - (3/4 + 1/12)

= (5+4)/ 6 - (9+1) / 12

= 9/6 - 10/12

= 3/2 - 5/6

= (9-5) / 6

= 4/6

= 2/3

Consequently, the answer to the given fraction in its simplest form is 2/3

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See the graph. It shows the sketch.

The number of men and women that work at the company are;

Number of men = 36

Number of women = 18

Let the total number of employees in the company be x.

Now, we are told that 75% of the employees were men. Thus;

Number of men = 75% * x = 0.75x

Number of women = 0.25x

Now, we are told that after 6 women joined, the ratio of men to women became 2: 1.

Thus;

New total employees = x + 6

New total number of women = 0.25x + 6

Thus;

0.75x/(0.25x + 6) = 2/1

Cross multiply to get;

0.75x = 2(0.25x + 6)

0.75x = 0.5x + 12

0.75x - 0.5x = 12

0.25x = 12

x = 12/0.25

x = 48

Number of women = 0.25(48) + 6 = 18

Number of men = (48 + 6) - 18 = 36

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The volume V generated by rotating the region bounded by the given curves is V = 960π/7.

Given:

the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8.

27y= x³, y=0, x=6

dV = π(8^2-(8-y)^2)dx

y = [tex]x^{3} /27[/tex]

= π*([tex]8^2-(8-(x^3/27)^2)dx[/tex]

= π(64 - 64+16*[tex]x^3/27[/tex]-[tex]x^6/729[/tex])dx

[tex]= \int\limits^6_0 {16x^3/27-x^6/729} \, dx[/tex]

= π(4.[tex]6^6/27 - 6^7/7.729[/tex])

= π(5184/27 - 384/7)

= π(960)/7

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Answer:

7a-7b

Step-by-step explanation:

we distribute the 7 by multiplying it to each term

7(a)-7(b)

7a-7b

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Answer:

7a - 7b

Step-by-step explanation:

Given expression,

→ 7(a - b)

Let's simplify the expression,

→ 7(a - b)

→ (7 × a) - (7 × b)

→ 7a - 7b

Hence, the answer is 7a - 7b.

The error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

It is defined as the representation of a set of values that satisfy a relation or a function. It can be represented as open brackets and close brackets the close brackets mean the value at the close bracket is also included, and the open bracket means the value at the open bracket does not include.

It is given that, the number is 3.7.

We have to find the error interval for x rounded to 1 decimal place for the number 3.7.

Thus, the error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

When a number has been rounded or truncated, error intervals are the upper bounds of accuracy. They represent the range of values that a number might have had before being rounded or truncated.

This is so that we may round the range of 3.65 to 3.75 to one decimal place, and as 3.74 or less is considered to be below 3.75, rounding to one decimal place gives us 3.7.

Thus, the error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

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The diagram of the parabolic graph in the question indicates that responses are;

Vertex; (1, -9)

Axis of symmetry; x = 1

Y-intercept; (0, -8)

X-intercept(s); (-2, 0), (4, 0)

Concavity; opens up

A graph is a pictorial representation of the variation of one variable with respect to other variables.

Vertex

The vertex point of a parabolic graph represents the point where the parabola intersects the axis of symmetry

The vertex point of the parabolic graph in the question is; (1, -9)

Axis of symmetry

The axis of symmetry divides the graph of the parabola into two halves of the same dimensions, such that each side is a mirror reflection of the other.

The axis of symmetry is the line represented by the x-coordinate of the vertex, which is x = 1.

Y-intercept

The y-intercept is the point where the graph intersects the y-axis.

The y-intercept in the parabolic graph in the question is (0, -8)

X-intercept

The x-intercept is the location or point where the graph intersects the x-axis. The x-intercept of the graph in the question are (-2, 0) and (4, 0)

Concavity

The concavity of a graph is the rate of change of the derivative of the function.

If the derivative is increasing, the graph is concave upwards, and has a U-shape

The graph in the question is concave upwards

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sin(x+5pi/4) sin(x+5pi/4) in terms of sin(x) and cos(x) can be rewritten as cos (x) . sin [tex](\frac{x + 5\pi }{4} )[/tex] .sin (x)

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles

Let find the common multiplier of sin

[tex](\frac{x + 5\pi }{4} )[/tex]sin (x), cos(x); cos (x) sin[tex](\frac{x + 5\pi }{4} )\\[/tex] sin (x)

Find the least common Multiplier of sin [tex](\frac{x + 5\pi }{4} )[/tex] sin (x) , cos (x)

Lowest common multiplier (LCM)

The LCM of a, b is the smallest multiplier that is divisible by both a and b

Factor sin [tex](\frac{x + 5\pi }{4 } )[/tex]sin ( x)

sin[tex]( \frac{x + 5\pi }{4} )[/tex]. sin(x)

Multiplier each factor with the highest power;

cos (x) .sin [tex](\frac{x + 5\pi }{4} )[/tex].sin (x)

Therefore, the trigonometry sin(x+5pi/4) in terms of sin(x) and cos(x) can be rewritten as cos (x) . sin [tex](\frac{x + 5\pi }{4} )[/tex] .sin (x)

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Answer: [tex]7.39466666[/tex]

Step-by-step explanation:

Setting [tex]x=2.2[/tex] and [tex]n=3[/tex],

[tex]e^{2.2} \approx \sum^{3}_{k=0} \frac{2.2^{k}}{k!}=\frac{2.2^0}{0!}+\frac{2.2^1}{1!}+\frac{2.2^2}{2!}+\frac{2.2^3}{3!} \approx 7.39466666[/tex]

Answer:

7.39466667 (8 d.p.)

Step-by-step explanation:

We can approximate the value of eˣ for any x using the following sum formula:

[tex]\boxed{e^{x} \approx \displaystyle \sum^n_{k=0}\dfrac{x^k}{k!}}[/tex]

To approximate [tex]e^{2.2}[/tex] with n = 3, substitute x = 2.2 and n = 3 into the given sum formula:

[tex]e^{2.2} \approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}[/tex]

To calculate the sum, substitute k with each value from 0 to 3 and add the results together:

[tex]\begin{aligned}e^{2.2} &\approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\\\\&= \dfrac{2.2^0}{0!}+\dfrac{2.2^1}{1!}+\dfrac{2.2^2}{2!}+\dfrac{2.2^3}{3!}\\\\&= \dfrac{1}{1}+\dfrac{2.2}{1}+\dfrac{4.84}{2}+\dfrac{10.648}{6}\\\\&= 1+2.2+2.42+1.774666666...\\\\&=7.39466667\; \sf (8\;d.p.)\end{aligned}[/tex]

Therefore, the approximate value of [tex]e^{2.2}[/tex] is:

[tex]\large \textsf{$e^{2.2}$}=\boxed{7.39466667}\; \sf (8\;d.p.)}[/tex]

Note: To obtain a more accurate approximate value, increase the value of n.

The number of Kid's Launches that are possible is 128. This is solved using Combination Principle.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.

Hence,

The number of possible "Sizes" from the specified 4 sizes are ⁴C₁

The number of sorts of bun that is possible from the specified two bun types is:  ²C₁

From the four sides, the number of possible side purchases is:  ⁴C₁

Of the available four drinks, the number of the possible drinks is: ⁴C₁

Now the possible number of all lunches are:

⁴C₁ x  ²C₁ x  ⁴C₁ x  ⁴C₁

= 4 x 2 x 4 x 4

= 128

Hence the number of Kid's Lunches that are possible are 128.

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Answer:

Step-by-step explanation:

well, you have to determine what the variables are first. this question cannot be answered unless the variables are defined. If x=3 then it is 3(3) +5 which is 9 + 5. Then you add the numbers together which equals 14.

Answer:

the answer is 12

explanation 12x12= 144

The required place values in the chart are as Hundred: 9, Tens: 5, Ones: 0, Tenths: 0, Hundredths: 4, and Thousandths: 8. The number in standard form is 950.048.

The number is given in the question as:

(9 × 100) + (5 × 10) + (4 × 1/100) + (8 × 1/1000)

900 + 50 + 4/100 + 8/1000

1040 + 1/25 + 1/125

118756/125

950.048

As per the requierd place values in the chart are:

Hundred: 9

Tens: 5

Ones: 0

Tenths: 0

Hundredths: 4

Thousandths: 8

Now, the number in standard form is 950.048.

Thus, the required place values in the chart are as Hundred: 9, Tens: 5, Ones: 0, Tenths: 0, Hundredths: 4, and Thousandths: 8. The number in standard form is 950.048.

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Answer:

8

Step-by-step explanation:

Multiply the two radicals and then square it.

Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

Loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

When energy moves through a medium (such as air, water, or any other liquid or solid matter), it creates a pattern of disturbance known as a sound wave that propagates away from the sound source.

When an object vibrates, sound waves are produced that are similar to pressure waves, like when a phone rings.

Pitch, intensity, and timbre are three key components of the field of sound psychology or psychoacoustics. People can distinguish the harmonics of a complex periodic sound wave under certain conditions thanks to the way that humans perceive sound and music.

Thus, loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

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As per the concept of matrix multiplication, the value AB is [tex]\begin{bmatrix}11 &15 &-17 \\ -1&-4 &-4 \\ 17&15 &-22 \end{bmatrix}[/tex]

Matrix multiplication:

Matrix multiplication states that "The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix."

Given,

Here we have the matrix A and B.

And we have to perform the multiplication operation on it.

The value of matrix A is written as,

[tex]\begin{bmatrix} -4& 1 &-4 \\3 & 3 & 1 \\2 & 5 & 5\end{bmatrix}[/tex]

And the value of the matrix B is written as,

[tex]\begin{bmatrix} -4& -5 &4 \\3 & 3 & -5 \\2 & 2 & -1\end{bmatrix}[/tex]

Now, we have to multiply these two matrix, then we get the following,

[tex]\begin{bmatrix} -4& 1 &-4 \\3 & 3 & 1 \\2 & 5 & 5\end{bmatrix}\times\begin{bmatrix} -4& -5 &4 \\3 & 3 & -5 \\2 & 2 & -1\end{bmatrix}[/tex]

And the multiplication of the matrix is written as,

[tex]\begin{bmatrix} -4\times-4+1\times3-4\times2& -4\times-4+1\times3-4\times2 &-4\times4+1\times-5-4\times-1 \\3\times-4+3\times3+1\times2 & 3\times-5+3\times3+1\times2 & 3\times4+3\times-5+1\times-1 \\2\times-4+5\times3+5\times2 & 2\times-5+5\times3+5\times2 & 2\times4+5\times-5+5\times-1\end{bmatrix}[/tex]

When we simplify this one then we get the value of AB is,

[tex]\begin{bmatrix}11 &15 &-17 \\ -1&-4 &-4 \\ 17&15 &-22 \end{bmatrix}[/tex]

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The graph of y=1.4log (x) is black, graph of y=1.2ln(x) is green, graph of y=log(2.25-x) is blue, graph of y=log(0.75-x) is red.

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.

To determine the color of each function, plot the graph of each function,

The graph of y=1.4log (x) is black.

The graph of y=1.2ln(x) is green.

The graph of y=log(2.25-x) is blue.

The graph of y=log(0.75-x) is red.

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The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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The equation that represent the proportional relationship is t = 2 / 5 H.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x if:  

y = kx

for some constant k , called the constant of proportionality .

The equation that represent the proportional relationship can be represented as follows:

t = KH

using

t = 2

H = 5

Hence,

2 = 5k

k = 2 / 5

Therefore,

t = 2 / 5 H

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Answer:

HNO3. AND H3O

Step-by-step explanation:

BECAUSE THE TWO OF THEN GIVE AN (H) to the base

The expression of 602.16 dam in decimeters can be written as 60216 decimeter.

The concept that will be used in the calculation is conversion. to perform this conversion, it is important to note that 1 Decimeter (dm) is equal to 0.01 dekameter (dam).

Then, if 1dm = 0.01 dam

               Xdm     = 602.16 dam

Where x is the value in decimeter.

Then we can cross multiply as :

X= (602.16 dam * 1dm)/ 0.01 dam

= 60216 decimeter.

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Answer:

x = 55

x = 13

Step-by-step explanation:

Use the distributive property to solve.

0.5(x+9)=32

0.5x + 4.5 = 32

0.5x = 27.5

x = 55

Solve by dividing first

0.5(x+9)=32

x + 9 = 32/0.5

x + 9 = 64

x = 55

Use the distributive property to solve.

2(x+12)=50

2x + 24 = 50

2x = 26

x = 13

Solve by dividing first

2(x+12)=50

x + 12 = 50/2

x  + 12 = 25

x = 13

Answer:

[tex]x \geqslant 360[/tex]

We will see that the functions are inverses by proving that the composition is equal to the identity.

Two functions are inverses if their composition is equal to the identity, this means that if h(t) and k(t) are inverses, then we can write:

h(k(t)) = t

and

k(h(t)) = t

Proving one of these will be enough.

Here the functions are:

h(t) = (3t + 5)/t

k(t) = 5/(t - 3)

Let's find h(k(t))

We will get:

h(k(t)) = (3*k(t) + 5)/k(t)

Now we can replace the function k(t) there.

h(k(t)) = (3*5/(t - 3) + 5)/(5/(t - 3))

Now we can simplify this using algebra.

h(k(t)) = ( 15/(t - 3) + 5)*(t - 3)/5

h(k(t)) = (15/(t - 3))*(t - 3)/5 + 5*(t - 3)/5

h(k(t)) = 3 + (t - 3) = t

h(k(t)) = t

So yes, the two functions are inverses.

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The number of pupils altogether that said cola was their favorite is 26.

From the question:

The total number in pupils in the class = 60

Number of  Boys in the  classroom =32

Number of Girls in the classroom=Total number of pupils - Number of  Boys in the  classroom

Number of Girls in the classroom= 60-32

                                                       = 28

Number of Boys that like Cola only= 12

Number of Boys that like water best = 4

Number of Girls that like water best = 9

 The number of pupils altogether that said Milk was their favorite =21

The number of pupils altogether that said Water was their favorite =  9 boys+  4girls

The number of pupils altogether that said Water was their favorite =13

Thus,

The number of pupils altogether that said cola was their favorite =Total number of pupils  -The number of pupils altogether that said Water was their favorite -  The number of pupils altogether that said Milk was their favorite

= 60 - 21 - 13

=26

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Answer:

[tex]r=12, y=12x[/tex]

Step-by-step explanation:

[tex]\frac{y}{x}=\frac{48}{4}=12 \\ \\ \therefore r=12 \implies y=12x[/tex]

Answer:

12

Step-by-step explanation:

y=rx

For me it will be easier to use y=xr

So let’s fill in one of the points

48=4r

Now solve for r

48=4r

/4.  /4

12=r

Now let’s try another point to see if we get the same thing

60=5r

/5.  /5

12=r

We get the same thing so the constant of proportionality is 12

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