What is the length of DE?

A. 10
B. 22
C. 18
D. 12

Answer:

[tex]\frac{2x-y}{x(x-y)}[/tex]

Step-by-step explanation:

To express as a single fraction

multiply numerator/denominator of [tex]\frac{1}{x}[/tex] by (x - y) and

multiply numerator/ denominator of [tex]\frac{1}{x=y}[/tex] by x

= [tex]\frac{x-y}{x(x-y)}[/tex] + [tex]\frac{x}{x(x-y)}[/tex]

Add the numerators leaving the denominator

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

Answer:

36x² + 24x + 4

Step-by-step explanation:

Given

(6x + 2)² = (6x + 2)(6x + 2)

Each term in the second factor is multiplied by each term in the first factor, that is

6x(6x + 2) + 2(6x + 2) ← distribute both parenthesis

= 36x² + 12x + 12x + 4 ← collect like terms

= 36x² + 24x + 4

The answer is 84 degrees because d and f both are 48 degrees so that adds up to 96. So that means you add 84 plus 96 which is 180 so the answer is 84 degrees.

Answer. The answer is 84

Answer:

Front section tickets: $40

Back section tickets: $25

Step-by-step explanation:

If x is the price of back section tickets, and x + 15 is the price of front section tickets, then:

275 (x + 15) + 325 x = 19125

275 x + 4125 + 325 x = 19125

600 x = 15000

x = 25

So back section tickets are $25, meaning front section tickets are $40.

Answer:

Left 4 units

Step-by-step explanation:

h(x) is a line with slope 2.  Let's say it has y-intercept b.  So:

h(x) = 2x + b

d(x) is h(x) shifted up 8 units.  So:

d(x) = h(x) + 8

d(x) = 2x + b + 8

We want to shift h(x) left or right to get d(x).  If we say that shift is a units to the right, then:

h(x−a) = d(x)

2(x−a) + b = 2x + b + 8

2x − 2a + b = 2x + b + 8

-2a = 8

a = -4

a is negative, so the shift is to the left.

h(x) should be shifted to the left 4 units.

The h(x) should be Left 4 units

Since

h(x) represent a line with slope 2.  

Let's assume it has y-intercept b.  

Therefore,

h(x) = 2x + b

d(x) represent h(x) shifted up 8 units.  

So,

d(x) = h(x) + 8

d(x) = 2x + b + 8

Now

h(x−a) = d(x)

2(x−a) + b = 2x + b + 8

2x − 2a + b = 2x + b + 8

-2a = 8

a = -4

Since a is negative, so the shift is to the left.

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Answer:

C. The domain is all real numbers, and the range is non-negative real numbers( [tex]y\ge0[/tex])

Step-by-step explanation:

The absolute value parent function is [tex]y=|x|[/tex]

The domain of a function refers to all values of x for which the function is defined.

The parent absolute value function is defined for all values of x.

Therefore the domain is all real numbers.

The range refers to the y-values for which x is defined.

The parent has a v-shape and its vertex is at the origin.

Therefore the least y-value is 0 and there is no maximum y-value.

The range is [tex]y\ge0[/tex]

See attachment.

Answer:

The boy has 28 blue pencils

Step-by-step explanation:

Given

Total pencils = 40

The ratio of red to blue= 0.15:0.35

We have to find the number of blue pencils

For that we need the sum of ratio = 0.15+0.35 = 0.5

So, the number of blue pencils = (ratio of blue/sum of ratio) * total pencils

=0.35/0.5 * 40

=0.7*40

=28 pencils

Therefore, the boy has 28 blue pencils ..

Final answer:

The ratio of red to blue pencils is 0.15 to 0.35. By converting the ratio into parts and calculating the pencils per part, we conclude that the boy has 28 blue pencils in his pencil case.

Explanation:

Calculating the Number of Blue Pencils

To find out how many blue pencils the boy has, we start by understanding the ratio of red to blue pencils, which is given as 0.15 to 0.35. This ratio can also be represented as a fraction, so for every 0.15 red pencils, there are 0.35 blue pencils. To find out the total parts the ratio represents, we add them up: 0.15 (red) + 0.35 (blue) = 0.5 parts. We then divide the total number of pencils (40) by the total parts (0.5) to find out how many pencils each part represents: 40 pencils / 0.5 parts = 80 pencils per part. Since we are looking for the number of blue pencils, we multiply the blue part (0.35) by the number of pencils per part (80): 0.35 * 80 pencils per part = 28 blue pencils.

Answer: The black hole is [tex]3.302\times10^{6}[/tex] times more masive than the sun.

Step-by-step explanation:

Given : The mass of black hole =  [tex]6.57\times10^{36}\ kg[/tex]

The mass of Sum is approximately [tex]1.99\times10^{30}\ kg[/tex]

Now, the number of times the mass of black hole more massive than the mass of sun is given by :-

[tex]n=\dfrac{6.57\times10^{36}}{1.9\times10^{30}}[/tex]

i.e.[tex]n=\dfrac{6.57}{1.9}\times\dfrac{10^{36}}{10^{30}}[/tex]

Using the division law of exponent :-

[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]

[tex]=\approx3.302\times10^{36-30}}\\\\=3.302\times10^{6}[/tex]

Hence, the black hole is [tex]3.302\times10^{6}[/tex] times more masive than the sun.

Answer:

side GH is proportional to segment CD

Step-by-step explanation:

Corresponding sides are those sides that are in the same spot in two different  shapes.

Since parallelogram EFGH is dilated form of Parallelogram ABCD and Side BC is proportional to side FG.

So, side GH is proportional to segment CD

Answer: 0.999548

Step-by-step explanation:

If the probability that a person will die next year is 425/1,000,000

The the probability of them not dying is:

(1,000,000-425)/1,000,000=999548/1,000,000

Next let’s move the decimal 6 spots to the left.

The answer would be 0.999548

Answer:

The chord is bisected.

Step-by-step explanation:

see the attached figure to better understand the problem

In the circle of the figure

The diameter is the segment DE

The chord is the segment AB

PA=PB=r ----> radius of the circle

Triangles PAC and PBC  are congruent right triangles by SSS

Because

PA=PB

PC is a common side

AC=BC ----> Applying Pythagoras Theorem

therefore

The chord AB is bisected

Answer:

The chord is bisected

Step-by-step explanation:

So you're asking to evaluate this equation?

mk/m+k for m = 6 and k = 2

Answer:

The graph of g(x) is equal to the graph of f(x) shifted 3 units to the right and 4 units above.

Step-by-step explanation:

we know that

[tex]f(x)=x^{3}[/tex] ----> the turning point is the point (0,0)

[tex]g(x)=(x-3)^{3}+4[/tex] ----> the turning point is the point (3,4)

The rule of the translation of f(x) to g(x) is equal to

(x,y) ------> (x+3,y+4)

That means-----> The translation is 3 units at right and 4 units up

therefore

The graph of g(x) is equal to the graph of f(x) shifted 3 units to the right and 4 units above.

Answer:

Step-by-step explanation:

Y/1 = 2x + 5

Y = 2x + 5

Y = 2x + 5

When x = 1

Y = 2 ×1 +5

Y = 2 + 5

Y = 7

When x =0

Y = 2 × 0 + 5

Y = 5

When x = -2

X = 2 × -2 + 5

X = 1

( Make a table in the side of the page)

X | 1 0 -2

_ _______

Y 7 5 1

The graph for the coordinate points (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7) is plotted below.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation of a line is y=1/2x+5.

Substitute x=0, 1, 2, 3, 4, 5,....in a equation y=1/2x+5, we get

When x=0, y=5

When x=1, y=5.5

When x=2, y=6

When x=3, y=6.5

When x=4, y=7

So, the coordinate points are (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7)

Therefore, the graph for the coordinate points (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7) is plotted below.

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f(x-5) because when it's with the x, + indicates a translation to the left and - indicates a translation to the right.

Answer:

f(x−3)+1, f(x−5)

Step-by-step explanation:

I took the checkpoint and got it right.

Step-by-step explanation:

rearrange the equations first

y=-3x-2---eq(1)

y=-3x+1-4

y=-3x-3---eq(2)

In first eq slope is -3x and y-intercept is -2

In second equation, the slope is -3x and y-intercept is -3

the slopes are the same in both equations but the y-intercepts are different

so the lines are parallel. The system is inconsistent

For this case we have the following system of equations:

[tex]3x = -2-y\\4 + y = -3x + 1[/tex]

By clearing "y" from both equations we have:

Equation 1:

[tex]3x + 2 = -y\\y = -3x-2[/tex]

Equation 2:

[tex]y = -3x + 1-4\\y = -3x-3[/tex]

It is observed that the slopes of both equations are equal. Recall that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where "m" is the slope.

If the slopes are equal, then the lines are parallel.

Answer:

Parallel

Answer:

[tex]x=\sqrt[3]{10}-2[/tex]

Step-by-step explanation:

The composite function (f(x+1)) is moved in the x-axis by -1, you know this by solving x+1=0.

The equivalent expresion for f(x+1) is

[tex]f(x+1)= (x-1+3)^{3}+4[/tex]

[tex]f(x+1)=(x+2)^{3}+ 4[/tex]

Eval the above expression in g(x)

[tex]g(x)=(x+2)^{3}+4-2[/tex]

We must find x that gives g(x)=12

The equation is the following

[tex]12=(x+2)^{3}+2[/tex]

Grouping terms>

[tex](x+2)^{3} =10[/tex]

To solve for x, must apply cubic root in both sides of equation:

[tex]\sqrt[3]{(x+2)^{3} } =\sqrt[3]{10}[/tex]

it then turns in the following>

[tex]x+2=\sqrt[3]{10}\\[/tex]

Giving the stated answer

Answer:

A. Parabola

Step-by-step explanation:

Parabola best describes the locust of points equidistant from a given directrix and focus.

Parabola is the curve that best describes the locus of points equidistant from a given directrix and focus. This can be obtained by understanding what a parabola is.

The equation is y² = 4ax, when directrix is parallel to the y-axis, a is distance from origin to focus.

Hence parabola is the curve that best describes the locus of points equidistant from a given directrix and focus.

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[tex]\huge{\boxed{\text{No.}}}[/tex]

Unless the points are both the same point, there is only one straight line to connect them both. Any other line would either only touch one point or touch neither of the points.

Answer:

x=7

Step-by-step explanation:

The given equation is:

[tex]\frac{x}{3}+\frac{x}{6} = \frac{7}{2}[/tex]

Multiplying both sides by LCM of 3 and 6

So,

[tex]\frac{x}{3}*6+\frac{x}{6}*6 = \frac{7}{2}*6\\2x+x=7*3\\3x=21\\\frac{3x}{3} =\frac{2}{3}\\ x=7[/tex]

Hence, the solution of the equation is x=7 ..

Answer: x = 7

Step-by-step explanation:

(x/3)+(x/6)=7/2

add variables

(2x+x)/6=7/2

combine like terms

3x/6=7/2

simplify

x/2=7/2

multiply denominators by 2

x=7

Answer:

Step-by-step explanation:

[tex]A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] \\\\\det A=\left|\begin{array}{ccc}a&b\\c&d\end{array}\right|=ad-bc[/tex]

[tex]\left\{\begin{array}{ccc}x+2y=5\\x-3y=7\end{array}\right\\\\A=\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] \\\\\det A=A=\left|\begin{array}{ccc}1&2\\1&-3\end{array}\right|=(1)(-3)-(1)(2)=-3-2=-5[/tex]

Answer:

-5

Step-by-step explanation:

Answer: B. 36

Step-by-step explanation: Round each number.

11.72 -> 12

3.01 -> 3

Multiply the rounded numbers.

12 x 3 = 36

The answer would be 36.

Answer:

x+2

5x-2

Step-by-step explanation:

There is only 2 binomials that will multiply together that will give the given trinomial.

ax^2+bx+c

5x^2+8x-4

Goal: Find two numbers that multiply to be a*c and add up to be b.

We will use this goal to factor our trinomial.

a=5

b=8

c=-4

--------

a*c=-20

b=8

Can you think of two numbers that multiply to be -20 and add up to be 8? I hope you said 10 and -2.

So we are going to replace 8x with -2x+10x.

5x^2+8x-4

5x^2-2x+10x-4

We are going to pair the first terms together and the second two terms together like so:

(5x^2-2x)+(10x-4)

Now we are going to factor each pair.

x(5x-2)+2(5x-2)

(5x-2)(x+2)

So (x+2) is a factor of the given trinomial and (5x-2) is a factor of the given trinomial.

Answer

x+2 and 5x-2

Step-by-step explanation:

The symmetric property of equality justifies the statement 'If m₁ = m₂, then m₂ = m₁'.

Property of Equality: The property that justifies the statement 'If m₁ = m₂, then m₂ = m₁' is the symmetric property of equality. This property states that if a = b, then b = a. It is a fundamental property of equality in mathematics.

Hii!

__________________________________________________________

Answer:

Step-by-step explanation:

Note that both terms, 4x and -16, have something in common.

In math, this "something" is known as the greatest common factor (g.c.f.).

The g.c.f. of 4x and -16 is 4, so that's what we factor out.

First, we divide both 4x and -16 by 4.

We obtain.

x-4

Put parentheses around x-4

(x-4)

Now put 4 outside the parentheses

4(x-4)

--

Hope that this helped! Best wishes,

--

The factored form of the expression 4x - 16 is 4(x - 4).

To factor the expression 4x - 16, we can look for the greatest common factor (GCF) of the terms. In this case, both terms have a common factor of 4.

We can factor out the GCF of 4 from each term:

4x - 16 = 4(x - 4)

Therefore, the factored form of the expression 4x - 16 is 4(x - 4).

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2.375 is 0.95% of 250

Equation: Y = P% multiplied by X

Y = 0.95% multiplied by 250

Converting percent to a decimal:

P = 0.95%÷100 = 0.0095

Y = 0.0095 × 250

Y = 2.375

Therefore, 2.375 is 0.95% of 250

Answer:

D. I, II, III

Step-by-step explanation:

Let us look at the definition of set:

A set is a collection of well-defined and distinct objects

I: The collection of all the days in a week.

The set will consist of seven elements.

II: The collection of all teachers in a school.

Also a set.

III: The collection of all integers more than -5.

This is a set.

Therefore, Option D is correct ..

Answer:

Step-by-step explanation:

Look at the picture.

We know: the sum of the angles measure in the triangle is 180°. Therefore we have the equation:

[tex]35^o+35^o+\alpha=180^o[/tex]

Solve it:

[tex]70^o+\alpha=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\\alpha=110^o[/tex]

Angle α and β = x are the supplementary angles. Supplementary angles add up to 180°. Therefore:

[tex]\alpha+\beta=180^o[/tex]

[tex]110^o+\beta=180^o\qquad\text{subtract}\ 110^o\ \text{from both sides}\\\\\beta=70^o[/tex]

[tex]\beta+\gamma+\gamma=180^o[/tex]

[tex]70^o+2\gamma=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\2\gamma=110^o\qquad\text{divide both sides by 2}\\\\\gamma=55^o[/tex]

Answer:

Step-by-step explanation:

We know: the angles measures in a triangle add up to 180°.

(look at the picture)

z + 50 + 60 = 180

z + 110 = 180    subtract 110 from both sides

z = 70°

x + 50 + 70 = 180

x + 120 = 180         subtract 120 from both sides

x = 60°

Angles x, y and z are on one side of a straight line. Therefore they add to 180°.

x + y + z = 180

60 + y + 70 = 180

y + 130 = 180         subtract 130 from both sides

y = 50°

Answer:

x = 60°, y = 50°

Step-by-step explanation:

We know: the angles measures in a triangle add up to 180°.

z + 50 + 60 = 180

z + 110 = 180    subtract 110 from both sides

z = 70°

x + 50 + 70 = 180

x + 120 = 180         subtract 120 from both sides

x = 60°

Angles x, y and z are on one side of a straight line. Therefore they add to 180°.

x + y + z = 180

60 + y + 70 = 180

y + 130 = 180         subtract 130 from both sides

y = 50°

[tex]\bf \sqrt{x+11}-x=-1\implies \sqrt{x+11}=x-1\implies \stackrel{\textit{squaring both sides}}{(\sqrt{x+11})^2=(x-1)^2} \\\\\\ x+11=\stackrel{\mathbb{F~O~I~L}}{x^2-2x+1}\implies 11=x^2-3x+1\implies 0=x^2-3x-10 \\\\\\ 0=(x-5)(x+2)\implies x= \begin{cases} 5\\ -2 \end{cases}[/tex]

Gives x = -5 or x = 2.

Learn how to solve radical equations step by step by isolating terms and squaring, resulting in solutions to the given equation.

To solve the equation (square root of x+11)-x=-1, follow these steps: