ABCD is a rectangle. What is the value of X?

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\\\ ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{10}{10^{\frac{3}{4}}}\implies \cfrac{10^1}{10^{\frac{3}{4}}}\implies \cfrac{10^{\frac{4}{4}}}{10^{\frac{3}{4}}}\implies 10^{\frac{4}{4}}\cdot 10^{-\frac{3}{4}}\implies 10^{\frac{4}{4}-\frac{3}{4}}\implies 10^{\frac{1}{4}}\implies \sqrt[4]{10}[/tex]

Answer:

9 < n < 21

Step-by-step explanation:

15-6 < n < 15+6

9 < n<21

We are limited by the other two sides of the triangle

It can be no smaller than the other two sides subtracted and no larger than the other two sides added

Answer:

1.35 or 27/20

Step-by-step explanation:

(2/5) + (1/4) + (7/10)

= 0.4 + 0.25 + 0.7

= 1.35 or 27/20

Answer with explanation:

A function is said to attain maximum in the interval , if you consider any two points on the curve suppose (a,b) and (c,d)

if , c>a

Then , f(d) > f(a).

A function is said to attain minimum in the interval,

if ,c>a

Then,f(d)< f(a).

A function can have more than one relative Maximum and more than one relative Minimum.

The function whose graph is given here has following Characteristics

    •Two relative minima

     •Two relative maxima

is True .

For this case we must factor the following equation:

[tex]x ^ 2 + x-6 = 0[/tex]

We must find two numbers that, when multiplied, obtain -6 and when summed, obtain +1. These numbers are: +3 and -2

So, we have to:

[tex](x + 3) (x-2) = 0[/tex]

The roots are:

[tex]x_ {1} = - 3\\x_ {2} = 2[/tex]

ANswer:

[tex](x + 3) (x-2) = 0[/tex]

Answer:

5 boxes

Step-by-step explanation:

Given:

Total crayons : 98

Capacity of each box : 24

Number of boxes of 24 crayons needed to hold 98 crayons,

= 98 ÷ 24

= 4.08 boxes.

However since we cannot have 0.08 of a box, we must round this up to the next larger whole number of boxes.

4.08 rounded up to next whole number = 5

Hence he will need 5 boxes to hold all 98 crayons

Answer:

1 = 2

3 = 14

10 = 56

Step-by-step explanation:

y = 6x - 4

y = 6 - 4

y = 18 - 4

y = 60 - 4

Step-by-step explanation:

In first there is 2

ln second there is 14

ln third there is 56

I hope this is right answer!

For this case we must solve [tex]x + 2 <5[/tex]intersected with [tex]x-7> -6[/tex]

So, we have:

[tex]x + 2 <5\\x <5-2\\x <3[/tex]

The solutions are given by all strict minor numbers to 3.

[tex]x-7> -6\\x> -6 + 7\\x> 1[/tex]

The solutions are given by all the major strict numbers to 1.

If we intersect the solutions of both equations we have [tex]x <3[/tex] ∩ [tex]x> 1[/tex].

The intersection is given by [tex]1 <x <3[/tex]

Answer:

 The solution interval is (1,3)

Answer:

A''(1,-1) B''(3,2) C''(3,2)

Step-by-step explanation:

A(−5,0) B(−3,3) C(−3,0)

reflection over x=-2

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 3,1 and 1

after reflections, the perpendicular distance will be 6,2,2, and the points will be at

A'(1,0) B'(−1,3) C'(−1,0)

again  reflection over x=1

Perpendicular distance between points y-coordinates of points (A', B' and C') and y=1 are 0,2,2

after reflections, the perpendicular distance will be 0,4,4 and the points will be at

A''(1,-1) B''(3,2) C''(3,2)!

Step-by-step explanation:

range is all the y values

{y|y=-9, -3, 0, 5, 7}

The range of a function are all the ys included in the graph. In this case that would be:

(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)

Remember to order it from least to greatest:

{yly = -9, -3, 0,5,7}

Hope this helped!

~Just a girl in love with Shawn Mendes

To find the coordinates of point C, divide the x- and y-coordinates of AB in the ratio 2:1.

To find the coordinates of point C, we can use the concept of dividing a line segment in a given ratio. Given that AC:CB is 2:1, we can divide the x- and y-coordinates of the line segment AB in the same ratio.

The x-coordinate of point C is calculated by dividing the difference between the x-coordinates of points A and B by the sum of the ratio (2+1).

The y-coordinate of point C is calculated by dividing the difference between the y-coordinates of points A and B by the sum of the ratio (2+1).

Therefore, the coordinates of point C are (-2, 3).

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The correct option is d. [tex]\((4, 0)\)[/tex]. The coordinates of point [tex]\(C\)[/tex] are [tex]\((4, 0)\)[/tex].

To find the coordinates of point [tex]\(C\)[/tex] that partitions the segment [tex]\(AB\)[/tex] in the ratio [tex]\(AC:CB = 2:1\)[/tex], we use the section formula. Given points [tex]\(A(x_1, y_1)\)[/tex] and [tex]\(B(x_2, y_2)\)[/tex] with a ratio [tex]\(m:n\)[/tex], the coordinates [tex]\((x, y)\)[/tex] of the point dividing the segment in the ratio [tex]\(m:n\)[/tex] are given by:

[tex]\[x = \frac{mx_2 + nx_1}{m + n}, \quad y = \frac{my_2 + ny_1}{m + n}\][/tex]

For this problem:

- [tex]\(A(-8, 4)\)[/tex]

- [tex]\(B(10, -2)\)[/tex]

- Ratio [tex]\(m:n = 2:1\)[/tex]

Plugging in the values:

[tex]\[x = \frac{2 \cdot 10 + 1 \cdot (-8)}{2 + 1} = \frac{20 - 8}{3} = \frac{12}{3} = 4\][/tex]

[tex]\[y = \frac{2 \cdot (-2) + 1 \cdot 4}{2 + 1} = \frac{-4 + 4}{3} = \frac{0}{3} = 0\][/tex]

Thus, the coordinates of point [tex]\(C\)[/tex] are [tex]\((4, 0)\)[/tex].

The complete question is:

What are the coordinates of point C on the directed segment from A(−8,4) to B(10,−2) that partitions the segment such that AC:CB is 2:1 ?

A. (1,1)

B. (−2,2)

C. (2,−2)

D. (4,0)

Answer:

[tex]\large\boxed{10x^2-5x+10\ -\ \bold{quadratic\ trinomial}}[/tex]

Step-by-step explanation:

[tex]\text{quadratic trinomial}\ -\ ax^2+bx+c\\\\\text{cubic monomial}\ -\ ax^3\\\\\text{not a polynomial}\ -\ \dfrac{a}{x}\\\\\text{fourth-degree binomial}\ -\ ax^4+bx[/tex]

[tex]10x^2-5x+10\\\\\text{the highest power of variable (x) is 2}\to \boxed{x^2}\ \to\ \bold{quadratic}\\\\\text{polynomial has 3 terms}\ \to\ \boxed{10x^2,\ -5x,\ 10}\ \to\ \bold{trinomial}[/tex]

The solutions to the linear equations in variable x and unknown constant [tex]\alpha[/tex] are [tex]\frac{-\alpha}{6}[/tex], [tex]\frac{3}{\alpha}[/tex] and [tex]\frac{-6}{\alpha}[/tex].

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

We are given linear equations in variable x with an unknown constant [tex]\alpha[/tex] and we have to solve for x.

[tex]4 = \frac{6}\alpha}x + 5\\\\\frac{6}{\alpha}x = - 1\\\\x = \frac{-\alpha}{6}[/tex].

[tex]7 + 2\alpha{x} = 13.\\\\2\alpha{x} = 6.\\\\x = \frac{3}{\alpha}[/tex]

[tex]-\alpha{x} - 20 = -14.\\\\-\alpha{x} = 6.\\\\x = \frac{-6}{\alpha}[/tex]

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Answer:

195

Step-by-step explanation:

9 times 10 is 90 and 7 times 15 is 105  

so 105+90=195

Answer:

195 cm

Step-by-step explanation:

The area of ABCD is 195 cm.

Multiply the sides together:

9 ⋅ 10 = 90

7 ⋅ 15 = 105

Add them together:

105 + 90 = 195

Therefore, the area of ABCD is 195 cm.

Answer:

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct

Step-by-step explanation:

step 1

Find the area of the base of the rectangular pyramid

we know that

The volume of the rectangular pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base

H is the height of the pyramid

we have

[tex]V=40\ units^{3}[/tex]

[tex]H=6\ units[/tex]

substitute and solve for B

[tex]40=\frac{1}{3}B(6)[/tex]

[tex]120=B(6)[/tex]

[tex]B=120/6=20\ units^{2}[/tex]

step 2

Find the volume of the rectangular prism with the same base area and height

we know that

The volume of the rectangular prism is equal to

[tex]V=BH[/tex]

we have

[tex]B=20\ units^{2}[/tex]

[tex]H=6\ units[/tex]

substitute

[tex]V=(20)(6)=120\ units^{3}[/tex]

therefore

The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct

Answer:

C

Step-by-step explanation:

Got it right one the test! <3

Answer:

Third choice

Step-by-step explanation:

They are asking us to find the inverse of y=5x. To do this you just switch x and y and then remake y the subject of the equation (solve for y.)

y=5x

x=5y (I switch x and y)

x/5=y ( I divided both sides by 5)

Then you just replace y with the f^-1(x) thing

f^-1(x)=x/5

or

f^-1(x)=1/5x

If f(x) = 5x, then the inverse of the function, f⁻¹(x) is x/5.

Given that :

f(x) = 5x

Let y = f(x).

So, y = 5x

Now, interchange the values for x and y.

Then,

x = 5y

Now, solve for y.

Divide both sides of the equation by 5.

x/5 = y

So, the inverse of the function is x/5.

Hence f⁻¹(x) = x/5.

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Answer:

Option C) b=6

Step-by-step explanation:

we know that

If two linear equations of a system of equations have an infinite of solutions, then both equations are identical

we have

[tex]y=6x-b[/tex] -----> equation A

[tex]-3x+(1/2)y=-3[/tex]

Multiply by 2 both sides

[tex]-6x+y=-6[/tex]

Adds 6x both sides

[tex]y=6x-6[/tex] ------> equation B

equate equation A and equation B

[tex]6x-b=6x-6[/tex]

solve for b

[tex]b=6[/tex]

Answer:

The correct answer would be 34

Step-by-step explanation:

When solving an expression, we would first solve the operator with the highest precedence. In mathematics, there are four basic operators. Addition, subtraction, multiplication and division. The precedence of Division and multiplication is higher than the precedence of Addition and subtraction. So by solving this with the precedence, we would first solve the multiplication operator which is 25 * 2, it will give 50, then we will subtract 16 from it like 50-16, which will give us 34.

Answer:

(5x+4)(5x-4)

Step-by-step explanation:

The product expression can be obtained by factorizing the expression 25x²-16 provided in the question.

The expression is a difference of two squares whose factors are generally

(a-b)(a+b)

√25x² is 5x

√16 is 4

Therefore the product required is (5x+4)(5x-4)

25x²-16 is equivalent to (5x+4)(5x-4)

Answer:

(-1,-1)

The square needs to be all side with the same value when you graph the vertices on x-y plot, you obtain (x is the dot that correspond a vertice and y the forth vertice )

                            x       2 |                        x

                                      1 |

                                       |                                  

      -2                  -1         |          1              2

                            y        -1|                       x

                                     -2 |

If you draw a line between vertices the value it will be 2 +  (-1) so the forth vertice has to be (-1,-1)

The complete table of values for the equation y = x/4 is

x   4   2  9

y  1   1/2  9/4

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

y = x/4

The missing y values are at x = 4, 2 and x = 9

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

y = 1/4 * 4 = 1

y = 1/4 * 2 = 1/2

y = 1/4 * 9 = 9/4

So, the missing values are 1, 1/2 and 9/4

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Final answer:

The rule 'y = X/4' describes division of X by 4 to find Y. The student completes the table by dividing each X value by 4 to find the corresponding Y values, providing an organized data set.

Explanation:

The student is asking about the operation indicated by the rule y = X/4, which involves division. The fraction bar signifies division. Given this rule, we can complete the table for y when x-values are provided.

For x = 4: y = 4/4 = 1

For x = 2: y = 2/4 = 0.5

For x = 9: y = 9/4 = 2.25

To organize the data in the table, you simply divide the x-value by 4 to find the corresponding y-value.

Firstly see what they are in mixed fraction form:

[tex]7 \frac{9}{7} = \frac{58}{7} [/tex]

therefore, 7 9/7 is equal to 58/7

[tex]8 \frac{2}{7} = \frac{58}{7} [/tex]

Answer:

C. 24

Step-by-step explanation:

In a right triangle, the sum of the squares of the two legs of the triangle is equivalent to the square of the  hypotenuse.

a²+b²=c²

a=10

b=?

c=26

Let us substitute with the values given in the question.

10²+b²=26²

100+b²=676

b²=676-100

b²=576

b=√576

=24

The other leg of the triangle is 24 units long.

Answer: option c.

Step-by-step explanation:

You need to use the Pythagorean Theorem. This is:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse and "b" and "c" are legs of the triangle.

In this case you know that:

[tex]a=26\\b=10[/tex]

Then, you need  to substitute values into  [tex]a^2=b^2+c^2[/tex] and then solve for "c".

So, this is:

[tex]26^2=10^2+c^2\\\\26^2-10^2=c^2\\\\576=c^2\\\\\sqrt{576}=c\\\\c=24[/tex]

Answer:

The answer should be the last one.

Step-by-step explanation:

Answer:

=2√2 the fourth choice.

Step-by-step explanation:

We can use the Pythagoras theorem to calculate the value of y.

a²+b²=c²

a=1

b=y

c=3

Therefore substituting for the values in the theorem above we get:

1²+y²=3²

Leave y on one side.

y²=3²-1²

y²=9-1

y²=8

y=±2√2 in surd form.

Since we expressing length, a scalar quantity, we take the modulus of our answer. Thus y=2√2

Answer:

26.6 degrees

Step-by-step explanation:

Use the converting formula:

(-3°C × 9/5) + 32 = 26.6°F

-3 degrees to Fahrenheit would be 26.6

The formula is attached in the image below

-3 × 1.8 = -5.4

-5.4 + 32 = 26.6

Answer:

∠A, ∠B, ∠C

Step-by-step explanation:

In a triangle the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side, therefore:

∠A < ∠B < ∠C

Answer:

a,b,c

Step-by-step explanation:

The angle opposite the longest side has the largest angle measure, the angle opposite the shortest side has the most small angle measure etc.

Since BC is the shortest line, the angle opposite will have the smallest measure, this is ∠a.

CA is in the middle with length this means that the angle opposite of it will have an angle measure in between that of the other angle measures.  This is ∠b

AB has the longest length, therefore, the angle opposite it will have the largest measure, this is ∠c

The distance between the points (2, 8) and (-7, -4) is 15 units.

Using the distance formula derived from the Pythagorean theorem, the distance between the points (2, 8) and (-7, -4) is found to be 15 units.

The distance between two points in the coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. For points (2, 8) and (-7, -4), the distance can be calculated as follows:

Therefore, the distance between the points (2, 8) and (-7, -4) is 15 units.

Answer:

Option B. The value of x is 20

Step-by-step explanation:

we know that

The intersecting chords theorem  states that the products of the lengths of the line segments on each chord are equal.

so

In this problem

[tex](x)(x-11)=(x-8)(x-5)\\x^{2}-11x=x^{2}-5x-8x+40\\-11x=-13x+40\\2x=40\\x=20[/tex]

Answer:

[tex]y-6=-\frac{5}{4}(x+2)[/tex]

[tex]y-1=-\frac{5}{4}(x-2)[/tex]

[tex]y-3.5=-1.25x[/tex]

Step-by-step explanation:

step 1

Find the slope of the linear equation

with the points (-2,6) and (2,1)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{1-6}{2+2}[/tex]

[tex]m=-\frac{5}{4}[/tex]

step 2

Find the equation of the line into point slope form

The equation of the line in slope point form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{5}{4}[/tex]

1) with the point (-2,6)

substitute

[tex]y-6=-\frac{5}{4}(x+2)[/tex]

2) with the point (2,1)

substitute

[tex]y-1=-\frac{5}{4}(x-2)[/tex]

3) with the point (0,3.5)

substitute

[tex]y-3.5=-\frac{5}{4}(x-0)[/tex]

[tex]y-3.5=-\frac{5}{4}x[/tex] -------> [tex]y-3.5=-1.25x[/tex]

Answer:

A, D, E

Step-by-step explanation:

[tex](f+g)(x)=3x+\sqrt{x-4}[/tex]

Answer:

Table B

Vertex is (3,-5)

Step-by-step explanation:

We are given with an equation of a parabola [tex]y=x^2-6x+4[/tex]

Let is convert it into standard form of a parabola

[tex]y=x^2-6x+4[/tex]

adding and subtracting 9 in the right hand side of the =

[tex]y=x^2-6x+9-9+4[/tex]

[tex]y=x^2-2\times 3\times x+ 3^2-9+4[/tex]

the first three terms of the right hand side forms the expression of square of difference

[tex]a^2-2 \times a \times b+b^2 = (a-b)^2[/tex]

Hence

[tex]y=(x-3)^2-5[/tex]

adding 5 on both sides we get

[tex](y+5)=(x-3)^2[/tex]

Comparing it with the standard equation of a parabola

[tex]X^2=4\times \frac{1}{4} \times Y[/tex]

where [tex]X=x-3[/tex] and [tex]Y=y+5[/tex]

The vertex of [tex]X^2=4\times \frac{1}{4} \times Y[/tex] will be (0,0)

and thus vertex of

[tex](y+5)=(x-3)^2[/tex] will be (3,-5)

Hence the Table B is our right answer