The total area of two rectangles can be represented by the expression (x)(3x+1) + (2x)(x+3). Which expression represents the total area of the two rectangles?

Answer:

Part 1) [tex]z=4\sqrt{3}\ units[/tex]

Part 2) [tex]y=4\sqrt{2}\ units[/tex]

Part 3) [tex]x=4\sqrt{6}\ units[/tex]

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the value of z

In the right triangle DBC

[tex]cos(C)=\frac{4}{z}[/tex] ----> equation A

In the right triangle ABC

[tex]cos(C)=\frac{z}{12}[/tex] ----> equation B

equate equation A and equation B

[tex]\frac{4}{z}=\frac{z}{12}[/tex]

[tex]z^{2}=48[/tex]

[tex]z=4\sqrt{3}\ units[/tex]

step 2

In the right triangle DBC

Applying the Pythagoras Theorem

[tex]z^{2}=y^{2}+4^{2}[/tex]

we have

[tex]z=4\sqrt{3}\ units[/tex]

substitute

[tex](4\sqrt{3})^{2}=y^{2}+4^{2}[/tex]

[tex]48=y^{2}+16[/tex]

[tex]y^{2}=48-16[/tex]

[tex]y^{2}=32[/tex]

[tex]y=4\sqrt{2}\ units[/tex]

step 3

Find the value of x

In the right triangle ABC

Applying the Pythagoras Theorem

[tex]12^{2}=x^{2}+z^{2}[/tex]

we have

[tex]z=4\sqrt{3}\ units[/tex]

substitute

[tex]12^{2}=x^{2}+(4\sqrt{3})^{2}[/tex]

[tex]144=x^{2}+48[/tex]

[tex]x^{2}=144-48[/tex]

[tex]x^{2}=96[/tex]

[tex]x=4\sqrt{6}\ units[/tex]

Answer:

B

Step-by-step explanation:

Test Yourself

Answer:

x cannot equal -3, and x cannot equal -2

Step-by-step explanation:

Answer:

The excluded values of the rational expression are -3 and -2.

Step-by-step explanation:

If a ration function is defined as [tex]R(x)=\frac{p(x)}{q(x)}[/tex], then the excluded values of the rational function are those values for which q(x)=0.

The given rational expression is

[tex]\frac{x^2+2x-3}{x^2+5x+6}[/tex]

Factories the numerator and denominator.

[tex]\frac{x^2+3x-x-3}{x^2+3x+2x+6}[/tex]

[tex]\frac{x(x+3)-1(x+3)}{x(x+3)+2(x+3)}[/tex]

[tex]\frac{(x+3)(x-1)}{(x+3)(x+2)}[/tex]                .... (1)

Equate the denominator equal to 0.

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

Using zero product property,

[tex]x+3=0\Rightarrow x=-3[/tex]

[tex]x+2=0\Rightarrow x=-2[/tex]

Therefore the excluded values of the rational expression are -3 and -2.

Cancel out the common factors of equation (1)

[tex]\frac{x - 1}{x + 2}[/tex] for (x≠-3)

It means x=-2 is vertical asymptote and x=-3 is hole.

Answer:

100pi in^2, or 314.16 in^2 to nearest hundredth.

Step-by-step explanation:

The areas of the surface of water for  full basin and area for the surface when the depth is 10 inches are in the ratio 25^2 : 10^2 = 6.25 : 1. (because the depth of the water = radius of the water when the basin is full).

The area for a full basin =  pi r^2 = 625pi in^2.

So the area  when depth is 10 inches =  625pi / 6.25 = 100pi in^2.

Step-by-step explanation:

Whole numbers means 0,1,2,3,4,5 ........................................ up to infinity.

We need to find graph of whole number greater than 3

The numbers are 4, 5 , 6 , 7 , 8 , 9 ............................................... up to infinity.

The graph representing this is the second graph.

Second graph is the correct answer.          

Answer: graph number 2 is correct

Step-by-step explanation:

i just wanted to verify for others

[tex]\bf \stackrel{\textit{let's recall that }}{a+a \implies a(1+1)\implies a(2)\implies 2a} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{a}{\cfrac{9}{12}}+\stackrel{a}{\cfrac{9}{12}}\implies \stackrel{a}{\cfrac{9}{12}}(1+1)\implies \cfrac{9}{12}(2)\implies 9\cdot \cfrac{2}{12}\implies 9\cdot \cfrac{1}{6}\implies \cfrac{9}{6}\implies \cfrac{3}{2}[/tex]

Answer:

is the last one if not the second option would  be the 2 second

Step-by-step explanation:

Answer:

0.27

Step-by-step explanation:

Red marbles = 4

Yellow marbles = 16

Purple marbles = 5

Blue marbles = 16

Green marbles = 10

Total marbles

= 4 + 16 + 5 + 16 + 10

= 51

Red and Green marbles

= 4 + 10

= 14

P(Red or green marbles)

= 14/51

= 0.27

Answer:

0.27

Step-by-step explanation:

Red marbles = 4

Yellow marbles = 16

Purple marbles = 5

Blue marbles = 16

Green marbles = 10

Total marbles

4 + 16 + 5 + 16 + 10 = 51

Red and Green marbles

= 4 + 10

= 14

P(Red or green marbles)

= 14/51

= 0.27

hope this helps pls make my answer the brainliest

Answer:

[tex]6T+4Z\leq 49[/tex]

Step-by-step explanation:

Let

T----> the number of tomatoes

Z---> the number of zucchinis

we know that

The inequality that represent this situation is

[tex]6T+4Z\leq 49[/tex]

using a graphing tool

The solution is the triangular shaded area

see the attached figure

50 F

32 F - - 18 = 32 F + 18= 50 F

Answer:

A.

Step-by-step explanation:

First, let's define the types of numbers.

Real numbers: a value that represents a quantity along a continuous line

ex: 1, 5, -6, 0.125, 45.5258,

Integer: Zero, any positive or negative number

ex: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5....

Whole numbers: a number without fractions [not negative]

ex: 0, 1, 2, 3, 4, 5.....

Rational numbers: any number that can be expressed as the quotient or fraction

ex: 1, 2, 3, 4, 5

Irrational numbers: any number that can't be expressed at the quotient or fraction

ex: pi, [3.14.... (never ending decimal)]  square root of 2....

Based on this information, the false statment would be A. I believe, because

pi is a real number and it is an irrational number.

I hope this helps!!! :)

Answer:

[tex]\large\boxed{\vec{u}\circ\vec{v}=121}[/tex]

Step-by-step explanation:

[tex]\vec{a}=<x_a,\ y_a>,\ \vec{b}=<x_b,\ y_b>\\\\\vec{a}\circ\vec{b}=x_ax_b+y_ay_b\\\\====================================\\\\\vec{u}=<8,\ 7>,\ \vec{v}=<9,\ 7>\\\\\vec{u}\circ\vec{v}=(8)(9)+(7)(7)=72+49=121[/tex]

Answer:

Data set B has a higher range than data set A and thus B has a higher degree of variability than A.

Step-by-step explanation:

There are several measures of variability in Statistics among them being;

The range

The inter-quartile range

Variance and standard deviation

To compare the variability of two or more sets of data, we can compute any of the above measures of dispersion and compare them across the various data sets.

In this question we have been given two data sets;

Data Set A: 18, 24, 29, 30, 39

Data Set B: 26, 29, 39, 40, 52

The simplest measure of variability or dispersion is the range. The range is defined as the difference between the maximum and the minimum values in a data set.

The range of data set A is; 39 - 18 = 21

The range of data set B is; 52 - 26 = 26

Data set B has a higher range than data set A and thus B has a higher degree of variability than A.

the answer would be -3,1,2

Hello!

From Least To Greatest Your Numbers Would Be

now divide 76.5 by 8.5

76.5/8.5 = 9 hours

ANSWER

Midline y=-1

Period= 2π

Amplitude=3

Frequency=1

EXPLANATION

The given function completes one cycle on the interval 0 to 2π.

Therefore the period of the function is

[tex]2 \pi[/tex]

The midline divides the graph into two equal halves.

This line is y=-1

The cycle repeated once on the interval [0,2π] hence the frequency is 1.

The amplitude is the distance from the midline to the peak.

=2--1=3

Polygons are categorized according to their side count. The following are the designations for polygons depending on the number of sides they exhibit:

3 sides: Triangles

4 sides: Quadrilaterals

Special cases of quadrilaterals include rectangles, squares, parallelograms, rhombuses, and trapezoids.

5 sides: Pentagons

6 sides: Hexagons

7 sides: Heptagons or Septagons

8 sides: Octagons

9 sides: Nonagons

10 sides: Decagons

Polygons are classified based on the number of sides they possess. Here are the names for polygons with different numbers of sides:

Triangles: The simplest polygon with three sides, often classified based on angles as equilateral, isosceles, or scalene.

Quadrilaterals: Four-sided polygons, encompassing various shapes with specific characteristics. For example, squares have equal sides and right angles, while rectangles have opposite sides of equal length and right angles.

Pentagons: Five-sided polygons, commonly found in geometry and nature.

Hexagons: Six-sided polygons frequently seen in beehives and some crystal structures.

Heptagons or Septagons: Seven-sided polygons, less commonly encountered in everyday geometry.

Octagons: Eight-sided polygons, often used in architecture and design.

Nonagons: Nine-sided polygons, less commonly discussed but still defined geometrically.

Decagons: Ten-sided polygons, exhibiting symmetry and regularity in shape.

The question probable may be:

What is the name of the polygon​

Which has :

3 sides - ?

4 sides - ?

5 sides - ?

6 sides - ?

7 sides - ?

8 sides - ?

9 sides - ?

10 sides - ?

A frequency polygon is a statistical tool used in mathematics to represent the distribution of data visually, much like a line graph, but specifically connected to a histogram. They are particularly helpful for interpreting continuous data and spotting trends within datasets.

Although the question seems to be incomplete, it appears to ask about the terminology used in mathematics, particularly pertaining to polygons. However, if we connect the dots with the provided reference, it seems the actual topic is 'frequency polygons' in the context of statistics. A frequency polygon is a graphical representation of data in statistics, where it's used to illustrate the distribution of a dataset and is similar to a line graph. It is typically made by connecting the midpoints of the tops of bars of a histogram with straight lines, making the data visually easy to interpret. By doing so, it helps in understanding how values are distributed over an interval and is often used to compare different sets of data on the same graph.

Continuous data can sometimes be difficult to analyze, but frequency polygons simplify this by offering a clear, visual interpretation. They are helpful in identifying trends and patterns in data which are not immediately obvious when looking at a table of values or a histogram alone.

Answer:

No Solutions

Step-by-step explanation:

-5x+10x+3=5x+6

5x+3=5x+6

5x=5x+3, which isn't true

ANSWER

The equation has no solution.

EXPLANATION

The given equation is

-5x+10x+3=5x+6

Group similar terms

-5x-5x+10x=6-3

-10x+10x=6-3

0=3

This statement is not true.

Hence the equation has no solution.

the answer is I think -10.2

To find out how many pounds of apples Meredith has left after 4 hours, we need to subtract the total change in apples from the original amount.

To find out how many pounds of apples Meredith has left after 4 hours, we need to subtract the total change in apples from the original amount. Let's calculate step-by-step:

To find the total change, we need to add the individual changes:

Total Change = -8.5 + (-12 2/3) + (-16 1/5) + (-10.2) = -47 61/60 pounds

Now, we subtract the total change from the original amount:

Final Amount = 85.4 - 47 61/60 pounds

Calculate the final amount to find out how many pounds of apples Meredith has left.

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50% is ur answer your welcome

The area is the length x the height.

Length = 11.40 cm

Height = 6.90 cm

Area = 11.40 * 6.90 = 78.66 cm^2

The answer is D.

Answer:

[tex]f(x)=log_ex[/tex]

Step-by-step explanation:

By definition, we can write ln instead of log. WHEN??

Whenever the base of the logarithm is the number "e".

Hence, when we have:

[tex]Log_e[/tex]

We can write it in shortcut as:

[tex]Log_e=ln[/tex]

Hence, ln x can also be written as [tex]Log_ex[/tex]

Fourth answer choice is right.

Answer:

[tex]f(x) = log_e(x)[/tex]

Step-by-step explanation:

[tex]f(x) = ln x[/tex]

For logarithmic function ln(x) the base of ln is 'e'

[tex]f(x) = log_3(x)[/tex]

The base of log is 3 . so it is not equivalent to [tex]f(x) = lnx[/tex]

[tex]f(x) = log_{10}(x)[/tex]

The base of log is 10 . so it is not equivalent to [tex]f(x) = lnx[/tex]

[tex]f(x) = log_b(x)[/tex]

The base of log is b . so it is not equivalent to [tex]f(x) = lnx[/tex]

[tex]f(x) = log_e(x)[/tex]

The base of log is e . so it is equivalent to [tex]f(x) = lnx[/tex]

Answer:

Here the slope is 2.

Step-by-step explanation:

The first step here is to solve for y.  This will lead us to the correct slope value.  Subtracting 4x from both sides, we get -2y = 7 - 4x.

Dividing both sides by -2, we get y = -7/2 + 2x.  The coefficient of x is the slope.  Here the slope is 2.

The slope of a line parallel to the line 4x - 2y = 7 is 2. This is calculated by modifying the given equation into the form y = mx + b and determining the value of 'm', which represents the slope, and parallel lines share the same slope.

To find the slope of a line parallel to the given line, 4x - 2y = 7, we first need to put the given equation in the standard form y = mx + b, where 'm' represents the slope of the line.

We can do this by isolating 'y' in the equation. So, 4x - 2y = 7 becomes 2y = 4x - 7. Then, we divide the entire equation by 2 to solve for 'y', which gives us y = 2x - 7/2. Thus, the slope 'm' of this line is 2.

Lines that are parallel to each other have the same slope, so the slope of the line parallel to the given line is also 2.

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Answer: 1/6

Step-by-step explanation:

1/6+1/6+16 hope this helps!

For this case we must simplify the following expression:

[tex]\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}[/tex]

We rewrite:

[tex]64 = 4 ^ 3\\a ^ 6 = (a ^ 2) ^ 3\\b ^ 6 * b = ((b ^ 2) ^ 3 * b)\\c ^ 9 = (c ^ 3) ^ 3[/tex]

So:

[tex]\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}[/tex]

Answer:

Option B

Answer:

Part A) The perimeter of the court is [tex]P=139.25\ ft[/tex]

Part B) [tex]5\ cans[/tex]

Step-by-step explanation:

Part A) we know that

The perimeter of the court is equal to the perimeter of the square plus the perimeter of semicircle

[tex]P=4D+\frac{\pi D }{2}[/tex]

we have that

[tex]D=25\ ft[/tex]

substitute

[tex]P=4(25)+\frac{(3.14*25)}{2}[/tex]

[tex]P=139.25\ ft[/tex]

Part B)

Find the area above the foul line (labelled II)

The area of a semicircle is equal to

[tex]A=\frac{\pi r^{2}}{2}[/tex]

we have

[tex]r=25/2=12.5\ ft[/tex]

substitute

[tex]A=\frac{(3.14)(12.5)^{2}}{2}[/tex]

[tex]A=245.31\ ft^{2}[/tex]

Round to the nearest whole number

[tex]A=245\ ft^{2}[/tex]

One can of paint covers 50 square feet of floor

so

Calculate how many cans of blue paint does the school need to purchase

[tex]245/50=4.9\ cans[/tex]

Round up

[tex]5\ cans[/tex]

Answer:

x = 4 in

Step-by-step explanation:

scale factor of reduction is

[tex]\frac{6}{18}[/tex] = [tex]\frac{1}{3}[/tex], thus

x = [tex]\frac{1}{3}[/tex] × 12 = 4

Answer:

1) 48

C) It corresponds to the 48-degree angle

Step-by-step explanation:

k║l

1) <1 = 48

because corresponding angles are equal

Why?

C) It corresponds to the 48-degree angle

Answer:

1) 48 and C) It corresponds to the 48-degree angle.

Step-by-step explanation:

Seeing the parallel lines k and l, and the transversal line m, we have that 48° and angle 1 are corresponding angles because k and l are parallel, then, the angle formed with the same transversal line will have the same measure.

So, the measure of angle 1 is 48 (option 1) and the reason is C) It corresponds to the 48-degree angle.

Answer:

I don't know either

Step-by-step explanation:

you can get 12 quarters

Answers

Part a: Opposite

Part b: cos

Part c: Adjacent

Explanation

If you doing sine, cosine, and tangent, just remember SOHCAHTOA.