Find the missing length for both questions

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Answer: [tex]y \leq -\frac{x}{2}-\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]-x-2y \geq 7\\\\x+2y \leq -7\\\\2y \leq -x-7\\\\y \leq -\frac{x}{2}-\frac{7}{2}[/tex]

The measure of one of the congruent base angles is 65°.

It's important to note that any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. A triangle has three sides, three angles and the sum of the angles equal 180°.

It should be noted that a triangle has 3 side, 3 angles and a sum of 180°.

In this situation, DEF is an isosceles triangle. If m∠D = (3x + 5)° , m∠E = (4x − 15)° and m∠F = (2x + 10)°.

The value will be illustrated thus:

3x + 5 + 4x - 15 + 2x + 10 = 180

Collect the like terms

9x = 180 - 5 + 15 - 10

9x = 180

x = 180 / 9

x = 20

The measure of one of the congruent base angles will be:

= 4x - 15

= 4(20) - 15

= 65°

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Subtract 3

2y + 2xy – x + 4 from 9 - 7x + 3xy - 4

2y

Answer:

Step-by-step explanation:

teaj

Answer:

√192

Step-by-step explanation:

12 cos 30° + 2 tan 60°

Substitute the trig functions of the special angles.

12 (½√3) + 2 (√3)

Simplify.

6√3 + 2√3

8√3

Move under the radical.

√(8² · 3)

√192

0-4 can be the domain of positive real numbers but can not be the domain of whole numbers.

Numbers an arithmetical value used in counting and calculating that is expressed as a word, symbol, or figure that represents a specific quantity.

Let's understand what is positive real numbers.

That is all the real numbers that are greater than or equal to zero.

real numbers are numbers which include both rational and irrational numbers.

whole numbers are positive integers that mean only positive integers.

that means 0-4 can be the domain of positive real numbers but can not be the domain of whole numbers because 0.5 and 0.6 these numbers are not whole numbers.

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The value of y in the given diagram is 6cm.

What is triangle?

Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.

Consider, the given triangle the two base angles are same.

So, the triangle is a isosceles triangle.

Since, when the base angles of an isosceles triangle are equal, the sides that face these angles are also equal.

Hence, the value of y in the given diagram is 6cm.

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Answer:

(2½,1)

Step-by-step explanation:

(-1+6/2,5+-3/2)

(5/2,2/2)

(2½,1)

Answer:

  960.50 feet

Step-by-step explanation:

You want to know the height of a balloon if it is 1424 feet horizontally from a landmark at an angle of depression of 34°.

The geometry of the problem can be modeled as a right triangle with a base angle of 34°, the adjacent leg 1424 feet, and the opposite leg being the height of the balloon. The tangent relation tells us ...

  Tan = Opposite/Adjacent

  Opposite = Adjacent·Tan

  height = (1424 feet)·tan(34°) ≈ 960.50 feet

The balloon's vertical distance from the ground is 960.50 feet.

__

Additional comment

If the angle is measured to the nearest degree, then the height of the balloon is somewhere between 943 feet and 979 feet. The only purpose served by reporting the distance to the nearest 0.01 foot is to see if you can use your calculator correctly.

To make that precision for the height meaningful, the angle would need to be measured with an error less than 0.00014°, about 1/2 arc-second. This is better resolution than the best surveying instruments offer, by a factor of about 30.

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The length of the other leg is (c) √43

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

Hypotenuse = 7

One leg = √6

The length of the other leg can be calculated using

The length of the other leg = √(Hypotenuse^2 - One leg^2)

So, we have

The length of the other leg = √(7^2 - √6^2)

Evaluate

The length of the other leg = √43

Hence, the length is (c) √43

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Complete question

A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.

The requried equivalent fraction is 7/4. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Fraction is defined as the number of compositions that constitutes the Whole.

here,
7/6 divided by 2/3
= 7/6 ÷ 2/3
= 7/6 × 3/2
= 7/4

Thus, the requried equivalent fraction is 7/4. Option B is correct.

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The value of x and y at which function P = 3x+2y becomes maximum are

(9,0), data from given graph.

What is the graph?

Graph is the pictorial representation of given data.

Graph is defined as to create a diagram that shows a relationship between two or more things. An example of graph is to create a series of bars on graphing paper.

The four most common are

1. Probably line graphs,

2. Bar graphs and histograms,

3. Pie charts, and

4. Cartesian graphs

To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.

Note: (5,4) is not a vertex.

(0,8) :

P = 3*0 + 2*8

  = 16

(5,4):
P = 3*5 + 2*4

  = 23

(9,0):

P = 3*9 + 2*0

  = 27.

So, the maximum value = 27 at (9,0).

So, the x value = 9 and

      the y value = 0.

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Answer:

$9,712.12 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies A=9544\left(1+\frac{0.0525}{12}\right)^{12 \cdot \frac{1}{3}}[/tex]

[tex]\implies A=9544\left(1.004375\right)^{4}[/tex]

[tex]\implies A=9544\left(1.017615179\right)[/tex]

[tex]\implies A=9712.119269[/tex]

The balance of the account at the end of August will be $9,712.12 (nearest cent).

The constant amount that Carson makes every hour is $16.25.

It is important to note that this question has to do with a proportional relationship. Since Carson earns $113.75 for 7 hours of work and he makes a constant hourly wage.

The amount that he makes per hour will be:

= Amount / Number of hours

= $113.75 / 7

= $16.25

Therefore the constant amount he makes every hour is $16.25.

Note that the options weren't given but the question has been solved accordingly.

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Answer: [tex]9x+4y=-20[/tex]

Step-by-step explanation:

Standard form is ax+by=c. What we can do is put the given point and slope into slope-intercept point, and then manipulate it to standard form.

[tex]y=-\frac{9}{4} x-5[/tex]                  [add both sides by [tex]\frac{9}{4} x[/tex]]

[tex]\frac{9}{4} x+y=-5[/tex]                   [multiply both sides by 4]

[tex]9x+4y=-20[/tex]

Therefore the standard form is [tex]9x+4y=-20[/tex].

Answer:

C would be the answer

Step-by-step explanation:

constants are the numbers with no terms.

The relation (10, 8), (7, 9), (9, 13), (8, 5) is representing a function. (option B)

A function defines relations between input and output, where all input has a distinct output.

Given are the relations,

A) (14, 12), (10, 12), (-13, 7), (11, 15)

In this, two inputs 14 and 10 have same output 12, so it can not be a function.

B) (10, 8), (7, 9), (9, 13), (8,5)

In this, we can see, every input have distinct outputs, so it can be considered as a function.

Hence, (10, 8), (7, 9), (9, 13), (8,5) is a function.

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The value of x for the expression is equal to -5 and -2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the logarithmic expression is log₂ (x+4) + log₂ (x + 3) = 1. The value of x will be calculated as,

log₂ (x+4) + log₂ (x + 3) = 1

log₂ { (x+4)(x + 3) } = 1

x² + 7x + 12 = 2

x²+ 7x + 10 = 0

Solve the above quadratic equation,

x²+ 7x + 10 = 0

x² + 5x + 2x + 10 =0

x ( x + 5 ) + 2 ( x + 5 ) = 0

(x + 5 ) ( x + 2 ) = 0

x  = -5 and -2

The values of x are -5 and -2.

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Answer:

Step-by-step explanation:

• 12a - 2b - 4b - 15a + 2 (a = 0, b = 3)

→ apply the values

• 12x0 - 2x3 - 4x3 - 15x0 + 2

• 0 - 6 -12 - 0 + 2

→ use BODMAS formulae

• 0 - 6 - 12 - 2

= 0 - 6 - 10

→ zero wouldn't be counted so

- 6 - 10

(-) + (-) = (+) so:

= -16

Answer: last option

Step-by-step explanation: every value can be divided by 21

Answer: D)

Step-by-step explanation: 21 x 6 = 126, 21 x 8 = 168, and 21 x 9 = 189

Emma needs 8 seed packets to grow 16 plants.

What is unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Finding the value of a single unit using the unitary technique, then extrapolating from this value.

Given that,

Emma grew 6 plants with 3 seed packets.

To grow 6 plants Emma needs 3 seed packets.

Applying unitary method:

To grow 1 plants Emma needs 3/6 seed packets.

To grow 16plants Emma needs (3 × 16)/6 seed packets.

                                                   = 8 seed packets.

The unitary method is used to unite rate.

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The coordinates of Point E are (-4,2) and Point E is a reflection of point D across the X-axis.

Point E has the same y-coordinate as point D, which is 2. However, the x-coordinate of point E is the opposite of the x-coordinate of point D. The x-coordinate of point D is 4, so the x-coordinate of point E must be -4. Therefore, the coordinates of Point E are (-4,2).

As for the reflection, you can imagine a mirror placed on the x-axis (horizontally) and Point D and E being on the same side of that mirror.

Therefore, As Point D is reflected on the mirror, it will be flipped and the x-coordinate changes its sign and becomes -4. Therefore Point E is a reflection of point D across the X-axis.

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See full question below

Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x- coordinate of point D. Drag tiles to complete the statements. (4,2) (4,-2) (-4,2) (-4,-2) X-axis y-axis The coordinates of Point E are --- &Point E  is a reflection of point D across the ---

In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.

Central Limit Theorem:

The sampling distribution of the sample percentage for a proportion p in a sample of size n will be roughly normal with a mean (μ = p) and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n} }[/tex].

In a given year, 3% of books checked out from the library are downloaded.

That means p = 0.03

and n = 75

By the Central Limit Theorem

Mean = μ = p = 0.03

Standard deviation =  [tex]s = \sqrt{\frac{p(1-p)}{n} }[/tex]

                                   [tex]s = \sqrt{\frac{(0.03)(0.97)}{75} }[/tex]

                                   [tex]s=0.0197[/tex]

Hence,

         In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.

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The expression which represents the composite function (f - g) (x) as required in the task content is; 11x - 10.

It follows from the task content that the expression which represents the composite function (f - g) (x) as required in the task content be determined.

Since the given functions are;

f(x) = 6x − 8 and g(x) = −5x + 2

The composite function; (f - g) (g) is equivalent to;

f (x) - g (x)

Therefore, we have;

(f - g) (x) = 6x - 8 - (-5x + 2)

(f - g) (x) = 6x + 5x - 8 -2

(f - g) (x) = 11x - 10.

On this note, the required expression which represents (f - g) (x) is; 11x - 10.

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Answer:

Two blue = 6

Step-by-step explanation:

Let r = red

Let b = blue

2r + r + b = 21

r - b = 3    Can we rewritten  r = 3 + b  Substitute 3 + b  for r into the first equation

2r + r + b = 21

2(3 + b) + 3 + b + b =  21   Distribute the 2

6 + 2b + 3 + b + b = 21  Combine like terms

9 + 4b = 21  Subtract 9 from both sides

9 - 9 + 4b = 21 - 9

4b = 12  Divide both sides by 4

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

b = 3

2 blues would equal 6.

Answer:

6

Step-by-step explanation:

Define the variables:

From the given blackboard, create a system of equations from the first three equations:

[tex]\begin{cases}3x + y = 21\\\;\:x - y = 3\\2x + y = 15\end{cases}[/tex]

Add the first equation to the second equation to eliminate y:

[tex]\begin{array}{lrcccr}& 3x & + & y & = & 21\\+ & (x & - & y & = & 3\\\cline{2-6} &4x &&&=&24\end{array}[/tex]

Solve the equation for x:

[tex]\implies \dfrac{4x}{4}=\dfrac{24}{4}[/tex]

[tex]\implies x=6[/tex]

Substitute the found value of x into the second equation and solve for y:

[tex]\implies 6-y=3[/tex]

[tex]\implies y=3[/tex]

Therefore, the value of the red pencil is 6 and the value of the blue pencil is 3.

Finally, substitute the found value of y into the last equation:

[tex]\implies 3 + 3 = \boxed{6}[/tex]

Answer:

j = 4

Step-by-step explanation:

calculate the slope of the line passing through the goven points and equate to 2

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 7, - 10 ) and (x₂, y₂ ) = (0, j )

m = [tex]\frac{j-(-10)}{0-(-7)}[/tex] = [tex]\frac{j+10}{0+7}[/tex] = [tex]\frac{j+10}{7}[/tex] then equating gives

[tex]\frac{j+10}{7}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )

j + 10 = 14 ( subtract 10 from both sides )

j = 4

Given that e1 and e2 have a high spearman correlation, what we can say about the Pearson correlation of e1 and e2 is; The Pearson correlation must be high

A correlation coefficient is defined as the measurement of the extent to which two variables tend to change together.

Now, the Pearson correlation is the type that evaluates the linear relationship that exists between two continuous variables. A relationship is said to be linear as a result of a change in one variable being associated with a proportional change in the other variable.

Meanwhile, the spearman correlation is one that evaluates the monotonic relationship between two continuous or ordinal variables.

If the relationship described above tells us that one variable increases when the other increases, but then the amount is not consistent, then it means that the Pearson correlation coefficient is positive but less than +1. However, the Spearman coefficient still equals +1 in this case.

Thus, we conclude that as the spearman correlation is high, then the Pearson correlation is also high.

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Answer:

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.

The Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:

  c² = a² +b²

  RQ² = PQ² +PR²

  RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root

The distance between planets Q and R is 1.64×10⁷ km.

__

Additional comment

The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.

You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.

Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.

Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)

The distance QR is :

[tex] \qquad \sf \rightarrow d = \sqrt{(1.6 \times 10 {}^{7}) {}^{2} + (3.6 \times 10 {}^{6} ) {}^{2} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{2.56 \times 10 {}^{14} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{256\times 10 {}^{12} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(268.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex]\qquad \sf \rightarrow d = 16.4\times 10 {}^{6} {}^{} [/tex]

The constraints to represent the incoming students at the college is B. 0 < x ≤ 100 and 0 < y ≤ 400

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this situation, the college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students.

Let x = the number of out-of-state students and

y = the number in-state students.

The constraints is 0 < x ≤ 100 and 0 < y ≤ 400.The correct option is B.

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Answer:

  $360

Step-by-step explanation:

You want the amount of simple interest earned by $6000 in 3 years at the rate of 2%.

The simple interest formula is ...

  I = Prt

where P is the principal invested at rate r for t years.

$6000 invested at 2% for 3 years earns ...

  I = $6000·0.02·3 = $360

Chris will be paid $360 in interest in the first 3 years.