tool to form the correct answer on the provided number line.
ven functions.
Function 1
f (x) =-52 + 1 + 10
-6
-2
Function 2
g(x)
30-
20+
the interval where both functions are decreasing on the number line provided.

Answer:

Sides:

MX = 4cm

BX = 8cm

BM = 6.928...cm

Angles:

m = 90°

b = 30°

x = 60°

Step-by-step explanation:

We've been given 3 pieces of info that we can use, which is more than enough

Using the sine rule, we can find the hypotenuse:

[tex]\frac{4cm}{sin30} = \frac{BXcm}{sin90}[/tex]→[tex]\frac{4sin90}{sin30} =BX = 8cm[/tex]

Now we can use Pythagoras' theorem to find the last side:

[tex]a^2+b^2=c^2[/tex] →  [tex]b^2\ = c^2-a^2[/tex] → [tex]64 - 16 = b^2 = 48[/tex] → [tex]\sqrt{48} =6.928...cm[/tex]

And since we know two of the angles, we can find the third:

[tex]x = 180 - (30 + 90) = 180 - 120 = 60[/tex]°

Answer:

Below

Step-by-step explanation:

REMEMBER: for a right triangle  sin (30) = opposite LEG/ hypotenuse

 so sin 30 =  4 / hypotenuse         now, with a calculator sin 30 = 1/2

           1/2   = 4 / hypotenuse      so hypotenuse = 8

Now it is a right triangle so Pythagorean theorem applies

 hyp ^2 = 4 ^2   +   BM^2

  8^2 = 4^2 + BM^2

     48 = BM^2     so  BM = sqrt (48 ) = 4 sqrt 3

Finally, all of the internal angles of ANY triangle sum to 180 °

  so angle x = 180 - 90 - 30 = 60°

The required maximum point of the function [tex]$f(x)=-x^2+8x+40$[/tex] is (4,24).

A quadratic equation is an algebraic equation with a maximum degree of two. Where a 0, the equation is provided by ax² + bx + c = 0.

To find the maximum point of the quadratic function [tex]$f(x)=-x^2+8x+40$[/tex], we can use the formula for the x-coordinate of the vertex, which is given by [tex]x=-\frac{b}{2a}$[/tex], where a is the coefficient of the [tex]x^2$[/tex] term and b is the coefficient of the x term.

In this case, a=-1 and b=8, so the x-coordinate of the vertex is:

[tex]$x=-\frac{b}{2a}=-\frac{8}{2(-1)}=4$$[/tex]

To find the y-coordinate of the vertex, we can plug this value of x into the original function:

[tex]$$f(4)=-4^2+8(4)+40=24$$[/tex]

Therefore, the maximum point of the function [tex]$f(x)=-x^2+8x+40$[/tex] is (4,24).

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The right angles would be named as:

3. ∠PNL 4. ∠PNO

Right angles can be named in a few different ways, depending on the context in which they are being used. One common way is:

Using three points: use the names of the three points that form the angle, with the vertex of the angle in the middle. For example, if the right angle is formed by the line segments AB and BC, you could name it angle ABC.

The sign "∠" means angle, therefore, it can be named also as ∠ABC.

Thus, the right angles in the given diagram can be named accordingly as:

∠PNL and ∠PNO

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The answer of the given question based on the cost of mailing is , the cost of mailing a 2.5-ounce letter to Vienna, Austria would be $6.63 (rounded to the nearest cent).

An equation is  mathematical statement that shows  two expressions are equal. It contains variables, constants, and mathematical operations like  addition, subtraction, multiplication, and division.

For example, a simple equation could be:

2x + 3 = 9

The equation y = 0.25x + 6.00 represents the cost y of mailing a letter to Vienna, Austria based on the weight x of the letter in ounces. The flat rate of $6.00 is represented by the constant term 6.00 in the equation, and the additional charge of $0.25 per ounce is represented by the coefficient of x, which is 0.25.

To use this equation to determine the cost of mailing a specific letter, you would need to know the weight of the letter in ounces. You could then substitute this value for x in the equation and solve for y, which would give you the cost of postage in dollars.

For example, if a letter weighs 2.5 ounces, you could plug in x = 2.5 into the equation:

y = 0.25(2.5) + 6.00

y = 0.625 + 6.00

y = 6.625

So the cost of mailing a 2.5-ounce letter to Vienna, Austria would be $6.63 (rounded to the nearest cent).

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The minimum score Chen can earn on the final test to get at least 80 percentage avg. on the tests is 41.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

As a percentage, "%" is read as "percent" or "percentage" in this context. This percent symbol can always be converted to a fraction or decimal equivalent by "dividing by 100".

Now in the given question,

Chen has total no of tests = 4

Total marks of the tests = 4 × 50 (Each test is worth 50 points)

= 200 marks.

So, to secure at least 80% average Chen has to score:

80% of 200

= 80/100 × 200

= 80 × 200/100

= 160

Now Chen has already secured 45, 38 and 36 points in 3 tests.

So, the points he has to secure in the last test =

160 - 45+ 38 + 36

= 41

Therefore, the minimum score Chen can earn on the final test to get at least 80% avg. on the tests is 41.

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Answer:

There is a direct relationship, in which the value of the division of the circumference by the diameter is a constant. This constant is know as Pi.

Proof for the given statement is given below.

Vertical angles are the angles formed on two opposite sides of intersecting lines.

The measure of a pair of vertical angles are equal.

Given are two line segments intersected each other.

The line segments are KM and JN.

Consider ΔJKL and ΔLMN.

Given JL / NL = KL / ML

This means that two corresponding sides of ΔJKL and ΔLMN are proportional.

In a similar triangles, corresponding angles are equal.

So they are similar triangles.

∠JLK and ∠MLN are a pair of vertical angles.

So they are equal.

Corresponding angle of J in ΔJKL is angle N in ΔLMN.

So ∠J = ∠N

Or, ∠J ≅ ∠N

Hence it is proved.

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Answer:

To find the cube root of a number, you want to find some number that when multiplied by itself twice gives you the original number. In other words, to find the cube root of 8, you want to find the number that when multiplied by itself twice gives you 8. The cube root of 8, then, is 2, because 2 × 2 × 2 = 8.

Step-by-step explanation:

The actual value of cos θ is -(51)/10 based on the information provided.

Noun. Values in plural. Definition of value from the Britannica dictionary. 1.: the monetary value of something, often known as its price or cost.

The Pythagorean identity can be used to determine the value of cos θ if sin θ = 7/10 and is θ in quadrant II:

cos² θ + sin² θ = 1

cos² θ + (7/10)² = 1

cos² θ + 49/100 = 1

cos² θ = 51/100

cos θ = ±√(51/100)

Since θ is in quadrant II, cos θ is negative. Therefore,

cos θ = -√(51/100)

Putting it more briefly,

cos θ = -(√51)/10

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Answer:

Jennifer went grocery shopping; She purchased supplies to make sandwiches.

Step-by-step explanation:

Out of all the other sentences, "Jennifer went grocery shopping; She purchased supplies to make sandwiches." is the only grammatically correct answer.

Answer:

the present value that must be invested to have a future value of $6000 after 6 months at a simple interest rate of 1.45% is approximately $5957.00.

Step-by-step explanation:

To determine the present value P that must be invested to have a future value A at a simple interest rate r after time t, we use the formula:

A = P (1+r)^t

P = A / (1+r)^t

where P is the present value, A is the future value, r is the simple interest rate as a decimal, and t is the time period in years.

In this case, the future value is $6000, the simple interest rate is 1.45% or 0.0145 as a decimal, and the time period is 6 months or 0.5 years.

Substituting these values into the formula, we get:

P = 6000 / (1+0.0145)^0.5 = 5,957.00

= $5957.00 (rounded to two decimal places)

Therefore, the present value that must be invested to have a future value of $6000 after 6 months at a simple interest rate of 1.45% is approximately $5957.00.

The present value P to be invested can be calculated using the reverse of the simple interest formula A = P * (1 + r * t). Given A = $6000, r = 1.45%, and t = 6 months, we can find P by rearranging the formula to P = A / (1 + r * t) and substituting the given values.

To calculate the present value P, which needs to be invested under simple interest to amount to a future value A, we use the formula for simple interest in reverse. The formula is:

A = P * (1 + r * t)

Re-arranging for P:

P = A / (1 + r * t)

where,

Given that A = $6000, r = 1.45% = 0.0145 (per year), and t = 6 months = 0.5 years, the present value P can be calculated as:

P = 6000 / (1 + 0.0145 * 0.5)

Calculate the above expression to determine P.

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The answer of the given question based on linear equations what is the y intercept of the line b =4.

In  linear equation of  form y = mx + b, where m is slope and b is  y-intercept, the y-intercept is  point at which  line intersects the y-axis. It is  value of y when x is equal to a zero.

To find the y-intercept of the line, we need to identify the point at which the line intersects with the y-axis. This is the point where x=0.

From the given graph, we can see that when x=0, the point on the line is (0, 4). Therefore, the y-intercept (b) of the line is 4.

So, the answer is:

b = 4

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Answer:

b=2

Step-by-step explanation:

its 2 not 4 the dot is located on 2 in between the first and second quadrant.

Answer: A

Step-by-step explanation:

Using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.

The height abοve οr belοw a specified reference pοint, mοst frequently a reference geοid, which is a mathematical representatiοn οf the Earth's sea level as an equipοtential gravitatiοnal surface, determines a lοcatiοn's elevatiοn.

A frequently used idea in relatiοn tο height and distance is the angle οf elevatiοn, particularly in trigοnοmetry. It is described as a relatiοnship between an οblique line frοm the οbserver's eye tο an item abοve his eye and the hοrizοntal plane.

This angle eventually develοps abοve the surface. The angle οf elevatiοn is made in such a way that it is abοve the οbserver's eye, as the name suggests.

Using the given infοrmatiοn, we drew a right triangle as given belοw.

The hypοtenuse οf the triangle is the length οf the sheet.

The angle οf elevatiοn is 20°.

The base οf the triangle is the grοund.

The hypοtenuse l = 19 inches

Angle Ф = 20°

We have tο find the elevatiοn h.

sin  Ф = h/l

sin 20 = h/19

0.342 = h /19

h = 6.49 inches

Therefοre using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.

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Answer:

only opposite anglesare

Step-by-step explanation

Z

. . . . . . .. . . . . .. . . . . . . . Y

. .

. .

. .

. .

. .

. . . . . .. . . . . . . . . . .. . . . X

The value of the polynomial equations are

f ( -10 ) = 20201

f ( 2 ) = 17

f ( 3 ) = 142

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial equation be represented as A

Now , the value of A is

f ( x ) = 2x⁴ + x² - 10x + 1   be equation (1)

Now , when the value of x = -10

f ( -10 ) = 2 ( -10 )⁴ + ( -10 )² - 10 ( -10 ) + 1

On simplifying , we get

f ( -10 ) = 2 ( 10000 ) + 100 + 100 + 1

f ( -10 ) = 20000 + 201

f ( -10 ) = 20201

Now , when the value of x = 2

f ( 2 ) = 2 ( 2 )⁴ + ( 2 )² - 10 ( 2 ) + 1

On simplifying , we get

f ( 2 ) = 2 ( 16 ) + 4 - 20 + 1

f ( 2 ) = 32 - 15

f ( 2 ) = 17

Now , when the value of x = 3 , we get

f ( 3 ) = 2 ( 3 )⁴ + ( 3 )² - 10 ( 3 ) + 1

f ( 3 ) = 2 ( 81 ) + 9 - 30 + 1

f ( 3 ) = 162 - 20

f ( 3 ) = 142

Hence , the polynomial equations are solved

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The function has a range of all real numbers less than or equal to 2.

Quadratic functions form parabolas, which look like a U-shape.

What is Range

Range describes the y-values covered by a function. So, the range contains every y-value that is a possible output of a function. You can find the range of a function from the graph by looking at what y-values are or will be covered by the function.

The range of a quadratic is always all real numbers greater than/less than the y-value of the vertex. Positive quadratics have ranges greater than the vertex, and negative quadratics have ranges less than the vertex.

Finding the Range

The parabola given is negative. We know this because the graph opens downward. This means that the graph has a maximum, and the range is less than the vertex.

By looking at the graph we can tell that eventually, the graph will cover all y-values under y-value 2. Note that 2 is the y-value of the vertex. So the range is all real values less than or equal to 2. This means that any number less than or equal to 2 is a possible output of the function.

The histogram has a longer right tail since skewed right side

The distribution of data is positively skewed distribution

A histogram with a longer right tail indicates that the data is skewed to the right, which means that the majority of the data points are on the left side of the graph, and there are fewer data points on the right side. This is also known as a positively skewed distribution.

In a positively skewed distribution, the mean is typically greater than the median, and the mode is less than the median. This is because the presence of outliers on the right side of the graph can pull the mean towards higher values, while the median remains closer to the bulk of the data.

The graph that represents this is D.

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Answer:

a) 15, 25

Step-by-step explanation:

Finding the average is to find the sum and divide it by the quantity of the numbers.

(15 + 25) / 2 = 40 / 2 = 20, 20 is the average of two numbers.

However standard deviation includes at least one degree of 2.

x1 + x2 = 40

SD = 5

= [tex]\sqrt{[(x_1 - 20)^2 + (x_2 - 20)^2]/2 \\}= 5\\ x_1 = 15, or x_1 = 25\\x_2 = 15 or x_2 = 25[/tex]

Answer:

27 blocks not used in the castle

Step-by-step explanation:

35+18= 53

53-26=27

The measures of the angles in the parallel lines is

m∠a = 97°

m∠b = 15°

m∠c = 68°

m∠d = 68°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the two parallel lines be represented as l and m

Now , the transversal line is t

The measure of m∠a = 97° ( corresponding angles )

The measure of m∠d = 180° - 112° ( angles in a straight line = 180° )

So , the measure of m∠d = 68°

The measure of m∠c = measure of m∠d ( alternate interior angles )

So , the measure of m∠c = 68°

From the triangle formed by the intersection of lines ,

The measure of m∠b = 180° - ( a + d ) ( angles of a triangle = 180° )

So , the measure of m∠b = 180° - ( 97° + 68° )

The measure of m∠b = 15°

Hence , the measures of angles are solved

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Answer:

y=9

Step-by-step explanation:

y=7x+2

y=7(1) +2

y=7+2

y=9

Answer:

29n - 39/2.

Step-by-step explanation:

To simplify the expression 8(3n-2) + 1/2 (10n-7), we can start by using the distributive property of multiplication over addition to simplify the terms inside the parentheses:

8(3n-2) + 1/2 (10n-7) = (83n - 82) + (1/2 * 10n - 1/2 * 7)

This gives us:

24n - 16 + 5n - 7/2

Next, we can combine like terms:

24n + 5n - 16 - 7/2 = 29n - 16 - 7/2

Finally, we can simplify the expression by finding a common denominator for -16 and -7/2:

29n - 16 - 7/2 = 29n - 32/2 - 7/2 = 29n - 39/2

Therefore, 8(3n-2) + 1/2 (10n-7) simplifies to 29n - 39/2.

The number that can be placed in the blank to make the number sentence true is given as follows:

1/316.

The number sentence for this problem is given as follows:

"316 times which number equals 1".

The number is unknown, hence the variable that represents the number is given as follows:

x.

The times word means a multiplication operation, hence the expression is given as follows:

316x = 1.

Now we must simply solve the expression 316x = 1 for the variable x, applying the division, which is the inverse operation of the multiplication, hence:

x = 1/316.

Which is the number that satisfies the number sentence.

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Answer:

a=50-40

a=10

lxb

answer

Based on the relative frequency tables, the correct options are

Relative frequency is a statistical concept that refers to the proportion or percentage of times an event occurs in relation to the total number of times the event could occur. It is calculated by dividing the number of times an event occurs by the total number of observations or trials.

For example, if you flip a coin 10 times and it lands on heads 6 times, the relative frequency of heads would be 6/10 or 0.6, which is equivalent to 60%. This means that heads occurred 60% of the time in the sample of 10 coin flips.

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The lengths DG and GC are 12 and 24 units respectively

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

G is the centroid and DC = 36.

The centrod divides the triangle in 1 : 2

Using the above as a guide, we have the following:

DG : GC = 1 : 2

Multiply by 12

So, we have

DG : GC = 12 : 24

12 and 24 add uo to 36

This means that

DG = 12 and GC = 24

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