Hicro
children in a class are asked about the animals they own.
between them, they only have cats, dogs, rabbits and hamsters.
the pictogram shows information about the numbers of cats, dogs and rabbits
owned by members of the class.
a total of 33 animals are kept as pets. complete the pictogram.

The vertex of the function is at (5, 10) .For the function, the domain exists on all real numbers while the range exist for the value f(x) ≥ 10

Vertex, domain and range of a function

The vertex of a quadratic or linear function is in the form

y =  a(x – h)^2 + k

where;

(h, k) is the vertex of the function

Given the function expressed as;

f(x) = |x-5| + 10

On comparison, you can see that h = 5 and k =10, hence the vertex of the function is at (5, 10)

For the domain and range

Domain are the dependent variable for which a function exist while the range is the independent variable for which a function exist.

For the function, the domain exists on all real numbers while the range exist for the value f(x) ≥ 10

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The equation in slope-intercept form is y = (-2/5)x - 9/2.

Slope-intercept form is an equation of a line that is written in the form of y=mx+b, where m is the slope of the line and b is the y-intercept. The slope-intercept form makes it easy to identify the slope and y-intercept of a line from an equation.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Therefore, for a line with a slope of −2/5 that passes through the point (15, −9/2), we can solve for b using the point-slope formula.
Point-slope formula:  y - y1 = m(x - x1)
Plugging in the given information, we get:
-9/2 - (-9/2) = (-2/5) (15 - 15)
Solving this equation yields b = -9/2.
Therefore, The equation in slope-intercept form is y = (-2/5)x - 9/2.

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Water fills the cone to a capacity of 75%. 0.75 is the decimal equivalent of 75%.

Find the whole amount of what you're looking for to get a percentage of.

To calculate the percentage, divide the number.

Add 100 to the value.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, 35% is equal to the fraction 0.35 or the decimal 0.35.

The value of the number out of 100 is the proportion of the number. For instance, there are 26 females and 24 boys in a class. As a result, 52 out of 100 students in the class are females, or 52% of the class.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Percentages.

According to our question-

volume of water  =  (3/4) * (1/3)(a)(h)

volume of water  =  (3/4) * volume of cone

volume of water  =  75% of the volume of cone

75% of the cone's volume is filled with water.

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Answer: 23

Step-by-step explanation: Both triangles are the same in measurements so whatever number - 4 that equals 19 is the answer. 23-4=19

The average rate of change of the given function is 20.

It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.

The average rate of change of a function f(x) over the interval [a,b] is given by the formula:

(f(b) - f(a)) / (b - a)

So, for the function f(x) = x² + 2 as x changes from 5 to 15, we can plug in the values to find the average rate of change:

(f(15) - f(5)) / (15 - 5) = (15² + 2 - 5² - 2) / (15 - 5) = (225 - 25) / 10 = 200 / 10 = 20

So the average rate of change of the function is 20.

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It defines conclusions or rounding a number to the nearest decimal place or to the nearest ones, tens, hundreds, and so on.

Estimation refers to obtaining a result that is close to the correct or actual result. It involves conclusions or rounding a number to the nearest decimal place or to the nearest ones, tens, hundreds, and so on.

There are various reasons, the estimate is especially useful when there is not enough information to calculate an exact value. Accountants use estimates when they want to calculate transaction amounts.

To estimate the quotient, we round the dividend to the nearest tens, hundreds, or thousands.

There are two methods for estimating the quotient:

let us consider an example:

for 371 nearest value is 400 because in the tens place it is equal to 400.

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0.5  is the best estimate of the correlation coefficient for the variables in the scatter plot.

What is the short definition of a scatter plot?

A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they can display the degree of connection, if any, between values of observable quantities or events (called variables).

What is the purpose of a scatter plot?

To illustrate how much one variable affects another, scatter plots are used to exhibit data points on a horizontal and vertical axis.

                       A marker is used to represent each row in the data table, and the position of the marker depends on the values of the columns that are set up on the X and Y axes.

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Answer:

y = 43, x = 23

Step-by-step explanation:

[tex]180 - 63 = 3y - 12\\117 = 3y - 12\\129 = 3y\\y = 43[/tex]

Supplementary angles add up to 180 and alternative angles (Z-pattern) are the same

[tex]180 - 63 = 5x + 2\\117 = 5x + 2\\115 = 5x\\x = 23[/tex]

A linear function is one that visualizes a straight line on the coordinate plane.

When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear. A linear function is, for instance, the progression in the number of ticks of a clock's second hand through time.

Any function that depicts a straight line on the coordinate plane is said to be linear. For instance, the equation y = 3x – 2 indicates a straight line on a coordinate plane, indicating that it is a linear function. This function can be expressed as f(x) = 3x - 2 since f(x) can take the place of y.

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The statement '15 more than the sum of 5 and a number' is equivalent to the mathematical expression (5+n)+15.

Therefore the answer is (5+n)+15.

The statement "15 more than the sum of 5 and a number" is asking for an expression that represents the value that is 15 greater than the result of adding 5 and a number together. The mathematical way to express this is:

15 + (5 + n)

Where n is the number that we are adding to 5.

15 is being added to the sum of 5 and n. The parentheses around the 5 and n indicate that those two values are being added together before the 15 is added to them.

In other forms of representation

15+(5-n) or (5+n)+15 or (5-n) +15 or 15+5n does not convey the meaning you want it to convey as these forms does not represent "15 more than the sum of 5 and a number"

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The Mixed number is -6 1/6, an integer is -6.16, proper fraction is -13/6

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The polynomial function in given graph for g(x) is

g(x)= -x^2.

What are polynomial functions?

Polynomial is made up of two words, poly and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms"

Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants. for e.g.

f(x) = 3x^2 - 5.

Types of Polynomial Function:

Constant Polynomial Function -  A constant polynomial function is a function whose value does not change. It remains the same and also it does not include any variables.

Zero Polynomial Function - Polynomial functions with a degree of 0 are known as zero Polynomial functions.

Linear Polynomial Function - Polynomial functions with a degree of 1 are known as Linear Polynomial functions.

Quadratic Polynomial Function - Polynomial functions with a degree of 2 are known as Quadratic Polynomial functions.

Cubic Polynomial Function - Polynomial functions with a degree of 3 are known as Cubic Polynomial functions.

Quartic Polynomial Function - Polynomial functions with a degree of 4 are known as Quartic Polynomial functions.

Now,

In given graph, We fill find g(x) by putting value of x and seeing the corresponding result of y.

As for    x      y is

            1       -1

             2      -4

            3       -9

            -1       -1

            -2      -4

Therefore, from given values we can conclude that polynomial function for g(x)= -x^2.

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Answer:

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Since lines n and p intersect, they must have different slopes.  Lets say they have slopes 2 and 4, as an example.  They will intersect.  Lines m and l are perpendicular to n and p, so their slopes will be the negative inverse of 2 and 4.  That gives them slopes of -(1/2) and -(1/4).  These slopes are different, so they will intersect.

The attached graph illustrates this intersection with lines having the above slopes.  Lines m and l intersect at (-1,1) in this example.  Lines m and l also intersect, off the graph at the top left.

The center point formula,  (x h) 2 + (y k) 2 is r, must be converted into standard form in order to get the center and radius. 2 (x-h)2 + (y-k)2 is r2 (x-h)2 + (y-k)2 =is r2).

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The line TU is parallel to QR and SQR is dilated version of STU by a scale factor of 4.

What is midpoint theorem?

The line segment of a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.

Through the diagram it can be seen that T and U are midpoints of SQ and SR respectively.

And it can also be seen that TU is parallel to QR.

It is given that ST = 2, TQ = 6, SU = 3 and UR = 9

The length of side SQ -

SQ = ST + TQ

SQ = 2+6

SQ = 8

The length of side SR -

SR = SU + UR

SR = 3+9

SR = 12

The measurement of QR = SQ as seen in the diagram.

According to midpoint theorem the mid points line segment TU measures half of its parallel third side of triangle QR.

Now, to find the scale factor -

= QR - TU

= 8 - 4

= 4

Therefore, the scale factor is 2.

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Although there are other factors to take into account, a model is worth your attention if its R-Squared is more than 0.6: R-squared values lower than 0.5 are normal for any science that tries to predict human behavior, such as psychology.

There are multiple phases involved in the actual R-squared computation. Finding the line of best fit, frequently from a regression model, entails taking the data points (observations) of dependent and independent variables.

Predicted values would then be calculated, actual values would be subtracted, and the results would be squared.

You would deduct the average actual value from each of the actual values, square the findings, and add them to determine the overall variance.

The R-squared is obtained by dividing the first sum of mistakes (unexplained variance) by the second sum (total variance) and deducting the result from one.

Hence, Although there are other factors to take into account, a model is worth your attention if its R-Squared is more than 0.6: R-squared values lower than 0.5 are normal for any science that tries to predict human behavior, such as psychology.

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Answer:

<a=113, <b=67, <c=126, <d=54

Step-by-step explanation:

<a= 180-67=113 degrees. Why? Angles on a straight line add up to 180

<b=67 degrees Why? Because it is an alternate interior angle with 67degrees and alternate interior angles are equal

<d = 54 degrees Why? Because it is an alternate interior angle with 54 degrees and alternate interior angles are equal

<c=180-54=126 degrees Why? Because it is a co-interior angle with <d which is 54 degrees and co-interior angles add up to 180 degrees

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The distance flown by the plane East of the starting point is (60 minutes * 500 km/h * cos(120°))/60 minutes/hour = 250 * cos(120°) km.

What is the Pythagorean theorem in plain English?

Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The distance flown by the plane South of the starting point is (60 minutes * 500 km/h * sin(120°))/60 minutes/hour = 250 * sin(120°) km.

To find the distance of the plane from the starting point, we need to use the Pythagorean theorem.

The distance would be √((250 * cos(120°))^2 + (250 * sin(120°))^2) = √(62,500 + 62,500) = √125,000 = approximately 111.8 km

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The expression that shows time, t, it will now take Rashid to make the trip relative to the speed, v with which he slows down is t = (240 - (v/120) * 240) / (120 - v)

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

The relation between time, t, and the speed at which Rashid slows down, v, is given by the formula:

t = (240 - (v/120) * 240) / (120 - v)

t = time

v= speed.

This formula can be derived by using the distance formula (distance = speed x time) and the fact that the distance traveled is constant (240 km).

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Answer:

Image 1 answer → not a polygon

Image 2 answer → n = 49 degrees

Image 3 answer → Square

Step-by-step explanation:

Image 1 explanation: Circles and ovals aren't polygons because their area and perimeter are calculated differently. So the answer is not a polygon.

Image 2 explanation: All complementary angles add up to 90 degrees, so 131 and 139 are incorrect. 41 and 49 add up to 90 degrees, which makes 49 degrees your answer.

Image 3 explanation: All options listed are quadrilaterals, but a square is the only shape that has 4 congruent sides and angles. Therefore, a square is a shape that possesses all the characteristics listed.

Have a great day! :)

Answer: To find out which loan option will have the least interest, you need to calculate the interest amount for each option. You can do this by using the formula:

Interest = Principal x Interest Rate x Time (in years)

For option A, the interest amount would be:

Interest = $12,000 x 0.05 x (48/12) = $2,400

For option B, the interest amount would be:

Interest = $12,000 x 0.045 x (60/12) = $3,000

For option C, the interest amount would be:

Interest = $12,000 x 0.0375 x (66/12) = $2,970

For option D, the interest amount would be:

Interest = $12,000 x 0.04 x (72/12) = $3,840

As we can see the lowest interest amount is option C which is $2,970. Thus Ciara will pay the least interest if she chooses option C.

Step-by-step explanation:

The range of possible values of the third side of the triangle is 3 < x < 25. That is, the possible whole number values are 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24.

From the given information, we are to determine all possible values for the length x of the third side of the given triangle

From the given information,

One of the sides of the triangle is 11 centimeters in length

and

The length of the other side is 14 centimeters

From one of the properties of a triangle,

The third of a triangle is greater than the positive difference of the other two sides and the third side is lesser than the sum of the other two sides.

if the third side of the triangle is x

Then,

x < 14 + 11

x < 25

and

x > 14 - 11

x > 3

Thus,

x > 3 and x < 25

3 < x and x < 25

3 < x < 25

Thus, the range of possible values is 3 < x < 25.

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The compound inequality given is "and" inequality.

Compound inequalities are inequalities which consist of more than two expressions connected with two or more inequality signs.

Compound inequality can be divided into two or more simple inequalities.

"And" inequalities are those compound inequalities where both the inequalities need to be true for the statement to be true.

"Or" inequality needs only any one of them true.

Given inequality is,

6 > x + 1 > 3

Subtracting 1 throughout,

5 > x > 2

Here x lies between 2 and 5 where x > 2 and x < 5.

Hence this inequality is "and" inequality.

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The average rate of change of f(x) over -6≤x-4 is -70.

The average rate of change of g(x) over -6≤x-4 is -140.

The average rate of change of g(x) is 2 times that of f(x)

The average rate of change of an equation can be determine by using the formula below:

average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]

From the given information, f(x) = 7x², g(x) = 7x² and  x₁ = -6, x₂ = -4

For f(x) = 7x²:

average rate of change =  ([7(-4)²] - [7(-6)²]) / (-4-(-6))

                                       = (112-252)/2

                                      = -70

For g(x) = 14x²:

average rate of change =  ([14(-4)²] - [14(-6)²]) / (-4-(-6))

                                       = (224-504)/2

                                      = -140

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Yes, the given equation y = 10x is a direct variation.

Direct variation is a type of proportionality in which one quantity directly varies with respect to a change in another quantity. This means that if one quantity increases then the other quantity will also experience a proportionate increase.

Similarly, if there is a decrease in one quantity then the other quantity also decreases. Direct variation is a linear connection hence, the graph will be a straight line. Further, if the two entities are in a direct variation relationship then one will be a constant multiple of the other.

A direct variation equation has the form

y = kx  

Here, k is the constant of variation

Now, y = 10x is in this form, thus it is a direct variation.

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Dante deposited $5,000 into an account with an annual interest rate of

3.5%. He plans to deposit an additional $200 each year, just after the

interest is compounded. His balance will be $9,838.44 after 16 years.

It displays the actual percentage rate of interest owed on any outstanding debts, including credit card debt and loans.

Because it takes compounding effects into account, the effective annual interest rate is the real interest rate on an investment or loan. The rate increases as the compounding periods get more frequent. Advertisements for loans or savings accounts may include both the nominal interest rate and the effective yearly interest rate. The rate that should be used to compare loan and investment rates of return is the effective annual interest rate.

We can substitute the known values into the formula and calculate the final balance:

A = $5,000 (1 + 0.035)¹⁶

We can calculate the final balance by using a calculator, or we can use the formula of compound interest:

A = P(1 + r/n)ˣ

where, A= Amount

P= Principle($5,000 )

x= Time(16 years)

n= Rate(3.5%)

A = $5,000 (1 + 0.035/1)¹⁶

Now we can add the $200 deposit each year for 16 years:

A = $5,000 (1 + 0.035)¹⁶ + $200 × 16

A = $9,838.44

Dante's balance will be $9,838

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Using trigonometric ratios,  tree is leaning 106.1°-90° = 16.1° away from the vertical.

Pythagorean identities, reciprocal identities, sum and difference identities, double angle and half-angle identities are the main trigonometric identities. We must apply the sine rule and the cosine rule to the non-right-angled triangles.

6² = 3.5²+4² -2(3.5) (4) cos θ

36 = 12.2.5+16 - 28 cos θ

36 = 28.25 - 28 cos θ

7.75 = -28cos θ

7.75 / 28 = cos θ

Cos⁻¹ (7.75/28) = θ

106.1°=θ

So, the tree is leaning 106.1°-90° = 16.1° away from the vertical

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