The dashed triangle is the image of the solid triangle for a dilation with center at the origin. What is the scale factor?

Answer:

C

Step-by-step explanation:

The equation that shows the whole amount of pizza Miah ate on Saturday is 3/32 of the whole pizza

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted to mathematical equation

The left over is calculated is 3/8

therefore 5/8 of the pizza is left for Saturday

On Saturday she ate 1/4 of the pizza

= 1/4 × 3/8

= 3/32

therefore Miah ate 3/32 of the whole pizza on Saturday.

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The expression b²/b⁻⁷ when simplified with a positive exponent only will become b⁹.

To simplify the expression b²/b⁻⁷, we can use the rules of exponents. The rules of exponents, also known as laws of exponents, are a set of mathematical rules that govern the manipulation of exponential expressions. These rules are essential in simplifying and solving various mathematical problems involving exponents.

Quotient rule of exponent states that when dividing two exponential expressions with the same base, we subtract their exponents, such that:

xᵃ / xᵇ = xᵃ⁻ᵇ.

In this case, we can simplify the expression b²/b⁻⁷ as follows:

b²/b⁻⁷ = b²⁻⁽⁻⁷⁾ = b⁹.

So, the simplified expression is b⁹. This answer is written with a positive exponent only, as requested.

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c) 2x^-3 + 5x^-1 - x

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, and raised to non-negative integer powers.

Answer:

Only the (a) and (c) can be classified as polynomials here.

Reason is that  a polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division by a variable. A polynomial can have one or more terms, where each term contains a product of a coefficient and a variable raised to a non-negative integer power. For example, 2x^3 + 5x^2 - 3x + 7 is a polynomial with four terms.

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Answer:

To find how many more items the first plant produces daily than the second plant, we need to subtract the daily production levels of the two plants.

First plant: 5x + 11

Second plant: 2x - 3

Difference: (5x + 11) - (2x - 3)

= 5x + 11 - 2x + 3

= 3x + 14

Therefore, the first plant produces 3x + 14 more items daily than the second plant.

The pair of equations is y = 25x + 8 and y = 12 + 5x where 'x' is the number of months and 'y' is the total cost.

A system of equations refers to a set of two or more equations that need to be solved simultaneously. The solution of a system of equations is a set of values that satisfy all the equations in the system.

To represent the following situations use variables like x, y, z.. etc. to represent the number of months and total cost and form the equations.

Here we have

An online video streaming service offers two plans for unlimited streaming.

Plan A has a one-time $8 membership fee and is $25 per month.  

Let Plan A run for 'x' number of months and 'y' be the total cost

Total cost for 'x' months, y = 25x + 8  

=> y = 25x + 8

Plan B has a $12 membership fee and is $5 per month.

Let Plan B run for 'x' number of months and 'y' be the total cost

Total cost for 'x' months, y = 12 + 5x

=> y = 12 + 5x

Therefore,

The pair of equations is y = 25x + 8 and y = 12 + 5x where 'x' is the number of months and 'y' is the total cost.

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So the values of a, h, and k in the vertex form of the parabola are a = 6/11, h = -1/2, and k = 3.

A parabola's vertex form is given by:

y = a(x - h)^2 + k

where an is a constant that governs the parabola's shape and (h, k) is the parabola's vertex.

The vertex is (-1/2, 3), and the directrix is x = -13/24, according to the information provided.

The value of a can be calculated using the common parabola formula:

4a = 1/ (distance from vertex to directrix) (distance from vertex to directrix)

4a = 1 / (|(-1/2) - (-13/24)|)

4a = 1 / (11/24)

4a = 24/11\sa = 6/11

The vertex form of the parabola can now be simplified by substituting the vertex and a values:

y = (6/11)(x + 1/2)^2 + 3

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Answer:

In the image

Hope this helps!

Step-by-step explanation:

Yes, the logistic regression model is adequate to the response variable y. The parameter Beta 1 in this model measures the change in the log odds of the response variable when the independent variable (household income) increases by one unit. This is a measure of how the likelihood of home ownership changes in response to an increase in household income.

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The value of the Upper quartile is 12.5 for the set of data represented by the box and whisker plot.

When presented in increasing order, the value that 75% of data points fall within is known as the upper quartile, or third quartile (Q3). As the second quartile, the median is used (Q2). Interquartile range (IQR) refers to the space between the upper and lower quartiles.

Median, representing or having to do with a value or quantity that sits in the middle of a frequency distribution of observed values or quantities, with an equal chance of falling above or below it.

In box and whiskers plot, The upper quartile is the point at the right border of the box. In this case, that value is 12.5. It reflects the median of the data set's upper half.

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The greatest number of 0.25 pounds hamburgers Sonia can make using the hamburger meat she has is 16.

What is Average total cost?

The average total cost is calculated by dividing the total cost of production by the total output.

To find the total amount of hamburger meat Sonia has, we need to add the weights of the two packages:

Total weight = 1.76 + 2.29 = 4.05 pounds

To find the greatest number of 0.25 pounds hamburgers that Sonia can make, we need to divide the total weight of hamburger meat by the weight of each hamburger:

Number of hamburgers = Total weight / Weight of each hamburger

Number of hamburgers = 4.05 / 0.25

Number of hamburgers = 16.2

Since Sonia cannot make a fraction of a hamburger, she can make a maximum of 16 hamburgers. Therefore, the greatest number of 0.25 pounds hamburgers Sonia can make using the hamburger meat she has is 16.

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The statement "It is valid because Victoria added the same amount to each side of the equation" correctly explains whether equation 3 in Victoria's work is valid in solving the equation.

In equation 3, Victoria added 3 to both sides of the equation x-3=4/21. This operation is valid because she added the same amount (3) to both sides, which maintains the equality between the two sides of the equation. The resulting equation is x-3+3=4/21+3, which simplifies to x=4/21+63/21 or x=67/21.

Therefore, equation 3 is a valid step in solving the equation x-3=4/21.

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Answer: y = -15/14x - 1/2

Step-by-step explanation:

Start:

15x + 14y = -7

Subtract 15x from each side:

14y = -15x - 7

Divide 14 on each side:

y = -15/14x - 1/2

If you want to simplify the slope, it would be:

y = -1 1/14x - 1/2

Hope this helps!

Answer:

To find the total area of the figure, we need to find the area of each of the individual triangles and rectangles and then add them up.

The rectangle on the left has a length of 6 and a width of 3, so its area is 6 x 3 = 18 square units.

The triangle on the left has a base of 6 and a height of 5, so its area is 1/2 x 6 x 5 = 15 square units.

The triangle on the right has a base of 6 and a height of 3, so its area is 1/2 x 6 x 3 = 9 square units.

The rectangle on the right has a length of 3 and a width of 6, so its area is 3 x 6 = 18 square units.

Adding up the areas of each shape, we get:

18 + 15 + 9 + 18 = 60 square units

Therefore, the total area of the figure is 60 square units. Answer: (d) 60 units squared.

The ball traveled a horizontal distance of roughly 75.6*cos(theta) feet. Keep in mind that this is supposing a level, homogeneous surface and that the ball has no spin.

What is the equation?

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14.

To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific program typically correspond. An illustration would be 2x - 4 = 2.

75.6 feet are equal to ymax = 472/(2*32.2) + 4.

As the ball's motion is symmetrical, the time it takes to reach its highest point is equal to half the length of its flight. As a result, the total flight time is:

[tex]\frac{Sin(\theta)}{g} = 247;[/tex]

[tex]t_{total} = 2[/tex];

[tex]t_{max} = 247[/tex]

[tex]\frac{cos(\theta)*y_{max}}{vi^{2}},\\[/tex]

where t max is the time needed to reach the highest point. Again, we cannot precisely solve for theta, but we may leverage the knowledge that the ball's horizontal travels as follows:

[tex]Vi \ \times cos(\theta)\times t_{total} = x.[/tex]

Hence, by entering the data we are aware of, we can determine x:

x = 47cos(θ) (θ)

75.6/47 = [tex]\frac{2y_{max}}{vi}[/tex]

= 47cos(θ)75.6cos (θ).

Hence, the ball traveled a horizontal distance of roughly 75.6*cos(θ) feet. Keep in mind that this is supposing a level, homogeneous surface and that the ball has no spin.

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Answer:

see below

Step-by-step explanation:

put paragraph of words into summarised information 1st.

ie

black : red : total

7 : 2 : 7+2 = 9 is total units

total units = 9 (which is 144 markers)

so 1 unit is .....

144 ÷ 9 = 16 markers

black = 7units

7 x 16 markers = ans

red = 2 units

2 x 16 = ans

The given histogram is right skewed type.

A histogram is a graphic representation of data in a grouped frequency distribution with continuous classes.

They are similar to a bar graphs, but there are no gaps between the consecutive rectangles.

Histograms are widely used for ranging data into groups. It is a highly practical graph due to its clarity and simplicity.

Histogram :-

It is a collection of rectangles next to one another, where each bar represents a different type of data.

In this context, frequency refers to the number of times a number appears in statistical data.

It is known as a frequency distribution when shown in a table.

Here, the distribution here is skewed to the left. Therefore, it is also referred to as a negatively skewed histogram graph.

Hence, the given histogram is right skewed type.

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(a) The possible number of positive real zeros of P(x) can be determined using Descartes' Rule of Signs. The Rule of Signs states that a polynomial with real coefficients can have at most as many positive real zeros as its leading coefficient has sign changes in the coefficients. This means that the polynomial has at most 3 positive real zeros.

(b) Descartes' rule of signs can also be used to prove that 1-2 cannot be a zero of P(x). According to the Rule of Signs, the number of positive real zeros of P(x) is limited to 3. However, if 1-2 is a zero of P(x), then the polynomial would have 4 sign changes, which is not possible. Therefore, 1-2 cannot be a zero of P(x).

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Answer:

X = 1

Step-by-step explanation:

[tex]2x + 8 = 4x + 6 \\ collect \: the \: like \: terms \\ 8 - 6 = 4x - 2x \\ 2 = 2x \\ x = 1[/tex]

Answer:

x = 1

Step-by-step explanation:

first subtract 6 from both sides

2x + 8 = 4x + 6

     -6           -6

2x + 2 = 4x

Now get the variable on to one side by subtracting 2x from both sides

2x + 2 = 4x

-2x         -2x

2 = 2x

Now divide both sides by two to get the value of x

2 (÷ 2) = 2x (÷ 2)

1 = x

x = 1

to check your work, plug in one for x

2x + 8 = 4x + 6

2(1) + 8 = 4(1) + 6

2 + 8 = 4 + 6

10 = 10

this statement is true which means the solution is true

Hope this helps!

An expression to represent the total amount of juice left in the jar is "Total amount of juice left in jar = Total amount of juice in jar before Celina drinks any - Amount of juice Celina drinks"

First, let's start by labeling the quantities of juice we have. We have 0.85 liters of strawberry juice, 0.50 liters of mango juice, and 0.15 liters of watermelon juice. When we combine these three quantities, we get the total amount of juice in the jar before Celina drinks any of it. We can express this as:

Total amount of juice in jar before Celina drinks any = 0.85 + 0.50 + 0.15

Simplifying this expression, we get:

Total amount of juice in jar before Celina drinks any = 1.50 liters

Now, we know that Celina drinks 0.30 liters of the mixture. So, the total amount of juice left in the jar after she drinks some can be expressed as:

Total amount of juice left in jar = Total amount of juice in jar before Celina drinks any - Amount of juice Celina drinks

Substituting in our values, we get:

Total amount of juice left in jar = 1.50 - 0.30

Simplifying this expression, we get:

Total amount of juice left in jar = 1.20 liters

Therefore, the expression that represents the total amount of juice left in the jar after Celina drinks 0.30 liters of the mixture is:

Total amount of juice left in jar = 1.50 - 0.30 = 1.20 liters

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Complete Question:

A jar contains 0.85 liter of strawberry juice and 0.50 liter of mango juice. Celina poured 0.15 liter of watermelon juice into the jar. She then drank 0.30 liter of the mixture.

Part A: Write an expression to represent the total amount of juice left in the jar.

The graphs of y = x and y = -1 are related to each other because they intersect at the point (-1, -1)

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

The standard equation of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Given the graphs of y = x and y = -1.

As we can see from the graphs, they intersect at the point (-1, -1)

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Considering  A, B, C, and D are colinear the length of line BC is 7cm.

In mathematics, a circle is a geometric shape that consists of all points that are the same distance from a fixed point called the center. This distance is called the radius of the circle. A circle is a two-dimensional object and is usually represented by a curved line, often drawn as a closed shape.

Since line DE is tangent to circle A at point E, we know that line AE is perpendicular to line DE. Therefore, we can use the Pythagorean theorem to find the length of AE:

AE² = AD²- DE²

Since A, B, C, and D are collinear, we can find AD by subtracting CD from BC:

AD = BC - CD

Substituting this into the equation above, we get:

AE² = (BC - CD)² - DE²

We are given that CD = 8cm and DE = 12cm, so we can substitute these values into the equation:

AE² = (BC - 8)² - 12²

We also know that AE = BE, since E is the point of tangency. Therefore, we can use the Pythagorean theorem again to find the length of BE:

BE² = AE² + AB²

Substituting AE^2 with the expression we found above, we get:

BE² = (BC - 8)² - 12² + AB²

Since A, B, C, and D are collinear, we know that AB + BC = CD = 8cm. Solving for AB, we get:

AB = 8 - B

Substituting this into the expression for BE², we get:

BE² = (BC - 8)² - 12² + (8 - BC)²

Simplifying this expression, we get:

BE^² = -16BC + 256

We want to find the value of BC, so we set BE equal to 12cm (since DE = 12cm):

12² = -16BC + 256

144 = -16BC + 256

-112 = -16BC

BC = 7 cm

Therefore,considering  A, B, C, and D are colinear the length of line BC is 7cm.

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Based on the given information, the equation that can be used to find the n^(th) term in the sequence, a_(n) is a_(n) = 18n + 6.

To find the equation for the sequence, we need to first determine the common difference between the terms. We can do this by subtracting a_(3) from a_(4), a_(4) from a_(5), and so on:

66 - 48 = 18
84 - 66 = 18
102 - 84 = 18
120 - 102 = 18

The common difference between the terms is 18. This means that the sequence is an arithmetic sequence with a common difference of 18.

Now, we can use the formula for the n^(th) term of an arithmetic sequence, which is:

a_(n) = a_(1) + (n - 1)d

Where a_(1) is the first term, n is the term number, and d is the common difference.

We can plug in the values we know into the formula:

a_(n) = a_(1) + (n - 1)18

We don't know the value of a_(1), but we can use one of the given terms to find it. For example, we can use a_(3) = 48:

48 = a_(1) + (3 - 1)18
48 = a_(1) + 36
a_(1) = 12

Now, we can plug in the value of a_(1) into the formula:

a_(n) = 12 + (n - 1)18

We can simplify the formula by distributing the 18:

a_(n) = 12 + 18n - 18

And then combining like terms:

a_(n) = 18n - 6

So, the equation for the n^(th) term of the sequence is a_(n) = 18n - 6.

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The measure of the central angle indicated is 60°.

The central angle of a circle is the angle that an arc takes up in the centre. The radius vectors are what make up the angle's arms.

The formula for calculating a central angle is: Central Angle = Arc length (AB) / Radius (OA) = (s 360°) / 2r, where "s" stands for arc length and "r" for circle radius.

Now here in the given diagram,

Let x equal the desired angle.

The central angle that we need to find is:

Now x = 360-120-(90+90)

⇒ x = 360-300

⇒ x = 60°

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a) The equation of the circle is x² + y² 169.

b) The coordinates of the other endpoint of the diameter are (-5, 12).

The equation of a circle is given by:

(x-a)² + (y-b)² = r²

Where (a, b) is the centre of the circle and r is the radius.

In this case, the centre of the circle is at (0, 0), so the equation of the circle simplifies to: x^2 + y^2 = r^2

To find the radius, we can use the distance formula between the centre and the point

P: r = √((5-0)^2 + (-12-0)²) = √(25 + 144) = √169 = 13

Therefore, the equation of the circle is: x² + y² = 13^2 or x² + y² = 169

To find the coordinates of the other endpoint of the diameter that passes through the point P, we can use the fact that the diameter is a straight line that passes through the centre of the circle. The slope of this line is: m = (-12-0)/(5-0) = -12/5

The equation of this line is: y = -12/5x

Since the other endpoint of the diameter also lies on the circle, we can substitute this equation into the equation of the circle: x² + (-12/5x)² = 169

Solving for x, we get: x = -5 or x = 5. Since the point P has an x-coordinate of 5, the other endpoint of the diameter must have an x-coordinate of -5.

Substituting this value of x back into the equation of the line, we get: y = -12/5(-5) = 12

Therefore, the coordinates of the other endpoint of the diameter are (-5, 12).

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The required solutions are as follows,
(a) The parabola will open downwards and have a maximum.
(b) The axis of symmetry for this function is t = 15.

A parabola is a cross-section cut out of the cone and represented by an equation shown in the question.

Here,
(a) The function C(t) is a quadratic function with a coefficient of -0.2 in front of the t² term. Since this coefficient is negative, the parabola will open downwards and have a maximum.

(b) The axis of symmetry of a quadratic function in the form of f(x) = ax² + bx + c is given by the formula x = -b/2a.

In this case, the function is C(t) = -0.2t² + 6t + 28.5, so a = -0.2 and b = 6. Thus, the axis of symmetry is:

t = -b/2a = -6/(2*(-0.2)) = 15

Therefore, the axis of symmetry for this function is t = 15.

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A group of 10 people would raise a total value of  $160 if they worked 16 hours.

According to the given information, the amount of money raised, R, varies jointly as the square root of hours worked, h, and the number of people working, p. This means that R = k√h * p, where k is the constant of proportionality.

We are given that six people raise $72 when working 9 hours, so we can use this information to find the value of k:
72 = k√9 * 6
72 = k * 3 * 6
72 = 18k
k = 4

Now that we know the value of k, we can use it to find the amount of money that 10 people would raise if they worked 16 hours:
R = k√h * p
R = 4√16 * 10
R = 4 * 4 * 10
R = 160

Therefore, 10 people would raise $160 if they worked 16 hours.

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Answer: 5.25

Step-by-step explanation:

In the picture there is a smaller triangle inside a bigger triangle. You have to find the size it grows by dividing a side of the bigger triangle to the same side of the smaller triangle.

16.8/6.4 = 2.625

Then you find x by multiplying the adjacent side by the size it grows.

2*2.626 = x

2*2.626 = 5.25

Answer:

720

Step-by-step explanation:

The number of permutations of the letters of the word MAKABAYAN is 720. This is because the word MAKABAYAN has 9 letters, and the formula for calculating the number of permutations of a word with n letters is n! (n factorial). Therefore, 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 720