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There are 8 half dollars and 9 quarters inside the cup.

We can set up a system of equations to represent the number of half dollars (h) and quarters (q) in the cup and the total value of the coins.

Let h be the number of half dollars and q be the number of quarters.

The first equation represents the total number of coins in the cup:

The second equation represents the total value of the coins:

To solve for h and q, we can use either the substitution or elimination method.

By substitution, we can solve for one variable in terms of the other in one of the equations and substitute it into the other equation.

So, q = 17 - h

then substitute it into the second equation:

0.5h + 0.25(17 - h) = 5.50

By solving for h, we get h = 8, then we can substitute it back into the first equation to get q = 9

So, there are 8 half dollars and 9 quarters inside the cup.

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Answer:x=20

Step-by-step explanation: <2 and <3 must be equal, so set 3x-10 equal to x+30, once simplified you get x equal to 20.

Answer:

x = 20

Step-by-step explanation:

Angle 2 and 3 are alternate (interior) angles which means that they are equivalent to each other.

3x-10=x+30

-x       -x

2x-10=30

  +10  +10

2x=40

x=20

Answer in explanation:

although there's an addition sign, you subtract the two because a

(+) + (-) = (-) subtract

[This is a general rule, writing down the "rules" for reference is a good way to help if your having trouble]

subtract to find your answer (you keep the sign of 1.8 because it's the larger number.)

1.3 + (-1.8) =

-0.5

-0.5 is your answer

Hope this is clear!

Answer: -14

Step-by-step explanation:   When you have a problem like this all you do in multiply the answer and the number your given.

 7x-2 that would by -14

You want to check your answer by changing X for -14 and you solve from there. Plus 2 negatives equal a positive.

Hope this helps!

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{x}{-2} = 7}[/tex]

[tex]\text{Multiply } \rm{ -2}\text{ to both sides}[/tex]

[tex]\mathsf{\dfrac{x}{-2}\times -2 = 7\times -2}[/tex]

[tex]\text{Simplify it}[/tex]

[tex]\mathsf{x = 7\times -2}[/tex]

[tex]\mathsf{x = -14}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = -14}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Step-by-step explanation:

(-2,4)

(0,5)

(2,6)

(4,7)

Answer: 4, 5, 6, 7,

Step-by-step explanation: From the formula   y = x / 2 + 5

substitute x with the value -2

It becomes -2 / 2 + 5

that equals 4

then do the same for the rest

when x = 0

y = 0 / 2 + 5

y = 5

when x = 2

y = 2 / 2 + 5

y = 1 + 5

y = 6

when x = 4

y = 4 / 2 + 5

y = 2 + 5

y = 7

I hope this was helpful

The area of a polygon with the given vertices is calculated by adding the areas of the individual triangles that make up the polygon.

A polygon is a closed figure in a plane consisting of a set of straight line segments connected end-to-end. The sides of a polygon are all of equal length, and the angles between them are all of equal measure. Polygons are one of the most fundamental shapes in geometry. They include triangles, squares, rectangles, hexagons, and many more.

The area of triangle WXZ is calculated as (1/2) × |XW × ZY|,

where XW is the vector from W to X and ZY is the vector from Z to Y.

In this example,

XW = (3, -2) and ZY = (-2, -4).

Therefore, the area of triangle

WXZ is (1/2) ×|(3, -2) × (-2, -4)| = (1/2) × 14 = 7.

The area of triangle XYA is calculated similarly,

where XY = (2, 3) and YA = (-2, -4).

Therefore, the area of triangle

XYA is (1/2) ×|(2, 3) ×(-2, -4)| = (1/2)× (-14) = -7.

The area of the polygon is calculated by adding the areas of the individual triangles, which in this example is 7 + (-7) = 0. Therefore, the area of the polygon with the given vertices is 0.

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Inequalities represent Susan's weekly goal of earning money are:

c + e ≤ 20

15c + 10e ≥ 240

The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.

The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.

Given that,

Susan earns $10 per hour tutoring elementary students in math.

She also earns $15 per hour cleaning in the library.

Her goal each week is to earn at least $240 while working not more than 20 hours.

Thus, the equation of inequality:

c + e ≤ 20

15c + 10e ≥ 240

Here, e represent the number of hours Susan works in one week tutoring elementary students.

c represent the number of hours Susan works in one week cleaning the library.

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Submarine must descend 17 feet in the 5th minute.

What is the average of the data?

Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.

Let the distance descended by submarine in 5th minute = x feet

Average distance descended by the submarine

= (Total distance distended/ Duration or time)

= (6 + 8 + 14 + 15 + x) / 5

= (43 + x) / 5

Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"

So the inequality for the statement will be,

(43 + x) / 5 ≥ 12

43 + x ≥ 60

x ≥ 17

Therefore, submarine must descend 17 feet in the 5th minute.

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g(6) must be greater than 21 which is 22 only.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable.

Since g'(x) > 0 for all x and we know that g(x) is an increasing function.

Additionally, since g"(x) > 0 for all x, we know that g(x) is a concave-up function.

Since g(x) is increasing, we know that g(6) > g(5) = 18.

Now, we can use the fact that g(x) is concave-up to find a lower bound on g(6).

By the definition of concave-up, we know that the slope of the tangent line to g(x) is increasing.

This means that the slope of the line connecting (3,g(3)) to (5,g(5)) is less than the slope of the line connecting (5,g(5)) to (6,g(6)).

Using this information, we can find a lower bound on g(6):

g(5)- g(3) / (5-3) < g(6)- g(5)/ (6-5)

18- 12/2 < g(6)- 18

3 < g(6) - 18

g(6) > 21

Therefore, g(6) must be greater than 21.

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Probability of Two people was born on Friday = 1/49

Possibility of happening an event is called probability. It is given by the ratio of favorable outcome to the total possible outcome. Probability is different kinds such as independent probability, dependent probability, conditional probability and so on.

Assume that birthdays are equally distributed throughout the week.

probability of one people having birthday on Friday = 1/ 7

probability of another people has birthday on Friday = 1/7

probability of two people was born on Friday = 1/7× 1/7 = 1/ 49

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1) false

2) false

3) true

4) true

5) true

Answer:

1 false,2 false,3 true,4 true,5 true

If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of  inequality is [tex]x > 1[/tex] .

The inequality that Line is solving is [tex]15-x < 14[/tex] ,

the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;

we have to find the value of x for which the given inequality expression is true ,

Case(i) , let us take [tex]x > 1[/tex] ,

So , putting x = 2 , in the inequality ,

we get ; [tex]15-2 < 14[/tex]

= 13 < 14 , that is TRUE .

Case(ii) , let us take [tex]x < 1[/tex] ,

So , putting x  = 0 in the inequality ,

we get ; [tex]15-0 < 14[/tex]

= 15 < 14 , that is FALSE .

Therefore , the solution of the inequality is x > 1 .

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Answer:

To determine the number of miles Coroline runs per minute, we need to first convert the distance she runs to a fraction of a mile and the time it takes her to run that distance to a fraction of an hour.

3 1/2 miles is equivalent to 3 + 1/2 = 3 + 1/(2*1) = 7/2 miles.

22 1/4 minutes is equivalent to 22 + 1/4 = 22 + 1/(4*1) = 23/4 minutes.

To convert the time to hours, we can divide the number of minutes by the number of minutes per hour. There are 60 minutes per hour, so we have:

23/4 minutes / (60 minutes/hour) = (23/4) / (60/4) = 23/60 hours

To determine the number of miles Coroline runs per minute, we can divide the distance she runs by the time it takes her to run that distance:

(7/2 miles) / (23/60 hours) = (7/2) / (23/60) = (760) / (223) = 420/46

Simplifying, we have:

420/46 = 9 1/23

Therefore, Coroline runs approximately 9 1/23 miles per minute.

Step-by-step explanation:

Answer:

she runs 0.078 miles  per minute.

Step-by-step explanation:

Step-by-step explanation:

it means that the graph of the function above y=x must be the mirrored image of the graph under y=x.

it means that the function applied to itself gives x.

f(f(x)) = x

e.g.

f(x) = 5 - x

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

so, this f(x) is its own inverse.

When we reverse the integration and evaluation orders, we obtain: [tex]\frac{c}{2}-1[/tex]

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

So, we have:
[tex]$$\int_0^1 \int_x^z e^{\frac{x}{y}} d y d x$$\\[/tex]

Here:  [tex]z=\sqrt{x}[/tex]

Next, reverse the sequence:

[tex]$$\int_0^1 \int_m^y e^{\frac{x}{y}} d y d x$$ $m=y^2$$$\\\\\begin{aligned}\\& \int_{=0}^1\left(e^{\frac{x}{y}} y\right) \| \begin{array}{l}y \\y^2\end{array} d y \\& \int_{=0}^1(e y)-\left(e^y y\right) d y\end{aligned}$$[/tex]

The following section uses integration by parts,

[tex]$$\begin{aligned}& \mathbf{u}=\mathbf{y}, \\& d v=e^y\end{aligned}$$$$\mathrm{d} u=1$$$$v=e^y$$$$\begin{aligned}& =\left(\left(\frac{e y^2}{2}\right)-\left(y e^y\right)\right)||_0^1+\int_0^1 e^y d y \\& = \\& =\frac{e}{2}-e+e-1=\frac{e}{2}-1\end{aligned}$$[/tex]

Therefore, when we reverse the integration and evaluation orders, we obtain: [tex]\frac{c}{2}-1[/tex]

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Correct question:

Evaluate the integral by reversing the order of integration.

8 0 2 3ex4 dx dy 3 y

rate of change for this linear equation, y = 5x - 1 is +5

the initial value of the linear equation, y = 5x + 2 is +2.

A linear equation is an algebraic equation of the form y = mx+c, where m is the slope and c is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on.

Non-linear equations are those that do not produce a straight line. It has a changeable slope value and resembles a graphed curve.

Given that,

y = 5x - 1 is a linear equation.

As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.

Therefore, for the given equation, rate of change is 5 and initial value is -1.

Given that,

y = 5x + 2

is a linear equation.

As we know, when linear equation is in the form of y = mx + c, here m is the slope or the rate of change, and c is the Y-axis intercept, or value of y when x is zero, or initial value.

Therefore, for the given equation, rate of change is 5 and initial value is + 2.

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On solving the provided question, we can say that -  here in graph we have on solving equation [tex]x^2+ 3y^2 \\[/tex]  =  [tex]4+3 = 7[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here-

from graph, x= 2

y = 1

[tex]x^2+ 3y^2 \\[/tex]

[tex]4+3 = 7[/tex]

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Answer:

the answer is. The answer is

57

Step-by-step explanation:

Yes, the horizontal asymptote is at y = 4.

The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.

Here we have given the expression y = 4.

In order to find whether it is an horizontal asymptote or not, we have to plot it on the graph,

The first process is to label the graph with x and y axis.

And then we have to defines the scale for the for the graph.

Now, we have to input the expression y = 4 on the graph then we get the graph like the following.

While we looking into the given graph we have identified that the expression y = 4 makes the horizontal asymptote on the graph.

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On solving the provided question, we can say that - the value of the function is f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]; f(x) = x= it doesn't factor

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

f(x) = [tex](x+3)^2 - 5[/tex]

f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]

f(x) = x= it doesn't factor



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Answer:

Step-by-step explanation:

factoring

e =

(a+1)(a-1-3(a+1))
= (a+1)(a-1-3a-3)

= (a+1)(-2a-4)

= -2(a+1)(a+2)

The ratios on the double line are 3:7, 6:14, 12:28 and 15:35.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line.

From the given double line, the ratio is 9:21.

Completed double line has the following ratios

3:7, 6:14, 12:28, 15:35

Therefore, the ratios on the double line are 3:7, 6:14, 12:28 and 15:35.

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Answer:

Translate(1.3, -1)

Scale Factor: 2/3

Step-by-step explanation:

First, perform a dilation about the origin. This will make the original shape smaller.

From the given diagram, we can see that R'S' is 10 units long. RS is 15 units long. Using this information, we can create this ratio.

[tex]\frac{10}{15}[/tex]

This means that Triangle R'S'T' is 2/3 of Triangle RST. Construct lines from the origin (the center of dilation) to each point on the original triangle. Then, find two thirds of that line. The new point will be the new y-coordinate.

The new coordinates will (approx.) be:

R = (-2, 4.7)

S = (-2, -5.3)

Only two coordinates are necessary to perform this translation. As per the graph, this triangle must shift approximately 1.3 units up and 1 unit to the left. Thus, the final translation is:

Translate(1.3, -1)

Scale Factor: 2/3

Answer:B or A depending on if it went per year or overall

Step-by-step explanation:100 137, 137-100=37

37/5=7.4

The answers to each part of the question are mentioned above.

        y = a(x – h)² + k    or     x = a(y – k)² +h.

        where - (h, k) denotes the vertex.

Given is the equation of a parabola as -

(x - 1)² = y + 2​

We can write the equation as -

y = (x - 1)² - 2

        [tex]$y=\frac{1}{4 \left(f - k\right)} \left(x - h\right)^{2} + k[/tex]

        [tex]$y=\frac{1}{4 \left(\frac{-7}{4} - (-2)\right)} \left(x - h\right)^{2} + k[/tex]

        - 2 - (- 7/4) = d - (- 2)

        d = - 9/4

        y = d

        y = -9/4

Therefore, the answers to each part of the question are mentioned above.

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It can be written in standard form as [tex]5x^2-2+3[/tex] and the degree of polynomial is 2 with leading coefficient as 2.5.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). When attempting to solve systems of two linear equations, this form is also very helpful.

The values on which mathematical operations take place in an algebraic expression are known as terms in mathematics. Let's explain with the help of a term example. This algebraic expression has terms 8x and 9, respectively.

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y=­−12(x+4)(x−1) A quadratic function that satisfies the requirement and passes through the points (4, 2) and has the equation +2 (1,2) .

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.

given

a )a vertex at (­−2,−­5) :

y=[tex](x+2)^{2}[/tex]−5

y=­−[tex](x+2)^{2}[/tex]−5

y=3[tex](x+2)^{2}[/tex]−5

b) a y-­intercept of (0,−­6) :

y=[tex]x^{2}[/tex]−6

y=[tex]x^{2}[/tex]+13x−6

y=2[tex]x^{2}[/tex]−6

c)  the points (−­4,2) and (1,2):

y=(x+4)(x−1)+2

y=2(x+4)(x−1)+2

y=­−12(x+4)(x−1)+2

y=­−12(x+4)(x−1) A quadratic function that satisfies the requirement and passes through the points (4, 2) and has the equation +2 (1,2).

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Answer:

the equation of line parallel to y=-3x+2

is y=-3x+k---(1)

Since,line(1) passes through point (4,3).

3=-3(4)+k

or,3=-12+k

or,k=3+12

:.k=15

Putting value of k in line (1), we get

y=-3x+15,which is the required eqn.

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When ABCD is dilated by a factor of the coordinate of D' and the size of the coordinate point is, A"s coordinate would be (-6, -2) (-3, -1) .

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

The coordinate point's size is specified as (-3, -1).

The coordinate A' will be supplied as follows if the coordinate A is dilatable by a factor of two: A' = (2(-3), 2(-1)) = (-6, -2)

Consequently, A"s coordinate would be (-6, -2)

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