Five student government officers want to go to the state convention. It will cost them $115 for registration, $365 for transportation and food, and $55 per person for the hotel. There is $485 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $6 per car, how many cars must they wash in order to have enough money to pay for the trip?

In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.

given

Use similar triangles,

BAC and DAB are similar

therefore

CA/AB = BA/AD

CA/20 = 20/10

cross multiply

AC = CA = 20*20/10 = 40

Or use metric relations

CA*AD = BA^2

CA = BA^2/AD = 20^2/10 = 40

In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.

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Answer:  An equation has two solutions when it has two distinct values that can be assigned to the variable to make the equation true.

In this case

equation A. W=-1 is a single solution

equation B. W=1 is a single solution

equation C. W=-2 is a single solution

equation D. W=0 is a single solution

So none of the given equations have two solutions. they all have only one solution.

It's worth mentioning that, if the equation is a quadratic equation (in the form of ax² + bx + c = 0) and it has a non-zero discriminant (b² - 4ac) then the equation will have two distinct real solutions.

In this case the equations are not in that form, and also doesn't show any signs of having two solutions.

Step-by-step explanation:

Answer:

2 2/4 or 2 1/2

Step-by-step explanation:

3-1=2

3/4-1/4=2/4

2/4=1/2

The amount of rain required would be 2.5 inches.

What is the addition?

Addition is a mathematical operation that represents the process of combining two or more numbers together. The result of this operation is called the sum. The addition operation is often represented using the symbol "+", and it can be used to add any two or more numbers together.

To beat the record by one-tenth of an inch, an additional 0.1 inches of rain must fall.

Currently, the average amount of rain per day is 12 inches / 5 days = 2.4 inches per day.

So, the amount of rain that must fall on Friday to beat the record by one-tenth of an inch is 2.4 inches + 0.1 inches = 2.5 inches

Hence, the amount of rain required would be 2.5 inches.

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The solution for y in the equation √(7 - x)² + (9 - y)² is infinite many solutions

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

√(7-x)²+(9-y)²

Express tthe equation properly

So, we have the following representation

√(7 - x)² + (9 - y)²

The above is an expression, not an equation

This means that the value of the variable y can take any value and the equation will be true

In other words, it means that the variable y has infinite many solutions because it is not an equation but it is an expression

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Step-by-step explanation:

a probability is always

desired cases / totally possible cases.

now in our case the totally possible area is the area of the triangle XYZ (when D = Z).

the desired case is the area of 20 (which contains also the possibilities of smaller areas).

so, the probability is 20/area.

now, let's find the area of XYZ :

Pythagoras tells us the length of the Hypotenuse :

XZ² = XY² + YZ² = 12² + 6² = 144 + 36 = 180

XZ = sqrt(180)

the area based on all 3 sides we get via Heron's formula

s = (a+b+c)/2

A = sqrt(s(s-a)(s-b)(s-c))

s = (12+6+sqrt(180))/2 = 9 + sqrt(180/4) = 9 + sqrt(45)

sqrt(180) = 2×sqrt(45)

A = sqrt((9+sqrt(45))(-3+sqrt(45))(3+sqrt(45))(9-sqrt(45)))

(a+b)(a-b) = a² - b²

so,

(9+sqrt(45))(9-sqrt(45)) = 81 - 45 = 36

(-3+sqrt(45))(3+sqrt(45)) = 45 - 9 = 36

A = sqrt(36×36) = 6×6 = 36

the probability that the area of XYD is max. 20 is

20/36 = 5/9

Answer:

Here

Step-by-step explanation:

Step by step solution:

Fractions with the same denominators can be added together by simply adding the numerators while retaining the common denominator.

The numerators should be added together while maintaining a common denominator. Add fractions with the same denominators by following the methods shown below:

Given:

=2/4 + 1/4

=(2+1)/4

=3/4

Therefore, 2/4 + 1/4=3/4 and not 3/8

Note:

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On solving the provided question, we got to know that - arbitrary number So the money she earns is equal to 10 times w plus 15, which can be expressed as: 10w + 15

A number is considered arbitrary if its only unique characteristic is that it has a high value. You can think of them informally as the numbers that your opponent picked. Any number appears to be worthless intuitively.

Since the question allows us to use any number, we decide to make the money she makes from washing the car equal $10. We'll also assume that she gets paid $15 to wax the car.

So the money she earns is equal to 10 times w plus 15, which can be expressed as:

10w + 15

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Answer:

She spent 37.05

Step-by-step explanation:

multiply both values

Answer:

parallel line: y = 8x - 26

perpendicular line: y = -1/8 x - 13/8

Step-by-step explanation:

1.

Lines are parallel, so slopes are equal, and y-intercepts are different.

Given line:

y = 8x - 2

New line:

y = 8x + b

Use point (3, -2) and solve for b.

-2 = 8(3) + b

-2 = 24 + b

b = -26

Equation: y = 8x - 26

2.

Lines are perpendicular, so slopes are negative reciprocals.

Given line:

y = 8x - 2

New line:

m = -1/8

y = -1/8 x + b

Use point (3, -2) and solve for b.

-2 = -1/8 × 3 + b

-2 = -3/8 + b

b = -16/8 + 3/8

b = -13/8

Equation: y = -1/8 x - 13/8

Answer:

Step-by-step explanation:

If there are 12 cookies in a package and you want to buy 4 packages, you will need a total of 12 x 4 = 48 cookies.

If you have a dozen eggs and you want to make 4 omelets, you will need a total of 12 x 4 = 48 eggs.

If you have 12 pieces of fruit and you want to make 4 fruit salads, you will need a total of 12 x 4 = 48 pieces of fruit.

Answer:

Based on the given equation, the function g is an exponential function with base 2. The y-intercept of the function g is at (0, 4).

The graph of function f is not described, so it is not possible to accurately compare the two functions. In order to accurately compare the two functions, it would be helpful to have more information about the graph of function f, such as the vertex and any other points that the graph passes through.

Answer:

Step-by-step explanation:

Given L is the line through A(1, 2, -1) and B(5, -3, 4), you want its direction vector, a parameterization of L, 2 points on L that are 2 units from A, and a unit speed parametrization of L.

A direction vector for L will be the vector AB.

  [tex]\overrightarrow{AB}=B-A=(5,-3,4)-(1,2,-1)\\\\\boxed{\overrightarrow{AB}=(4, -5,5)}[/tex]

The parameterized equation will be ...

  [tex]L=A+t\cdot\overrightarrow{AB}\\\\\boxed{L=(1+4t,2-5t,-1+5t)}[/tex]

The direction vector has length √66, so we can find two points on L that are 2 units from A by using t = ±2/√66 in the parameterized equation.

Here, they are:

  P1 = L(2/√66) = (1 +8/√66, 2 -10/√66, -1 +10/√66)

  P2 = L(-2/√66) = (1 -8/√66, 2 +10/√66, -1 -10/√66)

In the Answer section above, these are written with rationalized denominators.

The unit speed parametrization uses the unit direction vector instead of the unnormalized direction vector in the parameterized equation. Effectively, t is scaled by a factor of 1/√66.

  L = (1 +4t/√66, 2 -5t/√66, -1 +5t/√66)

In the Answer section above, this is written with rationalized denominators.

You might notice here that it is easier to answer part 3 if you have this equation. You need only substitute t=±2 to get the points 2 units from A.

For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.

domain : (x | x  3/2)

range : (-∞ , 2)

For these values, Option B , C and E holds that they exists when x  3/2 and it's output that is y exists between  (-∞ , 2).

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In the sample compound interest rate tables presented in your reading material, the first column on the left-hand side of each table shows you the number of periods. Option C

When interest is computed, it is done so on the initial principal as well as all of the accrued interest from prior periods.

The ability of compound interest is defined as producing "interest on interest."

Any frequency schedule, including continuous, daily, and yearly, can be used to compound interest.

Money increases more quickly when compounded.

Formula is given as :
[tex]A = P(1 + \frac{r}{n})^n^t[/tex]

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Step-by-step explanation:

I said it I knew it I did it I submit for you so I'm the one that is if if you know me.

On solving the provided question, we can say that - here in the slope intercept [tex]2y / 2 = -4x /2 + 24 / 2 = > y = -2x + 12\\[/tex]

The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.

y = mx + c

m = slope, c = y-intercept

[tex]4x + 2y = 24\\2y = -4x + 24\\2y / 2 = -4x /2 + 24 / 2\\y = -2x + 12\\[/tex]

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Answer:

  1400

Step-by-step explanation:

You want to know the number of customers in April if the number in May was 10% lower. That number was 140 fewer.

The problem statement is telling us ...

  April - (10% × April) = April - 140

  10% × April = 140 . . . . . . . . subtract April, multiply by -1

  April = 140/10% = 1400 . . . . divide by 10%

The number of customer visits in April was 1400.

__

Additional comment

The 1400 customers in April fell by 140 to 1260 in may. That's 10% fewer than in April.

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There are 36 pieces in one case. The store has 90 loose storage units. The store manager requested an inventory count where 2.5 units would fill her 90 units.

Typically, this process involves the retailer (or team of employees) walking through the retailer's warehouse and storefront, counting each item. Information is captured manually using pen and paper or electronically using a mobile device.

Create a storage location map showing each shelf, bin, drawer, receiving dock, and return area. Place geographic divisions, not product lines, between each storage area. Let's start counting! After each counter completes a certain range, allow a manager or someone else to check the count.

90/36 = 2.5

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When Malia joined a gym 14 weeks after Jane did, the value of b was 5.

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them.

A car's fuel capacity and efficiency, as well as how far it can go on a single charge of its electric battery, are important considerations. A nonproportional connection can be used to describe this.

a + b = 14

9 + b = 14

b = 14-9 = 5

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First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.

The product of the given numbers can be represented in a scientific notation form as = 6418 × 10^19 (approximately)

Multiplication can be defined as the repeated addition of a given value with the purpose of arriving to an expected value.

The multiplication of two given numbers is the same thing as the products of the given number and it's represented by the sign (X)

The product of 6,789,694,976 x 9,452,569,132 = 6418 × 10^19

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Answer:

theres three possible answers, they either QUACK, HONK, or hum

Step-by-step explanation:

Answer: 571.11111...(Fraction: 9/28)

Step-by-step explanation:

5,140÷9 = 571.11111...

Answer:

1

Step-by-step explanation:

1/1260 = 0.00079365079

0.00079365079 * 1260 = 1

When Nancy wanted to find the volume of a cuboid, the volume is 352cm³.

Word problem simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Since Nancy wanted to find the volume of a cubiod she measured the length of the cubiod as 11 cm and width as 8cm and the height as 4cm.

The volume will be:

= Length × Width × Height

= 11cm × 8cm × 4cm

= 352cm³

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Complete question

Nancy wanted to find the volume of a cubiod she measured the length of the cubiod as 11 cm and width as 8cm and the height as 4cm. Find the. volume

Answer:

0.02083333333