At the beginning of the year, Valeria had $20 in savings and saved an additional $15 each week thereafter. Jackson started the year with $70 and saved $5 every
week. Let V represent the amount of money Valeria has saved t weeks after the beginning of the year and let J represent the amount of money Jackson has saved t
weeks after the beginning of the year. Graph each function and determine at what week do Valeria ands Jackson have the same amount of money?

Answer:

The square root of -10 is already in the simplest radical form. Therefore, the answer is:

√10

-10 in simplest radical form is written as -√10.

Answer: 15

Step-by-step explanation:

Let x be the first of the consecutive integers.

So, the consecutive integer after x would be x+1. The one after this one would be x+2. Continue this until there are nine consecutive integers.

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) = 99

Simplify:

9x + 36 = 99

9x = 63

x = 7

The largest of these consecutive integers is the last one, x+8. Plug in x to this expression:

(7) + 8 = 15

The largest of these consecutive integers is 15.

Answer:

See answer below

Step-by-step explanation:

See drawing I made:

The submarine's final positions expressions are

Generally, An expression is a finite combination of symbols that is well-formed according to principles that rely on the context in which it is used. In mathematics, an expression is also known as a mathematical expression.

3F + 4A = -5 units

Working:

3 floats * -1 unit/float + 4 anchors * -1 unit/anchor

= -3 units + -4 units

= -7 units

3F - 4A = -5 units

Working:

3 floats * -1 unit/float - 4 anchors * 1 unit/anchor = -3 units - 4 units

= -7 units

F + 2A = -5 units

Working:

1 float * -1 unit/float + 2 anchors * -1 unit/anchor

= -1 units + -2 units

= -3 units

5F - A = -5 units

Working: 5 floats * -1 unit/float - 1 anchors * 1 unit/anchor

= -5 units - 1 unit = -6 units

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Answer:

474.119 kilometers

Step-by-step explanation:

The class traveled 474.119 kilometers in total. You can find this by adding the distance traveled by train (471.459 km) to the distance traveled by bus (2.66 km).

471.459 + 2.66 = 474.119

Step-by-step explanation: :)

Answer:

19.990

Explanation:
You can find this by rounding 19.992 on a number line to the nearest tenth. Tens is the first 2 numbers in a number.

Example: 2.535.783
Eighty-Three would be the tenth number.

15 more than the sum of 5 and a number a, when translated into a mathematical expression will become b. (5 + n) + 15.

An algebraic expression is a mathematical expression that can contain numbers, variables, and operations.

An algebraic expression can represent a specific value for a given value of the variable, and can be used to describe mathematical relationships and solve equations.

Algebraic expressions can be simplified, added, subtracted, multiplied and divided.

Algebraic expressions can also be represented in different forms, such as polynomials, rational expressions, exponential expressions and logarithmic expressions.

"15 more than the sum of 5 and a number a" can be represented algebraically as:

15 + (5 + a)

or

(5 + a) + 15

which can also be simplified as

a + 20

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Mean and Variance of the given table are 3.43672 and 7.837755 respectively.

What is probability ?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

a)E(x) = ∑ xᵢp(xᵢ)

∑ xᵢp(xᵢ) = 1(0.3870) + 2(0.038062) + 3(0.0968) + 4(0.06913) + 5(0.0968) + 6(0.04846) + 7(0.01252) + 8(0.1935)

∑ xᵢp(xᵢ) = 3.43672

Mean = 3.43672

b) Variance = E(x²) - [E(x)]²

E(x²) = ∑ x²ᵢp(xᵢ)

∑ x²ᵢp(xᵢ) = 1²(0.3870) + 2²(0.038062) + 3²(0.0968) + 4²(0.06913) + 5²(0.0968) + 6²(0.04846) + 7²(0.01252) + 8²(0.1935)

∑ x²ᵢp(xᵢ) = 19.6488

∴ Variance = 19.6488 - (3.43672)² = 7.837755

Hence , Mean and Variance of the given table are 3.43672 and 7.837755 respectively.

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On solving the provided question we can say that - the linear equation of .25x + 3y = 1 +3 = 4

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation  two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, x= 4 and = 1

.25x + 3y

= 1 +3

= 4

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Answer:

y = 23x - 43

Step-by-step explanation:

y - 9 = 23 (x + 7)

y - 9 = 23x + 161

y = 23x + 170

y = 23x + b

3 = 23(2) + b

3 = 46 + b

y = -43

y = 23x - 43

In order to dilate a line segment by 1/ 2, every coordinate point of the end point of the line segment is multiplied by the scale factor ½.

Dilation refers to a process of changing the size of an object or shape by either increasing or decreasing its dimensions by some scaling factors. It is a type of transformation, which is used to resize the object, making the objects larger or smaller. This transformation produces an image that is the same in shape as the original but there is a difference in the size. A dilation should either stretch or shrink the original shape and is expressed by the term “scale factor.”

When a dilation creates a larger image, it is called enlargement and when a dilation creates a smaller image, it is called reduction. If the scale factor is 1/2, every coordinate point of the original segment line is multiplied by the scale factor 1/2.

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When a swimming coach needs to choose a team for a relay race then the number of ways they can arrange 444 of the 666 swimmers is 3.53×[tex]10^{1735}[/tex]

There are a total of 444[tex]C_{444}[/tex] (or 6.64 x [tex]10^{847}[/tex]) ways to select 444 swimmers from the pool of 666.

Once the swimmers have been chosen, they need to be arranged in a strategic sequence.

This can be done in 444! (or 5.34 x [tex]10^{906}[/tex]) ways.

Therefore, the total number of unique ways to arrange 444 of the 666 swimmers is

6.64 x [tex]10^{847}[/tex] x 5.34 x [tex]10^{906}[/tex]

3.53 x [tex]10^{1735}[/tex]

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Based on the graph which shows the relationship between pounds and euros, the value of a is €0 and the value of b is €1.45.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the relationship between pounds (£) and euros (€) must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 1.45/1

Constant of proportionality (k) = 1.45.

When x = 0, the value of a is given by:

y = a = 1.45x

a = 1.45(0)

a = €0.

When x = 1, the value of b is given by:

y = a = 1.45x

b = 1.45(1)

b = €1.45.

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The given triangles GEF and HKJ are congruent by the AAA test of congruency and the value of a = √2.

The two triangles are proved to be congruent and the value of a is to be determined.

Both triangles are right-angled triangles.

We know that similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

In triangle GEF,

since the sum of the angles in a triangle is 180

∠ G + ∠ F + ∠ E =180

90 + 45 + E = 180

∠ E = 45

similarly, ∠ J = 45

In Triangle GEF and Triangle HKJ,

∠ G = ∠ K (both are 90)

∠  F = ∠ H  (both are 45)

∠ E = ∠ J  (both are 45)

So, Triangle GEF and Triangle HKJ are congruent triangles by AAA congruency.

Now in triangle GEF,

cos 45 = 3a/6

1/√2 = a/2

a = √2

Thus, the given triangles are congruent by AAA . and the value of a = √2.

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The complete question is -

Given right triangles EFG and HJK. find the value of a that satisfies the congruency of the triangles. in two or more complete sentences, explain the relevance between the congruency of the triangles and the calculations made in finding the value of a.

All properties that apply to the differential equation dy/dx+sin²(x)y = cos²(x)y are following

(A) homogeneous

(B) ODE

(D) first order

(G) linear

(I) separable

Ordinary Differential equation: A differential equation consisting an unknown function and its derivatives with respect to a single independent variable.

Partial Differential equation: A differential equation consisting an unknown function and its partial derivatives with respect to a two or more independent variables.

First order Linear differential equation: The standard form of first order Linear differential equation is dy/dx + p(x)y = q(x)

and if q(x)=0, then this linear differential equation is homogeneous.

Separable Differential equation: A differential equation, y′ = f(x,y)

is said to be in separable form if the function f(x,y) can be written as

fx,y) = g(x)h(y). Now, we have an equation

dy/dx+sin²(x)y=cos²(x)y --(1)

As we see differential equation (1) contains derivative with respect to a single independent variable, x only, therefore this is an Ordinary differential equation. Also, the order of the differential equation (1) is one, i.e. first order differential equation. Now the given differential equation can be written as

dy/dx + ysin² x - ycos²x = 0

=> dy/dx − y(sin²x−cos²x) = 0

This is the standard form of first order Linear differential equation with q(x) = 0 . Therefore, there is not a candidate for integrating factors. The right side function is zero, therefore the the differential equation is homogeneous and dy/dx = y(sin²x−cos²x) = f(x,y)

= g(y) h(x) , so, it is a separable one . Hence, we check all properties for equation (1) .

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System sequence diagram is the best model to use to document the inputs and the outputs to a system.

In the realm of software engineering, a sequence diagram, also known as a system sequence diagram (SSD), depicts process interactions grouped in chronological order. It illustrates the processes involved and the order in which messages must be exchanged for the processes to provide the functionality. In the 4+1 architectural perspective model of the system under development, sequence diagrams are often connected to use case realizations. Event diagrams and event scenarios are other names for sequence diagrams.

The diagrams display the events that external actors produce, their order, and any potential inter-system events for a given scenario of a use case. [1] The diagram emphasizes events that cross the system boundary from actors to systems and treats all systems as black boxes. The main success scenario of the use case, as well as frequent or complex alternate situations, should be represented using a system sequence diagram.

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1.
In the triangle that contains x (call the other 2 angles as a and b, where a is the angle that is supplemetary to the center angle.)

a = 180 - 110 = 70 (supplemetary angles add up to 180)

b = 30 (b and the angle measures 30 are in the same segment.)

-> x = 180 - 70 - 30 = 80.

2. In triangle PRT, v = 180 - 40 - 70 = 70.

Since P,Q,S,T all lies on the circumference, PQST is a cyclic quadrilateral.

-> w = 180 - PQS = 180 - (180 - 70) = 70.

3.
i) A 1:2 scale means that all sides of P must be shortened by twice the lengths.

Since D is the only shape with the sides shortened from P, it's the correct option.

ii) A 1:1/2 scale means that all sides of P must be enlarged by twice the lengths.

Therefore, the measures of the sides become sqrt(20),6,4,6 (clockwise from diagonal), which is B.

4. Using the Pythagoras' theorem, we can find the hypotenuse PR : [tex]\sqrt{12^{2} + 5^{2} } = 13[/tex]

sin(x) = QP/PR = 5/13 = 0.385 (rounded to 3 d.p)
tan(y) = QP/QR = 5/12 = 0.417 (rounded to 3 d.p)

The value of x will be;

⇒ x = 50

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

Two parallel lines cut by a transversal.

Now,

Since, Two parallel lines cut by a transversal.

Hence, By definition of co-interior angle, we get;

The sum of co-interior angle in supplementary.

Hence, We get;

⇒ (2x + 10)° + (2x - 30)° = 180°

⇒ 4x - 20 = 180

⇒ 4x = 180 + 20

⇒ 4x = 200

⇒ x = 200/4

⇒ x = 50

Thus, The value of x = 50

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Statement                                     Reason

∠1 = ∠2, WX = ZY                            Given

WP = ZP                                         converse of isosceles triangle  theorem

△WXP ≅ △ZYP                              SAS

XP = YP                                           CPCT

∠3 = ∠4                                          Isosceles triangle  teorem

What is the isosceles triangle?

A triangle's corresponding angles are congruent if its two sides are.

Given that ∠1 = ∠2, WX = ZY.

Statement 1 is given.

According to the converse of the isosceles triangle theorem:

WP = ZP  

SAS rule: If the two sides and an included angle of one triangle match the two sides and an included angle of the other, then two triangles are said to be congruent. This is referred to as SAS congruency.

In triangles △WXP and △ZYP:

∠1 = ∠2

WX = ZY.

WP = ZP

According to SAS rule,  △WXP ≅ △ZYP

By CPCT, XP = YP

Again the isosceles triangle theorem ∠3 = ∠4.

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Answer: 161

Step-by-step explanation: 23 + 3 times 46 (since the first 4 numbers are already there) is 161

An example of a complex number in standard form is (5 + 4i), where i is the imaginary unit.

example to solve (x + 5i)(2x - 3i):

Step 1: Multiply the real numbers together:

x × 2x = 2x²

Step 2: Multiply the imaginary numbers together:

5i × -3i = -15i²

Step 3: Multiply the real and imaginary parts together:

x × -3i = -3ix and 2x × 5i = 10xi

Step 4: Add all the terms together:

2x² - 15i² + -3ix + 10xi = 2x² - 15i² - 3ix + 10xi

Step 5: Simplify the terms:

2x² - 15i² - 3ix + 10xi = 2x² - 18ix - 15i²

The product of two complex numbers (x + 5i)(2x - 3i) can be found by multiplying the real numbers together, the imaginary numbers together, and the real and imaginary parts together, then adding all of the terms together and simplifying.

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The total distance travelled covered by the Daren is greater than that of  Umberto.

Distance travelled is the product of speed of the body and the time for which it moved. Mathematically -

Distance = Speed x Time

Given is that Daren can run 8.55 kilometers in one hour. Umberto can run 9.5 kilometers in one hour. Now, Daren plans to run for 3.5 hours and Umberto plans to run for 3 hours.

Total distance travelled by Daren is -

d₁ = 8.55 x 3.5

d₁ = 29.925 Km

Total distance travelled by Umberto is -

d₂ = 9.5 x 3

d₂ = 28.5 Km

It can be seen that -

d₁ > d₂

Therefore, the total distance travelled covered by the Daren is greater than that of  Umberto.

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Answer:

She sold 8 bracelets

Step-by-step explanation:

I knew the number of bracelets would have to be an even number otherwise the total cost would have a decimal. Then I just went down the list doing 3.5*16 + 6*2, etc. until I got the answer (she sold 10 necklaces btw)

I think it is W(week)...........

Answer:

2004 to 2012

Step-by-step explanation:

The probability of getting 2 red marbles will be 0.298.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

In this case, there is a bag filled with 5 blue and 6 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced.

The probability of getting 2 reds will be;

= 6/11 × 6/11

= 0.298

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Answer:

3/2

Step-by-step explanation:

7 x 3/14 can be simplified to 21/14, which is written in simplest form as 3/2.

Hope can help :)

The simplest form of the fraction of the expression is 3/2.

We have,

The expression:

7 x 3/14

Now,

14 is a multiple of 7.

i.e

7 x 2 = 14

So,

7 x 3/(7 x 2)

7 gets canceled.

= 3/2

Thus,

The simplest form of the fraction of the expression is 3/2.

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The factorization of the quadratic equation:

x^2 + 3x - 54

Is (x + 9)*(x - 6).

To factorize the quadratic equation we first need to find the roots:

x^2 + 3x - 54 = 0

Using the quadratic formula we will get:

[tex]x = \frac{-3 \pm \sqrt{3^2 - 4*1*(-54)} }{2} \\\\x = \frac{-3 \pm15 }{2}[/tex]

So the two roots are:

Then the factorized form of the quadratic equation is:

(x - (-9))*(x - 6)

(x + 9)*(x - 6)

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Answer: 103.96

Step-by-step explanation: