A family buys a studio apartment for$180,000 . They pay a down payment of $18,000 .
a. Their down payment is what percent of the purchase​ price?
b. What percent of the purchase price would a ​$9,000 down payment​ be?

Answer:

57

Step-by-step explanation:

x = 6

10x - 3

10(6) - 3

60 - 3

57

Answer:

57

Step-by-step explanation:

10x-3

10(6)-3

10(6)=60

60-3=57

The corrrect statements about angle are:

Please refer to the attached picture below for visualization of the angles.

Based on the attached picture, we can consider the relationship of each angle, such as:

Alternate interior angles and congruent:

Angle 4 and angle 5

Angle 3 and angle 6

Alternate exterior angles and congruent:

Angle 1 and angle 8

Angle 2 and angle 7

Consecutive interior angles and supplementary:

Angle 3 and angle 5

Angle 4 and angle 6

Corresponding angles and congruent:

Angle 1 and angle 5

Angle 2 and angle 6

Angle 3 and angle 7

Angle 4 and angle 8

Vertical angles and congruent:

Angle 1 and angle 4

Angle 2 and angle 3

Angle 5 and angle 8

Angle 6 and angle 7

Supplementary angles:

Angle 1 and angle 2

Angle 3 and angle 4

Angle 5 and angle 6

Angle 7 and angle 8

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Answer:

468

Step-by-step explanation:

A sequence is arithmetic sequence when the first differences are all the same non-zero number.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.

As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.

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Answer:

10 < x

Step-by-step explanation:

ten (10) less than (<) a number (x)

Answer:

This is a often mistake when being asked to write an expression. The words "is less than" and "less than" have different meaning. The phrase, "is less than" means 6 < k. The phrase "less than" means 6 - k.

I'll make a example with your problem. (I am adding a "x" on it cause it's easier for me to interrupt. But means the same as yours.)

"10 less than a number x"

10 - x

"10 is less than a number x"

10 < x

Answer:

663.

Step-by-step explanation:

Answer:The boat is traveling at a rate of 3 ft/s.

Step-by-step explanation:

The perimeter of ΔAEB is 18.5 feet.

A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.

As,  side AB║DF hence we will use Triangle Proportionality theorem to calculate the length of side AE.

Since, AE/AD = EB/ BF

AE/2 = 7.2/8.4

AE = 6.5 feet

So, the perimeter of ΔAEB is

= AE + EB + BE

=6.5+4.2+7.8

=18.5 ft.  

Hence, the perimeter  is 18.5 feet.

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The correct answer is A. True

A linear equation represents a line in the xy-plane. In the form of y = mx + b, where m is the slope and b is the y-intercept, a linear equation defines a straight line relationship between x and y. Each x value corresponds to a unique y value on the line.

By plotting the points that satisfy the equation, a line can be formed. The slope determines the steepness or direction of the line, while the y-intercept represents the point where the line intersects the y-axis.

Therefore, a linear equation does determine a line in the xy-plane.

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True. A linear equation determines a line in the xy-plane.

A linear equation is an equation that describes a straight line in the xy-plane. It is an equation of the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. The slope-intercept form of a linear equation is commonly used to graph lines.

The equation y = mx + b shows that for every value of x, there is a corresponding value of y that lies on the line. The slope, m, determines the steepness of the line, while the y-intercept, b, represents the point where the line crosses the y-axis.

Therefore, it is true that a linear equation determines a line in the xy-plane.

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Answer:

  -43

Step-by-step explanation:

The additive inverse of 43 is its opposite, -43.

The sum of a number and its additive inverse is the additive identity element:

  43 + (-43) = 0

1 1/2 can be split apart into 1 as the whole part and 3/2 as the fractional part.

To split apart the mixed number 1 1/2 into its whole part and fractional part, we need to understand the components of a mixed number.

A mixed number consists of a whole number part and a fractional part. In this case, 1 1/2 is a mixed number where 1 is the whole number part and 1/2 is the fractional part.

To separate the whole part and fractional part, we can rewrite the mixed number as an improper fraction.

The whole number part, 1, can be written as a fraction with a denominator of 1:

1 = 1/1

Now, let's convert the fractional part, 1/2, into an improper fraction. To do this, we multiply the whole number part, 1, by the denominator of the fraction and add the numerator:

1 x 2 + 1 = 2 + 1 = 3

The improper fraction is 3/2.

So, we have the whole part as 1 and the fractional part as 3/2.

It's worth noting that the whole part represents the whole number portion of the mixed number, while the fractional part represents the remaining portion of the number that is less than a whole unit.

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==================================================

Explanation:

Use the slope formula to find the slope of line E

m = (y2-y1)/(x2-x1)

m = (10-8)/(4-7)

m = 2/(-3)

m = -2/3

The slope of line E is -2/3

The slope of line F is also -2/3 since parallel lines have equal slopes but different y intercepts.

Answer:

approx. 0.083 m/s

Step-by-step explanation:

Velocity * Time = Distance

Velocity = Distance/Time

Our change in position, our distance, over 60 seconds is 5 meters.

Distance: 5 meters

Time: 60 seconds

Velocity = 5/60 = 0.083333...

Answer: approx. 0.083 m/s

Answer:

Number of sundaes = 36

Number of banana split = 28

Step-by-step explanation:

On that day, let the number of sundaes sold be x

Now, since they sold 8 more sundaes than banana, the number of bananas sold is x-8

So the cost of sundaes sold will be 2 * x = 2x

the total cost of banana splits sold will be 3(x-8) = 3x -24

The addition of both equals 156

Hence;

2x + 3x-24 = 156

5x -24 = 156

5x = 156 + 24

5x = 180

x = 180/5

x = 36

So

number of sundaes sold is 36 while the number of bananas split sold is 36-8 = 28

None of the given options matches this general solution, so the answer is E. None of the options.

To solve the given ordinary differential equation:

y'' + 2y' + 5y = e^t sin(t)

We first find the characteristic equation:

r^2 + 2r + 5 = 0

Using the quadratic formula, we find the roots to be:

r = (-2 ± sqrt(4 - 4(1)(5))) / 2

r = -1 ± 2i

The characteristic equation has complex roots, so the general solution is:

y(t) = e^(-t)(Acos(2t) + Bsin(2t))

Next, we find the particular solution by guessing a solution of the form:

y_p(t) = Ae^t sin(t) + Be^t cos(t)

Taking the first and second derivatives, we get:

y_p'(t) = Ae^t sin(t) + Ae^t cos(t) + Be^t sin(t) - Be^t cos(t)

y_p''(t) = 2Ae^t cos(t) - 2Be^t sin(t)

Substituting these expressions into the original equation and simplifying, we get:

(2A - B) e^t sin(t) + (-2B - A) e^t cos(t) = e^t sin(t)

We need the coefficients of e^t sin(t) and e^t cos(t) to be equal to 1 and 0, respectively, in order to obtain a particular solution. This gives us the system of equations:

2A - B = 1

-2B - A = 0

Solving for A and B, we get:

A = 1/5

B = -2/5

Therefore, the particular solution is:

y_p(t) = (1/5) e^t sin(t) - (2/5) e^t cos(t)

The general solution is then the sum of the homogeneous and particular solutions:

y(t) = e^(-t)(Acos(2t) + Bsin(2t)) + (1/5) e^t sin(t) - (2/5) e^t cos(t)

To solve for the constants A and B using the initial conditions, we can substitute y(0) = 0 and y'(0) = 1 into the general solution and solve the resulting system of equations. However, since the question asks us to avoid solving for the constants, we can simply write the general solution as:

y(t) = e^(-t)(Acos(2t) + Bsin(2t)) + e^t (Csin(t) + Dcos(t))

where A, B, C, and D  are constants that we do not need to solve for.

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The most appropriate choice for matrices will be given by-

Required Equation

\(y = 2x^2 - 3x + 1\)

What are matrices?

If the numbers are arranged in the form of rows and columns, then the arrangement is called matrix.

Here,

The equation is \(y =Ax^2 + Bx + C\)

The function contains the points (0, 1), (-2, 15), (3,10).

On putting these coordinates in the equation,

C = 1

\(15 = A(-2)^2 + B(-2) + 1\\4A - 2B = 15-1\\2(2A - B ) =14\\2A - B = \frac{14}{2}\\2A -B = 7\)................ (1)

\(10 = A(3)^2 + B(3) + 1\\9A + 3B = 10-1\\3(3A + B ) =9\\3A + B =\frac{9}{3}\\3A + B = 3\).................... (2)

Here matrix method will be used

Let

\(P = \begin{bmatrix} 2 & -1\\ 3 & 1 \end{bmatrix}\), \(Q = \begin{bmatrix} x \\ y\end{bmatrix}\), \(R = \begin{bmatrix} 7\\3 \end{bmatrix}\)

PQ = R

\(Q = P^{-1}R\)

Adjoint P =

\(\begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}^T\\\\\begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix}\)

Det P = \(\begin{vmatrix} 2 & -1\\3&1\end{vmatrix}\)

          = \(2\times 1 - 3 \times (-1)\\5\)

\(P^{-1} = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}\)

\(Q = \frac{1}{5}\begin{bmatrix} 1 & 1\\-3 &2\end{bmatrix}\begin{bmatrix}7\\3\end{bmatrix}\)

\(Q = \frac{1}{5}\begin{bmatrix} 10\\-15\end{bmatrix}\\Q= \begin{bmatrix} 2\\-3\end{bmatrix}\)

A = 2, B = -3

Required Equation

\(y = 2x^2 - 3x + 1\)

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Complete Question

Use matrices to write the equation of the function in the form \(y = Ax^2 + Bx + C\)that contains the points (0, 1), (-2, 15), (3,10).

The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.

Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.

Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.

All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).

The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.

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Answer:

LMJ and NMO

Step-by-step explanation:

Think of it as an X, top and bottom are vertical, and so are both sides together.

Answer:

LKJ and NMO

Step-by-step explanation:

Vertical angles are formed from the same lines and are opposite each other

LKJ and NMO are formed from the same lines and are opposite each other

Answer:

Irrational

Step-by-step explanation:

Not repeating

A probability model gives information about the likelihood of different outcomes of a random event or experiment.

A probability model is a mathematical tool used to describe the likelihood of different outcomes in a random event or experiment. It provides information about the distribution of probabilities associated with the different possible outcomes, and can be used to make predictions about the likelihood of specific events occurring.

Probability models can be simple or complex, depending on the nature of the event or experiment being modeled, and can be used to make predictions in a wide range of fields, from finance to physics. By providing a framework for understanding the distribution of probabilities associated with different outcomes, probability models allow us to make informed decisions and assess risk in a variety of contexts.

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Answer:

£84.5

Step-by-step explanation:

Given ratio = 2:5:6

Amount that Louis got from the total amount = £39

Step 1: Add the ratio together

2+5+6=13

Step 2: covert the given ratio into fraction

George ratio=2/13

Charlotte ratio=5/13

Louis ratio= 6/13

✓LET THE AMOUNT THAT WAS SHARED AMONG THEM= Y

But we know that Louis got £39, then we can compute How much did they shared using "Louiz" shrare as

Louis ratio= 6/13 × Y= £39

= 6Y/13 = 39

Cross multiply

13×39= 6Y

507= 6Y

Y= 84.5

Hence, the amount they shared was £84.5

Note that  the x-values where the height of the tunnel is zero feet are x = -6 and x = 6.  See the graph attached.

To find the x-value where the height of the tunnel is a maximum, we can use the   fact that the maximum point of a quadratic function occurs at its vertex.

The vertex of the equation y = -x² + 36 corresponds to the maximum height of the tunnel.

The x-coordinate of the vertex can be found using the formula

x = -b / (2a),

where the quadratic equation is in the form

y = ax² + bx + c.

In  our case, a = -1 and b = 0, so the x-coordinate of the vertex is

x = - 0 / (2 * (-1))

= 0.

Height of Zero

To find the x-values where the height of the tunnel is zero feet, we can set the equation y = -x^2 + 36 equal to zero and solve for x.

-x² + 36 = 0

x² = 36

= ±√36 hence,

x = ±6

By plotting these points on the graph, you will have the points    where the height of the tunnel is a  maximum ( 0, maximum height) and where the height of the tunnel is zero (- 6, 0) and (6, 0).

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Answer:

894.14 mm^2.

Step-by-step explanation:

i did this.

Answer:

What are the bases and heights?

It doesnt make sense because i got 104 but thats not one of the options.

Answer:

$292.74 :)

Step-by-step explenation

i searchd it

~inequality

3(8 - 4x) < 6(x - 5)

= 24 - 12x < 6x - 30

= -12x - 6x < - 30 - 24

= -18x < - 54

= x > 3 ✔️

~ nice to help you ^^

Answer:

50

Step-by-step explanation:

................

..............

Answer:

13 dog's and 6 children

Step-by-step explanation: