Find the area of the triangle below. Be sure to include the correct unit in your answer.​

6a. The equation for the graph is y = 2√(x + 5).

6b. The equation for the graph is y = -|x + 1| + 5

In Mathematics and Geometry, the standard form of a square root function can be modeled as follows;

y = a√(x - h) + k

Part 6a.

Next, we would determine value of a as follows;

4 = a√(-1 + 5) + 0

4 = a√4

4 = 2a

a = 2

Therefore, the required square root function is given by;

y = 2√(x + 5)

Part 6b.

Since the line representing the absolute value function has a y-intercept at (0, 4) and vertex at (-1, 5), the absolute value equation for the graph is given by:

y = a|x - h| + k

y = -|x + 1| + 5

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Answer:

Option D

Hope this helps!

Answer: A

Step-by-step explanation: just took the test

The solution of the system of equations would be = y= 16.4, X = 6.76

The substitution method of solving equation is defined as the method whereby a known value is substituted into an equation to find the value of the unknown.

The given equations are as follows:

-8x + 4y = -8 ---> equation 1

5x - 2y = 1 --->. equation 2

From equation 2 make X the subject of formula;

x = 1 + 2y/5

Substitute X = 1 + 2y/5 into equation 1

-8 ( 1 + 2y/5) + 4y = -8

-8 + 16y/40 + 4y = -8

-8 +16y + 4y = 40×-8

-8 + 20y = -320

20y = -320+8

y = 328/20

y = 16.4

Substitute y = 16.4 into equation 2 to find X.

5x - 2(16.4) = 1

5x - 32.8 = 1

5x = 33.8

X = 33.8/5

X = 6.76

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Answer:

29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

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

We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.

Answer:The symbolism of angel number 1119 is usually related to generosity. It means that you may be a very generous person, but there are people who are ready to abuse your generosity. Angel number 1119 is warning you to be careful because not all people around you have good intentions.

Step-by-step explanation:

The values of x and y are -12.5  and  -5.5  respectively

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

-2x+4y=3 -----(1)

c--------(2)

(1)=> 4y = 3 +2x

         y= 3/4 + (1/2)x

(2) => 3x-7 ( 3/4 + (1/2)x  ) =1

         3x - 21/4 - (7/2)x = 1

        (-1/2)x = 1+ 21/4 = 25/4

=> x= -50/4 = -12.5

y= 0.75 +0.5(-12.5) = 0.75 - 6.25 = -5.5

The values of x and y are -12.5  and  -5.5  respectively

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Answer:

8/4

Step-by-step explanation:

to do slope is y2 - y1 over x2 - x1, so it would be 11 - 3 for 8, then 6 - 2, leaving 8/4.

The slope of the line passing through the points A ( 2 , 3 ) and B ( 6 , 11 ) is Option A . 8/4

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the two points be A and B , where

A ( x₁ , y₁ ) = A ( 2 , 3 )

B ( x₂ , y₂ ) = B ( 6 , 11 )

Let the slope of the line be m

Now , the slope of the line passing through two points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values of x₁ , y₁ , x₂ and y₂  in the above equation we get

Slope m = ( 11 - 3 ) / ( 6 - 4 )

Slope m = 8 / 4

Hence , the slope of the line passing through the points

A ( 2 , 3 ) and B ( 6 , 11 ) is 8/4

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hello

to solve this question, we need to plot the graph of this equation

Answer:

Answer: There is 1 1/2 times more juice than ginger ale; there is 2/3 as much ginger ale as there is punch.

Step-by-step explanation:

Answer:

Answer A:

Step-by-step explanation:

2 parts ginger ale to 3 parts raspberry juice.

Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

64 decrease by twice the number then the algebraic expression be

64 - 2m.

The algebraic expression exists acquired by a finite number of the fundamental functions of algebra upon characters expressing numbers. Algebraic expressions contain at least one variable and at least one operation (addition, subtraction, multiplication, division).

From the given information, we get

Let, Matt's savings be denoted by the variable m.

Twice the number be 2m.

64 decrease by twice the digit then the algebraic expression be 64-2w.

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Answer:

x = 2 I hope this helped you :)

\( \qquad \qquad\qquad\large\overbrace{\underbrace{\underline{ \boxed{ \sf \:Aƞsweɾ }}}}\)

Let's solve ~

\(\qquad \sf  \dashrightarrow \: 5(4 - 3x) = - 10\)

\(\qquad \sf  \dashrightarrow \: 20- 15x = - 10\)

\(\qquad \sf  \dashrightarrow \: - 15x = - 10 - 20\)

\(\qquad \sf  \dashrightarrow \: - 15x = - 30\)

\(\qquad \sf  \dashrightarrow \: x = - 30 \div ( - 15)\)

\(\qquad \sf  \dashrightarrow \: x = 2\)

Therefore, the value of x is 2

Answer:

y = $11.25 and (5, $11.25)

Step-by-step explanation:

x = # of videos

y = total monthly cost

5 videos:

y = $1.25(5) + $5.00

y = $6.25 + $5

y = $11.25

Ordered pair:

x = 5

y = $11.25

(5, $11.25)

The polynomial\(1-x x^2-x^3 \ x^{16}-x^{17}\) can be written in the form \(a0 + a1(x+1) + a2(x+1)^2 + ... + a16(x+1)^{16} + a17(x+1)^{17}\) where y = x + 1 and a1's are constants.

a polynomial can be written in the form

\(a0 + a1x + a2x^2 + a3x^3 + ... + anx^n\)

where a0, a1, a2, ..., an are constants (also known as coefficients) and x is the variable.

In this case, we are given a polynomial in the form \(1-x x^2-x^3 \ x^{16}-x^{17}\) and we want to express it in the form \(a0 + a1y + a2y^2 + ... + a17y^{17}\), where y = x + 1 and a1's are constants.

By substituting y = x + 1 into the polynomial, we get:

\(1 - (x + 1) + (x + 1)^2 - (x + 1)^3 + ... + (x + 1)^{16} - (x + 1)^{17}\)

Each term in this polynomial is a function of y, which is in turn a function of x.

We can then match the coefficients a0, a1, a2, ..., a17 with the corresponding powers of y in the polynomial, i.e, a0 = 1, a1 = -1, a2 = -1, a3 = 0, ..., a16 = -1, a17 = -1, and we get the polynomial

It's important to note that the value of a1's are constants, meaning that they are not dependent on the variable x.

Did you mean: The polynomial \(1-x x^2-x^3 \ x^{16}-x^{17}\) may be written in the form \(a 0 a 1y a 2y^2 \a {16}y^{16} a {17}y^{17}\), where y = x + 1 and a1's are constants?

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The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08

Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.

Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\)  2. 2\(x^{0}\)\(y^{-2}\)

Expression for x =2 and y=5

-4x-2 + 3y0

= -4(2)-2 + 3(5)0

= 16+3

=19

Now

2x0y-2

= 2(2)0x(5)-2

= 2 x (1/25)

= 2 x 0.04

= 0.08

Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08

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Answer:

Slope: 1/2

y-intercept: (0, 4.5)

Slope Intercept = y = mx + b

Slope Intercept = y = 1/2x + 4.5

Step-by-step explanation:

The slope is 1/2 based on our rule, "Rise over Run" Based on the two points listed on the graph, we can say that we "rise" once and "run" twice. This makes our slope 1/2.

The y-intercept is where the line crosses the y-axis. If use our slope, we can determine that if we "rise" half of our slope in the opposite direction (0.5) and run half of our run in the opposite direction (1) we will intersect at (0, 4.5).

With this information, we can construct our slope-intercept equation:

The slope-intercept formula is as follows: y = mx + b

m is our slope, and b is out y-intercept.

y = 1/2x + 4.5

The sum of the series b 2 b 4 b 6 b 8 b {10} is \($\dfrac{180}{3}$\) since it is a geometric series with a common ratio of \($\dfrac{7}{4}$\).

Since the given series \($b 1 b 2 b 3 \cdots b {10}$\) has a sum of 180, it can be deduced that the series is a geometric series with a common ratio of\($\dfrac{7}{4}$\). This means that the ratio of any two consecutive terms in the series is a constant, \($\dfrac{7}{4}$\). Therefore, the sum of the series b 2 b 4 b 6 b 8 b {10} can be calculated as follows:

\($S = b2 + b4 + b6 + b8 + b_{10}$\)

\($= b2\left(\dfrac{7}{4}\right)^0 + b2\left(\dfrac{7}{4}\right)^2 + b2\left(\dfrac{7}{4}\right)^4 + b2\left(\dfrac{7}{4}\right)^6 + b2\left(\dfrac{7}{4}\right)^8$\)

\($= b2 \left[1 + \left(\dfrac{7}{4}\right)^2 + \left(\dfrac{7}{4}\right)^4 + \left(\dfrac{7}{4}\right)^6 + \left(\dfrac{7}{4}\right)^8\right]$\)

\($= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{1-\left(\dfrac{7}{4}\right)^2}\right]$\)

\($= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{\dfrac{3}{4}}\right]$\)

\($= \dfrac{4b2}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

Since the sum of the series\($b 1 b 2 b 3 \cdots b {10}$\) is 180, we can substitute $b2$ with \($\dfrac{180}{3}$\)nd calculate the sum of the series $b 2 b 4 b 6 b 8 b {10}$:

\($S = \dfrac{4\left(\dfrac{180}{3}\right)}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

\($= \dfrac{180}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$\)

Therefore, the sum of the series \($b 2 b 4 b 6 b 8 b {10}$ is $\dfrac{180}{3}$\).

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The vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).

A quadratic functiοn is a functiοn οf the fοrm  where a, b, and c are cοnstants, and a is nοt equal tο 0. It is a type οf pοlynοmial functiοn that can be graphed as a parabοla, which is a symmetric curve that οpens either upwards οr dοwnwards.

Given the table οf pοints fοr the cοntinuοus quadratic functiοn h(x), we can find the vertex and range οf the functiοn. Since the functiοn is quadratic and cοntinuοus, it can be represented in the standard fοrm \($f(x)=a(x-h)^{2}+k,$\), where (h, k) is the vertex οf the parabοla.

Tο find the vertex, we can use the fact that the x-cοοrdinate οf the vertex is given by -b/2a, where a and b are the cοefficients οf the quadratic term and the linear term, respectively. In this case, a = 1 (since the functiοn is cοntinuοus and quadratic), and b can be fοund using any twο pοints οn the parabοla:

\(\rm b=(h(x_2)-h(x_1))/(x_2-x1)=(4-7)/(-2+1)=3$\)

Therefοre, the x-cοοrdinate οf the vertex is x = -b/2a = -3/2. Tο find the y-cοοrdinate οf the vertex, we can evaluate the functiοn at this value οf x:

\($\rm h(-3/2)=(1)(-3/2-h)^{2}+k$\)

Tο sοlve fοr k, we can use οne οf the pοints οn the parabοla, say (-6, 12):

\($12=(1)(-6-h)^{2}+k\,$\)

Expanding and simplifying, we get:

\($12=(h-6)^{2}+k$\)

Substituting -3/2 fοr h, we get:

\($\begin{array}{l}{{12=(-(3/2)-6)^{2}+k}}\\\\ {{12=81/4+k}}\\\\ {{k=-21/4}}\end{array}$\)

Therefοre, the vertex οf the parabοla is at the pοint (-3/2, -21/4).

Tο find the range οf the functiοn, we can lοοk at the shape οf the parabοla. Since the cοefficient οf the quadratic term is pοsitive, the parabοla οpens upwards, and the vertex is the lοwest pοint οn the graph. Therefοre, the range οf the functiοn is all real numbers greater than οr equal tο the y-cοοrdinate οf the vertex, which is -21/4. In interval nοtatiοn, we can write the range as (-21/4, infinity).

Hence, the vertex οf the parabοla is at the pοint (-3/2, -21/4) and the range οf the functiοn wοuld be (-21/4, infinity).

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Answer:

btfrt34598fc

Step-by-step explanation:

Answer:

7.50$

Step-by-step explanation:

49.98÷100=0.4998=1%

0.4998×15= 7.497 which is 15%of their bill

The perimeter of the triangle is 30 units

The vertices are (−7,−1), (5,−1), and (5,4).

Start by calculating the distance between the vertices using:

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2\)

So, we have:

\(d1 = \sqrt{(-1 + 1)^2 + (5 + 7)^2\)

d1 = 12

\(d2 = \sqrt{(-1 - 4)^2 + (5 - 5)^2\)

d2 =5

\(d3 = \sqrt{(-1 - 4)^2 + (-7 - 5)^2\)

d3 = 13

The perimeter is then calculated as:

P = d1 + d2 + d3

This gives

P = 12 + 5 + 13

Evaluate

P = 30

Hence, the perimeter of the triangle is 30 units

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Answer:

5040

Step-by-step explanation:

7*6*5*4*3*2*1=5040

The correct number of different 7-person committees that can be made is,

⇒ 5,040

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

7 students from a class of 10 are going to be chosen to be on the dance committee.

Hence, the number of different 7-person committees that can be made is,

⇒ 7!

⇒ 7 × 6 × 5 × 4 × 3 × 2 × 1

⇒ 5,040

Thus, The correct number of different 7-person committees that can be made is,

⇒ 5,040

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Answer:

Step-by-step explanation:

To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction.

How to Convert a Percent to Fraction. Divide the percentage by 100 to get a decimal number. Use that number as the numerator (top) of a fraction. Put a 1 in the denominator (bottom) of the fraction.

Answer:

Imperial Units

155/8 Inches (fraction) 

15.625 Inches 

1.302083 Feet

Metric Units

396.875 Millimeters 

39.6875 Centimeters 

0.396875 Meters

Answer:

B. \( \frac{4}{(d - 6)} \)

Step-by-step explanation:

\( \frac{2d - 6}{d^2 + 2d - 48} \div \frac{d - 3}{2d + 16} \)

Change the operation from ÷ to ×, then flip the fraction by your right upside down.

\( \frac{2d - 6}{d^2 + 2d - 48} \times \frac{2d + 16}{d - 3} \)

\( \frac{2d - 6}{d^2 + 8d - 6d - 48} \times \frac{2d + 16}{d - 3} \)

\( \frac{2(d - 3)}{d(d + 8) - 6(d + 8)} \times \frac{2(d + 8)}{d - 3} \)

\( \frac{2(d - 3)}{(d + 8)(d - 6)} \times \frac{2(d + 8)}{d - 3} \)

\( \frac{2(1)}{(1)(d - 6)} \times \frac{2(1)}{1} \)

\( \frac{2}{(d - 6)} \times \frac{2}{1} \)

\( \frac{2 \times 2}{(d - 6) \times 1} \)

\( \frac{4}{(d - 6)} \)

Thus, after approximately 66 months, Darren will have saved enough money to recover his $20,000 down payment through his monthly savings. The answer is (B) 66 months.

The term "principal" has multiple meanings, depending on the context in which it is used. Here are a few possible definitions:

Principal as a noun refers to the person who holds the highest position or authority within an organization, such as a school principal or a company principal.

Principal can also refer to the original amount of money borrowed or invested, excluding any interest or other charges that may accrue over time.

In the context of finance or investments, principal can refer to the sum of money that is invested or borrowed, on which interest is calculated.

Principal can also be used as an adjective to describe something that is most important or essential, such as the principal reason for a decision or the principal goal of a project.

given by the question.

To determine the monthly mortgage payment, we first need to calculate the principal amount that Darren will be borrowing. He will be borrowing the purchase price of the house ($125,000) minus the down payment he plans to make ($20,000), which is $105,000.

We can then use the formula for calculating the monthly mortgage payment:

M = P [  I \((1 + i)^{n}\)] / [ \((1+i)^{n-1}\)]

where:

M is the monthly mortgage payment

P is the principal amount

I is the monthly interest rate (which is the annual interest rate divided by 12)

n is the total number of payments (which is the number of years multiplied by 12)

In this case, we have:

P = $105,000

I = 5.5% / 12 = 0.00458

n = 30 years x 12 = 360

Plugging in these values, we get:

M = $105,000 [ 0.00458(1 + 360] / [ (1 + 0.00458) ^360 – 1]

M ≈ $596.55

Therefore, Darren's monthly mortgage payment will be approximately $596.55.

The difference between Darren's current rent payment and his mortgage payment will be:

$900 - $596.55 = $303.45

So, Darren plans to save $303.45 per month.

To determine how long it will take for Darren to recover his down payment through his monthly savings, we can set up an equation:

$20,000 / $303.45 per month = 65.8 months

Rounding up to the nearest whole number, we get 66 months.

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The Brady & Matthew Camera Company has recently introduced its latest high-quality digital camera designed for professional use.

1. The Brady & Matthew Camera Company: The company known as Brady & Matthew Camera is the manufacturer of the newly released digital camera.

2. Newest professional quality digital camera: The recently launched camera by Brady & Matthew Camera Company is their latest product in their lineup of professional-grade digital cameras.

3. Features: The new camera is equipped with advanced features that cater to the needs of professional photographers, such as high-resolution image sensors, a wide range of ISO sensitivity, and customizable shooting modes.

4. Image Quality: The camera is designed to deliver exceptional image quality with sharp details, accurate colors, and low noise, ensuring professional-grade results.

5. Durability: The camera is built to withstand the rigors of professional use, featuring a robust body construction and weather sealing to protect against dust and moisture.

6. Ergonomics: Brady & Matthew Camera Company has paid attention to ergonomic design, ensuring that the camera is comfortable to hold and operate for extended periods.

7. Connectivity: The camera is equipped with various connectivity options, including Wi-Fi and Bluetooth, allowing photographers to transfer images wirelessly and control the camera remotely.

8. Accessories: Brady & Matthew Camera Company offers a range of compatible accessories for their new camera, including lenses, external flashes, and battery grips, expanding the capabilities of the camera system.

9. Market Availability: The new professional-quality digital camera by Brady & Matthew Camera Company is now available for purchase from authorized retailers and their official website.

10. Customer Support: The company provides reliable customer support services, including warranty coverage, technical assistance, and firmware updates to ensure a satisfying user experience.

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Answer:

2=x

Step-by-step explanation:

34 = -2 + 9x + 16 + x

+2     +2             add to both sides

36=9x+16+x

36=10x+ 16        simplify

-16        -16         subtract from both sides

20=10x      

/10  /10               divide on both sides

2=x

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