Is 3 a solution of 2n - 6 = 5n - 15

The vertex is [tex](-1,1)[/tex]

Explanation:

The equation is [tex]f(x)=2x^{2} +4x+3[/tex]

To find the vertex, we need the equation in the form of [tex]f(x)=a (x-h)^{2}+k[/tex]

Dividing each term by 2 in the equation [tex]f(x)=2x^{2} +4x+3[/tex]

[tex]f(x)=2(x^{2} +2x+\frac{3}{2} )[/tex]

Now, completing the square by adding and subtracting 1, we get,

[tex]f(x)=2(x^{2} +2x+1-1+\frac{3}{2} )[/tex]

The first three terms can be written as [tex](x+1)^{2}[/tex],

[tex]f(x)=2[(x+1)^{2}+\frac{1}{2} ][/tex]

Multiplying 2 into the bracket, we get,

[tex]f(x)=2(x+1)^{2} +1[/tex]

This equation is of the form [tex]f(x)=a (x-h)^{2}+k[/tex]

Now, we shall find the vertex [tex](h,k)[/tex]

Thus, [tex]h=-1[/tex] and [tex]k=1[/tex]

Thus, the vertex is [tex](-1,1)[/tex]

Answer:

Step-by-step explanation:

Horizontal

Answer:

slope = 0

Step-by-step explanation:

A horizontal line is parallel to the x- axis.

Since the x- axis has a slope of zero then the slope of a horizontal line is 0

Answer: 1) 56 cents. 2) 30 CDs

Step-by-step explanation:

1.68 ÷ 3 = 56 cents

60 x 7 = $420

$420/ 14 = 30 CDs

The price per ounce of tomato sauce is 56 cents. Edward can buy 30 CDs for $14 each with the same amount that would buy 60 CDs for $7 each.

To calculate the price per ounce, we take the total cost of the can in cents, which is $1.68 or 168 cents, and divide it by the number of ounces, which is 3 ounces. Thus, the price per ounce is: 168 cents / 3 ounces = 56 cents per ounce.

Edward wants to spend the same amount to buy CDs at $14 each as he would buying 60 CDs at $7 each. The total cost for 60 CDs at $7 each is: 60 CDs x $7/CD = $420. We divide this total cost by the price of one CD at $14: $420 / $14/CD = 30 CDs. Therefore, Edward can buy 30 CDs for $14 each with the same amount of money.

Answer:

width: 7 cm

length: 56 cm

Step-by-step explanation:

Let:

x=width

8x=length

P=2l+2w

126=2x + 2(8x)

126=2x+16x

18x=126

x=7

width: 7 cm

length: 56 cm

hope this helps!!

Answer:

Each side of the frame is 12.35 centimeters long.

Answer:

  Emma

Step-by-step explanation:

Emma ran (3 1/2)×(1000 m) = 3500 m compared to Grace's 380 m. 3500 m is farther, so Emma ran farther.

Final answer:

The pencil is 11 centimeters shorter now than when it was new, which is determined by subtracting the current length (8 centimeters) from the original length (19 centimeters).

Explanation:

The subject of this question is Mathematics. The question involves calculating the length by which a pencil has become shorter, which is a basic arithmetic problem dealing with subtraction.

To find how much shorter the pencil is now compared to when it was new, we subtract the current length of the pencil from its original length. Given that the new pencil was 19 centimeters long and now measures 8 centimeters, the calculation would be:

Original length - Current length = Length difference

19 cm - 8 cm = 11 cm

Therefore, the pencil is 11 centimeters shorter now than when it was new.

The unit of measurement is particularly important here to provide clarity and accuracy to the measurement. For example, while measuring the length of a classroom, you might use meters or feet, but for small objects like a pencil, centimeters or inches are more appropriate.

Answer:

28) 120 x 20y

30) 3w x 36

Step-by-step explanation:

28) 20 x (6 x y)

20 x 6 = 120

y x 20 = 20 y

120 x 20y

30) (w x 12) x 3

3 x w = 3w

12 x 3 = 36

3w x 36

Answer:

120 x 20y               3w x 36

Step-by-step explanation:

Distributive Property

Answer:

36 apples

Step-by-step explanation:

First, divide 72 by 6 to find out how many apples are in 1 basket.(Answer 12)

There will be 12 apples in one basket.

Mrs. Doolan wants 3 baskets so multiply 12 by 3 to get 36.

72/6= 12

12X3=36

Answer:36 apples

Step-by-step explanation: dividing that will each be 12 apples in a basket. mrs. doolan will recieve three baskets so 12x3. that will equal 36

The length of ladder is 17 feet

Solution:

Given that, ladder touches a wall 15 ft off the ground, and the base of the ladder is 8 feet from the base of the wall

To find: length of ladder

The ladder, wall and ground forms a right angled triangle

Where, ladder is "hypotenuse" and "ground' forms the base

The figure is attached below

ABC is a right angled triangle

AC = length of ladder = ?

AB = height of wall = 15 feet

BC = distance between base of ladder and base of wall = 8 feet

Apply pythogoras theorem for right angled triangle

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above theorem,

[tex]AC^2 = AB^2+BC^2[/tex]

Substituting the values we get,

[tex]AC^2 = 15^2 + 8^2\\\\AC^2 = 225 + 64\\\\AC^2 = 289\\\\\text{Take square root on both sides }\\\\AC = \sqrt{289}\\\\AC = 17[/tex]

Thus length of ladder is 17 feet

Answer:

56x² + 6x - 36

Step-by-step explanation:

(8x-6)(7x+6) = 8x*(7x + 6) - 6*(7x + 6)

= 8x*7x + 8x*6 - 6*7x - 6*6

=56x² + 48x - 42x - 36

= 56x² + 6x - 36

Answer:

The ratio of food costs to take home is 1 : 6.

Step-by-step explanation:

Given:

Carol's monthly take home pay is 1500$. She spends $250 a month on food.

Now, to find the ratio of food costs to take home pay.

Take home pay = $1500.

Cost of food = $250.

So, getting the ratio:

Cost of food : take home pay

$250 : $1500

[tex]=\frac{250}{1500}[/tex]

[tex]=\frac{1}{6}[/tex]

[tex]=1:6[/tex]

Therefore, the ratio of food costs to take home is 1 : 6.

Final answer:

Carol's food costs to take home pay ratio is 1:6, meaning for every six dollars she takes home, she spends one dollar on food.

Explanation:

To calculate the ratio of Carol's food costs to her take home pay, we compare the amount she spends on food to her total monthly take home pay. This can be represented by the ratio 250:1500 or simplified by dividing both numbers by the common factor of 250, which results in the simplified ratio of 1:6. Hence, for every dollar Carol takes home, she spends about one-sixth of it on food.

Answer:

The graph is attached.

Step-by-step explanation:

The graph of the line with the slope [tex]m[/tex] and the y-intercept [tex]b[/tex], has the form

[tex]y=mx+b[/tex]

In our case the rate of change [tex]m[/tex] is [tex]0.4[/tex]; therefore we have the equation

[tex]y=0.4x[/tex]

The graph of which is attached.

P.S: we have set [tex]b=0[/tex]  by default, because we are not given any information for it.

The line that represents a proportional relationship between y and x where the unit rate of change (or slope) is 0.4 can be plotted on a graph. Start from the origin and for each increase of 1 in x, y increases by 0.4. Plot these points and draw a straight line which represents this proportional relationship.

To graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4, you can start by creating a plot with an x- and y-axis. The y-axis represents the dependent variable and the x-axis represents the independent variable.

In this case, we're looking at a linear relationship, which means the line produced on the graph will be straight. This kind of straight-line graph typically uses the equation y = mx, where m is the slope (or unit rate of change) and x is the independent variable.

For this graph, the slope or unit rate of change is 0.4. This means that with every increase of 1 in x, y increases by 0.4. Plot some points on the graph starting from the origin (0,0). If x is 1, y will be 0.4 (1*0.4). If x is 2, y will be 0.8 (2*0.4). Keep plotting these points and connect them to draw the line. This line demonstrates the proportional relationship between x and y.

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Answer:

The correct answer is D. 30°, 60°, 90°; 1,  √3, 2

Step-by-step explanation:

Let's find out the solution to this question:

Arc cos (β) = √3/2 = 1.732/2 = 0.866

β = 30°

Let's recall that the ratio of the sides of a triangle 90 - 60 - 30 is:

1 : 2 : √3

β = 30°, α = 60°, r = 2, h = 1, k = √3

The correct answer is D. 30°, 60°, 90°; 1,  √3, 2

[tex]\frac{8}{35}[/tex] of all claims were paid in the second month.

Step-by-step explanation:

Step 1; In the first month [tex]\frac{3}{7}[/tex] of all expenses were paid. So to find the expenses that were not paid in the first month we subtract [tex]\frac{3}{7}[/tex] from 1 i.e. 1-[tex]\frac{3}{7}[/tex]= [tex]\frac{4}{7}[/tex]. So in the first month  [tex]\frac{4}{7}[/tex] of total expenses were not paid.

Step 2; In the second month [tex]\frac{2}{5}[/tex] of the remaining claims were paid i.e. [tex]\frac{2}{5}[/tex] of the remaining claims which is  [tex]\frac{4}{7}[/tex] of the total claims. So to find out the number of claims paid in the second month it's just a case of multiplying [tex]\frac{2}{5}[/tex] with [tex]\frac{4}{7}[/tex].

Fraction of all claims paid in second month = [tex]\frac{2}{5}[/tex]  * [tex]\frac{4}{7}[/tex]= [tex]\frac{8}{35}[/tex].

Example; If $ 70,000 was the total claim amount, [tex]\frac{3}{7}[/tex] of that which equals $30,000 was paid in the first month. So $40,000 was still to be paid. In the second month [tex]\frac{2}{5}[/tex] of $40,000 was paid which equals $16,000 paid in the second month which is [tex]\frac{8}{35}[/tex] of total claims i.e. $70,000

Answer:

159n - 43

Step-by-step explanation:

Write as an equation

159 * n - 43

Multiply

159n - 43

Hope this helps :)

Answer:

A force is a vector quantity. As learned in an earlier unit, a vector quantity is a quantity that has both magnitude and direction. To fully describe the force acting upon an object, you must describe both the magnitude (size or numerical value) and the direction.

Step-by-step explanation:

Answer:

The height of the triangle is: [tex]H = (5x^2 + x +3)[/tex]

Step-by-step explanation:

Here, the area the triangle  is given as: [tex]15x^4 + 3x^3 + 4x^2 - x - 3[/tex]

Also, base of the triangle  = [tex](6x^2 -2)[/tex]

Let us assume the height of the triangle = H units

Now, AREA of TRIANGLE =  [tex]\frac{1}{2} \times B \times H[/tex]

[tex]\implies (15x^4+3x^3+4x^2-x-3 ) = \frac{1}{2} \times ( 6x^2-2) \times H\\\implies H =\frac{ (15x^4+3x^3+4x^2-x-3 )}{(3x^2-1)}[/tex]

Solving by LONG DIVISION, we get:

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

Hence, the height of the triangle is: [tex]H = (5x^2 + x +3)[/tex]

Margot needs 3/4 pounds of turkey to make 1 liter of turkey chili. To make 4 liters of turkey chili, which is 4 times the recipe, she will need 3 pounds of turkey.

Margot used 1/2 pound of turkey to make 2/3 liters of turkey chili. To find out how much turkey she will need for 4 liters of turkey chili (4 times the 1-liter recipe), we need to calculate the amount of turkey needed per liter first and then multiply it by 4.

First, we determine the amount of turkey needed for 1 liter by setting up a proportion. Since 1/2 pound of turkey makes 2/3 liters, we have:

1/2 pound / (2/3) liter = x pounds / 1 liter

By cross-multiplication, we find that x = (1/2) * (3/2) = 3/4. Therefore, Margot needs 3/4 pounds of turkey for 1 liter of chili.

To make 4 times the recipe, or 4 liters, Margot will need 4 * 3/4 pounds of turkey = 3 pounds of turkey.

Answer:

[tex]p(Not\ 5) = \frac{8}{9}[/tex]

Step-by-step explanation:

Given:

Txo six-sided dice are rolled.

Total number of outcomes n(S) = 36

We need to find the probability that the sum is not equal to 5 p(Not 5).

Solution:

Using probability formula.

[tex]P(E)=\frac{n(E)}{n(S)}[/tex]  ----------------(1)

Where:

n(E) is the number of outcomes favourable to E.

n(S) is the total number of equally likely outcomes.

The sum of two six-sided dice roll outcome is equal to 5 as.

Outcome as 5: {(1,4), (2,3), (3,2), (4,1)}

So, the total favourable events n(E) = 4

Now, we substitute n(E) and n(s) in equation 1.

[tex]P(5)=\frac{4}{36}[/tex]

[tex]p(5) = \frac{1}{9}[/tex]

Using formula.

[tex]p(Not\ E) + p(E) = 1[/tex]

[tex]p(Not\ 5) + p(5) = 1[/tex]

Now we substitute p(5) in above equation.

[tex]p(Not\ 5) + \frac{1}{9} = 1[/tex]

[tex]p(Not\ 5) = 1-\frac{1}{9}[/tex]

[tex]p(Not\ 5) = \frac{9-1}{9}[/tex]

[tex]p(Not\ 5) = \frac{8}{9}[/tex]

Therefore, the sum of two six-sided dice roll outcome is not equal to 5.

[tex]p(Not\ 5) = \frac{8}{9}[/tex]

Answer:

F(a) =2a^2+4a+5

Step-by-step explanation:

just put x= a

The probability of getting the number 4 and the multiple of 5 is 1 / 4.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that an adventure game has a number cube with 12 equal-size faces. Each face is labelled with a number from 1 to 12.

The probability will be calculated as:-

Number of favourable outcomes = { 4, 5 , 10 } = 3

Number of samples = 12

Probability = 3 / 12

Probability  = 1 / 4

Therefore, the probability of getting the number 4 and the multiple of 5 is 1 / 4.

To know more about probability follow

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[tex]\dotfill[/tex]

To find the value of the given function, substitute x = 12 instead of x and evaluate.

Given function:

[tex]\sf f(x)=\cfrac{2}{3} x+14[/tex]

Substitute 12 for x:

[tex]\sf f(12)=\cfrac{2}{3}\times12+14[/tex]

Convert 12 to a fraction to make multiplying easier:

[tex]\sf f(12)=\cfrac{2}{3}\times\cfrac{12}{1}+14[/tex]

[tex]\sf f(12)=\cfrac{2\times12}{3\times1}+14[/tex]

[tex]\sf f(12)=\cfrac{24}{3}[/tex]

[tex]\sf f(12)=8[/tex]

>>> Therefore, the value of the function is 8.

The value of  [tex]\( f(x) = \frac{2}{3}x + 14 \)[/tex] is 22.

To find the value of f(12), you simply need to substitute (x = 12) into the function f(x) and evaluate it:

Given: [tex]\( f(x) = \frac{2}{3}x + 14 \)[/tex]

Substituting x = 12:

[tex]\[ f(12) = \frac{2}{3} \times 12 + 14 \][/tex]

Now, let's calculate:

[tex]\[ f(12) = \frac{2}{3} \times 12 + 14 \]\[ = \frac{2}{3} \times 12 + 14 \]\[ = 8 + 14 \]\[ = 22 \][/tex]

So, [tex]\( f(12) = 22 \)[/tex].

Theorem .

Basically you already know this, and it can also be proven.

Answer:

- 6

Step-by-step explanation:

its negative so I divided —12 by 2 to get -6 also You have to get the F by itself so you have to divide the sides by 2 but bringing the negative is important

Answer:

  t = 36

Step-by-step explanation:

If one of the roots is "a", the equation can be factored as ...

  (5x -a)(x -a) = 0

  5x^2 -6ax +a^2 = 0

Comparing terms to the given equation, we see that ...

  -6ax = -36x

  a = 6 . . . . . . . . divide by -6

Then ...

  a^2 = t

  36 = t . . . . . . . substitute 6 for a

_____

The roots are 6 and 6/5.

Answer:

[tex]42x + 49 \\ = 7(6x + 7)[/tex]

hope this helps..!

Answer:

A

Step-by-step explanation:

The interval of 0-19 will increase by 20 of either Hay Bale Toss or Pie Eating Contest.

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.

Given that, a class of 20 students is visiting the fair today. Each student is 16 years old or younger and will participate in either the Pie Eating Contest or the Chili Cookoff.

Number of students visiting the fair = 20

Age group = 0-16

In the histogram, this age group falls in the first interval which is 0-19.

If all 20 students joined the Hay Bale Toss then the bar of 0-19 of Hay Bale Toss will increase from 40 to 60 and the graph of Pie Eating Contest will remain the same.

If all 20 students joined the Pie Eating Contest then the bar of 0-19 of Hay Bale Toss will increase from 20 to 40 and the graph of Hay Bale Toss will remain the same.

Therefore, only one if the graph's interval of 0-19 will increase by 20 whereas the other graph would remain the same.

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This is a combinatorial geometry problem involving the probability of forming a triangle with an integer area from randomly selected lattice points within a square grid. It requires analyzing the properties of lattice point triangles and applying combinatorial mathematics.

The problem given discusses the selection of random points within a square on a coordinate system to form a triangle, and it questions the probability of the triangle's area being an integer. This involves combinatorics, geometry, and number theory within the field of mathematics. To approach the problem of calculating the probability that the area is an integer, one must consider the distribution of lattice points and use combinatorial analysis.

Area of a triangle with vertices at lattice points can be expressed using the formula derived from the determinant of a matrix. The triangle's area, if non-degenerate, can be half of the odd integer, which upon doubling to remove the half, leaves an integer area. Thus, the problem reduces to a combinatorial question concerning lattice points, selected at random, and forming a triangle whose twice the area is an odd integer.

However, a direct count of the favorable vs. total possibilities may be complex due to the large number of possible point combinations and the chance of degenerate triangles (where the area is zero). Thus, a systematic probabilistic and combinatorial approach is necessary to resolve this question, likely involving a careful analysis of the geometric configurations and properties of integer triangles on a lattice grid.

Answer:

45

Step-by-step explanation:

The sum of angle in a straight line is 180

=> 3n + (4n - 15) + 90 = 180

3n + 4n + 75 = 180

7n = 180 - 75 = 105

n = 15

Angle ZLQK = 4n - 15 = 4*15 - 15 = 60 - 15 = 45