What is negative 1/4 to the 3rd power

The vertex form is [tex]y=(x-1)^{2} -6[/tex]

Step-by-step explanation:

The given equation [tex]y=x^{2} -2x-5[/tex] is a parabola. The vertex of the parabola is of the form [tex]y=ax^{2} +bx+c[/tex]  

The parameters of the parabola are [tex]a=1, b=-2[/tex] and [tex]c=-5[/tex]

The vertex of the x-coordinate is given by [tex]x=\frac{-b}{2a}[/tex]

Thus, substituting the values of a and b in [tex]x=\frac{-b}{2a}[/tex], we get,

[tex]\begin{aligned}x &=\frac{-(-2)}{2(1)} \\&=\frac{2}{2} \\x &=1\end{aligned}[/tex]

Now, substituting [tex]x=1[/tex] in [tex]y=x^{2} -2x-5[/tex], we get,

[tex]\begin{aligned}y &=1^{2}-2(1)-5 \\&=1-2-5 \\y &=-6\end{aligned}[/tex]

Thus, the vertex is [tex](1,-6)[/tex]

The equation of parabola to be in vertex form is [tex]y=a(x-h)^{2} +k[/tex]

where a is the coefficient of [tex]x^{2}[/tex], h is vertex of the x-coordinate and k is the vertex of the y-coordinate.

Hence, [tex]a=1, h=1[/tex] and [tex]k=-6[/tex]

Thus, substituting the values in the equation of the vertex form,

[tex]y=1(x-1)^{2} -6\\y=(x-1)^{2} -6[/tex]

Hence, the vertex form is [tex]y=(x-1)^{2} -6[/tex]

Answer:

1) 5.6 cents

2) 30 cds

Step-by-step explanation:

For both problems we can use the Rule of Three:

1) If 3 ounces of tomato sauce cost [tex]\$1.68[/tex], how many will cost 1 ounce?:

3 oz ---[tex]\$1.68[/tex]

1 oz --- ?

Then:

[tex]?=\frac{(1 oz)(\$1.68)}{3 oz}[/tex]

[tex]?=\$ 0.056[/tex]

This is the price in dollars, now we have to calculate it in cents, taking into account that [tex]100 cent=\$1[/tex]:

[tex]$ 0.056 \frac{100 cent}{\$1}=5.6 cents[/tex]  This is the price in cents of 1 ounce of tomato sauce

2) If Edward buys 60 cds for [tex]\$ 7[/tex] each, what is the cost of 60 cds?:

60 cds ---?

1 cd --- [tex]\$7[/tex]

[tex]?=\frac{(60 cds)(\$7)}{1 cd}[/tex]

[tex]?=\$ 420[/tex] This is what Edward spends in 60 cds for [tex]\$7[/tex] each

Now, we have to calculate how many cds Edward can buy for [tex]\$14[/tex] each and spend the same [tex]\$ 420[/tex]:

1 cd --- [tex]\$14[/tex]

? cds ---[tex]\$ 420[/tex]

[tex]?=frac{(\$ 420)(1 cd)}{\$14}[/tex]

Finally:

[tex]?=30 cds[/tex]

I think it's histograms for the first blank; distribution for the second blank; frequency for the third and final blank.

Hope this helps please let me know if I'm wrong :)))

Histograms show the distribution and frequency for a set of values. Distribution is how the values are spread out or grouped, and frequency is how often a value occurs in a set of numbers.

A frequency distribution is like a detailed count of all the different values or groups of values in a data set. When data are collected, a histogram provides a visual representation of this distribution. The distribution of the data can be divided into various classes or bins, where the count or frequency of data falling into each bin is tallied. This tally helps to visualise patterns such as the center, spread, and overall shape of the data.
The histogram consists of contiguous rectangles, with the height of each bar corresponding to the frequency of data points within that class interval. The horizontal axis (x-axis) typically represents the values or categories of the dataset, while the vertical axis (y-axis) represents the frequency of occurrences. This graphical tool allows us to quickly ascertain which values are more prevalent and identify the spread or variability of the data, as well as the center, which is considered the middle or typical value of the dataset.

Answer:

17

Step-by-step explanation:

The sum of all the angles of this polygon is

(n-2)180

Where m is the number of corners

(5-2)180

3*180

540

Hence

Sum of all angles=540

139+92+71+9x+5x=540

302+14x=540

14x=540-302

14x=238

Dividing both sides by 14

x=17

Answer:

3x-3y+4z+2=0

Step-by-step explanation:

Answer:

3x-3y+4z+2=0

Step-by-step explanation:

Answer: w = 4[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Let the unknown number be w , then

the product of w and 3 = 3w

Nine less than the product of 3 and the number = 3w - 9

completing the equation , we have

3w - 9 = 4

add 9 to both sides

3w = 13

w = 13/3

w = 4[tex]\frac{1}{3}[/tex]

Answer:

The correct answer is C. 3 (-64 ÷ 8) + 25

Step-by-step explanation:

Let's solve the four expressions to find out the positive one, this way:

A. - 4 + (-5) (-6) ÷ (-3)

= -4 + 30 ÷ -3

= - 4 - 10 = - 14

B. 8 [10 ÷ (2) (-2)]

= 8 [10 ÷ -4]

= 8 * - 2.5 = -20

C. 3 ( -64 ÷ 8) + 25

= 3 ( -8) + 25

= - 24 + 25 = 1

D. -2 (-5) (-3) ÷ 10

= - 30 ÷ 10 = -3

As we can see, after solving the four expressions, the only with a positive result is C. 3 ( -64 ÷ 8) + 25

Answer:

The correct option is first one.

Therefore,

[tex]4(-1) = (-1)(4)[/tex] .. illustrates the associative property of multiplication.

Step-by-step explanation:

Associative property:

The associative property states that you can add or multiply regardless of how the numbers are grouped.

For example A x B = B x A

Therefore,

[tex]4(-1) = (-1)(4)[/tex] .. illustrates the associative property of multiplication.

Answer:

Option (-2-1)(8)=-2(1-8) is correct

The expression (-2-1)(8)=-2(1-8) represents the associative property of multiplication .

Step-by-step explanation:

Given expression is (-2-1)(8)=-2(1-8)

Associative property of multiplication is given by

(a+b)c=a(b+c)

Comparing the equations (-2-1)(8)=-2(1-8) and (a+b)c=a(b+c)  we get that the given expression is in the form of (a+b)c=a(b+c)

Therefore the given equation represents the associative property of multiplication .

Therefore option (-2-1)(8)=-2(1-8) is correct

The expression (-2-1)(8)=-2(1-8) represents the associative property of multiplication .

Answer:

a.III

Step-by-step explanation:

We solve for x:

4x > 15

it gives

x > 3.75

Now we have to analyze our choices and see which solutions satisfy this inequality.

[tex]3\frac{1}{2} =3.5[/tex]

is not greater than 3.75; this isn't a solution.

[tex]3\frac{3}{4}=3.75[/tex]

is not greater than 3.75; this isn't a solution.

[tex]4\frac{1}{4}=4.25[/tex]

is greater than 3.75; this is a solution.

Thus only choice III is correct.

Answer:

[tex]FJ=18\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

[tex]\frac{FE}{FH}=\frac{FG}{FJ}[/tex]

we have

[tex]FE=HF+EH=12+8=20\ units[/tex]

[tex]FH=HF=12\ units[/tex]

[tex]FG=30\ units[/tex]

substitute the given values

[tex]\frac{20}{12}=\frac{30}{FJ}[/tex]

[tex]FJ=12(30)/20\\FJ=18\ units[/tex]

[tex]-3-2(5+1)-1-1\\-3-(2)(6)-(1-1)\\-3-12-(1-1)\\15-(1-1)\\15-0\\{Answer=-15 \checkmark[/tex]

Answer:

3x+4=19 x is 5 3(5)=15+4=19

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

let the percent be p

rewriting the expression:

p% of 170 is 34

or mathematically,

p% x 170 = 34

(p / 100) x 170 = 34   (divide both sides by 170)

p/100 = 34/170  (multiply both sides by 100)

p = (34 / 170)  x 100

p = 20

hence 34 is 20% of 170

Answer:

see work attached and shown

Answer:

D. No solution.

Step-by-step explanation:

2x - 3 = 2x - 5

2x - 2x - 3 = 2x - 2x - 5

-3 = -5   which is absurd so there is No Solution.

Answer:

D no solution

Step-by-step explanation:

2x-3= 2x-5  means  : -3=-5   ...false

Answer:

Therefore the probability that in one turn James could roll an odd number and fip a heads on the quarter is  = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex].

Step-by-step explanation:

i) There are three odd numbered faces on the cube, that is the faces having 1, 3, and 5.

Therefore the probability of rolling an odd numbered face is = [tex]\frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{1}{2}[/tex] since the probability of rolling 1 = probability of rolling 3 = probability of rolling 5 = [tex]\frac{1}{6}[/tex]

ii) The probability of flipping a head on the quarter = probability of flipping a tail on the quarter = [tex]\frac{1}{2}[/tex]

iii) Therefore the probability that in one turn James could roll an odd number and fip a heads on the quarter is  = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{4}[/tex]

The probability that James could roll an odd number on a fair six-sided die and flip heads on a quarter in one turn is 1/4 or 25%.

The student is asking about the probability of two independent events happening simultaneously: rolling an odd number on a fair six-sided die and flipping heads on a quarter. To calculate the probability of both independent events occurring, we multiply the probabilities of each event.

The probability of rolling an odd number (1, 3 or 5) on a die is 3 out of 6 possibilities, which simplifies to 1/2 since there are three odd numbers out of six total numbers. The probability of flipping heads on a quarter is 1/2, as there are two sides to a coin and it is fair, meaning each side has an equal chance of landing face up.

Now, to find the combined probability, we multiply the probabilities of the independent events:

Combined probability = (1/2) x (1/2) = 1/4 or 0.25, which means there is a 25% chance to roll an odd number and flip heads in one turn.

a. The solution set is (-3,2)

b. The solution set is (2,6)

c. The solution set is (1,1)

d. The solution set is (-0.5,1.5)

e. The solution set is (7.5, -4.5)

f. The solution set is (-2,7)

Step-by-step explanation:

a. x+2y=1   Eqn 1

   x=y-5      Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex](y-5)+2y=1\\y-5+2y=1\\3y=1+5\\3y=6[/tex]

Dividing both sides by 3

[tex]\frac{3y}{3}=\frac{6}{3}\\y=2[/tex]

Putting y=2 in Eqn 2

[tex]x=2-5\\x=-3[/tex]

The solution set is (-3,2).

b. y-x=4    Eqn 1

   y=3x     Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]3x-x=4\\2x=4[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{4}{2}\\x=2[/tex]

Putting x=2 in Eqn 2

[tex]y=3(2)\\y=6[/tex]

The solution set is (2,6)

c. y = x     Eqn 1

  y = -x+2   Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]x=-x+2\\x+x=2\\2x=2[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{2}{2}\\x=1[/tex]

Putting x=1 in Eqn 1

[tex]y=1[/tex]

The solution set is (1,1)

d. y=5x+4    Eqn 1

   x+3y=4     Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]x+3(5x+4)=4\\x+15x+12=4\\16x=4-12\\16x=-8[/tex]

Dividing both sides by 16

[tex]\frac{16x}{16}=\frac{-8}{16}\\x=-0.5[/tex]

Putting x= -0.5 in Eqn 1

[tex]y=5(-0.5)+4\\y=-2.5+4\\y=1.5[/tex]

The solution set is (-0.5,1.5)

e. x-y=12   Eqn 1

   y = 3-x   Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]x-(3-x)=12\\x-3+x=12\\2x=12+3\\2x=15[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{15}{2}\\x=7.5[/tex]

Putting x=7.5 in Eqn 2

[tex]y=3-7.5\\y=-4.5[/tex]

The solution set is (7.5, -4.5)

f. 2x+y=3      Eqn 1

  x+y=5       Eqn 2

From Eqn 2;

y = 5-x

Putting in Eqn 1

[tex]2x+(5-x)=3\\2x+5-x=3\\x=3-5\\x=-2[/tex]

Putting x=-2 in Eqn 1

[tex]2(-2)+y=3\\-4+y=3\\y=3+4\\y=7[/tex]

The solution set is (-2,7).

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

Julian is using the concept testing method of advertising which involves testing ad ideas before product development. It helps in determining consumer reactions and minimizing errors.

The method Julian is using is called the concept testing method in advertising. In concept testing, ad ideas and concepts are tested by companies before the actual development of the product. Concept tests are ways for advertisers to determine the reaction of consumers to a proposed product or service before it hits the market, thus minimizing errors and financial risks. For instance, in Julian's case, this would imply presenting his ad idea, which showcases a new mobile phone, to a selected group of people and then collecting their feedback. The feedback can then be used to refine the ad and the product itself, ensuring that the mobile phone meets the expectations and needs of the targeted consumers.

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75 % free throws are made by Morton

Solution:

Given that Morton made 36 out of 48 free throws last season

To find: Percent of free throws made by Morton

From given statement,

total number of throws = 48

throws made by morton = 36

Thus the percent of free throws made by Morton is given as:

[tex]percent = \frac{\text{number of throws made}}{\text{total number of throws}} \times 100[/tex]

Substituting the values, we get

[tex]percent = \frac{36}{48} \times 100\\\\percent = 0.75 \times 100 = 75 %[/tex]

Thus 75 % of his free throws are made by Morton

Answer:

7/10

Step-by-step explanation:

4 1/2=9/2

3 4/5=19/5

9/2-19/5=45/10-38/10=7/10

Answer:

Option C. is the correct option.

Step-by-step explanation:

Clara found the product of (3 - 6y²) and (y² + 2) and she did it as below

(3 - 6y²)(y² + 2) = 3(y²) + (-6y²)×2 = 3y² - 12y² = -9y²

She did the step wrong as highlighted above. She did not use the distributive property correctly.

Now we will do it in a correct way.

(3 - 6y²)(y²+2) = 3(y² + 2) - 6y²(y² + 2)

= 3y^{2}+6-6y^{4}-12y^{2}=-6y^{4}-9y^{2}+6

Therefore Option C. is the correct answer.

Hope it helps:)

Step-by-step explanation:

1.

Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex]

Here m = 1500 kg and v = 14 meter / second

Kinetic energy = [tex]\frac{1}{2} mv^{2}[/tex]= [tex]\frac{1}{2}\times 1500 \times 14^{2}[/tex] joule =147000 joule

2.

Here m = 2 unit and v = 5 units

Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex] =[tex]\frac{1}{2}\times 2 \times 5^{2}[/tex] units =25 units

3.

Here m= 2 units and v = 5 units

Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex] =[tex]\frac{1}{2}\times 4 \times 5^{2}[/tex]=5 0 units

4.

Here m= 2 units and v= 10 units

Kinetic energy =[tex]\frac{1}{2} mv^{2}[/tex]=[tex]\frac{1}{2}\times 4 \times 10^{2}[/tex]units = 200 units

Answer:

C

Step-by-step explanation:

Slope-intercept form is y=mx+b. Y is y, m is the slope, x is x, and b is the y-intercept. The first thing you do is figure out the slope. The equation is (y2-y1)/(x2-x1). Then take 2 points from the table and substitute them in. I'll use the bottom two points: (4-2)/(2-1). You should get 2 as your answer. Substitute this in for m. Take a point from the table and substitute y in for y, x in for x. I'll use the last point: 4=2(2)+b. If I simplify further, I get 4=4+b, which means b is 0, and we won't need to put it in the equation.

Figure out the answer using the process of elimination: we know that because b=0, the answer can't be A or B. The slope is positive 2, which means that the answer can't be D. So it has to be C.

Answer:

-10y - 11x

Step-by-step explanation:

First you need to distribute -7 through the parentheses.

-7y - 14x - 3y + 3x

then you need to collect the like terms (terms with the same variable)

-10y - 11x

Answer:-10y - 11x

Step-by-step explanation:

Expanding , we have

-7y - 14x -3y  + 3x

collecting the like terms , we have

- 7y - 3y - 14x + 3x

Simplifying , we have

-10y - 11x

Answer:

why?

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

[tex] \frac{2}{6} \times 3 = \frac{2}{6} \times \frac{3}{1} [/tex]

[tex] \frac{2}{6} \times \frac{3}{1} = \frac{6}{6} = 1[/tex]

To multiply 2/6 and 3 in its simplest form, multiply the numerators and denominators together. The resulting fraction is 6/6, which simplifies to 1.

To multiply fractions, multiply the numerators together and multiply the denominators together. In this case, multiplying 2/6 and 3 gives a result of (2 * 3) / (6 * 1), which simplifies to 6 / 6. Since the numerator and denominator are the same, the fraction is equal to 1 in its simplest form.

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Answer: yes , it is possible

Step-by-step explanation:

Let the first number be x and the second number be y .Then , the sum of the two numbers will be x + y , and their difference will be x - y.

Combining the two , we have :

x + y = 1 ............................... equation 1

x - y = 8 ................................. equation 2

solving the system of linear equation by substitution method. From equation 1 , make x the subject of the formula ,

x = 1 - y ...................... equation 3

Substitute equation 3 into equation 2 ,

1 - y - y = 8

1 - 2y = 8

add 2y to both sides

1 = 8 + 2y

subtract 8 from both sides

1 - 8 = 2y

- 7 = 2y

divide through by 2

y = [tex]\frac{-7}{2}[/tex]

y = - 3.5

substitute y = -3.5 into equation 3 to find the value of x , we have

x = 1 - y

x = 1 - ( - 3.5 )

x = 1 + 3.5

x = 4.5

Let us check :

x + y will be

4.5 + (-3.5) = 1

Also ,

x - y will be

4.5 - (-3.5)

⇒ 4.5 + 3.5 = 8

Answer:

The algebraic expression for this problem is [tex]T=15x+3y[/tex].

Step-by-step explanation:

Given:

15 students fit in a van and 3 students will be traveling in a car.

So we can say that;

Number of students travelling by van = 15

Number of students travelling by car = 3

Now Let the number of vans be 'x'.

also Let the number of cars be 'y'.

Let the Total number of students bayside middle school be 'T'.

Solution:

now we can say that;

Total number of students going on field trip is equal to sum of Number of students travelling by van multiplied by the number of vans and Number of students travelling by car multiplied by the number of cars.

framing in equation form we get;

[tex]T=15x+3y[/tex]

Hence, The algebraic expression for this problem is [tex]T=15x+3y[/tex].

Answer:

B. It was the document Jefferson referred to when writing the Declaration of Independence.

Step-by-step explanation:

Virginia's Declaration of Rights was drawn upon by Thomas Jefferson for the opening paragraphs of the Declaration of Independence. It was widely copied by the other colonies and became the basis of the Bill of Rights. Written by George Mason, it was adopted by the Virginia Constitutional Convention on June 12, 1776.

Hope  I helped answer the question:)

The Virginia Declaration of Rights influenced the Declaration of Independence through its content and circulation as a pamphlet.

The Virginia Declaration of Rights influenced the Declaration of Independence in several ways:

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Answer:

Max

Step-by-step explanation:
what is this question