1. Put the numbers 1-7 in the seven
circles so that the numbers in each
group of three circles connected
with a straight line add up to 12.
Use each number only once?

Answer:

y = - 2(x - 3)² + 4

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (3, 4 ) , then

y = a(x - 3)² + 4

to find a substitute (1, - 4 ) into the equation

- 4 = a(1 - 3)² + 4 ( subtract 4 from both sides )

- 8 = a(- 2)² = 4a ( divide both sides by 4 )

- 2 = a

y = - 2(x - 3)² + 4 ← equation in vertex form

The new balance in Jackie's account after 2 days will be -$27.50.

It should be noted that for each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day.

Since her current balance in the account is –$12.50, the new balance after 2 days will be:

= -12.50 + (-7.50 × 2)

= -12.50 + -15

= -27.50

The balance is -27.50

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[tex]\displaystyle\\Answer:\ y=\frac{7}{16}x^2 -\frac{7}{4}x-\frac{5}{4}[/tex]

Step-by-step explanation:

The vertex is also the symmetry point of the parabola. The formula for finding the x-coordinate of the parabola: x = -b/2a  (2,-3)

Hence,

[tex]\displaystyle\\2=\frac{-b}{2a} \\[/tex]

Multiply both parts of the equation by -2a:

[tex]\displaystyle\\-4a=b\ \ \ \ \ (1)[/tex]

[tex]y=ax^2+bx+c\ \ \ \ \ -\ \ \ \ \ the\ quadratic\ equation\\\\Thus,[/tex]

You can make a system of equations on two points belonging to the quadratic equation:

[tex]-3=a(2)^2+b(2)+c\\4=a(6)^2+b(6)+c\\\\-3=4a+2b+c\ \ \ \ (2)\\4=36a+6b+c\ \ \ \ (3)\\\\[/tex]

Substitute (1) into equations (2) and (3):

[tex]-3=4a+2(-4a)+c\\4=36a+6(-4a)+c\\\\-3=4a-8a+c\\4=36a-24a+c\\\\-3=-4a+c\ \ \ \ (4)\\4=12a+c \ \ \ \ (5)\\\\\\[/tex]

Subtract equation (4) from equation (5):

[tex]7=16a[/tex]

Divide both parts of the equation by 16:

[tex]\displaystyle\\\frac{7}{16} =a\ \ \ \ (6)[/tex]

Substitute (6) into equations (1):

[tex]\displaystyle\\-4(\frac{7}{16} )=b\\\\-\frac{4*7}{4*4}=b\\\\-\frac{7}{4}=b[/tex]

Substitute values a and b into equation (2):

[tex]\displaystyle-3=4(\frac{7}{16})+2(-\frac{7}{4})+c\\\\ -3=\frac{7}{4} -\frac{14}{4}+c\\\\ -3=-\frac{7}{4}+c \\\\-3+\frac{7}{4}=-\frac{7}{4}+c+\frac{7}{4} \\\\ \frac{-3*4+7}{4} =c\\\\\frac{-12+7}{4}=c\\\\ -\frac{5}{4}=c[/tex]

Thus,

[tex]\displaystyle\\y=\frac{7}{16}x^2 -\frac{7}{4}x-\frac{5}{4}[/tex]

Answer: 16+d>20

d>4

Step-by-step explanation:

d=digs

16+d>20

16-16+d>20-16

d>4

Answer:

a) y = 6

b) y = 3x + 3

Step-by-step explanation:

a.)

plug 1 into x in the equation:

[tex]-12+4y=12[/tex]

add 12 to both sides to isolate 4y:

[tex]4y=24[/tex]

divide both sides by 4 to simplify x:

[tex]y=6[/tex]     [24/4=6]

b.)

add 12x to both sides to isolate 4y:
[tex]4y=12x+12[/tex]

divide both sides by 4x to simplify x:

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

The correct form of the partial fraction decomposition for given expression 7x+18/x^2+9x is A/x + B/(x + 9)

The correct answer is an option(B)

In this question, we have been given an expression x² + 9x = x (x + 9),

We need to write the correct form of the partial fraction decomposition for given expression.

Suppose, (7x + 18) / (x² + 9x) = A/x + B/(x + 9)

where A and B are some constants.

To find them, multiply both sides by x² + 9x :

7x + 18 = A (x + 9) + Bx

and then we solve for A and B.

Therefore, the correct form of the partial fraction decomposition for given expression 7x+18/x^2+9x is A/x + B/(x + 9)

The correct answer is an option(B)

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Answer:

The correct answer is option B

Step-by-step explanation:

The solutions associated with each case are listed below:

According to the statement, we find that the two functions are f(x) = x + 2 and g(x) = 2 · x and we are asked to perform on the functions to obtain all resulting expressions and, if possible, to evaluate on each case:

Case 1

(f + g) (x) = f (x) + g (x) = (x + 2) + 2 · x = 3 · x + 2

Case 2

(f - g) (x) = f (x) - g (x) = (x + 2) - 2 · x = 2 - x

Case 3

(f · g) (x) = f (x) · g (x) = (x + 2) · (2 · x) = 2 · x² + 4 · x

Case 4

(f / g) (x) = f (x) / g (x) = (x + 2) / (2 · x) = 1 / 2 + 1 / x

Case 5

(f ° g) (x) = f [g (x)] = 2 · x + 2

Case 6

(g ° f) (x) = g [f (x)] = 2 · (x + 2) = 2 · x + 4

Case 7

(f ° f) (x) = f [f (x)] = (x + 2) + 2 = x + 4

Case 8

(g ° g) (x) = g [g (x)] = 2 · (2 · x) = 4 · x

Case 9

(g ° g) (- 2) = 4 · (- 2) = - 8

Case 10

(f ° f) (- 2) = - 2 + 4 = 2

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Answer:

x = -1, PR = 38.

Step-by-step explanation:

As Q is the midpoint of PR

PQ = QR

6x + 25 = 16 - 3x

9x = -9

x = -1.

PR

= 6x + 25 + 16 - 3x

= 6(-1) + 25 + 16 - 3(-1)

= -6 + 25 + 16 + 3

= 38.

Answer:

x = 10

Step-by-step explanation:

We are given the following equation:

[tex]8x + 5(2x+3) = 195[/tex],

and told to find [tex]x[/tex].

In order to calculate the value of [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] the subject:

[tex]8x + 5(2x+3) = 195[/tex]

⇒ [tex]8x + (5 \times 2x) + (5 \times 3) = 195[/tex]       [Distributing 5 into the brackets]

⇒ [tex]8x + 10x + 15 = 195[/tex]

⇒ [tex]18x + 15 = 195[/tex]

⇒ [tex]18x + 15 - 15 = 195 - 15[/tex]       [Subtracting 15 from both sides of equation]

⇒ [tex]18x = 180[/tex]

⇒ [tex]\frac{18}{18}x = \frac{180}{18}[/tex]                  [Dividing both sides of equation by 18]

⇒ [tex]x = \bf 10[/tex]

Therefore, the value of x is 10.

Answer:

$100.25 total

100.25-15-20= $65.25 total for three days

For three Dayan three hours so 3*3 = 9 hrs total

65.25/9=7.25

Hence per hour $7.25

Step-by-step explanation:

The correct interpretation regarding the solution of the compound inequality is given as follows:

Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.

To solve a compound inequality involving the or operation, we solve each inequality, then apply the union operation to their solutions.

In this problem, the following inequalities help us find the miles x in which the drivers are never pulled over.

The solutions are found as follows:

2x - 18 ≥ 122

2x ≥ 140

x ≥ 140/2

x ≥ 70.

5x + 15 < 250.

5x < 235

x < 235/5

x < 47.

Hence the correct option is given by:

Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.

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Point R' is located at (28, -20)

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

Reason:

The translation rule is [tex](\text{x},\text{y})\to (\text{x}+4,\text{y}-7)[/tex]

It says to add 4 to the x coordinate, and subtract 7 from the y coordinate.

If we apply the rule to point R(24, -13), then we have...

[tex](\text{x},\text{y})\to (\text{x}+4,\text{y}-7)\\\\(24,-13)\to (24+4,-13-7)\\\\(24,-13)\to (28,-20)\\\\[/tex]

This rule shifts the point 4 units to the right and 7 units down.

Using it's concept, the probabilities are given as follows:

A. 1/4.

B. 11/16.

C. 0.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the number of marbles is given by:

7 + 5 + 4 = 16.

Then:

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The resulting polynomials are listed below:

Herein we find two cases of addition of polynomials and the two cases of subtraction of polynomials. Each operation must be done by taking algebra properties into account. Complete procedures are shown below:

Addition - Case 1

(a - 5) + (2 · a - 3)              Given

(a + 2 · a) + [- 5 + (- 3)]       Associative and commutative properties

3 · a - 8                              Distributive property / Definitions of addition and subtraction

Addition - Case 2

(5 · t² - 6 · s · t + 8 · t - 3) + (7 · t² + 8 · s · t - 2 · t + 9) + (3 · t² + 2 · s · t + 5 · t + 5)                                         Given

(5 · t² + 7 · t² + 3 · t²) + (- 6 · s · t + 8 · s · t + 2 · s · t) + (8 · t - 2 · t + 5 · t) + (- 3 + 9 + 5)                                   Associative and commutative properties

15 · t² + 4 · s · t + 11 · t + 11       Distributive properties / Definitions of addition and subtraction / Result

Subtraction - Case 1

(10 · m - 2 · n - 1) - (5 · m - 2 · n + 2)          Given

(10 · m - 5 · m) + (- 2 · n + 2 · n) + (- 1 - 2)   Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b

5 · m - 3                                                      Distributive property / Cancellative property / Definition of addition and subtraction / Modulative property / Result

Subtraction - Case 2

(- 5 · x³ + 3 · x² + 6 · x) - (3 · x³ + 9 · x² + 4 · x)              Given

(- 5 · x³ - 3 · x³) + (3 · x² + 9 · x²) + ( 6 · x + 4 · x)           Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b

- 8 · x³ + 12 · x² + 10 · x                                                  Distributive property / Definition of addition and subtraction / Result

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Reason:

-4 - (-10) = -4 + 10 = 6

The two negatives cancel to form a positive.

Here's how to visualize what's going on: Draw a number line. Plot a marker at -4. Then move 10 units to the right and you should arrive at 6. This visually indicates -4+10 = 6

Another way to visualize: Imagine you are on basement level 4 of a tall building. If you move up 10 floors, then you'll arrive at the 6th floor. We treat the ground floor as floor 0. It might help to draw a vertical number line.

Answer:

f(x)=2x+1

Step-by-step explanation:

Use formula:

f(x)=a(x-h)+k

a=shrinking/stretching

h= horizontal translation

     left (+)

   right (-)

k= vertical translation

    left (-)

 right (+)

The total number of students in Ridgewood Junior High School is 2500 students

It is given that all students in Ridgewood Junior High School either get lunch in the school cafeteria or brought it from home on Tuesday.

No. of students who brought their lunch on Tuesday= 2% = 50 students

Let x be the total number of students in the Ridgewood Junior High School, therefore formulating the equation we get:

2% of x = 50

2/100*x = 50

x = 2500

Total number of students in the school = 2500

Hence, the total number of students in Ridgewood Junior High School is 2500 students

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The probability that it was an HH coin is [tex]\frac{1}{50}[/tex]

Conditional Probability P(B/A) is defined as probability of occurrence of B given that A has already occurred  .

Baye's Theorem describes the probability of an event based on conditions that might be related to event .

P(A/B)={P(B/A)*P(A)}/P(B)

Total number of coins =100

Total number of HH coins = 1

P(HH) =Probability of getting HH=1/100

P(H/HH)=Probability of H knowing that HH has already occurred=1

Next to find Probability Of H

We need to find two thing

(i) Probability H appears and is a fair coin= [tex]\frac{1}{2} *\frac{98}{100} =\frac{98}{200}[/tex]

(ii)Probability H appears and is a HH coin = [tex]\frac{1}{100}[/tex]

P(H)= (i)+(ii) =100/200=1/2

BY Baye's Theorem

P(HH|H)={P(H|HH)∗P(HH)}/P(H)

[tex]=\frac{1*\frac{1}{100} }{\frac{100}{200} }[/tex]

[tex]=\frac{2}{100}[/tex]

[tex]=\frac{1}{50}[/tex]

Therefore , The probability that it was an HH coin is [tex]\frac{1}{50}[/tex]

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Answer: 25%

Step-by-step explanation:

Answer:

Step-by-step explanation:

6+4=10

10/2

answer =5

Answer:

2/3

Step-by-step explanation:

6 divided by 3 is 2, so you have to divided 4 by 2, which is 2.

Answer:

⅔

Step-by-step explanation:

4 divide by 2 = 2

6 3

therefor 2/3 is equvelet too 4/6.

Hope this helped

Analyzing the given data, it cab be concluded that Option D, that is, mL3 = 126° is most likely being shown by the proof.  

It can be observed from the given diagram, angle 1 and angle 2 are complementary. By the definition of complementary angles, we get the sum of angle 1 and angle 2 equal to 90°.

=> mL1 + mL2 = 90°

The value of angle 1 is given as 36.

=> mL1 = 36⁰

Using the first observed condition and the value of angle 1, we can obtain the value of angle 2.

=> 36⁰ + mL2 = 90°

=> mL2 = 90 - 36 = 54°

Therefore, the value of angle 2 is obtained as 54°.

From the diagram given in the question, it can also be inferred that angle 2 and angle 3 form a linear pair. Using the linear pair theorem, we get the sum of angle 2 and angle 3 as 180°.

=> mL2 + mL3 = 180°

Previously, we have obtained the value of angle 2 as 54°.

Hence, by substituting the value of angle 2 in the above equation, we get,

54° + mL3 = 180°

=> mL3 = 180 - 54 = 126°

Therefore, By researching all the data and the results, we can conclude that all other options are discarded and the correct option is option D.

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smaller x value (x, y)=(-15,-8)

larger x value (x, y)=(+15,-8)

[tex]\sqrt{x^{2} + y^{2} } = 17[/tex]

[tex]x^{2} +y^{2} = 289[/tex]

y= -8

[tex]x^{2} =289-64[/tex]

[tex]x^{2} =225[/tex]

x= ±15

The points are (15, -8) and (-15, -8)

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematics, scientists, and engineers frequently employ a variety of coordinate systems. The positions of points in 2D or 3D are defined by two or three straight-line axes known as cartesian coordinates, sometimes known as rectangular coordinates. All scales are linear, which means that they are all graduated in uniform-sized increments. The positions of points in 2D are defined by a different coordinate system called semilog coordinates. The other scale is logarithmic while the first is linear.

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B is the y- intercept of the equation B = 28 - 7t, where B is the percentage of the battery.

What is a linear graph?

Linear graphs are straight line graphs to represent the relationship between two quantities. This graph helps in depicting a result in single straight lines. There is no use of curves, dots, bars, etc., and a straight line is denoted by the term linear. Let's represent the given example in the form of a data table.

Given equation,

B = 28 - 7t

B represents the battery percentage of the phone.

t represents time,

According to the equation, with passing of time the percentage of the battery drops.

28 is the highest amount of battery present at 0 time hours.

With passage of time the battery decreases.

So, in t = 1 hr,

battery, B = 28 - 7*1 = 28 -7 = 21%

similarly, t = 4 hrs,

B = 28 -7*4 = 28 -28 = 0%

The battery completely drains and becomes 0%

Therefore, B is the y- intercept of the equation B = 28 - 7t, where B is the percentage of the battery.

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Selena is right. This relation represents a function.

The set of points given is {(2,-4),(3,-4),(4,-4),(5,-4),(6,-4)}.

We can consider 2, 3, 4, 5, 6 as x-values and -4 as the y-value.

Here, the values 2, 3, 4, 5, 6 are related to -4.

This relation represents a function.

Because no two same x-values are related to different y-values. In other words, different x-values can be mapped to same y-value. But two same x-values should not be related to different y-values for the map to be a function.

So here all the x-values are related to the y-value -4. So this is a many-to-one function.

Function is a relation which maps a particular set of points(Domain) to another set of values(Codomain) through which one domain value has exactly one image in the co-domain.

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[tex]Let$p_1$ - true proportion of California residents who reported insufficient rest or sleep during the preceding 30 days$p_2$ - true proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days$\hat{p}_1$ - sample proportion of California residents who reported insufficient rest or sleep during the preceding 30 days $=0.08$$\hat{q}_1=1-\hat{p}_1=1-0.08=0.92$$n_1$ - sample size of CA residents $=11,545$[/tex][tex]$\hat{p}_2$ - sample proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days $=0.088$$\hat{q}_2=1-\hat{p}_2=1-0.088=0.912$$n_2$ - sample size of OR residents $=4,691$The $95 \%$ Confidence Interval for $\left(p_1-p_2\right)$ is given by,$$[/tex][tex]\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{p_1 q_1}{n_1}+\frac{p_2 q_2}{n_2}}$$if $p_1$ and $p_2$ are unknown we use$$\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}}$$where $Z^*=Z_{\frac{\alpha}{2}}=Z_{0.0250}$[/tex][tex]Plugging in, we get$$\begin{aligned}\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}} \\(0.08-0.088) & \pm 1.96 \sqrt{\frac{0.08(0.92)}{11545}+\frac{0.088(0.912)}{4691}} \\&-0.008 \pm 0.009498026 \\&(-0.017498026,0.001498026) \\& \approx(-0.0175,0.0015)\end{aligned}$$[/tex][tex]a) For the Hypothesis Test we have,- i) State the hypotheses.$$\begin{aligned}&H_0: p_1-p_2=0 \\&H_1: p_1-p_2 \neq 0\end{aligned}$$[/tex]

A hypothesis test examines a suggested mathematical model to see if a sample of data contains enough evidence to disprove the null hypothesis.

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Answer:

watashiwa ana men toire ne duse ka

fipinjin desu

The value of y = 5 and CD = 4 cm in the segment.

The point D is the midpoint of a segment CF. CF = 2y-2 and CD = 3y - 11.

CD = (1/2) CF

3y - 11 = (1/2) (2y -2)   (multiply both sides by 2)

6y - 22 = 2y - 2

6y - 2y = -2 + 22

4y = 20

y = 5

Substitute with the value of y in the equation of CD, you get:

CD = 3y-11 = 3(5) - 11 = 15 - 11 = 4 cm

In geometric terms, a line segment is a section of a straight line that is bordered by two clearly defined end points and contains all of the points on the line that lie inside that segment. The Euclidean distance between two endpoints of a line segment provides the length of the segment.

Between two points of a line or curve. a portion of a plane or solid figure that is eliminated due to the intersection of a line, plane, or planes, particularly one that occurs between a chord and a circle's arc.

A line segment in geometry is bordered by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points.

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Answer:

3

Step-by-step explanation:

33 - 2[3(3 + 12) - (5 x 2)3] =

= 33 - 2[3(15) - (10)3]

= 33 - 2[45 - 30]

= 33 - 2[15]

= 33 - 30

= 3