Solve the equation by identifying the quadratic form. Use a substitute variable(t) and find all real solutions by factoring.

Type your answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. When typing exponents do not use spaces and use the carrot key ^ (press shift and 6). For example, x cubed can be typed as x^3.



(x^2-1)^2+(x^2-1)-12=0
Step 1. Identify the quadratic form

Let t= Answer
. We now have:

t^2+t-12=0


Step 2. Factor

Factor this and solve for t to get t=Answer
and Answer




Step 3. Solve for x

We have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your real solutions (no extraneous) from smallest to largest.

x=___ and ___

Answer:

26

Step-by-step explanation:

you are given 45° and 90° so you know the third angle will also be 45° because the sum of all angles always is 180°
with all 3 angles you apply the sine law
a / sin( α ) = b / sin( β ) = c / sin( γ )
then you'll see that a = 26

The largest integer value of x in the solution of the following inequality is 7/4.

We have given equation is 4x+6 ≥13

In the question we have to determine the largest integer value of a in the solution of the following inequality.

So first we have to solve this inequality equation:

4x+6 ≥13

4x≥13-6

4x≥7

x≥7/4

So the largest value of x is 7/4

Hence, the largest integer value of a in the solution of the following inequality is 7/4.

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The right answer is

Determine the largest integer value of x in the solution of the following inequality.

4x+6≥13

The value of y coordinate of the unit circle is given by [tex]\sqrt{7}/4[/tex]

Given that,

x - coordinate of p =-3/4 . Let the co-ordinate of point P = (-3/4 , y).

To find : The y coordinate in Quadrant IV

By using the formula for unit circle,

Unit circle means a circle whose radius is one or 1

x²+ y² = 1

y²+ (-3/4)² = 1

y²+ (9/16) = 1

y² = 1 -9/16

y² = 7/16

y= [tex]\sqrt{7/16}[/tex]

y =  ± [tex]\sqrt{7}/4[/tex]

It is given that point P is in quadrant IV so in IV quadrant y is positive.

Therefore, y =  [tex]\sqrt{7}/4[/tex]

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Answer:

3n³ + 2n + 3

Step-by-step explanation:

(3+6n³ + 3n) - (3n+3n³-2n¹)

3 + 6n³ + 3n - 3n - 3n³ + 2n

3n³ + 2n + 3

The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0 thus option (A),(B), and (E) is correct.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

The given graph of the number of mice in the number of weeks the cat adopted.

The asymptote of the graph is y = 0.

The asymptote tells that the number of the mouse will become zero when the number of cats becomes infinite.

Hence "The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0".

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The coefficient would be 3.6

Answer:

He is using the commutative property of multiplication.

The confidence interval estimate is (6.41, 7.11) of the population mean rating for Miami

The question includes a sample of the data.

The sample size, n = 50

The sample mean:

x= ∑X /n

= 6.76

The sample standard deviation;

s= √∑(X-x)²/(n-1)

=2.55

The confidence level =0.95

The significance level , α = 0.05

The sample mean, X

= 6.76

The sample standard deviation, s = 2.55

The sample size , n= 50

Degree of freedoms :

Df = n-1

=49

Using the t-distribution table, the critical value of t is:

t critical = t α/2, df

= t 0.025,49

= 0.098

95% confidence interval :

μ =  X ± t.s/√n

 t.s /

= 6.76  2.01  2.55 / √50

= 6.76  0.7249

Therefore, The confidence interval is ( 6.41, 7.11)

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So, for this question, there are two answers possible that you could put in.

-25 < 4y + 3 < 19 in inequality form: -7<y<4

-25 < 4y + 3 < 19 in interval notation form: (-7,4)

The graph that goes alongside it should be attached to this answer as well.

Hope this helps! :)

The interpolations;

(a) 81st

= NORM.INV(0.81;0;1)

0.878

(b) 19th

=NORM.INV(0.19;0;1)

-0.878

(c) 76th

=NORM.INV(0.76;0;1)

0.706

(d) 24th

=NORM.INV(0.24;0;1)

-0.706

(e) 11th

=NORM.INV(0.11;0;1)

-1.227

Given,

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.

"A numerical measurement used in statistics of a value's relationship to the mean (average) of a set of values, assessed in terms of standard deviations from the mean," according to Wikipedia, is the Z-score.

For this case we can find the percentiles with the Norm.inv function in Excel and we got:

(a) 81st

= NORM.INV(0.81;0;1)

0.878

(b) 19th

=NORM.INV(0.19;0;1)

-0.878

(c) 76th

=NORM.INV(0.76;0;1)

0.706

(d) 24th

=NORM.INV(0.24;0;1)

-0.706

(e) 11th

=NORM.INV(0.11;0;1)

-1.227

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0.1367 percent of randomly chosen cookies will weigh less than 14 grams.

Given data;

Is it possible to calculate the likelihood that a randomly selected cookie weighs less than 14g using the information provided above?

Let,

X = Average cookie weight in a pack of 30

E (X) = μ = 15

Var (X) = σ²/n

           = 1²/30 =  0.0333

⇒ Standard Deviation (X) = √0.0333 = 0.1826

P(X ≤ 14.8) = (X-15 / 0.1826 < 14.815/0.1826)

= P(14.815 - 0.1826)

= P(Z-1.1)

= 0.1367

Hence, the probability that a randomly selected cookie has a weight less than 14g is 0.1367

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The decimal that Juanita can use to update her report is 1.6.

A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent numerical value for whole plus some fraction of a whole.

The decimal numeral system is the most widely used system for representing both integer and non-integer numbers. It is the Hindu-Arabic numeral system's extension to non-integer numbers. Decimal notation refers to the method of representing numbers in the decimal system.

In this case, the the pitcher threw a total of 384 pitches and used a fastball 240 times. The decimal will be:

= Number of throws / Fastball

= 384 / 240

= 1.6

The decimal is 1.6.

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The expression that represents a 20% discount off the price of an item that originally cost d dollars include:

0.8d

d - 0.2d

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, the cost of the item is d. Since there's a 20% discount, the new cost will be:

= d - (20% × d)

= d - 0.2d

= 0.8d

The cost is 0.8d.

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First number 79 about friction is correct statement with initial velocity .

What is friction?

Friction is a force that opposes motion between any surfaces that are touching. Friction can work for us yet against of us .

It is the action of one surface or object rubbing against another .

According to the given question in this case force of friction has a tendency to rotate the cube in anticlock wise direction. So normal reaction will shift in forword direction to balance the force due to torque of friction.

Thus, During motion the normal reaction shift towards posetive x- axis from the centre of mass is correct.

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By applying the exterior angle property, the measure of the exterior angle to ∠G in triangle EFG is 120.7°

In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.

To determine the value of ∠G in triangle EFG (ΔEFG), we would have to apply exterior angle property.

Then, the exterior angle property can be used to model triangle EFG (ΔEFG)  is given by:

∠G = m∠E +m∠F

Now Substituting the given parameters into the formula, we have

∠G = 84.3° + 36.4°.

∠G = 120.7°.

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Answer:

3x7

Step-by-step explanation:

product is multiplication so 3x7 is only correct answer

Hopes this helps please mark brainliest

Answer:

it needs to be written step by step

Since more than 4 vans will be required in total, at least 4 vans should be reserved.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal. The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It is an illustration of inequality. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3.

Here,

Since the total number of people is at least 28, then the total number of people must be 28 or more, so

7v≥28

v≥4

The total number of vans needed will be more than 4 that is at least 4 vans should be booked.

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The total amount of money that farmer will make to sell the tomatoes for $2 per tomato will be $14720.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Multiplication = to multiply any two or more numbers or variables called multiplication.

The number of red tomato = 128 × 32

The number of yellow tomato = 102 × 32

The total cost will be,

2(128 × 32) + 2(102 × 32)

⇒ 2(4096) + 2(3264)

⇒8192 + 6528

⇒$14720

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Error = (10-9)°C & Error percentage = 10%.

Given that temperature today in Chicago is 50°F

Standard conversion formula

°C = [tex]\frac{5}{9} *(T^{0}F-32)[/tex]   - 1

Given T = 50°F

Put the value in equation 1

[tex]^{0}C = \frac{5}{9} *(50-32) \\\\= \frac{5}{9}*18\\ \\= \frac{90}{9}[/tex]

= 10°C

Tommasa's grandmothers rule is to subtract 32 from the value in °F and multiply the result by 0.5

i.e. [tex]^{0}C = 0.5(T^{0} F-32)[/tex]   - 2

Given temperature is T = 50°F

Put the value of T in equation 2

[tex]^{0}C = 0.5*(50-32)[/tex]

= 0.5 * 18

= 1/2 * 18

= 9°C

Temperature obtained by standard conversion Formula is 10°C and the temperature obtained by Tammaso's grandmother rule is 9°C.

So error = (10-9)°C

= 1°C

Error percentage = [tex]\frac{1}{10}*100[/tex]

= 10%

Hence the answer is Error = (10-9)°C & Error percentage = 10%.

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Answer:

8 hours

Step-by-step explanation:

2 cars will be $400 since 2x200=400

500-400=120

He made $120 from hours alone so now we divide by 15

120/15=8

He worked 8 hours

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The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

What is the intermediate value theorem?

Intermediate value theorem is theorem about all possible y-value in between two known y-value.

x-intercepts

-x^2 + x + 2 = 0

x^2 - x - 2 = 0

(x + 1)(x - 2) = 0

x = -1, x = 2

y intercepts

f(0) = -x^2 + x + 2

f(0) = -0^2 + 0 + 2

f(0) = 2

(Graph attached)

From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3

For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.

Your question is not complete, but most probably your full questions was

Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?

Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

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The set of probabilities for the number of eaglets is the

probabilities for how many eaglets will survive.

The table that shows the probability distribution is the option C;

X      0         1         2

p(x)   0.35   0.60   0.05

  P(O) = 0.5 is the likelihood that the elder eaglet will live.

  Therefore;

   P(O') = 1 - 0.5 = 0.5 is the probability that the older eaglet won't survive.

  The likelihood that the younger eaglet will survive if the older eaglet              does not P(Y|O) = 10%

Therefore;

The likelihood that the elder eaglet will live while the younger eaglet does not survive is P(Y'|O) = 1 - 10% = 90%.

When the older eaglet does not survive, the younger eaglet has a 30% survival chance (P(Y|O')).

Therefore;

The likelihood that the younger eaglet will not survive, compared to the elder eaglet, is P(Y'|O') = 1 - 30% = 70%

The collection of potential probabilities for the number of eaglets that survive is expressed as the probability distribution, or P(X)

The range of potential results includes:

Never survives:

The likelihood that no eaglets survive is equal to P(O') × P(Y'|O') = 0.5 × 0.7 = 0.35.

The only survivor is:

The likelihood that only one eaglet survives is determined by P(O) = P(Y'|O) × P(O') = P(Y|O'), which results in P = 0.5 × 0.9 + 0.5 × 0.3 = 0.6 Both survive:

The odds of both eaglets surviving are P(O) ×P(Y|O) = 0.5 × 0.1 = 0.05.

The table of the probability distribution is therefore;

X      0         1         2

p(x)   0.35   0.60   0.05

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Answer:

Step-by-step explanation:

It A (x,y) (0.4x,0.4y)

8.1^4 x 8.1^8 will be equal to 8.1^12. But, 8.1^12 will not be equal to 8.1^6.

Some laws of exponents are:

We are given:

8.1^4 x 8.1^8

We need to check if 8.1^4 x 8.1^8 be equal to 8.1^12 and if 8.1^12 be equal to 8.1^6.

We will use laws of exponents to solve the given expression:

8.1^4 x 8.1^8 = 8.1^(4 + 8) = 8.1^12

So, 8.1^4 x 8.1^8 = 8.1^12

Also,

8.1^12 = 8.1^(2 * 6) = (8.1^2)^6

So, 8.1^12 ≠ 8.1^6.

Thus, 8.1^4 x 8.1^8 will be equal to 8.1^12. But, 8.1^12 will not be equal to 8.1^6.

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Answer:Total time minute Casey can talk= 689 Minute

Step-by-step explanation:Total charges of flat rate per month= $3. 99

Total Additional charge per minute = $0.05

Total monthly bill = $38. 44

Total additional charge=Total monthly bill - Total charge of flat rate

=$38.44-$3.99

=$34.45

Total time minute Casey cann talk=Total additional charge÷Total additional charge per minute

=$34.45÷$0.05

=689 Minute

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689 minutes long If Casey's monthly bill was $38.44, she would talk on her cell phone.

Given;

A cell phone provider charges a set monthly fee of $3. 99 plus an extra $0.05 per minute.

If Casey's monthly phone bill was $38.44, how many minutes did she use? 

The total charges of the flat rate per month = $3.99

The total additional charge per minute = $0.05

Total monthly bill = $38.44

Total additional charge = Total monthly bill - Total charge of flat rate

                                       = $38.44 - $3.99

                                       = $34.45

Total time per minute Casey can talk = Total additional charge/Total additional charge per minute

                                                       = $34.45 / $0.05

                                                       = 689 Minutes

Therefore, for 689 minutes Casey talk on her cell phone if her monthly bill was $38.44

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The transformation f(x)—>f(1/3x) due to the graph of f(x), will be dilation horizontally and vertically.

What is Transformation of Function?

Transformation of functions refers to the graph's curve moving to the left, right, up, or down, expanding, contracting, or reflecting. Just dilation, out of these three transformations, alters the size of the original shape; the other two only adjust the position.

A translation happens when each point on a graph (which represents a function) travels in the same direction and by the same amount. There are two kinds of function translations.

Stretching or compressing is a dilation. The x-values on a graph are all scaled up by the same amount when a dilation that is parallel to the x-axis occurs. The y-values are all increased by the same scale factor if it is dilated parallel to the y-axis.

f(x) to become f(1/3x), Then it will go dilation "vertically and horizontally".

Referring to the graph mentioned below we can conclude the same.

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Answer:

11-k

Step-by-step explanation:

if you are asking what is as a equation its 11-7 because decreased means minus

The required mathematical expression for the given statement is 11-k.

A mathematical statement containing variables, numbers and related by at least one mathematical operator is considered as an expression.

Given that, a statement, what's eleven decreased by k,

Converting it into a mathematical expression,

Here, a value k is being extracted or subtracted by 11, that mean, the expression should be like k is being subtracted by 11.

That is = 11-k

Hence, the required mathematical expression for the given statement is 11-k.

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The value of sin θ of the given right angle triangle using trigonometric ratios is; A: 5/13

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). They are based on the angles formed from the ratio of sides of a right angle triangle. Thus;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

From the given image, we see that;

Hypotenuse = 13

Adjacent = 12

Opposite = 5

Thus;

tan θ = 5/12

θ = tan⁻¹(5/12)

sin θ = 5/13

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Answer:

Step-by-step explanation:

3 because at the bottem it is 3 away and top three away.