How do you solve for x in a quadratic equation?

Considering the figure drawn using the formula given a = 40 cm

information given in the question

hypotenuse = 85 cm

opposite = 75 cm

adjacent =  a

The problem is solved using the Pythagoras theorem is applicable to right triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let a be the required dimension

85² = 75² + a²

7225 = 5625 + a²

7225 - 5625  = a²

a² = 1600

a = √1600

x = 40

The adjacent of the right triangle is solved to be 40 cm

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Answer: Quarter or 25%

Step-by-step explanation:

1/4 = 25%/ 100%

Or quarter

Answer:

1/4 is also called:

One Fourth

One quarter

One percent of Four

The vertical distance of the balloon from the ground will be 960.50 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

From a sight-seeing balloon, Justin estimates a 34° point of sadness to a milestone that is 1424 feet away, estimating on a level plane.

The vertical distance of the balloon from the ground will be given as,

tan 34° = h / 1424

Simplify the equation, then we have

h = 1424 tan 34°

h = 960.50 feet

The upward distance of the inflatable starting from the earliest stage is 960.50 feet.

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Therefore , the upper bound of the confidence interval is  - 8.82 .

A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.

Here,

n1 = 17 ; X1' = 78.4 ; s1² = 90.3

n2 = 13 ; X2' = 92 ; s2² = 107.8

Confidence interval :

(x1 - x2) ± Tcritical * [tex]\sqrt{[(sp^{2} /n1 + sp^{2}/n2)]}[/tex]

Pooled variance = Sp²

=> Sp² = (df1*s1² + df2*s2²) / (n1 + n2 - 2)

df = n - 1

Sp² = (16*90.3 + 12*107.8) / 28

Sp² = 97.8

Tcritical, 90%, df = n1 + n2 - 2 = 28 (1 - tail)

Tcritical = 1.313

(78.4-92)±1.313*sqrt[(sp²/n1 + sp²/n2)]

Margin of Error = Tcritical *[tex]\sqrt{[(sp^{2} /n1 + sp^{2}/n2)]}[/tex]

Margin of Error = (1.313 * √(97.8/17 + 97.8/13)) = 4.7771473

Upper boundary :

(78.4-92) + 4.7771473

-13.6 + 4.7771473

= -8.8228527

= - 8.82

Therefore , the upper bound of the confidence interval is  - 8.82 .

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The equation is 128 + 2x = 180.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

The sum of the same-side interior angles between two parallel lines is supplementary

This means,

128 + 2x = 180

2x = 180 - 128

2x = 52

x = 26

Thus,

The value of x is 26.

The equation is 128 + 2x = 180.

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write the factors out with reverses signs like this

y = (x+3/2)(x)(x-2)

solve for x = 1

y = -2.5

what can we add to this to get 3

5.5

so

y = (x+3/2)(x)(x-2) + 5.5

at x = 1, y = 3

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

The probability of getting at least one even number and at least one odd number is (3/4).

What is the probability of getting an even number in a single-dice throw?

If we throw a die, we have six possible outcomes: {1,2,3,4,5,6}. Now:

P(E) = Favourable outcomes / Total outcomes

     = 3/6

     = 1/2

As per the question, we need at least one even number and one odd number in three throws. We know that for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

Let A be the event of getting an even number and B be the event of getting an odd number on the dice.

P(A) = P(B) =  1/2

So, we need to have events occur like:

ABA or ABB (with all their possible combinations)

So, P(A∩B∩A) = (1/2)*(1/2)*(1/2) = 1/8

P(A∩B∩B) = (1/2)*(1/2)*(1/2) = 1/8

Possible number of combinations of ABA = 3

Possible number of combinations of ABB = 3

So, required probability = 3*(1/8) + 3*(1/8)

= 6/8

= 3/4                          

So, the Required probability is (3/4)

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Answer:

[tex]\textsf{a)} \quad \dfrac{1}{2}[/tex]

[tex]\textsf{b)} \quad -2[/tex]

[tex]\textsf{c)} \quad a = -4,\;\; a = 6[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9cm}\underline{Gradient Formula}\\\\Gradient $=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Given points:

Substitute the given points into the gradient formula to find the gradient of line PQ:

[tex]\textsf{Gradient}=\dfrac{-a-(a-2)}{(4-3a)-a}=\dfrac{-a-a+2}{4-3a-a}=\dfrac{2-2a}{4-4a}=\dfrac{2(1-a)}{4(1-a)}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

If two lines are perpendicular to each other, their gradients are negative reciprocals.

Therefore, the gradient of a line perpendicular to PQ is:

[tex]\implies \textsf{Gradient}=-2[/tex]

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Substitute the points and the given distance 10√5 into the formula and solve for a.

[tex]\implies 10\sqrt{5}=\sqrt{((4-3a)-a)^2+(-a-(a-2))^2}[/tex]

[tex]\implies 10\sqrt{5}=\sqrt{(4-3a-a)^2+(-a-a+2)^2}[/tex]

[tex]\implies 10\sqrt{5}=\sqrt{(4-4a)^2+(2-2a)^2}[/tex]

[tex]\implies 500=16-32a+16a^2+4-8a+4a^2[/tex]

[tex]\implies 500=20a^2-40a+20[/tex]

[tex]\implies 25=a^2-2a+1[/tex]

[tex]\implies a^2-2a-24=0[/tex]

[tex]\implies a^2-6a+4a-24=0[/tex]

[tex]\implies a(a-6)+4(a-6)=0[/tex]

[tex]\implies (a+4)(a-6)=0[/tex]

Apply the zero-product property:

[tex]\implies a+4=0 \implies a=-4[/tex]

[tex]\implies a-6=0 \implies a=6[/tex]

Therefore, the two possible values of a are:

The snail travels at rate 0.528 in/sec.

What is rate?

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

Given that,

A snail travels at a rate of 31.68 in./min.

This means

In 60 sec the snail travels 31.68 in.

In 1 sec the snail travels (31.68/60) in = 0.528 in.

This implies that the snail travels at rate 0.528 in/sec

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Answer:

θ = 35°

tanθ = 1

Step--step explanation:

using SOH CAH TOA

Hypotenuse = 7

opposite = 4

adjacent = needs to be found

θ = needs to be found

According to Pythagoras theorem

Hyp² = opp² – Adj²

7² = 4² – Adj²

Adj² = 49 – 16

Adj ² = 33

Adj = 5.7

what connects Hypotenuse and opposite os SOH

sinθ = opposite/Hypotenuse

sin θ = 4/7

sinθ= 0.57

divide bith sides by sin

θ = sin-¹ 0.57

θ = 34.75°

to find Tan θ TOA

Tanθ = opposite / adjacent

Tanθ = 4/5.7

Tan θ= 0.7018

Tanθ = 1

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The solutions to the inequalities are x ≤ -5, x ≥ 1 and x > 1

From the question, we have the following parameters that can be used in our computation:

-4x ≥ 20

8 ≤ -4(x - 1)

3x - 2 > 4 - 3x

Next, we solve the inequalities

Inequality 1

-4x ≥ 20

Divide both sides of the inequality by -4

So, we have the following representation

x ≤ -5

Inequality 2

8 ≤ -4(x - 1)

Divide both sides of the inequality by -4

So, we have the following representation

-2 ≥ -x - 1

Rewrite as

x + 1 ≥ 2

Evaluate the like terms

x ≥ 1

Inequality 3

3x - 2 > 4 - 3x

Add to both sides of the inequality 3x

So, we have the following representation

6x - 2 > 4

Add to both sides of the inequality 2

So, we have the following representation

6x  > 6

Divide by 6

x > 1

Hence, the solution is x > 1

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The minimum sales price Zion Sun Chairs must sell each chair to earn a monthly profit of $75,000, given total monthly fixed costs of $17,363.50 and variable cost per chair of $52.17, is D. $78.01.

To compute the minimum sales price, we determine the expected total sales revenue to meet the target profit.

The total sales revenue equals the total costs and the target profit.

Using division operation, the sales price is the quotient of the total sales revenue and the number of units.

The number of beach chairs produced monthly = 3,575

Target monthly profit = $75,000

Total monthly fixed costs = $17,363.50

Variable cost per chair = $52.17

Total variable costs = $186,507.75 ($52.17 x 3,575)

Total costs (variable and fixed) = $203,871.25 ($186,507.75 + $17,363.50)

Expected total sales revenue to earn a profit = $278,871.25 ($203,871.25 + $75,000)

Selling price per unit to earn a profit of $75,000 = $78.01 ($278,871.25 ÷ 3,575)

Thus, the minimum sales price is not Options A to C, but D.

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Answer:  4

Step-by-step explanation:

-1+-10 is -11

5+2 is 7

-11+7 is 4

The height of the tree to the nearest hundredth of a meter = 7.54 m

What are similar triangles?

If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.

From the figure,

AB= 21.15 meters

AE = AB - BE = 21.15 - 16.8 = 4.35 meters

BC= height, h

The triangles ABC and ADE are similar triangles

So,

AE/DE  = AB/BC

4.35 / 1.55 = 21.15/  h

h = ( 21.15 * 1.55 ) / 4.35

  = 32.78/4.35 = 7.54 m

So, the height of the tree to the nearest hundredth of a meter = 7.54 m

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The division of the two numbers in scientific notation 5.07 × 10⁹ ÷ 1.087 × 10⁻⁴ is 4.664 × 10¹³

Scientific notation is a means in which we use to represent numbers based on a standard measure.

In this problem, we have to perform a mathematical operation with two numbers expressed in scientific notation.

To divide 5.07 × 10⁹ by 1.087 × 10⁻⁴;

We need to divide 5.07 by 1.087

The result given is 5.07 ÷ 1.087 = 4.664

The second step is to note that when 10⁹ ÷ 10⁻⁴,

Using law of indices, it becomes 10⁹ ÷ 10⁻⁴ = 10⁽⁹⁺⁴⁾ = 10¹³

We can now rewrite our answer as

5.07 × 10⁹ ÷ 1.087 × 10⁻⁴ = 4.664 × 10¹³

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Answer: 4/5

Step-by-step explanation:

Let's start with what we know:

4 blue

6 red

10 purple

5 green

So, we have 25 total and 5 green. But we are trying to find the probability it won't be green, in which we have 20 marbles. So the probability it won't be green is 20/25 = 4/5.

The equation should she use was k = 2p/x²

Potential energy is the power that an object can store due to its position in relation to other things, internal tensions, electric charge, or other circumstances.

Common kinds of potential energy include the gravitational potential energy of an object, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field. The joule, denoted by the letter J, is the energy unit in the International System of Units (SI).

p=1/2kx²

To get the equivalent formula, we make k the subject

p=1/2kx²

Multiply both sides by 2

2p = kx²

Divide both sides by x²

2p/x² = k

∴ the equivalent formula is;

k = 2p/x² .

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The equation of the least-squares line when y is expressed in kilograms is y = 2114.20 + 18.96x.

What is the linear system?

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more two variables.

The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern.

Given the least square regression model equation:

y hat = -959.00 + 8.60x

weld diameter x ; shear strength y (in pounds)

1 lb = 0.4536 kg

To express shear strength y in kilogram:

y is multiplied by 0.4536

(y hat × 0.4536) = -959.00 + 8.60x

Divide both sides by 0.4536

(y hat × 0.4536) / 0.4536= (-959.00 + 8.60x) / 0.4536

y hat = 2114.1975 + 18.959435x

y hat = 2114.20 + 18.96x

The equation of the least-squares line when y is expressed in kilograms is y = 2114.20 + 18.96x.

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Disclaimer

The question given by you is incomplete, the above answer is done as per a similar question

The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern. The least-squares line is y hat = -959.00 + 8.60x. Because 1 lb = 0.4536 kg, strength observations can be re-expressed in kilograms through multiplication by this conversion factor: new y = 0.4536(old y). What is the equation of the least-squares line when y is expressed in kilograms? (Give the answer to two decimal places.)

Answer: - 7 1/3 or -88/12 (it depends)

Step-by-step explanation:

To solve this equation, multiply the second number using it's reciprocal. A reciprocal is a flipped version of a fraction.

(3/4 to 4/3)

-22/4  x  4/3 = -88/12

Change it to a mixed number.

-7 1/3

Therefore, - 7 1/3 is the answer to this problem or keep it as -88/12.

The value of test statistic for test of independence is 62.5

The Chi-square test of independence checks that two variables are related or not. We have to count for two nominal variables. We also believe that the two variables are unrelated. The test allows us to determine whether or not our idea is plausible.

The sections that follow go over what we need for the test, how to perform it, understanding the results, statistical details, and p-values.

Given,

the table shows the beverage preferences for random samples of teens and adults.

For calculating the test statistics,

First wee need to calculate the expected values of every observed values.

Expected values for teens,

[tex]E(50)=\frac{250*400}{1000}=100\\\\E(100=)\frac{250*400}{1000}=100\\\\E(200)=\frac{400*400}{1000}=160\\\\E(50)=\frac{100*400}{1000}=40[/tex]

Expected values for adults,

[tex]E(200)=250-100=150\\\\E(150)=250-100=150\\\\E(200)=400-160=240\\\\E(50)=100-40=60[/tex]

Now, the test statistic is given by:

[tex]X^2=\frac{\sum\limits^n_{i=1}(O_i-E_i)^2}{E_i}[/tex]

Where, Ei=expected value and Oi = observed value

[tex]X^2=\frac{(50-100)^2}{100}+\frac{(100-100)^2}{100}+...\frac{(200-240)^2}{240}+\frac{(50-60)^2}{60}=62.5[/tex]

So, the value of test statistic for this test independence is 62.5.

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Your question is incomplete, here is the complete question

The table below gives beverage preferences for random samples of teens and adults.

                  teens adults total

coffee      50 200        250

tea              100 150        250

soft drink      200 200        400

other       50 50        100

                     400 600        1000

we are asked to test for independence between age (i.e., adult and teen) and drink preferences. the test statistic for this test of independence is ?

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.

You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).

Given,

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.

Let s represent the truck's speed and (s+20) represent the car's speed.

to determine each vehicle's time

Time = Speed / Distance

truck time = 350/s

Time in an automobile is 350/(s+20)

Truck time - car time = 2 hours

So,

(350/s) - [350/(s+20)] = 2

LCM is s(s+20)

[350(s+20) - 350s]/s(s+20) = 2

Cross multiplying,

350(s+20) - 350s = 2s(s+20)

Simplifying the equation,

350s + 7000 - 350s = 2s² + 40s

Now, we have quadratic equation to simplify,

2s² + 40s - 7000 = 0

Dividing the equation by 2

s² + 20s - 3500 = 0

Factorizing,

s= 50

s= -70 (impossible because of the sign)

Hence the truck's speed is s = 50 km/h.

The speed of the car is s + 20 = 70 km/h.

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The basic difference between the addition and subtraction of polynomials has been explained below.

A polynomial is a mathematical expression containing two or more algebraic terms containing variables and their coefficients that involve operations such as addition, subtraction, and multiplication.

The basic difference between the addition and subtraction of polynomials is that since subtraction is the inverse of addition, all terms get the opposite sign upon subtraction. For example -

In addition - 2x²+3x+4 and 3x²+7x+9 are added and we get = 6x²+10x+13

In subtraction - The same polynomials are subtracted = -x²-7x-5

Henceforth, we see that the signs have changed to the opposite.

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Micah increased his practice time by 80%.

What is percent?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

Given:

Micah is preparing for a piano recital .

He practices for 50 minutes on Monday and 90 minutes on Wednesday.

Micah increased his practice time by 40%.

%increase = (Final value - starting value) / |starting value| x 100

                 = (90 - 50) / |50| x 100

                  = 40/50 x 100

%increase = 80%

Hence, Micah increased his practice time by 80%.

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Complete question:

C.( $100.00) is the correct answer.

If you want to know how to get that answer, simply add all of the Cash and Checks together.

Answer:

56$

Step-by-step explanation:

8$x7=56.

you just need to multiply it

Answer:

Step-by-step explanation:

[tex]\frac{9}{24} = \frac{3}{i} \\9i = 72\\i = 8[/tex]

∴ i is 8.

By using multiplication, it can be calculated that

3 [tex]\times[/tex] 9423 = 28269

What is multiplication of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.

Here the given multiplication is 3 [tex]\times[/tex] 9423

3 [tex]\times[/tex] 9423 = 28269

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