Solve -32x + 3 < 5.
A. > 3 and x < 3
OB. > -3 and x < 1
OC. x > 3 or x ≤ 1

The equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5

The equation of a line in pint slope form is expressed as:

y - y1 = m(x-x1)

where

m is the slope = -7

(x1, y1) = (7, -54 ) is the point on the line

Substitute

y + 54 = -7(x -7)

Write in slope intercept form

y + 54 = -7(x -7)

y + 54 = -7x + 49
y = -7x - 5

Hence the equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5

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Answer:

[tex] \large {\boxed{ \sf{y = 2x + 5}}}[/tex]

Step-by-step explanation:

Suppose the slope of the line is k.

So,

[tex] \large {\bold {k = \frac{7 - ( - 1)}{1 - (3)} = \frac{7 + 1}{1 + 3} = \frac{8}{4} = 2 }}\\ [/tex]

So the line:

[tex] \large \bold{ \frac{y - 7}{x - 1} = k = 2 } \\ [/tex]

[tex] \: [/tex]

So,

[tex] \large \bold{y - 7 = 2(x - 1)}[/tex]

[tex]\large \bold{y - 7 = 2x - 2}[/tex]

[tex]\large \bold{y = 2x - 2 + 7}[/tex]

[tex]\large \bold{y = 2x + 5}[/tex]

[tex]{\rule{200pt}{4pt}}[/tex]

[tex] \large \bold{-N} \frak{unx-}[/tex]

Answer:

multiply the probability of the first event by the second.

Step-by-step explanation:

Use the specific multiplication rule formula. Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.

Answer:

[tex]\frac{1}{26} * \frac{1}{26} = \frac{1}{676} = .00148.[/tex]

Step-by-step explanation:

Multiply the probability of P by the probability of Q.

In which the probability of P is equal to [tex]\frac{R}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]

In which the probability of Q is equal to [tex]\frac{P}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]

There's a 1 in 676 chance that you'd randomly pick R, put the tile back in, and then pick P in a sack of 26 letters of the latin alphabet.

By taking a common factor, we will see that the equivalent expression is:

[tex]12*\sqrt[3]{6c}[/tex]

Here we start with the expression:

[tex]5*\sqrt[3]{6c} + 7*\sqrt[3]{6c}[/tex]

Notice that if we define:

[tex]\sqrt[3]{6c} = u[/tex]

We can rewrite our expression as:

[tex]5u + 7u[/tex]

Now we can take the common factor u to write:

[tex](5 + 7)u = 12u[/tex]

Now if we replace u y the cubic root, we will get:

[tex]12*\sqrt[3]{6c}[/tex]

So the correct option is the third one.

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Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

[tex](\frac{1}{4}) ^{2}[/tex] can also be written as [tex](\frac{1}{4} )(\frac{1}{4} )[/tex]

So the answer is just [tex]\frac{1}{16}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1-cos^2\theta}{cos^2\theta}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{sin^2\theta}{cos^2\theta}[/tex]

[tex]\\ \rm\Rrightarrow tan^2\theta[/tex]

Option C

Answer:

Trigonometric identities

[tex]\large \begin{aligned}\cos^2 \theta + \sin^2 \theta & = 1\\\implies \quad \quad \sin^2 \theta & = 1 - \cos^2 \theta\\\\\tan \theta=\dfrac{\sin \theta}{\cos \theta} \end{aligned}[/tex]

Therefore, using the identities, the given expression can be simplified as follows:

[tex]\large\begin{aligned}\implies \dfrac{1- \cos^2 \theta}{\cos^2 \theta} & = \dfrac{\sin^2 \theta}{\cos^2 \theta}\\\\& = \tan^2 \theta\end{aligned}[/tex]

Answer:

b = -8

Step-by-step explanation:

-2b + 9 =25

-9 = -9

-2b = 16

/-2 /-2

b = -8

Answer: See attached

Step-by-step explanation:

   [] Since the inequality uses greater than (>) and not greater than or equal to (≥), the line will be dashed.

   [] The inequality is greater than (>) so we will shade above the line as values "above" are greater.

Answer:

here is what i got

Step-by-step explanation:

Answer:

1.42 cm

Step-by-step explanation:

2.5 m = 98.4251 inches

98.4251 in / 11.5 in =8.5587

  .5587 inches left over =1.42 cm

There will be 18.87 centimeters of rope left over.

It is the conversion of one unit to another unit with its standard conversion.

Examples:

1 hour = 60 minutes

1 minute = 60 seconds

1 km = 1000 m

We have,

Let's convert the length of the rope to inches.

1 meter = 39.37 inches

2.50m = 98.43 inches

Now,

The number of 1.5-inch pieces.

=  98.43 / 11.5

= 8.55 pieces

Now,

11.5 inches pieces are cut.

This means,

= 98.43 - (8x11.5)

= 7.43 inches

Now,

1 inch = 2.54 cm

7.43 inch = 18.87 cm

Thus,

There will be 18.87 centimeters of rope left over.

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Answer:

I don't know it

Step-by-step explanation:

try with an textbook you have

Let's consider the information at hand:

         ⇒ has some special property about its side length

             ⇒ look at the diagram I attached

Using the same ratios of side length as seen in the diagram:

  ⇒ we get the equation:

        [tex]\frac{1}{\frac{\sqrt{2} }{2} } =\frac{x}{3\sqrt{2} } \\\frac{\sqrt{2} }{2}*x=3\sqrt{2} \\\frac{x}{2}=3\\ x=3*2\\x=6[/tex]

Thus x = 6.

Answer: x = 6

Hope that helps!

The purpose of using slang is mostly for social purposes such as:

Slangs is often used in the Sharing and keeping  of a constantly altering vocabulary aids.

It is used to show group solidarity and it is often used to include or exclude members.

The common sports slangs are:

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Answer:

The quadratic equation 3x² - 12x + 9 = 0 has two real roots when solved:

x₁ = 1 and x₂ = 3

Step-by-step explanation:

✍ An equation of type ax² + bx + c = 0, can be solved, for example, using the quadratic formula:

[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{b^{2}-4ac } }{2a} }[/tex]

either

[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} }[/tex]

where

[tex]\bf{\Delta=b^{2}-4ac }[/tex]

Identify the coefficients

a = 3, b = -12 and c = 9

Calculate the discriminant value

Δ = b² - 4ac

Δ = (-12)² - 4.3.9 = 144 - 12.9

Δ = 144 - 108 = 36

Enter the values of a, b and the discriminant value in the quadratic formula

[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta } }{2a} }[/tex]

[tex]\boldsymbol{x=\dfrac{-(-12\pm\sqrt{36} }{2\cdot3 } }[/tex]

[tex]\boldsymbol{x=\dfrac{(12\pm\sqrt{36} }{6 } \ ==== > \ (Solution \ general) }[/tex]

As we can see above, the discriminant (Δ) of this equation is positive (Δ> 0) which means that there are two real roots (two solutions), x₁ and x₂.

[tex]\boldsymbol{x_{1}=\dfrac{-12-\sqrt{36} }{6}=\dfrac{12-6}{6}=\dfrac{6}{6}=1 \ === > (First \ solution) }[/tex]

To find x₁, just choose the positive sign before the square root. Later,

[tex]\boldsymbol{x_{1}=\dfrac{12+\sqrt{36} }{6}=\dfrac{12+6}{6}=\dfrac{18}{6}=3 \ === > (Second \ solution) }[/tex]

Answer:

10

Step-by-step explanation:

give brainliest please!

hope this helps :)

so these two angles add up to 180 degrees

7x -3 + 12x -7 = 180

7x+12x=180+7+3

19x=190

x=10

to check if this is true we can input 10 for x in each side.

7(10)-3 = 67

12(10)-7 = 113

113+67 = 180

Answer:

see explanation

Step-by-step explanation:

since the triangles are congruent, then corresponding angles are congruent.

∠ B = ∠ F

∠ FCE ≅ ∠ BDA

∠ EFC ≅ ∠ ABD

∠ FEC ≅ ∠ BAD

note that the order of letters in Δ ABD follows the same order as those in Δ BDA

The estimate for the number of people in the town who have not been to their doctor in the last year is 7062.

It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Total population = 1819 + 6150 + 2003 + 5918 = 15890

Emily takes a random sample of 90 people from the town.

40 of these people have not been to their doctor in the last year.

The estimate for the number of people in the town who have not been to their doctor in the last year:

= (40/90)×15890

= 7062.22 ≈ 7062

Thus, the estimate for the number of people in the town who have not been to their doctor in the last year is 7062.

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The number of 1/3 cm-cubes that would fill the rectangular prism is approximately 20 cubes.

Volume = a³, where a is the side length.

Volume = lwh

Given the following:

Volume of the rectangular prism = (1/2)(1)(3/2)

Volume of the rectangular prism = (1/2)(1)(3/2) = 0.75 cm³

Volume of the cube = (⅓)³ = 0.037 cm³

Number of cubes that would fill the prism = 0.75/0.037 ≈ 20 cubes.

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Answer:

x = -2.5
x = 2

Step-by-step explanation:

Hello!

We can remove the denominators by multiplying everything by it.

Solve:

Let's make one side equal to 0.

Solve by factoring, and then the zero product property.

Multiply 2 and -10. You get -20. Think of two number that multiply to -20, and add to 1. If we think about the standard form of a quadratic, [tex]ax^2 + bx + c[/tex], think two numbers that equal "ac" and add up to "b".

Using the zero product property, set each factor to 0 and solve for x.

The two answers are x = -2.5, and x = 2.

Answer:

x = -5/2, 2

Step-by-step explanation:

Given:

[tex]\displaystyle \large{\dfrac{5}{x+3}+\dfrac{4}{x+2} = 2}[/tex]

With restriction that x-values cannot be -3 and -2 else it will turn the expression as in undefined.

First, multiply both sides by (x+3)(x+2) to get rid of the denominator.

[tex]\displaystyle \large{\dfrac{5}{x+3}\cdot (x+2)(x+3)+\dfrac{4}{x+2} \cdot (x+2)(x+3) = 2 \cdot (x+2)(x+3)}\\\\\displaystyle \large{5(x+2)+4(x+3) = 2(x+2)(x+3)}[/tex]

Simplify/Expand in:

[tex]\displaystyle \large{5x+10+4x+12 = 2(x^2+5x+6)}\\\\\displaystyle \large{9x+22=2x^2+10x+12}[/tex]

Arrange the terms or expression in quadratic equation:

[tex]\displaystyle \large{0=2x^2+10x+12-9x-22}\\\\\displaystyle \large{2x^2+x-10=0}[/tex]

Factor the expression:

[tex]\displaystyle \large{(2x+5)(x-2)=0}[/tex]

Solve like linear equation as we get:

[tex]\displaystyle \large{x=-\dfrac{5}{2}, 2}[/tex]

Since both x-values are not exact -2 or -3 - therefore, these values are valid. Hence, x = -5/2, 2

A straight line is represented by a linear equation given below.

The points are given as (1, 2) and (4, 4).

Start by calculating the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So, we have

[tex]m=\frac{4-2}{4-1} \\m=\frac{2}{3}[/tex]

The equation in slope-intercept form is then calculated as:

[tex]y=m(x-x_1)+y_1[/tex]

So, we have:

[tex]y=\frac{2}{3}(x-1)+2\\ \\y=\frac{2}{3}(x-4)+4\\[/tex]

Expand

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

Take LCM

[tex]y=2/3x+4/3[/tex]

Multiply through by 3

3y=2x+4

So, the possible equations are:

.[tex]3y=2x+4\\y=\frac{2}{3}x+\frac{4}{3} \\y=\frac{2}{3}(x-1)+2\\y=\frac{2}{3}(x-4)+{4}[/tex]

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Answer:

B

C

E

Step-by-step explanation:

other dudes are  wrong

Answer: C. y - 1 = 1/2(x-5)

Step-by-step explanation:

point-slope form: y - y1 = m(x - x1)

m = 1/2

y1 = 1

x1 = 5

y - 1 = 1/2(x-5)

Answer: C

Step-by-step explanation:

Complementary angles have measures that add to 180 degrees, so since angle EAD measures 20 degrees, we need an angle that measures 70 degrees. This is angle DAB.

Answer:

The answer to this is 9.

Step-by-step explanation:

First of all, you wrote the expression wrong, but that's okay. It's supposed to be written as (-3)².

Second of all, since multiplying two negatives makes a positive and squaring is just multiplying the integer to itself, then -3×-3=9. I hope this helps! :)

Answer:

cost of a doughnut is $0.75

cost of a cookie is $0.60

Step-by-step explanation:

As you wrote:
Let x = doughnuts

Let y = cookies

The first sentence of the problem (alexandra) can be written as:

[tex]2x + 3y = 3.30[/tex]

The second sentence of the equation (briana) can be written as:

[tex]5x + 2y = 4.95[/tex]

We must now solve for either [tex]x[/tex] or [tex]y[/tex] in this system of equations.

I will solve for [tex]x[/tex] in this example.

First we need to multiply the first equation by [tex]2[/tex] and the second equation by [tex]3[/tex]. This is so both equations have [tex]6y[/tex] as a term.

Equation 1:

[tex]2(2x + 3y) = (3.30)2\\4x + 6y = 6.60[/tex]

Equation 2:

[tex]3(5x + 2y) = (4.95)3\\15x+6y=14.85[/tex]

Now that both equations have [tex]6y[/tex] as a term, we can subtract Equation 1 from Equation 2. This will remove y from the equation and allow us to solve for x.

[tex](15x+6y) - (4x+6y) = (14.85) - (6.60)\\11x = 8.25\\\boxed{x = 0.75}[/tex]

We now know the cost of a doughnut is $0.75. Now we can solve for the cost of a cookie through substitution.

[tex]2x + 3y = 3.30\\2(0.75) + 3y = 3.30\\1.50 + 3y = 3.30\\3y = 1.80\\\boxed{y = 0.6}[/tex]

Now we know the cost of a cookie is $0.60.

These are the answers,

- Kan Academy Advance

The least expensive is the Stock Transportation charges $500 to cover the cost for the drivers plus $6 per student.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.

For example, if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.

If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Let the number of students the bus carries be x.

First Student charges $350 per bus. They will need 7 buses.

Therefore, the cost of the school hiring the bus is:

C = 7*350

C = 2450

The charge of per student

= 2450 / 260

= $ 9.4

Stock Transportation charges $500 to cover the cost for the drivers plus $6 per student.

C = 500 + 6*260

C = 500 + 1560

C = 2060

Switzer-Carty costs $7 for every student that they bus.

Therefore, the cost of the school hiring the bus is:

C = 7 * x

C = 7x

To bus 260 students, then, the cost will be:

C = 7 * 260

C = $1820

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Answer: C i think.

Step-by-step explanation:

8 different trees multipled by s equal to 6 meters tall in total.

The step of Talia that's incorrect.The step that is incorrect is: C. Step 3

The slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

Thus, we get:

Slope = rise/ run

Calculating the slope using two points on the line, (2, 5) and (1, 3), we have:

Slope (m) = (5 - 3)/(2 - 1)

Slope (m) = (2)/(1)

Slope (m) = 2

This shows that the ratio of the slope calculated by Talia was wrong. The step that is incorrect is: C. Step 3

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Answer:

C) [tex]3x^2-14x-5[/tex]

Step-by-step explanation:

[tex](5x^2-5x+1)-(2x^2+9x-6)\\\\5x^2-5x+1-2x^2-9x-6\\\\3x^2-14x-5[/tex]

The subtraction of the given expressions gives D. 3x² - 14x + 7.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are two expressions.

5x² - 5x + 1 and 2x² + 9x - 6

We have to find the difference of the given expression.

(5x² - 5x + 1) - (2x² + 9x - 6)

= 5x² - 5x + 1 - 2x² - 9x + 6

Operating the like terms together,

= (5x² - 2x²) + (-5x - 9x) + (1 + 6)

= 3x² - 14x + 7

Hence the correct option is D.

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The probability that he would have done at least this well if he had no ESP is 0.99979

To determine the probability, we need to first find the probability of doing well with ESP.

The probability of having 20 correct answers out of 23 coin flips is:

[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]

Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:

[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]

There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.

Therefore, the probability of doing well with ESP is:

[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]

= 0.00021

The probability that he would have at least done well if he had no ESP is:

= 1 - 0.00021

= 0.99979

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