the point slope form of X-3Y=-27

we know that

The Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides. The formula is equal to

[tex]Area=\sqrt{p(p-a)(p-b)(p-c)}[/tex]

where

a,b,c -----> are the lengths of the sides of a triangle

p ----> is half the perimeter

we have

[tex]J(-2,1)\ K(4,3)\ L(-2,-5)[/tex]

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Step 1

Find the distance JK

[tex]J(-2,1)\ K(4,3)[/tex]

Substitute the values in the formula of distance

[tex]d=\sqrt{(3-1)^{2}+(4+2)^{2}}[/tex]

[tex]d=\sqrt{(2)^{2}+(6)^{2}}[/tex]

[tex]dJK=\sqrt{40}\ units[/tex]

Step 2

Find the distance KL

[tex]K(4,3)\ L(-2,-5)[/tex]

Substitute the values in the formula of distance

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

[tex]d=\sqrt{(-8)^{2}+(-6)^{2}}[/tex]

[tex]dKL=10\ units[/tex]

Step 3

Find the distance JL

[tex]J(-2,1)\ L(-2,-5)[/tex]

Substitute the values in the formula of distance

[tex]d=\sqrt{(-5-1)^{2}+(-2+2)^{2}}[/tex]

[tex]d=\sqrt{(-6)^{2}+(0)^{2}}[/tex]

[tex]dJL=6\ units[/tex]

Step 4

Find the perimeter of the triangle

we know that

the perimeter of a triangle is the sum of the length sides of the triangle

so

[tex]P=dJK+dKL+dJL[/tex]

substitute the values

[tex]P=\sqrt{40}\ units+10\ units+6\ units=22.32\ units[/tex]

Find half the perimeter

[tex]p=22.32/2=11.16\ units[/tex]

Step 5

Find the area of the triangle

Applying the Heron's Formula

[tex]Area=\sqrt{p(p-a)(p-b)(p-c)}[/tex]

we have

[tex]p=11.16\ units[/tex]

[tex]a=dJK=\sqrt{40}\ units=6.32\ units[/tex]

[tex]b=dKL=10\ units[/tex]

[tex]c=dJL=6\ units[/tex]

substitute the values

[tex]Area=\sqrt{11.16(11.16-6.32)(11.16-10)(11.16-6)}[/tex]

[tex]Area=\sqrt{11.16(4.84)(1.16)(5.16)}[/tex]

[tex]Area=17.98\ units^{2}[/tex]

[tex]Area=18\ units^{2}[/tex]

therefore

the answer is

The area of the triangle is [tex]18\ units^{2}[/tex]

The area of the triangle with given vertices is 18 units squared.

To find the area of a triangle with given vertices, we can use the formula:

Area =  1/2 * |(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))|

Plugging in the coordinates of the vertices:

A = 1/2 * |(-2 * (3 - (-5)) + 4 * (-5 - 1) + (-2) * (1 - 3))|

Simplifying the expression:

A = 1/2 * |(-2 * 8 + 4 * (-6) + (-2) * (-2))|

A = 1/2 * |(-16 - 24 + 4)|

A = 1/2 * |-36|

A = 1/2 * 36

A = 18

Therefore, the area of the triangle is 18 units squared.

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Answer:

  2√42 ≈ 12.961

Step-by-step explanation:

All of the right triangles are similar, so ...

  short leg/long leg = BC/AC = AC/CD

  AC² = BC·CD = 7·24 = 168

  AC = √168 = 2√42

Answer:

m∠A = 70°

Step-by-step explanation:

The given figure is nothing but parallel lines cut by a transversal.

We use property of transversal to find the value of angle A.

Here ∠A and 110° are pair of interior angles on the same side.

The pair of interior angles on the same side add upto 180 degrees.

Therefore, ∠A + 110 = 180

Subtract 110 from both sides, we get

∠A + 110 - 110 = 180 -110

∠A = 70°

m∠A = 70°

[tex]\text{Answer: a) }P(\text{ getting an orange )}=\frac{7}{20}[/tex]

b) Blue color had an experimental probability that matched its theoretical probability.

Explanation:

Since we have given that

Number of times this spinner is spinned = 60

Number of times black occur = 17

Number of times blue occur = 15

Number of times orange occur = 21

Number of times purple occur = 7

a) So, Experimental probability of a spin of orange is given by

[tex]P(\text{ getting an orange }=\frac{\text{ Number of times orange occur}}{\text{total number of times the spinner spins}}\\\\P(\text{ getting an orange})}=\frac{21}{60}=\frac{7}{20}[/tex]

b) which color had an experimental probability that matched its theoretical probability.

According to theoretical probability ,

Every event must have equal probability, i.e. [tex]\frac{1}{4}[/tex]

And,

[tex]P(\text{ getting blue color)}=\frac{15}{60}=\frac{1}{4}[/tex]

So, Blue color had an experimental probability that matched its theoretical probability.

Answer:

[tex]18^{\circ}C[/tex]

Step-by-step explanation:

Given :The temperature is 64.4 degrees Fahrenheit

To Find : What is the temperature in degrees Celsius?

Solution:

The temperature is 64.4 degrees Fahrenheit

To convert in into Celsius

Formula : [tex]T(^{\circ}C) =(T(^{\circ}F)-32) \times \frac{5}{9}[/tex]

Substitute the vale

[tex]T(^{\circ}C) =(64.4-32) \times \frac{5}{9}[/tex]

[tex]T(^{\circ}C) =(32.4) \times \frac{5}{9}[/tex]

[tex]T(^{\circ}C) =18^{\circ}C[/tex]

So, Option A is true

Hence the temperature in degrees Celsius is [tex]18^{\circ}C[/tex]

divide total miles by speed

1650 / 50 = 33

 it will take 33 hours

If two chords are the same distance from the center of a circle then they are congruent.

Given that, two chords are the same distance from the center of a circle.

The chord of a circle is a line that connects two points that are located on the circumference of the circle. These two points can be located anywhere on the same circumference.

Chords are equidistant from the center if and only if their lengths are equal. Equal chords are subtended by equal angles from the center of the circle.

Hence, if two chords are the same distance from the center of a circle then they are congruent.

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Answer:

-18

Step-by-step explanation:

Answer:

6 over 13

Step-by-step explanation:

its right i took the test

Answer:

slope of perpendicular line = [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

Find  the slope of a line that is perpendicular to the line shown on the graph

To find slope of the given line , we pick two points from the graph

(0,1) and (1,3)

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{3-1}{1-0} = 2[/tex]

Slope of given line = 2

slope of perpendicular line = negative reciprocal of slope of given line

slope of perpendicular line = [tex]-\frac{1}{2}[/tex]

Final answer:

The expression 3√54−4√24 simplifies to √6 after factoring out the perfect squares under the radicals and combining like terms.

Explanation:

The student's question requires simplifying the expression 3√54−4√24. To simplify a square root, we look for perfect squares that are factors of the number under the root. For √54, we can notice that 54 = 9 * 6, and since √9 is a perfect square, we have 3√54 = 3*√9*√6 = 3*3*√6 = 9√6. Similarly, for √24, it is 24 = 4 * 6, so √24 = √4*√6 = 2*√6, and thus -4√24 = -4*2*√6 = -8√6. Combining these two results, we have 9√6− 8√6, which simplifies to √6. Therefore, the simplified expression is √6.

Answer:  A flowchart proof presents a logical argument using boxes and arrows.

Step-by-step explanation:

We know that a flowchart proof is a way of representation of a mathematical proof that includes a logical series of statements ( or can say arguments) in boxes with connecting arrows.

i.e. we use boxes and arrows in a flow chart proof.

By the definition of flowchart proof, the complete sentence will be : A flowchart proof presents a logical argument using boxes and arrows.

The quadratic equation r² – 94 = 0 has two real solutions, as the discriminant is positive when applying the quadratic formula.

The question deals with the quadratic equation r2 – 94 = 0. To determine how many real solutions this equation has, we can rearrange it into the standard quadratic form ar2 + br + c = 0, where a = 1, b = 0, and c = -94. The real solutions of a quadratic equation are found using the quadratic formula, which is r = −b ± √(b2 - 4ac) / (2a). In this case, the discriminant (b2 – 4ac) becomes (02 – 4(1)(-94)) which simplifies to 376. This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 1, b = 0, and c = -94. To find the number of real solutions, we need to determine the discriminant, which is given by the formula: discriminant = b² - 4ac. If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution. If the discriminant is less than zero, the equation has no real solutions. In this case, the discriminant is: 0 - 4(1)(-94) = 376. Since the discriminant is greater than zero, the equation r² - 94 = 0 has two real solutions. Since the discriminant is positive, this equation has two real solutions.

The equation has two real solutions.

This expression is a quadratic equation of the form  where the constants are To find the number of real solutions, we can use the discriminant, which is given by . If Δ > 0, there are two real solutions. If Δ = 0, there is one real solution. If Δ < 0, there are no real solutions. Let's calculate the discriminant:

Δ = 0² - 4(1)(-94) = 376

Since Δ > 0, the equation has

To evaluate tan(sin(90°)), first determine sin(90°) which equals 1. However, tan(1) is not a standard unit circle value, and if the question intended to find tan(90°), this would be undefined.

The correct option is (d).

The question is asking to use the unit circle to find the value of tan(sin(90°)).

Firstly, the sin(90°) on the unit circle is 1, as the sine function corresponds to the y-coordinate of the unit circle at that angle. Therefore, sin(90°) = 1.

Now, we need to find the tangent of this value, which is tan(1). However, tan(1) is not solvable by standard unit circle values, so it seems we may have a misunderstanding in the question. If the intention was to find tan(90°) instead, then the answer would be undefined as the tangent function at 90 degrees is undefined due to division by zero.

Answer:

B. Angle PTR and angle PTS are supplementary angles.

Step-by-step explanation:

As R, T, S are collinear and PQ intersects RS at T, so ∠RTP and ∠STP are supplementary angles.

[tex]\Rightarrow m\angle RTP+m\angle PTS=180^{\circ}[/tex]  -------1

As P, T, Q are collinear and RQ intersects PQ at T, so ∠PTS and ∠QTS are supplementary angles.

[tex]\Rightarrow m\angle PTS+m\angle QTS=180^{\circ}[/tex]  ------2

Subtracting equation 1 and 2,

[tex]\Rightarrow m\angle RTP+m\angle PTS-m\angle PTS-m\angle QTS=180^{\circ}-180^{\circ}[/tex]

[tex]\Rightarrow m\angle RTP-m\angle QTS=0[/tex]

[tex]\Rightarrow m\angle RTP=m\angle QTS[/tex]

[tex]\Rightarrow m\angle PTR=m\angle STQ[/tex]

Therefore, to prove that angle PTR is always equal to angle STQ the statement needed is angle PTR and angle PTS are supplementary angles.

The measure of each base angle is 81.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

Sports a pennant for the sports teams at lincoln high school is in the shape of an isosceles triangle.

An  isosceles triangle is a triangle in which two sides are equal.

Given that  the measure of the vertex angle is 18

We need to find the measure of each base angle.

By angle sum property the sum of three angles is 180 degrees.

x+x+18=180

2x+18=180

Subtract 18 from both sides

2x=180-18

2x=162

Divide both sides by 2

x=81

Hence, the measure of each base angle is 81.

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Answer:

1   1/4 or 5/4 gallon per hour.

Step-by-step explanation:

Fuel used in 2 1/4 hour = 2  13/16 gallon

Fuel used in 9/4 hour = 45 / 16 gallon

Fuel used in one hour = [tex]\frac{\frac{45}{16}}{\frac{9}{4}}[/tex]

                                     = 5 / 4 gallon per hour = 1  1 /4 gallon per hour

Thus, teh fuel used in each hour is 1  1/4 gallon or 5 / 4 gallon.

The value of x in 5(x + 1) = 4(x + 8) is 27.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

5(x + 1) = 4(x + 8)

Now, applying distributive property

5x+ 5 = 4x+ 32

5x - 4x = 32- 5

x= 27

Hence, the value of x is 27.

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5.4 x 0.18 can be expressed as [tex](54 * 18) * (1/10 * 1/10)[/tex], where each 1/10 returns the decimal point stripped from 5.4 and 0.18 initially. So the correct answer is option B.

The appropriate approach to solving this question is by acknowledging how numbers with decimal points function on multiplication. To express 5.4 x 0.18 in another form, we can take the decimal points away and multiply the resultant figures, 54 and 18. Then, we introduce the decimal points back using fractions equivalent to 0.1 and 0.01 (that is, 1/10 and 1/100, respectively). Hence, the correct equivalent is option B: [tex](54 * 18) * (1/10 * 1/10).[/tex] The 1/10 accounts for the decimal in 5.4, and the other 1/10 accounts for the decimal in 0.18.

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