An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 21 inches, and the length of the base is 18 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

Answer: (-1, 4)

Step-by-step explanation: y=-2x+2, y=-4x Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer this question using SUBSTITUTION:

Substitution is a method to solving a system of equations through substituting one of the variables for another equation.

y + 2x = 2

y + 4x =0 (rewrite this equation so y is isolated: y =4x)

Since y=4x you can substitute the y in y +2x =2 and solve for x:

4x + 2x =2

6x = 2

x = [tex]\frac{1}{3}[/tex]

Now, plug in x into y =4x:

y = 4 ([tex]\frac{1}{3}[/tex]) = [tex]\frac{4}{3}[/tex] or [tex]1\frac{1}{3}[/tex]

x= [tex]\frac{1}{3}[/tex]

y = [tex]\frac{4}{3}[/tex] or [tex]1\frac{1}{3}[/tex]

a) the maximum error in surface area  and  the relative error  is 25.4 cm² and 1.25%

b) the maximum error in the volume and  the the relative error  is 162.1 cm³ and 1.875%

As we know  the  formula for surface area is

                                    Surface Area , S= 4*π*r^2.

So  differentiating both sides we get

                                     dS/dr = 8*π*r .....1

and  the  formula for  the circumference is :2*π*r

, so the error on the circumference will be respect to radius

=> Δc = 2*π*Δr  

=> Δr = ΔC / (2*π)

substituing the value ofΔr in  the equation 1, we get

The maximum error in surface area which is :

ΔS = 8*π*r*Δr = 4*r*Δc

      = (2/π)*c*Δc.

    = 25.4

where for the relative error

                 ΔS/S = 4*r*Δc/(4*π*r^2)

                          = Δc/(π*r)

                          = 2*Δc/c

                        = 1.25%

Now Since  the formula for  the volume of a sphere  is :

                                       V = 4/3*π*r^3

dofferentiating both sides we get ,

                           => dV/dr = 4*π*r^2.

So,  the   the maximum error in the calculated volume  will be :

ΔV = 4*π*r^2*Δr

       = 2*r^2*Δc

       = 1/(2*π^2)*c^2*Δc

      =162.1

Where as the relative error for the volume will be

ΔV/V = 3*Δr / r = 3*ΔC/C = 1.875%

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The absolute value function graphed in this problem is given as follows:

A. y = |x - 5| - 4.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The leading coefficient a does not influence the vertex of the absolute value function.

The vertex of the graph is the turning point, hence it is given as follows:

(5, -4).

Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:

y = |x - 5| - 4.

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The factor pairs which matches the number of tents to sleep exactly 40 boys with each tent having an equal number of boys are;

Since 40 students are to be equally distributed in each of the number of tents arrangement.

It follows that first, one must list the integer pairs whose products yield 40 as follows;

Hence, we have;

Hence, the factor pairs for each scenario of number of tents are as listed in the answer section above.

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Answer:

Step-by-step explanation:

The time interval of interest is 6 hours

There is an average of 18 trains per 24 hours or 18/(24/6)=49/12 trains per 6 hours.

The probability can be found using the Poisson distribution with parameter

λ=49/12

a) The linear regression equation is y = 1.360x + 6.540

b) The linear regression equation is y = -0.8909x + 37.59

Given,

a) The data;

Time in years, x ; 1, 1.5, 3, 5, 6, 7, 8.5, 10

Price, y ; 8, 9.75, 10.25, 11.80, 13.90, 17, 18, 20.75

We have to find the linear regression equation to the above given data.

We can use regression calculator ;

There are 8 xy pairs.

The linear regression equation is;

y = 1.360x + 6.540

b) The data

Time in years, x ; 1, 1.5, 3, 5, 6, 7, 8.5, 10

Price, y ; 32.5, 35, 37.3, 36.4, 35.7, 32.4, 29, 25

We have to find the linear regression equation to the above given data.

We can use regression calculator ;

There are 8 xy pairs.

The linear regression equation is;

y = -0.8909x + 37.59

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Answer:

Step-by-step explanation:

Given a transversal crossing parallel lines and supplementary angles (x+8°) and (2x-5°), you want to find the measures of angles L and O, supplementary to each of these.

Where a transversal crosses parallel lines, consecutive interior angles are supplementary. Using the given expressions, this means ...

  (x +8°) +(2x -5°) = 180°

  3x +3° = 180° . . . . . . . . . simplify

  x +1° = 60° . . . . . . . divide by 3

  x = 59°  . . . . . . subtract 1°

Then the acute angle is ...

  x+8° = 59° +8° = 67°

and the obtuse angle is ...

  2x -5° = 2(59°) -5° = 113°

Angle L corresponds to angle (2x-5°), so is congruent:

  ∠L = 113°

Angle O is an alternate interior angle with respect to angle (x+8°), so is congruent:

  ∠O = 67°

The expression to simplify is

We will simplify by combining like terms.

• There are FIVE x's and TWENTY-SIX more x's. We add.

5x + 26x = 31 x

• There is 1 constant, NEGATIVE THIRTEEN. No combining required so leave it as is.

•

• There is 1 term with y, which is SEVEN y. No combining required, so we leave it as is.

The final expression is

The volume of the given rectangular prism is V = 5x⁵ + 4x⁴ + x³ cubic units.

What is the volume of the rectangular prism?
Four rectangular faces and two parallel rectangular bases make up a rectangular prism. We are aware that a rectangular prism's cross section is a rectangle. The term "Cuboid" is another name for the rectangular prism.
Therefore, the following formula is provided to determine a rectangular prism's volume: Volume = l*b*h cubic units.

Given, the length of the rectangular prism = l = x
Also, the width of the rectangular prism = w = x²
Again, the height of the rectangular prism = h = 5x² + 4x + 1
Volume of the rectangular prism = l*w*h = x*(x²)*(5x² + 4x + 1)
= x³(5x² + 4x + 1) = 5x⁵ + 4x⁴ + x³
Thus, the volume of the given rectangular prism is V = 5x⁵ + 4x⁴ + x³ cubic units.

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The polynomial with zeros of −3, −1, and 2, and passes through the point (3,11) is:

P(x) = (11/24)*(x + 3)*(x + 1)*(x - 2)

We know that the zeros are −3, −1, and 2, so if we define the leading coefficient as A, the polynomial can be written as:

p(x) = A*(x + 3)*(x  + 1)*(x - 2)

Now we want this to pass through the point (3, 11), then we get:

p(3) = 11 = A*(3 + 3)*(3 + 1)*(3 - 2)

         11 = A*6*4*1

         11 = A*24

         11/24 = A

Then the polynomial is:

P(x) = (11/24)*(3 + 3)*(3 + 1)*(3 - 2)

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Answer:

ojsjsnajnbaknrkmlamsl

Answer:

y to the power of -8

:) hope this help

Answer: y^8

Step-by-step explanation:

You see that the equation has two negative numbers, so it will become positive.

(y^-2)^-6 = y^8

The base of it will cancel each other out and left with y^8

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Answer:

x ≥ 97

Step-by-step explanation:

Average = Sum of values divided by the amount of numbers in a data set

Data Set: {75, 82, 94, 77, ?}

75 + 82 + 94 + 77 + ? = ? ÷ 5 = 85

85 x 5 = 425

75 + 82 + 94 + 77 + ? = 425 ÷ 5 = 85

75 + 82 + 94 + 77 = 328

425 - 328 = 97

Ray must score greater than or equal to 97, or x ≥ 97 in order to have an average of at least 85.

if we replace y for -3 in the given equation and then we despejate x, we wiil going to have a values for the ordered pair that satisfy the equation:

then

the ordered pair woul be (4,-3)

The percentage of red pins in total pins ordered by Eric is 30%.

According to the question,

We have the following information:

Eric received 70 pins in all.

21 of the pins are red.

Now, we will find the percentage of red pins:

Percentage of red pins = (Number of red pins*100/total number of pins)

Percentage of red pins = (21*100)/70

Percentage of red pins = 2100/70

Percentage of red pins = 30%

(In the same way, we can also find the number and percentage of yellow pins from the total pins.)

Hence, the percentage of red pins in total pins ordered by Eric is 30%.

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Step-by-step explanation:

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

Arithmetic progression is S = 1/2n[2a+(n-1)d]

----------------------------------------

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Geometric progression is Uₙ = arⁿ ⁻ ¹

The equation of the line is g(x) = -1/4x + 9.

Given,

g(0) = 9

g(8) = 7

Here,

We can consider this as points:

(x₁, y₁) = (0, 9)

(x₂, y₂) = (8, 7)

Now lets find the slope of the line.

Slope, m = (y₂ - y₁) / (x₂ - x₁)

Slope, m = (7 - 9) / (8 - 0)

Slope, m = -2/8

Slope, m = -1/4

Now, the slope-intercept form:

y = mx + b

here,

9 = -1/4 × 0 + b

9 = b

Now,

equation of line,

y = -1/4x + 9

That is,

g(x) = -1/4x + 9

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This can be solved using the properties of a parallelogram.

What is a parallelogram?

A parallelogram is a basic (non-self-intersecting) quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. The congruence of opposing sides and angles is a direct result of the Euclidean parallel postulate, and neither condition can be established without resorting to the Euclidean parallel postulate or one of its equivalent formulations. A quadrilateral having just one set of parallel sides is known as a trapezoid in American English or a trapezium in British English. A parallelepiped is a parallelogram's three-dimensional counterpart.

1. If ABCD is a parallelogram, then

(A) Opposite sides of the parallelogram are congruent

2. In a parallelogram opposite sides are equal, so

 6x = 4x + 19

or, 6x - 4x = 19

or, 2x = 19

or, x = 19/2 = 9.5

Hence, x =

(C) 9.5

3. CD = 6x9.5 = 57 units

(D) 57

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Answer:

y = [tex]\frac{28+3x}{4}[/tex]

Step-by-step explanation:

- 3x + 4y = 28 ( add 3x to both sides )

4y = 28 + 3x ( isolate y by dividing both sides by 4 )

y = [tex]\frac{28+3x}{4}[/tex]

The line DE is parallel to line PQ and line DE is parallel to XY.

If any one line is parallel to any other line and any of one line (from two parallel line) is parallel to third line then all three line are parallel to each other.

So line PQ, line XY and line DE all three parallel to each other.

Option B is correct.

Answer:

245

Step-by-step explanation:

6 - 42

35 - x

cross multiply

6x = 35 × 42

6x = 1470

x = 1470 ÷ 6

x = 245

Answer:

Classification by Angles: Obtuse

Classification by Sides: Scalene

Step-by-step explanation:

    ➜ This triangle has an obtuse angle, or an angle greater than 90°, so it is an obtuse triangle. This is the classification by angles.

    ➜ This triangle's sides are all different lengths, as shown by the three different angle measurements. This means this triangle is scalene, and scalene is the classification by sides.

Answer:

a. 57 m

Step-by-step explanation:

The figure is not shown here---please draw and label it. Additionally, make sure your calculator is in degree mode.

[tex] \tan(67) = \frac{134}{x} [/tex]

[tex]x \tan(67) = 134[/tex]

[tex]x = \frac{134}{ \tan(67) } = 57[/tex]

Answer:

> -24.32 I hope that help so it is a on your screen

The perimeter of the triangle is 46.4 and the length of a triangle's boundary taken as a whole is referred to as its perimeter.

Calculate the perimeter of a triangle:

Perimeter of a triangle = a +b + c

Therefore, the triangle's perimeter is 46.4, and the whole length of a triangle's boundary is referred to as the triangle's perimeter.

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Given the expression:

using the distributive property we get the following:

therefore, the simplified expression is 0

Step-by-step explanation:

The total number of cars=24

Number of black cars=12

Divide 12 by 24,multiplied by 100%

12÷24 ×100=50%

Therefore, 50% of the cars are black

Answer:

15

Step-by-step explanation:

6.65:5=1.33

1.33х15=19.95$

we need to around the 19.95 and we get a 20$

have a nice day