Two positions of an open gate are shown.
The triangles show the position of the gate in relation to its closed position. The distance from G to H in Position 1 is less than the distance from G to H in Position 2.
What can you conclude about the angles opposite these sides?

[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -3 ) = \stackrel{0}{y}}\hspace{4em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{5em}1( x +2 )( x -3 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-x-6=y \end{array}}~\hfill[/tex]

Answer: 56 cm

Step-by-step explanation:

Answer:

x=522/163

Step-by-step explanation:

14(12x−36)=5x+18

168x-504=5x+18

168x-504+504=5x+18+504

163x=522

163x/163=522/163

x=522/163

x=3.20

Answer:

I got 3.2 in decimal form or 522/163 in a fraction

Answer:

2 * 3 * 5

Step-by-step explanation:

The factors of 30 are 1,2,3,5,6,10,15, and 30. Lets just pick out the prime numbers from this and see if they multiply to 30.

[tex]2\times 3\times 5=30[/tex]

Answer:

PS=21.3

Step-by-step explanation:

please mark as brainliest

Answer:

368.49 cm3

Step-by-step explanation:

[tex]2.9kg=(2.9)(1000)=2900g[/tex]

[tex]V=2900/7.87[/tex]

[tex]368.49 cm^{3}[/tex]

nearest hundredth

Hope this helps.

Using algebra, Marty can make 4 triangles from a rope with 7 knots.

Algebra, a branch of mathematics, facilitates the representation of situations or issues as mathematical expressions. Mathematical operations like addition, subtraction, multiplication, and division are combined with variables like x, y, and z to produce a meaningful mathematical expression.

All branches of mathematics, such as trigonometry, calculus, and coordinate geometry, employ algebra. Algebraically, 2x + 4 = 8 is a simple expression.

Now here in the question,

3 knots form the vertices of a triangle.

Remaining 4 knots out of the 7 can be distributed as:

4+0+0 .......(on 3 sides)

3+1+0

2+2+0

2+1+1

Therefore, Marty can make 4 triangles from the rope with 7 knots.

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The amount of change that the customer will be given when payment is made with a $20 bill would be = $7.15. That is option G.

The total number of items purchased by the customer = 10

The cost for 5 items = $1.60× 5 = $8

The cost of 3 items = $1.25×3 = $3.75

The cost of 2 items = $0.55×2 = $1.1

The total cost = 8+3.75+1.1 = $12.85

Therefore, the change of the customer when $20 bill is used = 20-12.85

= $7.15.

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Individual insurance is designed tο prοtect individuals and their families against the financial impact οf events such as illness, disability, accidents, οr death.

Individual insurance and business insurance are similar in that bοth prοvide financial prοtectiοn against risks and uncertainties. Hοwever, there are alsο significant differences between the twο types οf insurance.

Individual insurance is designed tο prοtect individuals and their families against the financial impact οf events such as illness, disability, accidents, οr death.

Business insurance is designed tο prοtect businesses against the financial impact οf events such as prοperty damage, liability claims, οr lοss οf incοme due tο interruptiοn οf business οperatiοns.

The similarities between individual insurance and business insurance include:

The differences between individual insurance and business insurance include:

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The area of trapezoid ABCD is 39 ft².

A trapezοid is a quadrilateral with twο sides that are parallel. It has fοur sides, fοur angles, and twο pairs οf οppοsite sides that are equal in length. The nοn-parallel sides, οr legs οf the trapezοid, are usually referred tο as the bases οf the trapezοid. The twο parallel sides are referred tο as the bases, the nοn-parallel sides are referred tο as the legs, and the line cοnnecting the twο parallel sides is called the midline. The angles created by the bases and the legs are called the base angles

Area of trapezoid = [tex]\dfrac{a + b}{2} h[/tex]

Here, a = 5ft

b = 21 ft

h = 3ft

Area of trapezoid = [tex]\dfrac{5 + 21}{2} (3)[/tex]

Area of trapezoid = 39 ft²

Thus, The area of trapezoid ABCD is 39 ft².

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Answer:

According to the recipe, the ratio of flour to water is 4:0.5 or 8:1 (since 1/2 can be simplified to 0.5).

To determine how much water is needed for 5 cups of flour, we can use this ratio:

8:1 = 5:x

where x represents the amount of water needed.

To solve for x, we can cross-multiply:

8x = 5 * 1

8x = 5

x = 5/8

Therefore, you will need 5/8 cup of water for 5 cups of flour, using the given recipe.

Step-by-step explanation:

Answer: To estimate the mean score for all the students in the district, we can use a confidence interval. We are given that the sample size is 400, the sample mean is 110, the population means is 100, and the population standard deviation is 15. We are asked to find a 99% confidence interval for the population mean.

The formula for a confidence interval for the population mean with known population standard deviation is:

Confidence interval = sample mean ± z*(σ/√n)

where:

sample mean = 110 (given)

σ = 15 (given)

n = 400 (given)

z = the critical value from the standard normal distribution for a 99% confidence level, which is 2.576.

Substituting the values, we get:

Confidence interval = 110 ± 2.576*(15/√400)

Confidence interval = 110 ± 1.92

Therefore, the 99% confidence interval for the population mean score is (110 - 1.92, 110 + 1.92), or (108.08, 111.92). We can be 99% confident that the true population mean score for all the students in the district falls between 108.08 and 111.92.

Step-by-step explanation:

After answering the presented question, we can conclude that equation  Therefore, f(x) + g(x) = [tex]-x^3 + x^2 + 3x - 1.[/tex]

An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

To find f(x) + g(x),

[tex]f(x) = 8 - 4x - x^3\\g(x) = x^2 + 7x - 9\\f(x) + g(x) = (8 - 4x - x^3) + (x^2 + 7x - 9)\\f(x) + g(x) = -x^3 + x^2 + 3x - 1\\[/tex]

Therefore, f(x) + g(x) = [tex]-x^3 + x^2 + 3x - 1.[/tex][tex]-x^3 + x^2 + 3x - 1.[/tex]

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Answer: Since the alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper, we can express the weight of zinc and copper needed to make the alloy as a ratio to the weight of aluminum needed. Let x be the weight of aluminum needed in pounds, then we have:

Weight of aluminum: Weight of zinc: Weight of copper = 93.5: 5 : 1.5

We know that the foundry has 164 pounds of aluminum available, so we can substitute x = 164 into the above ratio and solve for the weights of zinc and copper:

164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5

Cross-multiplying, we get:

164 × 5 = 93.5 × Weight of zinc

Weight of zinc = (164 × 5) / 93.5

Weight of zinc = 8.76 pounds (rounded to two decimal places)

Similarly, cross-multiplying the above ratio gives us:

164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5

164 × 1.5 = 93.5 × Weight of copper

Weight of copper = (164 × 1.5) / 93.5

Weight of copper = 2.63 pounds (rounded to two decimal places)

Therefore, the weight of zinc needed to make the alloy is 8.76 pounds and the weight of copper needed is 2.63 pounds.

Step-by-step explanation:

Therefore , the solution of the given problem of circle comes out to be the circle's radius is about 5.2 centimetres.

A circle is formed by each region of a plane that is a certain distance from this extra point (center). It thus consists of spots that are isolated from one another by the surface and is curved. It also revolves about the centre equally from all angles. In the constrained, the double sphere of a circular, every group of endpoints is uniformly separated from the "centre." By tracing a thread through a circle, one can create a line to circular symmetry. Additionally, it rotates evenly in all directions around the centre.

Here,

The following equation determines the extent of a circle's arc:

=> arc length = radius * central angle

We can determine the radius by solving for the centre angle,

which is known to be 2.3 radians, and the arc length, which is 12 cm:

=> radius = arc length / central angle

=> 12 cm / 2.3 radians

=> 5.22 cm

We calculate the radius to be 5.2 cm by rounding to the closest tenth. As a result, the circle's radius is about 5.2 centimetres.

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Answer:

12

Step-by-step explanation:

7+5

Answer:

.

Step-by-step explanation:

The distance between two points (x1, y1) and (x2, y2) is given by the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Here, (x1, y1) = (-7, 3) and (x2, y2) = (5, 3).

Substituting these values, we get:

d = sqrt((5 - (-7))^2 + (3 - 3)^2)

= sqrt((12)^2 + (0)^2)

= sqrt(144)

= 12

Therefore, the distance between (-7, 3) and (5, 3) is 12 units.

The side x = 16.72 approximately to two decimal places using the cosine rule.

In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Considering the given triangle, we shall calculate for the side x is using the cosine rule as follows;

a² = b² + c² - 2(b)(c)cosA

x² = 7² + 12² - 2(7)(12)cos121°

x² = 49 + 144 - 168(-0.5150)

x² = 193 + 86.52

x² = 279.52

x = 16.7189 {take square root of both sides}

Therefore, using the cosine rule, we can conclude the value of the side x of the triangle is 16.7189.

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The area of the trapezoid is 176 square units.

What is a trapezoid?

A trapezoid, which is also referred to as a trapezium, is a flat, closed shape with four straight sides and one set of parallel sides.

A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the length of the parallel sides measured perpendicularly.

The height of the trapezoid is 4 units.

The parallel sides of the trapezoids are 17 units and (5+17+5) = 27 units.

The area of a trapezoid is half of the product of the height and the sum of parallel sides.

The area of the trapezoid is

1/2 × 4 ×(17+27)

= 176 square units

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The total number of outcomes in the quiz is 8

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

Using the above as a guide, we have the following:

For each question, there are two possible outcomes: true or false.

So, the total number of outcomes for all three questions is:

Total = 2 x 2 x 2

Evaluate

Total = 8

Hence, there are 8 possible outcomes in total.

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Complete question

Find the total number of outcomes of the following experiment

There are 3 true-false questions on a quiz.

Answer: 1, 5, 11, 55

Step-by-step explanation:

Answer:

Traingle=180 degrees

U=54

180-54

=126

126/2

=63

R=63

U=54

T=63

Therefore , the solution of the given problem of volume comes out to be  has a volume of 256 cubic centimetres.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 are two examples of cubic measures. However, the bulk of an item may be employed to estimate its size. Usually, the weight of an item is converted into mass measures like grams and kilos.

Here,

The formula: gives the capacity of a pyramid.

=> V = (1/3)Bh

where B is the base's size and h is the pyramid's height.

The ratio of the volumes of the dilated pyramid to the initial pyramid is (1/4)3 = 1/64 if the scale factor of dilation is 1/4. In other terms, pyramid B's volume is 1/64 that of pyramid A's.

Let V(A) represent the pyramid A's volume. Then:

=> V(B) = (1/64)

=> V(A) = 4

When we multiply both parts by 64, we obtain:

=> V(A) = 256

Pyramid A, the preimage, therefore, has a volume of 256 cubic centimetres.

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Answer:

1.  8

2. 24

3.  15

4.  135

b. 135 x 1/9

5. the answer is 24

The base length of the parallelogram found using the area formula is 4 units.

What is a parallelogram?

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees. 360 degrees is the sum of all interior angles.

A parallelogram's area is the area that it takes up in a two-dimensional plane. The parallelogram's area is calculated by multiplying the base length by the height.

Each shape's perimeter can be defined as either the entire length or total distance encircling the object. The entire distance between a parallelogram's boundaries is also known as the parallelogram's perimeter.

Given,

The area of the parallelogram A =36 sq. units

The height of the parallelogram  h = 9 units

We are asked to find the base length b.

Now the formula for the area of the parallelogram is:

A = b * h

36 = b * 9

b = 36/9 = 4 units.

Therefore the base length of the parallelogram, found using the area formula is 4 units.

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Answer:

Step-by-step explanation:

Let the age of the son be $s$ and the age of the father be $f$. From the first equation, we have $2s + f = 56$, and from the second equation, we have $f + 2s = 82$. Solving this system of equations, we get $s = 12$ and $f = 32$, so the son is 12 years old and the father is 32 years old.

Let the two-digit number be $10t+u$, where $t$ is the tens digit and $u$ is the units digit. We are given that $t+u=13$ and $2t-u=1$. Solving this system of equations, we get $t=7$ and $u=6$, so the two-digit number is $76$.

Let the two-digit number be $10x+y$, where $x$ is the tens digit and $y$ is the units digit. We are given that $2(10+x+y) = 27(10x+y)$, or $20+2x+2y = 270x+27y$. Simplifying this equation, we get $268x-25y = 10$. Since $y$ is a digit, we know that $0 \leq y \leq 9$. We can check that $x=1$ is too small, so we try $x=2$. Plugging in $x=2$, we get $536-25y=10$, which gives $y=21/5$, which is not a digit. Thus, there is no solution for a two-digit number.

Therefore , the solution of the given problem of triangle  comes out to be segments LM and MN have equal 10x measures.

A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.

Here,

Given that RS and LM are the respective sides of the two triangles, if we set x as the length of RS, then LM's length is 5x and ST's length is 2x. The duration of MN is five times that of ST, which is ten times longer.

We can now calculate the length of RS using the tangent of angle R:

=> tan R=RS/ST

=> 5/2.5=2

We thus have:

=> RS = 2

=> ST = 2x

We can determine the length of RT using the Pythagorean theorem:

=> RT/ST = sin R

=> RT = ST sin R

=>  2.5 (2/29) = 4.337 sin R = 2.5

We can now determine the lengths of LM and MN using the similarity of the triangles:

=> RM = 5 (2x) LM = 5 = 10

=> MN = 5 ST = 5 (two times) = 10

As a result, segments LM and MN have equal 10x measures.

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The values of LM = 12.5 and MN = 25

A triangle is a closed geometric figure consisting of three line segments or sides, connected to each other at three endpoints or vertices. Each side of a triangle intersects with exactly two other sides, and the vertices are the points where the sides meet.

From the given figures, both the triangles are right angle triangle.

[tex]tan R=\frac{5}{2.5} = \frac{ST}{RS}[/tex]

So, ST = 5 and RS = 2.5

Since, ΔRST is 5th to create ΔLMN,

its corresponding sides are 5 times the length LM corresponding sides of RS. So, its length

LM = 5×2.5 = 12.5

LM = 12.5

MN corresponding sides of ST. So, its length

MN = 5×5 = 25

MN = 25

Therefore, The values of LM = 12.5 and MN = 25.

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Answer:

Since Khrysteen is paid semimonthly, she receives 24 paychecks in a year (12 months x 2 pay periods per month).

To calculate her annual pay, we can multiply her semi-monthly pay by the number of paychecks she receives in a year:

Annual pay = Semi-monthly pay x Number of paychecks in a year

Annual pay = $1,978.50 x 24

Annual pay = $47,484

Therefore, Khrysteen's annual pay is $47,484.

Hope This Helps!

In response to the given question, we can state that As a result, Igbo expressions experienced a N50.00 loss.

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.  

Igbo spent N40.00 on 5 books, for a total of N40.00.

N200.00 = 5 books x N40.00 each

Igbo lost money since he sold the books for N150.00. To find the amount of the loss, subtract the selling price from the cost price:

Cost Price - Selling Price = Loss

N200.00 - N150.00 = Loss

Loss = N50.00

As a result, Igbo experienced a N50.00 loss.

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