Quadrilateral DEFG is a rhombus and angle CED=s-25. What is the value of s?

Quadrilateral DEFG Is A Rhombus And Angle CED=s-25. What Is The Value Of S?

Answers

Answer 1

The value of s, considering that quadrilateral DEFG is a rhombus, is given as follows:

s = 55.

How to obtain the value of s?

To obtain the value of S, we must consider triangle CED, and the fact the sum of the measures of the internal angles of a triangle is of 180º.

The measures of the internal angles of triangle CED are given as follows:

<C = 90º. (the diagonals of the rhombus are perpendicular).<D  = 60º. (the center of the rhombus is a bisection).<E = s - 25.

As the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle E is given as follows:

90 + 60 + <E = 180

150 + <E = 180

<E = 30º.

As <E = s - 25, the value of s is obtained as follows:

s - 25 = 30

s = 30 + 25

s = 55.

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Related Questions

Bounce Club surveyed a random sample of 555555 of their members about their favorite type of music. Of the members surveyed, 222222 said that jazz is their favorite type of music. There are 422422422 Bounce Club members. Based on the data, what is the most reasonable estimate for the number of Bounce Club members whose favorite type of music is jazz music

Answers

This is calculated by multiplying the proportion of members who said jazz is their favorite type of music (222222/555555) by the total cost number of Bounce Club members (422422422).

1. Calculate the proportion of members who said jazz is their favorite type of music:

222222/555555

= 0.4

2. Multiply the proportion (0.4) by the total number of Bounce Club members (422422422):

0.4 x 422422422

= 400,000

The survey asked 555555 members of the Bounce Club about their favorite type of music and 222222 said that jazz was their favorite type of music the proportion of members who said jazz is their favorite type of music (222222/555555) was multiplied by the total number of Bounce Club members (422422422). This calculation resulted in a most reasonable estimate of 400,000 members whose favorite type of music is jazz.

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Is it necessary to
ename 4 to subtract ? Explain.

Answers

Yes, It is necessary to rename 4(1/4) to 3(2/4) when 3/4 is subtracted with 4(1/4).

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4(1/4) - 3/4

= 17/4 - 3/4

= (17 - 3) / 4

= 14 / 4

= 3(2/4) or 3(1/2)

Thus,

We can rename 4(1/4) to 3(2/4).

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The complete question:

Explain Why It Is Necessary To Rename 4 1/4 If You Subtract 3/4 From It?

In 25 words or fewer, describe one thing the Fed can do to help
businesses.

Answers

The Federal Reserve helps small businesses access the technical and financial resources they need, by conducting research and data analyses, forging partnerships amongst industry stakeholders, and promoting

Drag each tile to the correct box. Not all tiles will be used.
Consider the following function.
Place the steps for finding f-¹(x) in the correct order.
f(x) = 4x + 7

Answers

Answer:

P.E.M.D.A.S

(PARENTHESIS .1

(EXPONETS .2

(MULTIPLICATION .3

(DIVISION .4

(ADDITION .5

(SUBTRACT .6

Step-by-step explanation:

Write the mission power of 10 in exponent form 0.007 X_____=7

Answers

On solving the provided question we cans ay that - the value of the following exponent is [tex]10^-5[/tex]

what are exponents?

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

here,

[tex]10^-5[/tex] = [tex]\frac{1}{10^5}[/tex]

= 1/100000

=0.00001

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HELP ME PLEASE!!! WORTH 10 POINTS!!
drag and drop each expression to correctly classify it as having a positive or negative product ( just put the ones in a positive group in that group and sam for the other one)

(5/6)(5/6) (-5/6)(5/6)

(5/6)(-5/6) (-5/6)(-5/6)

Answers

Answer:

Step-by-step explanation:

(5/6)(5/6) (-5/6)(5/6)

(5/6)(-5/6) (-5/6)(-5/6)  they  are they same but  you can also change them  and they will  still be the  same just backwords

Hope that helps

Select all pairs that are like terms.
1.) -4n and 18n
2.) 15ab and 2ab
3.) 17f and 17
4.) 3w and 3y
5.) 14h and -3h
6.) 5w and 5w²

Answers

All the pairs that are like terms are given as follows:

1.) -4n and 18n

2.) 15ab and 2ab

5.) 14h and -3h

What are like terms?

Like terms are terms that share these two features:

Same letters. (algebraic variables).Same exponents.

If two terms are like terms, then they can be either added or subtracted.

The like terms for this problem are given as follows:

1.) -4n and 18n -> algebraic variable of n, exponent of 1.

2.) 15ab and 2ab -> algebraic variable of ab, exponent of 1.

5.) 14h and -3h -> algebraic variable of h, exponent of 1.

For example, the pair in item 3 is of terms that are not like terms, as they have different algebraic variables, f and 1.

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convert 180 grams to ounces

Answers

The answer is 6.349 ounces

Mariella compared 9 brands of ice cream and found that the average price of the 9 brands is equal to 254 as she was going to another store she found two other brands that cost 282 and 292 respectively.What will be the resulting average?

Answers

260

An average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

how to calculate the average(avg) = sum of all terms/number of terms.

According to the question:

Mariella had compared 9 brands later on she wanted to even compare the other 2 brands so the average has to be calculated to 11 brands (9+2).

We can formulate it as (292 +282+ 9*254)/11

As we simplify the question we equate it as:

 (292 +282 +2286)/11

  2860/11 = 260

hence, the average is 260.

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frank can mow his own yard in $45$ minutes. joe's yard is $40\%$ larger than frank's, but joe can mow his own yard in an hour. how long would it take them, working together, to mow both yards? express your answer as mm:ss, where mm is the number of minutes and ss is the number of seconds, rounded to the nearest whole number, it would take them.

Answers

Working together, Frank and Joe could mow both of their yards in a fraction of the time it would take them individually.

Frank can mow his own yard in 45 minutes.

Joe's yard is 40% larger than Frank's.

Therefore, Joe's yard would take 56 minutes (45 x 1.4) to mow.

The combined time for both yards would be 101 minutes (45 + 56).

This can be expressed as 01:15 (1 minute and 15 seconds).

Frank can mow his own yard in 45 minutes. Joe's yard is 40% larger than Frank's, so it would take Joe 56 minutes to mow his yard. If Frank and Joe worked together, it would take them a combined 101 minutes (45 + 56) to mow both yards. This can be expressed as 01:15 (1 minute and 15 seconds). This is the time it would take them to mow both yards, rounded to the nearest whole number. Working together, Frank and Joe could mow both of their yards in a fraction of the time it would take them individually.

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I need help finding the domain and range of a parabola. The vertex is (-2,1).

Answers

The domain is the set of all x-values that lead to a range value (y-value). In other words, it’s the set of all acceptable x-values. The range is the set of all y-values produced from the domain values. You can think of the domain as how far left or right the function goes, and the range as how far up and down the function goes.

Looking at the parabola, we see that it extends left and right to negative and positive infinity, hence the arrows at at the “tails” of the function.

So, the domain (D) is:

D: (-∞, ∞)

Note: we use ( ) because infinity is not a defined number, so it’s not a starting point nor end point.

The vertex is where the lowest or highest point of the parabola, so this is where the lowest or highest range value is found. Looking at the parabola’s vertex, 1 is the y-coordinate. So, the highest point the parabola reaches is y=1. It extends all the way down to negative infinity, hence the arrows at the “tails” of the function.

So, the range (R) is:

R: [1, -∞)

Note: we use [ for 1 because it is a defined endpoint since it is the y-coordinate of the vertex.

Hope that helps! I like your name btw!

The table shows the length and area of a square
patio whose equation is y = 12x - x² where x
represents the length of the side of the patio and y
represents the area of the patio.
What does the point (6, 36) represent
graphically?

Answers

The equation provided in the problem is a parabola whose maxima is at (6, 36)

What is the equation of the parabola?

To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(x-h)²+k, and then to determine the value of the coefficient a.

Given that an equation y = 12x - x² where x represents the length of the side of the patio and y represents the area of the patio.

Since the given equation is parabolic it must have a maxima point

dy/dx = 12-2x

for maximum point dy/dx = 0

Thus,

12 - 2x = 0

x = 6

substituting this value in the function

f(x) = 12*6 + 6*6

f(x) = 36

Therefore, (6, 36) points are the maxima point of the given parabolic function. These given points show that the patio will have a maximum area at the length of 6.

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Look at picture 30 points

Answers

Answer:

It's a IQ based question

if you focus you'll see first is 1 then 3, 6,9

difference is increasing 2, 3, 4 then next one will be 5. it's quite simple

Roberta cites the following statement as evidence for a claim. "the chicken genome has about 17,000 genes, and the grape has about 30,000 genes. " which claim about human genes would be most strongly supported by this statement?.

Answers

The assertion that there aren't many extra genes in humans compared to other organisms would be the one this statement would most strongly support.

Genes are stretches of DNA that aid in the precise determination of each trait. The primary biological factor transmitted from parent to child. Genes are composed of DNA sequences and are organised sequentially at specified sites on chromosomes in the cell nucleus.

The human genome project estimates that we contain between 20,000 and 25,000 genes. Daphnia, a microscopic eating flea, contains 31,000 genes, the most of any animal.

Therefore, the claim that there are not particularly many genes in humans compared to other organisms would be most strongly supported by this statement.

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The claim that humans have more number of genes than chickens and grapes

The statement provided by Roberta states that the chicken genome has about 17,000 genes, and the grape has about 30,000 genes. This statement indicates that grapes have more genes than chickens. Therefore, it can be inferred that humans have more genes than chickens and grapes, as humans typically have more complex genomes than other species.

Roberta cites the following statement as evidence for a claim. "the chicken genome has about 17,000 genes, and the grape has about 30,000 genes. " From this statement, it can be inferred that humans have more genes than chickens and grapes. This is because humans typically have more complex genomes than other species, and the statement provided suggests that grapes have more genes than chickens. Therefore, the claim that humans have more number of genes than chickens and grapes would be most strongly supported by this statement.

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Guys please help me with this question ASAP!!
Leah and Lee hiked last weekend.
Day
Saturday| 7 3/4
Sunday| 5/ 25
Distance (Miles)

How much farther did Leah and Lee
hike on Saturday than on Sunday?

Answers

27 /20 miles farther Leah and Lee hike on Saturday than on Sunday.

How much farther did Leah and Lee?

Leah and Lee hiked last weekend.

Day Saturday| 7 3/4 ,Sunday| 5/ 25 ,Distance (Miles)

Solution: lean and lee hiked last weekend and on saturday 7  3 / 4 mileson Sunday = 5 2/5 miles

so,

distance leah and lee hiked farther on Saturday than Sunday = (7 3/4 miles - 5 2/5 miles)

Leah and Lee hike on Saturday than on Sunday:

31 / 4 miles - 27 / 5 miles

( 155 - 108 )  / 20 miles

47 / 20  miles

= 27 /20 miles

27 /20 miles farther Leah and Lee hike on Saturday than on Sunday.

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For questions 9-12, use the ellipse having foci located at (3,1) and (7,1), and a major axis length of 10.
9. what are the coordinates of the vertices.
10. What is the length of the minor axis.
11. find the eccentricity of the ellipse.
12. draw a sketch of the ellipse. PLEASE HELP AND SHOW WORK!

Answers

Answer:

[tex]\textsf{9.} \quad \textsf{Vertices}:\;\;(0, 1) \;\; \textsf{and} \;\; (10, 1)[/tex]

[tex]\textsf{10.} \quad \textsf{Minor axis}:\;\;2\sqrt{21}[/tex]

[tex]\textsf{11.} \quad \textsf{Eccentricity}:\;\;\dfrac{2}{5}[/tex]

[tex]\textsf{12.} \quad \sf See\;attachment[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.2 cm}\underline{General equation of an ellipse}\\\\$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center\\ \phantom{ww}$\bullet$ $(h\pm a,k)$ or $(h,k\pm b)$ are the vertices\\ \phantom{ww}$\bullet$ $(h\pm c,k)$ or $(h,k\pm c)$ are the foci where $c^2=a^2-b^2$\\\end{minipage}}[/tex]

Given:

Foci:  (3, 1) and (7, 1)Major axis:  10

The center of an ellipse is the midpoint of the foci.

Therefore, the center (h, k) of the ellipse is (5, 1), so:

h = 5k = 1

The foci are on the major axis of an ellipse.

Given that the y-values of the given foci are the same, the ellipse is horizontal.

The foci of a horizontal ellipse are (h±c, k)

[tex]\implies 5-c=3 \implies c=2[/tex]

[tex]\implies 5+c=7 \implies c=2[/tex]

The major axis of a horizontal ellipse is 2a.

If the major axis is 10, then a = 5.

The vertices of a horizontal ellipse are (h±a, k).  

Therefore the coordinates of the vertices are:

(5-5, 1) = (0, 1)(5+5, 1) = (10, 1)

The minor axis of a horizontal ellipse is 2b.

As c² = a² - b² then b = √(a² - c²).

[tex]\implies b=\sqrt{5^2-2^2}=\sqrt{21}[/tex]

Therefore, the minor axis is 2√(21).

The eccentricity of the ellipse is:

[tex]\implies e=\dfrac{c}{a}=\dfrac{2}{5}[/tex]

Is the relation in the problem in the image a function? explain i will mar you brainliest

Answers

Yes it is

Because it has a domain and range

Solve for x: 2 4
— = —
5 x

Answers

Therefore ,we can state that after resolving the given problem of equation, x = 3 .

What is an equation?

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. An equation is an empirical statement that proves the equality among two mathematical expressions, according to the definition of an explanation in algebra. The variables 69x + 7  and 14 are divided by an equation in the solution 56 + 5 = 14, as example. Mathematical equations are used to express the relationship between two words from either end of a letter. In most cases, the symbol serves as the sole variable. a good example

is 2x - 4 = 2.

Here,

At this location, we have

=> x + 2 = 5

=> x = 3

now,

=> 5x= 15

=> x = 15/5

=>x =3

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The question is "Solve for x for the equations  x+ 2 = 5  and 5x =15"

Express y in terms of x. Find the value of y when x = −1. 0.5y - 2 = 0.25x

Answers

Answer:

y = 3.5

Step-by-step explanation:

0.5y - 2 = 0.25x ( add 2 to both sides )

0.5y = 0.25x + 2 ( divide through by 0.5 )

y = 0.5x + 4

when x = - 1 , then

y = 0.5(- 1) + 4

  = - 0.5 + 4

  = 3.5

Answer:

Step-by-step explanation:

step 1.  0.5y-2=0.25x

step 2 0.5 y-2=0.25(-1)

step 3 0.5y = 1.75

step 4 y = 3.5

A paint mixer wants to mix paint that is 40% gloss with paint that is 25% gloss to make 5. 25 gallons of paint that is 30% gloss. How many gallons of each paint should the paint mixer mix together?.

Answers

It needs 1 [tex]\frac{3}{4}[/tex]gallons of 40% gloss and 3 [tex]\frac{1}{2}[/tex] gloss gallons of 25% gloss.

System of equations is a set or collection of equations that are dealt together. These equations can be solved graphically and algebraically. The point where two lines intersect is the solution to the system of equations. This article elaborates on Algebraic Technique To Solve System Of Equations.A linear equation is the one which has one or more variables and when plotted gives a straight line. Two or more linear equations consisting of two or more variables such that all equations are considered at the same time is called the system of linear equations.

Asume it needs x gallons of 40% gloss and y gallons of 25% glass

x+y=5.25

40% X+25% y = 30%×5.25

So x+y=5.25 ----------(i)

0.4x+0.25y = 15.75----------(ii)

(ii)*4 - (i)

4*(0.4x+0.25) -  (x+y)=15.75*4 - 5.25

0.6x=1.05 (elimination y)

x=1.75=1 [tex]\frac{3}{4}[/tex] So

y=5.25-X=3.5 = 3 [tex]\frac{1}{2}[/tex]

So,it needs 1 [tex]\frac{3}{4}[/tex] gallons of 40% gloss and 3 [tex]\frac{1}{2}[/tex] glass gallons of 25% gloss.

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To mix paint that is 40% gloss with paint that is 25% gloss to make 5.25 gallons of paint that is 30% gloss, the paint mixer should mix 1.75 gallons of paint that is 40% gloss with 3.5 gallons of paint that is 25% gloss.

Let x be the number of gallons of paint that is 40% gloss and y be the number of gallons of paint that is 25% gloss. To mix paint that is 40% gloss with paint that is 25% gloss to make 5.25 gallons of paint that is 30% gloss, we can set up the following system of equations:

0.40x + 0.25y = 0.30 × 5.25

x + y = 5.25

To solve this system of equations, we can first multiply the second equation by 0.4 to eliminate the x term, and then we can subtract the first equation from the resulting equation to solve for y:

0.4x + 0.25y = 0.3×5.25

0.4x + 0.4y = 0.4×5.25

0.15y = 0.1×5.25 = 0.525

y = 0.525/ 0.15

y = 3.5

Then we can substitute this value of y back into one of the original equations to solve for x:

x = 5.25 - y

x = 5.25 - 3.5

x = 1.75

Therefore, the paint mixer should mix 1.75 gallons of paint that is 40% gloss with 3.5 gallons of paint that is 25% gloss to make 5.25 gallons of paint that is 30% gloss.

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Given the figure below, find the values of x and z.

75°
(8x+19)
Please help I’m really stressing

Answers

Using the concept of angle in a straight line and the vertically opposite angles, The answer is x= [tex]7^o[/tex] and z =[tex]105^o[/tex].

What is an angle?

An angle is a measure of the amount of rotation between two lines or planes. It is typically measured in degrees or radians. An angle can be defined as the amount of rotation needed to bring one line or plane into coincidence with another. Angles are often represented graphically as a central point, called the vertex, and two rays that extend from the vertex in different directions. The angle is the amount of rotation needed to rotate one ray so that it coincides with the other ray.

What is vertically opposite angle and angle in a straight line?

Vertically opposite angles are a pair of angles that are opposite each other and have the same vertex, with the rays of the angles extending in opposite directions. They are formed when two lines intersect at a right angle. For example, in the letter "L" shape, the angles in the corner of the "L" shape are vertically opposite angles. They are congruent angles and supplementary angles, meaning they add up to 180 degrees.

An angle in a straight line is when two lines are in the same straight line and forms an angle of 180 degree. It is also called a straight angle. A straight angle is formed when a line is bent so that its two endpoints are in the same location, creating an angle of 180 degrees. The rays of the angle are in the opposite direction, hence it is also known as straight angle.

75 = 8x+19 (Vertically opposite angles)

75-19 = 8x

x=56/8 = [tex]7^o[/tex].

75+z =180 (Angle in a straight line)

z=180-75 = [tex]105^o[/tex].

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The drawing plan for an art studio shows a rectangle that is 11.2 inches by 8 inches. The scale in the plan is 4 in.: 5 ft. Find the length and width of the actual studio. Then find the area of the actual studio.

The length is ________ feet, the width is _____ feet, and the area is _______ square feet.

Answers

The length is 14 ft, the width is 10 ft, and the area of the rectangle is 140 square feet.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Given that the scale of the plan is:

Scale = 4 in: 5 ft = [tex]\frac{5ft}{4in}[/tex]

Multiply the length of the studio with the given scale:

[tex]l= 11.2\cancel{\text{ in}} (\frac{5\text{ ft}}{4 \text{ in}}) \\\\l = 14 ft[/tex]

Multiply the width of the studio with the given scale:

[tex]w= 8\cancel{\text{ in}} (\frac{5\text{ ft}}{4 \text{ in}}) \\\\w = 10 ft[/tex]

The area of the rectangle is given by the formula:

[tex]A= l * b[/tex]

Substitute the value of l = 14 and w = 10:

[tex]A= (14)(10)\\\\\\A= 140 ft^2[/tex]

Hence, the length is 14 ft, the width is 10 ft, and the area is 140 square feet.

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Help it is due tomorrow

Answers

Answer:

The dependent variable is n (outs). The number of outs depends on the number of innings.

Anna, Bertie and Carl share some money.

Anna gets 30% less than Carl.

Bertie gets

of what Anna gets.

Everyone gets a whole number of pounds.

Given that Bertie gets over £40, what is the least amount of money Carl can recieve?

Answers

Step-by-step explanation:

$60 as Carl gets more than the other 2

20 PIONTS!!!!


Which set of ordered pairs does NOT represent a function? Responses
A (-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)(-3, 6), (2, 7), (0, 5), (1, 5), (4, 9), (5, 4)
B (0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)(0, 1), (2, 2), (4, 8), (2, 7), (5, 8), (7, 9)
C (-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)(-4, 2), (-3, 2), (-2, 2), (-1, 2), (0, 2), (1, 2)
D (0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)(0, 1), (2, 2), (4, 8), (-2, 7), (5, 8)
E (1, 4), (3, 7), (5, 8), (4, 9), (6, 2), (7, 8), (2, 5)

Answers

Answer:

C

Step-by-step explanation:

two - 4s

Share 18£ in ratio 4:5

Answers

well, we can simply divide £18  by (4 + 5) and then distribute accordingly

[tex]\stackrel{\text{\LARGE }}{4\cdot \frac{18}{4+5}}~~ : ~~\stackrel{\text{\LARGE }}{5\cdot \frac{18}{4+5}}\qquad \implies\qquad \stackrel{\text{\LARGE }}{4\cdot 2}~~ : ~~\stackrel{\text{\LARGE }}{5\cdot 2}\qquad \implies\qquad \stackrel{\text{\LARGE }}{8}~~ : ~~\stackrel{\text{\LARGE }}{10}[/tex]

I need help please
[tex]18+2y=34\\-18 -18\\__0______\\[/tex]
I need help with the rest

Answers

Answer:

y = 8

Step-by-step explanation:

18 + 2y = 34  Subtract 18 from both sides

18 - 18 + 2y = 34 - 18

2y = 16  Divide both sides by 2

[tex]\frac{2y}{2}[/tex] = [tex]\frac{16}{2}[/tex]

y = 8

Check:

18 + 2y = 34

18 + 2(8) = 34

18 + 16 = 34

34 = 34

Adding and Subtracting Polynomials terms. Giving out brainlest. ​

Answers

The terms related to the definition are given below.

What is Polynomial?

Polynomials are expressions of the form,

a₀ + a₁ x + a₂ x² + ................. + aₙ₋₁ xⁿ⁻1 + aₙ xⁿ

where a's are the coefficients, x is the variable and n is the number of terms.

1. A term or a sum or difference of terms is AB) Polynomial

2. A polynomial that contains one term is E) Monomial

3. The number factor of a term that contains a variable is B) Coefficient

4. A polynomial written in descending order is D) Descending order.

5. A number, a variable or a product of numbers and variables is AD) Term.

6. A polynomial that contains two terms added or subtracted is A) Binomial.

7. A term that contains a number only is C) Constant

8. A polynomial that contains three terms added or subtracted is AE) Trinomial.

9. The arrangement of the terms of a polynomial in one variable in decreasing powers of the variable is AC) Standard form of a polynomial.

10. A symbol, usually a letter of the alphabet, that can be used to represent any number is BC) Variable.

Hence the terms related to the definitions are matched.

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Examine the system of equations. x 3y = 7, 2x 4y = 9 which variable would be the most efficient to solve for? x in the first equation y in the first equation x in the second equation y in the second equation

Answers

It would be  more efficient to solve for x in the first equation

The most efficient variable to solve for is the one which appears in one equation only because if solved for the variable that appears in both the equations, it will require more steps.

In the given equation both x and y appear in both the equation, so solving for x or y in either equation would be same, but solving for x in the first equation will be more efficient as the coefficient of x is 1.

It will be solved as:-

x=7-3y

2(7-3y)+4y=9

14-6y+4y=9

-2y=9-14

y=(-5)/(-2)=2.5

x=7-3(2.5)=7-7.5=-0.5

Solving for x in the first equation will be the most efficient approach.

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The solution to the given system of equations is (-0.5, 2.5).

So, x in the first equation

Now, According to the question:

Let's know:

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The  system of equations are:

x + 3y = 7 ---(1)

2x + 4y = 9---(2)

From equation (1), we have x=7-3y

So, substitute x=7-3y in equation (2), we get

2 × (7-3y)+4y=9

⇒ 14-6y+4y=9

⇒ 14-2y=9

⇒ 2y=5

⇒ y=2.5

Substitute y=2.5 in equation (1), we get

x+3 × (2.5)=7

⇒ x + 3 × (2.5)=7

⇒ x= -0.5

So, the solution to the given system of equations is (-0.5, 2.5)

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Geometry please help fast

Answers

We’ll use the Pythagorean Theorem since we are given a right triangle.

a²+b²=c²

Substitute the values in for a and b, and we’ll solve for c (hypotenuse).

(8)²+(8)²=c²

Simplify:

64+64=c²

128=c²

Take the positive square root of both sides:

√128=√c²

Simplify:

(√2•64)=c

Apply the multiplicative radical rule:

√2•√64=c

√2•8=c

c=8√2

So, your answer is: 8√2



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