Johnny oeders 5 cheese pizzas and 6 pepperoni pizzas for his son's birthday party. He paid $136. Mid party he realized he was going to run out of pizzaz, so he decided to place a second order. This time johnny ordered 2 cheese pizzas and 2 pepperoni pizzas and paid $49.00. Write a linear system that could be used to find the cost of each type of pizza?

Answers

Answer 1

Step-by-step explanation:

Let x = cost of cheese pizza

Let y = cost of pepperoni pizza

x + 6y = 136

2x + 2y = 49

Solve the system:

x = $14

y = $15


Related Questions

Given the equation four ninths plus h equals eleven over nine, determine the value of h. nine over seven, seven ninths, forty four over eighty one, fifteen over ninetee,n

Answers

The required value of h in the equation 4/9 + h = 11/9 is 7/9 or seven ninths.

What is an equation?

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

4/9 + h = 11/9    (1)

To determine the value of h, solve the equation,

Subtract 4/9 from both the sides,

4/9 + h - 4/9 = 11/9 - 4/9

h = 7/9

The value of h is 7/9 or seven ninths.

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standard deviation for 6,8,10,4?

Answers

Standard deviation for 6,8,10,4 will be;

⇒ 2.58

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

The data set is,

⇒ 6, 8, 10, 4

Now,

Since, The data set is,

⇒ 6, 8, 10, 4

Hence, Mean = 6 + 8 + 10 + 4 / 4

                     = 7

So, The standard deviation= √ (6 - 7)² + (8 - 7)² + (10 - 7)² + (4 - 7)² / (4 - 1)

                                        = √20/3

                                        = 2.58

Thus, Standard deviation for 6,8,10,4 will be;

⇒ 2.58

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What is 7/10 divided by 3.4

Answers

Answer: 0.20588235294 or ≈0.21

Step-by-step explanation: First, we should change the 7/10 into a fraction. (Divide numerator by the denominator) You should get .7 or 0.7. Then, when dividing, it would be 0.7 divided by 3.4 and I got 0.20588235294. I rounded it to the nearest hundredth to get ≈0.21. I hope this helped! Please, mark brainliest! (If can)

The slope of the line shown below is 3/2. What is the value of a? 2, 3, 5, 6

Answers

The solution is Option D.

The value of a from the equation of slope is a = 6

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second poin

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the value to be determined be = a

Now , the slope of the line be = m

The value of m = 3/2

So , Slope m = 3/2

And , the value of a is calculated by

Slope = rise / run

Slope = y/x

Since , the value of x = 4

3/2 = y/4

Multiply by 4 on both sides of the equation , we get

y = 3 x 2

y = 6

Therefore , the value of a = 6

Hence , The value of a from the equation of slope is a = 6

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PLS HEEEEEEELP For 100 Points!!!!

Ana was washing dishes at the end of her shift at a restaurant. She washed 40 plates from 7:20 to 7:30.
When she finishes washing all the plates, her shift will end.
(a) If she started washing plates at 7:10 and ended at 7:35, estimate how many plates she washed in
total. Explain your reasoning.
(b) Write an equation to represent how many plates Ana has left to wash at a particular time after her
start at 7:10. Explain your reasoning.

Answers

Answer:

If Ana started at 7:20, ended at 7:38, and she washes 6 dishes per minute, than she has 108 dishes left to wash.

Step-by-step explanation:

Answer:

Step-by-step explanation:Answer: 138 plates are to be washed by her if she started at 7:15 and ends at 7:38, and the function will be f(x)=6x.

Step-by-step explanation:

Since we have given that

She washed 30 plates from 7:30 to 7:35,

That means in 5 minutes, the number of plates get washed here = 30

We need to find the number of plates from 7:15 to 7:38

First, we count the number of minutes

In 1 minute, the number of plates gets washed by her is given by

In 23 minutes, the number of plates gets washed by her is given by

The equation to represent how many plates Ana has left to wash at a particular time after her start at 7:15  is given by

Hence, 138 plates are to be washed by her if she started at 7:15 and ends at 7:38, and the function will be f(x)=6x.

Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a ____________ to be verified by the auditors.

Answers

Income taxes that are withheld from employees' pay and not remitted as of the balance sheet date will constituted a liability to be verified by the auditors.

A tax placed on people or organizations in relation to their income or profits is known as an income tax. Tax rates multiplied by taxable income are typically used to calculate income taxes.

Tax rates might change depending on the taxpayer's attributes and source of income. As taxable income rises, the tax rate can also. Corporate tax, which is often assessed at a fixed rate, is the name given to the tax charged on businesses. Individual income is frequently subject to progressive taxation.

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4x-2(3x+7)=____x-_____

Answers

Answer: x = -9

Step-by-step explanation: 4

x

+

2

=

3

x

7

4x−3x=−7−2⇒x=−9

URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!

Answers

Answer: b. The radius is the same as a cylinder with a volume of 500(3) and the same height.

Step-by-step explanation:

The volume of a cylinder is 3 times that of a cone (assuming they have the same perpendicular height and radius).

HELP?!!? You’ve been hired to help a car company with analyzing sale trends to help them with figuring out what direction development of new products should go. Due to rising fuel costs the industry is seeing a rise in people purchasing compact cars, but the kind of features and thus price people are targeting is less clear.
Based on your initial analysis the average cost of a compact car over the last 10 years has ranged from $12,000 to $28,000. Your job is to assist your team with plotting this data on a graph to help your team with visualizing potential trends in the data. The years will be on the x-axis and the cost will be on the y-axis.
(a) What is a good maximum and minimum value along the y-axis that would be a good fit for your data on this graph? Explain your reasoning.
(b) What is a good distance between the marks along the y-axis on the graph to ensure that you have appropriate resolution for your data set? Explain your reasoning. Too few means you can’t reasonably read the data, too many will make your graph too cluttered.
(c) What is a good maximum and minimum value along the x-axis which would be a good fit for your data on this graph? Explain your reasoning.
(d) What is a good distance between the marks along the x-axis on the graph to ensure that you have appropriate resolution for your data set? Explain your reasoning. Too few means you can’t reasonably read the data, too many will make your graph too cluttered.

Answers

183844.ii887777777788

Question 1(Multiple Choice Worth 1 points)
(05 04 LC)
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows
First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9,2,4,3,0
Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1,0, 2, 1, 3.
Which is the best measure of center for first period, and why?
O Mean, because there are no outliers that affect the center
O Median, because there is one outier that affects the center
O
Interquartile range, because there is one outier that affects the center
O Standard deviation, because there are no outliers that affect the center

Answers

Answer:uu

Step-by-step explanation:

Mike drinks of a litre of juice each day.
Juice costs £4.40 for a 2 litre carton and £2.60 for a 1 litre carton.
Mike buys enough juice to last for 7 days.
What is the lowest price Mike can pay for this juice?
Show how you decide.

Answers

lowest price Mike can pay for this juice is £15.8

What is an integer?

An integer (pronounced IN-tuh-jer) is an integer (not a fraction) that is positive, negative, or zero.

An example of an integer is:

-5, 1, 5, 8, 97, 3,043.

Examples of non-integers are:

-1.43, 1 3/4, 3.14, 0.09, and 5643.1.

The set of integers denoted by Z is formally defined as:

Z = {...,-3,-2,-1,0,1,2,3,...}

It is given that Mike drinks of a litre of juice each day.

Juice costs £4.40 for a 2 litre carton and £2.60 for a 1 litre carton.

Mike buys enough juice to last for 7 days.

Total litre of milk needed = 7 × 1 = 7 litre

7l = 2l + 2l + 2l + 1l

Lowest cost = 4.40 + 4.40 + 4.40 + 2.60 = 15.8

Therefore,   lowest price Mike can pay for this juice is £15.8

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what is the product to 6.5x9.5

Answers

Answer: 61.75

Step-by-step explanation:

The answer is 61.75

ABCD is a square with four congruent sides and four congruent angles. triangle BAD is congruent to

Answers

ΔBAD is congruent to ΔBCD by the ASA rule.

What is the ASA congruency of triangles?

If any two angles and sides included between the angles of one triangle are equivalent to the corresponding two angles and sides included between the angles of the second triangle, then the two triangles are said to be congruent by the ASA rule.

In the given figure ABCD is a square.

In ΔBAD and ΔBCD

∠B ≅ ∠B ----Common Angle

∠A ≅ ∠A  ------Each of 90° angle

Side BD ≅ Side BD ----Common Side

So we can say that ΔBAD ≅ ΔBCD -----(ASA rule)

Hence, ΔBAD is congruent to ΔBCD by the ASA rule.

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200-8.(2x+7)=112
(2x-123):3=33

Answers

is it two questions?

if it is then.....

Is answer correct?

Select all true statements if n || m.

Parallel lines M and N cut by two transversals, A B and B C. Along line M, three angles are labeled 2, 3, and 4, which together form a straight angle. Transversal A B forms two angles below line N, one labeled 20 degrees and the other labeled A. Together, these angles form a straight angle. Transversal B C forms two angles below line N, one labeled C and the other labeled 60 degrees. Together, these angles form a straight angle. Angle 1 is vertical to the 60-degree angle and is an alternate interior angle to angle 4. Together, angles 1, 3, and an unlabeled angle that is vertical to the 20-degree angle form a triangle between the two parallel lines.
A. m∠2 = 60°
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
D. m∠2 + m∠3 = 80°
E. m∠2 = 20°

Answers

Answer:

Hi,  the correct answer is A) m∠2 = 60°.

let me put it in this way.

Step-by-step explanation:

Since parallel lines M and N are cut by transversals A B and B C, corresponding angles are formed. Corresponding angles are pairs of angles that are formed by intersecting lines and are on opposite sides of the transversal. In this case, angles 2 and C are corresponding angles, as are angles 3 and A.

We know that angles 2 and C form a straight angle along line M, and angles C and 60 degrees form a straight angle along line N. Since corresponding angles are congruent (have the same measure), this means that angle 2 must have the same measure as the 60-degree angle

Write an equation for a line passing through points (-2,3) and (3,5)

Answers

Answer:

[tex]y=\frac{2}{5}x+\frac{31}{5}[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{3-5}{-2-3}=-\frac{2}{5}[/tex].

So, the equation is:

[tex]y-5=-\frac{2}{5}(x-3) \\ \\ y-5=-\frac{2}{5}x+\frac{6}{5} \\ \\ y=\frac{2}{5}x+\frac{31}{5}[/tex]

suppose a researcher finds that the p-value of a test statistics is 0.08. which of the following significance levels gives you a chance of finding a statistically significant result? -0,01 -0,001 -0,1 -0,05

Answers

the best chance of finding a statistically significant result would be 0.1. This is because the p-value of 0.08 is less than the significance level of 0.1, but greater than the significance levels of 0.01, 0.001, and 0.05

The p-value of a test statistic is a measure of the probability of obtaining a result that is at least as extreme as the one observed, given that the null hypothesis is true. In other words, it is a measure of the strength of the evidence against the null hypothesis.

If the p-value of a test statistic is 0.08, it means that there is an 8% chance of obtaining a result at least as extreme as the one observed, given that the null hypothesis is true. This does not necessarily mean that the result is statistically significant at any particular significance level.

To determine whether a result is statistically significant, you need to compare the p-value to a predetermined significance level, also known as the alpha level. The alpha level is the probability of rejecting the null hypothesis when it is actually true (also known as a type I error).

If the p-value is less than the alpha level, then the result is considered statistically significant. For example, if the alpha level is set at 0.05, and the p-value of the test statistic is 0.03, then the result would be considered statistically significant.

In the case of the options you provided, the significance level that gives you the best chance of finding a statistically significant result would be 0.1. This is because the p-value of 0.08 is less than the significance level of 0.1, but greater than the significance levels of 0.01, 0.001, and 0.05.

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Evaluate 15/r -1 when r = 5.

Answers

The value of the expression 15/r -1 when r = 5 will be equal to 2.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 15/r -1. The value of r is 5. The value of the expression at r=5 will be calculated as,

E = 15/r - 1

E = 15 / 5- 1

E = 3 - 1

E = 2

Therefore, the value of the expression 15/r -1 when r = 5 will be equal to 2.

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Factorise the following:
a) x + 3x-4
b) x - 2x - 3
c) x + 2x - 8

Answers

By Factorise the equations we get 2 points for each equation:

for a) we get (x+4),(x-1)

for b) we get (x-3),(x+1)

for c) we get (x+4),(x-2)

a) x^2 + 3x-4

for this equation we have to take factors of -4:

x^2+4x-x-4

Taking common in the equation we get:

x(x+4)-1(x-4)

After taking common, Now we get two points:(x+4,)(x-1)

b) x^2 +-2x-3

for this equation we have to take factors of -3:

x^2-3x+x-3

Taking common in the equation we get:

x(x-3)+1(x-3)

After taking common, Now we get two points:(x-3,)(x+1)

c) x^2 + 2x-8

for this equation we have to take factors of -8:

x^2+4x-2x-8

Taking common in the equation we get:

x(x+4)-2(x+4)

After taking common, Now we get two points:(x+4,)(x-2)

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"The correct question is":

Factorise the following:

a) x ^2+ 3x-4

b) x^2 - 2x - 3

c) x ^2+ 2x - 8

A school is arranging a field trip to the zoo. The school spends 835.19 dollars on passes for 45 students and 2 teachers.

Answers

Answer: $17.77 per pass

Step-by-step explanation:

$835.19 / (45 + 2)

$835.19 / 47

= $17.77 price per pass

Could someone help me with my math?? Neville says, "I add because of the words
in all. The answer is 9 pencils." Anthony says,
"I multiply because there are equal groups.
The answer is 18 pencils." Who is correct?
Explain.

Answers

From the statement, Anthony is correct because 3*6=18

How to determine the number of pencils she bought?

We should know that the problem is to determine the number of pencils he bought

The given parameters are that

You can draw a 3 packages of pencils with 6 pencils in each to represent t package.

Now let us do the following:

For Neville

3*6 = 18

And also,

18÷3 = 6

For Anthony

6*3 =18 and

18÷6 = 3

In conclusion, looking at the two analysis, it seems that Anthony is more correct knowing fully well that each of the multiplications and divisions give us 18 or 6

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Complete question:

Critique Reasoning Neville and Anthony are solving this problem: Barbara bought You can draw a 3 packages of pencils with 6 pencils in each to represent t package. How many pencils did she buy in all? Neville says, “I add because of the words in all. The answer is  9 pencils.” Anthony says, “I multiply because there are equal groups. The answer is  18 pencils.” Who is correct? Explain.

Jackson has $650 in their account and uses their debit card to take out $40 cash each week. Their card has a $5 ATM fee.

Write an equation to express their balance, y, after x weeks.
What will their balance be after 8 weeks?
After 8 weeks, how much will Jackson have paid in ATM fees alone?

Answers

The word problem have the following answers:

y = $650 - $45x is an equation to express their balance, y, after x weeks

$290 will their balance be after 8 weeks.

After 8 weeks, Jackson would have paid $40 in ATM fees alone.

Word problems in mathematics

Word problems are mathematical problems which involves the use ofordinary words, instead of mathematical symbols.

From the question, if y is the balance after x weeks, this implies Johnson took out $45 multiplied by x in total including ATM fees, and their balance will be the equation;

y = $650 - $45x

After 8weeks, their balance will be;

y = $650 - $45(8)

y = $650 - $360

y = $290

After 8 weeks, Jackson will pay in ATM fees alone;

$5 × 8 = $40

Therefore, the equation y = $650 - $45x is to express their balance, y, after x weeks and $290 will be their balance after 8 weeks. While Johnson would have paid in $40 in ATM fees alone after 8 weeks.

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An arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 6 feet and a span of 22 feet. Find an equation for the ellipse. (Assume a center at (0, 0)). Use the equation to find the height of the arch at a distance of 3 feet from the center. (Round your answer to two decimal places.)

Answers

The equation of ellipse is [tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex] and height of arch is 5.77 feet

Assume that the center of the ellipse is at the origin.

So,  The general equation for an ellipse is:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

Where:

x is Horizontal distance, in feet.

y is Vertical distance, in feet.

a is Horizontal semiaxis length (half-width), in feet.

and b is Vertical semiaxis length (height), in feet.

According to the question,

x = 3 , a = 11 and b = 6

Putting all the values ,

So , the equation of ellipse will be

[tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]

Putting x = 3,

[tex]\frac{3^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]

Solving for y,

[tex]\frac{y^2}{36} = 1 - \frac{9}{121}[/tex]

=> [tex]y^2 = \frac{(121 - 9)36}{121}[/tex]

=> y² = 4032 / 121

=> y = √33.32

=> y = 5.77 feet

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Martin will receive a pay raise of 6%. He currently makes $30 per hour. What will be his new hourly rate?

Answers

Answer:

New hourly rate is $31.8

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

GivenCurrent rate is $30,Pay raise is 6%,

Solution

New rate is:

$30 + 6% = $30 + $30*6/100 =$30 + $1.8 = $31.8

Evaluate the following:

Logn(-n)2 = ?

Answers

The value of the logarithm expression logₙ (n)⁻² will be negative 2.

What is the value of the expression?

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ logₙ (n)⁻²

Simplify the expression, then we have

⇒ logₙ (n)⁻²

⇒ -2 logₙ (n)

⇒ - 2

The value of the logarithm expression logₙ (n)⁻² will be negative 2.

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The approximate length of side XY is
units
The approximate length of side YZ
units.
The approximate length of side ZX is
v units.
The approximate perimeter of triangle XYZ is
units

Answers

please mark me brainlieset and click the stars i spent so long on this :>

Answer:

ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ  = 14√5 units

Step-by-step explanation:

1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units

2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX =  √18 units = 3√2.

3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.

4. YZ is visualized to have a length of 4 units.

5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ  = 14√5 units

ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ  = 14√5 units

What are coordinates?

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle,

the length of this altitude would be: 3 units

2. The length of ZX can be determined through Pythagorean Theorem.

If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW.

ZW clearly = 3,

thus

[tex]ZX^2 = 3^2 + 3^2 = 18[/tex],

and ZX =  √18 units = 3√2.

3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW.

Knowing XW to have a length of 3 units, and YW to have a length of 1 unit [tex]= > XY^2 = XW^2 + YW^2 \\= > 3^2 + 1^2[/tex],

and XY = √10.

4. YZ is visualized to have a length of 4 units.

5. Knowing that

ZX = 3√2, XY =√10, and YZ = 4

⇒ Perimeter of ΔXYZ = ZX + XY + YZ

⇒ Perimeter of ΔXYZ = 3√2 + √10 + 4

⇒ Perimeter of ΔXYZ = 14√5 units.

To simplify this, it would be that the Perimeter of ΔXYZ  = 14√5 units

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If the discriminant of an equation is positive, which of the following is true of
the equation?

Answers

Step-by-step explanation:

For this case suppose that we have a quadratic equation of the form:

 

 The solution to the quadratic recuacion is given by:

 

 Where,

 The discriminant is:

 

 When the discriminant is greater than zero, then the root is positive, and therefore, we have two positive real solutions.

 Answer:

 B. it has two real solutions

The Chess Club wants to raise a total of $150 for a group trip.
They earn $1.25 for each box of pies they sell. They have
already made $16.25. Which equation could be used to find
how many more boxes of pies they must sell?

Answers

Answer:

Step-by-step explanation:

The number of boxes of pies that the Chess Club must sell to reach their goal of $150 can be represented by the variable x. We can create the following equation to represent this relationship:

1.25x + 16.25 = 150

To find the number of boxes of pies that the Chess Club must sell, we can solve this equation by subtracting 16.25 from both sides and then dividing both sides by 1.25:

1.25x = 150 - 16.25

1.25x = 133.75

x = 133.75 / 1.25

x = 107.

Therefore, the Chess Club must sell 107 more boxes of pies to reach their goal of $150.

Simplify:
O
O
O
O
(3) ²
9
4
9
(())
9
< Previous
-12
-7
9
(4)
-3
6help

Answers

The simplified form of the given expression is, [tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex].

What is simplifying an expression?

To simplify an expression, create an equivalent expression without any terms that are similar. The expression will then be rewritten using the fewest terms possible.

Consider, the given expression,

[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5[/tex]

To simplify this using the exponent rule:

[tex]((a)^b)^c = a^b^.^c[/tex]

[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9})^(^-^4^*^-^3)(\frac{4}{9})^-^5\\ ((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9})^1^2(\frac{4}{9} )^-^5[/tex]

Now use the exponent rule:

[tex]a^ba^c = a^(^b^+^c^)[/tex]

[tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^(^1^2^-^5^)\\((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex]

Hence, the simplified form of the given expression is, [tex]((\frac{4}{9} )^-^4)^-^3(\frac{4}{9})^-^5 = (\frac{4}{9} )^7[/tex].

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. If F F G H text is a rhombus, find each missing value
J G=
F J=
m ∠ E F H=
m ∠H G E=

2. If J K Z If is a square, find each missing value
J L=
M A=
m ∠ R N L=
R∠ M E U=

Answers

The value of JG = 24,

                      FJ = 7,

                     ∠EFH = 74°,

                     ∠HGE = 16°

What are the properties of a diagonal of rhombus?

In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.

Solution:

Given :

EJ = 24

∴ GJ = 24

∠FHG = 74°

∴ ∠EFH = 74° by alternate angle properties

Now, we know

FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other

Substitute FG = 25, GJ = 24, we get

25² = FJ² + 24² - 2FJ × GJ × cos(90)

FJ² = 49

∴FJ = 7

180 =∠GHJ  +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°

∴ ∠HGE = ∠HGJ = 180 - 90 - 74

∴ ∠HGE = 16°

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2. The value of JL = 14

                         ML = 7√2

                         ∠KNL = 90°

                          ∠MKJ = 45°

What are the properties of diagonals of a square?

The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.

Solution:

Given; NM = 7

We know that diagonals of the square are equal

∴ NM = NL = NK = NJ = 7

∵ JL = JN + NL

∴ JL = 7 + 7

∴JL = 14

∠KNL = 90° ----- as we know that diagonals bisect each other at 90°

For ∠MKJ

we know that KM = KN + NM = 14

KJ = JM = 7√2------- property of isosceles triangle

∠KJM = 90° ----- all angles of square are 90°

We know that diagonals of a square dissects the square into two equal isosceles triangle.

∴ ∠MKJ = JMK = ∠KJM/2

∴ ∠MKJ = 90/2

∴ ∠MKJ = 45°

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The value of JG = 24 ,   FJ = 7,   ∠EFH = 74°,   ∠HGE = 16°

What are the properties of a diagonal of rhombus?

In a rhombus, diagonals bisect each other at right angles. Diagonals bisect the angles of a rhombus. The sum of two adjacent angles is equal to 180 degrees. You will get a rectangle when you join the midpoint of the sides.

Given :

EJ = 24

∴ GJ = 24

∠FHG = 74°

∴ ∠EFH = 74° by alternate angle properties

Now, we know

FG² =FJ² + GJ² - 2FJ × GJ × cos(90) ------ diagonals of the rhombus are perpendicular to each other

Substitute FG = 25, GJ = 24, we get

25² = FJ² + 24² - 2FJ × GJ × cos(90)

FJ² = 49

∴FJ = 7

180 =∠GHJ  +∠HGJ + ∠GJH ------ sum of all angles of a triangle is 180°

∴ ∠HGE = ∠HGJ = 180 - 90 - 74

∴ ∠HGE = 16°

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2. The value of JL = 14

              ML = 7√2

                        ∠KNL = 90°

                         ∠MKJ = 45°

What are the properties of diagonals of a square?

The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other. The diagonal of the square divide it into two similar isosceles triangles.

Given; NM = 7

We know that diagonals of the square are equal

∴ NM = NL = NK = NJ = 7

∵ JL = JN + NL

∴ JL = 7 + 7

∴JL = 14

∠KNL = 90° ----- as we know that diagonals bisect each other at 90°

For ∠MKJ

we know that KM = KN + NM = 14

KJ = JM = 7√2------- property of isosceles triangle

∠KJM = 90° ----- all angles of square are 90°

We know that diagonals of a square dissects the square into two equal isosceles triangle.

∴ ∠MKJ = JMK = ∠KJM/2

∴ ∠MKJ = 90/2

∴ ∠MKJ = 45°

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