In rectangle QRST , QS=30-2x and RT=9+x . Find the lengths of the diagonals of QRST

Answer:

one apple: 75 cents

one orange: 60 cents

Step-by-step explanation:

let x be price of one apple

let y be price of one orange

3x + 4y = 4.65

5x + 8y = 8.55

we can do elimination, substitution, or graphing.

this is elimination: (we're eliminating the x in this case to find y, and then use y to find x)

ORIGINAL EQUATIONS: (we're multiplying by 5 so we can eliminate x)

3x + 4y = 4.65

5x + 8y = 8.55

5(3x + 4y = 4.65) = 15x + 20y = 23.25

3(5x + 8y) = 8.55 = 15x + 24y = 25.65

(distribute, and then subtract to get one equation and eliminate x)

  15x + 20y = 23.25

-  15x + 24y = 25.65

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

  0    -    4y = - 2.4

so we got that, now we make it this:    -4y = -2.4

divide both sides by -4.

-4y = -2.4

-----    -----

-4          -4

y (orange variable) = 0.60

therefore, one orange cost 60 cents.

plug y (the 60 cents) back into one of the original equations (either works) and solve for x.

3x + 4y = 4.65

5x + 8y = 8.55

let's use this equation:  5x + 8y = 8.55

5x + 8(0.6) = 8.55

5x + 4.8 = 8.55

     -4.8      -4.8

5x = 3.75

----    ------

5        5

x = 0.75

therefore, one apple cost 75 cents.

(also, there was an easier number to multiple the equations by)

3x + 4y = 4.65

5x + 8y = 8.55

We could have multiplied (3x + 4y = 4.65) with 2, distributing and bringing it to 6x + 8y = 9.30

Then subtract 6x + 8y = 9.30 from 5x + 8y = 8.55, and you would have solved and gotten x just fine, then plugged x back in to find y)

sorry this answer is so long...good luck :))

The sοlutiοn(s) οn the graph are x = -4, 2.

In mathematics, a graph is a diagram οr visual representatiοn οf facts οr values that is οrdered. The pοints οn a graph are typically used tο depict the relatiοnships between twο οr mοre things. Graph theοry is the study οf graphs, which are mathematical structures that are used tο depict pairwise interactiοns between οbjects. A graph in this sense is made up οf vertices and edges.

A graph is an οrdered graphic οr visual representatiοn οf facts οr values in mathematics. The relatiοnships between twο οr mοre οbjects are οften shοwn by the pοints οn a graph.

The study οf graphs, which are mathematical representatiοns οf pairwise interactiοns between things, is knοwn as graph theοry. Vertices and edges make up a graph in this cοntext.

From the given graph we conclude following -

[tex]\frac{1}{4}x^2 = -\frac{1}{2}x + 2\\x^2 + 2x - 8 = 0\\x^2 + 4x - 2x - 8 = 0\\x(x + 4) - 2(x + 4) = 0\\(x + 4)(x - 2) = 0\\x = 2, -4[/tex]

On the graph, the solutiοns are the x-coοrdinates of the points of intersection

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Answer:

0.85 m

Step-by-step explanation:

Model dimension : Real dimension

3 : 74

x : 21

[tex] \frac{21}{74} = \frac{x}{3} \\ x = 3 \times \frac{21}{74} \\ = \frac{63}{74} \\ = 0.851...[/tex]

Answer:

85.54 cm

Step-by-step explanation:

To find the height of the scale model, we need to use the scale ratio given: 3 : 74. This means that every 3 units on the model represent 74 units on the real building.

First, we need to determine the ratio of the heights. Let x be the height of the scale model. Then:

3 / 74 = x / 21

Solving for x, we get:

x = 21 * 3 / 74

x = 0.8554 m

To convert this to centimeters, we multiply by 100:

x = 85.54 cm

Therefore, the height of the scale model is 85.54 cm to 2 decimal places.

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The probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.

The given distribution is λxe-λx! where λ is the expected number of flood events in a year. In order to calculate the probability of not more than two flood events in a particular year at that location.

The expected number of flood events in a year is given by: λ = (5 flood events) / (2 years) = 2.5 flood events per year

The given distribution is:λxe-λx! = 2.5xe-2.5x!

We need to find the probability of occurring not more than two flood events in a particular year at that location.

Therefore, the required probability is:P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)Here, P(x) represents the probability of x flood events.

The probability of x flood events can be calculated using the Poisson distribution formula:

P(x) = λxe-λx!Substitute λ = 2.5 and x = 0 in the above formula to get:P(0) = (2.5)0e-2.5 / 0! = e-2.5 ≈ 0.082Substitute λ = 2.5 and x = 1 in the above formula to get:P(1) = (2.5)1e-2.5 / 1! = 2.5e-2.5 ≈ 0.206Substitute λ = 2.5 and x = 2 in the above formula to get:P(2) = (2.5)2e-2.5 / 2! = 3.125e-2.5 ≈ 0.258Step 5

Now, add the above probabilities to find the required probability:P(x ≤ 2) = P(0) + P(1) + P(2)≈ 0.082 + 0.206 + 0.258 = 0.546Therefore, the probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.

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Answer:

Step-by-step explanation:

First we sould factor out the function:

y=x^2+5x-6

y=(x+6)(x-1)

Note: if you multiply out the factored equation, you will get your original equation.

Now, find what we need to plug in to make it equal 0.

If we plug in -6, then the (x+6) part equals 0. Since we are multiplying by 0, the whole thing equals 0.

If we plug in 1, then the (x-1) part equals 0. Since we are alo multiplying by 0 here, the function comes out to 0.

This means that at x=-6 and x=1 the function comes out to 0.

Answer:

k=11/3

Step-by-step explanation:

Use distributive property.

3k+4=15

Subtract 4 from both sides.

3k=11

Divide 3 from both sides.

k=11/3

Answer: k=11/3 or 3.66

Step-by-step explanation:

3k+4=15 --Distribute 1/3 to 9k and 12.

3k=11 --Subtract 4 from both sides.

k=11/3 or 3.66

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The family needs 15 cubic feet of sand to fill the mold completely.

The volume of the square pyramid sand castle mold can be calculated as V = (1/3) * b² * h, where b is the length of one edge of the square base and h is the height from the base to the apex.

In this case, b = 3 feet and h = 5 feet.

Plugging these values into the formula, we get:

V = (1/3) * 3² * 5

V = 15 cubic feet

Therefore, the family needs 15 cubic feet of sand to fill the mold completely.

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Answer:

The answer is 4/17

Step-by-step explanation:

Answer:

1440 ft²

Step-by-step explanation:

The roof is made up of 4 congruent triangles.

We first solve for the area of one of the triangles using the formula:

A = (1/2) · b · h

↓ plugging in given values

A = (1/2) · 40 ft · 18 ft

A = 20 ft · 18 ft

A = 360 ft²

Now, we can solve for the surface area of the entire roof by multiplying the area of one of the triangles by 4 (because there are 4 congruent triangles).

SA = 360 ft² · 4 = 1440 ft²

—

Note that we can solve for the area of the triangles using the formula {A = (1/2) · b · h} because the slant height of a pyramid is perpendicular to the side of the pyramid's base that it connects to, thereby making it the height of the triangle that is the pyramid's side.

—

The two sets of data are

Set 1: 5, 6, 7, 8, 9, 10, 20

Set 2: 1, 2, 3, 4, 5, 15, 16

The median is a measure of central tendency in a data set that represents the middle value of the data when arranged in order.

To find the median of a data set, we need to arrange the values in ascending or descending order and then find the middle value.

The IQR (Interquartile Range) is a measure of variability in a data set that represents the difference between the 75th percentile (third quartile) and the 25th percentile (first quartile).

To calculate the IQR of a data set, we need to find the values of the first quartile (Q1), and third quartile (Q3), and then subtract Q1 from Q3.

Here we have

Each data set has 7 values, -

The median of set 1 is greater than the median of set 2, -

The IQRs of the data sets are the same.

To create the sets assume a positive value as the median of the data and make sure that the value is in the middle of the data.

Similarly, take another positive value that is greater than the previous value and make sure that the value is also in the middle.

Now arrange the remaining values such that both sets of data have the same IQRs.  

Here are two sets of data that meet the given characteristics:

Set 1: 5, 6, 7, 8, 9, 10, 20

Median: 8

IQR: 4 (Q3 = 9, Q1 = 5)

Set 2: 1, 2, 3, 4, 5, 15, 16

Median: 4

IQR: 4 (Q3 = 5, Q1 = 1)

Therefore,

The two sets of data are

Set 1: 5, 6, 7, 8, 9, 10, 20

Set 2: 1, 2, 3, 4, 5, 15, 16

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According the given question the value οf x is (b+1)/(d-a).

Tο simplify simply means tο make anything easier. In mathematics, simplifying an equatiοn, fractiοn, οr prοblem means taking it and making it simpler.

Calculatiοns and prοblem-sοlving techniques simplify the issue. Simplifying shοuld have twο essential characteristics: it shοuld be algοrithmic, and it shοuld result in the same simplified fοrm when twο expressiοns fοr the same thing are simplified. These characteristics οf a simplificatiοn apprοach prοvide an algοrithm fοr determining whether twο expressiοns are equivalent.

Here, we have

Given: ax+b=dx-1,  if a≠d

We have tο find the value οf x.

We apply simplificatiοn here and we get

ax+b = dx-1

b + 1 = dx - ax

b +1 = x(d-a)

x = (b+1)/(d-a)

Hence, the value οf x is (b+1)/(d-a).

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Step-by-step explanation:

Her interest earned will be   p r t    

p = principal = amount of deposit = 1100 dollars

r = decimal  interest rate = .09

t = time in years = 3

$ 1100 * .09 * 3 = $ 297 .

The amount of fertilizer needed for the garden is 508600 grams.

In the middle of the garden is a pond that is approximately circular with a diameter of 40 m. Therefore, the fertilizer will not be applied in the pond area.

The villagers will only apply the fertilizer in the garden area. The recommended rate of application of the fertiliser is 25 g/m².

Therefore, let's find the fertilizer required for the garden.

area of the garden to be fertilized = area of trapezium - area of a circle

area of the garden to be fertilized = 1 / 2 (a + b)h - πr²

area of the garden to be fertilized = 1 / 2 (124 + 196)135 - 3.14(20)²

area of the garden to be fertilized = 1 / 2 (320)(135) - 1256

area of the garden to be fertilized = 43200 / 2 - 1256

area of the garden to be fertilized = 21600 - 1256

area of the garden to be fertilized = 20344 m²

Therefore,

1 m² = 25 grams

20344 m² = ?

Hence,

amount of fertiliser needed  = 20344 × 25 = 508600 grams

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Answer:

Answer  = 21 Sacks

Step-by-step explanation:

First, we need to calculate how much flour the baker will use in 20 days:

Amount of flour used per day for 64 loaves = 64 loaves/day x 400 g/loaf = 25,600 g/day

Amount of flour used in 20 days = 25,600 g/day x 20 days = 512,000 g

Next, we need to convert the amount of flour used into kilograms:

512,000 g ÷ 1000 g/kg = 512 kg

Finally, we need to calculate the minimum number of 25 kg sacks the baker should order:

Number of 25 kg sacks = 512 kg ÷ 25 kg/sack ≈ 20.48

Since the baker cannot order a fraction of a sack, he will need to order at least 21 sacks to last him for 20 days.

Answer:

the amount will give 69 percentage of nothing thanks

The shape shοwn is a a parallelοgram as  twο sides are parallel and οppοsite angles are same. Thus, οptiοn D is cοrrect.

A parallelοgram is a quadrilateral in which the οppοsite sides are parallel and equal. Parallelοgrams are classified intο three main types: square, rectangle, and rhοmbus, and each οf them has its οwn unique prοperties.

A parallelοgram is a special kind οf quadrilateral that is fοrmed by parallel lines. The angle between the adjacent sides οf a parallelοgram may vary but the οppοsite sides need tο be parallel fοr it tο be a parallelοgram. A quadrilateral will be a parallelοgram if its οppοsite sides are parallel and cοngruent. Hence, a parallelοgram is defined as a quadrilateral in which bοth pairs οf οppοsite sides are parallel and equal.

Given that:

One οf the twο οppοsite sides are equal

The οther twο sides are parallel

These are the traits οf a parallelοgram.

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Complete question:

What type of shape is show below:

he volume of the drum can be calculated as follows:

Volume of drum = πr²h

= π(4.2m)²(3.5m)

≈ 246.33 m³

To find out how many full bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the volume of one wheat bag:

Number of full bags of wheat = Volume of drum ÷ Volume of one bag

= 246.33 m³ ÷ 5.39 m³

≈ 45.72

Therefore, the circular drum can hold approximately 45 full bags of wheat.

Answer: 45 Full of bags.

Step-by-step explanation:

The volume of the drum can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.

V = π(4.2m)^2(3.5m)

V ≈ 246.73 m³

To find out how many bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the space required for one bag:

246.73 m³ ÷ 5.39 m³/bag ≈ 45.81 bags

Since we can't have a fraction of a bag, we need to round down to the nearest whole number:

Number of bags = 45

Therefore, 45 full bags of wheat can be emptied into the drum.

The Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.

The distance between the Sun and the Earth is approximately 9.29 x 10^7 miles, and the distance between the Moon and the Earth is approximately 2.389 x 10^5 miles.

To find how much farther the Sun is from the Earth than the Moon, we can subtract the distance between the Moon and the Earth from the distance between the Sun and the Earth:

9.29 x 10^7 miles - 2.389 x 10^5 miles = 9.2661 x 10^7 miles

Therefore, the Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.

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We can say that after answering the offered question As a result, the equation for the circle with centre (7, -7) and point (11, -3) i[tex](x - 7)2 + (y + 7)2 = 32.[/tex]

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

Determine the radius:

The radius of the circle is the distance between the circle's centre (7, -7) and any point on it (11, -3).

We may calculate the distance using the distance formula:

[tex]r = \sqrt((11 - 7)^2 + (-3 - (-7))\\v^2)\\r = \sqrt(4^2 + 4^2)\\r = \sqrt(32) (32)[/tex]

In the standard form equation of a circle, substitute the centre and radius:

A circle with centre (h, k) and radius r has the following standard form equation:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

With h = 7, k = -7, and r = sqrt(32), we get:

[tex](x - 7)^2 + (y + 7)^2 = 32[/tex]

As a result, the equation for the circle with centre (7, -7) and point (11, -3) is[tex](x - 7)2 + (y + 7)2 = 32.[/tex]

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Answer:

C. (6r + 5)

Step-by-step explanation:

You would multiply (3r - 7) with (6r + 5) to get the value.

According to the algebraic expression 1.50x + 0.75y:

An algebraic expression is a combination of variables, values, numbers, and constants.

An algebraic expression is short of an equation, which consists of two or more algebraic expressions that are equated to each other.

The cost of hot dogs per unit = $1.50

The cost of cans of soda per unit = $0.75

Let the number of hot dogs bought = x

Let the number of cans of soda bought = y

1.50x + 0.75y = Customer's total expenses

Thus, the variables x and y in the algebraic expression represent the number of units of each type of item sold during the BBQ fundraiser.

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Answer:

Red I think maybe we should try hi friends I am new to this app

The charged battery costs 16 dollars, which is denoted as -16. (negative number). The cost for  the savings for using a battery that can be recharged is +14(positive number).

A battery is an electrical energy storage instrument made up of one or more electrochemical cells connected to the outside world. The cathode and anode of a battery are the positive and negative terminals, respectively, when the battery is supplying electricity.                            The battery costs 16 dollars. You save 14 dollars each time you recharge the battery.  The cost of the rechargeable battery as a negative number is -16.The savings for using a battery that can be recharged is +14

The charged battery costs 16 dollars, which is denoted as -16. (negative number). Each refresh saves 14 dollars, which is symbolised as +14. (positive number). The charged battery costs 16 dollars, which is denoted as -16. (negative number). The cost for  the savings for using a battery that can be recharged is +14(positive number).

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Answer:

735.1 square meters

Step-by-step explanation:

total surface area (TSA) of a cone can be calculated by using this mathematical expression:

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)

Total surface area (TSA) of a cone = 3.142 × 6 × (39)

Total surface area (TSA) of a cone = 735.1 square meters.

Answer: ty

Step-by-step explanation:

Brainliest pls:)

The circular pan with a 16 inch diameter is 55.94 square inches (256-201.06) larger than the square pan with sides measuring 16 inches.

The area of a circle is given by the formula A=πr2, where r is the radius of the circle. The radius of a circle with a 16 inch diameter is 8 inches. Therefore, the area of this circle is A=π*82=201.06 square inches.

The area of a 16 inch square is given by the formula A=s2, where s is the length of the side of the square. The area of this square is A=162=256 square inches.

Therefore, the circular pan with a 16 inch diameter is 55.94 square inches (256-201.06) larger than the square pan with sides measuring 16 inches.

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Answer: 490.87 is the answer, rounded to a whole number is 491.

Step-by-step explanation: A≈490.87m²

Solving for A

A=1

4πd2=1

4·π·252≈490.87385m²

Not sure that's really an explanation but... Hope that makes since :)

Answer:

a)

=2×5+2×6

=10+12

=22

Ans. GCF (10, 12) = 2

The value of the test statistic is -1.75.

To test the claim that the percentage of uninsured patients is under the expected percentage of 32%, we can use a one-sample z-test. The null hypothesis is that the true percentage of uninsured patients is equal to 32%, while the alternative hypothesis is that the true percentage is less than 32%.

Using the sample data, we can calculate the sample proportion of uninsured patients as 40/160 = 0.25. We can then calculate the standard error of the sample proportion as sqrt[(0.32 x 0.68)/160] = 0.0385.

The test statistic can be calculated as (0.25 - 0.32)/0.0385 = -1.75.

To find the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator to find the probability of a z-score less than -1.75. The p-value is approximately 0.04.

Since the p-value is less than the typical significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that the percentage of uninsured patients is under the expected percentage of 32%.

Therefore, the correct answer is -1.75, which is the calculated value of the test statistic.

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Answer:

62.85 units

Step-by-step explanation:

s= rΘ

s= 4*5π/3= 20π/3

the perimeter= 20π/3*3

= 20π

= 20*22/7

= 440/7=62.85