What is the approximate length of the base of an isosceles triangle if the congruent sides are 3 feet and the vertex angle is 35°?

Answer:

I'm not quite sure but I believe he sold 39 Boxes for $3.50 a box.

Step-by-step explanation:

-You would divide 702 by 18 Since he puts them in boxes of 18.

702/18= 39

-Then you would divide $136.50 by 39

136.5/39= 3.5

Which means each box was $3.50 a piece

Tyler sold 39 boxes of cookies, with the price of each box is $3.5

Further explanation

Given:

Tyler baked 702 cookies

He sold them in boxes of 18 cookies

Tyler earned $136.50

Question:

How many boxes of cookies did Tyler sell?

to find out how many boxes of cookies he sold we are going to divide the total cookies he made with the number of cookies in each box

[tex]\boxed {= \frac{702}{18} = 39 }[/tex]

so there were 39 boxes of cookies. He sold all of them and earned $136.50. Price per box would be:

[tex]\boxed {\frac{136.50}{39} = 3.5 }[/tex]

With total earned $136.50, Tyler sold 39 boxes of cookies at $3.5/box

Mixed fraction brainly.com/question/213168

Division big numbers brainly.com/question/1955444

Division brainly.com/question/11688736

Keywords: mixed fraction, fraction, division, division big numbers, math word problem, multiplication

If a, b and c are the lengths of a right triangle and c is the longest side, then:

[tex]a^2+b^2=c^2[/tex]

We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:

[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]

Answer:

$200 will be price of 2 pairs

Step-by-step explanation:

It is given that the price of one pant is $80

The second is given at half price which is $40

but in the case of pants buying or anything buying when we are given an off then after buying an item the same discount is given for all

so as he bought one pant then the other pant will be given at half price

now the third pant will also be given at half price i.e: $40

fourth price will also be given at $40

so four pants will become 2 pairs

price of 2 pairs = $80+$40+$40+$40

                         =$200

Answer: 8

Step-by-step explanation:

60 dowels - each 6 inches (1/2 foot) in length = 30 feet of wood

30 feet of wood ÷ 4 foot boards = 7.5 boards

Since he can't buy half of a board, you must round up to 8 boards.

The question involves a conversion of measurements. After converting 4 feet to 48 inches, it's calculated that one piece of wood can produce 8 dowels. To make 60 dowels, you would need 7.5 pieces of wood, but this rounds up to 8 pieces since half a piece cannot be bought.

To answer this question, we first need to understand that all measurements need to be in the same units. Since our dowels are in inches (6 inches long) and our wood lengths are in feet (4 feet long), we need to convert one to the other. For simplicity's sake, let's convert the feet to inches as follows: 1 foot = 12 inches, therefore, 4 feet = 48 inches.

Then, we can find out how many dowels we can get from just one piece of wood: 48 inches / 6 inches per dowel = 8 dowels per one piece of 4-foot wood.

Lastly, to find out how many pieces of wood are needed to make 60 dowels, we divide the total number of dowels by the number of dowels per wood: 60 dowels / 8 dowels per wood = 7.5. Since we can't purchase half a piece of wood, we have to round up, so the carpenter needs to buy a minimum of 8 pieces of 4-foot wood to have enough to make 60 dowels.

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Points A, B, and C are equidistant from point M, so lie on a circle centered at M. That makes BC a diameter, and it means that inscribed angle BAC intercepts an arc of 180°.

The measure of the inscribed angle is half the measure of the arc, so ∠BAC is 90° and ΔABC is a right triangle.

Final answer:

Given that the median AM of triangle ∆ABC is half the length of BC, by showing that triangles ADM and BMC are congruent with the right angle at A, we prove that ∆ABC is a right triangle because the median to the hypotenuse is half its length.

Explanation:

Given that the median AM of triangle ∆ABC is half the length of side BC, to prove that triangle ∆ABC is a right triangle, we can use the properties of triangles and the definition of a median.

Let's denote the midpoint of BC as D such that AD is the median and AD = DB = DC since AM is half of BC and M coincides with D.

Now, consider triangles ADM and BMC. They are right triangles because AD and DM are perpendicular to BC (definition of a median from a vertex to the midpoint of the opposite side). In ∆ADM and ∆BMC, we have AD = DB and DM is common.

Hence, triangles ADM and BMC are congruent by the Side-Side-Side (SSS) criterion. This implies that AM = MB and angle AMD (or AMB) is a right angle.

Since AM is also the median, for it to be equal in length to MB (half of BC), the only way this is geometrically possible is for triangle ABC to be a right triangle with the right angle at A. This is because the median to the hypotenuse of a right triangle is always half the length of the hypotenuse, which in this case is side BC.

Therefore, triangle ∆ABC must be a right triangle.

To calculate the thickness of one card from a stack of three hundred cards with a total height of 5/8 inch, you divide the total height by the number of cards, resulting in roughly 0.0020833 inches per card.

To compute the thickness of one card from a stack of three hundred cards, we must first determine the total height of the stack, which we already know is 5/8 of an inch. Then, we simply divide this height by the number of cards, which is 300, to find the thickness of a single card.

Here is the calculation:

Total height of the stack = 5/8 inch
Number of cards in the stack = 300

Thickness of one card = Total height of the stack
Number of cards

Thickness of one card = (5/8 inch)
300

Thickness of one card = 5/8
300

Thickness of one card = 0.0020833... inches (approx.)

Therefore, each card is approximately 0.0020833 inches thick.

Final answer:

The converse of the statement is "If two angles are equal, then the two angles are both obtuse."

Explanation:

Converse of the Statement:

To write the converse of the statement 'if two angles are both obtuse, the two angles are equal,' we need to swap the hypothesis and the conclusion.

The converse statement would be: 'If two angles are equal, then the angles are both obtuse.'

Example:

Let's consider two angles, Angle A and Angle B. If Angle A and Angle B are both equal, then we can conclude that both angles are obtuse.

Answer:

False

Step-by-step explanation:

If the angles are congruent then they have the same shape but the sides  could be of different length. The 2 triangles are SIMILAR but not necessarily congruent.

Answer:

b. [tex]e=25c+125[/tex]

Step-by-step explanation:

We are told that Mr. Shaw earned $250 for selling 5 cars. Mr. Shaw earned $400 for selling 11 cars.

We can see that earnings of Mr. Shaw depends on selling of car, so selling of cars will be independent (x) and total earnings will be dependent (y).

Let us find slope of our line with given points (5,250) and (11,400)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{400-250}{11-5}[/tex]

[tex]m=\frac{150}{6}=25[/tex]

This means that Mr. Shaw earns $25 for selling each car.

Now let us find equation of our line in slope intercept formula.

[tex]y=mx+b[/tex], where m= Slope and b= y- intercept.

Let us find b for our equation substituting coordinates of point (5,250) and m=25 in slope intercept form of equation.

[tex]250=25*5+b[/tex]

[tex]250=125+b[/tex]

[tex]250-125=b[/tex]

[tex]125=b[/tex]

[tex]y=25x+125[/tex]

Now let e represent the amount earned by Mr. Shaw and c represent the number of cars sold.

So our equation will be:  [tex]e=25c+125[/tex] and option b is the correct choice.

The correct equation that represents Mr. Shaw's earnings from selling cars, where c is the number of cars sold and e is the earnings, is Option b: e = 25c + 125, because it correctly translates the given scenarios into mathematical terms.

The equation correctly represents the situation where c represents the number of cars Mr. Shaw sold and e represents the amount he earned from selling those cars.

To solve this, let's plug the values given into the options provided and see which one fits. For the first scenario, selling 5 cars earned him $250, and selling 11 cars earned him $400.

Option a: e = 50c + 125
For 5 cars: e = 50(5) + 125 = 250 + 125 = 375 (Incorrect)
For 11 cars: e = 50(11) + 125 = 550 + 125 = 675 (Incorrect)

Option b: e = 25c + 125
For 5 cars: e = 25(5) + 125 = 125 + 125 = 250 (Correct for 5 cars)
For 11 cars: e = 25(11) + 125 = 275 + 125 = 400 (Correct for 11 cars)

Option c: e = 50c
This option does not include the fixed amount, thus incorrect based on the provided values.

Option d: e = 25c
This option also does not consider a fixed starting amount, making it incorrect for our situation.

Hence, the correct equation is Option b: e = 25c + 125.

Answer:

RS 34000

Step-by-step explanation:

Price of the car = RS 23500

Profit = RS 10500

Selling price of the car = Price of the car + Profit

= Rs 23500 + RS 10500

= RS 34000

Answer:

Elevation = [tex]39996-160=3836[/tex] meters (taking base of Mt. Armstrong as sea level)

Step-by-step explanation:

The midpoint will be the half of their total distance.

If we take base of Mt. Armstrong to be 0, then Maya's distance is 7832 meters ABOVE and Juan's distance is 160 meters BELOW that.

The distance between them is thus [tex]7832+160=7992[/tex] meters.

We take half of this, to find midpoint. So:

[tex]\frac{7992}{2}=3996[/tex] meters

This is 3996 meters from Juan or from Maya. If the picnic is going to be at 3996 meters ABOVE Juan and since base of mountain is where we start measuring, we subtract 160 (Juan's distance from base) from 3996 to get the ELEVATION.

Elevation = [tex]39996-160=3836[/tex]

Answer:

$450 is the original price

Step-by-step explanation:

We can create a proportion to find the sale on the original price. A proportion is an equation where two ratios are set equal to each other. We create two fractions using the prices and percents. It is marked down by 30% so we pay 70% of the original. The sale price is $315.

[tex]\frac{70}{100} =\frac{315}{x}[/tex]

We begin solving by cross multiplying numerator to denominator of each fraction.

[tex]70(x)=100(315)\\70x=31500\\\frac{70x}{70}=\frac{31500}{70}  \\450=x[/tex]

Total number of evening dresses, sundresses, cocktail dresses are 9 , 7, 10 respectively.

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.

Let the number of evening dresses produced be x , sundresses produced   be y and cocktail dresses produced  be z.

According to the problem,

∴ We can write 3x + y + 2z = 54........(1)

Again, according to the problem,

∴ We can write 2x + 1.5y + z = 38.5........(2)

Again,

∴  We can write, 5x + 3y + 2.5z = 91......(3)

We have to solve the three equations.

From equation (1) we can write , y = 54 - 3x - 2z

Putting the value of y in equation (2), we get,

   2x + 1.5(54- 3x - 2z) + z = 38.5

⇒ 2x + 81 - 4.5x - 3z + z = 38.5

⇒ 2z + 2.5x = 42.5.....(4)

Again, putting the value of y from equation (1) in equation (3), we get,

5x + 3(54- 3x - 2z) + 2.5z = 91

⇒ 5x + 162 - 9x - 6z + 2.5z = 91

⇒ 4x +3.5z = 71

⇒ x = (71 - 3.5z)/4

Putting the value of x in equation (4)

2z + 2.5{(71 - 3.5z)/4} = 42.5

⇒ 8z + 177.5 - 8.75z = 170

⇒ -0.75z = -7.5

⇒ z= 10

Again putting the value of z in equation (4)

x = (71 - 35)/4 = 9

Putting the value of x and z in equation (1)

y = 54 - 27 - 20

⇒ y = 7

Number of evening dress = 9

Number of sundresses = 7

Number of cocktail dresses= 10

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In that week, the employees produced 7 evening gowns, 7 sundresses, and 9 cocktail dresses in total.

Given equations:

[tex]\[3x + y + 2z = 54\] (1)[/tex]

[tex]\[2x + 1.5y + z = 38.5\] (2)[/tex]

[tex]\[5x + 3y + 2.5z = 91\] (3)[/tex]

We'll use the method of elimination to solve this system of equations.

Step 1: Multiply equation (2) by 2 to eliminate [tex]\(z\):[/tex]

[tex]\[4x + 3y + 2z = 77\] (4)[/tex]

Step 2: Subtract equation (1) from equation (4) to eliminate [tex]\(x\):[/tex]

[tex]\[(4x + 3y + 2z) - (3x + y + 2z) = 77 - 54\][/tex]

[tex]\[x + 2y = 23\] (5)[/tex]

Step 3: Multiply equation (1) by 2 and subtract equation (2) from it to eliminate [tex]\(y\):[/tex]

[tex]\[6x + 2y + 4z - (2x + 1.5y + z) = 108 - 38.5\][/tex]

[tex]\[4x + 3z = 69.5\] (6)[/tex]

Step 4: Multiply equation (5) by 2 and subtract equation (6) from it to solve for [tex]\(x\):[/tex]

[tex]\[2(x + 2y) - (4x + 3z) = 46 - 69.5\][/tex]

[tex]\[2x + 4y - 4x - 3z = -23.5\][/tex]

[tex]\[4y - 3z = -23.5\] (7)[/tex]

Step 5: Now, let's multiply equation (7) by 3 and add it to equation (6) to solve for [tex]\(z\):[/tex]

[tex]\[3(4y - 3z) + 4x + 3z = -23.5\][/tex]

[tex]\[12y - 9z + 4x + 3z = -23.5\][/tex]

[tex]\[4x + 12y - 6z = -23.5\] (8)[/tex]

[tex]\[4x + 3z = 69.5\] (6)[/tex]

Now, add equations (8) and (6):

[tex]\[4x + 12y - 6z + 4x + 3z = -23.5 + 69.5\][/tex]

[tex]\[8x + 12y - 3z = 46\][/tex]

Step 6: Plug in the values of [tex]\(x\) and \(z\)[/tex] into equation (6) to solve for [tex]\(y\):[/tex]

[tex]\[8x + 12y - 3(69.5 - 4x) = 46\][/tex]

[tex]\[8x + 12y - 208.5 + 12x = 46\][/tex]

[tex]\[20x + 12y = 254.5\][/tex]

[tex]\[20x = 254.5 - 12y\][/tex]

[tex]\[x = \frac{254.5 - 12y}{20}\] (9)[/tex]

Step 7: Substitute the value of [tex]\(x\)[/tex] from equation (9) into equation (5) to solve for [tex]\(y\):[/tex]

[tex]\[\frac{254.5 - 12y}{20} + 2y = 23\][/tex]

[tex]\[254.5 - 12y + 40y = 460\][/tex]

[tex]\[28y = 205.5\][/tex]

[tex]\[y = \frac{205.5}{28}\][/tex]

y ≈ [tex]7.34[/tex]

Step 8: Substitute the values of[tex]\(x\) and \(y\)[/tex] into equation (1) to solve for [tex]\(z\):[/tex]

[tex]\[3x + y + 2z = 54\][/tex]

[tex]\[3(\frac{254.5 - 12y}{20}) + y + 2z = 54\][/tex]

[tex]\[3(\frac{254.5 - 12(7.34)}{20}) + 7.34 + 2z = 54\][/tex]

z ≈ 8.72

Since we can't produce a fraction of a dress, we'll round [tex]\(y\)[/tex] down to 7 and [tex]\(z\)[/tex]up to 9.

So, the employees produced approximately:

- 7 evening gowns

- 7 sundresses

- 9 cocktail dresses

Complete Question:

x^2+y^2-2xy+1+2xy-x^2=y^2+1

Answer:

Too much caramel.

Step-by-step explanation:

Answer: [tex]\bold{(A): g=\dfrac{\sqrt{15}}{2},\quad h=\dfrac{\sqrt{5}}{2}}[/tex]

Step-by-step explanation:

This is a special triangle because the side lengths have the following relationship:

30° ⇄ side length "a"        represented as "h" in your picture

60° ⇄ side length "a√3"   represented as "g" in your picture

90° ⇄ side length "2a"     represented as "√5" in your picture

Step 1: solve for "a"    hypotenuse (2a) is given as √5

[tex]2a=\sqrt{5}[/tex]

 [tex]a=\dfrac{\sqrt{5}}{2}[/tex]

According to your picture, a = h, so [tex]h=\dfrac{\sqrt{5}}{2}[/tex]

Step 2: use the a-value from Step 1 to solve for the remaining side

[tex]g=a\sqrt{3}[/tex]

   [tex]=\bigg( \dfrac{\sqrt{5}}{2}\bigg)\sqrt{3}[/tex]

   [tex]=\dfrac{\sqrt{15}}{2}[/tex]

Answer:

8,600 acres are old-growth trees.

Step-by-step explanation:

You can find this by multiplying the percentage by the overall number of acres

20% * 43,000 = 8,600

Answer:

There are 86 acres of old-growth trees.

Step-by-step explanation:

In order to answer the question, we need to calculate the 0.2% of 43,000.

We can calculate this stating that exists a linear relationship between the percentage and the amount of acres. We also need to state that 43,000 acres are the 100% of the acres.

Therefore, we can write the following equation to calculate the percentage :

[tex]\frac{43,000}{100}=\frac{x}{0.2}[/tex]

If we solve the equation in terms of ''x'' :

[tex]x=(\frac{43,000}{100}).(0.2)=86[/tex]

[tex]x=86[/tex]

We find that if 43,000 acres are the 100% of the acres ⇒ The 0.2% of the acres are 86 acres (in which there are old-growth trees).

Answer: Third option

= (6w + 2)(6w - 2)

Step-by-step explanation:

36w^2 - 4

= (6w)^2 - 2^2

=(6w + 2)(6w - 2)

Answer:

B) 8, 800, 000

Step-by-step explanation:

The number of cars in year 1= 80,000,000

She found that the number of cars on the roads increases by 10% each year.

Now let's find 10% of 80,000,000

= [tex]\frac{10}{100} *80,000,000 = 8,000,000[/tex]

So the number of cars in year 2= 80,000,000 + 8,000,000

= 88,000,000

Now let's find 10% of 88,000,000.

=  [tex]\frac{10}{100} *88,000,000 = 8,800,000[/tex]

So the number of cars in year 3= 88,000,000 million+8,800,000= 96,800,000

Now we have to find difference in year 3 compared to in year 2.

The difference in the cars in  year 3 compared to year 2= 96,800,000 - 88,000,000

=  8,800,000

Therefore, the answer is B) 8, 800, 000

A function in mathematics is a mapping where each input has exactly one output. A mapping is not a function if any input in the mapping maps to multiple outputs.

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. So a mapping is not a function if any input maps to multiple outputs.

For instance, if we have a mapping {a -> 1, b -> 2, c -> 1}, it is a function because even if 'a' and 'c' have the same output '1', it's okay because each individual input ('a', 'b', 'c') relates to exactly one output. But if we have a mapping {a -> 1, a -> 2}, this is not a function because 'a' maps to two different outputs ('1' and '2').

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Answer:

(-4,1)

Step-by-step explanation:

A system of equations is 2 or more equations for which the same x,y solution exists. We can solve the system in three ways: elimination, substitution, or graphing. Substitution can be used by substituting the value of one variable into the equation.

Pair 2.5x-3y=-13 and 3.25x-y=-14

We can solve for y in 3.25x-y=-14. 3.25x+14=y.

Because y=3.25x+14, we can substitute 3.25x+14 into y in 2.5x-3y=-13.

2.5x-3y=-13

2.5x-3(3.25x+14)=-13

2.5x-9.75x-42=-13

-7.25x-42=-13

-7.25x=29

x= -4

We now substitute x=-4 into y=3.25x+14

y=3.25x+14

y=3.25(-4)+14

y=-13+14

y=1

To solve the system by substitution, solve one equation for one variable and then substitute that expression into the second equation. Solve the resulting equation and then substitute the solution back into one of the original equations to find the other variable.

Given the equations:

Let's find the value of 'x' from the second equation:

y = 3.25x + 14

This formula for 'x' can be substituted into the first equation, resulting in a new equation:

2.5(3.25x + 14) - 3y = -14,

This equation can be simplified and solved to find the variable 'y'. The value of 'y' can then be substituted back into the original equation to find the value of 'x'.

The solution to these two equations, (x, y), is the point of intersection which describes the system of the original equations.

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Answer:

Option B is correct.

Step-by-step explanation:

Confidence interval is the range of the values that the particular probability whose value will lie in the interval.

So, if a level is 0.90 confidence interval it means the value of the probability will lie in the given level.

Therefore, Option B is correct that is an interval computed from sample data by a method that has probability 0.90 of producing an interval containing the true value of parameter of interest.

A 0.90 confidence interval is an interval computed from the sample data, with a probability of 0.90 that it contains the true value of the parameter of interest. The margin of error may vary and is not necessarily ±0.90. No method can absolutely guarantee a 0.90 probability.

A 0.90 confidence interval, in statistical terms, is most accurately defined as an interval computed from sample data by a method that has a probability of 0.90 of producing an interval containing the true value of the parameter of interest. Therefore, the correct answer to this question is option B).

When we say that we're 90% confident, what we're implying is that if we were to repeat the same experiment 100 times, we'd expect the true parameter to lie within the confidence interval 90 times. The margin of error isn't necessarily ±0.90 as suggested by some of the other options (A and C) - it could be any value, depending on the data.

Option D suggests the method guarantees a 0.90 probability. It's crucial to understand that a confidence interval doesn't give such a guarantee; it provides an estimate and there’s always a certain amount of uncertainty.

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Answer:

A

Step-by-step explanation:

We can find the surface area of the object by adding the surface areas of each part. We have many rectangle faces to count and two triangular faces. Each has a formula for the area. We will find the area of each and then add them all together.

Triangle - 0.5 *b*h

Rectangle - b*h

Triangles

There are two triangles on either side. The height is 1.5. The base is 1.8.

0.5(1.5)(1.8)=1.35 meters squared

Since there are two, we will add 1.35+1.35 in our final calculation.

Rectangles

We will start by calculating the largest rectangle on the side. It has height of 4 and a base of 2.5 (shown above left).

4(2.5)=10

Since there are two (one we can see and one we can't), we will add 10+10 in our final calculation.

Next we calculate the top and bottom. The height is 3 and the base is 2.5 on top. But the bottom sticks out more and adds 1.8 to its base.

Top - 3(2.5)=7.5

Bottom-3(2.5+1.8)=12.9

Finally, we will calculate the front side and back(not visible) as well as the slant up front. The back side has height 4 and base 3. The front side has base 3 and height 4-1.5=2.5. The slant has base 2.3 and height 3.

Back - 4(3)=12

Front- 3(2.5)=7.5

Slant - 3(2.3)=6.9

We add all together for the total surface area: 1.35+1.35+10+10+7.5+12.9+12+7.5+6.9=69.5 meters squared.

When you divide you number actually gets bigger.

You flip the last number in the question and then turn it in to a multiplication problem and then solve!!

Hope I could help!!!

Brainiest??

Answer:

She can make nine gallons. (9)

Step-by-step explanation:

Just took the assignment!

Answer:

[tex]100:37[/tex]

Step-by-step explanation:

For every pound a company spends on advertising it spends £0.37 on its website.

Ratio of the the total amount spent on advertising to the amount spent on its website is,

[tex]=\dfrac{1}{0.37}[/tex]

[tex]=\dfrac{1\times 100}{0.37\times 100}[/tex]

[tex]=\dfrac{100}{37}[/tex]

[tex]=100:37[/tex]

Therefore, the ratio of the the total amount spent on advertising to the amount spent on its website is [tex]100:37[/tex]

y = -3x +2

The y-intercept is at +2, so that is the value of the added constant (b).

The line goes down 3 units for each unit to the right, so the slope (m) is ...

... m = ∆y/∆x = -3/1 = -3

Then in the form ...

... y = mx + b

with m=-3 and b=2, your line's equation is ...

... y = -3x +2

Answer:

90%

Step-by-step explanation:

We are told that 9/10 of alien races think invading Earth is a bad idea.

To find the percent of alien races that think invading Earth is a bad idea we will have to find 9 is what percent of 10.

[tex]\text{The percentage of alien races that think invading Earth is a bad idea}=\frac{9}{10}\times 100[/tex]

[tex]\text{The percentage of alien races that think invading Earth is a bad idea}=9\times 10[/tex]

[tex]\text{The percentage of alien races that think invading Earth is a bad idea}=90[/tex]

Therefore, 90% of alien races think invading Earth is a bad idea.

90%

Step-by-step explanation:

mark me branilest

Answer:

choice A

Step-by-step explanation:

Closed circles on the end of  the number line means we include it in our inequality  (has an equals)

-3 <= x <= 1

Answer:

The answer is A.

Step-by-step explanation: