Same items have same prices.
Different items have different prices.

1. How much is a helmet?
2. How much is a bell?
3.How much is a lock?
4. Explain how you figured out the prices.

Solving a system of equations we can see that the two numbers are-8 and -7.

Let's say that the two numbers are A and B, and we know that we can write:

A*B = 56

A + B = -15

So we have a system of equations.

Using the second equation we can write:

A=  -15 - B

And replace that in the first equation, then we will get:

(-15 - B)*B = 56

-15B - B² = 56

Now we can solve the quadratic equation:

-B² - 15B - 56 = 0

The solutions are:

[tex]B = \frac{15 \pm \sqrt{(-15)^2 - 4*-56*-1} }{2*-1} \\\\B = \frac{15 \pm 1 }{-2}[/tex]

The two possible solutions are:

B = (15 + 1)/-2 = -8

B = (15 - 1)/-2 = -7

And when B is one of these values, A will be the other one.

Then the two numbers are -8 and -7.

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Answer:

Let's call the distance between Cape Town and East London "d".

We know that the average speed on the outward trip was 108 km/h, so the time it took to travel from Cape Town to East London can be calculated using the formula:

time = distance / speed

So the time it took on the outward trip can be expressed as:

time = d / 108

We also know that the average speed on the return trip was 72 km/h, and we're told that this trip took 12 hours. So we can use the same formula to find the distance between Cape Town and East London:

d = speed * time

d = 72 * 12

d = 864 km

Now we can use the formula for time again to find how long the outward trip took:

time = d / 108

time = 864 / 108

time = 8 hours

Therefore, the outward trip took 8 hours.

Step-by-step explanation:

Answer: To find the indicated z-score for a shaded area of 0.1949 in the standard normal distribution, we need to use a z-table or a calculator with a built-in normal distribution function.

Using a z-table, we can find the z-score that corresponds to a cumulative area of 0.1949 in the standard normal distribution. The z-table gives us the area to the left of the z-score, so we need to look for the area closest to 0.1949 in the body of the table and then interpolate to find the exact z-score.

Looking at the z-table, we find that the area to the left of the z-score 0.88 is 0.8106, and the area to the left of the z-score 0.89 is 0.8159. Since 0.1949 is closer to 0.8106 than to 0.8159, we can estimate that the z-score corresponding to the area 0.1949 is approximately 0.88.

Therefore, the indicated z-score for a shaded area of 0.1949 in the standard normal distribution is approximately 0.88.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Firstly,

angles at the centre of a circle add to 360°. So

      [tex](15x-1)+\angle ZVX +(8x-2)+(7x+15)+(3x+5)=360[/tex]

                                                             [tex]33x+17+\angle ZVX=360[/tex]

                                                                               [tex]\angle ZVX=360-33x-17[/tex]

                                                                               [tex]\angle ZVX=342-33x[/tex]

Secondly,

[tex]\angle YVU+ \angle UVW + \angle WVX =180[/tex]°   (since YX is a diameter - angles on a

                                                           straight line sum to 180°)

[tex](3x+5)+(7x+15)+(8x-2)=180[/tex]

                                   [tex]18x+18=180[/tex]

                                           [tex]18x=162[/tex]

                                               [tex]x=9[/tex]

Substitute [tex]x=9[/tex] into [tex]\angle ZVX=342-33x[/tex]:

    [tex]\angle ZVX=342-33\times9=63[/tex]°

Solution: [tex]\angle ZVX=63[/tex]

The area of the composite figure is 122.5 square inches

Based on the problem statement, we have the following dimensions from the question

The area of the composite figure is the sum of individual areas

So, we have

Area = Isosceles right triangle + Rectangle + Another isosceles triangle

By applying the formulas, we have

Area = 0.5 * 11 * 11 + 14 * 4 + 0.5 * 4 * 3

Evaluate

Area = 122.5

Hence the area is 122.5 sq inches

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cos θ expressed as a ratio of given lengths of the right triangle is:

cos θ =  12/13

Trigonometry deals with the relationships between the sides and angles of triangles.

The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:

Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

Thus, cos θ as a ratio of given lengths of the right triangle can be expressed as:

cos θ =  12/13   (cos = adjacent/hypotenuse)

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Complete Question

The attached image completes the question

Step-by-step explanation:

ADCF and DEFG

the third pane AECG is perpendicular to line r.

The line's slope  on the graph will switch from being negative to positive.

The graph of the equation y = mx + c is a line with m as the slope and m and c as the y-intercept. The values of m and c are actual integers in the slope-intercept illustration of the linear equation.

The slope of a line, measured in m, tells us how steep it is. A line's gradient is also referred to as its slope sometimes. The y-coordinate of the point where the line's graph meets the y-axis is known as the y-intercept of a line, ab.

The slope-intercept form of the equation for the line, y = -5/4 x + 3, is written as y = mx + b. Where,

The line has a slope of m, a y-intercept of 3, a slope of -5/4, and a y-intercept of b.

As a result, the slope has changed from negative to positive if -5/4 is changed to 5/4.

As a result, the graph of the line's slope will switch from being negative to positive.

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Looking at the data, we can see that both the high as well as low temperatures of Monday, Tuesday, Thursday, & Friday were above [tex]O^{o}C[/tex]. The high on Wednesday was minus zero degrees Celsius.

The most popular scales are indeed the Celsius scale, sometimes known as centigrade, with the unit sign °C, the Franklin level (°F), and the Scale parameter (K), with the latter being mostly used for scientific reasons.

The total kinetic energy of a substance's particles is measured by its temperature. 2. An object's kinetic energy increases with increasing temperature. 3. If we add up the instances where the maximum and low temps were in excess of or below zero degrees Celsius, we find:

High temperature above [tex]O^{o}C[/tex]: 5 days

High temperature below [tex]O^{o}C[/tex]: 2 days

Low temperature above [tex]O^{o}C[/tex]: 3 days

Low temperature below [tex]O^{o}C[/tex]: 4 days

Therefore, we can see that overall, there were more days where the temperatures were below [tex]O^{o}C[/tex], both for the high and low temperatures.

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The complete question is:

In Vienna were more of the high and low temperatures above or below [tex]O^{o}C[/tex] justify your answer using a vertical number line

Days                        high temperature      low temperature

Monday                            8                           0

Tuesday                            9                          -4.5

Wednesday                      4.5                       -12

Thursday                           9                          4.5

Friday                                8.5                       -6

Saturday                           1                           -10

Sunday                             5                           -14

Answer:

That answer is -3

Step-by-step explanation:

The way you do this is Rise/Run

so you would do y2-y1/x2-x1

In this case it's 10-1/-4-(-1)

Simplified is 9/-3 which is -3

hope this helped

Therefore, the solutions to the equation [tex]p^{2} -4=21[/tex]are p = 3, -3, 7, and -7. Neither 1/4 nor 21 are solutions to this equation.

In mathematics, a factor is a number or expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers can all divide 12 evenly.

by the question.

We can solve this equation by first moving all the terms to one side of the equation:

[tex]p^{2}[/tex] - 4 = 21

[tex]p^{2}[/tex] = 25

Now, we can factor the left-hand side of the equation by using the difference of squares formula:

(p + 2) (p - 2) = 25

We can now solve for p by setting each factor equal to a possible value of the square root of 25:

p + 2 = 5 or p + 2 = -5

p - 2 = 5 or p - 2 = -5

Solving each of these equations, we get:

p = 3 or p = -7, p = 7 or p = -3

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The formula for the function is S(r) = -10r² + 130r.

A function can be represented as an equation, a graph, or a table of values. In an equation, the function is usually denoted as "f(x)", where "x" is the input value and "f(x)" is the output value. For example, the equation f(x) = 2x represents a function that takes an input value x and produces an output value that is twice the input value.

Functions can be used to model real-world phenomena and solve various problems in mathematics, science, engineering, economics, and other fields. They are an important concept in calculus and other branches of mathematics, and they have numerous applications in modern technology and industry.

Let the cost of admission be $a and the cost of each raffle ticket be $r. Then we can write the following equation based on the given information:

10r + a = 135

Solving for a, we get:

a = 135 - 10r

Thus, the function that relates the total amount spent to the number of raffle tickets bought is:

S(r) = ar + 5r = (135 - 10r)r + 5r = -10r² + 130r

Therefore, the formula for the function is:

S(r) = -10r² + 130r

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Answer:

629=500+120+9

Step-by-step explanation:

500+120+9=629

629=629

Answer:

The answer is 1/2

Step-by-step explanation:

3 and 6 are the known sides of the triangle as you can see three is half of six making it a 1/2 dilation

[tex]\dfrac{6}{3} = 2[/tex]

the scale factor is

1 : 2

The value οf the median MN fοr the given trapezοid is 70.59 units.

The law οf sines specifies hοw many sides there are in a triangle and hοw their individual sine angles are equal. The sine law, sine rule, and sine fοrmula are οther names fοr the sine law. The side οr unknοwn angle οf an οblique triangle is fοund using the law οf sine.

Any triangle that is nοt a right triangle is referred tο as an οblique triangle. At least twο angles and their cοrrespοnding side measurements shοuld be used at οnce fοr the sine law tο functiοn.

Given that, SPQR is a trapezοid with SP parallel tο QR,

Nοw, we knοw that MN is the average οf the lengths οf the bases SP and QR.

That is,

MN = (SP + QR) / 2.

Fοr the given values we have:

SP = PQ = 12, sο QR = 2MN - SP

Nοw, m∠QRS = 120 and m∠QPS = 135,

Thus,

m∠SPQ = 180 - 120 - 135 = -75.

Hοwever, angles cannοt be negative, sο we add 360 tο get 285 degrees.

Since SPQR is a trapezοid, we knοw that m∠SPQ = m∠QRN. Alsο, since MN is the median οf the trapezοid, it divides the trapezοid intο twο cοngruent triangles, sο m∠QMN = m∠RNM.

Using the law οf sines in triangle QMN tο find MN:

sin(m∠QMN) / MN = sin(m∠MQN) / QN.

Since QN = NR:

sin(m∠QMN) / MN = sin(m∠RNM) / NR.

sin(135) / MN = sin(285) / NR.

NR = sin(285) / sin(135) * MN.

2MN - SP = 2 * sin(285) / sin(135) * MN

2MN - 12 = 2.17MN

MN = 12 / 0.17 = 70.59

Hence, the value οf the median MN fοr the given trapezοid is 70.59 units.

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Every proper subgroup of G is cyclic.

In abstract algebra, a subgroup is a subset of a group that is itself a group under the same operation as the original group. More precisely, a subgroup H of a group G is a subset of G that satisfies the following three conditions:

A cyclic subgroup is a subgroup of a group that is generated by a single element. In other words, a subgroup H of a group G is cyclic if there exists an element a in G such that every element of H can be written as a power of a, and H is the smallest subgroup of G containing a.

In the given question,

Let H be a proper subgroup of G. Since H is a proper subgroup, we have lHl < lGl = 77.

Now, by Lagrange's Theorem, the order of any subgroup of G must divide the order of G. That is, lHl divides lGl = 77.

Since H is a proper subgroup, we have lHl > 1. Therefore, lHl can only be 7, 11, or 77 (the divisors of 77).

Suppose lHl = 7. Then, by Lagrange's Theorem, the elements of G are partitioned into disjoint cosets of H, each of size 7. But 77 is not divisible by 7, so there cannot be a whole number of cosets. Therefore, this case is not possible.

Similarly, suppose lHl = 11. Then, the elements of G are partitioned into disjoint cosets of H, each of size 11. But 77 is not divisible by 11, so there cannot be a whole number of cosets. Therefore, this case is also not possible.

Thus, we are left with the case where lHl = 77. But this implies that H = G, which contradicts the fact that H is a proper subgroup. Therefore, this case is also not possible.

We have exhausted all possibilities for the order of H, and in each case, we have arrived at a contradiction. Therefore, the assumption that there exists a proper non-cyclic subgroup of G must be false.

Hence, every proper subgroup of G is cyclic.

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There are 3150 distinct ways to arrange the marbles in a row.

What is Combination ?

In mathematics, combination is a way of selecting a group of objects from a larger set, without regard to the order in which the objects are selected. Combinations are also sometimes called "unordered selections" or "combinatorial subsets".

To solve this problem, we can use the formula for permutations with repetition. We have a total of 10 marbles, but some of them are repeated. Specifically, we have:

3 yellow marbles (repeated)

3 green marbles (repeated)

2 red marbles (repeated)

2 blue marbles (repeated)

So the number of distinct ways to arrange these marbles in a row is:

(10!) ÷ (3! x 3! x 2! x 2!)

The factorials in the denominator account for the repetition of each color. We divide by them to eliminate the overcounting that would occur if all the marbles were unique.

Simplifying this expression, we get:

(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)÷(3 x 2 x 1 x 3 x 2 x 1 x 2 x 1 x 1 x 1)

which equals:

(10 x 9 x 8 x 7 x 6 x 5 x 4) ÷ (3 x 3 x 2 x 2)

Simplifying further, we get:

(10 x 3 x 3 x 3 x 2 x 2 x 7 x 5) ÷ (3 x 3 x 2 x 2)

which equals:

(10 x 3 x 3 x 7 x 5)

which finally equals:

3150

Therefore, there are 3150 distinct ways to arrange the marbles in a row.

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The area of the triangle is 5/2 x sqrt(7) square units, or approximately 6.99 square units.

We need to know the triangle's base and height lengths in order to calculate its area.

Let's give the triangle's vertices the following names:

A is the bottom-left vertex.

B is the vertex at the bottom right.

C is the top vertex.

We can infer from the facts provided that the triangle's base measures AB, or 5 units.

We must draw a perpendicular line from the triangle's vertex C to its base AB in order to get the triangle's height. Let's give the intersection of the perpendicular line and the base the letter D.

Right triangle ACD with CD as the triangle's height now exists. The Pythagorean theorem can be used to determine CD's length:

[tex]AD^2 + CD^2 = AC^2[/tex]

We can determine that AC is 4 units and AD is 3 units based on the facts provided.

When we plug these figures into the formula, we get:

[tex]4^2 = 3^2 + CD^2[/tex]

Simplifying:

16 = 9 + [tex]CD^2[/tex]

[tex]CD^2[/tex] = 7

CD = √7

The triangle's height is therefore √7 units.

The area formula for triangles can now be used:

Area equals ([tex]\frac{1}{2}[/tex]) x base x height.

Adding the values we discovered:

Area equals ([tex]\frac{1}{2}[/tex]) x 5 sq (7)

Area = [tex]\frac{5}{2}[/tex] x sqrt (7)

Hence, the triangle has a surface area of [tex]\frac{5}{2}[/tex] x √7 square units, or roughly 6.99 square units.

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The missing reason for the following proof: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

A triangle is a closed two-dimensional figure with three straight sides and three angles. It is formed by connecting three non-collinear points with straight lines. The sum of the interior angles of a triangle always equals 180 degrees, and the exterior angles of a triangle always add up to 360 degrees. Triangles are one of the fundamental shapes in geometry and have many different classifications based on their side lengths, angles, and other properties.

Here,

In geometry, CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a property that states that if two triangles are congruent, then their corresponding parts (angles and sides) are also congruent. In other words, if two triangles are the same shape and size, then all of their corresponding angles and sides are equal in measure. This property is often used in geometric proofs to show that two triangles are congruent by demonstrating that their corresponding parts are equal.

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Step-by-step explanation:

Answer:

I'm sorry, but the question is unclear. Can you please provide more context or information so that I can understand what you are asking?

Answer:

D)  8 + 4 + 2 + 1 + 1/2 + ...

Step-by-step explanation:

The sum of an infinite geometric series can be found when the absolute value of the common ratio, r, is less than 1.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$,\quad $|r| < 1$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

To determine which of the given infinite geometric series can be summed using the formula, calculate the value of r for each series.  To do this, divide a term by the previous term.

Given infinite geometric series:

[tex]\implies r=\dfrac{6}{-2}=-3[/tex]

As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.

Given infinite geometric series:

[tex]\implies r=\dfrac{12}{3}=4[/tex]

As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.

Given infinite geometric series:

[tex]\implies r=\dfrac{2}{1}=2[/tex]

As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.

Given infinite geometric series:

[tex]\implies r=\dfrac{4}{8}=\dfrac{1}{2}[/tex]

As |r| < 1 the sum of the infinite series can be found using the formula.

Therefore, the infinite series for which the sum can be found by using the formula is:

The expressiοn a² + b² = a + b is true when a = 1 and b = 1.

An expressiοn is a cοmbinatiοn οf variables, numbers, and mathematical οperatiοns that represents a quantity οr value. Expressiοns can be simple οr cοmplex, and they can invοlve a variety οf οperatiοns such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and radicals.

a. It is impοssible tο cοmbine the expressiοn √√3x + 2√3x intο a single term because the twο terms have different radical expressiοns. The first term has a dοuble square rοοt, while the secοnd term has a single square rοοt. These cannοt be cοmbined unless simplified first.

b. Ratiοnalizing the denοminatοr means tο eliminate any radical expressiοns frοm the denοminatοr οf a fractiοn by multiplying bοth the numeratοr and denοminatοr by a suitable expressiοn that will result in an integer οr ratiοnal denοminatοr.

c. Let a = 1 and b = 1, then a² + b² = 1² + 1² = 2, and a + b = 1 + 1 = 2. Therefοre, a² + b² = a + b is true when a = 1 and b = 1.

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The answer of the given question based on the actual area of the park in meters squared answer is the actual area of the park is 593,442 square meters.

Width refers to measurement of  distance from one side of object to other side, perpendicular to its length. It is one of basic dimensions of  object or shape along with the length and height.

Width is often used in context of rectangular or parallelogram-shaped objects, where it refers to measurement of shorter sides of the shape. For example, in a rectangular picture frame,  width would be measurement of the shorter sides of the frame.

The scale of the drawing is 1 cm = 110 m, which means that every 1 centimeter on the drawing represents 110 meters in real life.

The length of the park on the drawing is 8.6 cm, so the actual length of the park in meters is:

8.6 cm x 110 m/cm = 946 meters

The width of the park on the drawing is 5.7 cm, so the actual width of the park in meters is:

5.7 cm x 110 m/cm = 627 meters

Therefore, the actual area of the park in square meters is:

946 meters x 627 meters = 593,442 square meters.

So, the actual area of the park is 593,442 square meters.

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Plugging in the values, we get: [tex]y - (-4) = (9/5)(x - (-9))[/tex]  simplifying and rearranging, we get the equation of the perpendicular line: [tex]y = (9/5)x + (16/5)[/tex]

To find the equation of a line that is parallel to   [tex]y = (-5/9)x - 2,[/tex]  we need to note that parallel lines have the same slope. The slope of   [tex]y = (-5/9)x - 2[/tex] is -5/9, so the slope of the parallel line will also be -5/9.

We can use this information and the given point (-9, -4) to find the equation of the parallel line using the point-slope form of the equation of a line:

[tex]y - y1 = m(x - x1)[/tex]

where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get:

[tex]y - (-4) = (-5/9)(x - (-9))[/tex]

Simplifying and rearranging, we get the equation of the parallel line:

[tex]y = (-5/9)x + (34/9)[/tex]

To find the equation of a line that is perpendicular to y = (-5/9)x - 2, we need to note that perpendicular lines have opposite reciprocal slopes. The slope of y = (-5/9)x - 2 is -5/9, so the slope of the perpendicular line will be 9/5 (the opposite reciprocal).

We can use this information and the given point (-9, -4) to find the equation of the perpendicular line using the point-slope form of the equation of a line:

[tex]y - y1 = m(x - x1)[/tex]

Therefore, where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get: [tex]y - (-4) = (9/5)(x - (-9))[/tex]  simplifying and rearranging, we get the equation of the perpendicular line: [tex]y = (9/5)x + (16/5)[/tex]

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the solved equation will be x=7.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

2/X-5 - 4/ x+5 =2/ x²-25

[tex]\frac{(x+5)2-4(x-5)}{x^{2} -25}[/tex] = [tex]\frac{2}{x^{2} -25}[/tex]

2x-4x+10+20 = 2

-4x=-28

x=7

Hence, the solved equation will be x=7.

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Answer:

To find the explicit formula for this sequence, we need to determine the common ratio between successive terms. To do this, we can divide any term by the previous term. For example:

6 ÷ 2 = 3

18 ÷ 6 = 3

54 ÷ 18 = 3

162 ÷ 54 = 3

So the common ratio is 3.

Next, we can use the general form of a geometric sequence to find the explicit formula:

a(n) = a(1) * r^(n-1)

where a(n) is the nth term of the sequence, a(1) is the first term, r is the common ratio, and n is the position of the term we want to find.

In this sequence, a(1) = 2 and r = 3. So the explicit formula for this sequence is:

a(n) = 2 * 3^(n-1)

For example, if we want to find the 6th term, we can plug in n = 6:

a(6) = 2 * 3^(6-1) = 2 * 3^5 = 2 * 243 = 486

Therefore, the 6th term of the sequence is 486.