Joyce paid $50 for an item at the store that was 45 percent of the original price. What was the original price?

Answer:

angle 2 = 90° {corresponding angles}

angle 7 + angle 5 = 180° {linear pair}

or, angle 7 + 100° = 180° {angle 5 is corresponding to 100°}

so, angle 7 = 80°

The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.

To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:

Area = (1/2) * a * b * sin(C),

where a and b are the lengths of the two sides adjacent to the given angle C.

In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:

c² = a² + b² - 2ab * cos(C),

where C is the angle opposite side c. Rearranging the formula, we have:

b² = a² + c² - 2ac * cos(C),

b² = 86² + 37² - 2 * 86 * 37 * cos(128°).

By substituting the given values and calculating, we find b ≈ 63.8.

Now, we can calculate the area using the formula:

Area = (1/2) * a * b * sin(C),

Area = (1/2) * 86 * 63.8 * sin(128°).

By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.

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Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

Answer:

poin J is (-3,-2.5)

point L is (2.5,3)

x-cord for M is 3

x-cord for K is -2.5

Answer:

$27.01

Step-by-step explanation:

100% + 19.3% = 119.3%.

$32.22 = 119.3%

divide both sides by 119.3:

(32220/1193) = 1

multiply by 100 to get 100% ie the bill before the tip:

$27.01 = 100%

$27.01 is bill to nearest cent

Answer:

$31.50

Step-by-step explanation:

To find the answer, you would divide.

$1,260 / 40 = 31.50

The answer is $31.50, hope this helps

Answer:

The two angles that are directly across the intersection point from each other are called vertical angles. Vertical angles are always congruent.

Step-by-step explanation:

brainliest???

Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

Vertical angles are angles opposite to each other where two lines cross.

When two lines intersect, they naturally form two pairs of vertical angles. Vertical angles share the same vertex or corner, and are opposite each other.

These pair of angles are congruent which means they have the same angle measure.

Hence, Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

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There will be 4,723,920 insects present after 10 days.

Given that a colony of insects triples every day, to determine, if the colony has 80 insects today, how many will be present in 10 days, the following calculation must be made:

Therefore, there will be 4,723,920 insects present after 10 days.

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The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.

It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.

Consequently, it follows from the sine law that;

4 / sin 20° = x / sin 109°

x = 4 sin 109° / sin 20°

x = 11.06.

Ultimately, the number that belongs in the green box is; 11.06.

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Answer:

a) Function A(x) =  (60*x - 1/2*x²)

b)Side length     x = 60 m      the other side   y = 30 m

c) A (max)  = 1800 m²

Step-by-step explanation:

Area of rectangular garden with length  " x " and wide "y"

A = x*y        

Perimeter of rectangular area ( only three sides 2*y and 1*x)

P(r)  = 2*y + x

P(r) = 120 = 2*y + x

y = ( 120 - x ) /2

Area of the garden as function of x is

A(x) = [( 120 - x ) /2]*x          ⇒     A(x) = (60*x - 1/2*x²)

Taking derivatives on both sides of the equation:

A´(x) = 60 - x

A´(x)  = 0            60  -  x  = 0

x = 60 m

Then

y = ( 120  -  x ) / 2                ⇒   y = (120 - 60 )/2

y = 30 m

A(max) = 30 * 60

A(max) = 1800 m²

The side length (x) is 30 m each

The maximum area is 1800 m².

He has 120 meters for fencing . He use it to form 3 sides of a rectangular garden.

Therefore,

let

the side parallel to the house = y

the sides perpendicular to the house = x (2 sides)

Therefore,

perimeter = 2x + y

120 = 2x + y

y = 120 - 2x

area = x(120 - 2x)

area = 120x - 2x²

area = -2x² + 120x

The leading coefficient is less than zero, therefore, the parabola is facing downward.  The maximum area is at (h, k).

where

h = - b / 2a

a = -2

b = 120

h = - 120 / 2 × -2

h = 120 / 4 = 30

The sides perpendicular to the building  = 30 meter

The side parallel to the building = 120 - 2(30) = 60 meters

The maximum area = 60 × 30 = 1800 m²

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Explanation

In the question, we are given that;

Since each of the vehicles is equally likely to leave;

Part A

Answer: 0.3

Part B

Answer: 0.1

Part C

First we find the probability of a lorry or van leaving

Next, we find the probability of a car; but remember that one of either a lorry or van has left the car park already, so the total number of vehicles will reduce by 1

Therefore, the probability of a car leaving second if either a lorry or van had left first is

Answer:

The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

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Answer:

3×2×1

Step-by-step explanation:

that is the answer

Answer:

see explanation

Step-by-step explanation:

The definition of factorial ! is

n! = n(n - 1)(n - 2) ...... × 3 × 2 × 1 , then

3! = 3 × 2 × 1

= 6

Answer:

\(840\)

Step-by-step explanation:

This is a good example of permutations. For the first slot on his shelf, Dylan has 7 trophies to choose from. Then 6, 5, and so on. Since he is only fitting 4 trophies on his shelf, we only continue until we have the slots filled. Thus, we have \(7\cdot 6 \cdot 5\cdot 4=\boxed{840\:\text{ways}}\) to do so.

*Note: We do not divide by \(4!\) because in this case, order matters. A different order of the same four books still produces different arrangements, so the order matters.

Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

The average number of likes will be 16.5. the correct option is D.

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is calculated by adding all the data points and dividing it by the total number of the data.

Given that Bethany has a photo website where she places photos that she has taken so others can see them. Below is how many likes each of her current photos was given: 10, 13, 15, 15, 17, 29.

The average will be calculated as:-

Mean = ( 10 + 13 + 15 + 15 + 17 + 29 ) / 6

Mean = 99 / 6

Mean = 16.5

Therefore, the average number of likes will be 16.5. the correct option is D.

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

The inequality corresponding to the equation -4x + y = -3 is either y > 4x - 3 or y < 4x - 3, depending on the relationship between 4x - 3 and 0.

To write the inequality represented by the equation -4x + y = -3, we first need to manipulate the equation to express y in terms of x.

Starting with -4x + y = -3, we isolate y by adding 4x to both sides:

y = 4x - 3

Now we have y expressed in terms of x. To form the inequality, we consider the relationship between x and y. The inequality depends on whether the expression 4x - 3 is greater than or less than 0.

If 4x - 3 is greater than 0, then y is greater than 0, and we can write the inequality as:

y > 4x - 3

If 4x - 3 is less than 0, then y is less than 0, and we can write the inequality as:

y < 4x - 3

The inequality represents a region in the coordinate plane where the y-values are either greater than or less than the expression 4x - 3, depending on the direction of the inequality sign.

For example, if we choose a point (x, y) in the region above the line y = 4x - 3, where y is greater than 4x - 3, the inequality y > 4x - 3 will hold true. On the other hand, if we choose a point below the line, where y is less than 4x - 3, the inequality y < 4x - 3 will be satisfied.

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Answer:

1080°

Step-by-step explanation:

sum = 180 ( n - 2)

note that octagon has 8 sides

therefore

sum = 180 ( 8 - 2)

sum = 1080°

Answer:

c.  1080

Step-by-step explanation:

= 180 x ( 8 - 2)

= 1080

\((\stackrel{x_1}{40}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{20}-\underset{x_1}{40}}} \implies \cfrac{ -2 }{ -20 } \implies \cfrac{ 1 }{ 10 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{ 1 }{ 10 }}(x-\stackrel{x_1}{40})\implies {\Large \begin{array}{llll} y=\cfrac{1}{10}x+4 \end{array}}\)

Answer:

hi hihthffffffffffffffffffssssssssssssssss

Step-by-step explanation:

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The slope of the line passing through points A and B is 1/3.

The formula for the slope of a line to find the slope passing through points A and B. The formula is:

slope = (change in y) / (change in x)

Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).

Then, substitute the values and calculate the slope:

slope = (y₂ - y₁) / (x₂ - x₁)

slope = (3 - 2) / (3 - 0)

slope = 1 / 3

Therefore, the slope of the line passing through points A and B is 1/3.

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Answer: go to I think it’s c but try a math solver to trust my answer

Step-by-step explanation:

Hope this helps

Answer:

Let's first define some variables:

Let P be the selling price of one loaf of bread in dollars (not including any price increases).

Let x be the number of $0.05 price increases.

Let Q be the number of loaves sold per day.

Let R be the revenue (income) per day.

Let C be the cost per day (the cost of the 50 loaves sold).

Using the given information, we can set up the following equations:

The selling price, P, can be written as:

P = 0.65 + 0.05x

The number of loaves sold, Q, can be written as:

Q = 50 - 2x

The revenue per day, R, can be written as:

R = P * Q

R = (0.65 + 0.05x) * (50 - 2x)

The cost per day, C, is simply:

C = 50 * 0.65

C = 32.50

The profit per day, which is the difference between revenue and cost, is:

Profit = R - C

Profit = (0.65 + 0.05x) * (50 - 2x) - 32.50

To find the vertex, we can either complete the square or use calculus. Let's use calculus:

Profit' = -0.1x^2 + 2.5x - 32.5

Setting Profit' = 0 and solving for x gives:

x = 12.5

Therefore, the vertex is at x = 12.5.

To find the cost that will maximize profit, we need to find the corresponding selling price:

P = 0.65 + 0.05x

P = 0.65 + 0.05(12.5)

P = 1.30

Therefore, the selling price that will maximize profit is $1.30 per loaf.

Step-by-step explanation:

The p-value of the test is 0.112

To determine whether the consumer group's belief is supported by the sample data, we can perform a one-sample t-test.

The null hypothesis is that the true average score improvement is equal to 50 points, while the alternative hypothesis is that it is less than 50 points.

Using the sample data, we can calculate the t-statistic as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (44 - 50) / (27 / √(31))

t = -1.24

The degrees of freedom for this test is 30 (sample size minus one).

Using a t-distribution table or calculator, we can find the p-value associated with this t-statistic and degrees of freedom, which is the probability of observing a t-statistic as extreme as -1.24 or more extreme, assuming that the null hypothesis is true.

The p-value is approximately 0.112.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence that the true average score improvement is less than 50 points.

Therefore, the consumer group's belief is supported by the sample data.

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The value of x in the secant intersection is 4.

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Therefore, let's find the value of x using the secant intersection theorem as follows;

4(4+x + 2) = 5(5 + x - 1)

4(6 + x) = 5(4 + x)

24 + 4x = 20 + 5x

24 - 20 = 5x - 4x

x = 4

Therefore,

x = 4

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\( \\ \\ \)

\( \\ \\ \)

Circumference of circle be C.

\( \\ \\ \)

\( \\ \\ \)

To find circumference of circle we have to use this formula:-

\( \\ \)

\( \bigstar \boxed{ \rm Cicumference \: of \: circle = 2\pi radius}\)

\( \\ \\ \)

Therefore:-

\( \dashrightarrow\sf C= 2\pi radius \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf C= 2 \times 3.14 \times 6\)

\( \\ \\ \)

\( \dashrightarrow\sf C= 2 \times \dfrac{314}{100} \times 6\)

\( \\ \\ \)

\( \dashrightarrow\sf C= \dfrac{314 \times 2 \times 6}{100}\)

\( \\ \\ \)

\( \dashrightarrow\sf C= \dfrac{3768}{100}\)

\( \\ \\ \)

\( \bf\dashrightarrow C=37.68 \: inches\)

\( \\ \\ \)

\( \therefore \underline{ \frak{ \red{Cicumference \: of \: circle = \blue{37.68 \: inches}}}}\)

Solution:

Given:

Formula to find circumference: 2πr

Use the formula to find the circumference.

The circumference of the circle is 37.68 in.