brandom bought a jacket that costs 7 dollars and a scarf that costs 22 dollars. At the counter, he received a discount. If he only paid 27 dollars total, how many dollars were the discount

Answer: 85

Step-by-step explanation:

\(100-3(3y-4x)\\\\=100-3(3 \cdot 7-4 \cdot 4)\\\\=100-3(21-16)\\\\=100-3(5)\\\\=100-15\\\\=85\)

Answer:

148

Step-by-step explanation:

use bidmas to get final solution

100-3(12-28)

100-3 × (-16)

=148

Answer: The measure of angle FHG = 42 degrees. This is the same as the arc length.

The measure of angle FEG = 21 degrees. This is half the value of the arc length.

Step-by-step explanation:

If a circle has center M and arc KL is 126 degrees then ∠KJL is 126 degrees and ∠KJL is 63 degrees

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Central angle is same as intercepted arc.

∠KJL = m(arc KL0

∠KJL =126 degrees

Inscribed angle  is equal to half of the intercepted arc.

To find inscribed angle , we divide the intercepted arc by 2.

∠KJL = 1/2(arc KL)

=1/2(126)

=63 degrees

Hence, if a circle has center M and arc KL is 126 degrees then ∠KJL is 126 degrees and ∠KJL is 63 degrees

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We have following associations:

In this question we need to fill the blanks of a given proof by understanding and taking advantage of the most important axioms and theorems of Euclidean geometry and real algebra. In this case, a linear pair is the combination of two angles whose sum equals 180°, and those angles are always supplementary.

Thus, we have following associations:

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This expression will give you the probability of drawing exactly two blue marbles.

To find the probability that she draws exactly two blue marbles, we need to consider the probability of drawing two blue marbles and one red marble in any order.

Let's assume the probability of drawing a blue marble is denoted by "P(B)" and the probability of drawing a red marble is denoted by "P(R)". Since she replaces only the blue marbles, the probability of drawing a blue marble remains the same for each draw.

To calculate the probability of drawing exactly two blue marbles, we can use the binomial probability formula:

P(2 blue marbles) = C(3, 2) * (P(B))^2 * (P(R))^1

Where C(3, 2) is the number of ways to choose 2 items out of 3, given by the combination formula:

C(3, 2) = 3! / (2! * (3 - 2)!) = 3

Since the probability of drawing a blue marble remains the same for each draw, we can simplify the formula:

P(2 blue marbles) = 3 * (P(B))^2 * (P(R))^1

Now, substitute the actual values of P(B) and P(R) into the formula. For example, if the probability of drawing a blue marble is 0.4 and the probability of drawing a red marble is 0.6, the calculation would be:

P(2 blue marbles) = 3 * (0.4)^2 * (0.6)^1

Simplifying this expression will give you the probability of drawing exactly two blue marbles.

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The correct option is for the value of c,  such that f(c) is the average value of the function on the interval [0, 2], is D.

The average value of a function on an interval [a, b] is given by:

R = (f(b) - f(a))/(b - a)

Here the interval is [0, 2], then:

f(2) = √(2 + 2) = 2

f(0) = √(0 + 2) = √2

Then here we need to solve the equation:

√(c + 2) = (f(2) - f(0))/(2 - 0)

√(c + 2) = (2 + √2)/2

Solving this for c, we will get:

c = [ (2 + √2)/2]² - 2

c = 0.9

Them tjhe correct option is D.

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Based on the fact that in the simple random variable, 5 is the sample mean, then it is a d. point estimate.

A point estimate refers to a specific value in a random group of variables that tell us more about the variables.

The mean is therefore a point estimate as it tells us the average value amounts the random sample of 31 observations.

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Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A.

Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A. This is due to the fact that for any symmetric matrix A, the image (column space) and kernel (null space) are orthogonal subspaces. Since v is in the image of A and w is in the kernel of A, their dot product must be zero, indicating orthogonality.

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0.35^3

or

0.105

I don’t know if you need the explanation or not

Answer:

a = 50

50*2=100

Step-by-step explanation:

Answer:

15.D

16.A

Step-by-step explanation:

Hello There!

For 15

We can find the slope given two points by using the slope formula

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

so given the two points (2,-3) and (-2,5)

we plug in the y values and x values into the formula

\(slope=\frac{5-(-3)}{-2-2} \\5-(-3)=8\\-2-2=-4\\slope=\frac{8}{-4}\)

Finally we want to simplify

8/-4=-2

so we can conclude that the slope of a line that passes through the points (2,-3) and (-2,5) is -2 (D)

For 16

The y intercept is at (0,0) meaning that at 0 hours there was no water in the pool

So we can conclude that the pool was originally empty

Answer:

Line

Step-by-step explanation:

Extends in two directions

The geometric term modeled by a bridge support beam is "cylinder."

Given data:

A bridge support beam often takes the form of a cylindrical shape to provide structural integrity and distribute the weight of the bridge and its load evenly. Cylinders have circular cross-sections.

A bridge support beam is often modeled as a "cylindrical" structure in geometry. Cylinders are three-dimensional geometric shapes characterized by their curved lateral surface and two circular bases of the same size and shape. When designing bridge support systems, engineers often opt for cylindrical beams due to their inherent strength and ability to distribute weight efficiently.

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Check the picture below.

The unknown values in the triangle are ;

a = 45.3

angle B = 7°

angle A = 28°

In a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.

Therefore,

a/sinA = b/sinB = c/sinC

So, we use the Sine rule to find the values of unknown lengths or angles of the triangle.

b/sinB = c/sinC

7/sinB = 33/sin145

33sinB = 7 sin145

33 sinB = 4.02

sinB = 0.122

B = 7°

angle A = 180-(145+7)

A = 180- 152

A = 28°

a/sinA = c/sinC

a/sin28 = 33/sin145

asin145 = 33sin128

0.574a = 26

a = 26/0.574

a = 45.3

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There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

There are 12 elements of the group     \(U_{13}\)   , namely all the positive integers less than 13, as these are relatively prime to 13. Now, if there are primitive roots, there are     \(\phi (\phi (n))\)    of them. So we must compute     \(\phi (12) = \phi (4\times 3) = \phi (4) \phi (3) = 2\times 2 = 4\)   . There are 4 incongruent primitive roots.

To find them, take the powers each element in turn:

1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1  (2 has order 12, it is a primitive root)

Of course, the higher powers of 2 cannot be.

Proceeding this way, we get next get that 6, 7, and 11 are also primitive roots.

For example, the powers of 6 give: 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1. We see 6 has order 12 and it is a primitive root. So 2, 6, 7, 11.

Therefore, There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

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The median household income after 5 years was approximately $51,040.

To solve the problem of finding the median household income in the US after 5 years, we can use the formula for compound interest. The given rate is 0.25% per month, which is the monthly interest rate. To find the annual interest rate, we multiply it by 12. So, the annual interest rate is:

0.25% × 12 = 3%

The compound interest formula is:

A = P(1 + r/n)^(nt)

where

A = the final amount

P = the principal

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

Substituting the given values, we have:

P = $42,050

r = 0.03 (3%)

n = 12 (monthly compounding)

t = 5 years

A = 42050(1 + 0.03/12)^(12×5) = 42050(1.0025)^60 = 42050(1.2155) ≈ $51,039.73

Therefore, the median household income after 5 years was approximately $51,040.

Note: The requested answer should be rounded to the nearest whole dollar. So, the final answer is $51,040.

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The correct option is, No, because HI and JK do NOT have the same slope and  HK and IJ have the same slope

Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.

Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.

Consecutive angles are supplementary: The consecutive angles of a parallelogram are always supplementary, meaning that they add up to 180 degrees.

Diagonals bisect each other: The diagonals of a parallelogram bisect each other, meaning that they intersect at the midpoint of each other.

The sum of the interior angles is 360 degrees: The sum of the interior angles of a parallelogram is 360 degrees.

No, because HI and JK do NOT have the same slope and HK and IJ have the same slope.

In order for a quadrilateral to be a parallelogram, opposite sides must be parallel, which means they have the same slope.

In this case, HI and JK do not have the same slope, and therefore, the opposite sides are not parallel.

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The complete question:

The vertices of parallelogram HUJK are H(0,-1),(2,3), J(7, -1),K(5,-5). Determine if HIJK is a parallelogram.

No, because HI and JK do NOT have the same slope and  HK and IJ have the same slope

Yes, because HI and JK have the same slope and HK and IJ have the same slope

Yes, because the image is tilted

No, because HK and JI have the same slope, but HI and JK do NOT have the same slope

To express the given vector c as a linear combination of given vectors a and b. We need to use the concept of linear independence or dependence of these given vectors.

The formula to get the linear combination is given by

c = ma + nb,

where m and n are the constants which we have to determine. As we can see from the given vectors, vector a and vector b lie in the same direction that is along the x-axis and hence they are linearly dependent. Therefore, we can get the values of m and n from the given coordinates of vectors a, b, and c. This is shown below:Substituting the values of a, b and c in the given equation we get

8 = 3m + 2n10

= 4m + 4n

Solving these two equations simultaneously we get m = 2 and n = 1

Therefore the linear combination of c with respect to a and b is given by c = 2a + b

We can prove this as follows:

2a + b = 2(3,4) + (2,4)

= (8,12) + (2,4)

= (10,16)

The above vector obtained is equal to the given vector c(8,10).

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The required width of the flower garden is 6 feet.

The area of a rectangular flower garden is 132 square feet.

Let us assume the length of the flower garden is l and its width is w (in feet).

The length of the flower is 10 feet more than twice the width of the garden.

That is, l = (10 + 2w ) feet

Thus the area of the flower garden is ,

length * width = 132 sq ft

⇒ (10+ 2w) w = 132

⇒2w^2 + 10w -132 = 0

⇒ w^2 + 5w - 66 = 0

⇒ w^2 + 11w - 6w - 66 = 0

⇒ w( w+ 11) - 6( w + 11) = 0

⇒ (w - 6)(w + 11) = 0

⇒ w = 6 and = -11

Since length or width of any garden can not be in negative, hence ignoring the negative value of w.

Thus, width of the flower garden is w=6  feet.

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Answer:

W=7

Step-by-step explanation:

Sin(x) / 7 = Sin(x) / w

W=7

Answer:

-3=-2/7(-14)+b

-3 = 4+b

-4    -4

-7 = b

= -3=-2/7x +-7

Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

With the help of the substitution method, we know that the value of x is 6 in the given linear equations.

The system of linear equations is:

Substitute the value of 'y' from (1) into (2):

Solve the result as follows:

Therefore, with the help of the substitution method, we know that the value of x is 6 in the given linear equations.

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The side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

The first such theorem is the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are equivalent to two sides and an included angle of another triangle.

Therefore, the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

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The solution to the expression in this problem is given as follows:

x = -1/3 + 1.7i and x = -1/3 - 1.7i.

The rational expression for this problem is defined as follows:

\(\frac{2x}{3x - 5} - \frac{x + 1}{3x + 5} = -\frac{4}{9x^2 - 25}\)

Applying the least common factor at the left side, we have that:

\(\frac{2x(3x + 5) - (x + 1)(3x - 5)}{9x² - 25} = -\frac{4}{9x^2 - 25}\)

\(\frac{6x^2 + 10x - 3x^2 + 5x - 3x + 5}{9x^2 - 25} = -\frac{4}{9x^2 - 25}\)

As the denominators are equal, the solution is obtained equaling the denominators, hence:

3x² + 2x + 5 = -4

3x² + 2x + 9 = 0.

Which is a quadratic function with coefficients given as follows:

a = 3, b = 2, c = 9.

Inserting these coefficients into a calculator, the solutions are given as follows:

x = -1/3 + 1.7i and x = -1/3 - 1.7i.

The rational expression is given by the image presented at the end of the answer.

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Answer:

A

Step-by-step explanation:

Set the equation equal to bx.

\((3x + 3)(ax - 2) - {x}^{2} + 6 = bx\)

\(3a {x}^{2} - 6x + 3ax - 6 - {x}^{2} + 6 = bx\)

Cancel out the constants

\(3 {ax}^{2} - 6x + 3ax - x {}^{2} = bx\)

In order to cancel out the quadratics, we must solve for a.

\(3 {ax}^{2} - {x}^{2} = 0\)

\(3 {ax}^{2} = {x}^{2} \)

\(3a = 1\)

\(a = \frac{1}{3} \)

So plug in 1/3 for a.

\(3( \frac{1}{3} ) {x}^{2} - 6x + 3( \frac{1}{3} )x - {x}^{2} = bx\)

\( - 6x + x = bx\)

\( - 5x = bx\)

\(b = - 5\)

Answer:

The area of the square is 15²

the area of a square and the length of its side are directly proportional because The area of the square is x²=> when its edge decreases, the area of ​​the figure decreases

Step-by-step explanation:

Answer:

≈3.99(simplified) or 3.98942

Answer:

\(\huge\boxed{r=4}\)

Step-by-step explanation:

The area of a circle is πr².  Thus, simply set that equation equal to 50 cm².

πr² = 50

r²=15.9154943

r=3.9894228

r ≈ 4

Hope it helps :)