In the figure shown, ABC is a right triangle with side lengths a, b, and c, and CD is an altitude to side AB. The side lengths of triangle ACD are b, h, and r, and the side lengths of triangle CBD are a, s, and h.


Which proportions are true?


A) c/a = a/s and c/b = b/r


B) c/a = s/a and c/b = r/b


C) c/b = a/s and c/a = b/r


D) c/b = s/a and c/a = r/b

Answer:

The Final Answer would be 14.9987.

Step-by-step explanation:

Given:

[tex]15-1.3\times 10^-3[/tex]

We need to Subtract the above number.

Since the larger number is standard Notation form and smaller number is in Scientific notation form

So first we will convert the Scientific notation Number in standard Notation form we get;

[tex]1.3\times 10^-3 = 0.0013[/tex]

Now Subtracting the smaller Number from larger number we get;

[tex]15-0.0013 = 14.9987[/tex]

Hence The Final Answer would be 14.9987.

The amount of Simon's monthly payment, rounded to the nearest cent, is approximately $240.17.

To calculate the monthly payment for Simon's loan, we need to use the formula for an annuity, which is derived from the amortization formula for loans. The formula to find the monthly payment (M) is:

[tex]\[ M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} \][/tex]

where:

- [tex]\( P \)[/tex] is the principal amount of the loan ($43,000)

- [tex]\( r \)[/tex] is the monthly interest rate (APR divided by 12)

- [tex]\( n \)[/tex] is the total number of payments (20 years times 12 months per year)

First, we need to convert the annual percentage rate (APR) to a monthly interest rate by dividing by 12:

[tex]\[ r = \frac{2.4\%}{12} = \frac{0.024}{12} = 0.002 \][/tex]

Next, we calculate the total number of payments:

[tex]\[ n = 20 \text{ years} \times 12 \text{ months/year} = 240 \text{ months} \][/tex]

Now we can plug these values into the formula:

[tex]\[ M = \frac{43000 \times 0.002 \times (1 + 0.002)^{240}}{(1 + 0.002)^{240} - 1} \][/tex]

[tex]\[ M = \frac{43000 \times 0.002 \times (1.002)^{240}}{(1.002)^{240} - 1} \][/tex]

Using a calculator, we find:

[tex]\[ (1.002)^{240} \approx 1.558 \][/tex]

Now we can calculate the monthly payment:

[tex]\[ M = \frac{43000 \times 0.002 \times 1.558}{1.558 - 1} \][/tex]

[tex]\[ M = \frac{43000 \times 0.002 \times 1.558}{0.558} \][/tex]

[tex]\[ M = \frac{134.034}{0.558} \][/tex]

[tex]\[ M \approx 240.17 \][/tex]

Therefore, the amount of Simon's monthly payment, rounded to the nearest cent, is approximately $240.17.

Answer:

241.16

Step-by-step explanation:

Answer:

9.28 Liters

Step-by-step explanation:

All we have to do is multiply the time by amount her time unit.

There is actually some tactics to this. I tried to find x and y first but they are very messy numbers but...

We know...

(x+y)²=x²+2xy+y²

In this case, (x+y)² = 11² = 121.

So, x²+2xy+y²=121

We also know that xy=15 and furthermore that 2xy=30.

x²+y² = 121-30 = 91

answer: 91

The value of x^2 + y^2 is 91.

To find the value of x^2 + y^2 given that x+y=11 and xy=15, we can use algebraic identities. We will use the fact that (x+y)^2 = x^2 + 2xy + y^2. We know that x+y=11, so (x+y)^2 = 11^2 = 121. Also given is xy=15, which we'll use in the identity mentioned.

Now, let's substitute the values into the identity:

(x+y)^2 = x^2 + 2xy + y^2

121 = x^2 + 2(15) + y^2

121 = x^2 + 30 + y^2

121 - 30 = x^2 + y^2

91 = x^2 + y^2

The distance between the y-intercept and the x-intercept of the line is 12.64911 units or [tex]\sqrt{160}[/tex] units

Solution:

Given equation is y = 3x + 12

We have to find the distance between y-intercept and the x-intercept of the line whose equation is y = 3x + 12

Let us first find the x - intercept and y - intercept

The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.

The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero

Finding x - intercept:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.

Substitute y = 0 in given equation

y = 3x + 12

0 = 3x + 12

3x = -12

x = -4

Thus the x - intercept is (-4, 0)

Finding y - intercept:

To find the y-intercept, plug 0 in for 'x' and solve for 'y'

Substitute x = 0 in given equation

y = 3x + 12

y = 3(0) + 12

y = 12

Thus the y - intercept is (0, 12)

Now let us find the distance between x intercept and y intercept

Distance between two points [tex]P(x_1, y_1) \text{ and } Q(x_2, y_2)[/tex] is given by:

[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]

Here the distance between (-4, 0) and (0, 12) is given as:

[tex]\begin{aligned}&d=\sqrt{(0-(-4))^{2}+(12-0)^{2}}\\\\&d=\sqrt{4^{2}+12^{2}}\\\\&d=\sqrt{16+144}=\sqrt{160}\\\\&d=12.64911\end{aligned}[/tex]

Thus the distance between the y-intercept and the x-intercept of the line is 12.64911 units or [tex]\sqrt{160}[/tex] units

The y-intercept of the line y=3x+12 is (0,12) and the x-intercept is (-4,0). The distance between these two points is approximately 12.65 units.

The equation given is y=3x+12. The x-intercept is the point where the line crosses the x-axis (where y=0), and the y-intercept is where the line crosses the y-axis (where x=0).

For the y-intercept, we simply replace x with 0, so y = 3(0) + 12 = 12. Thus, the y-intercept is (0,12).

For the x-intercept, we replace y with 0, so 0 = 3x + 12. Solving this equation for x gives x = -4. Thus, the x-intercept is (-4,0).

The distance between two points in the coordinate plane is given by the formula √[(x2-x1)² + (y2-y1)²]. Therefore, the distance between the x-intercept and the y-intercept is √[(-4-0)² + (0-12)²] = √(16 + 144) = √160 = 12.65.

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Answer:

Option b) is correct

3x+4(2x+4)=17  Substitute (2x+4) for y in the second equation

Step-by-step explanation:

Given Equations are

[tex]y=2x+4\hfill (1)[/tex] and [tex]3x+4y=17\hfill (2)[/tex]

To solve the given equations we have to find the value of

x and y values.

Here y value is given so that we can substitute  y=3x+4 value  in second equation

ie., Substitute equation (1) in (2) equation we can easily get x value.

Therefore  substitute (2x+4) for y in the second equation we get

3x+4(2x+4)=17

Option b) is correct

Answer:

Step-by-step explanation:

I think I've already answered this question.

She paid 80% of the regular price because it was 20% off so...

80% = £40

We want to get to the regular price (100%) so...

100% = £40 x 100/80 = £50

answer: £50

Answer:he paid 80% of the regular price because it was 20% off so...

80% = £40

We want to get to the regular price (100%) so...

100% = £40 x 100/80 = £50

answer: £50

Step-by-step explanation:

the product of (10x - 17) and (6y + 29)(8x + 1) is:

[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

you want to multiply the expressions (10x - 17) and (6y + 29)(8x + 1). Let's proceed with the multiplication:

First, distribute (6y + 29) into (8x + 1):

[tex]\[ (6y + 29)(8x + 1) = 6y \cdot 8x + 6y \cdot 1 + 29 \cdot 8x + 29 \cdot 1 \]\[ = 48xy + 6y + 232x + 29 \][/tex]

Now, multiply the result by (10x - 17):

[tex]\[ (10x - 17)(48xy + 6y + 232x + 29) \]\[ = 10x \cdot (48xy + 6y + 232x + 29) - 17 \cdot (48xy + 6y + 232x + 29) \]\[ = 480xy^2 + 60xy + 2320x^2 + 290x - 816xy - 102y - 3944x - 493 \]\[ = 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

So, the product of (10x - 17) and (6y + 29)(8x + 1) is:

[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

The probable question maybe:

multiply the expressions (10x - 17) and (6y + 29)(8x + 1).

The product of (10x - 17) and (6y + 29)(8x + 1) is: = [tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

You have to multiply the expressions (10x - 17) and (6y + 29)(8x + 1). Let's proceed with the multiplication:

First, distribute (6y + 29) into (8x + 1):

[tex]\[ (6y + 29)(8x + 1) = 6y \cdot 8x + 6y \cdot 1 + 29 \cdot 8x + 29 \cdot 1 \]\[[/tex]

= 48xy + 6y + 232x + 29

Now, multiply the result by (10x - 17):

[tex]\[ (10x - 17)(48xy + 6y + 232x + 29) \]\\\\ = 10x \cdot (48xy + 6y + 232x + 29) - 17 \cdot (48xy + 6y + 232x + 29) \]\\\\ = 480xy^2 + 60xy + 2320x^2 + 290x - 816xy - 102y - 3944x - 493 \]\\\\ = 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

So, the product of (10x - 17) and (6y + 29)(8x + 1) is:

[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

The complete question is:

Multiply the expressions (10x - 17) and (6y + 29)(8x + 1).

Answer:

102

Step-by-step explanation:

X=5 so from A to E is  5. 5 squared is 25 plus 4 = 29 then add 29 to 5 you get 34. Then multiply 34 times 6  you get 204 then divide by 2 because area of triangle is base times height divided by 2 you get 102.

Final answer:

Using the properties of isosceles triangles, the acute base angle of the isosceles trapezoid, which is part of an isosceles triangle with a 46° vertex angle, is found to be 67°.

Explanation:

To find the measure of an acute base angle of the isosceles trapezoid that is part of an isosceles triangle with a 46° vertex angle, we can apply the properties of isosceles triangles. By the Isosceles Triangle Theorem, we know that the angles opposite the equal sides are equal.

Since the given triangle is isosceles, the two base angles must also be equal. Additionally, we know that the sum of all angles in any triangle is 180°.

Let's call each of the base angles B. Then, the sum of all angles in the triangle is:

46° + B + B = 180°

Now we solve for B:

2B = 180° - 46° = 134°

B = 134° / 2 = 67°

Thus, each base angle of the isosceles triangle is 67°. Next, considering the isosceles trapezoid, we know the adjacent angles must be supplementary because they are on the same line. This means that one base angle of the isosceles trapezoid equals:

180° - 67° = 113°

However, since the student is looking for the measure of an acute base angle of the trapezoid and 113° is an obtuse angle, the acute base angle is the original 67° angle that we found. This is because the acute and obtuse angles in the trapezoid are adjacent angles around the same vertex, and the acute angle is the angle that's interior to the triangle.

Therefore, the measure of an acute base angle of the trapezoid is 67°.

Answer:

The correlation coefficient is 0.96

Step-by-step explanation:

The Given Table showing year and cost:

Year          Cost

1948           0.36

1963           0.86

1974           1.89

1978           2.34

1985           3.55

1991            4.21

1997           4.59

2005         6.41

2010          7.89

Regression table:

Regression table can be made if we rewrite the year column by associating

1948 with 0, and the years after 1948 to be associated with the number of years after 1948. For example, if 1948 is associated with 0, then 1963 would come after 15 years, hence 1963 would be represented by 15, and with the same way, we can associate other years as well. Have a look:

Year (X)          Cost  (Y)             X²                   XY  

0                         0.36                  0                    0

15                        0.86                225                 12.9

26                       1.89                 676                 49.14

30                       2.34                900                 70.2

37                        3.55               1369                 131.35

43                        4.21                1849                 181.03

49                        4.59               2401                 224.91

57                        6.41                3249                 365.37

62                        7.89               3844                  489.18

∑X= 319           ∑Y= 32.1           ∑X²= 14513        ∑XY= 1524.08            

As the correlation coefficient (r) can be determined as follows:

r = n (∑ XY) - (∑X) (∑Y)  ÷ √[n(∑X²)-(∑Y)²][n(∑Y²)-(∑Y)²]

But, we need an additional column Y²

So,

         Y²          

        0.1296            

         0.7396          

         3.5721        

         5.4756          

         12.6025          

         17.7241          

         21.0681            

         41.0881        

         62.2521  

   ∑Y² = 164.6518

As,

r = n (∑ XY) - (∑X) (∑Y)  ÷ √[n(∑X²)-(∑Y)²][n(∑Y²)-(∑Y)²]

So,

r = 9 (524.08) - (319)(32.1) ÷ √[9(14513 )-(319)²][9(164.6518)-(32.1)²]

[tex]r = \frac{3476.82}{\sqrt{(28856)(451.4562)}}[/tex]

[tex]r = \frac{3476.82}{\sqrt{(13027220.11)}}[/tex]

[tex]r = \frac{3476.82}{\sqrt{(3609.32)}} = 0.96[/tex]

So, the correlation coefficient is 0.96.

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Contraction. It gets smaller as the image is shrunk. It will be a fraction of the original triangle.

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Answer:

10

Hope this helps :)

Answer:

rthw aeenser is 20

Step-by-step explanation:

Answer:

is it 8 apples to her mother or 10 since I had this exact problem?

Step-by-step explanation:

Ashe started with 32 apples in the basket initially.

To find the half of something just multiply 1/2 with the given value.

According to the given question Linda picked a basket of apples.

Assuming she had x apples initially.

She gave half of the apples to the neighbour,Therefore she now has            (x - 1/2x) apples which is = 1/2x apples.

Then she gave 10 to her mother,So the remaining apples she has now is

= ( 1/2x - 10 ) apples

= (x - 20)/2.

Then she gave half of the apples to her best friend so the no. of apples she has now is (x - 20)/2×1/2 which is = (x - 20)/4 and she kept the remaining 3.

∴ (x - 20)/4 = 3

x - 20 = 12

x =32.

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Answer:

Number of hot dog packets = [tex]\frac{24}{12}[/tex] = 2

Number of bun packets = [tex]\frac{24}{8}[/tex] = 3

Step-by-step explanation:

Beverley is buying hot dogs and hot dog buns for a picnic. She wants to buy one got dog for each bun with none left over. The hot dogs come packed 12 in a package. The buns come packed 8 in a package.

We have to find the lowest common multiple of 8 and 12 and from observation we can see that it is 24.

So Beverly would have to buy around 24 pieces of hot dogs and buns.

Number of hot dog packets = [tex]\frac{24}{12}[/tex] = 2

Number of bun packets = [tex]\frac{24}{8}[/tex] = 3

Answer:

Beverly would have to buy around 24 pieces of hot dogs and buns.

Step-by-step explanation:

same hope this help

Final answer:

The correct answer is C. outside 45 degrees. In this question, we are asked to identify which directions are NOT vector directions. Options A, B, and D all describe vector directions, but option C does not.

Explanation:

The correct answer is C. outside 45 degrees.

In this question, we are asked to identify which directions are NOT vector directions. A vector direction is a specific direction or angle that describes the orientation of a vector.

Options A, B, and D all describe vector directions:

A. 35 degrees north of east: This describes a vector direction that is 35 degrees north of the east direction.

B. north: This is a vector direction that points directly north.

D. 35 degrees inside: This describes a vector direction that is 35 degrees inside the reference angle.

Option C, outside 45 degrees, does not describe a specific vector direction. It is not clear whether the direction is outside 45 degrees to the left or right. Therefore, option C is NOT a vector direction.

Answer:

Option A.

[tex]f(x)\leq 3x+4[/tex]

[tex]g(x) \leq-\frac{1}{2}x-5[/tex]

Step-by-step explanation:

we know that

If point C is a solution of the system of inequalities, then point C must satisfy both inequalities

Point C is located below the solid line f(x) and below the solid line g(x)

so

The shaded region of the solution set of the system must be below of the inequality f(x) and must be below of the inequality g(x)

therefore

The system is

[tex]f(x)\leq 3x+4[/tex]

[tex]g(x) \leq-\frac{1}{2}x-5[/tex]

Answer:

B

Step-by-step explanation:

Answer:

I think it's $1,349.86

Answer:

It's $1,349.86

Step-by-step explanation:

(trust me bro)

Answer:

40

Step-by-step explanation:

Least common multiple (lcm) = the smallest multiple that both numbers have.

Let's figure it out.

10 = 2 x 5

8 = 2 x 2 x 2

the ones I have highlighted, we will multiply them all together, except for a 2.

we didn't multiply one of the 2's because they both have a two, so we only keep one of them.

so it is 2 x 5 x 2 x 2

let me say it again, because they both share a same 2, that one is eliminated.

so the answer is 40 because:

2 x 5 x 2 x 2

= 10 x 4

= 40

Answer:

Step-by-step explanation:

list the multiples of 8 and 10 and mark wich one is the lowest number

Answer:

12

Step-by-step explanation:

When you subtract a negative number, the two negatives make a plus sign.

4 - (-8)

= 4 + 8

= 12

Answer:

$124.20 miles all you gotta do is add them together

Step-by-step explanation:

Answer: 213

Step-by-step explanation:

852/4 = 213

Answer:

213

Step-by-step explanation:

852/4 = 213

He is splitting 852 beads into 4 bracelets (groups)

Answer:

x = 100°

y = 125°

z = 55°

Step-by-step explanation:

A straight line is 180°

A triangle is 180°

Solve in this order:

X: 180 - 80 = 100

Z: 180 - 80 - 45 = 55

Y: 180 - 55 = 125

Answer:

4x-2y=2/5

Step-by-step explanation:

2y=4x-2/5

4x-2y=2/5

Answer:

Step-by-step explanation: when h(x) = 10

h(x)= 6-x

h(10)= 6-10

=-4

The expression √215x should be further simplified for (a) 35 as the value of x

How to determine the value of x

From the question, we have the following parameters that can be used in our computation:

√215x

Taking each value of x from the list of options, we have

√215x = √(215 * 35)

Expanding, we get

√215x = √(5 * 43 * 7 * 5)

This gives

√215x = 5√301

Next, we have

√215x = √(215 * 118)

Expanding, we get

√215x = √(5 * 43 * 2 * 59)

This gives

√215x = √(25370)

Next, we have

√215x = √(215 * 34)

Expanding, we get

√215x = √(5 * 43 * 2 * 17)

This gives

√215x = √7310

Next, we have

√215x = √(215 * 7)

Expanding, we get

√215x = √(5 * 43 * 7)

This gives

√215x = √1505

Hence, the value of x is 35

Answer:

15C is 59F

Step-by-step explanation:

As an equation, F = (1 4/5)C + 32. 1 and 4/5 is the same as 9/5.

Substitute 15 for C.

F = (9/5)C + 32

F = (9/5)(15) + 32   Multiply 15 by the top number in 9/5

F = 135/5 + 32       Convert 32 to a fraction over 5

F = 135/5 + 160/5     Add the numerators under the same denominator

F = 295/5        Divide

F = 59              Degrees in Farenheit

Therefore 15°C is 59°F.

Answer:

the remainder is 10

Step-by-step explanation:

Answer:

R=10

Step-by-step explanation:

1. 428/19=22

2. R=10

Steps for checking your work:

1. Multiply the divisor by the answer (aka quotient)

2. After that, add the remainder to the answer you got from doing step 1 for checking your work (aka proudct, since you multiplied)

Answer:

13.

Step-by-step explanation:

2g + 7

= 2(3) + 7

= 6 + 7

= 13.

Answer: 13

Step-by-step explanation: In this problem, we have the xpression 2g + 7 and we want to evaluate the expression when g is equal to 3.

To evaluate an expression, we simply plug the value of the variable into the expression and solve. So here, since g is equal to 3, we have 2 (3) + 7. 2 × 3 is equal to 6 so we have 6 + 7 which is equal to 13.

So the value of our expression when g is equal to 3 is 13.

Remember, when we see a variable like g next to a number, it means multiplication so you want to multiply by the value of the variable.