The ratio of the angle measures of the acute angles in a right triangle is 1:2 . What is the measures of these angles a. 30 and 60 b. 45 and 90 c. 60 and 120 d. 10 and 20

Final answer:

Kari had $13. We found this by dividing Penny's amount, $117, by 9, since Penny's amount is 9 times greater than Kari's.

Explanation:

The question is asking us to determine how much money Kari had if Penny had $117, which is 9 times as much as what Kari had. To do this, we need to perform a division, because if Penny's amount is 9 times Kari's, we can find Kari's amount by dividing Penny's $117 by 9.

 To solve for K, divide both sides of the equation by 9: K = $117 / 9.

Therefore, Kari had $13.

Answer:

True

Step-by-step explanation:

If you look at the different countries ranked based off of the size of their ecological footprint, you will see that Japan is ranked around 5 and china around 10.

This means The average ecological foot print of a person living in Japan is larger than a person living in China.

The given triangle can be known as a scalene triangle.

A triangle is a two dimensional shape bound by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.

The measures of the different angles are given as 15°, 44° and 121° respectively.

Since, all the angles have different measures.

The given triangle is neither equilateral or isosceles.

Thus, the given triangle is scalene triangle.

Hence, the given triangle can be called as a scalene triangle.

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y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We need to find the equation of line that includes the point (6, 3) has a slope of 2.

y minus y one equal to m time of x minus x one.

(y-y₁)=m(x-x₁)

x₁=6,y₁=3 and m is 2

y-3=2(x-3)

Apply distributive property on right hand side.

y-3=2x-6

Shift -3 to the RHS side

y=2x-6+3

y=2x-3

Hence y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2

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The larger frustum has a surface area of 1516.875cm². This is calculated by first finding the ratio of the heights, then cubing this ratio and finally multiplying the result by the surface area of the smaller frustum.

In Mathematics, similar frustums follow a rule in which the ratio of their dimensions is the cube root of their surface area ratio. Since the height of the larger frustum is 30cm, and the height of the smaller one is 20cm, their ratio is 30:20 or 1.5:1.

To find the ratio of the surface areas, you'll want to cube this ratio (1.5 ^ 3 = 3.375).

So, the surface area of the larger frustum is the surface area of the smaller frustum (which is 450cm² ) multiplied by this ratio. In mathematical terms, 3.375 * 450 = 1516.875cm².

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Answer:

Option B and E

Step-by-step explanation:

A line is given as 3x - 4y = 7

We have to find the equation of a line parralel to the given line which passes through point (-4, -2).

Let the equation is y = mx + c

Line parallel to 3x - 4y = 7 will have same slope

3x - 4y = 7

-4y = 7 - 3x

4y = 3x - 7

y = [tex]\frac{1}{4}[/tex] (3x - 7 ) ≈ [tex]\frac{3}{4}[/tex]x - [tex]\frac{7}{4}[/tex]

So slope of the line will be m = [tex]\frac{3}{4}[/tex]

Since the given line passes through (-4, -2)

So we put the values in y = mx + c to get the value of c.

-2 = [tex]\frac{3}{4}[/tex] (-4 ) + c

-2 = -30 +c

c = 3 - 2 = 1

Therefore, equation will be

y = [tex]\frac{3}{4}[/tex]x + 1 ----------(1)

We further solve equation (1)

4y = 3x + 4

3x - 4y = -4 ---Option B

By solving the equation (1) in other way

y + 2 = [tex]\frac{3}{4}[/tex]x + 1 + 2

[tex]\frac{3}{4}[/tex]x + 3

y + 2 = [tex]\frac{3}{4}[/tex] (x+4)  --Option E

Option B and E are the answers.

The total meat Elian bought is  4.33 pounds.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

Given, Elian bought 1.87 pounds of chicken and 2.46 pounds of turkey at the deli.

∴ The total meat Elian bought is the sum of pounds of chicken bought and pounds of turkey bought.

= (1.87 + 2.46) pounds.

= 4.33 pounds.

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Answer:

Option A - Non-linear              

Step-by-step explanation:

Given : Graph the function by the table.

x           y

1          12.3

2         19.6

3         26.6

4         34.2

5         41.5

To find : Is the function linear or nonlinear?

Solution :

The function is linear when there slopes are equal.

So, we find the slope of the points.

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

Taking point, [tex](x_1,y_1)=(1,12.3)[/tex] and [tex](x_2,y_2)=(2,19.6)[/tex]

[tex]m=\frac{19.6-12.3}{2-1}[/tex]

[tex]m=\frac{7.3}{1}[/tex]

[tex]m=7.3[/tex]

Taking point, [tex](x_1,y_1)=(2,19.6)[/tex] and [tex](x_2,y_2)=(3,26.6)[/tex]

[tex]m=\frac{26.6-19.6}{3-2}[/tex]

[tex]m=\frac{7}{1}[/tex]

[tex]m=7[/tex]

We have seen that slope between points are not equal.

Therefore, The given points are non-linear.

So, Option A is correct.

The equation of the line with a slope of 5 and a y-intercept of 7 is y = 5x + 7.

The equation of a line in slope-intercept form is given as y = mx + b, where m is the slope of the line and b is the y-intercept. Given that the slope (m) is 5 and the y-intercept (b) is 7, the equation of the line can be written as y = 5x + 7. This equation tells us that for every increase of 1 on the x-axis, the value of y rises by 5 units, and the line crosses the y-axis at the point (0, 7).

The variable will be a natural number according to the set of numbers that best describes its values, the amount of money m spent is a vending machine option (D) is correct.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The amount of money m spent is a vending machine.

As we know, in the vending machine we cannot insert money in negative quantity.

And integers range from (-∞, ∞)

The real number starts from 1 and continues 2, 3, 4,5 ,6 and so on

Thus, the variable will be a natural number according to the set of numbers that best describes its values, the amount of money m spent is a vending machine option (D) is correct.

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Factor out 4x from the given trinomial. Therefore, option C is the correct answer.

The factors are the polynomials which are multiplied to produce the original polynomial.

The given trinomial is 4x³-20x²+24x.

Here, 4x(x²-5x+6)

= 4x(x²-3x-2x+6)

= 4x[(x(x-3)-2(x-3)]

= 4x(x-3)(x-2)

Therefore, option C is the correct answer.

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Answer:

It's B

Step-by-step explanation:

20(102+159/2)

Answer:

The answer is 6 inches

Step-by-step explanation:

Since the angle is isosceles, angle A and angle B have the same measure, 

The sum of the angles of any triangle is 180°.

So 2 times the measure of angle B plus  120° = 180°, then the equation:

Solving for x we get: 

Now we use the law of sine on the triangle BMC like this:

Solving for BC we get : 

We apply the law of sin again on the isosceles triangle ABC like this:

Solving for AB we get:

6 inches

Answer:

Answer:

The answer is 6 inches

Step-by-step explanation:

Since the angle is isosceles, angle A and angle B have the same measure, 

The sum of the angles of any triangle is 180°.

So 2 times the measure of angle B plus  120° = 180°, then the equation:

Solving for x we get: 

Now we use the law of sine on the triangle BMC like this:

Solving for BC we get : 

We apply the law of sin again on the isosceles triangle ABC like this:

Solving for AB we get:

6 inches

Read more on Brainly.com - https://brainly.com/question/6638938#readmoreStep-by-step explanation:

True because their different

Answer:

Step-by-step explanation:

the right answer is a (-6,8) where x=-6 and y=8

We're going to use Cramer's rule to resolve this question.

First of all, we're going to give a number to the equations:

(1) -8x-8y=-16

(2) 6x-9y=-108

where constant 1=c1=-16 and the constant 2=c2=-108

now we need to find the next determinants:

D: system determinant,Dx and Dy.

now we're going to find "D."

for that, we're going to take the coefficients of  x and y in (1) and (2)

              x    y

D= [tex]\f\left[\begin{array}{ccc}-8&-8\\6&-9\end{array}\right][/tex]     

this is how we need to put the matrix, using the numbers next to x and y in the (1) and (2) equation.

to solve this matrix, we need to multiplicate in X, and subtract the results; so for D we have:

(-8*-9)-(6*-8)

72-(-48)=

72+48=120

now we're doing the same process to find Dx and Dy, but in each case, we're going to replace x or y with the constants (the constants are the numbers right to the "=")

to find Dx we're going to use the values of c1 and c2 instead of x

            C1&2      y

Dx= [tex]\f\left[\begin{array}{ccc}-16&-8\\-108&-9\end{array}\right][/tex]

Now we do the same as with D

(-16*-9)-(-108*-8)=

144-(864)

144-864=-720

and now for Dy=

            x      C1&2

Dy=  [tex]\f\left[\begin{array}{ccc}-8&-16\\6&-108\end{array}\right][/tex]

= (-8*-108)-(6*-16)=

864-(-96)=

864+96=960

now the last step is to find x and y .

x= [tex]\frac{Dx}{D}[/tex]   Y= [tex]\frac{Dy}{D}[/tex]

x= -720/120=-6

y=960/120=8

x=-6  y= 8

answer = (-6,8)

After applying the translation (x - 1, y - 3), the vertices of the triangle originally at (-4, 5), (0, 0), and (4, 5) will move to new locations (-5, 2), (-1, -3), and (3, 2).

The question is about translation in mathematics, specifically in geometry. A translation is a function that moves every point a constant distance in a specific direction. If we have a point at coordinates (x, y), a translation of the form (x - a, y - b) will shift that point a units to the left and b units down:

So, the vertices of the triangle after the translation (x - 1, y - 3) will be (-5, 2), (-1, -3), and (3, 2).

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Final answer:

The sequence of substitutions of the coins on the table results in a final arrangement of coins with a total value of 121 cents or $1.21. This problem combines sequence patterns with coin values to find the total.

Explanation:

We have a problem involving a series of substitutions of coins, and we need to calculate the total value of the coins on the table after these substitutions. We start with 12 pennies, which are initially worth 1 cent each.

Step 1: Every other coin is replaced with a nickel, so we replace every 2nd penny with a 5-cent coin (nickel). The sequence starts with a penny (P), so the even positions will now be nickels (N). The sequence now looks like P, N, P, N, P, N, P, N, P, N, P, N.

Step 2: Every third coin is replaced with a dime, which is worth 10 cents. This means the 3rd, 6th, 9th, and 12th positions will now be dimes (D). The sequence becomes P, N, D, N, P, D, P, N, D, N, P, D.

Step 3: Every fourth coin is replaced with a quarter, which is worth 25 cents. Positions 4, 8, and 12 are affected. The sequence is now P, N, D, Q, P, D, P, Q, D, N, P, Q.

Let’s calculate the total value of the coins:

6 Pennies (P): 6 * 1 cent = 6 cents

2 Nickels (N): 2 * 5 cents = 10 cents

3 Dimes (D): 3 * 10 cents = 30 cents

3 Quarters (Q): 3 * 25 cents = 75 cents

Adding all these values together: 6 cents + 10 cents + 30 cents + 75 cents = 121 cents or $1.21.

This problem requires understanding of sequence patterns and knowledge of United States coin values to determine the total value of the coins.