Find the volume of this Triangular Prism

9514 1404 393

Answer:

  the numbers are -10 and -11

Step-by-step explanation:

Let x represent the second number. Then the first number is x+1, and the relation can be written ...

  5(x+1) = 4x -6

  x = -11 . . . . . . . . subtract 4x+5

The first number is -10; the second number -11.

ANSAWER:

−15+8i

Explanation:

First, you can expand the square of the bynomial:

Answer:

decimal: 2.25

fraction: 9/4

Step-by-step explanation:

Answer:

Fraction: 15/4

Decimal: 3.75

Answer:

so the lines mean absolute value

which is the exact distance from zero that the number is

now

you subtract one from nine which makes it 2x=8

then

you divide nine by 2x which makes it

x=4

So the answer is four

if it helps mark me brainliest please

Answer:

-5,4

Step-by-step explanation:

I know that 2 numbers will work because it's an absolute function.

2x+1=9

2x=8

x=4

2(-5)+1=|-9| = 9

Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer:

it needs me to type more but answer is

-5,-4

Answer:

S will be at (-5,-4)

Step-by-step explanation:

T is located at (0,-4)

To move to the left, the x coordinate moves.

(0-5, -4)

S will be at (-5,-4)

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

<a=55° ,< b=55° and <c=70°

Answer:

\(Perimeter = 38.6\)

Step-by-step explanation:

Given

\(A\ B = 13\)

\(B\ F = 9\)

\(F\ C = 5.6\)

Required

Calculate the perimeter of A B C

To calculate the perimeter of A B C, we sum up the sides of the triangle

i.e.

\(Perimeter = A B + B\ C + A\ C\)

AB is given in the question already.

So, we need to calculate B F and F C

To solve for BF, we consider triangle B F C

Using Pythagoras Theorem, we have:

\(B\ C^2 = B\ F^2 + F\ C^2\)

Substitute values for BF and FC;

\(B\ C^2 = 9^2 + 5.6^2\)

\(B\ C^2 = 81 + 31.36\)

\(B\ C^2 = 112.36\)

\(B\ C^2= \sqrt{112.36\)

\(B\ C = 10.6\)

Next, we calculate A C.

To calculate A C, we need to calculate A F, considering triangle B F A

Using Pythagoras Theorem, we have:

\(A\ B^2 = B\ F^2 + A\ F^2\)

Substitute values for B F and A B;

\(13^2 = 9^2 + A\ F^2\)

\(169= 81 + A\ F^2\)

\(A\ F^2 = 169 - 81\)

\(A\ F^2 = 88\)

\(A\ F = \sqrt{88\)

\(A\ F = 9.4\)

Since F lies on line A C:

\(A\ C = A\ F + F\ C\)

\(A\ C = 9.4 + 5.6\)

\(A\ C = 15.0\)

Recall that:

\(Perimeter = A\ B + B\ C + A\ C\)

\(Perimeter = 13 + 10.6 + 15.0\)

\(Perimeter = 38.6\)

Hence, the perimeter is 38.6

Given that P is the orthocenter of triangle ABC, applying the properties of an orthocenter of a triangle and the Pythagorean Theorem, each measure and the perimeter of △ABC are:

Recall:

Given that P is the orthocenter of triangle ABC, where,

Perimeter of △ABC = AB + BC + AC

First, we need to find BC and AC.

△BFC is a right triangle, apply Pythagorean theorem to find BC:

\(BC = \sqrt{BF^2 + FC^2}\)

\(BC = \sqrt{9^2 + 5.6^2}\\\\\mathbf{BC = 10.6}\)

△BFA is a right triangle, apply Pythagorean theorem to find FA:

\(FA = \sqrt{AB^2 - BF^2}\)

\(FA = \sqrt{13^2 - 9^2}\\\\\mathbf{FA = 9.4}\)

AC = FA + FC

AC = 9.4 + 5.6

AC = 15

Perimeter of △ABC = AB + BC + AC

Perimeter of △ABC = 13 + 10.6 + 15

Perimeter of △ABC = 38.6 units

Therefore, given that P is the orthocenter of triangle ABC, applying the properties of an orthocenter of a triangle and the Pythagorean Theorem, each measure and the perimeter of △ABC are:

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Answer:

15:6

Step-by-step explanation:

Answer:

1500

Step-by-step explanation:

p = number of people who should be tested

.02p = 30

p = 30/.02

p = 1500

yes its a skill related mostly to math

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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There is no whole number by which you can multiply or divide 16087 to make it a perfect square.

To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.

In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.

To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.

A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.

Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.

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Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer:

Step-by-step explanation:

24   hope it helps you!!

Answer:

It would equal -3

Step-by-step explanation:

you are trying to find how to get a positive 21 so you would have to divide 21 by -7

21 ÷ -7 = -3

to make sure it's correct muiltply it

-7 × -3 = 21

So therefore n = -3

The value of x is 6

2/5 = 6/21-x

Cross multiply both sides

2(21-x)= 30

42-2x= 30

collect the like terms

-2x= 30-42

-2x= -12

Divide both sides by the coefficient of x which is 2

2x/2 = 12/2

x= 6

Hence the value of x is 6

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Answer:

The 2 is 200

The 3 is 3000

The 1 is 1

And if needed

The 6 is 60

Step-by-step explanation:

2 is in hundredths place

3 is in thousand place

6 is in tens place

1 is in ones place

hope this helps

Answer:

65º

Step-by-step explanation:

(the sum of the angles of a triangle) 180- 65= 115

65= 30+ 35

180- 115=65

Answer:

I'm pretty sure the answer is 65

Step-by-step explanation:

30+35=65

180-65=115

So the 3rd angle in the triangle is 115°

Then you subtract 115 from 180 and get 65°

So S equals 65°

Answer:

5/21 = 0.2381

Hope this helps!

Answer:

0.238095

Step-by-step explanation:

Answer:

y= |x|-9

Step-by-step explanation:

Answer:

Who knows!?

Step-by-step explanation:

Answer:

\(\implies \dfrac{80}{90}-\sqrt{50} \times 19^2 \div 23^2\)

Order of operations (PEDMAS)

Following the order of operations,
Carry out the exponents (and radicals) first:

\(\implies \dfrac{80}{90}-\sqrt{25 \cdot 2} \times 361 \div 529\)

\(\implies \dfrac{80}{90}-5\sqrt{2} \times 361 \div 529\)

Now the multiplication and division (from left to right):

\(\implies \dfrac{8}{9}-1805\sqrt{2} \div 529\)

\(\implies \dfrac{8}{9}-\dfrac{1805\sqrt{2}}{529}\)

Convert the fractions so that their denominators are the same:

\(\implies \dfrac{8 \times 529}{9 \times 529}-\dfrac{1805\sqrt{2} \times 9}{529 \times9}\)

\(\implies \dfrac{4232}{4761}-\dfrac{16245\sqrt{2}}{4761}\)

Answer as a fraction:

\(\implies \dfrac{4232-16245\sqrt{2}}{4761}\)

Answer as a number:

\(\implies -3.936546801... = -3.9\: \textsf{(nearest tenth)}\)

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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Answer:

What is the measure of angle D?

52o

Angle D = 360-128-126-54 = 52o

Step-by-step explanation: got it right on edge

Since the sum of the angles in a quadrilateral is 360 degrees then the angle D is 50 degrees.

A quadrilateral is a four sided figure. Examples of quadrilaterals include; square, parallelogram, rectangle, kite etc.

The sum of angles in a quadrilateral is 360  degree hence;

A + B + C + D = 360 (sum of angles in a quadrilateral)

128 + 126 + 54 + D = 360

D = 360 - ( 128 + 126 + 54)

D = 50 degrees

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