These shapes below are mathematically

Answer:

5c-5=45

Step-by-step explanation:

Since he didn't have the dessert you have to take away the five and the total was 45 which means something has to equal it.

5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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Answer:

Step-by-step explanation:

8) Find the LCM of 9 , 12

9 = 3* 3

12 = 3 * 2 *2

LCM = 3 * 3 * 2* 2 =36

Now  find equivalent fraction to make like fractions and then subtract

\(\dfrac{7}{9}-\dfrac{8}{12}=\dfrac{7*4}{9*4}-\dfrac{8*3}{12*3}\\\\\\=\dfrac{28}{36}-\dfrac{24}{36}\\\\\\=\dfrac{28-24}{36}=\dfrac{4}{36}\\\\=\dfrac{1}{9}\)

9)

\(6\dfrac{1}{2}-4\dfrac{3}{8}=\dfrac{13}{2}-\dfrac{35}{8}\\\\=\dfrac{13*4}{2*4}-\dfrac{35}{8}\\\\=\dfrac{52}{8}-\dfrac{35}{8}\\\\=\dfrac{17}{8}\\\\\\15\dfrac{1}{4}+\dfrac{17}{8}=\dfrac{61}{4}+\dfrac{17}{8}\\\\=\dfrac{61*2}{4*2}+\dfrac{17}{8}\\\\=\dfrac{122}{8}+\dfrac{17}{8}\\\\=\dfrac{122+17}{8}\\\\=\dfrac{139}{8}\\\\=17\dfrac{3}{8}\)

10)

\(48\dfrac{9}{10}-45\dfrac{4}{5}= \dfrac{489}{10}-\dfrac{229}{5}\\\\=\dfrac{489}{10}-\dfrac{229*2}{5*2}\\\\=\dfrac{489}{10}-\dfrac{458}{10}\\\\=\dfrac{31}{10}\\\\=3\dfrac{1}{10}\)

Answer

(7/9)-(8/12) = 1/9

15(1/4)+6(1/2=27(1/4)=(21/4)

48(9/10)-45(4/5)=(36/5)kg

Step-by-step explanation:

When working with fractions it is easiest to start with a common denominator.

Difference means to subtract:

8:

(7/9)-(8/12) = 1/9

First simplify 8/12 notice how both terms are even. so 8/12 = 2/3 see how 8 and 12 are divisible by 4 so you get 2/3.

Now the question will be (7/9)-(2/3). Now you can find an easy common denominator.

***** Finding the common denominator is important when adding or subtracting fractions*******

This will be (7/9)-(6/9) the common denominator here is 9. Notice how you only need to multiply (2/3) by three. Now the denominators match so you can subtract them easily.

You will get (7/9)-(6/9)=(1/9)

9: Sum means to add and subtracted obviously means to subtract. Remember find a common denominator than simplify. The easiest way todo this is work through the problem one fraction at a time. Remember to follow the order of operation. (In this case + and - are the same order of operations so it doesn't matter what you do first.)

(27/4)

So lets start with the first two 15(1/4)+6(1/2)

The common denominator here is 4 so multiply 6(1/2) by 2

15(1/4)+12(1/4)=27(1/4)

Now lets subtract

27(1/4)-4(3/8)=(27/4)-(12/8) notice the common denominator as 8.

lets multiply(27/4)) by 2

(54/8)-(12/8)=(42/8)

Notice how it divisible by 2

so (42/8) = (21/4)

so

15(1/4)+12(1/4)=27(1/4)=(21/4)

10: 48(9/10)-45(4/5)=(432/10)-(180/5)

Notice common denominator 10 so multiply (180/5)  by 2

(432/10)-(360/10)=(72/10)

Notice divisable by 2

so (72/10)=(36/5)

you could use the multiplication strategy such as 10x3 or 3x10

Answer : 10 x 3

Step - by - step explanation :

10 x 3 = How much time Denzel spends washing his car

Answer:

B. Multiply 6 by 3

Step-by-step explanation:

Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:

B. Multiply 6 by 3

Your step by step for getting the number Hannah started with:

First, multiply 6 with 3:

6 x 3 = 18

Next, subtract 4:

18 - 4 = 14

Next, divide by 2:

14/2 = 7

Hannah started with the number 7.

~

Answer: Hannah started with 7.

B. Multiply 6 by 3

Explanation:

Let the number be y

2 × y = 2y

(2y + 4)/3 = 6

2y + 4 = 6×3 = 18

2y + 4 = 18

2y = 18 - 4 = 14

y = 14/2 = 7

To solve the problem backward, the first step is to multiply 6 by 3.

The function g(x) is a quadratic function in vertex form. Its vertex is at (3, 9), and it opens upwards because the coefficient of the squared term is positive.

The function f(x) is also a quadratic function, but in standard form. It opens upwards because the coefficient of the squared term is positive.

Since both functions have a minimum value at the vertex, the graphs of g(x) and f(x) will be similar in shape. However, the vertex of f(x) is at (0,0), so it is shifted to the left of g(x). Also, the y-intercept of f(x) is (0,0), while the y-intercept of g(x) is (0,18).

In summary, the graph of g(x) is the graph of f(x) shifted 3 units to the right and 9 units up.

The solutions to the system of equations are x = 2 and 4

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

f(x) = x - 3

g(x) = 1/(x - 3)

The solution to the system of equations implies that

f(x) = g(x)

So, we have

x - 3 = 1/(x - 3)

Cross multiply the equation

This gives

(x - 3)² = 1

So, we have

x - 3 = ±1

Add 3 to both sides

x = 3 ± 1

So, we have

x = 2 and 4

Hence, the solutions to the system of equations are x = 2 and 4

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The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.

An acute triangle with sides measuring 7, 4, and 2

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .

According to the Pythagorean Theorem.

Here, 7² is greater than (4² + 2²).

So this is not possible.

An isosceles triangle with angles measuring 20° and 80°

In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,

Then the third angle measures is

180° - 20° - 80°= 80°

Two angles are congruent implies two sides are congruent.

It is possible to form isosceles triangle.

An obtuse triangle with sides measuring 5, 10, and 15

In an obtuse triangle, the longest side is opposite the largest angle.

Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.

However, 15²is greater than (5²+ 10²),

so this is not possible.

A scalene triangle with angles measuring 110° and 35°

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

so the third angle must measure

180° - 110° - 35° = 35°.

Two angles are congruent so it is isosceles triangle.

It is not possible to form scalene triangle.

Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.

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Refer to this previous solution set

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Problem 4

Like the three earlier problems, we'll place the kicker at the origin and have her kick to the right. The two roots in this case are x = 0 and x = 20 to represent when the ball is on the ground.

This leads to the factors x and x-20 and the equation \(y = ax(x-20)\)

We'll plug in (x,y) = (10,28) which is the vertex point. The 10 is the midpoint of 0 and 20 mentioned earlier.

Let's solve for 'a'.

\(y = ax(x-20)\\\\28 = a*10(10-20)\\\\28 = -100a\\\\a = -\frac{28}{100}\\\\a = -\frac{7}{25}\\\\\)

This then leads us to:

\(y = ax(x-20)\\\\y = -\frac{7}{25}x(x-20)\\\\y = -\frac{7}{25}x*x-\frac{7}{25}x*(-20)\\\\y = -\frac{7}{25}x^2+\frac{28}{5}x\\\\\)

The equation is in the form \(y = ax^2+bx+c\) with \(a = -\frac{7}{25}, \ b = \frac{28}{5}, \ c = 0\)

The graph is below in blue.

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Problem 5

The same set up applies as before.

This time we have the roots x = 0 and x = 100 to lead to the factors x and x-100. We have the equation \(y = ax(x-100)\)

We'll use the vertex point (50,12) to find 'a'.

\(y = ax(x-100)\\\\12 = a*50(50-100)\\\\12 = -2500a\\\\a = -\frac{12}{2500}\\\\a = -\frac{3}{625}\\\\\)

Then we can find the standard form

\(y = ax(x-100)\\\\y = -\frac{3}{625}x(x-100)\\\\y = -\frac{3}{625}x*x-\frac{3}{625}x*(-100)\\\\y = -\frac{3}{625}x^2+\frac{12}{25}x\\\\\)

The graph is below in red.

Answer: 0.8333

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1 or 6

Step-by-step explanation:

x² - 7x + 6

-6 and -1

x² -6x - 1x + 6

x( x - 6) + -1(x - 6)

(x - 1) (x - 6)

x = 1 or x = 6

Answer:

\( {x}^{2} - 7x + 6 \\ {x}^{2} - 6x - x + 6 \\ ( {x}^{2} - 6x) - (x - 6) \\x(x - 6) -1 (x - 6) \\ (x - 6)(x - 1)\)

The Compound Interest would be $1104.895

What is Compound Interest ?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even though the principal remains the same, the interest changes annually. We can observe that interest rises over time. As a result, we can infer that the interest the bank charges is compound interest, or CI, rather than simple interest.

Number of quarters in 5years =5×4=20

Quarterly rate of compound interest

r=24=0.5%

Initial amount

P=$1000

hence the total amount after 5years

=  P(1+r/100)n

=1000(1+0.5/100)^20

=1000(1.005)^20

=$1104.895

Hence, The Interest will be $1104.895

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Answer:

i dont know how to help you:(

Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

The percentage is 17% and the rotio is 7.5

Step-by-step explanation:

(a) 28000-20000=8000.

(8000/28000+20000)*100%

=16.66%=17%

(b) (28000/48000)

= 7/12.

(20000/48000)

=5/12.

so you take the numerators which are 7 and 5.so the ratio is7.5

Answer:

1/2

Step-by-step explanation:

Let's say the number is 1.5

1.5 = 1 + 0.5

(1.5 = 1 + 0.5)*10 ==> multiply by 10 to remove decimals

15 = 10 + 5

5 is half of 10

Hence, 0.5 is half of 1 ==> 0.5 = 1/2

66) The number of feet of fencing that Ms. Hamilton needs to buy is 75 feet.

67) The distance around a rectangle is called a perimeter.

The use of Mathematics skills is all-encompassing. Every activity involves some mathematical calculations and the use of mathematical operations, like additions, subtractions, divisions, and multiplication.

When you visit a Merchandise Store, you undertake some mathematical activities by computing how much is needed and the balance you will get. Future projections depend on maths skills.

For instance, budgeting how much it costs you weekly to maintain your hairstyle also involves maths skills.

As you return to school after the summer breaks, you decide how much savings you must spend. It is maths.  Any time calculations are involved, it requires maths.

Length of the yard = 24.75 feet

Width of the yard = 12.75 feet

Perimeter of the yard = 75 feet (24.75 + 12.75)2

Charges for a yard of iron fencing = $50 per yard

3 feet = 1 yard

75 feet = 25 yards (75/3)

The cost of 25 yards = $1,250

Thus, Ms. Hamilton will need to spend $1,250 on this decorative iron fence project.

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Answer:

67 Yards

Step-by-step explanation:

Have a nice day :)

Answer:

If neither of the two real numbers is zero, then their product is also not zero Suppose also that x is a real number that satisfies the equation The " / " symbol does not always give you a result of an integer, so be careful.pkek, and any other expression for n as a product of prime numbers is identical to this except,.

Step-by-step explanation:

Answer:2 hours, 15 minutes, and 0 second

2.25 hours

135 minutes

8,100 seconds

Answer:

The answer is 39.2

Step-by-step explanation:

The first thing you want to do is multiply both numbers by them selves like this: 9x8 and 4x8. Then after you do that, add the sum of those equations and you have your answer. Think about it like this, for 8x4, all it is is just 8+8+8+8. If solving it that way is easier for you, go for it! Hope I could help!

Answer:

Step-by-step explanation:

Given function:

The vertical stretch is the function with:

With a = 5 the function becomes:

Answer:

B v D v M ;

(B ٨ M) V (B ٨ D) V (M ٨ D) ;

B V (D ٨ M)

Step-by-step explanation:

Given :

B : Applicant present a birth certificate

D: Applicant presents a drivers license

M applicant presents a marriage license

1.)

This means that any one of the three must be presented :

Birth certificate OR Driver's license OR Marriage certificate

B v D v M

2.)

This means any two combination of the three certificates :

(birth certificate and marriage certificate) OR (birth certificate and driver's license) OR (marriage certificate and driver's license)

(B ٨ M) V (B ٨ D) V (M ٨ D)

3.)

That is birth certificate alone will suffice or a driver's incense and a marriage certificate

B V (D ٨ M)

Answer:

82°

Step-by-step explanation:

Answer: The ratio is 4:1

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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We have here two parallel lines, m, and n, cut by a transversal (t). In this case, we have that the corresponding angles are congruent.

We have that both equations represent corresponding angles. Then, we have that:

Now, we need to solve these equations for x. We can proceed as follows:

1. Subtract 5x from both sides of the equation:

2. Add 4 to both sides of the equation:

3. And finally, divide both sides of the equation by 2:

Therefore, the value for x is x = 7.

Answer:

Step-by-step explanation:

men

Answer:

A. 16 - 6i

Step-by-step explanation:

(14 - 9i)+(2+3i)

14 - 9i + 2 + 3i

-9i + 3i + 14 + 2

-6i + 16

Answer:

  about 1.1%

Step-by-step explanation:

Given a moon has a diameter of 22% of the diameter its planet, you want the volume of the moon as a percent of the planet's volume.

The ratio of moon diameter to planet diameter is given as 22%. The ratio of moon volume to planet volume will be the cube of this scale factor:

  moon volume / planet volume = (0.22)³ ≈ 0.0106 = 1.06%

The volume of the moon is about 1.1% of the volume of the planet.

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