What the possible outcomes

Answer:

Sample Response: Gerard determined that the squares of the two smaller sides did not equal the square of the longest side. The side lengths did not create a true statement of the Pythagorean theorem.

Gerard most likely came to the conclusion that the sides of the triangle do not conform to the Pythagorean Theorem.

Therefore, Gerard most likely came to the conclusion that the sides of the triangle do not conform to the Pythagorean Theorem.

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Answer:

x = 20

Step-by-step explanation:

Adjacent angles on straight line add up to 180º

7x + (x + 20) = 180

7x + x + 20 = 180

8x + 20 = 180

8x = 160

x = 20

Two angles whose sum is 180° are called supplementary angles. The value of x is 20°.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

The sum of the measure of the angle will be supplementary to each other because the two angles together will be a line. Therefore, the sum will be,

7x + (x+20°) = 180°

7x + x + 20° = 180°

8x = 160°

x = 20°

Hence, the value of x is 20°.

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The correct anwser would be 56

The volume of the prism filled with 30 cubes with side lengths of 1/2 unit is 3.75 cubic units.

To calculate the volume of a cube with a side length of 1/2 unit, we use the formula V = s³, where s is the side length of the cube.

For a side length of 1/2 unit, the volume of one cube is V = (1/2)³ cubic units.

Therefore, the volume of one such cube is 1/8 cubic units. If the prism is filled with 30 such cubes, we multiply the volume of one cube by the number of cubes:

Total Volume = Number of Cubes × Volume of One Cube = 30 × 1/8 cubic units = 30/8, which simplifies to 3.75 cubic units.

Answer:

The volume of oblique cylinders is the same volume as a right cylinder of the same radius and height. The height of cylinder must be the perpendicular height, but as long as the radius and height are the same the volume does not change, which is why the same formula can be used for both oblique and right cylinder.

For skewed and right prism, base length and height does not change, volume for both is calculated by area times height.

Answer:

See picture

Step-by-step explanation:

The equation f(x)=x+4 becomes f(3x) = 3x +4. The graphs are attached below. The original is in red and the blue is the new function.

Answer:

90

Step-by-step explanation:

add them all up and divide by how many there are

The answer is 90.

Add all the numbers then average them out by how many numbers there are.

Answer:

[tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69

Step-by-step explanation:

To solve this we are using the standard exponential growth equation:

[tex]f(t)=A(1+r)^t[/tex]

where

[tex]f(t)[/tex] is the final population after [tex]t[/tex] years

[tex]A[/tex] is the initial population

[tex]r[/tex] is the growth rate in decimal form

[tex]t[/tex] is the time in years

We know from our problem that the initial population is 5000, the final population is 10000, and the time is 10 years, so [tex]A=5000[/tex], [tex]f(t)=10000[/tex], and [tex]t=10[/tex].

Let's replace the values and solve for [tex]r[/tex]:

[tex]f(t)=A(1+r)^t[/tex]

[tex]10000=5000(1+r)^{10}[/tex]

Divide both sides by 5000

[tex]\frac{10000}{5000} =(1+r)^{10}[/tex]

[tex]2=(1+r)^{10}[/tex]

Take root of 10 to both sides

[tex]\sqrt[10]{2} =\sqrt[10]{(1+r)^{10}}[/tex]

[tex]\sqrt[10]{2} =1+r[/tex]

Subtract 1 from both sides

[tex]\sqrt[10]{2}-1=r[/tex]

[tex]r=\sqrt[10]{2}-1[/tex]

[tex]r=1.0718-1[/tex]

[tex]r=0.0718[/tex]

We can conclude that the growth rate of our exponential equation is [tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69

Step-by-step explanation:

I think the answer is x=-4,x=+6

The values of the x are +6 and -4. The values of the x are obtained by the factorization method.

They are mathematical formulas containing variables raised by non-negative integers, coefficient, and constants involving only addition, subtraction, multiplication, and non-negative exponentiation of variables.

The given expression is;

x²-2x-24= 0

By factorization;

x²-6x+4x-24=0

After taking common terms, we get ;

x²-6x+4x-24=0

x(x-6)+4(x-6)=0

(x+4)(x-6)=0

The value of the x is found as;

x-4=0

x=-4

x-6=0

x=+6

Hence, the values of the x are +6 and -4.

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The distance between two points on a number line is found using the absolute value of their difference. For instance, the distance between 2 and 14 is 12 units, and the distance between -10 and 8 is 18 units.

The concept of absolute value is crucial when determining the distance between two points on a number line. This distance is represented by the difference in their values, disregarding which one is larger or whether they are positive or negative.

The expression for the distance is |2 - 14|. Evaluating this, we find |2 - 14| = |-12| = 12. Therefore, the distance between the numbers 2 and 14 on the number line is 12 units.

The expression for the distance is |-10 - 8|. Evaluating this, we find |-10 - 8| = |-18| = 18. Therefore, the distance between the numbers -10 and 8 on the number line is 18 units.

Answer:

It's a - (minus) sign.

Step-by-step explanation:

This is because √9 is 3, and therefore 6-3=3.

Hope I helped :)

Answer:

Your picture is not clear enough.

Step-by-step explanation:

For this case we have that by definition, the volume of the prism shown is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex]It is the area of the base of the prism

h: It is the height of the prism

Substituting the values:

[tex]A_ {b} = 10 \ cm ^ 2\\h = 6 \ cm[/tex]

Then, the volume is:

[tex]A_ {b} = 10 \ cm ^ 2\\h = 6 \ cm[/tex]

ANswer:

60

Theoretically, each letter should have the same probability of occurring since there are 15 of each. There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability [tex]\dfrac{15}{75}=\dfrac15[/tex] of being drawn.

This means one would expect a theoretical frequency of [tex]\dfrac{1250}5=250[/tex], i.e. any given letter should get drawn 250 times, which means the answer is D.

Answer:

252 D-O

Step-by-step explanation:

250 and theoretically 252

Answer:

Area of Trapezoid is 88 Units^2

Step-by-step explanation:

Area of trapezoid = (a+b)/2 * h

where a and b are lengths of each base and h is the height of trapezoid.

In the question given:

a= 17 (because a is the upper base and value will be 17)

b= 27 (because b is the lower base and value will be 17+5+5 = 27)

h= 4

Area of trapezoid = (a+b)/2 * h

                             = (17 +27)/ 2 * 4

                             = 22 * 4

                             = 88 Units^2

Area of Trapezoid is 88 Units^2

Answer:

[tex]\large\boxed{y=0.470793x+2.13908}[/tex]

Step-by-step explanation:

The slope intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

From your picture we have:

[tex]m=0.470793[/tex]

and

[tex]b=2.13908[/tex]

Substitute:

[tex]y=0.470793x+2.13908[/tex]

Answer:

Step-by-step explanation:

For this, both sides added together will need to equal 180°.

So you need to set up an equation: p+28+3p=180

Now, solve for p

p+28+3p=180

    -28 .       -28

p+3p=152

combine p            (the single p counts as 1, so add it to 3p to get 4p)

4p=152

/4 .   /4

p= 38

You get p is equal to 38.

multiply the bracket by 2

-2x+18-x

Negative and Negative= positive

=-3x+18

Answer:A

Answer:

The answer is A

Step-by-step explanation:

Answer:

5. 24°

6. 30°

7. 49°

Step-by-step explanation:

5. You are given right triangle with known opposite leg and hypotenuse. By the sine definition,

[tex]\sin \theta=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{11}{27}\\ \\\theta=\sin^{-1}\left(\dfrac{11}{27}\right)\approx 24^{\circ}[/tex]

6. You are given right triangle with known opposite leg and hypotenuse. By the sine definition,

[tex]\sin \theta=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{12}{24}=\dfrac{1}{2}\\ \\\theta=\sin^{-1}\left(\dfrac{1}{2}\right)\approx 30^{\circ}[/tex]

7. You are given right triangle with known adjacent leg and hypotenuse. By the cosine definition,

[tex]\cos \theta=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{13}{20}\\ \\\theta=\cos^{-1}\left(\dfrac{13}{20}\right)\approx 49^{\circ}[/tex]

Answer:

21 articles of clothing are clean.

Step-by-step explanation:

If 2/5 clothes, or 40% of them, are dirty, then 3/5, or 60% of them are clean.

Multiply 35 by 0.60, and you get your answer.

35 x 0.60 = 21.

We can check this answer by multiplying 0.40 by 35 to get the amount of dirty clothes and adding that amount to 21, which should equal 35.

35 x 0.40 = 14

14 + 21 = 35

To find out how many articles of clothing were clean, we set up a ratio equation using the given ratio of 2 to 5. By representing the number of clean clothes with a variable and using the total count of 35 clothes, we determined that Meredith found 10 clean articles of clothing.

When Meredith cleaned her room, she found that the ratio of clean clothes to dirty clothes was 2 to 5. If there were 35 articles of clothing in total, the problem can be approached by assigning a variable to represent the number of clean clothes. Let's denote the number of clean clothes by c and the number of dirty clothes by d.

Based on the given ratio, we can write the equation as 2/5 = c/d. Since we know that c + d = 35, we can use these two equations to solve for c.

We express d in terms of c as d = 35 - c.

Substituting this into the ratio equation, we get 2/5 = c/(35 - c). Cross multiplying gives us 5c = 2(35 - c), which simplifies to 5c = 70 - 2c.

Solving for c, we add 2c to both sides to get 7c = 70. Dividing both sides by 7 gives us c = 10. Therefore, Meredith found 10 clean articles of clothing.

Answer:

B

Step-by-step explanation:

Given

pitchers of grape juice=g=4

picthers of orange juice=o=6

Each pitcher contains 64 oz of juice

So in order to calculate, we will calculate the total number of pitchers and then multiply it by 64 to get total oz.

=(6+4)*64

=10*64

=640 oz

We can see that we added count of pitchers and then multiplied the sum by 64.

So option B is the correct answer ..  

I think either A or D makes more sense

Answer:

[tex]\sqrt{5}\cdot\sqrt[3]{5} =\sqrt[6]{5^3} \cdot\sqrt[6]{5^2} =\sqrt[6]{5^5} =5^{(5/6)}[/tex]

Step-by-step explanation:

The rules of exponents apply, even when they are fractional exponents:

[tex]a^b\cdot a^c=a^{b+c}\\\\\sqrt[b]{x^a}=x^{(a/b)}[/tex]

Answer:

[tex] \frac{1}{2} \times 21.6 \times 5.9 = 63.72[/tex]

The area of this triangle is 63.72 square feet.

Answer: Equivalent

Step-by-step explanation:

[tex]y=-\dfrac{1}{3}x+\dfrac{2}{3}\\\\\text{Multiply by 3 to clear the denominator: }3y = -x + 2\\\text{Add x to both sides: }x+3y=2\\\text{Multiply both sides by 2: }2x+6y=4[/tex]

When given a system of equations, the definitions of the solution are:

In the given system, the equations are the same which means they have INFINITE solutions --> The system is Consistent & Dependent = Equivalent.

Answer:

[tex]\large\boxed{144^\frac{3}{2}=1728}[/tex]

Step-by-step explanation:

[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\144^\frac{3}{2}=144^{1\frac{1}{2}}=144^{1+\frac{1}{2}}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=144^1\cdot144^{\frac{1}{2}}=144\sqrt{144}=144\cdot12=1728[/tex]

Simplify using [tex]a\frac{n}{m} =\sqrt[m]{a^{n} } =\sqrt{144^{3} }[/tex]

Now, we will factor it and rewrite the radicand in exponential form:

                                  [tex]\sqrt{144^{2}*144 }[/tex]

Rewrite the expression using:

[tex]\sqrt[n]{ab} =\sqrt[n]a}*\sqrt[n]{b} =\sqrt{144^{2} } *\sqrt{144}[/tex]

Now, we will simplify the radical expression:

                        [tex]144*\sqrt{144}[/tex]

Now, factor it and rewrite the radicand in exponential form:

                       [tex]144*\sqrt{12^{2} }[/tex]

simplify the radical expression: [tex]144*12[/tex]

                                               [tex]=1728[/tex]

The expression which is equivalent to [tex]144^{\frac{3}{2} }[/tex] is 1728.

The exponential form is an easier way of writing repeated multiplication involving base and exponents. For example, we can write 5 × 5 × 5 × 5 as 54 in the exponential form, where 5 is the base and 4 is the power. In this form, the power represents the number of times we are multiplying the base by itself. 1.

2*2*3 will be its exponential form.

Hence, we have represented 243 as a product of prime given as 243=3×3×3×3×3, and in the exponential form as 243=35.

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solution here,

slope(m)=(y2-y1)/(x2-x1)

=(5-1)/(1-0)

=4/1 =4

Answer:

The correct answer is D) 4

Step-by-step explanation:

I took the test and this was correct!

Answer:

x =  15

Step-by-step explanation:

Given in the question an equation

31 = 3x - 14

Solution

rearrange the constant to the right of equation

3x = 14 + 31

3x = 45

divide 3 on both sides of the equation

3x/3 = 45/3

      x = 15

Answer:

x=15

Step-by-step explanation:

The given equation is;

31=3x-14

Group similar terms:

31+14=3x

Combine the left hand side to obtain;

45=3x

Divide both sides by 3 to get;

[tex]x=\frac{45}{3}[/tex]

x=15

209 seats were used by men and boys. i took 45% of 380 which = 171. I subtracted that by 380 which = 209.

Answer with Step-by-step explanation:

0.45 of the total seats were used by women and girls.

i.e. Remaining 0.55(1-0.45) of the total seats were used by men and boys.

Seats used by men and boys=55% of 380

                                               [tex]= \dfrac{55}{100}\times 380\\\\ =209[/tex]

Hence, Seats used by men and boys is:

209

and the fraction of total number of seats used by men and boys(0.55) is greater than that of total seats used by women and girls(0.45).

Answer:

all rectangles are square

Step-by-step explanation:

Answer:

80 inches

Step-by-step explanation:

8*10=80

Answer:

80 in.

Step-by-step explanation:

So we know that 1/8 is 10 in.

So to get 8/8 (Original length), we need to multiply 10 by 8, because 8 is the denominator.

10 in * 8 = 80 in.

Hope I beat Jarid lol

Answer:

7.85 m

Step-by-step explanation:

Circumference is 2πr.

The radius (r) is half of the diameter, but multiplying r by 2 is the same as just using the diameter in this formula, so:

2.5π

When you multiply you get 7.85 to the nearest hundredth.

Answer:

7.8539 m

Step-by-step explanation:

Multiply 2.5 by 3.14159

Answer:

True ~apex

Step-by-step explanation:

a point has zero dimension

True

A point has zero dimension.

Because every open cover in the space has a refinement made up of just one open set, a point is zero-dimensional in relation to the covering dimension.

So, A point is just a position in space and has no dimensions.

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