1. Which statement is not true? A. Rational numbers are closed under division. B. Odd numbers are closed under multiplication. C. Prime numbers are closed under subtraction. D. Integers are closed under addition​

Answer:

Similar

Step-by-step explanation:

We can say that the triangles are similar by looking at the angle measurements

Angle B = 35

Angle F = 55

Both angles A and D = 90 because these are right triangles

We can say the measure of angle E = 35 because the sum of angles in a triangle equal to 180

Same rule applies to angle C

Answer: 4.5 units

Step-by-step explanation:

Answer:

4.5 units

Step-by-step explanation:

You would use this equation to find the value of x: \(\frac{18}{x}\) = \(\frac{20}{5}\)

Answer:

The value of x is 15.

Step-by-step explanation:

Since the base is 40 inches long, and the two triangles are congruent - both are right triangles and have sides x and their bases equal - you know that each base of a triangle is 20 inches long. Using the Pythagorean Theorem, you can get that \(x^2+20^2=25^2\). Solve for x by isolating the variable on one side: \(x^{2} =25^{2} - 20^{2}\) ⇒ \(x^{2} = 625 - 400\) ⇒ \(x^{2} = 225\) ⇒ \(x^{2} =225\) ⇒ \(x=\sqrt{225}\) ⇒ \(x=15\) inches.

Weight is in Olivia's backpack is 5/6 pound.

As in the given problem olivia's  history book weights 1/2 of a pound and

her lunch weighs 2/3 of a pound.

As both the units are same,

Thus total weight must be summation of both history book and her lunch  box.

total weight is =1/2 +2/3 pound

= (3+2)/6

that is equal to 5/6 pound.

Learn more about summation here:

https://brainly.com/question/21021524

#SPJ4

Answer:

Step-by-step explanation:

496m=8h

Figure for 1 hour.

496/8=62

Now do

62x6=372m

Yes, you are correct.

Answer:

22 people

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

11/4

Applying the fractions formula for division,

11x8

4x1

Simplifying 88/4, the answer is

The rectangle that will side lengths of 5units and 4 units will have coordinate of A(3, 3), B(3, 7), C(8, 7), D(8, 3) ( option B)

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

For a rectangle, the opposite sides are equal this means AB = C D and CB = AD

To verify the answer, The distance between AB = √((3– 3)² + (7– 3)²).

line AB = √0+16= 4units

line AD = √((8– 3)² + (3– 3)²).

line AD = √25+0

line AD = 5 units

therefore the sides of the rectangle are 5units and 4 units.

learn more about distance between two points from

https://brainly.com/question/7243416

#SPJ1

When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include

A. 27, 22, 17, 12, 7

D. 100, 95, 90, 85, 80

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.

Learn more about expressions on:

https://brainly.com/question/723406

#SPJ1

Complete question

Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.

27, 22, 17, 12, 7

5, 10, 15, 20, 25

55, 50, 35, 30, 25

100, 95, 90, 85, 80

75, 65, 55, 45, 35

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer:

(A ruler) = X  (a pen) = Y

y = x+10

Step-by-step explanation:

Answer:

A ruler cost x pence.

Pen costs 10 pence more than the ruler

The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

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

\(\sqrt[4]{a}^3\)

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)

Apply the exponent rule of indices

\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)

Apply the power rule of indices

\(\sqrt[4]{a}^3 = a^\frac34\)

Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

Read more about expression at

https://brainly.com/question/32302948

#SPJ1

Answer:

6666

Step-by-step explanation:

Answer:

Amount of discount =80-70=10$

percentage:-

\({:}\longrightarrow\)\(\sf {\dfrac{10}{80}}\times 100 \)

\({:}\longrightarrow\)\(\sf {\dfrac {10}{4}}5 \)

\({:}\longrightarrow\)\(\sf {\dfrac {50}{4}}\)

\({:}\longrightarrow\)\(\sf 12.5\% \)

Answer: the answer is 12.5

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer:

the first term is 4

Step-by-step explanation:

Given

G(3) = 36

G(6) = 972

Solution:

General formula for geometric series

G(x) = AB^x

From given data: G(6)/G(3) = 972/36 = 27

From formula: G(6)/G(3) = AB^6/(AB^3) = B^3

Therefore

B^3 = 27

B=3

Hence

G(1) = AB^1 = AB^3/B^2=36/3^2=36/9=4

Ans: the first term is 4

Answer:

a₁ = 4

Step-by-step explanation:

The n th term of a geometric series is

\(a_{n}\) = a₁ \(r^{n-1}\)

where a₁ is the first term and r the common ratio

Given a₃ = 36 and a₆ = 972 , then

ar² = 36 → (1)

a\(r^{5}\) = 972 → (2)

Divide (2) by (1)

\(\frac{ar^{5} }{ar^{2} }\) = \(\frac{972}{36}\) , that is

r³ = 27 ( take the cube root of both sides )

r = \(\sqrt[3]{27}\) = 3

Substitute r = 3 into (1)

9a = 36 ( divide both sides by 9 )

a = 4

The first term is 4

Solution:

To arrange the following numbers in "smallest to biggest" form, look for the smallest number in the group. To see the smallest number in the group, look for a negative number. If there is more than one negative number, the number which is farthest from zero is the smallest. If there are no negative numbers, the closest to 0 will be the smallest number.

We can conclude that the rearranged from (smallest to biggest) is:

Hoped this helped!

Answer:

Step-by-step explanation:

5√10×4√6=(5×4)√(10×6)=20√60=20√(4×15)=(20×2)√15=40√15≈77.4596669241...

The result is irrational because it can not be written as the ratio of two integers and its decimal expansion 77.4596669241

Answer:

x=3.01667

Step-by-step explanation:

\(x+y=9.35\\5x-y=8.75\\By\ adding\ the\ system\ of\ equations:\\(x+y)+(5x-y)=9.35+8.75\\6x=18.1\\x=3.01667\)

bvmnb n m mn

b bn. Step-by-step explanation:

Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

for more questions on fraction

https://brainly.com/question/78672

#SPJ8

Answer:

C AND D

Step-by-step explanation:

JUST PRESS C AND D AND ITS RIGHT LOL

The equation that represents the situation will be 0.10d + 0.25 = 5 and 10d + 25q = 500. Then the correct options are C and D.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

Noah has a coin jar containing dimes (d) and quarters (q) worth a total of $5.00.

The equation that represents the situation will be given as,

0.10d + 0.25 = 5

10d + 25q = 500

The equation that represents the situation will be 0.10d + 0.25 = 5 and 10d + 25q = 500. Then the correct options are C and D.

More about the conversion of sentence into equation link is given below.

https://brainly.com/question/10606712

#SPJ5

The P-value is between 0.025 and 0.05. and t = -1.85

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.

Therefore tests the hypotheses:

\(H_0\) : μ = 25 versus Ha: μ < 25,

where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

The alternative hypothesis is:

\(H_1:\mu < 25\)

The test statistic is given by:

\(t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }\)

The parameters are:

the values of the parameters are:

x = 23.5 , \(\mu=25\) , s = 4.8, n = 35

Plug all the values in above formula of t- statistic is:

\(t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }\)

t = -1.85

Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

t = –1.85; the P-value is between 0.025 and 0.05.

Learn more about t-distribution at:

https://brainly.com/question/13574945

#SPJ1

Answer:

centre = (5, - 6 ) , radius = 7

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )

x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )

x² - 10x + y² + 12y = - 12

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36

(x - 5)² + (y + 6)² = 49 = 7² ← in standard form

with centre (5, - 6 ) and radius = 7

Answer:

Center = (5, -6)

Radius = 7

Step-by-step explanation:

To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.

To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:

\(x^2-10x+y^2+12y=-12\)

Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:

\(x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2\)

Simplify:

\(x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2\)

       \(x^2-10x+25+y^2+12y+36=-12+25+36\)

       \(x^2-10x+25+y^2+12y+36=49\)

Factor the perfect square trinomials on the left side:

\((x-5)^2+(y+6)^2=49\)

The standard equation of a circle is:

\(\boxed{(x-h)^2+(y-k)^2=r^2}\)

where:

Comparing this with the rewritten given equation, we get

Therefore, the center of the circle is (5, -6) and its radius is r = 7.

Answer:

C

Step-by-step explanation:

get the y alone on one side: 2y=8x-12

divide by two on both sides: y=4x-6

Answer:

y=4x-6

Step-by-step explanation:

Your goal is to isolate the y variable to get it back into function form.

Hence ,the sum of ∠1 and ∠2  is 90 degrees this is a relationship between ∠1 and ∠2.

In Euclidean geometry, an  angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles  formed by two rays lie in the plane that  contains the rays. Angles are also formed by the  intersection of two planes. These are called dihedral angles.

complementary angles are two angles that add up to 90 degrees, supplementary angles are two angles that add up to 180 degrees,

vertical angles are opposite angles at an intersection of two straight lines, and adjacent angles are two angles that are next to each other.

According to figure , the sum of ∠1 and ∠2  is 90 degrees and If the sum of the two angles is equal to the measurement of a right angle .

So, the pair of angles ∠1 and ∠2  is said to be complementary angles.

Learn more about angles here:

https://brainly.com/question/25716982

#SPJ1.

Answer:

15 points

Step-by-step explanation:

The start and end point of the caterpillar path are;

Start point = (-3, -4)

End point = (25, 38)

The slope of the caterpillar's path, 'm', given the 'x', and y-coordinates of two points is given by the following formula;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Therefore, m = (38 - (-4))/(25 - (-3)) = 1.5

The equation of the caterpillar's path in point and slope form is given as follows;

y - (-4) = 1.5 × (x - (-3))

y + 4 = 1.5 × (x + 3)

y + 4 = 1.5·x + 4.5

y = 1.5·x + 4.5 - 4 = 1.5·x + 0.5

y = 1.5·x + 0.5

Given that the 0.5 is added to the product of 'x' and 1.5, the points that have both integer points for 'x', and 'y' are the points that have odd number values of 'x', as follows;

(-3, -4), (-1, -1), (1, 2), (3, 5), (5, 8), (7, 11), (9, 14), (11, 17), (13, 20), (15, 23), (17, 26), (19, 29), (21, 32), (23, 35), (25, 38)

Therefore, we have 15 points counting the start and end points with integer coordinates