Your friend thinks that the triangles shown below are congruent by SAS. Is your friend​ correct? Explain.
Choose the correct answer below.
A.
​Yes, the figure indicates that two corresponding angles and their included side are all congruent.
B.
​No, the congruent sides are not the included sides.
C.
​No, the congruent angles are not the included angles.
D.
​Yes, the figure indicates that three corresponding sides are congruent.
E.
​No, the figure only indicates that two corresponding sides are​ congruent, not three as required by the SAS Postulate.
F.
​Yes, the figure indicates that two corresponding sides and their included angle are all congruent.

Answer:

Step-by-step explanation:

find x

7x+10=2x+40+3x

2x=30

x=15

ABD = 7(15)+10 = 115

ABD + ABC =180

115+ABC=180

ABC=65

The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

To know more about probability , visit:

brainly.com/question/13604758

#SPJ1

The value of R is 7 , we can find answer using concept of greatest integer and square root .

What is square root of a number ?

Square root , in mathematics , a factor of a number that , when multiplied by itself , returns the original number.

e.g. Square root of 9 are both 3 and -3.

Symbol = " √ "

In given que, we need to find greatest integer smaller than √51.

Root of 51 will not give exact integer value.

As we know root of 49 is 7 and root of 64 is 8.

And 51 lie between 49 and 64,

So, Square root of 51 will also lie between 7 and 8.

So, the greatest integer smaller than √51 will be 7.

Learn more about square roots using link :

https://brainly.com/question/3617398

#SPJ1

Answer:

x(x-2)

Step-by-step explanation:

The probability the researcher will make a type i error 0.10

The hypothesis testing, type I error involves rejecting true null hypothesis also referred to as 'false-positive' conclusion and type II error occurs when false null hypothesis is not rejected. It is also known as 'false negative' conclusion. And they are opposite to each other.

Here we have given that suppose a researcher plans to conduct a test of hypotheses at the 5% significance level. she designs her study to have power of 0.90 at a particular alternative value of the mean

And we need to find the probability the researcher will make a type i error

While looking into the given question,

We know that,

Significance level = 5%

alternative value of the mean = 0.90

Then the probability the researcher will make a type i error is calculated as,

mean = 1 - error

0.90 = 1 - error

=> error = 0.10

To know more about Probability here

https://brainly.com/question/11234923

#SPJ4

If f:RR, then Munkres' definition (f′(a) is a 11 matrix) is the definition of the derivative as it is presented in elementary calculus and real analysis. The linear map yf′(a)y must be defined as the derivative if the first definition from above must be used.

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value).

Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.

When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable.

The function closest to that input value is best approximated linearly by the tangent line. Because of this, the derivative is

According to our question-

The linear mapping Dfa:RmRn that obeys limh0f(a+h)f(a)Dfa(h)h2=0 is typically used to compute the derivative (or "total derivative") of a function f:RmRn at some point aRm.

both are true. If f:RR, then Munkres' formulation (f′(a) is an 11 matrix) is the definition of the derivative as taught in introductory calculus and real analysis. The linear map yf′(a)y must be defined as the derivative if the first definition from above must be used.

learn more about derivative click here:

brainly.com/question/23819325

#SPJ4

Answer: c

Step-by-step explanation:

P(tail) = Probability of getting a tail on the coin

P(tail)=1/2

P(4)=Probability of getting the number '4' on the dice.

P(4)=1/6

P(tail and 4)=Probability of getting tail on the coin and number '4' on the dice.

P(tail and 4)=p(tail multiply with 4)

P(tail and 4)= 1/2×1/6

P(trail and 4)=1/12

Hope this helps!

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

[tex]\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}[/tex]

Now, differentiate P with respect to x, and we get,

[tex]\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}[/tex]

Solving the above equation to zero, we get,

[tex]\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}[/tex]

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

[tex]\begin{aligned}y&=108-36\\y&=72\end{aligned}[/tex]

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

https://brainly.com/question/1635103

#SPJ4

Solving the given equations using substitution method we get (x,y) as (2, -1) i.e option (2) is correct answer.

Substitution method

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Given: 4x + 2y = 6      --------- (1)

            x = 2y + 4        ----------(2)      

Put the value of x from the 2nd equation in the 1st equation

4(2y+4) +2y = 6

8y + 16 + 2y = 6

10y + 16 = 6

10y = 6-16

10y = -10

y = -1 --------------- (3)

put the value of y in the (2) from (3)

x = 2(-1) + 4

x = -2+4

x = 2

Therefore, its solution is (2, -1)

To know more about how to solve system of linear equation visit the given link: https://brainly.com/question/25869125

#SPJ1

Answer: B

Step-by-step explanation: Did the test

Answer: It takes 3 cups of sugar for 4 cups of cranberry

Step-by-step explanation:

12 cups of sugar, 16 cups of cranberry

Divide both numbers by 4

12/4=3

16/4=4

It takes 3 cups of sugar for 4 cups of cranberry

Answer:

d

Step-by-step explanation:

First up is 5x+2y-2z=-57

5x+2y-2z=-57 /You gotta subtract 27 and 2z from both sides

5x+2y-2z- (2y-2z)=-57- (2y-2z) Then simplify-5x =-57-2y+2z

Then divide by both sides:

Answer is: x=-57-2y+2z / over 5

Answer:

The answer should be 8.

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

-6x - 9y = 0

-24x -36y = 0

Multiply the top equation by -4 and add that to the second equation

24x + 36y = -4

-24x - 36y = 0

0 + 0 = -4

0 ≠ -4  Since this is a false statement, the answer is no solution.

The probability that the entire batch will be accepted.

What is Acceptance Sampling?

Acceptance sampling is a statistical measure used in quality control. It allows a company to determine the quality of a batch of products by selecting a specified number for testing.

abc Electronics Company manufactured 1200 write-rewrite cds, and 150 are defective. Since 150 are defective, the number of write-rewrite cds that would be accepted is (1200 - 150 = 1050).

Since the items at selected without replacement, the number of write-rewrite cds will continue to decrease anytime a write-rewrite cds is taken out. For example if they are 1050 accepted write-rewrite cds if one is taken out they would then be 1049 accepted write-rewrite cds, and if another one is taken out they would be 1049 accepted write-rewrite cds and so on.

If 3 of these cds are randomly selected for testing without replacement,

The probability that the entire batch will be accepted

= (1050/1200) × (1049/1200) × (1048/1200) × (1047/1200)

= 0.8750 × 0.8742 × 0.8733 × 0.8725

=0.5828

The probability that the entire batch will be accepted is 0.5828 .

Learn more about Acceptance Sampling by :

https://brainly.com/question/7032011

#SPJ4

Answer:

Option B is the correct answer

Step-by-step explanation:

h(x) = 5x + 2, h(8)

h(8) = 5(8) + 2

h(8) = 40 + 2

h(8) = 42

Thus, The answer is 42

Look to the photo and you will find the answers there ✔️

start from left to right

Answer:

Step-by-step explanation:

3(15.50 + x) = 60

46.5 + 3x = 60

3x = 60-46.5

x = 13.5/3

x = 4.5 or $4.50

The value of x (B) 5 makes the inequality 5x + 6 ≤ 2x + 15 FALSE.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

The equal sign (=) indicates that two expressions in an equation are believed to be equivalent.

The symbols >, <, ≤ or ≥ indicate that the two expressions in inequality are not always equal.

So,  we have the inequality:

5x + 6 ≤ 2x + 15

Now put the given values and check as follows:

(A) -2

5x + 6 ≤ 2x + 15

-10 + 6 ≤ -4 + 15

-4 ≤ 11

TRUE

(B) 5

5x + 6 ≤ 2x + 15

25 + 6 ≤ 10 + 15

31 ≤ 25

Correct: 31 > 25

FALSE

Therefore, the value of x (B) 5 makes the inequality FALSE.

Know more about inequality here:

https://brainly.com/question/28964520

#SPJ4

Complete question:
Determine which integer will make the inequality 5x + 6 ≤ 2x + 15 false.

a:{−2}

b:{5}

c:{2}

d:{−5}

If 250 bricks are used to build a wall of 15 ft high then, there is total 1250 bricks will be used to build a wall that is 75 ft high.

Proportion:

A proportion is an equation between two ratios or rates that is useful in solving for a single unknown.

We have given that,

It takes 250 bricks to build a 15 ft high wall. Let us consider x bricks , is needed for a 75 ft high wall, use the ratio given for a 15 ft high wall and equate it to the ratio for the unknown number of bricks for a 75-ft high wall.

In making proportions, make sure that the rate on one side has the same units as the rate on the other as shown :

x/75 = 250/15

=> 15 × x = 250 ×75

=> x = 250×75/15

=> x = 1250

Thus, it will take 1250 bricks to build a wall 75 feet high.

To learn more about proportion , refer:

https://brainly.com/question/3371568

#SPJ4

The matrices A and B are not inverse matrices

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

[tex]A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right][/tex]

[tex]B = \left[\begin{array}{cc}1&-1&-1&2\end{array}\right][/tex]

To determine if the matrices are inverse matrices, we simply calculate the inverse of matrix A and then make the comparison.

The matrix A is given as

[tex]A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right][/tex]

Calculate the determinant of the matrix A

So, we have the following representation

|A| = -2 * -2 + 3 * 2

Evaluate the sum of products

|A| = 10

The inverse is then calculated as

[tex]A^{-1} = \frac 1{10} * \left[\begin{array}{cc}-2&3&-2&-2\end{array}\right][/tex]

Evaluate

[tex]A^{-1} = \left[\begin{array}{cc}-\frac 1{5}&\frac 3{10}&-\frac 1{5}&-\frac 1{5}\end{array}\right][/tex]

When compared to matrix B, both matrices are different

Hence, the matrices are not inverse matrices

Read more about matrices at

https://brainly.com/question/11989522

#SPJ1

Step-by-step explanation:

(3-2)^2+y^2=4

(9-4)+y^2=2^2

the power of y and 2 should be cut now

5+y=2

5-2=y

3=y

y=3

:. the area of enclosed by a circle is 3 cm

Answer:

a.  Area of rectangle: Length x Width or Base x height

b. The length of the base is 6

c. The height is 3

d. Area of the rectangle is 18

Step-by-step explanation:

a. Area of the rectangle formula is: L x W

b. We find the Length, which means we find the distance of the x; we see that to get from point A to point B the x change is 6, so the base is 6

c. We find the height, which means we find the distance of the y; we see that get from point B to point C, the y change by 3, so the height is 3

d. To find the area we take 6 times 3 = 18

Answer:

z = 11

Step-by-step explanation:

To find the answer we need to set up an expression with the two values they gave us:

8z = z + 77

This works because side IJ is the same length as side JK. So, all we have to do is solve for z:

8z = z + 77

-z    - z

7z = 77

/7     /7

z = 11

Answer: 3 sports drinks

Step-by-step explanation:

6 divde by 2= 3

36 divided by 12 =3

in other words

3x2=6

12x3=36

hope this helps

The given formula would be used to find the first quartile of a data set using the exclusive method.

What is quartile?

A quartile is a type of quantile used in statistics that divides the total number of data points into four roughly equal parts, or quarters. To compute quartiles, the data must be arranged from smallest to largest; therefore, quartiles are a type of order statistic.

The given formula is [tex]L_P = (n + 1)\frac{25}{100} \\[/tex]

This formula can also be written as,

[tex]R = (n + 1)\frac{25}{100}[/tex]

where 25 is the percentile of the data set.

So, the option (c) is correct.

The first quartile of a data set using the exclusive method.

Hence, the given formula would be used to find the first quartile of a data set using the exclusive method.

To know more about quartile, click on the link

https://brainly.com/question/28169373

#SPJ1

On solving the provided question, we got to know that - carpenter should make the diagonals 37 ft

A diagonal is a line connecting two vertices of a solid or polygon whose vertices do not share an edge in mathematics. The vertices of a shape are connected by oblique or sloping lines, which are known as diagonals. A horizontal shape with sides/edges, corners, and is called a diagonal.

We can answer this problem using Pythagoras' Theorem since the diagonal would turn the angle into a right angle.

[tex]12^2+35^2= d^2[/tex]

[tex]d^2 = 144 + 1225\\d^2 = 1369\\d = 37\\[/tex]

So, carpenter should make the diagonals 37 ft

To know more about diagonals visit:

https://brainly.com/question/12274248

#SPJ4

Answer: The correct answer is C

Step-by-step explanation: Let's find each equation without any inequalities first. We have a dotted line at y = 1, so we can already remove A and B. Now, a dotted line represents exclusivity and hence; it should not include the = sign.

Answer:  m∠5 = 116°

Step-by-step explanation:

Because m∠4 and m∠6 are consecutive interior angles, then we know

         m∠4 + m∠6 = 180

(106 - y) + (3y - 10) = 180

   104 - y + 3x - 10 = 180

                96 + 2y = 180

                         2y = 84

                           y = 42

And also the m∠4 and m∠5 are alternate interior angles, we get:

m∠5 = m∠4 = 3y - 10

Since we also calculate what y is, we just plugin.

mm∠5 = m∠4 = 3(42) - 10 = 126 - 10 = 116