please help im having a really hard time in math i could use some help

Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, Where the base of these triangles are same

And also given that the two angles are the same.

Since,

Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).

Thus, the third angle is also equal

From AAS:

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,

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The statements that are listed above that are not propositions include the following:

A proposition statement is defined as the statement that is either a true statement or false statement but can not be both.

From the given statements,the statement that is a true proposition include the following:

The statement that is a false proposition include the following:

The statement will you be my valentine? is not a proposition but a declarative question that needs to be answered.

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Answer:

converting to minutes

Step-by-step explanation:

3*60+20+40+2.75*60=405 min = 6 hours 45 minutes

Answer:

6 hours and 45 minutes

Step-by-step explanation:

2.75 hours = 2 hours and 45 minutes

3 hours 20 minutes

0 hours 40 minutes

2 hours 45 minutes

5 hours 105 minutes

6 hours 45 minutes

Answer:

Second option

Step-by-step explanation:

For a set to represent a function, each input value in the set domain should match with one and only one output value of set range.

The option that follows this rule os second option as 1 is matched with 2 only, and 3 is matched with 3 only, and 5 is matched with 7 only.

The ways to pack are

This is further explained below.

Generally, The science, art, and technology of packaging involves confining or safeguarding goods for distribution, storage, sale, and usage. The process of creating, analyzing, and designing packages is sometimes referred to as packaging.

In conclusion,

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Answer:VROOOOOOM

Step-by-step explanation:

E E E EE

Answer:

...............

Step-by-step explanation:

Answer:

(3,60),

Step-by-step explanation:

The Miles Is 20 Times

Dario's car can travel 240

Answer:

3,60),

The Miles Is 20 Times

Dario's car can travel 240

Step-by-step explanation:

Answer:

xy  - x + 5y - 1

Step-by-step explanation:

hope this helps

The measure of the angles in triangle ARST are: 28 degrees, 28 degrees, 124 degrees, 124 degrees. The measure of the angles in triangle ANSP are: 28 degrees, 51 degrees, 101 degrees, 129 degrees.

An angle is a geοmetric figure fοrmed by twο rays οr lines with a cοmmοn endpοint, called the vertex. Angles are typically measured in degrees οr radians and are used tο describe the amοunt οf turn οr rοtatiοn between twο intersecting lines οr οbjects. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), οbtuse (greater than 90 degrees), straight (exactly 180 degrees), οr reflex (greater than 180 degrees).

Here,

To find the measure of the angles in each triangle, we need to solve for the value of x in both equations.

For the first equation, we can simplify it as follows:

x + 14 = 2x

Subtracting x from both sides, we get:

14 = x

For the second equation, we can simplify it as follows:

3x + 9 = 2x + 23

Subtracting 2x and 9 from both sides, we get:

x = 14

Now that we know x = 14, we can find the measure of the angles in each triangle.

In triangle ARST, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle R = 2x

= 2(14)

= 28 degrees

angle S = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

angle T = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

In triangle ANSP, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle N = 3x + 9

= 3(14) + 9

= 51 degrees

angle S = 180 - (angle A + angle N)

= 180 - (28 + 51)

= 101 degrees

angle P = 180 - (angle N)

= 180 - 51 = 129 degrees

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Answer:

Step-by-step explanation:

Use the slope formula:

10.

11.

12.

Answer:

i think its 3 im not sure

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30/30

→ [ x = -1 ]

Hence, the value of x is -1.

The amount of extra money a month that Mrs. Laurence pays in her car payment is $72.

We can get the amount of extra amount that Mrs. Laurence pays each month when compared to Mr. Gannon by dividing the amount that they pay by the number of months they need to make these payments.

This can be done as follows:

26304 ÷ 24 = 1096

20480 ÷ 20 = 1024

1096 - 1024 - 72

So, the amount of extra money that Mrs. Laurence has to pay each month when compared to that of Mr. Gannon is $72.

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The union consists of all of the elements that are contained in each interval.

Inequality Form:

x<6

Interval Notation:

(−∞,6)

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

f(x) = 15

Step-by-step explanation:

"If f(x)= 5x + 40, what is f(x) when x = -5?"

Substitute x for -5:

f(x) = 5x + 40

f(x) = 5(-5) + 40

f(x) = -25 + 40

f(x) = 15

Answer:

y = 340e^0.0427276t ; 908

Step-by-step explanation:

Given that :

t = time in days since study began

Number of bacteria after 11 days = 544

y = number of bacteria at time t

Exponential growth model:

y = ae^rt

Where a = initial amount ; r = Growth rate

y = 544 ; t = 11 ; a = 340

544 = 340*e^11t

544/340 = e^11t

1.6 = e^11t

Take the In of both sides

In(1.6) = 11t

0.4700036 = 11t

t = 0.4700036 / 11

t = 0.0427276

y = 340e^0.0427276t

Number of bacteria after 23 days :

Using the formula above :

t = 23

y = 340e^0.0427276(23)

y = 340 * 2.6717529

y = 908.39600

y = 908

The required formula is \(y = 340e^{0.0427}\)

908 bacteria are there 23 days after the beginning of the study .

Given that,

A certain culture of bacteria has a population of 340.

The population grows according to a continuous exponential growth model. After 11 days, there are 544 bacteria.

We have to find,

Write a formula relating y tot. Use exact expressions to fill in the missing parts of the formula.

How many bacteria are there 23 days after the beginning of the study.

According to the question,

And let y be the number of bacteria at time,

t = time in days since study began

Number of bacteria after 11 days = 544

y = number of bacteria at time t

Then,

Exponential growth model:

\(y = a.e^{rt}\)

Where, a = initial amount ; r = Growth rate

y = 544 ; t = 11 ; a = 340

Then,

\(544 = 340.e^{11t}\\\\\dfrac{544}{340} = e^{11t}\\\\1.6 = e^{11t}\\\\Taking \ log \ on \ both \ sides,\\\\ln(1.6) = 11t\\\\0.47 = 11t \\\\t = \dfrac{0.47}{11}\\\\t = 0.0427\)

The required formula is \(y = 340e^{0.0427}\)

\(y = 340e^{0.0427}\)

Where, t = 23

\(y = 340e^{0.0427276(23)}\\\\y = 340 \times 2.6717529\\\\y = 908.39600\\\\y = 908\)

Therefore, 908 bacteria are there 23 days after the beginning of the study .

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answer TRUE because they would make a triangle

Given:

The function is:

\(f(x)=x^3-x\)

To find:

The average of change of f(x) over the interval [1,5].

Solution:

We have,

\(f(x)=x^3-x\)

At x=1, we have

\(f(1)=(1)^3-(1)\)

\(f(1)=1-1\)

\(f(1)=0\)

At x=5, we have

\(f(5)=(5)^3-(5)\)

\(f(5)=125-5\)

\(f(5)=120\)

The average of change of f(x) over the interval [a,b] is

\(m=\dfrac{f(b)-f(a)}{b-a}\)

Now, the average of change of f(x) over the interval [1,5] is

\(m=\dfrac{f(5)-f(1)}{5-1}\)

\(m=\dfrac{120-0}{4}\)

\(m=\dfrac{120}{4}\)

\(m=30\)

Therefore, the average of change of f(x) over the interval [1,5] is 30.

Answer:

it is three

Step-by-step explanation:

12/3+2/3=14/3

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

A = -6 and B = 65

From the question, we are to express the given expression in the form (x + A)^2+B by completing the square

The given expression is

x² -12x + 101

Using the completing the square method

x² -12x + 101

Divide the coefficient of x by 2 and then square it

The coefficient of x is -12

Dividing by 2, we get

-12/2 = -6

Squaring

(-6)²

Now, add and subtract this value from the expression

x² -12x + (-6)² + 101 - (-6)²

Then, we can write that

(x - 6)² + 101 - (-6)²

(x - 6)² + 101 - 36

(x - 6)² + 65

Thus,

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

By comparison,

A = -6

and

B = 65

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The error in the subtraction of the given fraction is that the LCM was not used before subtraction of numerators and as such if correctly answered the final fraction is; -15/4

We are given the subtraction of fraction expression as;

3/4 - 9/2

Now, the first step in this subtraction is to find the L.C.M of both denominators.

Factors of 2 ; 1, 2

Factors of 4; 1, 2, 4

Thus, the L.C.M of both denominators is; 2 * 2 = 4

Now, the next step is to divide the LCM by the denominator and multiply by the numerator while retaining the LCM as common denominator to get;

[(3 * 4/4) - (9 * 4/2)]/4

= (3 - 18)/4

= -15/4

The method used in the question to subtract the fraction did not take into account finding the LCM.

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Answer:

We know that the wire was cut into 24 equal pieces and the length of each piece is 70 cm.

So, the total length of the wire = 24 x 70 cm = 1680 cm

We also know that 100 cm = 1 meter. Therefore,

1680 cm = 16.8 meters

Hence, the length of the wire is 16.8 meters.

Answer:

the coefficient of the squared expression is 5.

Step-by-step explanation:

the equation of a parabola in its vertex form is y=a(x-h)²+k, where (h, k) is the vertex of the parabola.

in this case, h=3, k=-2, so y=a(x-3)-2

plug (4,3) in the equation: 3=a(4-3)²-2, a=5

Answer:

4+5/2

9/2= 4.5

Step-by-step explanation:

Answer:

$4.00

Step-by-step explanation:

the median is the middle term in a sequence

since there are an even number of terms and not an obvious median, we take the two middle terms, add them together, and divide by two

So, 5+3= 8

8÷2= 4

hope this helps chu

Answer:

Packs of hot dogs needed: 6    Packs of Hot dog buns needed: 5

Step-by-step explanation:

keep in mind that the number of hot dog buns bought, must be 10, 20 , 30, 40, 50, 70, 80, 90,ect, Since hot dogs are bought in packages of 10. The closest number we can multiply by 12 to get a number in the 10's place would be 5. proof =

12 x 5 = 60

since we have 60 buns, we need 60 hot dogs, so...

10 x 6 = 60

and there you have it, 6 hot dog packs, and 5 hot dog buns.

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The trigonometric ratios as a fraction in simplest form are

sin L = opposite side/hypotenuse  = 30/34 = 15/17

cos L = adjacent side/hypotenuse  = 16/34 = 8/17

tan L = opposite side/adjacent side  = 30/16 = 15/8

sin M = opposite side/hypotenuse  =  16/34 = 8/17

cos M = adjacent side/hypotenuse  = 30/34 = 15/17

tan M = opposite side/adjacent side  = 16/30 = 8/15

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

In the figure, find MK using hypotenuse theorem

hypotenuse² = sum of the squares of other two sides

=> 34² = 16² +MK²

=> MK² = 34² - 16²

=> MK² = 1156 - 256 = 900

=> MK =√900 = 30

sin L = opposite side/hypotenuse  = 30/34 = 15/17

cos L = adjacent side/hypotenuse  = 16/34 = 8/17

tan L = opposite side/adjacent side  = 30/16 = 15/8

sin M = opposite side/hypotenuse  =  16/34 = 8/17

cos M = adjacent side/hypotenuse  = 30/34 = 15/17

tan M = opposite side/adjacent side  = 16/30 = 8/15

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Answer:

The sample proportion \(\hat{p}\) is within 0.03 of the true proportion of customers who are under age 21 is 0.803

Step-by-step explanation:

Total no. of customers = n = 400

We are given that the true population proportion of customers under age 21 is 0.68.

So, p =0.68

q=1-p=1-0.68=0.32

Standard deviation =\(\sqrt{\frac{pq}{n}}=\sqrt{\frac{0.68 \times 0.32}{400}}= 0.023\)

We are supposed to find  the probability that the sample proportion \(\hat{p}\) is within 0.03 of the true proportion of customers who are under age 21 that is , what is the probability that \(\hat{p}\)is between 0.68 - 0.03 and 0.68+ 0.03

\(P(0.65 < X < 0.71) = P((\frac{0.65-0.68}{0.0233}) < Z < (\frac{0.71-0.68}{0.0233}))\)

Using Z table

\(= P(-1.2875 < Z < 1.2875)= 0.803\)

Hence  the sample proportion \(\hat{p}\) is within 0.03 of the true proportion of customers who are under age 21 is 0.803