i need help with this math question

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Given,

We have to state that the triangles are congruent;

Here,

Congruent state;-

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Conditions for congruent triangles;-

If two triangles satisfy one of the following conditions, they are congruent:

That is,

If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.

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The Formula of Area of Obtuse Triangle is equal to ½ × b× h .

and by using Heron's formula,

A = √(S(S-a)(S-b)(S-c)) ; S = (a+b+c)/2

A closed two-dimensional figure with three sides of equal or unequal length and three corners of equal or unequal angles is called a triangle.

Obtuse triangle: A type of triangle with the following properties:

Area formula of obtuse triangle :

Area of obtuse triangle = ½ × b × h

where b --> base of triangle

h ---> height of triangle.

The area of a triangle can also be found using Heron's formula.

A = √(S(S-a)(S-b)(S-c)),

where s is half the perimeter of the triangle and a, b, c are the three sides of the triangle.

the perimeter of the triangle = a + b + c cm then

S = (a + b + c)/2

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4 is the length of missing length of polygon.

Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides)

Similar polygons are two polygons with the same shape, but not the same size. Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.

16/2=8

15.4/2=7.7

16/2=8

8/2=4

Hence, 4 is the length of missing length.

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Taylor has to pay 0.7875 ounces for the macadamia nut.

What is the rule of multiplication?

If a, b, and c are three numbers given to us and any expression is expressed as [tex]a\frac{b}{c}[/tex] then it can be expressed as

                          [tex]a\frac{b}{c}[/tex]  = [tex]\frac{a*c + b}{b}[/tex]

It is given that, Taylor measures out [tex]1\frac{3}{4}[/tex] of macadamia nut.

                          [tex]1\frac{3}{4} = \frac{1*4 + 3}{4}\\\\ 1\frac{3}{4} = \frac{7}{4}[/tex]

                               = 1.75  macadamia nut.

Per ounce is at 0.45

then 1.75 macadamia nuts will cost her = 1.75 * 0.45

                                                                = 0.7875 ounces.

Hence, Taylor has to pay 0.7875 ounces for the macadamia nut.

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The three angles of the triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A, respectively.

What does ABC mean in a triangle?

In triangle ABC, the sides are AB, BC, and CA. The angle formed by any two sides of a triangle is the angle of the triangle, denoted by the symbol ∠. A triangle has three angles. The three angles of the triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A, respectively.

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Answer:

x = 71 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

180-109

x=71

The given statements are true or false as following:

We have given some statements about matrix and subspace and we have to check whether the statements are true or false .

1. True

The columns of U are linearly independent and thus form an orthonormal basis for Col U. So, projcolU y = UU^T*y for all y in R^n.

2. True

The statement is true because y can be written uniquely in the form y = projw y+z where y − projw y is in W and Z is in W⊥ and it follows that Z = projw y

3. True

since z is orthogonal to u1 and to u2 it is orthogonal to every vector in W = Span{u1, u2}, a set that spans W.

4. False

The uniqueness property of the orthogonal decomposition y = y^ + z indicates that, no matter the basis used to find it, it will always be the same.

5. True

For an orthogonal basis of W, B = u1, ..., uP y and projw y can be written as linear combinations of vectors in B with equal weights.

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Step-by-step explanation:

10 goals out of 27 attempts gives a ratio of

10/27 = 0.37037037... goals per shot.

now, for 35 shots we expect

35 × 10/27 = 350/27 = 12.96296296... ≈ 13 goals

The equation of a line passing through the point (a,0) and parallel to the y-axis is x = a

The equation of line parallel to y axis is of the form x = a, and it cuts the x-axis at the point (a, 0). Here all the points on this line parallel to the y-axis will have the same x coordinate of a. Further the equation of line parallel to y-axis and cutting the x-axis at point (a, 0) is at a perpendicular distance of 'a' units from the y-axis

The equation of line parallel to the y axis and cutting the positive x-axis passes through the first and the fourth quadrant. And the equation of line parallel to the y axis and cutting the negative x-axis passes through the second and the third quadrant of the coordinate axes.

To find the equation of line passing through the point and parallel to y-axis:

Let Line cut the x-axis at point a .

So , the equation of line will be x = a

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a)If  if 1 and 3 over 4 time 2 and 2 over 3 then our answer is  14/3 and

b) If 2 and 1 over 2 3 and 5 over 12 4 and 2 over 3 4 and 6 over 7,then our answer is 647/42

a)We have 1 and 3 over 4  or in other word if we convert this in improper fraction it is  7/4

Similarly, we have  2 and 2 over 3,in improper fraction it is 8/3

Now ,we multiply both the number to find the required answer =(7/4)×(8/3)=14/3

B) In b part we need to follow the same procedure which we followed in part a.

We have,2 and 1 over 2 3 and 5 over 12 4 and 2 over 3 4 and 6 over 7

On Converting all the mixed fraction into improper fraction

5/2,  41/12,  14/3 , 34/7

Take LCM of 2,12,3,7

LCM = 84

Convert all the fraction into proper fraction

(5×42)/(2×42)=210/84--------(eq1)

(41 × 7)/(12×7) =287/84----------(eq2)

(14 × 28)/(3×28)= 292/84--------(eq3)

(34 ×12 )(7×12) =408/84----------(eq4)

Now add all equations

(210+287+ 392+408)/84

= 1294/84=647/42

Hence, our answers are a)14/3 and b)647/42

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Some calculations of degrees of freedom with multiple number of parameters or relationships use the formula

Df = N - P,

where P is the number of different parameters or relationships.

For example, in a 2-sample t-test, N - 2 is used because there are two parameters to estimate.

What Are Degrees of Freedom?

The formula to determine degrees of freedom is:

Df = N − 1

where:

Df =degrees of freedom

N=sample size

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Line y=6x−2 and line 6y=−x are perpendicular.

Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.

In the equation of line y=mx+c, m represents the slope of the line.

The given lines are

a: y=6x−2           (1)

b: 6y= -x            (2)

and c: y+6x=1     (3)

To determine lines are parallel or perpendicular,

Find the slope of the lines, use the standard equation of line is y=mx+c,

Compare the given equations with standard equation of line,

Slope of line (1) m₁= 6

Slope of line (2) m₂ = -1/6

Slope of line (3) m₃ = -6

By multiplying slope of line (1) and (2), gives -1

Implies that line (1) and (2) are perpendicular to each other.

Therefore, Line y=6x−2 and line 6y=−x are perpendicular.

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It is possible to determine the theoretical probability of an occurrence without doing the event itself. A number cube has 6 alternative outcomes, giving each one a theoretical probability of 1 out of 6.

For example, the likelihood of drawing an ace at random is 4 out of 52 since there are 4 aces in a deck of cards. The probability of hitting a double bullseye on a regular dartboard is roughly 78 out of 100,000 because the area of the double bullseye in the center is 0.078% of the dartboard's overall area.

The likelihoods of potential possibilities are instead calculated using the frequencies of past outcomes in empirical probability. They are merely projections. The empirical chance of rolling a 4 or a 5 on the following roll is 58 out of 96 since you rolled 4s and 5s more often than any other number when you rolled the number cube.

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Answer: 1/6 is the probability

"Scatterplot is a quality controle tool",which shows us the increase or decrease of the function.Obviously it called the "Scatter Diagram".

It's totaly depand upon XY corelation.

In scatterplot the two variables are very important that are :

1. Indipendent

2. Dependent

To depict the values for two different numerical variables, dots are used in a scatter plot (also known as a scatter chart or scatter graph). Values for each data point are shown by the location of each dot on the horizontal and vertical axes. The relationships between variables are visualized using scatter plots.

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Answer:

The answer will always be 1

Step-by-step explanation:

The exponent is how many times the base number is multiplied by itself

For example 2^4 means 2 multiplied by itself 4 times or 2*2*2*2

But it doesn't matter how many times you multiply 1 by itself and it will always be 1

For example 1^5 is 1*1*1*1*1 which is equal to 1. you can even have 1^16 which is 1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1 but the answer is still 1 so the answer will always be 1

Must assume positive values

f is above this line outside [a, b]

So,  f(x)f′′(x)<0 cannot hold for all x.

Given,

In the question:

Let f be a twice-differentiable function on R such that f′′ is continuous. Prove that f(x)f′′(x)<0 cannot hold for all x.

Now, According to the question:

Assume that :

f"(0) > 0

Then, f(0) < 0 and as neither factor can change sign.

f"(x) > 0 > f(x) for all x ∈ R and f is strictly convex.

Pick a < b with f(a) ≠ f(b).

Then the line through (a f(b)) and (b f(b)) intersect the x - axis.

By convexity, f is above this line outside [a, b],

Hence, Must assume positive values

f is above this line outside [a, b],

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A system of linear equations is a collection of two or more linear equations that have two or more variables each. All of these equations are considered at once.

Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations. There could be an unlimited number of solutions for some linear systems, whereas others might not have any. There must be at least as many equations as there are variables for a linear system to have a singular solution. However, this does not ensure an original answer. There is always one answer to a set of equations that makes sense. A consistent system, like the one we just examined, is said to be an independent system if it only has one solution. The two lines cross at one location in the plane and have different slopes. If the equations' slopes and y-intercepts match, the system is said to be consistent and considered a dependent system.

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Answer: 7*[tex]\sqrt{3}[/tex]

Step-by-step explanation:

An equation for a parabola with x-intercept (-3,0) and (2,0) which pass through the point (1,-20) is  "[tex]5x^2+5x-30[/tex]".

parabola is a major conic section that has wide applications in science and technology. know according to the condition by following intercepts we begin with an equation

                            [tex]y=a(x+3)(x-2)[/tex]

where a is any number that restricts the parabola to pass through (1,-20)

know we have to choose a for what the above equation got its require achievements. substitute (1,-20) in   [tex]y=a(x+3)(x-2)[/tex] we get

                           [tex]-20=a(1+3)(1-2)\\\\-20=a(4)(-1)\\\\a=5[/tex]

substituting a back in the first equation we get the equation of the parabola. so, the parabola has an equation  y= f(x)=[tex]5x^2+5x-30[/tex].

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Answer:

triangle

Step-by-step explanation:

a quadrilateral is a four-sided figure, but a triangle is three-sided, so a triangle isn't a quadrilateral.

x=1, -29+√337/2 and -29-√337/2 are zeros of function f(x)=x²-3x³-27x² - 13x +42

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

We need to find zeros of f(x)=x²-3x³-27x² - 13x +42

f(x)=-3x³-26x²-13x+42

Use division method

1   -3    -26   -13     42

    0      -3     -29   -42

    -3     -29   -42     0

-3x²-42x-42=0

x=1 is a zero

Now use the quadratic formula to find zeros

x=42±√(42)²-4(-3)(-42)/-6

x=-29+√337/2

and x=-29-√337/2

Hence, x=1, -29+√337/2 and -29-√337/2 are zeros of function f(x)=x²-3x³-27x² - 13x +42

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Answer:

-3,-2,1,7

Step-by-step explanation:

That's what Acellus said it was <3

Answer:

You need to use a nested for loop. Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows.

Step-by-step explanation:

Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows overtime.

The total market value of all the assets, properties, and income in a given region or jurisdiction is what is referred to as the tax base. The tax base must be multiplied by the tax rate to determine the overall tax obligation: Tax Base x Tax Rate equals Tax Liability.

Describe the tax base?

The whole amount of income, property, assets, consumption, transactions, or other economic activity that a tax authority is allowed to tax is known as the tax base.

What is tax base formula?

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The value of y after solving the pair of similar triangle is 15.

Similar shapes are enlargements of each other using a scale factor.

To find the value of y from the similar triangle below, we use the formula below.

Note: The ratio of the corresponding sides of two similar triangle are equal

Formula:

make y the subject of the equation above

Hence, the value of y is 15

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The work done by the water from the reservoir, traveling a distance, h, meters, can be found using the expression; (2/3)·π·r³×ρ×g×h

Energy is the ability to do work, and power is the rate at which work is done.

The work done is the product of the force applied and the distance traveled in the direction of the force.

Radius of the reservoir = r

Density of the water = ρ

Height  of the upper elevation = h

Gravitational acceleration = g

The force is the weight of the water pumped

Weight = Mass × Gravity

Mass = Density × Volume

Therefore;

Volume of the water = (2/3)·π·r³

Mass of the water = (2/3)·π·r³ × ρ

Weight of the water = (2/3)·π·r³ × ρ × g

The work done by the water is therefore;

The work that should be done is, W = (2/3)·π·r³ × ρ × g × h

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1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

1 x 96 = 96 (1, 96)

2 x 48 = 96 (2, 48)

3 x 32 = 96 (3, 32)

4 x 24 = 96 (4, 24)

6 x 16 = 96 (6, 16)

8 x 12= 96 (8, 18)

By defining the SAS theorem of congruency, we have proved that SAS is congruent.

Congruency;-

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

Here,

We have to prove that SAS is congruent.

For that, lets consider the SAS theorem of congruence,

According to the side-angle-side (SAS) theorem of congruence, two triangles are congruent if their corresponding two sides and their included angles are precisely equivalent to those of the first triangle.

That is,

We proved by the definition SAS is congruent

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The speed of bullet just before the impact would be 1.28 x 10^3 meter per second.

Let the speed of the bullet before impact be 'V₀.'

According to the question, we are given the mass of the rod 'M' = 4 kg. Length of the rod 'l' = 0.5 meter. The angle of the bullet's path 'Θ' = 60 degree and the angular velocity 'ω' = 10 rad/s.

   For bullet, the mass 'M' = 3 g = 3 x 10^3 kg. and the velocity is V₀.

  According to the law of conservation of momentum, we get

L(bullet) = l (bullet + rod)

mV₀ (l/2 sinΘ) = Iω

mV₀ x (l/2 sinΘ) = [ ml²/ 12 + m (l/2) ²] x ω

By cancelling the like terms, we get the equation as,

V₀ = (m +3m) x l/6m sin Θ

  By calculating the above equation, we get,

V₀ = 1.28 x 10^3 meter per second.

  Therefore, the speed of bullet before the impact is 1.28 x 10^3 meter per second.

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Imani uses less flour in her cookies than Vic because vic uses 25 / 17 g of flour while Imani uses 25 / 21 g of flour.

How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.

A substance's density is a measurement of how heavy it is in relation to its size. When placed in water, an object will float if its density is lower than that of the water, whereas it will sink if its density is higher.

if we see Vic's recipe:

170 g of butter = 250 g of flour

1 g of butter = 250 ÷ 170

= 25 / 17 g of flour

and Imani's recipe:

630 g of butter = 750 g of flour

1 g of butter = 750 ÷ 630 = 25 / 21 g of flour

Compare:

25 / 21 < 25 / 17

so Imani uses less flour in her cookies than Vic

moreover imani's cookies are more dense.

Therefore, we get that Vic uses more flour than imani.

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Categorical data are the sort of variable that would need utilizing a population proportion hypothesis test rather than a population mean hypothesis test.

Data that cannot be easily gathered by counting is referred to as categorical data, which is another name for qualitative data. Hypothesis testing may be used with this type of data. Data are used in hypothesis testing to draw conclusions about population characteristics.

The findings are reached after first proposing a null hypothesis. Therefore, for qualitative or categorical data, a hypothesis test of the population is performed rather than a numerical test of the population mean.

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