Find the interval(s) over which the function is decreasing

The workers make 751 toys per day

They work for 5 days per week

Number of toys made in one week is;

751 × 5 = 3755 toys

Number of toys made in 3 weeks is;

3755 × 3 = 11,265 toys

For triangles to be congruent, they must have the same angles and same three sides, irrespective of what direction they are pointing to.

Following are the ways to find if two triangles are congruent:

1. SSS (side, side, side): If all three sides of a triangle are equal to the three sides of another triangle, the triangles are congruent.

2. SAS (side, angle, side): If the two sides and the included angle of a triangle are equal to the corresponding sides and the angle of another triangle, the triangles are congruent.

3. ASA (angle, side, angle): If the two angles and their shared side is equal to the corresponding angles and shared side of another triangle, the triangles are congruent.

4. AAS (angle, angle, side): If two angles and the non-included side of a triangle are equal to the corresponding angles and non-included side of another triangle, the triangles are congruent.

5. HL (hypotenuse, leg): If the hypotenuse and one leg (side other than hypotenuse) of a right angle triangle are equal to the corresponding hypotenuse and the leg of another right angle triangle, then the two triangles are congruent.

Congruent triangles are used in real world for construction purposes to ensure that the man-made structures are strong and stable enough.

Final answer:

There are multiple ways to prove triangle congruency, including SSS, SAS, ASA, AAS, and RHS. These concepts are important in real-world applications such as architecture and engineering for ensuring precision and safety in structures and components.

Explanation:

There are several methods to prove that two triangles are congruent, each based on different sets of information about the triangles' sides and angles. The following are commonly used:

These concepts are utilized in various real-world applications, such as architectural design, engineering, manufacturing, and construction, where precise measurements and shapes are critical for the safety and fit of structures and components.

The answer is not found among the options A, B, C or D.

The standard form of a quadratic equation is ax² + bx + c = 0. Here, a is the coefficient of x² (which is 1 in this case), b is the coefficient of x (which is 16), and c is the constant (which is  55).

To find the roots of a quadratic equation ax² + bx + c = 0, we use the quadratic formula, which is x = [ -b ± sqrt(b²-4ac) ] / 2a.

Here, b²-4ac = (16)² - 4x1x55 = 256 - 220 = 36,  which is a perfect square, so we can continue.

Then the quadratic formula gives us two solutions:

Solution1 = [ -16 + sqrt(36) ] / (2x1) = -16 + 6 / 2 = -5
Solution2 = [ -16 - sqrt(36) ] / (2x1) = -16 - 6 / 2 = -11

So, the roots of the equation are x= -5 and x= -11.

Matching our solutions with the options given, we do not find any that fits the result. Therefore, the answer is not found among the options A, B, C or D.

f(x):  y = 9x² - 12

f⁻¹(x):  x = 9y² - 12

    x + 12 = 9y²

     [tex]\frac{x+12}{9} = y^{2}[/tex]  

     [tex]\sqrt{\frac{x+12}{9}} = |y|[/tex]     ; x ≥ -12

     [tex]+/-\sqrt{\frac{x+12}{9}} = y[/tex]

Answer: C

If relationship is an inverse variation then the product of x and y is constant.

A)

2 · 6 = 12

3 · 9 = 27

NOT

B)

1 · 6 = 6

2 · 3 = 6

3 · 2 = 6

6 · 1 = 6

YES

C)

0 · 0 = 0

2 · 8 = 16

NOT

D)

-3 · 4 = -12

-4 · (-3) = 12

NOT

29, 30, 31

consecutive integers have a difference of 1 between them

let the 3 integers be n, n + 1, n + 2

then n + n + 2 = 60

2n  + 2 = 60 ( subtract 2 from both sides )

2n = 58 ( divide both sides by 2 )

n = 29 ← least integer

thus the 3 integers are 29, 30, 31

Answer:

400,000

Step-by-step explanation:

[tex]\frac{375}{14}=\frac{x}{16}:x=\frac{3000}{7}(Decimal: x=428.57143...)[/tex]

Answer:

This proof involves the definitions of congruence and supplementary angles, as well as some of the properties of equality.

∠1 and ∠2 are supplementary    // given

∠3 and ∠4 are supplementary    // given

∠1 ≅ ∠3    // given

m∠1 + m∠2 = 180°    // definition of supplementary angles

m∠3 + m∠4 = 180°    // definition of supplementary angles

m∠1 + m∠2 = m∠3 + m∠4    // transitive property of equality

m∠1 = m∠3    // definition of congruent angles

m∠1 + m∠2 = m∠1 + m∠4    // substitution property of equality (replaced m∠3 with m∠1)

m∠2 = m∠4    // subtraction property of equality (subtracted m∠1 from both sides)

∠2 ≅ ∠4    // definition of congruent angles

hope this helps

Step-by-step explanation:

Answer:

For the future students who need answer to this problem ....

Step-by-step explanation:

5. given

7.  Transitive property of equality

8.  Substitution Property

9.  Subtraction Property of Equality

10.  Converse of Angles Congruent Postulate

I am writing this test now and these are the answers I put in. It hasn't been graded yet but I'm pretty sure that they are correct. But pls lmk if anything is wrong. HOPE THIS HELPS

PLEASE RATE AND CLICK ON THANKS IF THIS WAS HELPFUL :))))

OK

I'll take a hypothetical case. Suppose one of the ordered pairs = (1, 6)  which means 'x = 1 when y = 6)'

we substitute  x = 1 and y = 6 into the equation and see if the left side = right side

left: y = 6

right: -9x + 4 = -9(1) + 4 = -9 + 4 = -5

Therefore this ordered pair is NOT a solution to the equation.

Answer: Hello mate!

we have the equation y = –9x + 4 and we want to find ordered a pair that is a solution of the equation.  Where a pair has the form (x, y)

First, you need to know that there are infinite ordered pairs that are a solution of this equation, if you want to find them, you need to replace the value of x (or the value of y) with a number, and solve the equation:

suppose x = 1

then y = -9*1 + 4 = -9 + 4 = 5

then the pair (1,5) is a solution of the equation.

The general form of the pairs is (x,y), then the pairs that are a solution for this equation are the pairs of the form (x, y(x)) = (x, -9x + 4)

x = 6 is correct

Focus on the right triangle EDF. The short leg is x = 6. The hypotenuse is 4+8 = 12. Since the hypotenuse is twice that of the short leg, we have a 30-60-90 triangle. Recall that the ratio of the short leg, long leg and hypotenuse is 1:sqrt(3):2 or you can think of it as x: x*sqrt(3): 2x. The 30 degree angle is opposite the short leg (smallest angle opposite smallest side). So the 60 degree angle is angle FED, which is the angle formed by the two chords.

This means angle BEC is 120 degrees since 120+60 = 180.

Now use the second part of the hint which says that the two arcs add up and are cut in half to get the angle formed by the intersecting chords. This means,

angle BEC = (1/2)*(arc BC + arc AD)

120 = (1/2)*(arc BC + arc AD)

2*120 = 2*(1/2)*(arc BC + arc AD)

240 = arc BC + arc AD

arc BC + arc AD = 240 degrees

Remark

You need a split statement like C or D. A and B would have to be considered if the ages were between 12 and 60.  However the discounts apply the other way. Up to 12 and over 60. You need two inequalities to describe this.

Under 12

x ≤ 12

The pointy end of the arrow points toward the x. x must be less than or at most equal to 12. The pointy end of the inequality must be directed towards the smaller number.

Over 60

x ≥  60

This time the pointy end is directed towards the 60. x must be at least 60 and then upwards.

So C is the correct answer.

Answer:

answer in c pls give brainlist

Step-by-step explanation:

Your answer should be D. 3

C. The answer is C because the total amount of students is 14, and there are 4 boys, which makes the ratio 4 boys to 14 students in total. 4 and 14 are both divisable by 2, so divide 4 to get 2 and divide 14 to get 7. This leaves you with 2 and 7. The ratio would be 2 boys to 7 total students. Hope this helped

Answer:2:5

[tex]4 divided by two = 2 10/2=5[/tex]

The Answer Is A. above me is the example.

The equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have:

[tex](x-2)^2+(y+3)^2=16\\\\(x-2)^2+(y-(-3))^2=4^2[tex]

Therefore:

[tex]h=2,\ k=-3\to\text{center:}\ (2,\ -3)\ \text{and}\ r=4[/tex]

The graph matches the circle defined by this equation (x-2)^2 + (y+ 3)^2 = 16 is option D.

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane,

then its equation is given as:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

The given equation of the circle is;

[tex](x-2)^2 + (y+ 3)^2 = 16[/tex]

Where, (h, k) - center

r - radius

here the radius of the circle is 4.

So, the graph matches the circle defined by this equation (x-2)^2 + (y+ 3)^2 = 16 is option D.

Learn more about equation of a circle here:

https://brainly.com/question/10165274

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answer is (2,1)

y = 6x – 11

-2x – 3y = -7

Substitute 6x - 11 for y in the second equation

-2x – 3(6x-11) = -7

-2x – 18x +33 = -7

-20x + 33 = -7

Now subtract 33 on both sides

-20x   = -7 - 33

-20x = -40 ( divide by -20 on both sides)

x= 2

We know y = 6x -11

Plug in 2 for x  and find out y

y = 6(2) -11= 12 -11 = 1

So answer is (2,1)

Distribute 2/3 to all terms within the parenthesis. Simplify

(2/3)(-9m) = ((2)(-9m))/(3) = -18m/3

(2/3)(12) = (24)/(3) = 8

-18m/3 + 8

Simplify. Divide.

-18m/3 = -6m

-6m + 8 is your answer

hope this helps

Hi,

Solution,

2/3(−9m+12)

=(2/3)(−9m+12)

=(2/3)(−9m)+(2/3)(12)

Answer,

=−6m+8

Answer:

its a snakes nest.

Step-by-step explanation:

yes

assuming the 2 expressions are 36 + 20 and 4(9 + 5)

36 + 20 = 56 and

4(9 + 5 ) = 4(14) = 4 × 14 = 56

Yes, the 2 expressions are 36 + 20 and 4(9 + 5) represent equivalent expressions.

An equation represents the equality of two or more mathematical expressions.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

Let assume the 2 expressions are 36 + 20 and 4(9 + 5).

36 + 20 = 56

and

4(9 + 5 )

= 4(14)

= 4 × 14

= 56

Yes, they are equivalent to each other.

Learn more about solving equations here:

https://brainly.com/question/18015090

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[tex]f(x)=\left\{\begin{array}{ccc}2-x&if&x\leq-5\\x+11&if&x > -5\end{array}\right\\\\-5\leq-5\ \text{therefore for}\ x=-5,\ f(x)=2-x\\\\f(-5)=2-(-5)=2+5=7[/tex]

Answer:

2x60, 4x30

Step-by-step explanation:

Given that the glee club has 120 cupcakes to sell.

These 120 cupcakes are to be arranged in a rectangle shape such that

there are even number of cakes lengthwise and even number of cakes breadthwise.

If l is the number of cakes along row, and m is the number of cakes along column, then we have both l and m as even.

Also lm=120

In other words, we must find 2 even  factors of 120 l and m such that lm = 120

2x60 is one such pair

Next is 4x30.

There cannot be any other pair satisfying this condition.

Hence answer is 2x60 or 4x30

The problem requires mathematical analysis to find the time intervals during which the outside temperature, represented by a function of time, exceeds the AC's set point, thus determining when the AC was actively cooling the castle.

The question presented to Princess Poly and Prince Digit by Wizard N. Gineer involves a mathematical analysis of an air conditioning (AC) system's performance based on outside temperature fluctuations over time. The outside temperature function provided by Mr. N. Gineer is f(t) = 24 - 5cos(rac{
pi}{12}t), where t is the number of hours past midnight. To determine when the AC was actively cooling the castle, one would need to identify the time intervals during which the temperature exceeded the set point at which the AC is triggered to cool. These intervals will be when the function values are above the temperature set point for the AC to start.

For example, if the AC is set to cool the castle at any temperature above 24 degrees Celsius, the solution would involve finding the values of t for which the function exceeds this limit. This involves solving inequalities and possibly using trigonometric identities and properties to find the appropriate time intervals. However, without the exact temperature set point at which the AC starts, we cannot solve for the specific hours during which the AC would be actively cooling.

3x + 32 + x + 48 = 180

4x + 80 = 180

4x = 100

x = 25

Angles

x + 48 = 25 + 48 = 73

3x + 32 = 3(25) + 32 = 75 + 32 = 107

Larger angle = 107

Answer

C) x = 25, 107 degrees

we know that

The scalar magnitude of the velocity vector is the speed. The speed is equal to

[tex]Speed=\frac{distance}{time}[/tex]

in this problem we have

[tex]distance=400\ m \\time=120\ sec[/tex]

substitute in the formula

[tex]Speed=\frac{400}{120}[/tex]

[tex]Speed=3.5\frac{m}{sec}[/tex]

therefore

the answer Part a) is

the speed is equal to [tex]3.5\frac{m}{sec}[/tex]

Part b) Find the velocity

we know that

Velocity is a vector quantity; both magnitude and direction are needed to define it

in this problem we have

the magnitude is equal to the speed

[tex]magnitude=3.5\frac{m}{sec}[/tex]

[tex]direction=North\ East\ (NE)[/tex]

therefore

the answer Part b) is

the velocity is [tex]3.5\frac{m}{sec}\ North\ East\ (NE)[/tex]

Part c)

we know that

the acceleration is equal to the formula

[tex]a=\frac{V2-V1}{t2-t1}[/tex]

in this problem we have

[tex]V2=0 \\V1=3.5\frac{m}{sec}[/tex]

[tex]t2=15\ sec\\t1=0[/tex]

substitute in the formula

[tex]a=\frac{0-3.5}{15-0}[/tex]

[tex]a=-\frac{3.5}{15}\frac{m}{sec^{2}}[/tex]

[tex]a=-\frac{7}{30}\frac{m}{sec^{2}}[/tex]

therefore

the answer Part c) is

the acceleration is [tex]-\frac{7}{30}\frac{m}{sec^{2}}[/tex]

This is an example of negative acceleration

Step-by-step explanation:

1. It is given that,

Distance covered by the cyclist, d = 400 m

Time taken, t = 120 s

Speed = distance / time taken

[tex]v=\dfrac{400\ m}{120\ s}[/tex]

v = 3.33 m/s

So, the speed of the cyclist is 3.33 m/s.

2. The cyclist comes to a stop position within 15 seconds. Its acceleration is given by :

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{0-3.33\ m/s}{15\ s}[/tex]  

[tex]a=-0.22\ m/s^2[/tex]

So, the acceleration of the cyclist is [tex]-0.22\ m/s^2[/tex]. It is an example of negative acceleration as the cyclist is decelerating. Hence, this is the required solution.              

Answer:  4:1, 8:2, 12:3, 16:4

Step-by-step explanation:

blue is 4 times white  

 blue: white

     4 : 1

multiply both numbers by 2 to get 8:2

multiply both numbers by 3 to get 12:3

multiply both numbers by 4 to get 16:4

The linear equation that represents the arithmetic sequence is[tex]a_n=10-2(n-1)[/tex]

Writing arithmetic sequence as a function of linear equations.

Arithmetic sequence is a progressive set of numbers with a common difference between each term. On the other hand a linear equation y =mx + b where m= slope and b = y-intercept.

In the given question, we have the arithmetic sequence;

10, 8, 6, 4 ...

Here the arithmetic sequence, the common difference is -2. So the common difference relates to the slope of the linear equation.

The first term is 10, the common difference is - 2. Using the general formula for arithmetic sequence, we have:

[tex]a_n=10-2(n-1)[/tex]