what is the answer of these two according to this piecewise function?
f(1)=?
f(5)=?​

The representation of the equation as a standard quadratic equation is given by:

x² + 16x + 71 = 0.

The standard representation of a quadratic equation is given by:

ax² + bx + c = 0.

In this problem, the equation is:

-7 = (x + 8)²

Then:

x² + 16x + 64 = -7.

x² + 16x + 71 = 0.

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By the Congruent Supplements Theorem, we can conclude that,

∠FBC ≅ ∠DBG.

What is Congruent Supplements Theorem?

The Congruent Supplements Theorem states that two angles are said to be congruent if they are supplements of the same angle or even congruent angles.

If there are 4 lines such that, right angles are created when a horizontal line with the points F, B, and G crosses a vertical line with the points A, B, and E at point B. Between angles F and B and A and G, a third diagonal line with the points D, B, and C is intersecting the other two lines at point B. At points A, C, and G, there is a fourth line that joins three other lines.

Drawing Conclusion

In case the angle FBC and angle CBG are supplementary angles, angle DBG and angle DBF are another pair of supplementary angles, and angle CBG is-congruent-to angle DBF, we can apply congruent supplement theorem and draw the following inference,

∠FBC ≅ ∠DBG

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Answer: tis B :D

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:  £5.36

Step-by-step explanation: You can find this by dividing £64.32 by 12

Answer:

areas of AXYZ=10 square units1

Answer:

10 units squared

Step-by-step explanation:

Area of a triangle = 1/2 × base × height

Use the distance between two points formula to find the measure of the height and base of ΔXYZ.

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]

Height of Triangle

Define the points:

Substitute the points into the distance formula to find the height of the triangle:

[tex]\begin{aligned}\implies \sf height & =\sqrt{(4-2)^2+(5-1)^2}\\& = \sqrt{2^2+4^2}\\& = \sqrt{20}\end{aligned}[/tex]

Base of Triangle

Define the points:

Substitute the points into the distance formula to find the height of the triangle:

[tex]\begin{aligned}\implies \sf base & =\sqrt{(4-0)^2+(0-2)^2}\\& = \sqrt{4^2+(-2)^2}\\& = \sqrt{20}\end{aligned}[/tex]

Area of Triangle

[tex]\begin{aligned}\implies \sf Area & = \dfrac{1}{2} \times \sf base \times height\\& = \dfrac{1}{2}\sqrt{20}\sqrt{20}\\& = \dfrac{1}{2}(20)\\& = 10 \sf \:\:units^2 \end{aligned}[/tex]

Answer:

38 legs

Step-by-step explanation:

dog=4 legs

horse=4 legs

giraffe= 4 legs

duck = 2 legs

2x4+4x4+1x4+1x2

8+16+4+2=38

Answer:

f(x)=-12

Step-by-step explanation:

Since x=-4 substitute -4 into the equation

f(x)=3*-4

f(x)=-12

Hope this helped!

Answer:

the arc length of a circle can be calculated with the radius Central angle using the arc length formula

1 length of an hour is equal to zero into hour where zero is in radian

2 length of an art is equal to zero into ratio upon 180 into hour where zero is in degree

Triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.

Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Also, corresponding angles are congruent.

Triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.

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Answer:

down below

Step-by-step explanation:

Hope this helps =)

Answer:

[tex]x=6+8i[/tex]

[tex]x=6-8i[/tex]

Step-by-step explanation:

[tex]x^2-12x+100=0[/tex]

solve by quadratic formula.

[tex]\frac{-b+-\sqrt{b^2-4(a*c)} }{2*a}[/tex]

[tex]\frac{12+\sqrt{(-12)^2-4*(1*100)} }{2*1}[/tex]

[tex]\frac{12-\sqrt{(-12)^2-4*(1*100)} }{2*1}[/tex]

which is

[tex]x=\frac{12+16i}{2}[/tex]

[tex]x=\frac{12-16i}{2}[/tex]

Simplify.

[tex]x=6+8i[/tex]

[tex]x=6-8i[/tex]

Solved.

Hope this helps.

The truth of the given function that we have here is  The function increases at a constant multiplicative rate.

The table is given as

x            0   1    2      3

f(x)         2   3   4.5   6.75

We have x ranging from 0 to 3 while y ranges from 2 to 6.75.

The observations that we can make about the y values is that they produce the next value at the same rate of multiplication.

This is shown here

2 x 1.5 = 3

3 x 1.5 = 4.5

4.5 x 1.5 = 6.75

Hence we can conclude that it increases at a constant multiplicative rate of 1.5.

A table representing the function f(x) = 2(three-halves) Superscript x is shown below. A 2-column table has 4 rows. The first column is labeled x with entries (0, 1, 2, 3). The second column is labeled f (x) with entries 2, 3, 4.5, 6.75. What is true of the given function? The function increases at a constant additive rate. The function increases at a constant multiplicative rate. The function has an initial value of 0. As each x value increases by 1, the y values increase by 1.

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Answer:

Caleb’s error was :

instead of selecting the least exponent ,Caleb took the highest exponent.

Step-by-step explanation:

3x² = 3 • x • x

(in this factorization the exponent of 3 is 1 and the exponent of x is 2)

9x = 3 • 3 • x

(in this factorization the exponent of 3 is 2 and the exponent of x is 1)

• The common factors of 3x² and 9x are 3 and x

In order to determine the GCF ,we have to Compare the exponents of the  common factors then take the numbers which have the least exponent value.

• in the factorization of 3x² the exponent of 3 is 1

and in the factorization of 9x the exponent of 3 is 2

The least exponent is 1 Then we take it.

• in the factorization of 3x² the exponent of x is 2

and in the factorization of 9x the exponent of x is 1

The least exponent is 1 Then we take it.

Conclusion:

GCF(3x² , 9x) = 3¹ × x¹ = 3x

The x intercept is ( 7π/12 , 11π/12 , 19π/12 ,23π/12) , Option B is the correct answer.

The x intercept is the point at which the function intersects the x axis , the point at which y = 0

The given function is

g(x) = 2sin2x +1

g(x) = 0 , for x intercept

2sin2x +1 = 0

sin 2x = -1/2

Therefore in the interval ( 0 , 2π) , the x intercept is ( 7π/12 , 11π/12 , 19π/12 ,23π/12)

This can also be seen in the graph attached.

Option B is the correct answer.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[ a ] $ 20 for 8 lb

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]❖ \: \sf \:unit \: \: rate = simplest \: \: ratio \: in \: which \: it\: exists[/tex]

[tex] \qquad◈ \: \: \sf \: \cfrac{5}{2} \: \: \$ \:per \: \: lb[/tex]

Now, check out the options -

[ a ]

[tex] \qquad◈ \: \: \sf \: \cfrac{20}{8} [/tex]

( on simplifying )

[tex] \qquad◈ \: \: \sf \: \cfrac{5}{2} \: \: \$ \:per \: \: lb[/tex]

Same as the given one.

[ b ]

[tex] \qquad◈ \: \: \sf \: \cfrac{16}{6} [/tex]

( on simplifying )

[tex] \qquad◈ \: \: \sf \: \cfrac{8}{3} \: \: \$ \:per \: \: lb[/tex]

Not the same.

[ c ]

[tex] \qquad◈ \: \: \sf \: \cfrac{24}{8} [/tex]

( on simplifying )

[tex] \qquad◈ \: \: \sf \: 3 \: \: \$ \:per \: \: lb[/tex]

Not the same.

[ d ]

[tex] \qquad◈ \: \: \sf \: \dfrac{12}{4} \: \: [/tex]

( on simplifying )

[tex] \qquad◈ \: \: \sf \: 3 \: \: \$ \:per \: \: lb[/tex]

Not the same.

[tex] \qquad \large \sf {Conclusion} : [/tex]

The Correct answer is [ a ] $ 20 for 8 lb

$194.97 is the cost of the credit loan.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

The total cost of the dishwasher with sales tax can be found by multiplying the price by 1.04:

$1249.99 × 1.04 = $1299.99

The cost of credit is the total amount paid through the installment loan minus the cost of the dishwasher:

12 × $124.58 = $1494.96

$1494.96 - $1299.99 = $194.97

Therefore, the cost of credit for this loan is $194.97.

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Frogs are at the pond = 12.

Given,

There are some frogs and some lily pads at a pond. If lily pads with frogs on them have two frogs each, then there are 3 lily pads with no frogs on them. If each lily pad has exactly one frog on it, then there are 3 frogs with no lily pad.

= 2( n-3) = n+3

= 2n -6 = n+3

=> n = 9

9 pads, 12 frogs.

Hence, Frogs are at the pond = 12.

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Answer:

(i) Total cost of the flat is Rs. 540000.

(ii) Expenditure incurred on labour is Rs. 150000

Step-by-step explanation:

According to the question, cement cost is Rs. 112500, which represents 75° in the pie chart.

(i) The total cost of the flat is represented by the total 360° in the pie chart.

∴ Using unitary method

75° represents Rs. 112500

⇒ 360° represents = [tex]\frac{112500}{75}[/tex]  ×  360

                                = Rs. 540000

∴  Total cost of flat = Rs. 540000

(ii) Similarly, to calculate the cost of labour, represented by 100° in the pie chart, we can use the unitary method:

75° represents Rs. 112500

⇒ 100° represents =  [tex]\frac{112500}{75}[/tex]  ×  100

                               = Rs. 150000

∴ Cost of labour = Rs. 150000

Answer:

16

Step-by-step explanation:

let x be a positive integer

mathematically, the statement: “The product of two consecutive positive integers is 194 more than the next integer” means  x(x + 1) - 194 = x + 2

………………………………

Solving the equation x(x + 1) - 194 = x + 2 for x :

x(x + 1) - 194 = x + 2

⇔ x² + x - 194 = x + 2

⇔ x² - 194 = 2

⇔ x² = 196

⇔ x = 14 or x = -14

Since -14 < 0 then the solution to our equation is x = 14

Therefore

The largest integer of the three is x + 2 = 14 + 2 = 16

Verification:

14 × 15 − 194 = 210 − 194 = 16

Answer:

60inches

Step-by-step explanation:

this because If you multiply 4 by 10 equals 40 add 40 to 20 equals 60

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line passing through the point (1,2) and (5,4)

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

Formula used, here  [tex]\bf{\dfrac{y2-y1}{x2-x1}[/tex]

_______________________________________________________

[tex]\bf{\dfrac{4-2}{5-1}[/tex] | simplify

[tex]\bf{\dfrac{2}{4}[/tex] | reduce

[tex]\bf{\dfrac{1}{2}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

         [tex]\bf{=Slope:\dfrac{1}{2}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer:

1/2

Step-by-step explanation:

Subtract the second point on the you axis and

Answer:

5

Step-by-step explanation:

10+5=15

20-15=5 . that is the solution

This histogram is skewed to the left and its distribution's center would be three (3).

A histogram is used to graphically represent a set of data points into user-specified ranges, especially through the use of rectangular bars.

In this scenario, we can infer the following about the histogram distribution's center, spread, and overall shape:

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Question - 1 :

[tex]\qquad \sf  \dashrightarrow \: - 2x + 3y = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 2x + 3y - 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: (- 2)x + (3)y + (- 6)[/tex]

comparing it to general equation, we get :

Similarly,

Question - 2 :

[tex]\qquad \sf  \dashrightarrow \: 2x = - 5y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 5y = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2)x + (5)y + 0 = 0[/tex]

comparing it with general equation, we get :

The graph of the inequality can be seen in the image below.

Here we have:

-3 < y - 7x < 15

Isolating y, we get:

-3 + 7x < y < 15 + 7x

So we need to graph two linear inequalities:

y > -3 + 7x

y < 15 + 7x

So we need to graph two parallel lines (with dashed lines, the lines aren't solutions) and shade the region above the first line and below the second line.

The graph is below:

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Answer:

jsjsjd b ebejisnskskhdbd zkzkz z.

Step-by-step explanation:

* start by finding the gradient/ slope of the line using the two points*

after finding the gradient you can now use the formula/ equation of any straight line which is *y = m×x + c*