Determine the equation, in vertex form, of a parabola that has been:

(a) reflected in the x-axis and horizontally shifted right 4 units.

(b) vertically compressed by a factor of 1/4 and vertically translated 5 units down

(c) vertically stretched by a factor of 4, translated 3 units left and 2 units up

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:

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

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:

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

By using the definitions of distance and number line, the distance between a and b on the number line is 10.97 units, not 0.47 units. (Right choice: A)

Herein we must determine what choice is false with respect to two integers, one negative and other positive. The first choice represents a false proposition as:

|a - b| = |- 5.72 - 5.25| = |- 10.97|

|a - b| = 10.97

By using the definitions of distance and number line, the distance between a and b on the number line is 10.97 units, not 0.47 units. (Right choice: A)

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40.2 percent of the customers at the beauty supply store choose brand B.

An equation is an expression that shows the relationship between two or more numbers and variables.

The percent of customers that choose brand B = (number of  brand B customers / total number of customers) * 100%

The percent of customers that choose brand B = (402/1000) * 100% = 40.2%

40.2 percent of the customers at the beauty supply store choose brand B.

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Hope this helps you

.......

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]

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\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 chocolate will last for 1 day, if she gets 4 more dragons

The expression can be represented using the following ratio:

Ratio = Dragons : Days : Chocolate

For the 2 dragons she has, we have:

Ratio = 2 : 12 : 300

When she gets 4 more dragons, we have:

Ratio = 6 : days : 300

Equate both ratios

6 : days = 12 : 2

Express as fraction

days/6 = 2/12

Multiply both sides by 6

days = 6 * 2/12

Evaluate

days = 1

Hence, the chocolate will last for 1 day

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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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Answer:

c

Step-by-step explanation:

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*

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:

x = - 6

Step-by-step explanation:

Answer:

the inclination of the line will decrease

Step-by-step explanation:

If Cassandra changes the amount she deposits from 18 to 14, the slope changes to 14. So the new equation is M=14n + 224. The 224 is still the same, because that is the initial amount, and the new situation hasn't said anything about changing that, so it will not have any vertical translations. With that being said, as a result the slope will be less, so you can see it as "less vertical", so the inclination of the line will decrease

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!

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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A significance level of 5% (more commonly referred to as 95%) corresponds to a statement that (only) a probability of 5% or less is that a particular randomly generated observation is accepted as significant.

In this example, the p-level (the true probability that the observations are randomly generated) is less than 5% (0.0421 <0.05), so we can draw the conclusion that the observations are significant.

p = 0.0421 means that the probability is only 0421/1000. The choice of significance level to reject the null hypothesis is optional. Traditionally, 5%, 1%, and 0.1% levels have been used. In rare situations, a 10% significance level is also used.

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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.

Answer:

not moving any spaces

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

[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

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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[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

The house would have slid 910 yards in 15 days.

A geometric progression is a sequence in which successive terms differ by a common ratio.

It is a sequence in which the ratio of two consecutive terms is a constant.

Analysis:

first term, a= 1

second term, ar = 2

third term, ar^2= 4

common ratio = ar/a = 2/1 = 2

Sum of the G.P where n = 15

sum of G.p = a([tex]\frac{r^{n} - 1}{r-1}[/tex])

= 1([tex]2^{15}[/tex] - 1)/2 - 1 = 32768 - 1 = 32768 inches

converting the inches to yard, where 1 yard = 36 inches

so 32768/36 = 910 yards

In conclusion, the house would slide 910 yards in  15 days.

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Answer:

128.4°, 51.6°

Step-by-step explanation:

x + x - 76.8 = 180

2x = 256.8

x = 128.4

x - 76.8 = 51.6