A mother and daughter decided to add their ages together. The sum of their ages is 76. Six years ago, the mother was 3 times the age of her daughter. How old is the daughter now?​

Answer:

[tex]y=\dfrac{1}{2}(x+5)^2-3[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

Parent function

[tex]y=-x^2[/tex]

Reflected in the x-axis

[tex]-f(x) \implies y=-(-x^2)\implies y=x^2[/tex]

Compressed vertically by a factor of 1/2

Multiply the whole function by the given scale factor:

[tex]\dfrac{1}{2}f(x)\implies y=\dfrac{1}{2}x^2[/tex]

Translated 3 units down

Subtract 3 from the whole function:

[tex]f(x)-3 \implies y=\dfrac{1}{2}x^2-3[/tex]

Translated 5 units left

Add 5 to the variable of the function:

[tex]f(x+5) \implies y=\dfrac{1}{2}(x+5)^2-3[/tex]

To sketch the parabola

Vertex = [tex](-5, -3)[/tex]

Axis of symmetry:  [tex]x = -5[/tex]

Plot points:

[tex]x=-9 \implies \dfrac{1}{2}(-9+5)^2-3=5 \implies (-9,5)[/tex]

[tex]x=-7 \implies \dfrac{1}{2}(-7+5)^2-3=-1 \implies (-7,-1)[/tex]

[tex]x=-3 \implies \dfrac{1}{2}(-3+5)^2-3=-1 \implies (-3,-1)[/tex]

[tex]x=-1 \implies \dfrac{1}{2}(-1+5)^2-3=5 \implies (-1,5)[/tex]

Answer:

Median

Order the data values from smallest to largest:

55, 57, 57, 57, 58, 58, 58, 59, 59, 60, 61, 61, 61, 62, 62, 62, 63, 63, 64, 64, 65, 65, 66, 67

As there is an even number of values, the median is the mean of the middle two values ⇒ Median = 61

Quartiles

55, 57, 57, 57, 58, 58, 58, 59, 59, 60, 61, 61 || 61, 62, 62, 62, 63, 63, 64, 64, 65, 65, 66, 67

The first quartile is the median of the data points to the left of the median  ⇒ first quartile = 58

The third quartile is the median of the data points to the right of the median  ⇒ first quartile = 63.5

Five-number summary

Draw a box from the first quartile (58) to the third quartile (63.5)

Add the median (61) as a the vertical line through the box.

The whiskers are horizontal lines from each quartile to the minimum (55) and maximum values (67).

Answer:

last option

Step-by-step explanation:

hope it helps

One way to determine the factors of x³ + 5x² - 6x - 30 by grouping is shown by option D. x² (x + 5) - 6(x + 5).

Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.

Given a cubic polynomial,

x³ + 5x² - 6x - 30

Taking the first two terms together and the other two terms together,

(x³ + 5x²) + (- 6x - 30)

Taking x² common from first and -6 common from second,

x² (x + 5) - 6(x + 5)

Hence the correct option is D.

Learn more about Polynomials here :

https://brainly.com/question/28315959

#SPJ7

The trip would have taken 6 hours.

(300 mi) / (50 mi/h) = 6 h

The number of seeds in 2 ounce package is 6.7 × 10⁷ seeds

From the question, we are to determine the number of seeds in 2 ounce package

From the given information,

An orchid seed weighs 3.2 × 10⁻⁸ ounces

If an orchid seed weighs 3.2 × 10⁻⁸ ounces

Then,

2 ounce package will contain [tex]\frac{2}{3\times 10^{-8} }[/tex] seeds

= 0.67 × 10⁸

= 6.7 × 10⁷ seeds

Hence, the number of seeds in 2 ounce package is 6.7 × 10⁷ seeds

Learn more on Calculating quantity here: https://brainly.com/question/11262670

#SPJ1

Answer:

yes they do

Step-by-step explanation:

they share a ray

Answer:

D / 242

Step-by-step explanation:

hope this helps!

Abby can make 5 complete groups with 9 extra bonus coupons.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here, Abby has total number of coupons = 159

        Number of coupons in a group = 30

Total number of groups = Total Coupons / coupons in a group

                                         = 159 / 30

                                         = 5.3

Thus, Abby can make 5 complete groups with 9 extra bonus coupons.

Learn more about Division from:

https://brainly.com/question/2273245

#SPJ1

Answer & explanation:

A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question.

Pls, choose me as brainliest!

Answer:

10.5

Step-by-step explanation:

quick math

The average rate of change of the function over the interval [-1, 2] is: C. 2.5.

The average rate of change over an interval of a function is: f(b) - f(a) / b - a.

Given the interval  [-1, 2]:

a = -1; f(a) = -5

b = 2; f(b) = 2.5

Average rate of change = (2.5 - (-5)) / (2 - (-1)) = 7.5/3

Average rate of change = 2.5 (option C).

Learn more about average rate of change on:

https://brainly.com/question/11627203

#SPJ1

Answer:

x=0

Step-by-step explanation:

Expand the equation 4 + [tex]\sqrt{x}[/tex]+1=5

[tex]\sqrt{x} +5=5[/tex]

        -5   -5

subtract 5 from both sides

[tex]\sqrt{x} = 0[/tex]

x=0

square both sides

True= x=0

Answer:

the answer is x=0

Step-by-step explanation:

[tex]4+\sqrt{x} +1=5[/tex]

add "4 +1" which equals 5

[tex]\sqrt{x} +5=5[/tex]

now -5 on both sides :)

[tex]\sqrt{x}[/tex]

now you're left with a square root

[tex]\sqrt{x}=0[/tex]

The correct answer is option D.The point 1.6 with bar will be lies between 1 and 2.

The image of the question is attached with the answer below:-

The number line is the line on which real numbers are marked with the same interval between them. Number lines are used to mark any point of the real number on the line.

We can see in the image that A, B, C and D points are marked on the number line. The line is marked with real numbers that are integers.1.6 bar number will lie between 1 and 2 numbers.

Therefore the correct answer is option D.The point 1.6 with a bar will be lies between 1 and 2.

To know more about Number line follow

https://brainly.com/question/24644930

#SPJ1

Answer:

D

Step-by-step explanation:

Answer:

The answer to the equation is B.

Step-by-step explanation:

Answer:

i took the test and its B

Step-by-step explanation:

Step-by-step explanation:

x is less than or equal to 0.

so click x than the choose the third option then click 0

Since the polyhedron is about 78.5 m², the radius of the sphere is 2.5 m

Since the sum of the faces of the polyhefron equals the surface area of the sphere, we find its surface area.

The surface area of sphere is given by A = 4πr² where r = radius of sphere

Making r subject of the formula, we have

r = √(A/4π)

Given that he sum of all the faces of the polyhedron is about 78.5 square meters, this is equal to the surface area of the sphere.

So, A = 78.5 m²

Substituting this into the equation for r, we have

r = √(A/4π)

r = √(78.5 m²/4π)

r = √(19.625 m²/π)

= √(6.246 m²)

= 2.499 m

≅ 2.5 m

So, the radius of the sphere is 2.5 m

Learn more about radius of sphere here:

https://brainly.com/question/13458041

#SPJ1

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{4}{x}~~ = ~~\cfrac{x}{9}\implies 36=x^2\implies \sqrt{36}=x\implies 6=x[/tex]

The first step that we must take before solving a problem is to understand what the problem statement is asking us to do and what is given to us to do so.  Looking at the problem they are asking what the slope of the line is. What is provided to us is an equation which was captured as [tex]y=-2x + 3[/tex].

The next step that we must take is to determine what the slope of the line is. Let us first define what slope is.

Slope-Intercept form is a form in which an equation can be expressed in and it follows the y = mx + b format.  M is equal to the slope while b displays the y-intercept of the expression.

The easiest way to determine the slope using slope-intercept form us by looking at the coefficient of the variable x (in this case) which is also known as m.  Looking at our equation, we can see that the coefficient in front of the variable x is -2.

Therefore, the option that would best match the details that we provided would be option B, -2.

Answer:

B. -2

General Formulas and Concepts:
Algebra I

Slope-Intercept Form:
[tex]\displaystyle y = mx + b[/tex]

Step-by-step explanation:

Step 1: Define

Identify given equation.

[tex]\displaystyle y = -2x + 3[/tex]

Step 2: Find Slope m

Let's compare our given equation to the general equation Slope-Intercept Form to identify our values for slope m and y-intercept b:

We can see that our y-intercept b is equal to 3 and that our slope m is equal to -2.

∴ the slope of the given line is equal to -2 and the answer choice that correlates with this is answer choice B.

___

Learn more about Slope-Intercept Form: https://brainly.com/question/24552408

Learn more about Algebra I: https://brainly.com/question/10664006

___

Topic: Algebra I

The results for the matching between function and its period are:

If a given function presents repetitions, you can define the period as the smallest part of this repetition. As an example of periodic functions, you have: sin(x) and cos(x).

[tex]\mathrm{Period\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}[/tex]

The period of sin(x) and cos(x) is 2π.

For solving this question, you should analyze each option to find its period.

1) Option 1

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi }{\frac{1}{2} }=4\pi[/tex]

Thus, the option 1 matches with the letter D.

2) Option 2

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{4} =\frac{\pi }{2}[/tex]

Thus, the option 2 matches with the letter A.

3) Option 3

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{2} =\pi[/tex]

Thus, the option 3 matches with the letter C.

4) Option 4

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{8} =\frac{\pi }{4}[/tex]

Thus, the option 4 matches with the letter B.

Read more about the period of a trigonometric function here:

https://brainly.com/question/9718162

#SPJ1

Answer:

48 units²

Step-by-step explanation:

Lateral Surface Area :

Answer:

48 units²

Step-by-step explanation:

The lateral area of a square based pyramid comprises the four triangular sides.

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

                             = 1/2 × 8 × 3

                             = 1/2 × 24

                             = 12 units²

Lateral SA = 4 × area of triangle

                 = 4 × 12

                 = 48 units²

Answer:(-8,0)

Step-by-step explanation:

Add (-1,-6) with translation move (-7,6)

-1 , -6

-7 , 6

____

-8 , 0

Answer:

D) x = 12

Step-by-step explanation:

Given:

[tex]\sf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 \implies \dfrac{10}{4}x-7=\dfrac{3}{4}x+14}[/tex]

1. Multiply both sides by 4

[tex]\sf{4\left(\dfrac{10}{4}x-7\right)=4\left(\dfrac{3}{4}x+14\right)}\\\\\implies 10x-28=3x+56[/tex]

2. Subtract 3x from both sides

[tex]\sf{10x-3x-28=3x-3x+56}\\\\\implies 7x-28=56[/tex]

3. Add 28 to both sides

[tex]\sf{7x-28+28=56+28}\\\\\implies 7x=84[/tex]

4. Divide both sides by 7 to isolate the variable:

[tex]\sf{\dfrac{7x}{7}=\dfrac{84}{7}}\\\\\implies x=12[/tex]

Learn more here:

brainly.com/question/27844194

Answer:

a) v>4.5

b) w<6.5

a) 0.3 recurring

b) 5/11

Answer:y=5x+1

Step-by-step explanation:the y intercept is the y value when x=0 which we can read off as run. Slope =rise/run=(change in y value)/(change in x value) for any two points.

Answer:

  obtuse

Step-by-step explanation:

A "form factor" can be computed whose sign will tell you the classification of the triangle. For short sides a, b and long side c, the form factor is ...

  f = a² +b² -c²

And the interpretation is ...

__

For the given side lengths, the form factor is ...

  f = 11² +15² -20² = 121 +225 -400

  f = -54

The value is less than zero, signifying an obtuse triangle.

_____

Additional comment

The value f/(2ab) = -54/(2·11·15) = -9/55 is the cosine of the largest angle. Here, the largest angle is arccos(-9/55) ≈ 99.4°. This is greater than 90°, hence an obtuse angle.

This cosine relation comes from the Law of Cosines. The interpretation of the "form factor" can be developed by considering the Pythagorean theorem (f=0 ⇒ right triangle) and the relationship between sides and angles. If the longest side is longer than necessary for a right triangle, the largest angle will be greater than 90°.

Answer: I think

Step-by-step explanation:Let the coordinate of the point be (x,y,z). Since the point is located 3 units behind the YZ− plane, 4 units to the right of XZ− plane and 5 units above the XY−plane ,x=−3,y=4 and z=5 Hence, coordinates of the required points are (−3,4,5)

Answer:

none of those are correct.

Step-by-step explanation:

5 red

7 blue

8 white

5 red + 7 blue= 12

5 red + 7 blue + 8 white= 20

=12/20

=6/10