|x - 7| ≥ 1?

what is the solution?

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given functions

STEP 2: Describe the transformations

Translation to the left/right: Horizontal translation refers to the movement toward the left or right of the graph of a function by the given units. The shape of the function remains the same. It is also known as the movement/shifting of the graph along the x-axis.

To shift, move, or translate horizontally, replace y = f(x) with y = f(x + c) (left by c) or y = f(x - c) (right by c).

Translations up/down: The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input. Adding to the output of a function moves the graph up. Subtracting from the output of a function moves the graph down.

To translate the function up and down, you simply add or subtract numbers from the whole function. If you add a positive number (or subtract a negative number), you translate the function up. If you subtract a positive number (or add a negative number), you translate the function down.

STEP 3: Define the first transformation

STEP 4: Define the vertical transformation

STEP 5: Define the final transformation

Hence, the transformations of f(x) to g(x) are:

Translated 2 units left

Translated 3 units down

Reflected over the x-axis (yes)

Given relation between height and time is:

Now put the value of h=85 ft in given relation:

Solving it for t:

Answer:

Below

Step-by-step explanation:

With roots   -4   and 6  

the equation is   a * (x+4)(x-6) = 0  

     'a' can be any real number (I'll choose '1')

Expand to  x^2 -2x - 24 = f(x)

Answer: To do that, we divide both sides by 3. Thus, the answer to "3 times what equals 27?" is 9. To double-check our work, multiply 9 by 3 to see that it equals 27.

Step-by-step explanation:

Answer: 175

Step-by-step explanation:

3(27)+94  =

81 + 94 = 175

we have

f(x)=6x+2

g(x)=-5x-9

Find out the product

so

f(x)*g(x)=(6x+2)*(-5x-9)

Applying distributive property

f(x)*g(x)=(6x)*(-5x)+(6x)*(-9)+(2)*(-5x)+(2)*(-9)

f(x)*g(x)=-30x^2-54x-10x-18

combine like terms

f(x)*g(x)=-30x^2-64x-18

Answer: Width = 3.4 meters, Length = 6.4 meters

Step-by-step explanation:

If the width is [tex]w[/tex], then the length is [tex]w+3[/tex].

[tex]w(w+3)=22\\\\w^2 +3w=22\\\\w^2 +3w-22=0\\ \\ w=\frac{-3 \pm \sqrt{3^2 -4(1)(-22)}}{2(1)}\\\\w \approx 3.4 \text{ } (w > 0)\\\\\implies w+3 \approx 6.4[/tex]

The distance travelled by the plane is 1365 miles.

Given,

Speed of the pane =455 miles per hour

Time taken =3 hours

To find distance covered by the plane use formula,

[tex]speed =\frac{Distance}{Time taken}\\ \\Distance=Speed * time taken\\\\Distance=455*3\\\\Distance=1365 miles[/tex]

Thus, the distance travelled by the plane is 1365 miles.

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To find the equation of the line that goes through the point (4, -7) and is perpendicular to the line y + 6 = -2/5 (x - 1), we can use the fact that two lines are perpendicular if their slopes are negative reciprocals of each other.

The slope of the line y + 6 = -2/5 (x - 1) is -2/5, so the slope of the line that is perpendicular to it must be -5/2. We can use this slope and the point (4, -7) to write the equation of the line in slope-intercept form.

To do this, we can use the point-slope formula, which is: y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes, and m is the slope of the line. In our case, the point is (4, -7) and the slope is -5/2, so the equation of the line is: y - (-7) = (-5/2)(x - 4).

We can simplify this equation to get: y + 7 = -5/2 x + 10. Finally, we can rearrange the terms to get the equation in slope-intercept form, which is: y = -5/2 x - 25/2.

Therefore, the equation of the line that goes through the point (4, -7) and is perpendicular to the line y + 6 = -2/5 (x - 1) is y = -5/2 x - 25/2 in slope-intercept form.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y+6=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{5}}(x-1)\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-2}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{-2}\implies \cfrac{5}{2}}}[/tex]

so we're really looking for the equation of a line whose slope is 5/2 and that it passes through (4 , -7)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ \cfrac{5}{2}}(x-\stackrel{x_1}{4}) \implies {\large \begin{array}{llll} y +7= \cfrac{5}{2} (x -4) \end{array}}[/tex]

Answer:

you have to use the formula of a line passing through a point, so: y-y0=m(x-x0)

We also know that m=8, because it is parallel to the line y=(8=m)x -1

so: y-2=8(x+6)

and you solve it, so:

y-2=8x+48

y=8x+48+2

y=8x+50

Shifts on x, where x and k form a binomial, are horizontal shifts. If k is positive, it is a left shift. If k is negative, it is a right shift.

The constant final term of the equation acts in the opposite way. It will be a vertical shift, and positive will mean up, negative will mean down.

So here, where there is a positive horizontal shift of 2 and a negative vertical shift of 7, the function is shifted 2 units to the left and 7 units down.

Area of a rectangle = Length x Breadth

Note that:

• All numbers whose final digit is 0 or an even number are divisible by 2

• All numbers whose final digit is 0 are divisible by 10

• 498 is divisible by 2 but not divisible by 5 and 10

• 151 is not divisible by any of 2, 5, or 10

• 150 is divisible by al of 2, 5, and 10

The complete table is uploaded below

In this question, we are given two similar triangles ABC and DEF.

Similar triangles:

The triangles are similar if they have congruent corresponding angles and the corresponding sides of triangles are in proportion.

Therefore, the proportion of all sides should be the same. To proportion (k) can be found using:

k = Side AB / side DE

k = 9/6

or

k = 3/2

Similarly, the 'k' should be the same for side BC and side EF. Therefore,

k = side BC/ side EF

Now, put the values in the equation

Therefore, the value of x would be 4.

The length of each strip is 4 cm

In this question, we have been given Noam had a length of 13 1/3 cm of ribbon and cut 3 1/3 equal sized strips the full width of the ribbon.

We need to find the length of each whole strip.

first we convert the improper fraction into a proper fraction.

13 1/3 = 40/3

3 1/3 = 10/3

To find  the length of each whole strip, we need to divide 13 1/3 by 3 1/3

i.e., 40/3 ÷ 10/3

= (40/3) / (10/3)

= 40/3 × 3/10

= 40/10

= 4

Therefore, the length of each strip is 4 cm

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Answer:

4

Step-by-step explanation:

Just did it on khan academy.

Distance travelled by remote controlled car is 32 feet in 8 sec

Speed is the rate and direction of an object's movement, whereas speed is the scalar at which an object moves along a path in time. Velocity is a vector, whereas speed is a scalar integer.

speed  = 4 feet/sec

distance = d feet

time = t sec

4 = d / t

t =  8 sec

d = 4 *8

d = 32 feet

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The mass of the object that the star is orbiting is 1.0659 × 10³⁷ kg.

One of the fundamental quantities and the most fundamental feature of matter is mass. The quantity of matter in a body is referred to as its mass. The SI unit of mass is the "kilogram," or kg, while there are other units for determining mass, such as grams, pounds, pounds, etc. A good conversion formula can be used to convert any mass unit to another without changing the meaning or essence of the quantity being measured.

Given, the speed of the orbiting star is 1400 km/s.

Converting the speed in meter per second.

speed = 1.4 × 10⁶ m/s

The radius of the circular orbit is 14-day light.

Converting the radius in meters,

radius = 3.626 × 10¹⁴ m

We know that the gravitational constant = 6.67 × 10⁻¹¹ N.m²/kg².

Now, find the mass of the object:

mass = ((1.4 × 10⁶)² × 3.626 × 10¹⁴)/6.67 × 10⁻¹¹

         = (1.96 × 10¹² × 3.626 × 10¹⁴)/6.67 × 10⁻¹¹

         = (7.10696 × 10²⁶)/6.67 × 10⁻¹¹

         = 1.0659 × 10³⁷ kg

Therefore, the mass of the object that the star is orbiting is 1.0659 × 10³⁷ kg.

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Answer

The missing number = 45

Explanation

Let the unknown number be x

x ÷ 5 = 9

Multiply both sides by 5

x ÷ 5 × 5 = 9 × 5

x = 45

Hope this Helps!!!

Answer: B

Step-by-step explanation:

For 2, we have the following triangle:

Using sine and cosine we have the following:

Therefore, the remaining sides are y= 10 and x = 10

Let's consider triangle ABC

Length AB can be obtained using Pythagoras

Similarly, we can consider triangle ACD, so that length AD will be obtained through Pythagoras

Considering triangle ABD, with BD being the hypotenuse

Expanding the parentheses

Divide both sides by 2

Option A is correct

Answer:

Let's consider triangle ABCLength AB can be obtained using PythagorasSimilarly, we can consider triangle ACD, so that length AD will be obtained through PythagorasConsidering triangle ABD, with BD being the hypotenuseExpanding the parentheses Divide both sides by 2Option A is correct

Step-by-step explanation:

We are looking at what type of variables are given. Let's analyze it one by one to check which one suits it best.

(a) Temperature

Temperature is measured by numbers, hence, this is categorized as a quantitative variable. Temperature does not have a non-finite value since it changes as time goes by, hence, the level of measurement for this type of variable is ratio.

Answer: Quantitative and ratio

(b) Dosage of the medication

The dosage of medication is measured in milligrams, which means we are dealing with numbers, hence, this is a quantitative variable. In the case of dosage, we are dealing with fixed values, hence, the level of measurement for this type of variable is interval.

Answer: Quantitative and interval

(c) Stock exchange

Stock exchanges are types of group variables. These are represented as categories, hence, this variable is classified as categorical. The exchanges are ranked in some specific order. When dealing with categorical variables that have rank order, we have ordinal variables.

Answer: Categorical and ordinal

Answer:

80 degrees

Explanation:

The sum of the measures of angles in a triangle is 18 degrees.

Given that the angle measures in a triangle are (3x+4), (5x), and (7x-4), then:

First, we solve the equation for x.

Therefore, the measures of the angles are:

The measure of the largest angle in the triangle is 80 degrees.

Problem

You have $6,000 to invest in a savings account for 15 years and you have hvo account options to choose from. You can invest in an account that offers 8% simple interest or you can invest in an account that offers 6% interest compounded once a year. Complete the table and write an equation for each situation Simple interest & Compound Interest. Will you choose simple or compound interest? Why?​

Solution

Case 1: Simple interest

We can use the formula:

y= 6000 + 6000(0.08 x)= 6000+ 480x

And replacing we got:

X Y

__________

0 6000

1 6480

2 6960

5 8400

10 10800

15 13200

__________

Case 2: Compound interest

We can use the following formula:

Y= 6000 (1+0.08)^x =6000 (1.08)^x

And replacing we got:

X Y

__________

0 6000

1 6480

2 6998.4

5 8815.97

10 12953.55

15 19033.01

__________

STEP - BY - STEP SOLUTION

What to find?

The similarity ratio of WXYZ to EFGD.

Given:

The ratio of WXYZ to EFGD can be determine by taking the ratio of any of the simila side of WXYZ to EFGD.

That is;

Since EFGD is a rectangle, using the property of the rectangle that state " opposite sides are congruent, we can deduce that ED = EG = 6

Hence,

ANSWER

1/2

Answer:  (c)  y = −1/3x −2

Step-by-step explanation:

I know it because I looked on brainly .

Let the width of the field = w

∵ The length is four times as the width

∵ The width = w

∴ The length = 4w

∵ The length is decreased by 10 feet

∴ The new length = 4w - 10

∵ The width is increased by 2 feet

∴ The new width = w + 2

The new perimeter is 80 feet

∵ The perimeter of the rectangle = 2(length + width)

Let us simplify it

Now equate it by 80

Add 16 to both sides

Divide both sides by 10

The length is 4 times the width

The length is 38.4 feet and the width is 9.6 feet

Answer:

[tex] C = \dfrac{5}{9}(F - 32) [/tex]

Step-by-step explanation:

[tex] F = \dfrac{9}{5}C + 32 [/tex]

Switch sides to have C on the left side.

[tex] \dfrac{9}{5}C + 32 = F [/tex]

Subtract 32 from both sides.

[tex] \dfrac{9}{5}C = F - 32 [/tex]

Multiply both sides by 5/9.

[tex] \dfrac{5}{9} \times \dfrac{9}{5}C = \dfrac{5}{9} \times (F - 32) [/tex]

[tex] C = \dfrac{5}{9}(F - 32) [/tex]

The rule of the length of the arc of a circle is

Where

x is the central angle subtended by the arc

r is the radius of the circle

From the given figure

The radius is 3 units, then

r = 3

The central angle of the highlight arc is a right angle, then

x = 90 degrees

Substitute them in the rule above

The length of the highlight arc is 1.5pi units

In order to solve the equation for x, we need to look at the side where the variable is, then, we apply the contrary operations to this operation on both sides.

In this case, x is being subtracted by 15, then we need to eliminate this 15 by adding 15 on both sides

Answer:

A. Adding 15 to both sides of the equation