The solutions of the equation are -12 and 16
Step-by-step explanation:
Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative, if IxI = a, where a > 0, then
x = ax = -a∵ 2Ix - 2I - 8 = 20
- At first add 8 to both sides
∴ 2Ix - 2I = 28
- Then divide both sides by 2
∴ Ix - 2I = 14
Now By using the notes above equate x - 2 by 14 and -14
∵ x - 2 = 14
- Add 2 to both sides
∴ x = 16
∵ x - 2 = -14
- Add 2 to both sides
∴ x = -12
The solutions of the equation are -12 and 16
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A set of laptop prices are normally distributed with a mean of 750 dollars and a standard deviation of 60
dollars.
What proportion of laptop prices are between 624 dollars and 768 dollars?!
You may round your answer to four decimal places.
Answer:
0.6
Step-by-step explanation:
it is right
The proportion of laptop prices that are between 624 dollars and 768 dollars would be: 0.3907 or 39.07%.
What is the proportion?To determine the proportion of laptop prices that are betwee the specified prices, we would ge the z scores in the following way:
624 dollars
Z1 = (624 - 750) / 60 = -2.1
768 dollars
Z2 = (768 - 750) / 60 = 0.3
Now, if we use the standard distribution table, we would arrive at;
P(-2.1 < Z < 0.3) ≈ 0.3907
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An equation of a line perpendicular to y=2/3x-6
Final answer:
The equation of a line perpendicular to y=2/3x-6 has a slope of -3/2. The general form of the equation is y = -3/2x + b, where b is the y-intercept.
Explanation:
The student has asked for an equation of a line that is perpendicular to the line given by y=2/3x-6. For two lines to be perpendicular, the product of their slopes must be -1. Since the slope (m₁) of the given line is 2/3, the slope of the line perpendicular to it (m₂) must satisfy the equation m₁×m₂ = -1. Therefore, m₂ must be -3/2 (since (2/3)×(-3/2) = -1).
An equation of a straight line can be represented by y = mx + b, where m is the slope and b is the y-intercept. To find an equation of a line perpendicular to y=2/3x-6, we can use the slope m₂ = -3/2. The general form of the equation of the line we are seeking would then be y = -3/2x + b, where b is the y-intercept that can be determined based on a specific point the line passes through.
A. Part 1 ......Quadrilateral ABCD is similar to Quadrilateral EFGH. Diagonal AC has length 7 and diagonal EG has length 13. What is the scale factor that describes a dilation from BC to FG? Give the exact scale factor and state whether the dilation is an expansion or a contraction.
B. Part 2..... If side AB has length 17/26 what is the length of side EF? Give the exact, un-rounded value.
C. Part 3........If the area of ABCD is 147 square inches, what is the area of EFGH? Give the exact answer.
I would deeply appreciate it if you could explain how to find the answer
(I'm specifically confused about scale factor and diagonals in part 1) and if you could do a step by step walk through. Will give Brainliest Answer!
A. Part 1- The scale factor from BC to FG is 7/13 . Since this ratio is less than 1, it indicates a contraction.
B. Part 2- The length of side EF is 221/182
C. Part 3- The exact area of EFGH is 7213127/33124 square inches.
Let's solve each part step by step:
A. Part 1:
To find the scale factor from BC to FG, we need to find the ratio of the lengths of the corresponding sides of the similar quadrilaterals.
Given:
Diagonal AC (in quadrilateral ABCD) has length 7.
Diagonal EG (in quadrilateral EFGH) has length 13.
Using the fact that the diagonals of similar quadrilaterals are proportional, we have:
BC/ FG = AC/ EG
Substituting the given values:
BC/ FG = 7/13
So, the scale factor from BC to FG is 7/13 . Since this ratio is less than 1, it indicates a contraction.
B. Part 2:
Given side AB has a length of 17/26 . To find the length of side EF, we use the scale factor found in Part 1.
If the scale factor from BC to FG is 7/13 , then the length of side EF can be found using the proportion:
EF/ AB = FG/ BC
Substituting the given values:
EF=7/13×17/ 26
Solving for EF:
EF= 13/ 7 × 17/ 26 = 221/ 182
So, the length of side EF is 221/182
C. Part 3:
If the area of quadrilateral ABCD is 147 square inches, and the scale factor is 7/13 , the area of quadrilateral EFGH can be found using the scale factor squared.
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.
So,
( EF/AB )^2 =( 7/13 )^2
( 221/ 182)^2 =( 7/13 )^2
Solving for ( 221/ 182 )^2 :
( 221/182 )^2 = 48841/ 33124
Now, if the area of ABCD is 147 square inches, then the area of EFGH would be:
147× 48841/ 33124 = 7213127 /33124
So, the exact area of EFGH is 7213127/33124 square inches.
m
m< B = 80 + x
m< C=110 - 3x
m
Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are equal. Prove that Quadrilateral ABCD is
a parallelogram by finding the value of x.
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
The complete question is
m ∠ A = 100 - x
m ∠ B = 80 + x
m ∠ C = 110 - 3x
m ∠ D = 75 + 2x
Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are equal. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
Options
A) x = 5
B) x = 7
C) x = 10
D) x = 15/2
we know that
In a parallelogram, opposite angles are parallel and consecutive angles are supplementary
so
m ∠ A=m ∠ C
m ∠ B=m ∠ D
m ∠ A+m ∠ B=180°
m ∠ B+m ∠ C=180°
step 1
Find the value of x
we know that
m ∠ A=m ∠ C
substitute the given values
[tex](100-x)^o=(110-3x)^o[/tex]
solve for x
Group terms
[tex]3x-x=110-100[/tex]
Combine like terms
[tex]2x=10[/tex]
[tex]x=5[/tex]
step 2
Verify the measure of the angles
[tex]m\angle A=100-5=95^o[/tex]
[tex]m\angle B=80+5=85^o[/tex]
[tex]m\angle C=110-3(5)=95^o[/tex]
[tex]m\angle D=75+2(5)=85^o[/tex]
therefore
[tex]m\angle A=m\angle C[/tex] ---> is ok
[tex]m\angle B=m\angle D[/tex] ---> is ok
[tex]m\angle A+m\angle B=180^o[/tex] ---> is ok
[tex]m\angle B+m\angle C=180^o[/tex] ---> is ok
Which expression is the simplest form of 2(4x + 3) + 3(x - 63) + x??
OOO
A. x2 +11x-17y
B. x2 + 11x- 4y
C. x2 + 9x-17y
D. x2 +11x-16y
Answer:
12x-183
Step-by-step explanation:
2(4x+3)+3(x-63)+x
8x+6+3x-189+x
12x+6-189
12x-183
Hãy tưởng tượng từng chữ cái của từ Toán Toán học được viết trên từng mảnh giấy và đặt trong một cái túi. Bạn nên chọn một chữ cái ngẫu nhiên từ túi đó, xác suất bạn chọn một nguyên âm là gì
Answer:
25% or 1/4. I don't know how to type Vietnamese.
Database about trees include a height field. What kind of sort would list the data from tallest to shortest?
1) ascending sort
2) descending sort
3) mixed sort
4)random sort
A descending sort would list the data from tallest to shortest in the height field of a database about trees.
Explanation:The kind of sort that would list the data from tallest to shortest in the height field of a database about trees is a descending sort. This sort arranges the data in reverse order, with the tallest tree at the top and the shortest tree at the bottom. To perform a descending sort in a database, you can use the ORDER BY clause with the DESC keyword in the SQL query.
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The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal.
What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years?
a $60
b $80
c $90
d $100
Answer:
b $80
Step-by-step explanation:
Interest = Principal x Interest Rate x Time
$40 = P x 0.1 x 5
$40 = 0.5 P
Dividing the equation by 0.5 we get;
P = $40 / 0.5
P = $80
The perimeter of a triangle is 40 inches. Twice the length of the longest side minus the length of the shorted side in 30 inches. The sum of the length of the longest side and twice the sun of both the other side lengths is 61 inches. Find the side lengths
9514 1404 393
Answer:
8 inches, 13 inches, 19 inches
Step-by-step explanation:
Let's identify the side lengths (shortest to longest) as a, b, c. Then we have ...
a + b + c = 40 . . . . . . perimeter
2c -a = 30
2a +2b +c = 61
__
Subtracting the third equation from twice the first gives ...
2(a +b +c) -(2a +2b +c) = 2(40) -(61)
c = 19 . . . . . simplify
Using this in the second equation, we have ...
2(19) -a = 30
38 -30 = a = 8 . . . . add a-30
Then the first equation reveals b:
8 + b + 19 = 40
b = 40 -27 = 13
The side lengths are 8 in, 13 in, and 19 in.
If f(x) = 10x + 7 and g(x) = x^2 - 7x, find (f - g)(x)
A. (f - g)(x) = x^2 + 3x + 7
B. (f - g)(x) = 10x^3 - 63x^2 - 49x
C. (f - g)(x) = -x^2 + 17x + 7
D. (f - g)(x) = 10x + 7
Answer:
C
Step-by-step explanation:
note that (f - g)(x) = f(x) - g(x)
f(x) - g(x)
= 10x + 7 - (x² - 7x) ← distribute parenthesis by - 1
= 10x + 7 - x² + 7x ← collect like terms
= - x² + 17x + 7 → C
Final answer:
To find (f - g)(x), you need to subtract the function g(x) from the function f(x). The answer is -x^2 + 17x + 7.
Explanation:
To find (f - g)(x), we need to subtract the function g(x) from the function f(x).
Given f(x) = 10x + 7 and g(x) = x^2 - 7x, we substitute these values into (f - g)(x):
(f - g)(x) = f(x) - g(x) = (10x + 7) - (x^2 - 7x)
Expanding and simplifying, we get (f - g)(x) = -x^2 + 17x + 7.
Solve the following inequality.
9x−2>43
Answer:
x > 5
Step-by-step explanation:
Given
9x - 2 > 43 ( add 2 to both sides )
9x > 45 ( divide both sides by 9 )
x > 5
The solution to the inequality (9x - 2 > 43) is (x > 5).
To solve the inequality (9x - 2 > 43), follow these steps:
1. Add 2 to both sides of the inequality to isolate the term with x on one side:
[tex]\[ 9x - 2 + 2 > 43 + 2 \] \[ 9x > 45 \][/tex]
2. Divide both sides of the inequality by 9 to solve for x:
[tex]\[ \frac{9x}{9} > \frac{45}{9} \] \[ x > 5 \][/tex]
This means that any value of x greater than 5 will satisfy the original inequality. The solution set is all real numbers greater than 5.
7=x+3. What is being done to the variable?
Step-by-step explanation: If you take a look at the right side of the equation, a 3 is being added to our variable x.
If you were going to solve this equation, you must subtract 3 from the right side and the left side to isolate our variable.
You would end up with 4 = x.
How would you describe the location of the solutions in the
coordinate plane?
Answer:
The coordinates of a point are a pair of numbers that define its exact location on a two dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y axis. The coordinates of a given point represent how far along each axis the point is located.
Step-by-step explanation:
The location of solutions in the coordinate plane is described using a Cartesian coordinate system, involving movements either vertically (upward or downward) or horizontally (to the right or left) from the origin, represented by coordinates (x, y).
The location of the solutions in the coordinate plane can be described using a Cartesian coordinate system. This system is based on two perpendicular lines, the x-axis (horizontal) and the y-axis (vertical), intersecting at the origin (0,0). When we are looking at solutions on this grid, we can describe their positions in relation to the origin.
If a solution moves vertically upward from the origin, its y-coordinate increases while the x-coordinate remains the same.
Moving vertically downward means the y-coordinate decreases.
Horizontally to the right, the x-coordinate increases from the origin.
Horizontally to the left, the x-coordinate decreases.
The point at which the solution lies can be described by a pair of numbers, or coordinates, such as (x, y), where x is the position along the horizontal axis and y is the position along the vertical axis.
use an equation to find the value of k so that the line passes through (k,4) and (1,0) has a slope of m=-2
Answer:
(0-4)/(1-k)= -2
-4/(1-k)= -2
-2(1-k)= -4
-2 +2k = -4
2k = -2
k = -1
(-1, 4)
y - 4 = -2( x + 1)
y - 4 = -2x - 2
y = -2x + 2
40% of the memberships sold by Gym A were gold memberships.
25% of the memberships sold by Gym B were gold memberships.
Which statement must be true?
Answer:
a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.
Step-by-step explanation:
Here is the complete question: 40% of the memberships sold by Gym A were gold memberships. 25% of the memberships sold by Gym B were gold memberships.
Which statement must be true?
a) If both gyms sold 80 total memberships, Gym A sold 12 more gold membership.
b) If both gyms sold the same number of memberships, Gym A sold 15 more gold membership.
c) Gym A sold more gold membership than Gym A did.
d) If Gym B sold 50 membership, 25 would be gold memberships.
Given: Gym A have sold 40% gold membership of total membership.
Gym B have sold 25% gold membership of total membership.
Lets take option A first to find if it is true statement.
As per option A, There are total number of membership is 80.
∵ Gym A has sold 40% gold membership.
∴ Gym A gold membership= [tex]40\% \times 80[/tex]
⇒ Gym A gold membership= [tex]\frac{40}{100} \times 80= 32 member.[/tex]
∴ Gym A gold membership= 32.
Now, Gym B
∵ Gym B has sold 25% gold membership.
∴ Gym B gold membership= [tex]25\% \times 80[/tex]
⇒ Gym B gold membership= [tex]\frac{25}{100} \times 80=20 member.[/tex]
∴ Gym B gold membership= 20.
Next finding difference gold membership for Gym A and Gym B
[tex]32-20= 12 \ membership[/tex]
Hence, we can say option A is correct as Gym A have sold 12 more gold membership, if total number of membership sold by both Gym is 80.
Answer:maybve
Step-by-step explanation:
no
Solve for x: 2 over 5 (x − 4) = 2x. (1 point)
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
we have
[tex]\frac{2}{5}(x-4)=2x[/tex]
Solve for x
Multiply by 5 both sides
[tex]2(x-4)=10x[/tex]
Divide by 2 both sides
[tex]x-4=5x[/tex]
Subtract x both sides
[tex]x-4-x=5x-x[/tex]
[tex]-4=4x[/tex]
Divide by 4 both sides
[tex]x=-1[/tex]
A function is shown f=(x)=x^2+ 2X-3
show the X intercepts and maximum or minimum of the function
Answer:
x intercepts at (-3,0), and (1,0)
there is a minimum at (-1,-4)
Step-by-step explanation:
Please see attached image for the requested graph of the function [tex]f(x) = x^2+2x-3[/tex], and observe that the crossings of the x-axis are at the points (-3,0), and (1,0) , marked in red in the image.
We can also see that there is no maximum, but a minimum value, and located at the point (-1,-4) [marked in green in the image]
When Amy roller-skates, she moves 110 yards per minute. What is her speed in miles per hour? Round your answer to the nearest hundredth. (Hint: 1 yd= 3 ft; 5280 ft = 1 yd.; 60 min= 1 hr)
Answer:
Speed of Amy is 3.75 miles per hour.
Step-by-step explanation:
We have, speed of Amy = 110 yards per minute
This means, she covers 110 yards of distance in 1 minute.
Now, to convert the speed of Amy into miles per hour, we will first convert the distance from yards into miles and then convert time from minutes to hour.
We know that,
1 yard = 3 feet
∴ 110 yards = 3 × 110 feet = 330 feet
Now, we also know that,
5280 feet = 1 mile
∴ 1 feet = [tex]\frac{1}{5280}[/tex] miles
So, 330 feet = [tex]\frac{1}{5280}\times330[/tex] = [tex]\frac{1}{16}[/tex] miles
∴ 110 yards = 330 feet = [tex]\frac{1}{16}[/tex] miles
Now, 60 min = 1 hr
∴ 1 min = [tex]\frac{1}{60}[/tex] hrs
So, 110 yards = [tex]\frac{1}{16}[/tex] miles and 1 min = [tex]\frac{1}{60}[/tex] hr
So, we can say that, Amy covers a distance of [tex]\frac{1}{16}[/tex] miles in
[tex]\frac{1}{60}[/tex] hr.
We know that,
[tex]speed=\frac{distance}{time}[/tex]
[tex]speed=\frac{(\frac{1}{16}) miles}{(\frac{1}{60})hr}[/tex]
[tex]speed=\frac{60}{16} miles/hr = 3.75 miles/hr[/tex]
Therefore, the speed of Amy in miles/hr is 3.75 miles/hr.
Prime factorization of 1408
Answer:
There are 7 copies of 2 and 1 copy of 11 in the product:
1408 = 2^7×11
Step-by-step explanation:
Factor the following integer:
1408
The last digit of 1408 is 8, which means it is even. Therefore 1408 is divisible by 2:
1408 = 2 704:
1408 = 2×704
The last digit of 704 is 4, which means it is even. Therefore 704 is divisible by 2:
704 = 2 352:
1408 = 2×2×352
The last digit of 352 is 2, which means it is even. Therefore 352 is divisible by 2:
352 = 2 176:
1408 = 2×2×2×176
The last digit of 176 is 6, which means it is even. Therefore 176 is divisible by 2:
176 = 2 88:
1408 = 2×2×2×2×88
The last digit of 88 is 8, which means it is even. Therefore 88 is divisible by 2:
88 = 2 44:
1408 = 2×2×2×2×2×44
The last digit of 44 is 4, which means it is even. Therefore 44 is divisible by 2:
44 = 2 22:
1408 = 2×2×2×2×2×2×22
The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:
22 = 2 11:
1408 = 2×2×2×2×2×2×2×11
11 is not divisible by 2 since 11 is odd and 2 is even:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2)
The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2 or 3)
The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3 or 5)
Divide 7 into 11:
| | 1 | (quotient)
7 | 1 | 1 |
- | | 7 |
| | 4 | (remainder)
11 is not divisible by 7:
1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3, 5 or 7)
No primes less than 11 divide into it. Therefore 11 is prime:
1408 = 2×2×2×2×2×2×2×11
There are 7 copies of 2 and 1 copy of 11 in the product:
Answer: 1408 = 2^7×11
Final answer:
The prime factorization of 1408 is 2 raised to the power of 7 multiplied by 11, represented as 2^7 × 11. This is found by repeatedly dividing 1408 by 2 until we are left with the prime number 11, which cannot be divided further.
Explanation:
The prime factorization of 1408 involves breaking down the number into its prime factors until all the factors are prime numbers. To find the prime factors of 1408, we can use a factor tree or the method of division. We can start by dividing 1408 by the smallest prime number that divides it evenly, which is 2. If we keep dividing by 2, we get the following sequence of divisions:
1408 ÷ 2 = 704
704 ÷ 2 = 352
352 ÷ 2 = 176
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
Since 11 is a prime number, we cannot divide any further. Therefore, the prime factorization of 1408 is 27 × 11, since 2 was divided 7 times and 11 is the last prime factor found.
Ed Parker joined a health club. There was a $49 registration fee, and a $17.50 monthly fee. If Ed visits the club 2 times a week for a year, what does each workout cost him?
$ per visit.
Answer:
$2.49 per visit
Step-by-step explanation:
Mean or Average Value
It's referred to as the center of a numerical data set. In some circumstances, a list of values needs to be expressed as a single number who best represents them.
The registration fee of the health club is $49. It also charges a $17.50 monthly fee. In one year, the total cost will be $49 + 12*$17.50 = $259. If Ed Parker visits the club 2 times a week for a year, it will make an approximate of 2*52=104 visits a year. The mean cost by visit will be:
$259/104= $2.49 per visit
Answer:
3.55
Step-by-step explanation:
Juan fode his bike 2/3 mile to school,1/3 mile to the library,2/3 mile home far did he ride altogether
Answer:1 2/3
Step-by-step explanation:
2/3+1/3+2/3=5/3=1 2/3
I need the answer to the three questions I am struggling very hard to do this so I need help with the three questions
Answer:
Part 1) The slope is [tex]m=25[/tex] (the cost of the gym is $25 per month)
Part 2) The y-intercept is the point (0,-100) see the explanation
Part 3) [tex]y=25x-100[/tex], After 14 months the cost is [tex]\$250[/tex]
Step-by-step explanation:
Part 1) What is the slope of the line
Let
x ---> the number of months
y ---> the total cost in dollars
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
From the graph take two points
(0,-100) and (4,0)
substitute the values in the formula
[tex]m=\frac{0+100}{4-0}[/tex]
[tex]m=\frac{100}{4}[/tex]
[tex]m=25[/tex]
Remember that the slope is equal to the unit rate of the linear equation
That means ----> the cost of the gym is $25 per month
Part 2) What is the y-intercept of the line
we know that
The y-intercept is the value of y when the value of x is equal to zero
Looking at the graph the y-intercept is the point (0,-100)
In context this problem, the y-intercept represent the rebate of $100 that the gym was offering for sign up for a full year
Part 3) What is the linear equation for the line in this situation? What is the cost of the gym membership after 14 months
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]m=25[/tex]
[tex]b=-100[/tex]
substitute the values
[tex]y=25x-100[/tex]
For x=14 months
substitute
[tex]y=25(14)-100[/tex]
[tex]y=350-100=\$250[/tex]
I’m not to sure on how to find CEB can someone explain how to find it and what the answer would be,please
Answer:
m∠CEB is 55°
Step-by-step explanation:
Since ∠ADE = 55°, and ∠ADE is half of ∠ADC because ED bisects ∠ADC. Bisect means to cut in half.
∠ADC = 110° because it is double of ∠ADE.
Since AB║CD and AD║BC, the two sets of parallel lines means this shape is a parallelogram. In parallelograms, opposite angles have equal measures.
∠ADC = ∠CBE = 110°
All quadrilaterals have a sum of angles 360°. Since ∠DCB = ∠BAD and we know two of these other angles are each 110°:
360° - 2(110°) = 2(∠DCB)
∠DCB = 140°/2
∠DCB = ∠BAD = 70°
∠DCB was bisected by EC, which makes each divided part half.
∠DCE = ∠BCE = (1/2)(∠DCB)
∠DCE = ∠BCE = (1/2)(70°)
∠DCE = ∠BCE = 35°
All triangles' angles sum to 180°.
In ΔBCE, ∠BCE = 35° and ∠CBE = 110°.
∠CEB = 180° - (∠BCE + ∠CBE)
∠CEB = 180° - (35° + 110°)
∠CEB = 55°
Therefore m∠CEB is 55°.
What is the range of the function f(x) = –2|x + 1|?
all real numbers
all real numbers less than or equal to 0
all real numbers less than or equal to 1
all real numbers greater than or equal to 1
Answer:
Range [tex]\rightarrow[/tex] all real numbers less than or equal to 0 [tex]\rightarrow[/tex] ( - ∞ , 0 ]
Step-by-step explanation:
For visual understanding a graph of the function is attached with the answer.
For calculating the range of any modulus function you need to know that if modulus is there across any function then the output will be always positive.For example: x has a range of ( - ∞ , + ∞ ) but |x| has a range of [ 0 , + ∞ ). Similarly range of |x + 1| is [ 0 , + ∞ ).
If you multiply the modulus function with a negative sign then the output will always be negative.For example: Range of |x| is [ 0 , + ∞ ) but range of -|x| is ( - ∞ , 0 ]. Similarly range of -|x + 1| is ( - ∞ , 0 ]
Range in this case won't be affected on multiplying a positive constant with the modulus function.Therefore the range of f(x) = -2|x + 1| will be ( - ∞ , 0 ].
(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.
(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.
(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.
[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.
{a,b} means only 'a' and 'b'.
{a,b] or (a,b} doesn't mean anything. )
Answer:
B
Step-by-step explanation:
all real numbers less than or equal to 0
While on a business trip to Summerfield, Vera treated her co-workers to a meal that cost
$12. Vera knew that when the bill came, she would need to pay Summerfield sales tax of
11.75% and would want to leave a 15% tip on the original $12. Including tax and tip, how
much did Vera's meal cost?
Answer:
$15.21
Step-by-step explanation:
The tax and tip percentages are both being figured on the original bill amount, so they can be added. The tax and tip together come to ...
11.75% +15% = 26.75%
This is added to the original bill amount, so the final total will be ...
$12 + $12×0.2675 = $12×1.2675 = $15.21
Vera's meal cost $15.21.
UCULI
2 Points
When is a rhombus a square?
O
A. When its sides are parallel
B. When its angles are right angles
) C. When its angles are convex angles
O
D. When its sides are congruent
SUB
Answer:
B. When its angles are right angles.
Step-by-step explanation:
A rhombus is a quadrilateral with all 4 sides congruent. The sides can be slanted, which would keep it from being a square. If you make all the sides of a rhombus straight vertically and horizontally so you have 4 right angles, you have a square. A square is a quadrilateral with all 4 sides AND all 4 angles congruent.
Identify corresponding sides RGK=MQB
Final answer:
In geometry, corresponding sides are sides that have the same relative position in two similar figures. To identify the corresponding sides in the given question, we need to find the sides with the same position in the figures RGK and MQB. The corresponding sides of RGK and MQB are RG = MQ, RK = MB, and GK = QB.
Explanation:
In geometry, corresponding sides are sides that have the same relative position in two similar figures. To identify the corresponding sides in the given question, we need to find the sides with the same position in the figures RGK and MQB.
In this case, RGK and MQB are both triangles, so we need to compare their corresponding sides. The corresponding sides of a triangle are the sides that are in the same position (opposite vertices) in the two triangles.
Therefore, the corresponding sides of RGK and MQB are:
RG = MQ
RK = MB
GK = QB
In the figure shown, ABC is a right triangle with side lengths a, b, and c, and CD is an altitude to side AB. The side lengths of triangle ACD are b, h, and r, and the side lengths of triangle CBD are a, s, and h.
Which proportions are true?
A) c/a = a/s and c/b = b/r
B) c/a = s/a and c/b = r/b
C) c/b = a/s and c/a = b/r
D) c/b = s/a and c/a = r/b
Answer:
A
Step-by-step explanation:
In the figure shown, ABC is a right triangle with side lengths a, b, and c, and CD is an altitude to side AB. This altitude divides the triangle into two right triangles ADC and BDC. In these triangles,
[tex]\angle CBD\cong \angle ACD\cong \angle CBA[/tex][tex]\angle DCB\cong \angle DAC\cong \angle BAC[/tex]So,
[tex]\triangle ABC\sim \triangle CBD\sim \triangle ACD[/tex]
1. From the similarity [tex]\triangle ABC\sim \triangle CBD,[/tex] you have
[tex]\dfrac{AB}{BC}=\dfrac{BC}{BD}\\ \\\dfrac{c}{a}=\dfrac{a}{s}[/tex]
2. From the similarity [tex]\triangle ABC\sim \triangle ACD,[/tex] you have
[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}\\ \\\dfrac{c}{b}=\dfrac{b}{r}[/tex]
Hence, option A is true
Final answer:
The correct proportions for the right triangle ABC with altitude CD are c/a = b/r and c/b = a/s, derived from the similarity of the triangles ACD and CBD with triangle ABC.(Option c)
Explanation:
In the given right triangle ABC with altitude CD, we can apply similarity properties to find the true proportions related to the side lengths labeled a, b, and c, and the segments of the altitude, labeled h, r, and s. To solve the problem, we can consider the two right triangles ACD and CBD created by drawing altitude CD. Since these triangles are similar to ABC, their corresponding side ratios will be equal.
Applying the similarity of triangles (Theorem 22), two sets of proportions become evident:
Triangle ACD is similar to triangle ABC, which leads to the proportions:These proportions come from setting the sides of the smaller triangles against the hypotenuse c of the larger triangle ABC and using corresponding sides of similar triangles. Thus, the correct answer is that the true proportions are c/a = b/r and c/b = a/s, which match option C) in the question.
Which function has a domain of x 25 and a range of y s3?
g= x-5+3
9 = x+5 -3
y=-x-5+3
y=-x+5 -3
Answer:
[tex]y = - \sqrt{x - 5} + 3[/tex]
Step-by-step explanation:
The function [tex]y = - \sqrt{x - 5} + 3[/tex] has a domain x ≥ 5.
This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.
Hence, (x - 5) ≥ 0
⇒ x ≥ 5
Now, for all x values that are greater than equal to 5 the value of [tex]- \sqrt{x - 5}[/tex] will be negative.
So, [tex]- \sqrt{x - 5} \leq 0[/tex]
⇒ [tex]- \sqrt{x - 5} + 3 \leq 3[/tex]
⇒ y ≤ 3
Therefore, the range of the function is y ≤ 3. (Answer)
A rectangle has a height of 2y^3+5 and a width of y^3+6y.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answer:
in polynomial form
Step-by-step explanation:
if you have any question then reply me
The area of the rectangle can be found by multiplying its width by its height, which is a polynomial expression in this case.
Explanation:To find the area of a rectangle, we multiply its width by its height. In this case, the width of the rectangle is y3+6y and the height is 2y3+5. So, the area of the rectangle is:
A = width × height
A = (y3+6y) × (2y3+5)
A = 2y^6 + 5y^3 + 12y^4 + 30y
This is the area of the entire rectangle, expressed as a polynomial in standard form.
Learn more about Finding the area of a rectanglehttps://brainly.com/question/35549815
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