Answer: Negative two times z plus eight.
Step-by-step explanation:
The expression $-2z + 8$ represents "negative two times the quantity of z plus 8". To interpret this as a phrase, we can say "8 increased by the negative of two times the quantity of z."
construct triangle ABC if AB=8cm ABC=60degree and BC=6cm. measureA. measure AC
We kindly invite to check the image attached below to see the triangle constructed on Cartesian plane.
The measure of angle A is approximately equal to 46.102° and the measure of side AC is equal to 2√13 centimeters.
How to construct a triangle and determine missing angles and sides
Triangles are figures generated by three distinct points set on Cartesian plane, with three line segments (AB, BC, AC) and three internal angles. In this problem we show all steps to construct a triangle with the help of a graphing tool. First, set point B at origin.
B(x, y) = (0, 0)
Second, add point C along x-axis:
C(x, y) = (6, 0)
Third, determine point A and add it on Cartesian plane:
A(x, y) = (8 · cos 60°, 8 · sin 60°)
A(x, y) = (4, 6.928)
Fourth, draw all line segments in triangle ABC. The result is shown in the image attached below.
Finally, we determine the measure of angle A and side AC by trigonometry:
Angle A:
First, determine the length of line segment AC by law of cosine:
AC = √(AB² + BC² - 2 · AB ·BC · cos B)
AC = √(8² + 6² - 2 · 8 · 6 · cos 60°)
AC = 2√13
Second, calculate the angle A by law of cosine:
cos A = (BC² - AB² - AC²) / (- 2 · AB · AC)
cos A = [6² - 8² - (2√13)²] / [- 2 · 8 · 2√13]
A ≈ 46.102°
Side AC:
AC = 2√13
To learn more on triangles: https://brainly.com/question/17289163
#SPJ1
18. The numbers 1, 4, 9, 16, 25, 36...... are examples of ________________________
Step-by-step explanation:
squared numbers.
1 = 1² = 1×1
4 = 2² = 2×2
9 = 3² = 3×3
16 = 4² = 4×4
25 = 5² = 5×5
36 = 6² = 6×6
Enter the letter for the function graphed
below.
4
a) y = √x-5
b) y = √x - 5
c)y = 5-√√x
d) y = √x + 5
e) y = √x + 5
Answer:
C.
Step-by-step explanation:
correct answer is C:
[tex]y=5-\sqrt{x} ;[/tex]
where -sqrt(x) means one half of quadratic parabola, +5 means moving up the curve.
Please help me answer this
Extra points
Step-by-step explanation:
All you have to do is distribute the 2 and -2 to the inside of the parentheses. When you multiply it out, then combine all of your like terms, but remember to include the negative sign in the second set of parentheses.
2(7x+5)-2(4x+3)
(2*7x)+(2*5)-(2*4x)-(2*3)
14x+10-8x-6
This is the correct answer, but if you want to simplify it further, the answer would be 6x+4.
Option:-
[tex] \underline{ {\boxed{ \rm{ \red{\bold{C ) 14x + 10 - 8x - 6}}}}}}[/tex]
Ans:-
[tex] \rm{14x + 10 - 8x - 6}[/tex][tex] \: [/tex]
[tex] \rm{2( 7x + 5 ) - 2 ( 4x + 3 )}[/tex][tex] \: [/tex]
hope it helps! :)
Exit Ticket: At many county and state fairs, you must purchase
tickets if you wish to go on the rides. Different rides require
different numbers of tickets. The Ferris wheel, for example,
might require three tickets, while the bumper cars might require
two. Before you buy any tickets, it might be helpful to know
which rides you plan to ride, and how many tickets you will need.
Write about it! Each ride requires 3 tickets. If a ticket costs
$1.50, write an equation to find the total cost of y of x rides.
How much will it cost to ride 10 rides?
An equation to find the total cost of y of x rides is y = 3x.
The cost to ride 10 rides is equal to $15.
How to determine the total cost of y of x rides?In order to write an equation that model this situation, we would assign variables to the number of tickets and the total cost respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of tickets.Let the variable y represent the total cost.Next, we would translate the word problem into an algebraic equation based on the fact that each ride requires 3 tickets and a ticket costs $1.50 as follows;
y = 3x
For the cost of 10 rides, we have:
y = 10x
When x = 1.50, the total cost is given by:
y = 10(1.50)
y = $15.
Read more on equations here: brainly.com/question/3382177
#SPJ1
Drag each sentence to the correct category.
Determine the type of account that each description applies to.
If no deposits or withdrawals
are made, money held in this
account may increase or
decrease.
There is no risk of losing any
money put in this account.
Interest income is the only
way to earn money in this
type of account.
This account may generate
income from a variety of
sources.
Saving Account : Option B and Option C
Investment account : Option A and Option D.
Explain the terms Saving Account and Investment account?The savings account is an account of deposit account at which money you deposit earns interest. Savings accounts are trustworthy and secure given that they are insured accounts.An account that can store both cash and other investments that can be purchased and traded for financing is characterized as an investment account.Savings Account:
In this account, there is no chance that any money would be lost. An interestThe only method to make money in this kind of account is through income.Investment Account:
Money maintained in this account could rise or fall if no deposits or withdrawals are made.A number of sources may produce money for this account.To know more about the Saving Account, here
https://brainly.com/question/25787382
#SPJ1
The correct question is:
The table given in a similar question sourced on the site is presented as follows;
Saving Account || investment account
The options are;
A. If no deposit or withdrawals are made, money held in this account may increase or decrease
B. There is no risk of losing any money put in this account
C. Interest income is the only way to earn money in this type of account
D.This account may generate income from a variety of sources
If you run around a half-mile track at some average speed (s)( in miles per hour), at what average speed would you need to run a second lap to make your overall average three times as much as it was for the first lap?
Answer:
To calculate the average speed for the second lap, we need to know the overall average speed for the two laps. If the average speed for the first lap is s, then the overall average speed for the two laps is (s + x)/2, where x is the average speed for the second lap.
We are told that the overall average speed for the two laps is three times the average speed for the first lap, so we can set up the following equation:
(s + x)/2 = 3s
To solve for x, we can multiply both sides of the equation by 2:
s + x = 6s
Subtracting s from both sides:
x = 5s
So, to make the overall average speed for the two laps three times the average speed for the first lap, the average speed for the second lap should be 5 times the average speed for the first lap.
Define random error. Define random error. Random error has values that are consistent with one another. Random error has no probability of being too high or too low. Random error is an error that tends to be either too high or too low. Random error has an equal probability of being too high or too low. Random error has values that are close to the true value.
Define random error: B) Random error is an error that tends to be either too high or too low.
WHAT IS RANDOM ERRORRandom error, is an error caused by factors that cannot be predicted, you could even say that these factors seem temporary.
So, it is very difficult to predict, because it is still random. One might even say, this random error occurred, while the test was being conducted. Even worse, random errors do not have to occur in the first test, it could be in the second or third test and so on.
Random error is a very small and dissimilar effect in each test implementation, for example the effect of fluctuations in the voltage, temperature or humidity conditions of the accommodation and test environment.
Learn more about random error at
https://brainly.com/question/29445533.
#SPJ4
2. Refer to the figure to complete this proportion.
? b
bs
h
S
b
Area of a Triangle = A = ½ (b × h) square units
where b and h are the base and height of the triangle, respectively. Now, let's see how to calculate the area of a triangle using the given formula.
Define right triangle?
Right Triangle. A right triangle is a triangle with one right angle (one angle equal to 90°). The side opposite the right angle (the longest side) is called the hypotenuse. The remaining two sides (the sides that intersect to determine the right angle) are called the legs of the right triangle.A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.Theorem:In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. To prove: ∠B = 90° Proof: We have a Δ ABC in which AC2 = AB2 + BC2.To learn more about right triangle refers to:
https://brainly.com/question/19026964
#SPJ1
The correct ratio of right angled triangle is [tex]\frac{c}{b} = \frac{b}{s}[/tex]
There are a few unique varieties of right triangles, including the 45°-45° and the 30°-60° varieties.
Theorem: In a triangle, the angle across from the first side is a right angle if the square of one side equals the sum of the squares of the other two sides. To demonstrate: B=90° Proof: ABC has the formula [tex]AC^2 = AB^2 + BC^2[/tex]
The right triangle. A triangle with one right angle, or 90°, is referred to as a right triangle. The longest side, which is the side opposite the right angle, is referred to as the hypotenuse. The remaining two sides are referred to as the right triangle's legs because they intersect to form the right angle.
The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle. [tex]AC^2 = AB^2 + BC^2[/tex]
Given,
b/s = ratio of hypotenuse to height
c / b = ratio of hypotenuse to height
To learn more about right triangle refer to:
https://brainly.com/question/6322314
#SPJ1
how have surface processes shaped the landforms on earth? (not multiple choice)
What is the result when the number 32 is decreased by 25%?
Answer: 69 bozo LLLLLLLLLLLLLLLLLLLLLLLLLLL
Step-by-step explanation:
69
Please help me with this question.
The radius of the circle having an equation x²+ y²-10x+6y-47 = 0 is 9 units.
What is the radius of a circle?The radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary.
Given the general form of the equation of circle described as
x²+ y²-10x+6y-47 = 0, we need to find it radius,
The given equation is;
x²+ y²-10x+6y-47 = 0
Complete the squares so add 25 and 9 on both sides of the equation
x²+ y²-10x+6y-47+25+9 = 34
(x-5)² + (y+3)² -47 = 34
(x-5)² + (y+3)² = 81
(x-5)² + (y+3)² = 9²
Comparing with the standard form of the equation of a circle is (x - h)² + (y - k)² = r²,
r² = 9²
r = 9
Hence, the radius of the circle having an equation x²+ y²-10x+6y-47 = 0 is 9 units.
Learn more about radius, click;
https://brainly.com/question/13449316
#SPJ1
the passenger section of a train has width 2x-7, length 2x+3, and height x-2, with all dimensions in meters. solve a polynomial equation to determine the dimensions of the section of the train if the volume is 117m3
The polynomial equation is 4x³ - 16x² - 5x - 75 = 0.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The passenger section of a train has a width of (2x - 7), a length of (2x + 3), and a height of (x - 2).
Now,
Volume = 117 m³
Length x width x height = 117
(2x + 3) x (2x - 7) x (x - 2) = 117
(2x + 3) x (2x² - 4x - 7x + 14 = 117
(2x + 3) x (2x² - 11x + 14) = 117
4x³ - 22x² + 28x + 6x² - 33x + 42 = 117
4x³ - 16x² - 5x - 75 = 0
Thus,
The equation is
4x³ - 16x² - 5x - 75 = 0
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Which point best approximates the location of 78√?
point B
point A
point D
point C
The point that best approximates the square root of 78 is a point that is between 8 and 9.
How to estimate a non-exact square root?The estimate of a non-exact square root of x is done finding these two numbers listed as follows:
The greatest number less than x that is a perfect square(i.e., it has an exact square root), which we call a.The smallest number greater than x that is a perfect square(i.e., it has an exact square root), which we call b.For this problem, we have that these two parameters are given as follows:
8² = 64 < 78.9² = 81 > 78.Hence the point that best approximates the location of the square root of 78 is a point between 8 and 9.
More can be learned about the estimation of the non-exact square root of a number at brainly.com/question/28734995
#SPJ1
whitch figure is showig a ray
Answer: D.
Step-by-step explanation: It is a figure with no height or length, and it has indefinite length. Two rays are needed to make an angle.
Given any real number, there is a real number that is greater. a. Given any real number r, there is __________ s such that s is _______. b. For any _____, ______ such that s > r.
(a) Given any real number r, there is a real number s such that s is greater than r.
(b) For any real number r, there exists a real number s such that s > r.
(a) For some real number r, there exists another real number s such that s is greater than r.
Complete statement is, Given any real number r, there is a real number s such that s is greater than r.
(b) For real number r, there exists another real number s such that s is greater than r, represented as s> r.
Complete statement is, For any real number r, there exists a real number s such that s>r.
To know more about the real numbers, here
brainly.com/question/9876116
#SPJ4
The Dell Computer Company makes its own computers and delivers them directly to customers who order them via the Internet. To achieve its objective of speed, Dell makes each of its five most popular computers and transports them to warehouses from which it generally takes one day to deliver a computer to the customer. This strategy requires high levels of inventory that add considerably to the cost. To lower these costs the operations manager wants to use an inventory model. He notes demand during lead time is normally distributed and he needs to know the mean to compute the optimum inventory level. He observes 25 lead time periods and records the demand during each period. The manager would like a 95% confidence interval estimate of the mean demand during lead time. Assume that the manager knows that the standard deviation is 75 computers. Construct and interpret the confidence Interval Estimator.
The 95% confidence interval estimate of the mean demand during lead time is given as follows:
[tex]\overline{x} \pm 29.4[/tex]
The interpretation is that we are 95% sure that the sample mean is within 29.4 computers of the population mean.
What is a z-distribution confidence interval?The bounds of the confidence interval are given by the equation presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are given as follows:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameter values are given as follows:
[tex]\sigma = 75, n = 25[/tex]
Hence the interval is given as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]\overline{x} \pm 1.96 \times \frac{75}{\sqrt{25}}[/tex]
[tex]\overline{x} \pm 29.4[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Help thank you! A B C or D
Answer:
below
Step-by-step explanation:
'x' cannot be zero because you would then have an illegal fraction with a zero denominator
the only interval listed that does not include zero is ( 1, +inf)
Answer:
D.
Step-by-step explanation:
f(x) = |x|
|x| = x for x > or = 0
|x| = -x for x < 0
At x = 0
Left limit = Right limit = Function value = 0
|x| = is continuous at x = 0.
Left derivative (at x = 0) = -1
Right derivative (at x = 0) = 1
tumor is injected with 0.92
grams of Iodine-125. After 1 day, the amount of Iodine-125 has decreased by 1.15%
.
Write an exponential decay model with A(t)
representing the amount of Iodine-125 remaining in the tumor after t
days. Enclose arguments of the function in parentheses and include a multiplication sign between terms. For example, c*ln(t)
.
Then use the formula for A(t)
to find the amount of Iodine-125 that would remain in the tumor after 8.5
days. Round your answer to the nearest thousandth (3 decimal places) of a gram.
Answer:
A(t) = 0.92e^(-0.0115t)
The amount of Iodine-125 that would remain in the tumor after 8.5 days is 0.58 grams.
Step-by-step explanation:
A(t) = 0.92e^(-0.0115t)
To find the amount of Iodine-125 that would remain in the tumor after 8.5 days, we can plug in 8.5 for t in the exponential decay model:
A(8.5) = 0.92e^(-0.0115 * 8.5) = 0.92e^(-0.097875) = 0.92 * 0.9079 = 0.832
So, the amount of Iodine-125 that would remain in the tumor after 8.5 days is approximately 0.832 grams.
HELP I NEED ANSWER ASAP
The rule that best describes the dilation of triangle ABC to create triangle A'B'C' is given as follows:
a. (x,y) -> (2x, 2y).
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Considering a scale factor of k, the rule is given as follows:
(x,y) -> (kx, ky).
The scale factor for this problem is given as follows:
k = 2.
(as the larger triangle is formed as a dilation of the smaller triangle).
Hence the rule is given as follows:
(x,y) -> (2x, 2y).
Meaning that the correct option is given by option A.
More can be learned about dilation at brainly.com/question/3457976
#SPJ1
Please help me solve this
Extra points
Amber wrapped a gift for her daughter. The gift is shapped like a rectangular prism. Its base measures 9 inches by 0.5 feet. Part A: Amberly used exactly 408 square inches of paper to wrap the gift. Explain how tall the gift is assuming the paper does not overlap
Answer:
The gift is 4.5 feet tall, since 408 square inches is equal to a rectangular prism with dimensions of 9 inches by 0.5 feet by 4.5 feet.
Step-by-step explanation:
need help please, here is screenshot
A conversion of the expression (x - 3)² + 1 to the standard form of a quadratic function is x² - 6x + 10.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.
In Mathematics, the standard form of a quadratic function is given by ax² + bx + c = 0.
By applying the following binomial expression to the given quadratic function, we have:
(a - b)² = a² - 2ab + b²
(x - 3)² = x² - 2(x)(3) + 9
x² - 2(x)(3) + 9 = x² - 6x + 9
Therefore, the given expression can be rewritten as follows;
(x - 3)² + 1 = x² - 6x + 9 + 1
(x - 3)² + 1 = x² - 6x + 10.
Read more on quadratic functions here: brainly.com/question/24020644
#SPJ1
Tiffany has a goal to complete a triathlon. The race consists of a 2.4 -mile swim, a 112 -mile bike ride, and a 26.2 -mile run. In training, Tiffany can swim at an average pace of 2.2mph . She rides her bike at an average of 20.8mph and runs at 6.2mph . Estimate how long it will take her to complete the triathlon.
Answer:
10.7 hrs
Step-by-step explanation:
For each of the three legs time = distance / rate
so
2.4 / 2.2 + 112 / 20.8 + 26.2 /6.2 = 10.7 hrs
Part E
For any diagonal line segment on the coordinate grid, you can create two triangles that have the line segment as the hypotenuse. Are the lengths of the vertical line segments the same for both triangles? Are the lengths of the horizontal line segments the same for both triangles? What does that mean?
The triangle was created, using a diagonal as a hypotenuse, where the length of the horizontal and vertical lines is similar.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Step to create the triangle,
1. Draw a horizontal line parallel to the x-axis from the endpoints of the diagonal.
2. Draw a vertical line parallel to the y-axis from the endpoints of the diagonal.
3. The intersection point of these horizontal and vertical lines is the vertex of the triangle formed and the diagonal line is the common hypotenuse between the triangle.
4. When measuring the horizontal and vertical lines we will see they are equal for both the triangle formed.
Thus, the triangle was created, using a diagonal as a hypotenuse, where the length of the horizontal and vertical lines is similar.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
I have added a screenshot.
Answer:
none of the above
Step-by-step explanation:
May someone pls help me with this question? Thank you <3
Answer:
$100
Step-by-step explanation:
Use the example above and fill in the missing values.
Consider a three-year loan (so we'll assume the numbers 1 through 36) for $5,000 with interest at 10% per year. Using
standard amortization, the monthly payment is $161.33. In this example, we will not worry about exact or ordinary
interest because the total Interest to be paid is $808.13.
After the fifth month, the borrower decides to prepay the whole loan. Under a stándard amortization plan the borrower
would have paid $198.28 in cumulative interest. However, using the Rule of 78 a lender would calculate the fraction of
the total interest based on two series:
((n+35)+(n+34)+(n+33)+(n+32)+(n+31))
If you add 36, 35, 34, 33, and 32, the sum is
If you sum the numbers from 1 to 36, the sum is
{(n)+(n+1)+...+(n+35)}
The fraction (the first sum / the total sum) to the nearest tenth =
total interest.
%. The lender will multiply this fraction by the
The cumulative interest = (the percentage calculated above) x ($808.13) = $
The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78
plan is: $
The sum of the numbers 36, 35, 34, 33, and 32 is 36 + 35 + 34 + 33 + 32 = 160.
The sum of the numbers from 1 to 36 is (1 + 36) * 36 / 2 = 666.
The fraction (160 / 666) to the nearest tenth is 0.237, or 23.7%.
The cumulative interest using the Rule of 78 is (0.237 * $808.13) = $191.63.
The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is ($198.28 - $191.63) = $6.65.
What is a cumulative interest?Cumulative interest is the total amount of interest that has been accumulated on a loan or an investment over a certain period of time. It is the sum of all the interest charges that have been added to the original loan amount, and it increases with each passing period as interest is charged on the increasing balance.
This means that the cumulative interest will be higher at the end of a loan period than at the beginning, as more interest will have been charged. The cumulative interest can be used to calculate the total cost of a loan, including the interest charged, as well as to compare different loan or investment options.
learn more about cumulative interest: https://brainly.com/question/28020457
#SPJ1
A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of three popular options, air-conditioning (A), radio (R), and power windows (W), were already installed. The survey found:
15 had air-conditioning (A),
12 had radio (R),
11 had power windows (W),
5 had A and P,
9 had A and R,
4 had R and W,
3 had all three options.
A. Construct a Venn diagram to illustrate the sets.
Answer:
Step-by-step explanation:
15-12=03
3X 11 =33
33-5=28
28-9=19
19-3=16
16 divided by 4= 4
so the awser is 4
a square of area 81cm2 is cut to make 2 rectangles
Answer:
rectangle A
length = 9cm
width = 6cm
rectangle B
length = 9cm
width = 3cm
Step-by-step explanation:
