if PA=14 and PD=10 what is the length of PC
To find the length of PC when PA=14 and PD=10, apply the cosine rule formula in trigonometry.
The length of PC can be calculated using trigonometry and the given information.
Since PA=14 and PD=10, we can use the cosine rule to find the length of PC.Applying the cosine rule formula, PC = √(PA2 + PD2 - 2*PA*PD*cos(θ)).Calculate the length of PC by substituting the values: PC = √(142 + 102 - 2*14*10*cos(θ)).John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel. Write an equation to determine the total number of pages (p) in the novel. And find the total number of pages in the novel
Answer:
351
Step-by-step explanation:
If we add 3 pages to 114, we get a number that is [tex]\frac{1}{3}[/tex] the total number of pages in the novel (p). Thus, we can write:
[tex]114+3=\frac{1}{3}p[/tex]
Solving for p gives us the total number of pages in the novel. So:
[tex]114+3=\frac{1}{3}p\\117=\frac{1}{3}p\\p=\frac{117}{\frac{1}{3}}\\p=117*3=351[/tex]
Thus, total number of pages in the novel is 351.
which of the following describes the quotient of 2 and -12?
Walter had 2/4 yard of string. He used 3/6 of it on a school project. How much string did he use?
2/4 reduces to 1/2
3/6 reduces to 1/2
so he used 1/2 of 1/2 yard
1/2 * 1/2 = 1/4
he used 1/4 yard
You have a 5" by 7" photo that you would like to have enlarged to fit an 8" by 10" frame. Would the two photographs be similar? Explain
How can the order of operations be used to simplify expressions?
What is the slope of a line that is perpendicular to the line whose equation is 8y−5x=118y−5x=11?
Answer:
The slope of a line that is perpendicular to the line whose equation is [tex]8y-5x=11[/tex] is [tex]m=-\frac{8}{5}[/tex]
Step-by-step explanation:
Given : Equation [tex]8y-5x=11[/tex]
To find : What is the slope of a line that is perpendicular to the line whose equation is given?
Solution :
First we find the slope of the given line,
The general slope form of line is [tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept.
Re-write the given equation into general form,
[tex]8y-5x=11[/tex]
Take 5x to another side,
[tex]8y=5x+11[/tex]
Divide both side by 8,
[tex]y=\frac{5}{8}x+\frac{11}{8}[/tex]
On comparing with general form,
The slope of the line is [tex]m=\frac{5}{8}[/tex]
We know,
When two line are perpendicular one slope is negative reciprocal of another.
If the slope of line is [tex]m=\frac{5}{8}[/tex]
Then the slope of perpendicular line on this line is [tex]m=-\frac{8}{5}[/tex]
Therefore, The slope of a line that is perpendicular to the line whose equation is [tex]8y-5x=11[/tex] is [tex]m=-\frac{8}{5}[/tex]
According to the chart, from 1976-1986, unintentional drug overdose deaths per 100,000 population stayed relatively stable. The numbers for each year are, roughly, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2. What is the mean of these statistics?
Answer: 1.09
Step-by-step explanation:
Given that according to a chart from 1976-1986, unintentional drug overdose deaths per 100,000 population stayed relatively stable.
The numbers for each year are, roughly, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2.
We know that mean =[tex]\frac{\text{sum of all data values}}{\text{number of data values}}[/tex]
[tex]\\\Rightarrow\text{Mean}=\frac{1+1+1+1+1+1+1+1+1+1+2}{11}\\=\frac{12}{11}=1.09[/tex]
Thus the means of these statistics= 1.09
Why do some merchants, particularly smaller businesses, set a minimum purchase of $10 for any credit card transaction, or simply refuse to take any sort of bank card from consumers?
Answer:
Just look at the one above me
Step-by-step explanation:
Use <,>,or = to compare 0.36 and 0.4.
(05.01)A company makes triangular plates for individual slices of pizza. For each plate, the base is 9 inches and the height is 14 inches. The area of the top of the plate is ____ inches squared.
Answer:
63
Step-by-step explanation:
Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection?
ANSWER- 0.1(175-n)+0.05n=13.30
Answer:
The equation we can use is 0.1(175-n)+0.05 n=13.30
Step-by-step explanation:
Number of Dimes= d
Number of Nickels= n
n+d=175, so d=175-n
The value of the dime is $0.10 and the value of each nickel is $0.05 and the whole collection is worth $13.30, so
0.1 d+0.05 n=13.30
Replacing
0.1(175-n)+0.05 n=13.30 this is the equation we have to use to get the number of nickels.
Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below. x – y = 7 3x – 2y = 8 Step 1: x = y + 7 Step 2: 3(y + 7) – 2y = 8 Step 3: 3y + 7 – 2y = 8 Step 4: y + 7 = 8 Step 5: y = 1 In which step did Ernesto make the first error?
Answer:
answer C
Step-by-step explanation:
Question 4(Multiple Choice Worth 5 points)
(05.03 MC)A graph is shown below:
A graph is shown. The values on the x axis are 0, 3, 6, 9, 12, and 15. The values on the y axis are 0, 9, 18, 27, 36, and 45. Points are shown on ordered pairs 0, 36 and 3, 27 and 6, 18 and 9, 9 and 12, 0. These points are connected by a line
What is the equation of the line in slope-intercept form?
y = 36x − 3
y = −3x + 36
y = −3x + 12
y = −12x + 3
Answer:
y = -3x + 36
Step-by-step explanation:
first let's start with a formula.
y = mx + b
m equals the slope and b equals the y intercept.
slope can also be indetified as a rate of change.
so, looking at the graph we can see that the y intercept is (0, 36) or 36 and the rate of change is 3 subtracted.
sorry if this is wrong im not too sure myself. and sorry this is 5 years late, but alas it's too late to turn back now since i have already wrote all this.
A restaurant catered a party for 40 people. A child’s dinner (c) cost $11 and an adult’s dinner (a) cost $20. The total cost of the dinner was $728. How many children and adults were at the party? Use the table to guess and check.
8 children and 32 adults
9 children and 31 adults
10 children and 30 adults
12 children and 28 adults
a+c=40
c=40-a
11c +20a=728
11(40-a)+20a=728
440-11a +20a=728
440+9a=728
9a = 288
a=288/9 = 32
32 adults
8 children
(Write the rate as a fraction, then find each unit rate.)
A wheel rotates through 1,800 degrees in 5 revolutions.
From the computation, the rate per revolution will be 360°.
From the information given, it was stated that the wheel rotates through 1,800 degrees in 5 revolutions.
Therefore, the rate per revolution will be:
= 1800/5
= 360°
Therefore, the rate per revolution is 360°.
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A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket
If x = 49 , what is the value of x(x-10)
replace 49 for x so
x(x-10) becomes 49(49-10) =
49*39 = 1911
which statement is always true about an isosceles triangle A.it has 1 right angle B.it has 2 congruent angles C.it has no sides that are congruent D.the sum of all 3 angles in 360 degrees
It has 2 congruent angles, is always true about an isosceles triangle
What is Isosceles Triangle?
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
Angles of Isosceles Triangle:Contrary to the equal sides, two of the isosceles triangle's three angles have equal measures. One of the angles is therefore not equal. Assume that if we are given the measure of an unequal angle, we can quickly determine the other two angles using the angle sum property.
Properties of Isosceles Triangle:Since this triangle's two sides are equal, the base of the triangle is the side that is not equal.
The triangle's two equal sides' opposing angles are always equal.
The vertex (topmost point) of an isosceles triangle is where the altitude of the triangle is calculated.
The third angle of a right isosceles triangle is 90 degrees.
Hence, the answer (b) it has 2 congruent angles
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NEED HELP ASAP DUE TOMORROW AND ITS REALLY LATE WHERE I AM
How much is Pete's 12% commission on $50,00 in sales
The table shows the estimated number of deer living in a forest over a five-year period. Which type of function best models the data? Write an equation to model the data. Year Estimated Population 0 100 1 79 2 62 3 49 4 39
We are given the following data:
Year Estimated Population
0 100
1 79
2 62
3 49
4 39
Just by looking at the data we can see that the relationship of year and estimated population is not linear. The decrease in the population does not follow a linear path, that is:
79 – 100 is not equal to 62 – 79
-21 is not equal to -17
Therefore, the relationship must be exponential. Let us find the common ratio by dividing the population in year 1 and year 0:
common ratio, r = 79 / 100 = 0.79
This means that the population decreases by 21% every year.
So the model for this data can be written as:
yn = y0 * r^n
Where,
yn = is the population after n years
y0 = initial population
r = growth rate = decreasing
n = number of years
The following data points represent the number of chicken nuggets on each family member's plate. 1, 3, 0, 6? If the mean of the data set is 3 chicken nuggets, find the missing number of chicken nuggets.
The missing number of chicken nuggets will be 5.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
The following data points represent the number of chicken nuggets on each family member's plate.
1, 3, 0, 6, x
If the mean of the data set is 3 chicken nuggets. Then the missing number of chicken nuggets is calculated as,
3 = (1 + 3 + 0 + 6 + x) / 5
15 = 10 + x
x = 5
The missing number of chicken nuggets will be 5.
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You invest $300 in an account at 7.5% per year simple interest. How much will you have in the account at the beginning of the 11th year
By investing $300 at a 7.5% per year simple interest rate, the accrued interest over 11 years is $247.50. Adding this to the initial investment, the total in the account at the beginning of the 11th year will be $547.50.
To determine how much you will have in an account at the beginning of the 11th year with simple interest, you can use the formula for simple interest:
Simple Interest (I) = P × r × t
Where:
P is the principal amount ($300)r is the annual interest rate (7.5% or 0.075)t is the time in years (11 years)Let's calculate the simple interest first:
I = 300 × 0.075 × 11I = 247.50So, the interest earned over 11 years is $247.50. Now, add this to the principal amount to get the total amount in the account at the beginning of the 11th year:
Total Amount = Principal + Interest
Total Amount = 300 + 247.50
Total Amount = 547.50
what is the probability of flipping a coin 10 times and getting tails8 times? Round your answer to the nearest tenth of a percent
Answer:
4.4%
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line whose equation is 7x−3y=107x−3y=10?
Simplify by combining like terms: -18 + 3 (5x - 2) + 8
Please help me!! find the solution of this system of equations -x + 5y=-18 5x - 9y= 10
A television costs $270.25 including 15% tax. How much of cost is the tax
Final answer:
The tax on the television is $35.25.
Explanation:
To find the amount of tax, we first need to determine the original cost of the television. Since the total cost, including tax, is $270.25, we can set up the equation:
$270.25 = x + 0.15x
Where x is the original cost of the television. Combining like terms, we get:
$270.25 = 1.15x
To solve for x, divide both sides of the equation by 1.15:
x = $270.25 ÷ 1.15
Using a calculator, we find that x is approximately $235.00. Therefore, the tax on the television is:
$270.25 - $235.00 = $35.25
(k^3-8k^2+16k-5)/(k-5)
please use the "dividing polynomials format WILL GIVE BRAINIEST
if you do not use this format you will not become brainliest
The longest straight line that can be drawn to connect two point on the circumference of a circle whose radius is 9 inches is
Answer:
18 inches.
Step-by-step explanation:
We can connect two points of a circle in many ways, as you can see in the picture below.
The longest straight line that you can draw to connect two points is the diameter, that is, the straight line that passes through the center of the circle.
If the circle has 9 inches of radius the diameter will be 9+9 = 18 inches.