Answer:
PR = 39 cm
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
PR² + PQ² = QR² , that is
PR² + 80² = 89²
PR² + 6400 = 7921 ( subtract 6400 from both sides )
PR² = 1521 ( take the square root of both sides )
PR = [tex]\sqrt{1521}[/tex] = 39
Answer:
[tex]PR=39[/tex]
Step-by-step explanation:
The triangle (PQR) is a right triangle. This means the triangle has a (90) degree angle, such is indicated by the box around one of the angles in the triangle. One of the properties of the sides of a right triangle is the Pythagorean theorem. The Pythagorean theorem states the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs of the right triangle, or the sides adjacent to the right angle. (c) is the side opposite the right angle of the triangle triangle, in other words, the hypotenuse. Substitute the respective legs into the formula for the Pythagorean theorem and solve for the unknown,
[tex]a^2+b^2=c^2[/tex]
Substitute,
[tex]a^2+b^2=c^2[/tex]
[tex]PQ^2+PR^2=QR^2[/tex]
[tex]80^2+PR^2=89^2\\[/tex]
Simplify,
[tex]80^2+PR^2=89^2\\[/tex]
[tex]6400+PR^2=7921[/tex]
Inverse operations,
[tex]6400+PR^2=7921[/tex]
[tex]PR^2=1521\\\\PR=39[/tex]
which of the following represents 10 on a number line
Answer:
don't understand....................
Jeremy is buying a new car. The total cost, including tax, is $18275. If the tax rate is 7.5% , what is the sticker price of the car?
Answer:
$17000
Step-by-step explanation:
Given
[tex]Total = 18275[/tex]
[tex]Tax = 7.5\%[/tex]
Required
The original price
This is calculated using:
[tex]Price(1 + Tax) = Total[/tex]
Make Price the subject
[tex]Price = \frac{Total}{(1 + Tax)}[/tex]
So, we have:
[tex]Price = \frac{18275}{(1 + 7.5\%)}[/tex]
[tex]Price = \frac{18275}{1.075}[/tex]
[tex]Price = 17000[/tex]
18
The length of a rectangle is twice as long as the width of the rectangle.
The area of the rectangle is 32 cm.
Draw the rectangle on the centimetre grid.
.
4
54
B2
%
I did it wrong can someone help me
Answer:
Width = 4 cm
Length = 8 cm
Step-by-step explanation:
Hi there!
Let [tex]l[/tex] be equal to the length of the rectangle.
Let [tex]w[/tex] be equal to the width of the rectangle.
1) Determine equations to find the length and width
We're given that the length is two times the length of the width:
[tex]l=2w[/tex]
We're also given that the area of the rectangle is 32 cm². Recall that the area of a rectangle is [tex]A=lw[/tex]:
[tex]A=lw\\32=lw[/tex]
Now, we have our two equations:
[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]
2) Solve for the width using substitution
[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]
Replace [tex]l[/tex] in the second equation with [tex]2w[/tex] from the first equation:
[tex]32=(2w)w\\32=2w^2[/tex]
Divide both sides by 2 to isolate w²:
[tex]16=w^2[/tex]
Take the square root of both sides to isolate w:
[tex]\pm4=w[/tex]
Because width cannot be negative, w=4. Therefore, the width of the rectangle is 4 cm.
3) Solve for the length
[tex]\displaystyle \left \{ {{l=2w} \atop {32=lw}} \right.[/tex]
Now, that we have the width (4 cm), we can solve for the length by plugging it back into one of the equations. Either of the equations work, but we can use the first:
[tex]l=2w\\l=2(4)\\l=8[/tex]
Therefore, the length of the rectangle is 8 cm.
3) Draw the rectangle
We can use what you had before as a foundation. You drew a rectangle with width 4 cm and length 7 cm. To draw the correct rectangle, add another row on top to make it 4 cm by 8 cm.
I hope this helps!
A pendulum's height is modeled by the function h(t) = 4 cos(pi/4*t) + 8 where h is the
measure of the pendulum's height in feet and t is the number of seconds since the
maximum height. How many seconds does it take the pendulum to complete one
full swing?
===========================================================
Explanation:
The general cosine template is
y = A*cos(B(t - C)) + D
where in this case
A = 4B = pi/4C = 0D = 8We only really need to worry about the B value. To get the period T, we do the following
T = 2pi/B
T = (2pi)/(pi/4)
T = 2pi * (4/pi)
T = 8
Note how the pi terms canceled. The period is 8 seconds, which is the length of one full cycle. This is the time it takes for the pendulum to do one full swing (eg: start at the right, swing to the left all the way, then swing back to the right again).
The result of 8 we got has nothing to do with the D = 8 value (this D value could be any other number and T = 8 would still be the case as long as B doesn't change of course).
What is the probability of a red on this spinner?
Be sure to reduce.
Answer:
2/8 or 1/4 simplified
Step-by-step explanation:
If you count how many equal sections there are, you will see there are 8, and 2 or those 8 sections are red so that would easily give you your answer, 2/8.
And to simplify it divide both the top and the bottom by 2 and that gives you 1/4.
Hope the helps! :)
The probability of a red on this spinner would be 1/4.
Used the concept of probability that states,
The term probability refers to the likelihood of an event occurring. Probability means possibility.
Given that,
A spinner is shown in the image.
Since there are a total of 8 parts with different colors.
And, the number of red colors on this spinner is 2.
Hence, the probability of a red on this spinner would be,
P = 2 / 8
P = 1 / 4
Therefore, the probability is 1/4.
Learn more about the probability visit:
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The following ordered pairs represent a function: {(-3, 1), (1, -2), (3, 0), (4, 5)}.
True or False
Answer:
false
Step-by-step explanation:
this is because there is no function of an unknown in this set
Type the equation for the graph
below.
Answer:
Step-by-step explanation:
This is a "regular" sin graph that's "taller" than the original. The amplitude is 3; other than that, its period is the same and it has not shifted to the right or left, so the equation, judging from the graph, is
[tex]y=3sin(x)[/tex]
f(x)=square root 2x and g(x)=square root 50x find (f/g)(x)
Answer:
1/5
Step-by-step explanation:
(f/g)(x) = f(x)/g(x) = sqrt(2x)/sqrt(50x) = 1/5
helppppppppppppppp me
Answer:
42
Step-by-step explanation:
5²+3(2)+5+6
25+6+5+6
31+11
42
Hope it helps
ILL GIVE POINTS!! PLS HELP !!!
Which set of polar coordinates describes the same location as the
rectangular coordinates (1. - 1)?
A. (sqrt2,315°)
B. (-1,135°) C. (sqrt2,225°)
D. (1,45°)
Answer:
The polar coordinates appear in the form (r, θ), where r is the the radius from the center and θ is the angle. To get the radius, do the following.
[tex]r = \sqrt{x^2 + y^2} = \sqrt{1^2 + (-1)^2} = \sqrt{2}\\[/tex]
You can get the angle visually by drawing a point (1, -1) on a graph and seeing that it is 45 degrees from the top right quadrant (you can tell its 45 because both x and y have the same magnitude). Since there are 360 degrees, 360 - 45 = 315.
If you would like to find it mathematically, this is the way to do it
[tex]\theta = atan(y/x) = -45[/tex]
Notice that -45 degrees is just 360 - 45 = 315
Your answer would be
[tex](\sqrt{2}, 315)[/tex]
express y=2x²+9x+4 in the form a(x+b)²+c . where a ,b,c are constant
Answer:
2(x+9)^2 + 4
Step-by-step explanation:
.............
i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have. (Hint: one is the other simplified)
Answer:
Step-by-step explanation:
Total amount in cents (unsimplified): 5N +17(10-N)
Simplified: 170-5N
x+y=4 and 2x+3y=2 then find x and y
Answer:
x=10, y=-6
Step-by-step explanation:
1) express x from the first equation x+y=4 x=4-y
2) It is the system of equations, so both equations are simultaneous.
you can replace x to 4-y in the second one
2 *(4-y) +3y=2
8-2y+3y= 2
y=-6
x= 4-y=4-(-6)=10
The answer is x=10, y=-6
Find the measure of the indicated angle to the nearest degree
The Volume of a sphare is 28/3 times the surface area calculate The surface area and the Volume of the sphere, correct to the nearest whole number.
Given:
Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.
To find:
The surface area and the volume of the sphere.
Solution:
Volume of a sphere:
[tex]V=\dfrac{4}{3}\pi r^3[/tex] ...(i)
Surface area of a sphere:
[tex]A=4\pi r^2[/tex] ...(ii)
Where, r is the radius of the sphere.
Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.
[tex]V=\dfrac{28}{3}\times A[/tex]
[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]
Multiply both sides by 3.
[tex]4\pi r^3=112\pi r^2[/tex]
[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]
[tex]r=28[/tex]
Using (i), the volume of the sphere is:
[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]
[tex]V\approx 91989[/tex]
Using (ii), the surface area of the sphere is:
[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]
[tex]A=9856[/tex]
Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.
_(9)=(2(1-2(2)^(9)))/(1-2(2))
PLEASE HELP ME OUT.
Answer:
the answer = um ok
Step-by-step explanation:
The distance from Clinton to Greenville is 124 miles. To find the speed of a car, use the expression d divided t, where d represents the distance and t represents time. Find the speed of a car that travels from Clinton to Greenville in 2 hours
Step-by-step explanation:
time = 2 hours
distance travelled(d) = 124 miles
so
speed = d/t
= 124/2
= 62 miles per hour
Therefore, the speed of car is 62 miles per hour.
Can u help solve this
Answer:
- 5/3
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -1 -9)/(4 - -2)
= (-1-9)/(4+2)
= -10/6
- 5/3
Answer:
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 1 - 9}{4 - - 2} \\ \frac{ - 10}{6} \\ = - \frac{5}{3} \\ thank \: you[/tex]
find the length of BC
Answer:
13.3650978628
Step-by-step explanation:
Angle A=180-(Angle B+C)=180-117=63
Here,
b=BC, p=AC & AB=12
Using the relation of cos,
cosx=b/h
cos27=BC/15
15cos27=BC
Using a calculator,
BC=13.3650978628
if line 4x+ky=11 and line y=8x-3 are parallel find the value of k
pls help me asap thank you step by step please!!
Answer:
k=-1/2
Step-by-step explanation:
u have to change line 4x + ky=11 to this form:
y=11/k-4x/k
then, if 2 lines are parallel, their slopes have to equal
so: 8=-4/k -> k=-1/2
a man's income is rupees 12000 per month if the.If the rate of income tax ia rs2.50 per rs100,how much tax should he pay?
Answer:
don't know
Step-by-step explanation:
The rational number -13/-5 lies to the right of zero on the number true or false.
Answer:
true
hope it helps
PLEASE MARK BRAINLIEST
Given m \| nm∥n, find the value of x.
Answer:
53
Step-by-step explanation:
The value of x in the given figure is 127 degrees.
Given that;
The lines m and n are parallel lines.
Now by definition of vertically opposite angle,
Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other.
Hence from the figure we get;
Angle x and 127 degrees are vertically opposite angles.
Hence we get;
x = 127°
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trigonometric identities
Answer:
answer B:
[tex]x= \dfrac{\pi}{2}\ or\ \dfrac{\pi}{6}\ or\ x=\dfrac{5\pi}{6}[/tex]
Step-by-step explanation:
[tex]2cos^2 x + 3sin x=3\\\\\Longrightarrow\ 2*(1-sin^2 x)+3sin x -3=0\\\\\Longrightarrow\ 2-2sin^2 x+3 sin x -3=0\\\\\Longrightarrow\ -2sin^2 x+3 sin x -1=0\\\\\Longrightarrow\ 2sin^2 x-3 sin x +1=0\\\\\Delta=3^2-4*2*1=1\\\\sin\ x=\dfrac{3-1}{4} \ or\ sin\ x=\dfrac{3+1}{4}\\\\sin\ x=\dfrac{1}{2} \ or\ sin\ x=1\\\\\Longrightarrow\ x= \dfrac{\pi}{6}\ or\ x= \dfrac{5\pi}{6}\ or\ x=\dfrac{\pi}{2} \\[/tex]
What is the answer ? Help pls
Answer:
B. 4Step-by-step explanation:
Given,
[tex] {x}^{8} = {( {2}^{2} )}^{4} [/tex]
Since,
[tex] { ({a}^{x} )}^{y} = {a}^{xy} [/tex]
Then,
[tex] = > {x}^{8} = {2}^{2 \times 4} [/tex]
[tex] = > {x}^{8} = {2}^{8} [/tex]
(Since the exponents are same so the bases will be also same)
Therefore,
=> x = 2
As per condition,
[tex] {x}^{2} [/tex]
(Putting value of x = 2)
[tex] ={2}^{2} [/tex]
= 4 (Ans)
7/3 = 7 ÷
7 divided by blank equals 7/3
please help ?
Answer:
7/3 = 7 ÷ 7 ÷ 3/7 (i think)
Step-by-step explanation:
check mathpapa.com
https://www.mathpapa.com/algebra-calculator.html
From a group of three boys and six girls a boy and a girl will be selected to attend a conference and how many ways can the selection you made
Answer:
18
Girl = g
Boy = b
1g 1b 1g 2b 1g 3b
2g 1b 2g 2b 2g 3b
3g 1b 3g 2b 3g 3b
4g 1b 4g 2b 4g 3b
5g 1b 5g 2b 5g 3b
6g 1b 6g 2b 6g 3b
---------------------------------------
Another way you can do this,
6 × 3 = 18
In the end there will be 18 selections.
Please help!!! 20 points + brainliest!!
6 + (-47) =
Well, all we have to do is add, so:
6 + (-47) =
6 - 47 =
-41
Answer:
(-41)
Step-by-step explanation:
Subtract and write big numbers sign.
47 - 6= (-41)
What is the value of the expression below when x=3 and y=8?
6x +10y
Answer:
98
Step-by-step explanation:
The value of the expression below when x=3 and y=8 is 98.
1. Write an expression in simplest form for the area of the figure below:
(answer pls)
Answer:
(5x+6)(2x+5)-(2x+4)(x+8) simplified is 8x^2+17x-2
Step-by-step explanation:
Answer:
13x²+16x+28
Step-by-step explanation:
S=(5x+6)×(3x+2)=15x²+28x+12
2x+5-x-3=x-2
5x+6-3x+2=2x+8
(x-2)×(2x-8)=2x²-12x+16
15x²+28x+12-2x²-12x+16=13x²+16x+28
