Answer:
The solution to the system is (-6, -9)
Step-by-step explanation:
In order to graph the system, we can find two points belonging to each equation and join them with a line. We look then for the point at which the lines intersect.
(a) Two points for the first line defined by: 3 x + 2 y = -36
What is the value of y when x=0?
3 (0) + 2 y = -36
then y = -36/2 = -18, then one point on this line is (0, -18)
What is the value of x when y = 0?
3 x + 2 (0) = -36
then x = -12, then a second point for this line is: (-12, 0)
When can draw the line that represents this first equation by joining the two points as shown in the attached image with the two points found and the line depicted in orange.
(b) Two points for the second line defined by: - x + 2 y = -12
What is the value for y when x = 0?
- (0) + 2 y = -12
then y = -12/2 = -6, therefore one point for this line is: (0, -6)
What is the value of x when y = 0?
- x + 2 (0) = -12,
then x= 12,and therefore another point for this line is (12. 0)
When can draw the line that represents this second equation by joining the two points we found, as shown in the attached image with the two points found and the line depicted in blue.
We see that the intersection of the two lnes takes place at x= -6 and y = -9. That is at the point (-6, -9)
John who is 5 ft tall is standing 20 feet away from a tree, and you measure the angle of elevation to be 38. How tall is
the tree? Find your answer to the nearest tenth.
Find
45
Step-by-step explanation:
that would form a triangle
using tan
TOA tan = opp/adj
tan38 degree = 20/x
tan 38 =0.7813
so 0.7813 = 20/x
=cross multiply
= 0.7813x =20
divide both sides by 0.7813
so 20/0.7813
= 25.5983
which is 3 to the nearest tenth
The height of the tree is 20.6 feet.
How are the heights and distances problems solved?To solve problems of heights and distances, we use trigonometric ratios determining the given case by geometric shapes.
How do we solve the given question?We are given the following information: John who is 5 ft. tall is standing at a distance of 20 ft. from a tree, and you measure the angle of elevation to be 38°. We are asked to find the height of the tree.
To solve the problem, we will use heights and distances.
First, we define a figure:
Let AD be John, such that AD = 5 ft.
Let BE be the tree with its height = h ft.
The distance between John and the tree is determined by DE = 20 ft.
We drop a perpendicular from point A to BE at point C.
Now, ADEC is a rectangle. Hence,
CE = AD = 5 ft.
AC = DE = 20 ft.
We join A and B, to complete the right-angled triangle ACB, with ∠ACB = 90°, ∠BAC = 38° (the given angle of elevation).
In ΔACB,
AC = 20 ft. (already derived)
BC = BE - CE = h-5 ft. (∵ BE = height of the tree h, CE = 5, already derived)
Now, in ΔACB,
tan 38° = BC/AC = (h-5)/20
or, h-5 = 20*tan38° = 20*0.781286 = 15.6257
or, h = 15.6 + 5 = 20.6257.
∴ h = 20.6 (correct to the nearest tenth)
So, the height of the tree is 20.6 feet.
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Find the product h · k(x) if h(x) = 2(3x – 5) and k(x) = –2x + 1?
Answer:
The answer is option C.
Step-by-step explanation:
h(x) = 2(3x – 5) = 6x - 10
k(x) = –2x + 1
h • k (x) = (6x - 10) ( - 2x + 1)
= - 12x² + 6x + 20x - 10
The final answer is
= - 12x² + 26x - 10
Hope this helps you
Answer:
C) h · k(x) = –12x2 + 26x – 10
Step-by-step explanation:
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 563 randomly selected adults showed that 60% of them would erase all of their personal information online if they could. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.Find the value of the test statistic.
Answer:
a)Claims: P>0.5("MOST" of the adult erase their personal information)
b)Statistics test= 4.746
Step-by-step explanation:
we were given {p}=60% =0.60
where n= 563
since most of adults erase all their personal information online, then (p> 0.5
p=0.5
q=1-p=1-0.5=0.5
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
The value of the statistic test is 4.746 and this can be determined by using the given data.
Given :
A software firm survey of 563 randomly selected adults showed that 60% of them would erase all of their personal information online if they could.
It is given that [tex]\rm \bar{P}[/tex] = 60% = 0.60 and n = 563.
Claim: Most adults would erase all of their personal information online if they could that means (P > 0.5). Therefore:
q = 1 - P = 1 - 0.5 = 0.5
Now, to determine the value of the statistic test, the following formula can be used:
[tex]\rm \dfrac{\bar{P}-P}{\sqrt{\dfrac{Pq}{n}} } = \dfrac{0.6-0.5}{\sqrt{\dfrac{0.5\times0.5}{563}} }=4.746[/tex]
Therefore, the value of the statistic test is 4.746.
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Drag the tiles to the table. The tiles can be used more than once, but not all tiles will be used.
Emma and Jackson are helping their band raise funds for a trip to New York City. They've volunteered to call every
business owner in their small town to request donations. Emma can complete the calls in 6 days if she works alone.
Jackson can complete the calls in 4 days if he works alone. To complete the task, Emma and Jackson are going to work
together for the same amount of time. Use this information to complete the table.
Answer:
Emma can complete the calls alone in 6 days, which means she can complete [tex]\frac{1}{6}[/tex] of the calls in one day. So, Emma’s rate per day is [tex]\frac{1}{6}[/tex] . Jackson can complete the calls alone in [tex]4[/tex] days, which means he can complete [tex]\frac{1}{4}[/tex] of the calls in one day. So, Jackson’s rate per day is [tex]\frac{1}{4}[/tex] . Because they’re working together, the time, [tex]x[/tex] , is the same for both.
Multiply across the table to find the part of the task each has completed. Use the equation work completed = (rate)(time) to fill in the last column cells.
Step-by-step explanation:
f(x) = x2. What is g(x)?
Answer:
B
Step-by-step explanation:
Put x as 1 and the output will be 9.
y = (3x)²
y = (3(1))²
y = 3²
y = 9
True
Help please!!! Which of the following represents the area of the white (unshaded) region? * A.) Area of Big triangle - Square B.) Area of Circle + Area of Square C.) Area of small triangle + Area of Circle D.) Area of Circle - Square
Answer:
A.) Area of Big triangle - Square
Step-by-step explanation:
The triangle would have been all white if the square were not shaded. So the square must be subtracted from the area of the triangle. See diagram below.
The price of an antique car in 2020 is 200% of its original price in 1980. By what percentage did the price increase over this 40-year period?
Answer: 100%
Step-by-step explanation:
Given the following :
Price of antique car in 2020 is 200% of its original price in 1980.
By what percentage did the price increase over this 40-year period?
Let the original price = x
x = price of car in 1980
Price of car in 2020 = 200% of x = 2x
Percentage increase in price is given by:
(increase / original price) × 100%
Increase = (price in 2020 - price in 1980)
[(Price in 2020 - price in 1980) / original price] * 100%
[(2x - x) / x] * 100%
[(2x - x) / x] * 100%
(x /x) * 100%
= 1 × 100%
= 100%
100x%
The percentage that the price increase over this 40-year period is 100%.
Percentage increaseUsing this formula
Percentage increase=(Current price-Original price)÷Original price × 100%
Let plug in the formula
Percentage increase= (200% of x1-1)/1×100
Percentage increase= 1 × 100%
Percentage increase= 100%
Inconclusion the percentage that the price increase over this 40-year period is 100%.
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help pls, Find PG if JG=18.
The length of PG using the centroid property is 6 unit.
The centroid divides each median into segments in a 2:1 ratio.
This means that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.
Given:
JG = 18
As, the centroid divides each median into segments in a 2:1 ratio then
PG:PJ = 1:2
So, the length of PG
= 1/3 * (18)
= 18/3
= 6 unit
Thus, the length of PG is 6 unit.
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What are the coordinates of the terminal point determined by t=11pi/3 help please
Answer: The correct answer is B
Step-by-step explanation: (1/2,-sqrt3/2) just took quiz you’re welcome
By trigonometry functions, the coordinates of the terminal point are (1/2, -√3/2)
The given function is t = 11 pi / 3
How to find the coordinates of the terminal point?Given: t = 11 pi / 3
By the definitions of trigonometry functions, the point P has as coordinates P(x, y).
x=cos(11π/3) and y=sin(11π/3)
Trig table and unit circle give
x= cos(11π/3)=cos(-π/3+4π)
=1/2
y=sin(11π/3)=sin(-π/3+4π)
=-sin(π/3)=-√3/2
P is in Quadrant IV, (1/2, -√3/2) be the coordinates of the terminal point at t = 11π/ 3.
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#1 Billy stacked nine pieces of wood on top of one another. If each piece was 3/4 of a foot tall, how tall was the wood pile? Round your answer to the nearest hundredth of a foot.
#2 look at the photo
please help me as soon as you can it would be greatly appreciated I’m in a hurry.
Answer:
a. 6.75 ft
b. Exponent on w is w^4
Step-by-step explanation:
a. The best thing here is to work with decimals
each piece was 3/4 foot tall which means each piece is 0.75 ft tall
Now since he staked 9, the height of the wood pile would be 9 * 0.75 = 6.75 ft
b. Firstly let’s evaluate the denominator
That becomes; 2v^-3w^8 * v^4w = 2v^(-3+4)w^(8+1) = 2vw^9
So let’s now divide this by the numerator
Since we are concerned with only the exponent on w, we place w^13 over w^9 = w^(13-9) = w^4
Find lateral surface area in square units, of the following 3-
dimensional figure.
Enter just a number for your answer.
-
14 ft
7 ft
9 ft
Answer:
Lateral surface area of cuboid = 448 ft²
Step-by-step explanation:
Given:
Height of cuboid(h) = 14 ft
Length of cuboid(l) = 9 ft
width of cuboid(b) = 7 ft
Find:
Lateral surface area of cuboid
Computation:
Lateral surface area of cuboid = 2 h(l + b)
Lateral surface area of cuboid = 2(14)(9 + 7)
Lateral surface area of cuboid = 28(16)
Lateral surface area of cuboid = 448 ft²
simplify z^6x^7/z^5x
Answer:
[tex]\huge\boxed{\dfrac{z^6x^7}{z^5x}=zx^6}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{z^6x^7}{z^5x}=\dfrac{z^6x^7}{z^5x^1}=z^{6-5}x^{7-1}=z^1x^6=zx^6[/tex]
Answer:
[tex]zx^6[/tex] is the simplified answer.
Step-by-step explanation:
[tex]\frac{z^6x^7}{z^5x}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\=\frac{x^7z^{6-5}}{x}\\\\=\frac{zx^7}{x}\\\\\mathrm{Cancel\:the\:common\:factor:}\:x\\\\=zx^6[/tex]
Best Regards!
NEED HELP ASAP PLEASE WILL MARK BRANLIEST What would the equation of a hyperbola with directrices at x=±2 and foci at (6,0) (-6,0) be?
Answer:
The equation of the hyperbola can be presented as follows;
[tex]\dfrac{\left x \right ^{2}}{12} - \dfrac{\left y \right ^{2}}{24} = 1[/tex]
Step-by-step explanation:
We have the equation of an hyperbola given as follows;
[tex]\dfrac{\left (x - h \right )^{2}}{a^{2}} - \dfrac{\left (y - k \right )^{2}}{b^{2}} = 1[/tex]
The foal length = a² + b² = c²
c = focal length
The directrix = a²/c
The focal point are (h + c, k) and (h - c, k)
Therefore, by comparison with the given focal points, (6, 0) and (-6, 0), we have;
k = 0 and h + c = 6, h - c = -6
Therefore;
6 - c - c = -6
-2·c = -12
c = 6
h = 0
a²/c = 2
a² = 2 × 6 = 12
a = 2·√3
12 + b² = 6²
b² = 6² - 12 = 24
b² = 24
b = 2·√6
The equation of the hyper bola can then be written as follows;
[tex]\dfrac{\left (x - 0 \right )^{2}}{12} - \dfrac{\left (y - 0 \right )^{2}}{24} = 1[/tex]
Which gives
[tex]\dfrac{\left x \right ^{2}}{12} - \dfrac{\left y \right ^{2}}{24} = 1[/tex]
x² - y² = 12
y² = x² - 12.
what is the solution to the inequality below x<5
Answer:
The correct answer is B
Answer:
0 < x < 25
Step-by-step explanation:
Which part of the graph is the distance from home constant? PLEAS HELP ME VERY EASY
Un comerciante vende a un cliente 20kg de arroz 12,25 kilogramos de papa y 39, 16 kilogramos de frijol el peso de los artículos vendidos es
Respuesta:
71.41 kilogramos
Explicación paso a paso:
En este caso lo que debemos hacer para calcular el peso de los artículos vendidos, es sumar el peso individual de cada artículo, por lo tanto:
Peso total = peso del arroz + peso de la papa + peso del frijol
Ya que tienen la misma unidad de medida, no hay ningún problema para sumar, entonces reemplazamos:
Peso total = 20 + 12.25 + 39.16
Peso total = 71.41
Lo que quiere decir que el peso de los artículos vendidos es de 71.41 kilogramos
what is the formula for this equation?
hen spends 3 days baking 224 cookies. on the second day, he bakes twice as many as he did on the first day. on the third day, he baked half as many as he did on the first day. How many cookies did he bake o the 2nd day
Answer:
x + 2x + 1/2x = 224
Step-by-step explanation:
x + 2x + 1/2x = 224
3.5x = 224
x= 64
64×2=128
Hen baked 128 cookies on the second day
PLSSSS HELP ASAP MAYBE IF I SAY ICE CREAM I WILL GET UR GUYS' ATTENTION YOU GUYS WILL COME AND ANSWER IDK ANYWAY PLS HELP DO NOT LOOK IT UP ONLY UR OWN WORDS PLEASE THANK YOU SM!!!!
Answer:
Good very good
Step-by-step explanation:
Because my taste buds like it'
can someone help me answer this please
Answer: 19 degrees
Step-by-step explanation:
<FOE is the central angle of an arc of 52 degrees and is thus 52 degrees. Then by supplementary angles <COD is 71 degrees and angle BOA is thus also 71 degrees. Then by supplementary angles <BOC is 19 degrees and arc BC is thus also 19 degrees.
Hope it helps <3
Answer:
19 degrees
Step-by-step explanation:
3x-10-4
if x-3
3-164
if x=y=-25
88-y)
if =2 y = 6
6
2
if x=-12
9-10 +4
87-4
-32
4
3x + 4y - 3x
3,81-10) +5x
(2x + 6
if x = -2
-10x
1
ifr=
if x=-2
Kio-2+1
. 20th
2012
x+8y-(x)
(8x)+ 6x + 2
if x = -3
2x + 4y + xy
if x=y=2
8x + 2y
if x=1.5, y =-22
if x =-5, y =
ķ' +17-117
(x-6)+4
3r -8.rº + 7
if x = 4.5
-2x+8y
if x = 3, y = -9
(-5x) - 3x + x
if x=-3.5
if x=8
Answer/Step-by-step Explanation:
1. 3x - 10 +4 if x = 3
To evaluate, plug in the value of x in the expression given
3(3) - 10 + 4 = 9 - 10 + 4
= 3
2. [tex] \frac{x}{2} + 6x [/tex]
if x = -12
[tex] \frac{(-12)}{2} + 6(-12) [/tex]
- 6 - 72 = - 78
3. 8(x - y), if x = 2, y = 6
8(2 - 6) = 8(-4) = -32
4. x + xy, if x = 3, y = -2.5
3 + (3)(-2.5) = 3 + (-7.5)
= 3 - 7.5 = - 4.5
5. (2x)² + 6, if x = -2
(2*-2)² + 6 = (-4)² + 6
= 16 + 6 = 22
6. 3x + 4y - 3x, if x = 2, y = 4
3(2) + 4(4) - 3(2) = 6 + 16 - 6
= 16
7. [tex] -10x + \frac{4}{x} [/tex]
If x = -2
[tex] -10(-2) + \frac{4}{-2} [/tex]
20 + (-2) = 20 - 2 = 18
8. 3(8x - 10) + 5x, if x = ½
3(8*½ - 10) + 5(½)
3(4 - 10) + 2.5
3(-6) + 2.5 = -18+2.5 = - 20.5 or 20½
9. x + 8y - (x)², if x = -5, y = ¼
-5 + 8(¼) - (-5)² = -5 + 2 - (25)
= -3 - 25 = -28
10. (8x)² + 6x + 2, if x = -3
(8*-3)² + 6(-3) + 2 = (-24)² - 18 + 2
= 576 - 18 + 2 = 560
11. 2x² + 4y² + xy, if x = ½, y = 2
2(½)² + 4(2)² + (½)(2)
= 2(¼) + 4(4) + 1
= ½ + 16 + 1 = ½ + 17 = 17½
12. 8x + 2y, if x = 1.5, y = -2.2
8(1.5) + 2(-2.2)
12 - 4.4 = 7.6
13. [tex] \frac{5}{2}(x - 6) + 4 [/tex]
if x = 8.
[tex] \frac{5}{2}(8 - 6) + 4 [/tex]
[tex] \frac{5}{2}(2) + 4 [/tex]
= 5 + 4 = 9
14. 3x - 8x² + 7, if x = 4.5
3(4.5) - 8(4.5)² + 7
13.5 - 8(20.25) + 7
13.5 - 162 + 7 = -141.5
15. -2x² + 8y, if x = 3, y = -9
-2(3)² + 8(-9)
-2(9) - 72 = - 18 - 72 = 90
16. (-5x)² - 3x + x, if x = -3.5
(-5*-3.5)² - 3(-3.5) +(-3.5)
(17.5)² + 10.5 - 3.5
306.25 + 10.5 - 3.5 = 313.25
HELP ASAP!!! I WILL GIVE THE MOST BRAINIEST TO WHOEVER ANSWERS IT RIGHT PUT THE ANSWER IN A BOX
Answer:
4/3*PI
OR 4.186 (6 REPEATING0
OR 1.3(3 REPEATING )*PI
Step-by-step explanation:
BECAUSE
THE FORMULA IS 4/3*PI*R^3=V
4/3*3.14*1=V
4/3*PI=V
OR 4.186 (6 REPEATING
OR 1.3(3 REPEATING )*PI
HOPE I HELPED
BRAINLIEST PLS
-ZYLYNN JADE
Answer:
4.19 in³
Step-by-step explanation:
The volume of a sphere is given by the formula:
V = [tex]\frac{4}{3}[/tex]*π*r³ r is the radius here it's 1so the volume is:
V = [tex]\frac{4}{3}[/tex]*3.14*1³
V= 4.1866 ≈ 4.19 in³
A pencil cup is a cylinder made of plastic with one base missing. The cup is 5 inches tall and has a radius of 1.75 inches. Approximately how many square inches of plastic were used to make the cup? 54.98 in.2 74.22 in.2 48.11 in.2 64.60 in.2
Answer:
74.22
Step-by-step explanation:
a pencil cup is like a cylinder
A=2πrh+2πr2=2·π·1.75·5+2·π·1.752≈74.22013
hope this helps
correct me if this is wrong
Can someone please explain to me.
Answer:
A. 4.50 B. 1 : 3
Step-by-step explanation:
A.
First, think of Toby's money as 1/6x (x referring to the total amount of money) and Daoud's money as 1/2x.
It states that Toby gets 1.50, which means that 1/6x = 1.50.
To find what x is, multiply both sides by 6.
1/6x * 6 = 1.50 * 6
x = 9
Now that we know how much money there is in total, we can solve for Daoud's money. Daoud has 1/2x. We can substitute x for 9 and solve for Daoud's money.
1/2(9)
4.50
Daoud has 4.50.
B.
The problem states that Elsa gets the remaining money.
9 - (1.50 + 4.50)
9 - 6
3
Elsa gets 3.00.
Now, you can use turn solve the ratio of Toby's money and Elsa's money.
1.5 : 3
The problem states that they have to be whole numbers, so you can change the ratio to fit the requirements.
1 : 3
The ratio of boys to girls in a class of
45 pupils is 2:7. How many girls are
there in the dass?
(a) 35
(b) 20
(c) 18
(d) 15
le) 10
Answer:
The answer is option A.
35.Step-by-step explanation:
To find the number of girls in the class we must first find the total parts
That's
2 + 7 = 9
In the ratio 7 correspond to girls so the number of girls in the class are
7/9 × 45
= 7 × 5
= 35
Hope this helps you
easy question please help fast, i just want to check my answer!
Answer:
false
Step-by-step explanation:
its false I think
What is 14v14 divided by 72 in simplest form?
Answer:
About 2.72
Step-by-step explanation:
From reading the comments, I suppose you meant v actually means x so:
14 × 14 = 196
196 ÷ 72 ≈ 2.72
Hope this helped! :)
Answer:
Hello!
I'm not sure what the " v " means but I think you meant to put x instead of v
____________________
14 x 14 = 196
196 ÷ 72 = [tex]\frac{49}{18}[/tex]
Step-by-step explanation: Reduce the expression, if possible, by cancelling the common factors.
Hope I got this right.
NEED HELP ASAP *picture included* what percent of the area underneath this normal curve is shaded?
Answer:
68.26
Step-by-step explanation:
The symbol σ represents standard deviation. 1 standard deviation (in both directions) under a normal distribution= 68.26
Answer:
68%.
Step-by-step explanation:
The 68-95-99.7 rule (also know as the Empirical Rule) states that 68% of the data lies within 1 standard deviation of the mean. 95% of the data lies within 2 standard deviations of the mean. 99.7% of the data lies within 3 standard deviations of the mean.
According to the diagram, the area shaded shows data within 1 standard deviation of the mean (one standard deviation to the left, and one to the right). That means that 68% of the data is within the shaded area.
Hope this helps!
The painting shown is by Métis artist Leah Marie Dorion from Prince Albert, Saskatchewan. It is called Hawk Woman (2006). The frame is 2 in. wide on
each side of the square painting. Write an expression to represent the dimensions and area of the painting. Multiply, and then combine like terms.
Answer:
x^2-4x-4
Step-by-step explanation:
Dimension of the painting=x
Frame=2in wide is. Each side of the square painting
Length of the painting= x-2
Area of a square=lenght^2
=(x-2)^2
Multiply
=(x-2)(x-2)
=x^2-2x-2x+4
Combine like terms
Area of the square painting=x^2-4x-4
Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula Solve the problem using this formula. Find E, the voltage of a circuit, if I = (16 + i) amperes and R = (2 + 4i) ohms.
Answer:
E = (28 + 66i) Volts
Step-by-step explanation:
Note that: i = √-1 ; i² = -1
Ohm's law: E = IR
E = (16+ i) (2 + 4i)
Expand the equation.
E = 16x2 + 16x4i + ix2 + ix4i
E = 32 + 64i + 2i + 4i²
E = 32 + 64i + 2i + 4(-1)
E = 32 + 64i + 2i - 4
Collect like terms:
E = 32 -4 + 64i + 2i
E = (28 + 66i) Volts
Choose a number subtract 5 the result is 4
Answer:
3
Step-by-step explanation: