Answer:
The lines meet at (-1, -3)
Step-by-step explanation:
Line A :
[tex](x_1, y_1) = (3, 3) \ ; \ slope, \ m_A = \frac{3}{2}\\\\Equation \ of \ line \ A : (y - 3) = \frac{3}{2}(x - 3)[/tex]
[tex]2(y - 3) = 3(x-3)\\2y - 6 = 3x - 9\\2y = 3x - 9 + 6\\2y = 3x -3[/tex]
Line B :
[tex](x_2,y_2) = (-4, -2) \ ; \ slope , m_B = -\frac{1}{3}\\\\Equation \ of\ line \ B: (y -(-2)) = -\frac{1}{3}(x -(-4))[/tex]
[tex]3(y + 2) = -1(x+4)\\3y + 6 = -x -4\\3y = -x - 4 - 6 \\3y = -x - 10[/tex]
Solve for x and y from the linear equation to find where line A and line B meets :
2y = 3x - 3 => 3x - 2y = 3 ------- (1)
3y = -x - 10 => -x = 3y + 10
=> x = - 3y - 10 --------(2)
Substitute (2) in (1) : => 3(- 3y - 10) - 2y = 3
-9y - 30 -2y = 3
-11y = 3 + 30
-11y = 33
y = -3
Substitute y in (2) : => x = -3 (-3) - 10 = 9 - 10 = -1
Determine the area of a parallelogram if
its base is 16 cm and its height is 7 cm.
=====================================
Work Shown:
area = base*height
area = 16*7
area = 112 square cm
----------------
Extra info (optional section):
The area formula for a parallelogram is the same as the formula for a rectangle. Imagine tilting a rectangle so that it's slanted. The area has not changed.
Or another thing to imagine is that let's say we had a stack of 2 by 4s. If the stack is perfectly vertical, aka forming a rectangle, then we can nudge the beams so that we can form a slanted parallelogram instead. Both configurations involve the same amount of wood, and therefore would lead to the same frontal surface area.
Congruent angle pairs : Find m
Answer:
75
Step-by-step explanation:
x+60 and 5x are vertical angles, which means they are equal
x+60 = 5x
Subtract x from each side
x+60-x = 5x-x
60 = 4x
Divide by 4
60/4 = 4x/4
15 =x
We want to find x+60
x+60
15+60
75
Answer:
∠GH = 75°
Step-by-step explanation:
x + 60° = 5x° ( vertical angles )
subtract x from both side
x - x + 60° = 5x - x
60° = 4x
divide each side by 4
60°/ 4 = 4x / 4
15 ° = x
To calculate, ∠GH
∠GH = x + 60 °
15 ° + 60° .. ( x = 15°)
= 75°
6,347.2184 to the nearest thousandth
Answer: 6347.218
Step-by-step explanation:
Answer:6,347.218
Step-by-step explanation:
look at the thousandths place and then look at the number next to it if the number was 5 and above the answer would be 6,347.219 but in this situation it's not so you would keep everything the same but subtract the 0.0004
03.
(a)
Multiply out
3(2x-7)
Answer
Answer: -42 is the answer.
The terminal side of θ in standard position contains the point (3, 0). Find the exact values of the six trigonometric functions of θ
[tex]\textit{we know that }\theta \textit{ contains the point }(\stackrel{x}{3}~~,~~\stackrel{y}{0})\textit{, let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ r^2=a^2+b^2\implies r=\sqrt{a^2+b^2}\implies r=\sqrt{3^2+0^2} \qquad \begin{cases} r=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ r=\sqrt{3^2}\implies r=3[/tex]
[tex]\rule{34em}{0.25pt}\\\\ sin(\theta)=\cfrac{opposite}{hypotenuse} =\cfrac{y}{r}\implies \cfrac{0}{3}\implies 0 \\\\\\ cos(\theta)=\cfrac{adjacent}{hypotenuse} =\cfrac{x}{r}\implies \cfrac{3}{3}\implies 1 \\\\\\ tan(\theta)=\cfrac{opposite}{adjacent} =\cfrac{y}{x}\implies \cfrac{0}{3}\implies 0[/tex]
[tex]cot(\theta)=\cfrac{adjacent}{opposite} =\cfrac{x}{y}\implies \cfrac{3}{0}\implies und efined \\\\\\ csc(\theta)=\cfrac{hypotenuse}{opposite} =\cfrac{r}{y}\implies \cfrac{3}{0}\implies und efined \\\\\\ sec(\theta)=\cfrac{hypotenuse}{adjacent} =\cfrac{r}{x}\implies \cfrac{3}{3}\implies 1[/tex]
Marie made lasagna for dinner. She ate 1/6 of it, Morris ate 1/3 of it, and Larry ate 1/4 of it. How much of the lasagna was left?
Answer:
1/12 of the lasagna was left
Step-by-step explanation:
To find out how much of the lasagna has been eaten, you have to find the least common denominator (LCD) for the three fractions. The LCD of 1/3, 1/4, and 1/6 is 12 (3x4x6). Now convert all the fractions so that all of their denominators is equal to 72 (1/3=4/12, 1/4=3/12, 1/6=2/12), then add all of the fractions together (4/12 + 3/12 +2/12 = 3/4). 3/4 of the lasagna has been eaten and the remaining lasagna is 1/12 (1-3/4=4/4-3/4).
Answer:
[tex]\frac{1}{4}[/tex] of the lasagna
Step-by-step explanation:
[tex]\frac{1}{4} +\frac{1}{6}+ \frac{1}{3}[/tex]
4 = 2 × 2
3 = 3
6 = 2 × 3
LCM = 2 × 2 × 3
LCM = 12
4 × 3 × 6 = 72
[tex]\frac{18}{72} +\frac{12}{72}+ \frac{24}{72}[/tex]
[tex]\frac{18+12+24}{72}[/tex]
[tex]\frac{54}{72}[/tex]
54 = 2 × 3 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
GCF = 2 × 3 × 3
GCF = 18
[tex]\frac{\frac{54}{18} }{\frac{72}{18} }=\frac{3}{4}[/tex]
[tex]1-\frac{3}{4}[/tex]
[tex]\frac{4}{4} -\frac{3}{4}[/tex]
[tex]\frac{4}{4} -\frac{3}{4}=\frac{1}{4}[/tex]
Please help thank you! Sorry for spamming
Answer:
B
Step-by-step explanation:
because of order if operations.
Answer:
B
Step-by-step explanation:
The rule of PEMDAS states to start from parenthesis. To get your correct answer, you would need to prioritize what comes first going left to right.
If you were to select A, (/5) would be prioritized. D. Has the order placed in correctly, as well as C.
Please I need help with this!!!!!!!
Answer:
Step-by-step explanation:
1). Step 4:
[tex]x=5^{\frac{4}{3}}=(5^4)^{\frac{1}{3}}[/tex]
[tex]x=\sqrt[3]{5^4}[/tex] [Since, [tex]a^{\frac{1}{3}}=\sqrt[3]{a}[/tex]]
[tex]x=\sqrt[3]{5\times 5\times 5\times 5}[/tex]
Step 5:
[tex]x=\sqrt[3]{(5)^3\times 5}[/tex]
[tex]x=\sqrt[3]{5^3}\times \sqrt[3]{5}[/tex]
2). He simplified the expression by removing exponents from the given expression.
3). Let the radical equation is,
[tex](3x-1)^{\frac{1}{5}}=2[/tex]
Step 1:
[tex](3x-1)^{\frac{1}{5}\times \frac{5}{1} }=2^{\frac{5}{1}}[/tex]
Step 2:
[tex](3x-1)=2^5[/tex]
Step 3:
[tex]3x=32+1[/tex]
Step 4:
[tex]x=11[/tex]
4). By substituting [tex]x=11[/tex] in the original equation.
[tex](3\times 11-1)^{\frac{1}{5}}=(32)^\frac{1}{5}[/tex]
[tex]=(2^5)^\frac{1}{5}[/tex]
[tex]=2[/tex]
There is no extraneous solution.
1). Step 4:
x=5^{\frac{4}{3}}=(5^4)^{\frac{1}{3}}x=534=(54)31
x=\sqrt[3]{5^4}x=354 [Since, a^{\frac{1}{3}}=\sqrt[3]{a}a31=3a
x=\sqrt[3]{5\times 5\times 5\times 5}x=35×5×5×5
Step 5:
x=\sqrt[3]{(5)^3\times 5}x=3(5)3×5
x=\sqrt[3]{5^3}\times \sqrt[3]{5}x=353×35
2). He simplified the expression by removing exponents from the given expression.
3). Let the radical equation is,
(3x-1)^{\frac{1}{5}}=2(3x−1)51=2
Step 1:
(3x-1)^{\frac{1}{5}\times \frac{5}{1} }=2^{\frac{5}{1}}(3x−1)51×15=215
Step 2:
(3x-1)=2^5(3x−1)=25
Step 3:
3x=32+13x=32+1
Step 4:
x=11x=11
4). By substituting x=11x=11 in the original equation.
(3\times 11-1)^{\frac{1}{5}}=(32)^\frac{1}{5}(3×11−1)51=(32)51
=(2^5)^\frac{1}{5}=(25)51
=2=2
There is no extraneous solution.
[tex]\sqrt \frac{256}{4\\}[/tex]
Answer:
8
Step-by-step explanation:
[tex]\sqrt{\frac{256}{4} }[/tex]
[tex]\sqrt{\frac{16*16}{2*2} }[/tex]
[tex]\sqrt{(\frac{16}{2})^2 }[/tex]
square and root gets cancel . so ,
[tex]\frac{16}{2}[/tex]
8
x * 0.77 = 26
Solve for x.
Answer:
x = ~33.77
Step-by-step explanation:
divide .77 on both sides.
x = 26/0.77 = 33.766234 rounded to the nearest hundredth is 33.77.
lets check our answer by plugging it in:
33.77 * 0.77 = 26.0029 which is close enough
WUTY guerrITOSTITUTO PETTITUUTTOIVOITETTO
GO
Determine the equation of the line perpendicular to the line y = -8 through the point (-4,-2),
The line ys -8 is
The line perpendicular to the line y = -8 is
The equation of the line perpendicular to the line y = -8 through the point (-4,-2) is
Answer:
-x-6=y
Step-by-step explanation:
Perpendicular slope is -1
-1(-4)+b=-2
B=-6
Answer:
Determine the equation of the line perpendicular to the line y = –8 through the point (–4, –2).
The line y = –8 is
✔ horizontal
The line perpendicular to the line y = –8 is
✔ vertical
The equation of the line perpendicular to the line y = –8 through the point (–4, –2) is
✔ x = –4
Step-by-step explanation:
i got it right
Need answer fasttt
Find the volume of a pyramid with a square base, where the side length of the base is
11.5 in and the height of the pyramid is 6.7 in. Round your answer to the nearest
tenth of a cubic inch.
Answer:
295.4 [tex]in^3[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3}(b)^2(h)\\\\ =\frac{1}{3} (11.5)^2(6.7)\\\\=\frac{1}{3}(135.25)(6.7)\\\\[/tex]
= 295.358
≈ 295.4
Helppppppppp meeeeeeeeeeee
hii guys I'm sorry I am close to failin, and I sorry tay I'm asking a lot for questions :c
Answer:
A≈87.96
Step-by-step explanation:
A=2πrh+2πr2
= 2pi(2)(5) + 2pi(2)2
Answer:
Hello! answer: 87.92
Step-by-step explanation:
Im a little rusty on these but the answer I believe would be 87.92
2 × 2 × 3.14 = 12.56
2 × 2 × 3.14 = 12.56
4 × 3.14 = 12.56 12.56 × 5 = 62.8
12.56 + 12.56 + 62.8 = 87.92
Hope that helps!
Oof, I'm to tired to remember how to do this T-T
Can anyone help asap? This is timed. Brainliest for best answer!!
Answer:
D
Step-by-step explanation:
Equation of the line
y - y1 = m(x - x1)
y - (-4) = 1/3 (x - 3)
y + 4 = 1/3x - 1
y = 1/3 x - 5
the graph that intercept y axis in -5 is the graph D
Answer:
i can't remember how to do this rn because its like 2:30am
C seems like most accurate answer, if this is wrong im really sorry :C
Step-by-step explanation:
A company paid a ₦25200 electricity bill to NEPA. The bill included VAT at 5%. Calculate the amount of VAT paid
Answer:
1260
Step-by-step explanation:
5÷100=0.05
0.05×25200=1260
A 3-column table with 5 rows. Column 1 is labeled Tickets with entries 2, 4, 6, 8, 10. Column 2 is labeled Total Cost for Aquarium with entries 29, 58, 87, blank, blank. Column 3 is labeled Total Cost for Wave Pool with entries 33.5, 67, blank, blank, blank.
Gale found out that the wave pool has a money-saving deal: if more than 4 people attend, the tickets are discounted from $16.75 each to $12.25 each.
Calculate to determine how much 6 tickets to the wave pool will cost.
$
Answer
What event will cost the least for 9 tickets?
the wave pool
How much less will this event cost?
$20.25
Hope it helps :)
Step-by-step explanation:
X^2 +
1/x^2
+12(x+1/x) +38,
Answer:
44
Step-by-step explanation:
Help please! I really need it
Enter the explicit rule for the geometric sequence.
120,40,403,409,4027
Answer:
120(1/3)^n-1
This is the correct answer for sure.
please help 20 points
Answer:
Option C is correct
Step-by-step explanation:
[tex]a. - 3, - 12 \\ = 36[/tex]
[tex]b. - 6, - 6 \\ = 36[/tex]
[tex]c. \: \: 9, - 4 \\ = - 36[/tex]
[tex]d. \: \: 2,18 \\ = 36[/tex]
Hope it is helpful...Omar's gas tank is 1/3 full. after he buys 9 gallons of gas, it is 5/6 full. How many gallons can Omar's tank hold?
Answer:
18 gallons
Step-by-step explanation:
First get a common denominator (6). So 3/6 are added to the tank when Omar buys 9 gallons of gas. That means for every 1/6, three gallons are added to the tank.
List all the possible numbers for ALL 4 Quadrants (in terms of negative, positive).
What Quadrant would the following numbers be in:
-4, -6 ______
+5, +5______
-4, +1 ______
+3, -7 _____
Please please pleeeesse hurry if you see this and it’s right I with give brainliest
Answer:
forma is h * w / 2 and y and x have no value because there are no numbers to calculate.
Step-by-step explanation:
hope this helps!!!!!
Answer:
h * w/2 OR (base * height) / 2
/ = divide
* = multiply
Step-by-step explanation:
can somebody help me frl frl cause I'm failing
Black pens come in boxes of 12. Blue pens come in boxes of 10. Red
pens also come in boxes of 10. You need a total of 50 of each color of
pen. You have 2 boxes of black pens, 3 boxes of blue pens, and 1 box of
red pens. How many boxes of each color should you order?
Answer
12+10+10+50+2+3+1=88
Step-by-step explanation:
Answer:
Red pens: 4 boxes
blue pens: 2 boxes
black: 3 boxes
Step-by-step explanation:
A set of weights includes an 8 lb. barbell and 6 pairs of weight plates. Each pair of plates weighs 15 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 15x + 8. What is the range of the function for this situation?
Answer
8,98
Step-by-step explanation:
the minimum amount of weight you can use is the barbell alone which is 8lbs by itself and the maximum is 98 because there are 6 15lb plates which equal to 90lb total and when you add the 6 plates to the barbell you get 98lbs
Write an algorithm to find sum of first ten even numbers?
plz do it ... if you do i will mark brainliest
Answer:
n(n+1)
This is the answer I know
which point is a solution to the inequality shown in this graph
(0, 5)
(3, 2)
(-3, -6)
(5, 0)
Answer:
(0,5)
Step-by-step explanation:
if the point is graphed in the blue area then it is a solution to the inequality
Note: because the line is dashed points graphed on the line are not solutions
(0,5) is graphed in the blue region meaning that (0,5) is a solution to the inequality.
even though we may have found the answer let's check the rest just to be safe
(3,2) and (-3,-6) are graphed on the line
remember because the line is dashed points that fall on it are not solutions
therefore (3,2) and (-3,-6) are not Solutions
(5,0) when graphed is not in the shaded area and is therefore not a solution
we can conclude that a is the answer
Cost per item: $6.06 item sold: 64321 total profit: $25123.5 sale price:?
Answer:
0.39063241
Step-by-step explanation:
cost per item: 6.06
items sold: 64321
total profit: 25123.5
sale price: ?
x = number of items
64321x - 6.06x = 25123.5
64314.94x = 25123.5
x = 25123.5/64314.94 = 0.39063241
