Answer:
Hey there!
That would be the square root of 36, or 6.
Hope this helps :)
MATH HELP ME ASAP!!!!
Answer: Zak - Resp after 24 months = $4,344.00
Zak - Technology Fund after 24 months = $1,102.98
Zak's Technology Fund has enough money to buy a laptop.
Zak's Savings (Resp) will last less than 6 months
Step-by-step explanation for Zak:
January - June 2019
$15/hr x 20 hr x 4 wks x 6 months = $7200 Gross Income
Resp (15%): $7200(0.15) = $1080CPP(5%): $7200(0.05) = $360EI(2%): $7200(0.02) = $144Taxable Income is $7200 - $1080 = $6120 (Annual Income $12,240)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($6,120-$4,500)(0.08) = $129.60→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income
Tech Fund (5%): $5486.40(0.05) = $274.32
Food Expense (30%): $5486.40(0.3) = $1,645.92
Clothing Expense (30%): $5486.40(0.3) = $1,645.92
Entertainment Expense (25%): $5486.40(0.25) = $1,371.60
Miscellaneous Expense (10%): $5486.40(0.1) = $548.64
Other Expenses: $5,212.08
July - December 2019 (excluding August)
$16/hr x 20 hr x 4 wks x 5 months = $6400 Gross Income
Resp (15%): $6400(0.15) = $960CPP(5%): $6400(0.05) = $320EI(2%): $6400(0.02) = $128Taxable Income is $6400 - $960 = $5440 (Annual Income $11,560)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($5,440-$4,500)(0.08) = $75.20→ $6,400 - ($960 + $320 + $128 + $0 + $75.20) = $4,916.80 Net Income
Tech Fund (5%): $4916.80(0.05) = $245.84
Food Expense (30%): $4916.80(0.3) = $1,475.04
Clothing Expense (30%): $4916.80(0.3) = $1,475.04
Entertainment Expense (25%): $4916.80(0.25) = $1,229.20
Miscellaneous Expense (10%): $4916.80(0.1) = $491.68
Other Expenses: $4,670.96
January - June 2020
$17/hr x 20 hr x 4 wks x 6 months = $8160 Gross Income
Resp (15%): $8160(0.15) = $1224CPP(5%): $8160(0.05) = $408EI(2%): $8160(0.02) = $163.20Taxable Income is $8160 - $1224 = $6936 (Annual Income $13,872)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($6,936-$4,500)(0.08) = $194.88→ $8,160 - ($1224 + $408 + $163.20 + $0 + $194.88) = $6,169.92 Net Income
Tech Fund (5%): $6169.92(0.05) = $308.50
Food Expense (30%): $6169.92(0.3) = $1,850.98
Clothing Expense (30%): $6169.92(0.3) = $1,850.98
Entertainment Expense (25%): $6169.92(0.25) = $1,542.48
Miscellaneous Expense (10%): $6169.92(0.1) = $616.98
Other Expenses: $5,861.42
July - December 2020 (excluding August)
$18/hr x 20 hr x 4 wks x 5 months = $7200 Gross Income
Resp (15%): $7200(0.15) = $1080CPP(5%): $7200(0.05) = $360EI(2%): $7200(0.02) = $144Taxable Income is $7200 - $1080 = $6120 (Annual Income $13,056)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($6,120-$4,500)(0.08) = $129.60→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income
Tech Fund (5%): $4916.80(0.05) = $274.32
Food Expense (30%): $5486.40(0.3) = $1,645.92
Clothing Expense (30%): $5486.40(0.3) = $1,645.92
Entertainment Expense (25%): $5486.40(0.25) = $1,371.60
Miscellaneous Expense (10%): $5486.40(0.1) = $548.64
Other Expenses: $5,212.08
[tex]\boxed{\begin{array}{l|r|r|r|r||r}\underline{ZAK}&\underline{Jan-Jun'19}&\underline{Jul-Dec'19}&\underline{Jan-Jun'20}&\underline{Jul-Dec'20}&\underline{Totals\quad }\\Gross&\$7200.00&\$6400.00&\$8160.00&\$7200.00&\$28960.00\\Resp&\$1080.00&\$960.00&\$1224.00&\$1080.00&\$4344.00\\Net&\$5486.40&\$4916.80&\$6169.92&\$5486.40&\$22059.52\\Other&\$5212.08&\$4670.96&\$5861.42&\$5212.08&\$20956.54\\Tech&\$274.32&\$245.84&\$308.50&\$274.32&\$1102.98\end{array}}[/tex]
Is 5.7c-1.5+3.2c=7.8c-1.5+1.1c a one solution problem?
Answer:
This is NOT a one solution problem.
Step-by-step explanation:
Group all terms with a c in it to the left of the equal sign, and group all numbers to the right of the equal sign.
5.7c-1.5+3.2c=7.8c-1.5+1.1c
5.7c + 3.2c - 7.8c - 1.1c = - 1.5 + 1.5
8.9c - 8.9c = 0
0 = 0
No matter which number you substitute for c, it will always be true. Since you can find infinity of solutions, this is NOT a one solution problem.
solve for x, if a solution is extraneous identify in the final answer. thx :)
Answer:
x = 6 and x = 11.
Step-by-step explanation:
sqrt(x - 2) + 8 = x
sqrt(x - 2) = x - 8
(sqrt(x - 2))^2 = (x - 8)^2
x - 2 = x^2 - 16x + 64
x^2 - 16x + 64 = x - 2
x^2 - 17x + 66 = 0
We can use the discriminant to find whether there are solutions to the equation.
b^2 - 4ac; where a = 1, b = -17, and c = 66.
(-17)^2 - 4 * 1 * 66
= 289 - 264
= 25
Since the discriminant is positive, we know there are two valid solutions to the equation.
x^2 - 17x + 66 = 0
(x - 6)(x - 11) = 0
The solutions are when x - 6 = 0 and x - 11 = 0.
x - 6 = 0
x = 6
x - 11 = 0
x = 11
Hope this helps!
Answer:
x=11 solution
x=6 extraneous
Step-by-step explanation:
sqrt( x-2) + 8 = x
Subtract x from each side
sqrt(x-2) = x-8
Square each side
(sqrt(x-2))^2 = (x-8) ^2
x-2 = x^2 -8x-8x+64
x-2 = x^2 -16x+64
Subtract ( x-2) from each side
0 = x^2 -17x +66
Factor
0 = (x-6) ( x-11)
Using the zero product property
x=6 x=11
Checking the solutions
x=6
sqrt( 6-2) + 8 = 6
sqrt(4) +8 = 6
2 +8 = 6
False not a solution
x=11
sqrt( 11-2) + 8 = 11
sqrt(9) +8 =11
3 +8 = 11
solution
What is the simplest form for the expression (-12.7y-3.1x) Plus 5.9y-(4.2y Plus x)
Answer:
[tex]\boxed{-4.1x-11y}[/tex]
Step-by-step explanation:
[tex](-12.7y-3.1x) + 5.9y-(4.2y + x)[/tex]
Expand brackets.
[tex]-12.7y-3.1x+ 5.9y-4.2y - x[/tex]
Combining like terms.
[tex]- x-3.1x-12.7y+ 5.9y-4.2y[/tex]
[tex]-4.1x-11y[/tex]
Answer:
[tex] \boxed{\red{ - 11y - 4.1x}}[/tex]
Step-by-step explanation:
[tex] (- 12.7y - 3.1x) + 5.9y - (4.2y + x) \\ - 12.7y - 3.1x + 5.9y - 4.2y - x \\ - 12.7y + 5.9y - 4.2y- 3.1x - x \\ = - 11y - 4.1x[/tex]
Given the formula below, solve for x.
- Vi
ОА.
+ 11
B.
y – 9 + fi
O c.
Ử - VI
m
-fi
D.
mly – yy)
Answer:
Option (C)
Step-by-step explanation:
Given formula of a line passing through [tex](x_1, y_1)[/tex] and slope 'm' is,
[tex]y-y_1=m(x-x_1)[/tex]
Further solving this equation,
[tex]y-y_1=mx-mx_1[/tex] [By distributive property]
[tex]y-y_1+mx_1=(mx-mx_1)+mx_1[/tex] [By adding [tex]mx_1[/tex] on both the sides]
[tex]y-y_1+mx_1=mx[/tex]
[tex]\frac{y-y_1-mx_1}{m}=\frac{mx}{m}[/tex] [Divide the equation by m]
[tex]\frac{y-y_1}{m}-x_1=x[/tex]
Therefore, Option (C) will be the answer.
Choose the equation that is equivalent to the equation shown below. y = 2x + 4a/6b A. x = 2x - 3by B. c = ax-by/z C. b = 6y/2x+4a D. a = 3by-x/2
Answer:
Step-by-step explanation:
y = 2x + 4a/6b y=(12xb+4b )/6b
6yb=12x+4a
a=(-12xb+6yb)/4=
a=3yb/2 -3xb
x=y/2-a/3b
b=2a/(3y-6x)
the solution is for every variable
After eating at a restaurant Alyssa Dan and Nancy decided to divide the bill evenly if each person pay $38 what was the total of the bill
Answer:
$76
Step-by-step explanation:
$38 + $38 = $76
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9). What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 –4 –2 2 4
Answer:
-2
Step-by-step explanation:
The coordinate of a point that divides a line AB in a ratio a:b from A([tex]x_1,y_1[/tex]) to B([tex]x_2,y_2[/tex]) is given by the formula:
[tex](x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )[/tex]
Given that a line JK, with Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:
[tex]x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2[/tex]
Line segments can be divided into equal or unequal ratios
The x coordinate of the segment is -2
The coordinates of points J and K are given as:
[tex]J = (-6,-2)[/tex]
[tex]K = (8,-9)[/tex]
The ratio is given as:
[tex]m : n =2 : 5[/tex]
The x-coordinate is then calculated using:
[tex]x = (\frac{m}{m + n }) (x_2 - x_1) + x_1[/tex]
So, we have:
[tex]x = (\frac{2}{2 + 5 }) (8 - -6) -6[/tex]
[tex]x = (\frac{2}{7}) (14) -6[/tex]
Expand
[tex]x = (2) (2) -6[/tex]
Open bracket
[tex]x = 4 -6[/tex]
Subtract 6 from 4
[tex]x = -2[/tex]
Hence, the x coordinate of the segment is -2
Read more about line ratios at:.
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In 1833 a ship arrived inCalcutta with 120 tons remaining of its cargo of ice. One third of the original cargo was lost because it had melted on the voyage. How many tons of ice was the ship carrying when it set sail? A.40 B.80 C.120 D.150 E.180
Answer: 180
Step-by-step explanation:
Let the tons of ice the ship was carrying when it set sail be y.
We are told that one third of the original cargo was lost because it had melted on the voyage and that it arrived in Calcutta with 120 tons remaining of its cargo of ice.
This means that (1 - 1/3 = 2/3) remained which was the 120 tons remaining. This implies that:
2/3 × y = 120
2y/3 = 120
2y = 120 × 3
2y = 360
y = 360/2
y = 180
The ship was carrying 180 tons of ice when it set sail
Which option is equal to 7 1/5
Answer:
D. is the answerStep-by-step explanation:
Question:
7^1/5
The number given has an exponent of a fraction: fraction exponent = 1/5
So, when you have a fraction - you always have a square root - Important!!Since the top is one, the number 7 stays the same. = 7^1 = 7
The bottom is a 5. This means it is to the fifth root.
Answer = D
Hope this helped,
Kavitha
Answer: If 36/7 is one of the options, choose that one.
If the question involves an exponent, you should use the "caret" which is ^ found above the 6 on a keyboard. [Shift + 6]. That helps avoid confusion.
Step-by-step explanation: 7 is equal to 35/5 because 7×5=35
Add 1/5 and you end up with 36/5. A Common rational number.
7^(1/5) = the 5th root of 7. A very small irrational number!
A standard deck of of 52 playing cards contains 13 cards in each of four suits : diamonds, hearts , clubs and spades. Two cards are chosen from the deck at random.
Answer:
Probability of (one club and one heart) = 0.1275 (Approx)
Step-by-step explanation:
Given:
Total number of cards = 52
Each suits = 13
FInd:
Probability of (one club and one heart)
Computation:
Probability of one club = 13 / 52
Probability of one heart = 13 / 51
Probability of (one club and one heart) = 2 [(13/52)(13/51)]
Probability of (one club and one heart) = 0.1275 (Approx)
Answer:
D. 0.1275
Step-by-step explanation:
Justo took the Pre-Test on Edg (2020-2021)!!
Which is the best estimate of 90/7 divided by 1 3/4? 2 6 12 24
Answer:
6 is the best estimate.
Step-by-step explanation:
(90/7) / (1 & 3/4) == (90/7) / (7/4) == (90/7) * (4/7) == 360/49 > 7.
Choose 6 as your best approximation.
What is the point- slope of a line with slope -5 that contains the point (2,1) ? ( TOP ANSWER GETS BRAINLEST)
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 5 and (a, b) = (2, - 1), thus
y - (- 1) = - 5(x - 2) , that is
y + 1 = - 5(x - 2) → C
Answer:
y + 1 = - 5(x - 2)Option C is the correct option
Step-by-step explanation:
The general form of point slope form of line is :
[tex]y - y1 =m ( x - x1)[/tex]
Where ( x1 , y1 ) is one point on the line and m is the slope.
In the given problem,
The slope of line ( m ) = - 5
One point on the line = ( x1 , y1 ) = ( 2 , -1 )
The point slope form of the line is:
y - ( - 1 ) = - 5 ( x - 2 )
y + 1 = - 5 ( x - 2 )
Hope this helps..
Best regards!!
Solve the equation. \dfrac5{13}=t-\dfrac{6}{13} 13 5 =t− 13 6 start fraction, 5, divided by, 13, end fraction, equals, t, minus, start fraction, 6, divided by, 13, end fraction t=t=t, equals
Answer:
11 /13 = t
Step-by-step explanation:
5/13 = t -6/13
Add 6/13 to each side
5/13 + 6/13 = t -6/13+ 6/13
11 /13 = t
Answer:
[tex]t=\frac{11}{13}[/tex]
Step-by-step explanation:
[tex]\frac{5}{13} = t -\frac{6}{13}[/tex]
Add [tex]\frac{6}{13}[/tex] to both sides.
[tex]\frac{5}{13} + \frac{6}{13} = t -\frac{6}{13} + \frac{6}{13}[/tex]
[tex]\frac{11}{13} =t[/tex]
Please answer it now in two minutes
Answer: 3.2 yd
Step-by-step explanation:
Notice that TWV is a right triangle.
Segment TU is not needed to answer this question.
∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6
[tex]\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}[/tex]
A spinner is separated into 3 equal pieces, as shown below: Mary spins the spinner 6 times. What is the theoretical probability that it stops on the red sector on the last spin?
A.) 1/36
B.) 1/9
C.) 1/3
D.) 2/3
Answer:
C. 1/3
Step-by-step explanation:
Given:
Number of colors listed (Successful Outcome)
Red 1
Yellow 1
Purple 1
Total or Possible outcome= 3
Required:
What is the theoretical probability that it stops on the red sector on the last spin?
Formula:
Probability= Successful outcome ÷ Possible outcome
Solution:
Probability of the spinner stoping on red.
Probability= Successful outcome ÷ Possible outcome
Probability=1÷3
Probability=1/3
Hope it helps ;) ❤❤❤
The theoretical probability that spinner stops on the red sector on the last spin is option (C) [tex]\frac{1}{3}[/tex]
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given,
A spinner is separated into 3 equal parts.
Then Mary spins the spinner 6 times.
What is the theoretical probability that it stops on the red sector on the last spin. So only last spin is important, outcomes of first 5 spin is not important and it is independent.
Probability = Number of favorable outcome / Number of Total outcome
Probability (Red sector) = [tex]\frac{1}{3}[/tex]
Hence, the theoretical probability that spinner stops on the red sector on the last spin is option (C) [tex]\frac{1}{3}[/tex]
Learn more about Probability here
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find the area of equilateral triangle whose median is X cm
options:
a.x^2
b.(x^2)/2
c.(x^2)/√3
d.(x^2)/3
Evaluate A/B for a = 1/2 and b = -3/7
Answer:
-7/6
Step-by-step explanation:
If a = 1/2 and b = -3/7, then your given:
1/2 divided by -3/7=
-7/2*3=
-7/6
Sorry if its a bit unclears
Answer:
[tex]\frac{7}{-6}[/tex]
Step-by-step explanation:
To do this you are basically dividing the fractions so when you set up the equation it will look like this [tex]\frac{1}{2}/\frac{-3}{7}[/tex] now that we have this we will take the reciprocal of -3/7 which is 7/-3 and than multiply the 2 fractions we we get 7/-6
The sand used for sanding icy roads in the winter is stored in a conical-shaped structure with a radius of 10 m
and a height of 16 m. Calculate the maximum amount of sand which can be stored in this structure.
Answer:
[tex]V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3[/tex]
The maximum amount of sand that can be stored in this structure is 1675.52 m³.
Step-by-step explanation:
The volume of a conical-shaped structure is given by
[tex]V = \frac{1}{3} (\pi \cdot r^2 \cdot h)[/tex]
Where r is the radius and h is the height of the structure.
We are given that
radius = 10m
height = 16m
Substituting the above values into the formula, we get
[tex]V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3[/tex]
Therefore, the maximum amount of sand th can be stored in this structure is 1675.52 m³.
A tank contains 8000 liters of a solution that is 40% acid. How much water should be added to make a solution that is 30% acid?
Answer:
2,666.67 L of water
Step-by-step explanation:
Solve for W:
1) 3200 = 2400 + 0.3w
2) 800 = 0.3w
Divide both sides by 0.3 to get the variable alone
3) (800)/0.3 = (0.3w)/0.3
4) w = 2,666.67 L
[tex]Let $u$ and $v$ be the solutions to $3x^2 + 5x + 7 = 0.$ Find\[\frac{u}{v} + \frac{v}{u}.\][/tex]
By the factor theorem,
[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]
Now,
[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]
[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]
So we have
[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]
The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
What is quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.
What is the sum and product of the roots of the quadratic equation?If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then
Sum of the roots = [tex]\frac{-b}{a}[/tex]
And,
Product of the roots = [tex]\frac{c}{a}[/tex]
According to the given question.
We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]
On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].
We get
[tex]a = 3\\b = 5\\and\\c = 7[/tex]
Also, u and v are the solutions of the quadratic equation.
⇒ u and v are the roots of the given quadratic equation.
Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].
And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].
Therefore,
[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)
[tex]uv=\frac{7}{3}[/tex] ....(iii) (product of the roots)
Now,
[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex] ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])
Therefore,
[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex] (from (i) and (ii))
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]
Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
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which system of linear inequalities is represented by this graphed solution?
A. y > -1/2x + 2
y ≤ 3x - 1
B. y < -1/2x + 2
y ≥ 3x - 1
C. y > -2x + 2
y ≤ 1/3x - 1
D. y ≤ -1/2x + 2
y < 3x - 1
Answer:
B. y < -1/2x + 2 y ≥ 3x - 1Step-by-step explanation:
The gray shadowed area is below descending function and the line is dashed.
It means coefficient x is m<0 and the sign of inequality is y <
So the inequality wich fit it is y < -1/2x + 2
The blue shadowed area is above ascending function and the line is uninterrupted.
It means coefficient x is m>0 and the sign of inequality is y ≥
So the second inequality of system (y ≥ 3x - 1) also match.
The system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2 and y < 3x - 1
The standard equation of a line is expressed as y = mx + b;
m is the slope of the lineb is the y-intercept of the lineFor the blue line, the y-intercept is at y = -1. For the slope passing through (0, -1) and (2, 5):
m = 5+1/2-0
m= 6/2
m = 3
The equation of the line is y = 3x - 1
Since the line is dashed and the left part shaded, the inequality expression will be y < 3x - 1
For the black line, the y-intercept is at y = 2. For the slope passing through (0, 2) and (4, 0):
m = 0-2/4-0
m= -2/4
m = -1/2
The equation of the line is y = -1/2x + 2
Since the line is solid and the lower part shaded, the inequality expression will be y ≤ -1/2x + 2
Hence the system of linear inequalities represented by this graphed solutions are y ≤ -1/2x + 2 and y < 3x - 1
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The advertised size of a computer or television screen is actually the length of the diagonal of
the screen. A computer screen measures 30cm by 22.5cm. Determine the length of its
diagonal.
Answer:
37.5 cm
Step-by-step explanation:
See attached for reference.
let the diagonal be x,
By Pythagorean formula:
x² = (22.5)² + (30)²
x = √[(22.5)² + (30)²]
x = 37.5 cm
.
What is y + 3 = 7(2 – 2) written in standard form?
Answer:
y = -3
Step-by-step explanation:
y + 3 = 7(2 - 2)
y + 3 = 0
Subtract 3 from both sides
y + 3 - 3 = 0 - 3
y = -3
Answer:
7x - y = 17
Step-by-step explanation:
Maybe you want the standard form of the point-slope equation ...
y +3 = 7(x -2)
__
y + 3 = 7x -14 . . . . . eliminate parentheses
17 = 7x -y . . . . . . . . add 14-y
7x - y = 17
A.
The graph that represents x < 4 is
-
--
- 1
-H
-H
The graph that represents 4 sx is
0
2.
4
6.
8
10
12.
14
16
18 20
B.
1
--
--
1
-1
1
0
-5
4 -3
-2
1
2
3
4.
5
C.
--
---
--
--
-6
-4
-2
0
2.
4
6
8
10
12 14
Answer:
BAStep-by-step explanation:
The < symbol does not include the "or equal to" case, so will be graphed with an open circle at the boundary. x < 4 means that values of x less than 4 will be shaded, and there will be an open circle at x=4. Graph B shows this.
__
4 ≤ x means there will be a solid dot at x=4, and values of x greater than 4 will be shaded. Graph A shows this.
Answer: B & A
Step-by-step explanation:
If QR = 9 and ST = 13 calculate LM.
Answer:
[tex]\boxed{\sf LM = 11}[/tex]
Step-by-step explanation:
According to trapezoid mid-segment theorem:
[tex]LM = \frac{QR+ST}{2}\\ Given \ that\ QR = 9, ST = 13[/tex]
[tex]\sf LM = \frac{9+13}{2}[/tex]
LM = 22/2
LM = 11
Campus rentals rent 2 and 3 bedroom apartments for 700$ and 900$ a month respectively. Last month they had six vacant apartments and reported $4600 in lost rent. How many of each type of apartment were vacant?
Answer:
2 - bedroom apartment = 4
3 - bedroom apartment = 2
Step-by-step explanation:
Given the following :
2 - bedroom apartment = $700 / month
3 - bedroom apartment = $900 / month
Last month:
Number of vacant apartment = 6
Amount of Lost rent = $4600
Let a = 2 - bedroom apartment and b = 3 - bedroom apartment
Vacant apartment :
a + b = 6 - - - (1)
Lost rent :
700a + 900b = 4600 - - - (2)
From (1),, a = 6 - b
Substitute a = 6 - b into (2)
700(6 - b) + 900b = 4600
4200 - 700b + 900b = 4600
4200 + 200b = 4600
200b = 4600 - 4200
200b = 400
b = 400/200
b = 2
From (1) ;
a + b = 6
a + 2 = 6
a = 6 - 2
a = 4
a = 2 - bedroom apartment = 4
b = 3 - bedroom apartment = 2
Find the probability of choosing an item from the intersection of following sets Set A : {1, 5, 10, 14, 22} Set B : {5, 14, 20, 22, 27}
Answer:
1/3
Step-by-step explanation:
There are three elements that are intersecting: 5, 14, 22
Probability of choosing an item is 1/3
PLEASE help me with this question! This is urgent!
Answer:
second one
Step-by-step explanation:
Solve for x: (-1/2) x = 6
Answer: x = -12
Step-by-step explanation:
-1/2x=6
Divide by -1/2
x = -12
Hope it helps <3