( x - 2 )² + ( y + 4 )² = 49
.........................................
The length of a rectangle is 20cm longer than its width.
The area of the rectangle is 1000cm?
Find the width and length of the rectangle.
Give your answers in surd form.
[tex]\text{Width} ~= w ~ cm \\\\ \text{Length}~,l = (20+ w) ~ cm \\\\\text{Area of rectangle} = 1000 cm^2\\\\\\\text{Now,}\\\\l \cdot w = 1000\\\\\implies (20 + w) w= 1000\\\\\implies w^2 +20w -1000=0\\\\\\\implies w = \dfrac{-20 \pm \sqrt{20^2 - 4 \cdot 1 \cdot (-1000)}}{2 \cdot 1}\\\\\\\implies w = \dfrac{-20 \pm \sqrt{4400}}{2}= \dfrac{-20\pm 20\sqrt{11}}2 = -10 \pm 10\sqrt{11}\\\\\text{Width cannot be negative so,} \\\\w= -10+10\sqrt{11}=10\left(\sqrt{11} - 1 \right) ~ cm\\\\[/tex]
[tex]\text{And length,}[/tex]
[tex]l= 20+ 10\left(\sqrt{11} - 1} \right) = 20 + 10\sqrt{11} - 10 = 10 + 10\sqrt{11} = 10 \left(1+ \sqrt{11} \right)~ cm[/tex]
How do you write 7460 in standard form?
Answer:
7460
Step-by-step explanation:
To write a linear expression in standard form, rearrange the terms in alphabetical order.
7460
Answer:
a = 7.46
7.46 x 103
103 = 1,000 x 7.46 = 7,460
here your answer
hope it helps you
this graph shows how much lisa earns babysitting compared with thge number of hours she works
Answer:
For every hour she earns 12$
Step-by-step explanation:
If your question looks like the picture, then the answer above is the right answer. If it's not, oh well, show the picture next time!
PLEASE ANSWER NOWWWWW
340816.326531
Answer:
nearest whole number would be 340816
Answer:
340,816
Hope this helps :)
write the value of (2+root3)(2-root3)
Answer: 1
Step-by-step explanation: use foil and get 4-3.
A line passes through the point (-6,9) and has a slope of 3/2. Write an equation in slope-intercept form for this line.
Answer:
y=3/2x+18
Step-by-step explanation:
Hi there!
We are given a point (-6,9) and a slope of 3/2
We want to write the equation of this line in slope-intercept form
Slope-intercept form is written as y=mx+b, where m is the slope and b is the y intercept
Since we already know the slope of the line as 3/2, we can substitute it as m into the equation:
y=3/2x+b
Now let's find b
Since the equation of the line passes through (-6,9), we can use it to help solve for b
Substitute -6 as x and 9 as y:
9=3/2(-6)+b
Multiply
9=-9+b
Add 9 to both sides
18=b
Substitute 18 as b into the equation.
y=3/2x+18
Hope this helps!
2x+3y=15
x+y=6
work out the values of x and y.
Answer:
Step-by-step explanation:
Elimination sounds the easiest for y:
[tex]I - 2II: 2x+3y -2x -2y = 15-12 \rightarrow y= 3[/tex]
Now we got one value, let's replace in one of the two and find the second
[tex]II: x+(3)=6 \rightarrow x=3[/tex]
Answer:
[tex]2x + 3y = 15...(1) \\ x + y = 6...(2) \\ 2 \times (2) \\ 2x + 2y = 12...(3) \\ (1) - (3) \\ 0 + 3y - 2y = 15 - 12 \\ \color{red} \boxed{ y = 3 }\\ sub \: in \: (2) \\ x + 3 = 6 \rightarrow \: x = 6 - 3 \\ \color{green} \boxed{ x = 3 }[/tex]
Jack and Jill, trying to do math and chill, when they ran into a problem. They can't agree on what the answers should be, so now it's up to you to solve them.
In class, Jack thought as Jill she sought solve an absolute value... she removed the sign from her negative nine and said "the problem should be just about through".
But Jack he said, "no Jill you misread, the negative is on the outside". Still Jill didn't budge, so you be the judge, does this mean that the teacher lied?
Here's the problem Jack and Jill are trying to solve: -|9| = ?Jack thinks the answer is -9, because the negative is outside the absolute value signs. Jill thinks the answer is 9, because the teacher said absolute value is always positive.
Who is right and why? Explain your steps using sentences.
Answer:
-9
Step-by-step explanation:
the teacher was right
8. You have been asked to repaint the lateral surface area of cone-shaped pylons used for soccer drills. If they have a radius of 5" and a height of 12", calculate the slant height and lateral surface area to be painted to the nearest square inch.??
Answer:
See answer below.
Step-by-step explanation:
LA = π rl
1st find l
The radius is 5" and the height is 12" l = ?
h and the r is the two legs in the right triangle when drawn in a cone.
Use a² + b² = c² ⇔ h² + r² = l²
12² + 5² = l²
144 + 25 = l²
169 = l²
[tex]\sqrt{169} = l[/tex]
13 = l
Formula for LA = π r l
LA = 3.14 × 5 ×13 or with a calculator LA = π × 5 × 13
LA = 204.1 sq.in LA = 204.2035225 sq. in
I use 3.14 = for π but you know what the teacher uses in class.
0(-7) helppppppppppppppppppppp
Answer:
0
Step-by-step explanation:
anything multuplied by 0 is 0
A pool company is creating an image for a client that has the look of a 3-D image for a family pool and a similar dog pool. Find the value of a in the drawing below:
Answer:
a = 21
Step-by-step explanation:
Based on the information given, we can calculate that
WZ x 3 = a
so...
7 x 3 = 21
Hope that helped!! :)
Answer:
I think it is 21 since the relationship between 4 and 12 4 * 3 is equal to 12 so I did the same for each side but angles don't change so 7*3=21
Show that dividing a number by 5 1/2 gives the same answer as multiplying the number by 2/11 plz help!!!
Answer:
plz explain so i can help am i mutiplying the 2 numbers or...?
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
[tex]\frac{x}{5 \frac{1}{2} } \\\\ \frac{11}{11/2} \\\\11. \frac{2}{11}\\\\=2[/tex]
also,
[tex]x . \frac{2}{11} \\\\11 .\frac{2}{11} [x=11]\\\\=2\\[/tex]
Jeriel decides to research the relationship between the length in inches and the weight of a certain species of catfish. He measures the length and weight of a number of specimens he catches, then throws back into the water. After plotting all his data, he draws a line of best fit. Based on the line of best fit, how much would you predict a catfish with a length of 33 inches would weigh?
A catfish with a length of 33 inches would weigh 30 pounds.
Linear equationA linear equation is in the form of:
y = mx + b
where y,x are variables, m is the rate of change and b is the y intercept.
Let y represent the catfish weight with x inches length
From the line of best, it passes through (20, 4) and (23, 10), hence:
y - 4 = [(10 - 4)/(23 - 20)](x - 20)
y = 2x - 36
For a length of 33 inches:
y = 2(33) - 36 = 30 pounds
A catfish with a length of 33 inches would weigh 30 pounds.
Find out more on Linear equation at: https://brainly.com/question/14323743
what is the equation of a line when m=-7 and b=-8
the problem solving plan indentify step to organize your information which of the following answers choices are included in the steps to organize your information?
A) organize the problem and find the question
B) solve the problem and change your strategy if necessary
C) write the facts, organize your thoughts and define your strategy
D) organize the step and underline the question
that's the answer Just look at the picture's
100 POINTS
Given Point P(3,4), what is the resulting point after the following transformations?
Translate 3 up and 2 left
Rotation 180° around origin
Reflection over y-axis
Answer:
(1, -7)
Step-by-step explanation:
P(3,4)
3 up ---> y = 4 + 3 = 7
2 left ----> x = 3 - 2 = 1
new point (1, 7)
after 180 rotation around origin
point is (-1, -7)
now reflection over y-axis
(1, -7)
Answer:
[tex](1,-7)[/tex]
Step-by-step explanation:
Refer to the image below
Jamie and Raul both work at the Pizza House. Together, they work a total of 15 hours per week. Raul works 3 more than twice the hours as Jamie. How many hours does Jamie work per week?
Enter your answer in the box.
Answer:
Step-by-step explanation:
List the facts phrase by phrase.
Total = 15 hours
Let Raul's hours = x
Let Jamie's hours = y
Total = x + y = 15
x = 3 + 2y
From total, find x
x+ y = 15 Subtract y from both sides.
x = 15 - y Put the value for x in x = 3+ 2y
3 + 2y = 15 - y Subtract 3 from both sides
2y = 15 - 3-y Combine
2y = 12 - y Add y to both sides.
2y + y = 12 Combine
3y = 12
y = 12 / 3
y = 4
Jamie worked 4 hours
Raul worked 11
If your getting paid 5$ every week how long will it takes you to get 10,000$?
A person wins $25,000 on a game show and a trip to Costa Rica worth $5,700. Does he have any tax obligation from these winnings?
Answer:
Yes
Step-by-step explanation: All of these winnings become part of his gross income.
What are the ordered pairs of the
solutions for this system of equations?
f(x) = x2 – 5x + 3; f(x) = -3
(2, [?]); ( ), ( )
Given that
[tex]f(x) = -3\\\\\implies x^2 -5x +3 = -3 \\\\\implies x^2 -5x +6=0\\\\\implies x^2 - 3x -2x +6 =0\\\\\implies x(x-3) -2(x-3) =0\\\\\implies (x-2)(x-3)=0\\\\\implies x =2~ \text{or} ~ x =3[/tex]
Answer:
(2, - 3 ) and (3, - 3 )
Step-by-step explanation:
f(x) = x² - 5x + 3 and f(x) = - 3 , then equating
x² - 5x + 3 = - 3 ( add 3 to both sides )
x² - 5x + 6 = 0 ← in standard form
(x - 2)(x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 3 = 0 ⇒ x = 3
solutions are (2, - 3 ) and (3, - 3 )
sorry here is the question!! please help and Thank you!!
Answer:
B. 4
Step-by-step explanation:
[tex] \dfrac{\sqrt{32}}{\sqrt{2}} = [/tex]
[tex] = \dfrac{\sqrt{16 \times 2}}{\sqrt{2}} [/tex]
[tex] = \dfrac{\sqrt{16} \times \sqrt{2}}{\sqrt{2}} [/tex]
[tex] = \dfrac{4\sqrt{2}}{\sqrt{2}} [/tex]
[tex] = 4[/tex]
Which is the correct quotient with a letter as the remainder?
Answer:
A
Step-by-step explanation:
876 divided by 43 = 20
and the remainder is 16
in the case of other options, the quotients are correct but the remainders are wrong.
Therefore, A is the option with both correct quotient and remainder.
ashtons containor of water holds 80 milliliters. nelsons container holds 9/16 of that amont. how many milliniters of water do the two containors hokd together
Answer: Neither
Step-by-step explanation: Technically the containers hold no water at all as they hold only the bottles in which the water is actually contained. So the answer I suppose is 'Neither'.
Suppose that the function h is defined, for all real numbers, as follows
Somebody, please help me with this MATH question.
Please help I've never been more confused
Step-by-step explanation:
2.
Two pairs of corresponding angles
i. angle C angle D
ii. angle G angle F
Two pairs of alternate angles
i. angle B angle D
ii. angle H angle F
Two pairs of interior angles
i. angle C angle H
ii. angle D angle E
solve for g.
5.1g = 35.7
Answer:
g=7
Step-by-step explanation:
5.1 times 7 is 35.7
Answer:
Step-by-step explanation:
5.1g = 35.7
g = 35.7 / 5.1
= 7.
in figure below, lines r and s are parallel. If the m<1=47° , find:
Answer:
<3 = 47 degrees
<4 = 133 degrees
<5 = 47 degrees
<6 = 133 degrees
<7 = 47 degrees
<8 = 133 degrees
Angles 1 = 3 = 5 = 7 (vertical angles
Step-by-step explanation:
Jenifer is the high scorer on his basketball team. He made 36 free throws out of 50 free throws attempted. What was his percentage of free throw shots made?
Answer:
72%
Step-by-step explanation:
36/50 = 0.72
0.72 x 100 = 72%
Does the following relationship represent a function?