Answer:
1) x^2 - 14x + 44 = 0
(x^2 - 14x + 49) - 5 = 0
(x-7)^2 - 5 = 0
2)Assuming no complex number x...
(x-7)^2 = 5
x-7 = 5
x-7 = -5
x= 12, x=2
==============
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The answers to both the subparts of the equations are shown:
(A) Re-written equation by completing the square: (x-7)² - 5 = 0(B) Solutions of the equation: x = 12, x = 2What are equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.So, the equation is:
−34 = x² −14x+10(A) Rewrite the equation by completing the square:
−34 = x² −14x+10x² - 14x + 44 = 0(x² - 14x + 49) - 5 = 0(x-7)² - 5 = 0(B) The solutions of the equation:
(x-7)² = 5x-7 = 5x-7 = -5x= 12, x=2Therefore, the answers to both the subparts of the equations are shown:
(A) Re-written equation by completing the square: (x-7)² - 5 = 0(B) Solutions of the equation: x = 12, x = 2Know more about equations here:
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Pls help meee and thank you
Answer:
I believe the answer is y=4x+4
Step-by-step explanation:
because the 4 that is on the Y axis is the Y axis
and the 4 on the x axis will be the one with the variable
Hopefully this helps.
A manufacturer has cube shaped cardboard boxes with an exact volume of 12000 cubic inches. What is the volum of the largest sphere that can be packed inside the cube shaped box? Give you answer rounded to the nearest whole cubic inch
Answer:
6283 in³
Step-by-step explanation:
The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.
Since the cardboard box is in the shape of a cube, its volume V = L³
So, L = ∛V
Since V = 12000 in³,
L = ∛(12000 in³)
L= 22.89 in
So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2
So, V = 4π(L/2)³/3
= 4πL³/8 × 3
= πL³/2 × 3
= πL³/6
= πV/6
= π12000/6
= 2000π
= 6283.19 in³
≅ 6283.2 in³
= 6283 in³ to the nearest whole cubic inch
The table shows the costs
for 2, 3, 4, and 5 vegetable
seed packets. What is the
unit rate?
Find the volume of the con round you answer to the nearest tenth
Answer:
16.76 inch³
Step-by-step explanation:
volume of cone is 1/3 πr²h
h=4
r=2
then 1/3* 22/7* 2*2 *4
=352/21
=16.76
7. Would you expect the world population growth to be best modeled be a linear, quadratic, or exponential function?
Answer:
exponential
Step-by-step explanation:
since the rate of our population growth is relative to the amount of people already on our planet, the numbers will grow exponentially
Answer: exponential
Step-by-step explanation: exponential function don’t grow at a constant rate, like the world population
“Calculate the lengths of the 2 unlabeled sides”
Answer:
NL = 4.33
NM = 5
Step-by-step explanation:
tan 60° = NL/2.5
tan 60° = 1.7321
so:
1.7321 = NL/2.5
NL = (2.5)(1.7321)
NL = 4.33
cos 60° = 2.5/NM
cos 60° = 0.5
so:
0.5 = 2.5.NM
NM = 2.5/0.5
NM = 5
You must exert a force of 4.5 N on a book to slide it across a table. If you moved it 5 meters. How much work was done on the book?
Answer:
22.5 JStep-by-step explanation:
The work done by an object can be found by using the formula
workdone = force × distance
From the question we have
workdone = 4.5 × 5
We have the final answer as
22.5 JHope this helps you
A hot air balloon pilot begins to land her balloon. In the first minute the balloon's elevation -336 feet. In the second minute, the balloon's elevation changes by 1/16 of that amount. What is the balloon's elevation during the second minute?
Answer:
-21 Feet
Step-by-step explanation:
-336/16
The balloon's elevation during the second minute will be 21 feet.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A sight-seeing balloon pilot starts to land her inflatable. In the main moment the inflatable rise - 336 feet. In the subsequent moment, the inflatable's height changes by 1/16 of that sum.
Then the balloon's elevation during the second minute is given as,
⇒ - 336 x (1/16)
⇒ - 336 / 16
⇒ - 21 feet
The balloon's elevation during the second minute will be 21 feet.
More about the Algebra link is given below.
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There are 244 seventh grade students. The number of students enrolled in P.E. Is 8 fewer than three times the number of students enrolled in health
Answer:
No. of students enrolled in Health = 63
No. of students enrolled in P.E. = 181
Step-by-step explanation:
Given,
Total students in grade seven = 244 students
A.T.Q.
Let the number of students enrolled in Health be x
so, The number of students enrolled in P.E. = 3x - 8
As we know,
x + (3x - 8) = 244
4x = 244 + 8
x = 252/4
x = 63
Thus, the number of students enrolled in Health = 63
The number of students enrolled in P.E. = 3x - 8
= 3 * 63 - 8
= 189 - 8
= 181 students
2 qt 1 cup = ___ fl oz
A. 40
B. 72
C. 80
D. 136
Answer:
80 fl oz
2qts = 8 cups
Which graph represents all the real numbers, , where ≥−2? THIS IS LAST QUESTION PLEASE ANSWER! I WILL GIVE BRAINLYST.
Answer:
It's the one right under the first one
find x
answer choices
6
7
9
10
8
The answer should be 10
Jamar to the local snack shop near his school He bought 3 hotdogs and 2 bags of chips for $Kenny went to the same snack shop and bought 5 hotdogs and 6 bags of chips for $9.55 ordered 2 hotdogs and 3 bags of chips, then how much did she pay her order?
Answer:
Marcy paid $4.15
Step-by-step explanation:
Given
Represent hotdogs with x and chips with y.
So, we have:
Jamal
[tex]3x + 2y = 4.85[/tex]
Kenny
[tex]5x + 6y = 9.55[/tex]
See attachment for complete question
Required
Determine the amount for 2x and 3y
From Jamal's and Kenny's orders we have:
[tex]3x + 2y = 4.85[/tex] --- (1)
[tex]5x + 6y = 9.55[/tex] --- (2)
Multiply (1) by 3
[tex]3 * [3x + 2y = 4.85][/tex]
[tex]9x + 6y = 14.55[/tex] --- (3)
Subtract (2) and (3)
[tex]9x - 5x + 6y - 6y = 14.55 - 9.55[/tex]
[tex]9x - 5x = 5[/tex]
[tex]4x = 5[/tex]
Solve for x
[tex]x = \frac{5}{4}[/tex]
[tex]x = 1.25[/tex]
Substitute [tex]x = 1.25[/tex] in [tex]3x + 2y = 4.85[/tex]
[tex]3 * 1.25 + 2y = 4.85[/tex]
[tex]3.75 + 2y = 4.85[/tex]
Solve for y
[tex]y = \frac{4.85 - 3.75}{2}[/tex]
[tex]y = \frac{1.10}{2}[/tex]
[tex]y = 0.55[/tex]
So, the cost of 2x and 3y is:
[tex]Cost = 2x + 3y[/tex]
[tex]Cost = 2*1.25 + 3*0.55[/tex]
[tex]Cost = \$4.15[/tex]
PLEASE HELP ME OUT AND MAKE SURE TO SHOW YOUR WORK!!!! PLEASEEEEE
Answer:
1. 15
2. 16
3. 46
4. 59
Step-by-step explanation:
1. 44+30=74, 89-74=15
2. 90-74=16
3. 180-134=46
4. angles like that are the same
Answer:
1. x=5
2. x=16
3.x=46
4.x=59
Step-by-step explanation:
1. It says that the angle in total is 89 degrees (faded). then it shows the degrees 44 and 30. add them together to get 74 degrees. next subtract 89 by 74 to get the answer 5.
2. it shows a box at the corner of the angle (box means its a perfect 90 degree angle) so you need to subtract 90 by 74 to get the answer 16.
3. the whole entire angle is 180. so you need to subtract 134 from 180 to get the answer 46.
4. look focus on the one line that shows 59 degrees and right above it there is a blank. that arrow line represents 180 degrees. subtract 180 by 59 to get 121. next focus on the second line (the one that faces downward to the right) you then subtract 180 by 121 to get 59.
1. 44+30=74 89-74=5 x=5
2. box=90 90-74=16 x=16
3. 180-134=46 x=46
4. 180-59=121 180-121=59 x=59
are 2x-1 +3x=0 and 5x-1=0 equivalent
Answer:
yes
Step-by-step explanation:
they both equal 5x=1 where x = 1/5
9)
Consider
-196/14
Which THREE statements are correct?
A)
The quotient is 14.
B)
The quotient is -14.
The quotient is -
D)
- 196
is equivalent to the expression.
14
E)
196
-14
is equivalent to the expression.
A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32.What rule do you think the state park uses to decide the entrance fee for a vehicle?
Answer:
I think they charge a flat rate of $8 for a vehicle and $3 per person on top of that.
Step-by-step explanation:
There could be a multitude of rules, but let's try to find a simple one.
I would start by assuming that the park charges a fee for a vehicle and then for each person. Let's name those:
a - flat fee for a vehicle
b - fee per person
then a car with x people in it would be charged
a + bx
Let's see if the fees fit this assumption:
for x = 2
a + b*2 = $14
for x = 4
a + b*4 = $20
for x = 8
a + b*8 = $32
If so, we can subtract the second equation from the first and get
a + b*4 - a - b*2 = $20 - $14
b*2 = $6
b = 3$
a + b*2 = $14
a + $3*2 = a + $6 = $14
a = $8
so the first 2 equations gave us a = $8 and b = $3.
Let's see if these values fit the 3rd equation
a + b*8 = $32
$8 + $3*8 = $32
$8 + $24 = $32
$32 = $32
It fits!
That tells us that the rule is indeed very likely.
$12 with a 85% markup
12+85% is $22.20
80%x12=9.6
5%x12=0.6
9.6+0.6=10.2
12+10.2=22.20
Answer: $22.20
A box of macaroni & cheese says that it makes 25% more than a regular box. If a regular box makes 3 cups of macaroni & cheese, how many cups will this box make?
Thanks :)
Answer:
3.75
Step-by-step explanation:
25% = 0.25
3(0.25) = 0.75
3 + 0.75 = 3.75
At midnight, the temperature in Escondido was 68 degrees. The temperature was dropping at a steady rate of 2 degrees per hour. After how many hours was the temperature colder than -4 degrees?
Answer:
72 hours
Step-by-step explanation:
Answer: 34 hours
Step-by-step explanation: 68 divided by 34 is 2 and thats the rate the temperature is dropping.
I WILL GIVE BRAINLIEST!!!!!!
Write in complete sentences to explain what a budget is, how to make one, and how to balance it.
Solve the equation using either addition or substitution. Show all your work
Answer:
(x1, y1) = (1, 3)
(x2, y2) = (4, 12)
Step-by-step explanation:
y= x^2 - 4
y= 5x - 8
(substitute the value for y)
x^2 - 4 = 5x - 8
(solve the equation)
x = 1
x = 4
(substitute the values)
y = 5 × 1 - 8
y = 5 × 4 - 8
(solve the equations)
y = -3
y = 12
( the possible solutions are)
x1, y1 = 1, -3
x2, y2 = 4, 12
(check the solutions)
-3 = 1^2 - 4
-3 = 5 × 1 - 8
12 = 4^2 - 4
12 = 5 × 4 - 8
(simplify)
-3 = -3
-3 = -3
12 = 12
12 = 12
(the ordered pairs are the solutions)
Students set a goal for the
number of cans to collect
for the canned food drive.
They reached 120% of
their goal. What is 120%
expressed as a fraction
and as a decimal?
Answer:
Fraction = 120/100 | Decimal = 1.2
Step-by-step explanation:
Fraction:
100% is 100/100 but 120% is 20% over so the fraction is now 120/100 (20% = 20/100)
Decimal:
100% is 1 but as I said earlier, 120% is 20% over so the decimal is now 1.2 (20% = 0.2)
Solve the system of equations given below.
Answer:
The system of this equation is ( -1, 10) which is Option A.
Step-by-step explanation:
Solve for y in the first equation.
[tex]y = - 5x + 5 \\ - 2y = - x - 21[/tex]
Replace all occurrences of yy with -5x+5 in each equation.
[tex]10x - 10 = - x - 21 \\ y = - 5x + 5[/tex]
Solve for x in the first equation.
[tex]x = - 1 \\ y = - 5x + 5[/tex]
Replace all occurrences of x with -1 in each equation.
[tex]y = 10 \\ x = - 1[/tex]
The solution to the system is the complete set of ordered pairs that are valid solutions.
(−1, 10)
Hence, the system of this equation is (-1, 10).
Option A.
What is another way to express 52 + 24?
8 (6 + 3)
4(13+6)
6 (9+4)
13 (4+2)
Done
Answer:
it's the 2nd one
Step-by-step explanation:
hoped I helped:)
27 solid iron spheres, each of radius 'x cm' are melted to form a speher with radius 'y cm'. Find the ratio x:y
Answer:
My brain...
Step-by-step explanation:
Answer:
i believe its A on plato
Step-by-step explanation:
Need help on this one too
Answer:
sin(θ)=4√41/41
cos(θ)=5√41/41
tan(θ)=4/5
cot(θ)=5/4
sec(θ)=√41/5
csc(θ)=√41/4
Step-by-step explanation:
What's the slope and y intercept of 3x - y = 7
Answer:
the slope is 3
the y intercept is (0,-7)
Step-by-step explanation:
3x-y=7 solve for y
add y to both sides
3x=7+y
subtract 7 from both sides
y=3x-7
y=mx+b
m=slope
b=y-intercept
3=slope
-7=y-intercept
Hope that helps :)
i dont have a question for this. look at the photo
Answer:
first is no second is yes third is no fourth is yes
Step-by-step explanation:
I'm not sure btw
The playground at a park is shaped like a trapezoid the dimensions what is the area of the playground in square feet
Answer:
[tex]Area = 1560ft^2[/tex]
Step-by-step explanation:
Given
See attachment for playground
Required
Determine the area
The playground is a trapezoid. So;
[tex]Area = \frac{1}{2}(Sum\ parallel\ sides) * Height[/tex]
From the attachment, the parallel sides are: 68ft and 36ft
The height is: 30ft
So, the area is:
[tex]Area = \frac{1}{2}(68ft + 36ft) * 30ft[/tex]
[tex]Area = \frac{1}{2}(104ft) * 30ft[/tex]
[tex]Area = 52ft * 30ft[/tex]
[tex]Area = 1560ft^2[/tex]