Answer:a
Step-by-step explanation:
Answer:
length = 100
width = 25
Step-by-step explanation:
Let L = length of red rectangle
Let H = height of red rectangle
Equation1: L+H=125 : we know the perimeter is 250 so L+H is 125
Equation2: L*H=2,500 : we know the area is 2,500
Equation3: L=125-H : subtracted H from both sides of Equation1
Equation4: (125-H)*H=2,500 : substituted "125-H" for L into Equation2
Solve equation4:
(125-H)*H=2,500 multiple terms on left side of equation
125H - H^2 = 2,500 rearrange into standard form
H^2 - 125H + 2,500 = 0
At this point you can "brute force" the answer with the quadratic formula:
H = (125 ± SQRT(125^2 - 4*1*2500) ) / 2
H = 100 or H = 25 : actually these are L and H
You could also factor the equation:
(H - 100) * (H - 25) = 0 : gives same answe
PLEASE HELP!! what is the equation of a line that is perpendicular to y = 2x + 4 and passes through the point (4, 6)?
Answer:
The answer is B)
[tex]y = - \frac{1}{2}x + 8[/tex]
Answer:
B. y = -[tex]\frac{1}{2}[/tex]x + 8
Step-by-step explanation:
The line is perpendicular to line whose equation is:
y = 2x + 4 and;
passes through point (4,6) .
The product slopes of two perpendicular lines is -1.
The slope of the line whose equation is y = 2x + 4 is; 2
Let the slope of the perpendicular line (l2) be [tex]m_{l2}[/tex]
[tex]m_{l2} * 2 = -1[/tex]
[tex]m_{l2}[/tex] = [tex]-\frac{1}{2}[/tex]
Taking another point xy on line l2;
[tex]\frac{y - 6}{x - 4} = -\frac{1}{2}[/tex]
Cross multiplying this gives;
y = -[tex]\frac{1}{2}[/tex]x + 8 which is the equation of the perpendicular line!
The average weight of the three lion cubs at the zoo was 288 pounds. Two of the cubs weighed 261 and 252 pounds. What was the weight of the third cub?
Answer:
351 pounds
Step-by-step explanation:288 x 3 = 864 pounds
864 - 261 - 252 = 351 pounds
Therefore (261 + 252 + 351)/3 = 288.
So the answer is 351 pounds
7 liters of gasoline between their 4 cars. How many liters of gasoline should each car get?
Answer:
1.75 liters for each car.
Step-by-step explanation:
Divide:
*7 / 4 = 1.75.
Check:
*1.75 x 4 = 7.
Find the he value of n if 4n=6 4
Answer: 16
Step-by-step explanation:
64/4=16
n=16
Answer:
16
Step-by-step explanation:
4n = 64
n = 16 --------> Divide by 4 on each side
Which is the exponential form of log3 x= 11?
Answer:
[tex]x = 3^{11}[/tex]
Step-by-step explanation:
relation between logarithmic and exponential form is given by
[tex]\log_a x = y \\[/tex] is same as [tex]a^y = x[/tex] where a>0 and a is not equal to 1.
____________________________________________
[tex]\log_3 x = 11 \\\\x = 3^{11}[/tex]
Thus, exponential form is [tex]x = 3^{11}[/tex]
A police car drives with a constant speed of 64 mph. How far can it travel in 2 hours?
Answer:
128 miles.
Step-by-step explanation:
The police car is driving at a constant speed of 64 mph so you simply have to multiply the rate by the time to get the distance.
64 * 2 = 128 miles
Hope this helps!
The volume of a rectangular prism is the product of its dimensions. If the dimensions of a rectangular prism are
approximately 1.08 feet, 5.25 feet, and 3.3 feet, what is the approximate volume of the cube? Express your answer
using an appropriate level of accuracy.
Answer:
Hey there!
Volume of a rectangular prism: length (width) (height).
Volume: 1.08 (5.25) (3.3), or 18.71100.
However, because 3.3 is only two significant figures, we round our answer to: 19.
Hope this helps :)
Answer:
18.7 ft^3
Step-by-step explanation:
The volume is the product of the dimensions of the cube:
V = L*W*H, where L and W represent the length and width respectively.
Here,
V = (1.08 ft)(5.25 ft)(3.3 ft) = 18.7 ft^3, which is to 1 decimal place, because the least accurate dimension is also to 1 decimal place.
Which expression represents the prime factorization of 243?
Answer:
[tex]\boxed{3^5}[/tex]
Step-by-step explanation:
Hey there!
Look at the image below↓
By looking at the image we can tell the PR expression is [tex]3^5[/tex].
Hope this helps :)
Answer:
Below in bold.
Step-by-step explanation:
Dividing by primes:
3 ) 243
3 ) 81
3 ) 27
3) 9
3.
So the prime factors of 243 are 3 * 3 * 3 * 3 * 3 or 3^5.
PLEASE HELP!!
Complete the equation.
(13)^2 (13)^-14 (13)^5 = 13 [ ]a0
Answer:
(13)^2 (13)^-14 (13)^5
=2197
Answer:
13^3
Step-by-step explanation:
-4+2+5=3
is it . that or something else ??
PLEASE ANSWER ASAP!!!!!!!!!!!!!!!!!!!!! The price of coffee has dropped to $2.30. Yesterday's price was $2.55. Find the percentage decrease. Round your answer to the nearest tenth of a percent
9.8 percent. All you have to do is subtract 2.30 from 2.55 and then divide that answer by 2.55 and then multiply that by 100
Answer:
9.8%
Step-by-step explanation:
Step 1: Find the change in price
2.55 - 2.30 = $0.25
Step 2: Divide change with original price
0.25 / 2.55 = 0.098....%
Step 3: Multiple by 100 to get percent
0.098 x 100 = 9.8%
LESSON 2-1 PRACTICE
V 13. Attend to precision. Justify each step in the solution of 5x + 15 -
below by stating a property or providing an explanation for each
5x + 15 = 0
5x + 15 – 15 = 0 – 15
5x = -15
x = -3
Answer:
Value of x is -3
Step-by-step explanation:
Given:
5x + 15 = 0
Find:
Value of x
Computation:
5x + 15 = 0
From subtracting 15 from both side (LHS and RHS)
5x + 15 – 15 = 0 – 15
5x = -15
From dividing 5 from both side (LHS and RHS)
5x / 5 = -15 / 5
x = -3
So,
Value of x is -3
2. A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi.
21.2
31.8
7.9
24.7
Answer:
[tex] SA = 24.73~cm^3 [/tex]
Step-by-step explanation:
[tex] SA = 2\pi r^2 + 2\pi r h [/tex]
r = d/2 = (1.5 cm)/2 = 0.75 cm
[tex] SA = 2(3.14)(0.75~cm)^2 + 2(3.14)(0.75~cm)(4.5~cm) [/tex]
[tex] SA = 24.73~cm^3 [/tex]
Answer:
24.7
Step-by-step explanation:
took this exam and got it right
(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any
point on the remaining part of the circle.
Answer:
The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
Step-by-step explanation:
Let us consider the image attached.
Center of circle be O.
Arc AB subtends the angle [tex]\angle APB[/tex] on the circle and [tex]\angle AOB[/tex] on the center of the circle.
To prove:
[tex]\angle AOB = 2 \times \angle APB[/tex]
Proof:
In [tex]\triangle PAO[/tex]: AO and PO are radius of the circles so AO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So, [tex]\angle PAO = \angle OPA[/tex]
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
[tex]\angle AOQ = \angle PAO + \angle OPA=2 \times \angle APO .... (1)[/tex]
Similarly,
In [tex]\triangle PBO[/tex]: BO and PO are radius of the circles so BO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So, [tex]\angle PBO = \angle OPB[/tex]
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
[tex]\angle BOQ = \angle PBO + \angle OPB=2 \times \angle BPO .... (2)[/tex]
Now, we can see that:
[tex]\angle AOB = \angle AOQ+\angle BOQ[/tex]
Using equations (1) and (2):
[tex]\angle AOB = 2\angle APO+2\angle BPO\\\angle AOB = 2(\angle APO+\angle BPO)\\\bold{\angle AOB = 2(\angle APB)}[/tex]
Hence, proved.
Hope you could understand.
If you have any query, feel free to ask.
I WANT TO PASS HIGH SCHOOL PLEASE HELP
Given that the quadrilateral EFGH is a trapezoid, m∠H = 62° and m∠HEG = 64° calculate m∠FEG
Answer:
m∠FEG == 54°
Step-by-step explanation:
you should know that m∠FEG is equal m∠EGH. this is because sides HE and FG are equal this also means opposite angles of this sides (m∠FEG and m∠EGH) are equal.
first find the measure of m∠EGH from triangle EHG.
m∠H + m∠HEG + m∠EGH= 180°
62° + 64° + m∠EGH = 180°
m∠EGH=180° - 126°
m∠EGH=54°
due to the fact that sides HE and FG are equal thus opposite angles of sides HE and FG are also equal.
m∠FEG = m∠EGH = 54°
m∠FEG =54°
Jak policzyc: [tex](2x^2)^2[/tex] ?
What is the range of the function graphed below? PLEASE ANSWER ASAP
This is a more complicated way to write [tex]y < 2[/tex]
The range is the set of all possible y outputs of a function. So we use the graph to see what y values are possible. The graph shows that y can be anything smaller than y = 2. We can't actually reach y = 2 itself due to a horizontal asymptote here.
In interval notation, the answer would be [tex](-\infty, 2)[/tex] with the curved parenthesis to indicate "do not include y = 2 as part of the range".
How many triangles exist with the given side lengths? 2mm,6mm,10mm
Answer:
Zero
Step-by-step explanation:
2+6=8 which means it can't be. It has to be a length higher than 10
*PLEASE ANSWER* What is the volume of this prism?
Answer:
23.85
Step-by-step explanation:
→ Work out area of triangle
0.5 × 6 × 3 = 0.5 × 18 = 9
→ Multiply area of triangle by width of prism
9 × 2.65 = 23.85
The sum of 6 consecutive integers is 519. What is the third number in this sequence?
Answer:
86
Step-by-step explanation:
x+x+1+x+2+x+3+x+4+x+5 = 519
6x+15 = 519
6x = 504
x = 84
Third number = x+2 = 86
Answer:
86
Step-by-step explanation:
khan
A spinner has 3 red spaces, 5 white spaces, and 1 black space. If the spinner is
spun once, what is the theoretical probability of the spinner NOT stopping on
red?
P(Not red) =
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
If we have 3 red spaces, 5 white spaces, and one blank space, there are a total of 9 spaces.
Since there are 3 red spaces, there is a [tex]\frac{3}{9} = \frac{1}{3}[/tex] chance of getting a red. However, the question asks the probability of not getting a red, so the chances of not getting a red are [tex]1 -\frac{1}{3} = \frac{2}{3}[/tex].
Hope this helped!
Th sum of a number and two is equal to eight
The equation?
Answer:
2+n = 8
Step-by-step explanation:
2+ something must equal 8.
8 minus 2 = 6
n=6
Answer:
Let the number be n.
According to question,
2+ n =8
=) n = 8-2
=) n =6
hope you understand.
FORM A CUBIC POLYNOMIAL WHOSE ZEROS ARE -3,-1 AND 2
[tex](x+3)(x+1)(x-2)=\\(x^2+x+3x+3)(x-2)=\\(x^2+4x+3)(x-2)=\\x^3-2x^2+4x^2-8x+3x-6=\\x^3+2x^2-5x-6[/tex]
The graph shows the equation x2 + y2 = 5. Use the slider for a to move the vertical line on the graph. Based on the vertical
line test, is this equation a function? Why or why not?
Answer: This equation is not a function.
Step-by-step explanation:
Ok, a function is something like a "machine".
It takes an input value, x, and transforms it into an output value, y.
Such that for every input x, the function can transform it into only one value of y.
for example, if we have a "function" f(x)
such that f(2) = 3 and f(2) = 4
(for the same input, x = 2, we have two different outputs)
Then this is not a function.
Now, the given equation is:
x^2 + y^2 = 5
This is actually the equation for a circle, centered at the point (0, 0) and with a radius equal to √5.
Then, if we want to transform it into y(x), we can see a problem
If x = 0, we have:
0^2 + y^2 = 5
y^2 = 5
then we have two possible values for y:
y = +√5
y = -√5
Then for one value of x, we have two values of y.
This means that this is not a function.
Answer:
No. The vertical line touches the graph at more than one point at once.
Step-by-step explanation:
I just did it
Determine which one of the following statements is true. A. Exponential growth will always exceed linear growth. B. Linear growth will always exceed quadratic growth. C. Linear growth will always exceed exponential growth. D. Quadratic growth will always exceed exponential growth.
Answer:
A. Exponential growth will always exceed linear growth.
Step-by-step explanation:
The rate of growth of a linear function is always constant, that means it remains the same for any value of x or y. For an exponential growth, the rate of change is not constant, it continues to increase as the value of x increases. Therefore since the rate of growth of an exponential growth increases as the x value increases, while that of the linear growth remain constant there would be a point in which the exponential growth will exceed linear growth.
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.
Answer:
y = 100(3)^t
Step-by-step explanation:
Use the formula y = P(1 + r)^t where y is the new amount, P is the starting amount, r is the rate as a decimal, and t is the time.
Plug in the values given:
y = 100(1 + 2)^t
y = 100(3)^t
Answer:
Step-by-step explanation:
y = 100(3)^t
The graph of
is positive over the interval and negative over the interval . What happens on the graph when ? Explain.
Answer:
Positive and negative intervals on a graph
Step-by-step explanation:
The positive regions of a function are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero). The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero). hope this helps you :)
There are 9 classes of 25 students each, 4 teachers, and two times as many chaperones as teachers.
Each bus holds a total of 45 people.
What is the least number of buses needed for the field trip?
5 buses is the answer pls mark me brainliest
Least number of bus require for trip = 5 buses
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
Total number of classes = 9
Number of student in each class = 25
Number of teacher = 4
Number of chaperones = Double of teacher
Bus hold = 45 people
Now,
Total number of student = 9 × 25
= 225
Number of chaperones = 4 × 2
= 8
Total people = 225 + 8 + 4
= 237
Least number of bus require for trip = Total people / Bus hold
= 237 / 45
= 5.266
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
Bob has taken out a loan of $15,000 for a term of 48 months (4 years) at an interest rate of 6.5%. Using the amortization table provided, what will be his total finance
charge over the course of his loan?
Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77
$30.88
$23.95
$19.80
7.5% $86.76 $45.00
$31.11
$24.18
$20.04
8.0% $86.99 $45.23
$31.34
$24.41
$20.28
8.5% $87.22 $45.46
$24.65
$24.65
$20.52
9.0% $87.45 $45.68
$31.80
$24.89
$20.76
A.
$355.65
O
B.
$975.00
C.
$1,682.40
D.
$2,071.20
E. $17,071.20
Reset
Next
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Answer:
D. $2071.20
Step-by-step explanation:
The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be $23.71 per thousand borrowed. The sum of those 48 payments is ...
48 × $23.71 = $1138.08
That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000, so his total finance charge will be ...
finance charge = 15 × $138.08 = $2071.20 . . . matches choice D
Write the slope-intercept form of the equation for the line. (-1,-3) (1,1)
Answer:
y = 2 x − 1
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
We can find the slope from the slope equation
m = (y2-y1)/(x2-x1)
= ( 1- -3)/(1 - -1)
= (1+3)/(1+1)
= 4/2
=2
Assume all variables represent non negative numbers . Help please!!
Answer:
A). [tex]2p^{8}[/tex]
B). [tex]3m^{7}[/tex]
Step-by-step explanation:
A). [tex]\sqrt{4p^{16}}[/tex]
To get the square root of the given expression we will convert it into the square form.
[tex]4p^{16}=(2)^2(p^{8})^2[/tex] [Since 2×2 = 4 and [tex]p^{8}\times p^{8}=p^{16}[/tex]]
Therefore, [tex]\sqrt{4p^{16}}=\sqrt{2^{2}\times (p^{8})^2 }[/tex]
[tex]=2p^{8}[/tex]
B). [tex]\sqrt{9m^{44}}[/tex]
Since, [tex]9m^{14}=(3)^2\times (m^7)^2[/tex]
Therefore, [tex]\sqrt{9m^{44}}=\sqrt{(3)^2\times (m^7)^2}[/tex] [Since 3² = 9 and (m⁷)² = m¹⁴]
[tex]=3m^{7}[/tex]
