10 of 10
Work out the area of a rectangle with base, b = 38mm and perimeter, P =
100mm.
b
Answers
Let the height of the rectangle = h
2b + 2h = 100
2(38) + 2h = 100
2h = 100 - 76
h = 12mm
area of rectangle = base x height
= 38 x 12
= 456mm²
Answer:
456mm²
Step-by-step explanation:
using formula;
b/2( P - 2b) = A
substitute values
Related Questions
The polynomial 3x2 – 10x + 8 has a factor of 3x – 4. What is the other factor of 3x2 – 10x + 8?
x – 2
x – 4
x – 6
x – 8
Answers
Answer:
x-2
Step-by-step explanation:
Dividing 3x2 – 10x + 8 by 3x-4 we get x-2.
What’s and equation for a line that passes through (6,3) and (-6,6)?
Answers
Answer:
x + 5y -18=0
Step-by-step explanation:
Two points are given to us and we need to find the equation of the line. The given points are (6,3) and (-6,6) . Firstly let's find out the slope of the line .
Finding slope :-
[tex]\implies Slope = \frac{ y_2-y_1}{x_2-x_1} \\\\\implies Slope =\frac{ 3-6}{6+6} \\\\\sf\implies Slope =\frac{ -3}{12} \\\\\sf\implies Slope = \dfrac{-1}{4} [/tex]
Using point slope form :-
[tex]\implies y - y_1 = m( x - x_1 ) \\\\\sf\implies y - 3 = \dfrac{-1}{4}( x - 6)\\\\\sf\implies 4y - 12 = 6 - x \\\\\sf\implies x + 4y -12-6=0 \\\\\sf\implies\underline {\underline{ x + 5y -18=0}}[/tex]
Ben has twenty-six coins in her pocket are all dollars(1$ coins) and quarters, and they add up to seventeen dollars in value. How many of each coin does he have
Answers
Answer:
14 $1 coin
12 quarter coin
Step-by-step explanation:
Let :
x = $1 dollar coin
y = $0.25 (1 quarter) coin
x + y = 26 - - - (1)
1x + 0.25y = 17 - - - - (2)
From (1) :
x = 26 - y
Put x = 26 - y in (2)
1(26 - y) + 0.25y = 17
26 - y + 0.25y = 17
-y + 0.25y = 17 - 26
-0.75y = - 9
Divide both sides by - 0.75
-0.75y /- 0.75 = - 9 / - 0.75
y = 12
Put y = 12 in (1)
x = 26 - 12
x = 14
Factor 140c + 28 -14a to identify the equivalent expressions.
Answers
Step-by-step explanation:
140c+28-14a14(10c+2-a)hope it helps
stay safe healthy and happy...Graph the function f(x)= -5(x+5)^2–4.
Plot the vertex. Then plot another point on the parabola.
Answers
Answer:
Vertex= (-5,-4)
Another point=(0, -129)
Step-by-step explanation:
The vertex is also the maximum, and the point is also the y-intercept.
what is the inverse function f f(x)=radical x +7
Answers
Step-by-step explanation:
by switching the places of x and y ans solving for y
A new hospital tracked the number of births during its first 6 months of operation, as shown in the table.
A 2-column table with 6 rows. The first column is labeled month with entries 1, 2, 3, 4, 5, 6. The second column is labeled number of births with entries 137, 110, 93, 70, 65, 77.
Find a quadratic function that models the data. Round numerical values to the nearest whole number
Answers
Answer:
y = 4x² - 43x + 178
Step-by-step explanation:
Given that data:
1 __ 137
2 __ 110
3 __ 93
4 __ 70
5 __ 65
6 __ 77
Usibg technology, the quadratic regression equation obtained is written in the form:
Ax² + Bx + C
A = 4.34 = 4 ( nearest whole number)
B = - 43.46 = - 43 (nearest whole number)
C = 178.3 = 178 ( nearest whole number)
Hence, the quadratic model is
y = 4x² - 43x + 178
By rounding the coefficients to the nearest whole number, the quadratic function that models the data is[tex]f(x) = 5x^2 - 42x + 174[/tex]
How to Find a quadratic function that models the data.To find a quadratic function that models the data, use a quadratic equation of the form:
[tex]f(x) = ax^2 + bx + c[/tex]
Let's use the given data points to form a system of equations and solve for the coefficients a, b, and c.
Using the first data point (month 1 with 137 births):
[tex]f(1) = a(1)^2 + b(1) + c = 137[/tex]
a + b + c = 137 (Equation 1)
Using the second data point (month 2 with 110 births):
[tex]f(2) = a(2)^2 + b(2) + c = 110[/tex]
4a + 2b + c = 110 (Equation 2)
Using the third data point (month 3 with 93 births):
[tex]f(3) = a(3)^2 + b(3) + c = 93[/tex]
This simplifies to:
9a + 3b + c = 93 (Equation 3)
Solve this system of equations will give us the values of a, b, and c.
Subtract Equation 1 from Equation 2
3a + b = -27 (Equation 4)
Subtract Equation 1 from Equation 3
8a + 2b = -44 (Equation 5)
Now solve Equations 4 and 5 simultaneously.
Multiply Equation 4 by 2 and subtracting it from Equation 5:
8a + 2b - (6a + 2b) = -44 - (-54)
2a = 10
Divide both sides by 2:
a = 5
Now substitute the value of a back into Equation 4:
3(5) + b = -27
15 + b = -27
Subtract 15 from both sides:
b = -42
Finally, substitute the values of a and b into Equation 1
5 + (-42) + c = 137
-37 + c = 137
Add 37 to both sides:
c = 174
Therefore, the quadratic function that models the data is:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
Rounding the coefficients to the nearest whole number, the quadratic function becomes:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
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7x-49=y
Solve for x?
Answers
Add 49 to both sides
7x = y + 49
Diving both sides by 7
x =(y + 49)/7
The solution for x is x = (y + 49)/7.
Given that an equation 7x - 49 = y, we need to determine the equation in for of x,
To solve for x in the equation 7x - 49 = y, we'll isolate x on one side of the equation.
Here's the step-by-step process:
Start with the given equation: 7x - 49 = y.
Add 49 to both sides of the equation to isolate the term with x:
7x = y + 49.
Divide both sides of the equation by 7 to solve for x:
(7x)/7 = (y + 49)/7.
Simplify:
x = (y + 49)/7.
Therefore, the solution for x is x = (y + 49)/7.
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Find the coordinates of the
midpoint M. *
A(-4,-8) and B(-1,4)
Please provide an explanation
Answers
Answer:
M(-5/2, -2)
Step-by-step explanation:
Add the x-coordinates & divide by 2.
Add the y-coordinates and divide by 2.
x-coordinates: -4, -1
(-4 + (-1))/2 = -5/2
y-coordinates: -8, 4
(-8 + 4)/2 = -4/2 = -2
M(-5/2, -2)
rization
Vhat is the prime factorization of 180?
Select a composite number to break into factors. Continue
factoring until all factors are prime.
22•2•3•3.5
2.2.45
2.3.3.5
480
2.9.5
Answers
Answer:
5 3 3 2 2
Step-by-step explanation:
180
90 2
45 2 2
15 3 2 2
5 3 3 2 2
Answer:
180 = 5 × 3² × 2²
Step-by-step explanation:
Starting with 180, the prime factors are in bold
180 = 90 × 2
= 45 × 2 × 2
= 15 × 3 × 2 × 2
= 5 × 3 × 3 × 2 × 2
Then
180 = 5 × 3 × 3 × 2 × 2 = 5 × 3² × 2²
For every quarter in his pocket, John also has 5 pennies in his pocket. If the total of the coins in John’s pocket is $ 5.40, how many quarters does John have in his pocket.
Answers
If a student receives a score of 80, how many questions did this student answer ... (5). Let x = the first number, and y = the second number ... If John only has 25 coins in his pocket, how many of the coins are quarters?
Determine the measure of the interior angle at vertex C. PLEASE HELP ASAP
Answers
Answer:
B. 120°
Step-by-step explanation:
Sum of the measures of the interior angle of a polygon with n sides:
(n - 2)180
We have a pentagon, a 5-sided polygon, so n = 5.
We first find the sum of the measures of the angles of any pentagon.
(5 - 2)180 = 3(180) = 540
From the figure, we add the measures of the 5 angles and set the sum equal to 540°.
3x + 4x + 4x + 4x + 3x = 540°
18x = 540°
Divide both sides by 18.
x = 30°
The angle at vertex C measures 4x.
4x = 4 * 30° = 120°
Answer: B. 120°
is (12, 4), (36, 12), (-6, -2), (21, 7) directly proportional?
Answers
Answer:
I think yes
Step-by-step explanation:
12/4=3
36/12=3
-6/-2=3
and so on
Find the value of sin H rounded to the nearest hundredth, if necessary
Answers
Answer:
7/25 or .28
Step-by-step explanation:
sin=opp/hyp
7/25
Describe fully the transformation that maps triangle a onto triangle B
Answers
Answer:
The transformation that maps Triangle A onto Triangle B is a reflection of Triangle A across the axis "y=-1".
Step-by-step explanation:
The transformation that maps triangle A to triangle B is a reflection over the line y = -1.
Given are two triangles A, we need to determine the transformation performed to get the image of triangle A, i.e., triangle B.
The coordinates of the triangle A are:
(1, -5), (1, -2) and (3, -2)
The coordinates of the triangle B are:
(1, 3), (1, 0) and (3, 0)
By comparing the corresponding vertices, we can observe that the x-coordinates remain the same while the y-coordinates change.
The transformation that maps triangle A to triangle B is a reflection over the line y = -1.
This reflection flips the triangle across the line, resulting in the change of sign for the y-coordinates while leaving the x-coordinates unchanged.
Hence the transformation performed to obtain triangle B from triangle A is a reflection over the line y = -1.
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Given the points (-7, 9) and (5, 5) find the slope.
m=
Answers
Step-by-step explanation:
Hey sweetie!
We are given two points: (-7, 9) & (5, 5)
And we are asked to find the slope
To do this only given two points use the Slope-Formula to solve for the slope
m = slope
m = y2-y1/x2-x1
m = 5-9/5–7
m = -4/12
m = - 1/3
The slope will be - 1/3
Final Answer: m = - 1/3
3 miles. 128 yards. Converted to feet
Answers
If < W and < Y are supplementary, and < W = 121 °, then what would < Y measure?
Select one:
a. 121 °
b. 69 °
c. 59 °
d. 13 °
Answers
Answer:
Option c. 59°
Step-by-step explanation:
<W+<Y=180
121+<Y=180
<Y=180-121
<Y=59
Answered by GAUTHMATH
what single transformation maps triangle ABC onto A’B’C?
Answers
Answer:
the answer is rotation hope it helps ahhaha
true or false
is this a function 0 goes to 0 4 goes to 1 8 goes to 2 and 12 goe to 3
Answers
Answer:
Step-by-step explanation:
True. The function appears to be f(x) = x/4.
what is office personnel?
Answers
Answer:
Office personnel refers to the office chief, sectional chiefs and assistants that carry out all the administrative as well as clerical functions jointly to archive the objectives of an organization.
Which expression is equivalent to the given expression.assume the denominator does not equal zero
Answers
Answer:
you did not apply an expression
Step-by-step explanation:
Simplify
[tex]\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3} +...+\frac{1}{1+2+3+...+99}[/tex]
Answers
Answer:
65/264 or 0.2462
Step-by-step explanation:
The given series is
(1/1.2.3) + (1/2.3.4) + (1/3.4.5) + ………………
If we denote the series by
u(1) + u(2) + u(3) + u(4) +……………..u(n),
where u(n) is the nth term, then
u(n) = 1/[n(n+1)(n+2)] , n = 1,2,3,4,………n.
which can be written as
u(n) = (1/2) [1/n(n+1) - 1/(n+1)(n+2)] ………………………(1)
In the question, the number of terms n =10, thereby restricting us only to first 10 terms of the series and we have to find the sum for this truncated series. Let S(10) denote the required sum. We have then from (1),
u(1) = (1/2) (1/1.2 - 1/2.3)
u(2) = (1/2) (1/2.3 - 1/3.4)
u(3) = (1/2) (1/3.4 - 1/4.5)
u(4) = (1/2) (1/4.5 - 1/5.6)
u(5) = (1/2) (1/5.6 - 1/6.7)
u(6) = (1/2) (1/6.7 - 1/7.8)
u(7) = (1/2) (1/7.8 - 1/8.9)
u(8) = (1/2) (1/8.9 - 1/9.10)
u(9) = (1/2) (1/9.10 - 1/10.11)
u(10) = (1/2) (1/10.11 - 1/11.12)
Let us now add the terms on LHS and the terms on RHS independently. The sum of LHS is nothing but the sum S(10) of the series up to 10 terms. On the RHS, alternate terms cancel and we are left with only the first and the last term. Therefore,
S(10) = (1/2) (1/1.2 - 1/11.12) = (1/2) (66–1)/132 = [65/(132.2)]
= 65/264
= 0.2462 (correct to four decimal places)
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if a third plane could be drawn which contains both lines a and b .
Answers
Answer:
must be parallel
Step-by-step explanation:
They must be parallel.
I need help bad? What’s the answer
Answers
Answer:
76°,60°
Step-by-step explanation:
sum of angles of a triangle=180
x+64+x+80+44=180
2x+188=180
2x=180-188=-8
x=-8/2=-4
so angles are -4+60=60°
and -4+80=76°
PLEASE HELP, I WILL GIVE YOU BRAINLIEST!
Find the equation of a line that results in one real solution as part of a system with f(x)=x^2+2
Answers
Step-by-step explanation:
i hope this will help you
Answer:
give that person brainliest
Step-by-step explanation:
I am tired bestie. You are lucky we are friends. want sleep but homeworrkkk
If “the notation arcsin x represents the inverse function to sine” is true or false.
Answers
If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].
What is the sin function?The sine function is one of the three primary functions in trigonometry, the others being cosine, and tan functions.
The confusion is compounded by the fact that we use the notation sin⁻¹(x) interchangeably with arcsin(x), and we call it the inverse sine.
Here is a counterexample disproving your given statement:
Let x = π.
The value π is in the domain of sin(x).
arcsin[sin(π)] = arcsin(0) = 0
arcsin[sin(π)] ≠ π
Therefore arcsin(x) is not the inverse of sin(x).
If you restrict the sine function to the interval [ -pi/2, pi/2 ]. Otherwise, arcsin will not be a function.
Hence, If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].
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Ardi and Lei are both travelling by train. Ardi's train travels 70 km in 35 minutes. Lei's train travels 585 km. It leaves at 9:05 and arrives at 13:35. Work out the difference, in km/h, between the average speed of their trains.
Answers
Answer:
10 km/hr
Step-by-step explanation:
Average speed = Total distance travelled / Total time taken
Ardi:
Total distance travelled = 70 km
Total time taken = 35 minutes = 35/60 hour
Average speed = Total distance travelled / Total time taken
= 70 km ÷ 35/60 hr
= 70 × 60/35
= 4,200/35
= 120 km/hr
Lei:
Total distance travelled = 585 km Total time taken = 9:05 - 13:35 = 4 hours 30 minutes
= 4.5 hours
Average speed = Total distance travelled / Total time taken
= 585 km / 4.5 hours
= 130 km/hr
Difference, in km/h, between the average speed of their trains = Lei's train - Ardi's train
= 130 km/hr - 120 km/hr
= 10 km/hr
Christopher's car can drive 230 miles on a full tank of gas. He plans to drive with a full tank from Austin to Dallas, which is 195 miles. How many miles will be left once he arrives in Dallas?
Answers
Answer:
35 miles
Step-by-step explanation:
Total Miles driven at full tank = 230 miles
Miles drive at full tank from Austin to Dallas = 195 miles
How many miles will be left once he arrives in Dallas?
Number of miles remaining at full tank = Total Miles driven at full tank - Miles drive at full tank from Austin to Dallas
= 230 miles - 195 miles
= 35 miles
How many solutions exist for the given equation 3x+13=3(x+6)+1 zero one two infinity many
Answers
Answer:
Zero
Step-by-step explanation:
Given: 3x+13=3(x+6)+1
Step 1: Expand
3x+13=3x+19
Step 2: Subtract 3 from both sides
3x+13-13=3x+19-13
Step 3: Simplify
3x=3x+6
Step 4: Subtract 3x from both sides
3x-3x=3x-3x+6
Step 5: Simplify
0=6
NO REAL SOLUTIONS
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
Answer:
zero
Step-by-step explanation:
3x + 13 = 3(x + 6) + 1
3x + 13 = 3x + 18 + 1
3x - 3x = 18 + 1 - 13
0 = 18 + 1 - 13
0 = 6
NO SOLUTION
