The overall budget the Mr Hollis has is $12800.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Mr.Hollis determines that he gives away 800 each month and the fraction is 1/6 of his budget.
The value of the overall budget will be illustrated as x.
Therefore 1/16 × x = 800
x / 16 = 800
x = 16 × 800
x = 12800
Hollis has $12800 as budget.
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The area of rectangle abcd is 28 cm a) what is the length of side ab in terms of x? length of ab = 4 cm x cm 6 cm x cm b) if the area of rectangle abcd is 28 cm?, we can show that x2 + ax = b where a and b are integer values. work out the values of a and b. a : (1) b= (1) total marks: 3
The length AB of rectangle in terms of x is (4 + x) and values of a and b are 10 and 4.
The side AB measures (4 + x). Hence, the length of AB in terms of x is (4 + x).
The area of rectangle is calculated by the formula-
Area = length × breadth
Keep the values in formula -
28 = (4 + x) (6 + x)
Performing multiplication of both brackets with each other
28 = 24 + 4x + 6x + x²
Solving and rewriting the equation
x² + 10x = 4
Equation in question - x² + ax = b
Comparing both the equations, we get a = 10 and b = 4.
Thus, length of AB is (4 + x) and value fo a is 10 and b is 4.
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How to do this equation (1 + 3)²
Answer:
your answer is 16
Step-by-step explanation:
So, to solve (1 + 3)²
first add 1 and 3
then you will get 4
and your equation would be (4)²
then you just square 4.
(4)² > 4x4 = 16
hope this helps (can you mark as brainiest pls)
3. Functions f and g are shown below. Which
best represents
function g?
a. g(x) = f(x) - 3
b. g(x) = -f(x)
c. g(x) = f(x)
d. g(x) = f(x - 2)
Answer:
i think it might be c
Step-by-step explanation:
one class period at lily's school lasts for an hour and fifteen minutes, or $\frac{5}{4}$ hours. however, her biology class usually spends the first five minutes of that time talking and the next ten minutes reviewing old homework problems before they begin the lesson, which goes until the end of class. what fraction of lily's time is spent on the lesson itself?
Lily's time is spent in biology class on lesson is 1 hour or 60 minutes.
Time of one class = 1 hour and fifteen minutes
As we know, 1 hour = 60 minutes
So, time of a class = 60 + 15
Performing addition
Time of a class = 75 minutes
Time spent in talking in biology class = 5 minutes
Time spent in reviewing old homework = 10 minutes
Total time spent = 15 minutes
Remaining time = 75 - 15
Performing subtraction
Remaining time = 60 minutes
Hence, 60 minutes or 1 hour is spent on the lesson.
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I NEED HELP PLS I GIVE YOU POINTS
Answer:
Option D: 160 square feet
Step-by-step explanation:
Area of the lawn
= (7 feet × 8 feet) + (13 feet × 8 feet)
= 56 square feet + 104 square feet
= 160 square feet
It cost $4.50 for zoo parking, plus an additional $6.25 for admission per person into the zoo. If Jay starts off with $55.00 and buys 3 admission tickets, how much money will he have left?
Answer: he will be left with 31.74 dollars
Step-by-step explanation:
i first put 55.00 - 4.50 = 50.5
then you subtract 50.5 with 6.25 3 times so the and is 31.74
hope this helped !!
Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, , what is the predicted fuel efficiency for a speed of 30 mph?
17. 67 mpg
26. 50 mpg
30. 00 mpg
37. 74 mpg
The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.
What is the least-squares regression line?If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.
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These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two yellow marbels if the frist one is placed back in the bag before the second draw
The probability of drawing two yellow marbles if the first one is placed back in the bag before the second draw is 0.022
Since the formula we refer to in calculating probability is
P = no of possible outcomes/ total number of outcomes
Since we were provided with 10 marbles out of which 2 are yellow, 3 are pink and 5 are blue
So the total outcomes are = 1,The total number of yellow marble is 2
The probability that the first ball drawn is yellow :
P₊= 2/10= 1/5
the probability of drawing the second ball to be yellow is:
P₂= 1/9
the total probability of drawing two yellow marbles if the first one is placed back in the bag before the second draw is :
P= 1/5 * 1/9
= 1/45
= 0.022
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What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? There are 10 marbles total, 2 yellow, 3 pink, and 5 blue
What is the slope of a line that is perpendicular to y=4/5x+15 and passes through point (−3, 4)?
Answer:
Step-by-step explanation:
The slope of the line y = -5x-4 is -5 or -5/1 so the slope of the perpendicular line is +1/5 eg…
y = x/5 + c
To find c we substitute x=15, y=-2
-2 = 15/5 + c
-2 = 3 + c
C = -5
So the equation is
Y = x/5 - 5
125.8% of £188.83
Give your answer rounded to 2 DP.
The answer is 237.55
Define Percentage
A ratio or figure stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
Given expression is,
125.8% of £188.83
Rewrite it as,
⇒ 125.8 / 100 * 188.83
⇒ 1.258 * 188.83
⇒ 237.54814
⇒ 237.55 (rounded to 2 Decimal places)
Hence, the answer is 237.55
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quadrilateral rstu has vertices R(2,4) ,s (-2,2), T(-1,0)and (3,2)
Verify:
i) quadrilateral rstu is a rectangle
ii) the diagonals of the rectangle bisect each other and are equal in lengths .
As RS=TU and ST=UR by distance formula, The given quadrilateral RSTU is rectangle and The diagonals RT=US so they are equal and bisect each other at right angle.
What is rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.
Here,
Calculate the length of sides by distance formula.
RS=√(y2-y1)²+(x2-x1)²
=√(2-4)²+(-2-2)²
=√4+8
=√(12
=2√3 units
ST=√(y2-y1)²+(x2-x1)²
=√(0-2)²+(-1-(-2))²
=√(4+1)
=√5 units
TU=√(y2-y1)²+(x2-x1)²
=√(2-0)²+(3-(-1))²
=√(4+8)
=√12
=2√3 units
UR=√(y2-y1)²+(x2-x1)²
=√(4-2)²+(3-2)²
=√(4+1)
=√5 units
RT=√(y2-y1)²+(x2-x1)²
=√(0-4)²+(-1-2)²
=√(16+9)
=√25
=5 units
US=√(y2-y1)²+(x2-x1)²
=√(2-2)²+(-2-3)²
=√(0+25)
=√25
=5 units
Because the given quadrilaterals, RS=TU and ST=UR, are rectangles and the diagonals, RT=US, are equal and at right angles to one another, according to the distance formula.
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Solve for x:
[tex]\sqrt{x-3} =\sqrt{x} +3[/tex]
A. -2
B. 2
C. no solution
D. 4
Answer: The answer is C: No solution
Step-by-step explanation:
By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]
You then cancel out the equal terms, in this case x, to reach the equation:
[tex]-3=6\sqrt{x} +9[/tex]
This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.
Find the Area of the figure below, composed of a parallelogram and two semicircles. Round to the nearest tenth place.
Answer:
550.4 square units.
Step-by-step explanation:
This problem is easier than it seems.
To find the area of the parallelogram, multiply 11 and 32 to get 352 sq. units
The two semicircles must be equal because the sides of a parallelogram must be equal.
So if you add the semicircles together, you get a circle.
So we're really finding parallelogram+circle.
The area of a circle is [tex]\pi[/tex]x[tex]r^{2}[/tex], and the circle's radius is 8 because the radius is half of the diameter.
[tex]\pi[/tex]≈3.1 because you're rounding to the nearest tenth.
3.1x64=198.4 sq. units
198.4+352=550.4 square units.
Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
However, the graph has no maximum or minimum
This means that there is absence of a vertex in the graph
The transformationHere, we have:
The graph is translated 4 units to the left of the origin The graph is translated 2 units below the originThis transformation can be represented as (x - 4, y - 2)
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An object attached to a coiled spring is pulled down a distance of 10 centimeters from its rest position and then released.
Assuming that the motion is simple harmonic
with a period of 2 seconds, write an equation that relates the displacement d of the object from its rest position after t seconds.
Also assume that the positive direction of
the motion is up. At time t=0 the object is at its resting position and moving down.
Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.
In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).
Step-by-step explanation:
assume the state of arkansas placed a tax on playing cards of 6 cents per pack. if the state generated $48600 in revenue, how many packs of cards were sold?
The number of pack of cards sold at the state of Arkansas is 8100.
Describe the term division?Multiplication is the complete reverse of division. If participants of 4 add up to 12, then 12 divided into three classes of equally sized results in 4 in each group.For the values given in question.
The tax on playing card in state of Arkansas = 6 cents per pack.
Total revenue generated = $48600.
Divide total revenue by one pack price to get the number of packs.
Number of pack = Total revenue/price of each pack
Number of pack = $48600/6
$48600.Number of pack = 8100
Thus, the number of pack of cards sold at the state of Arkansas is 8100.
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What is the area of the parallelogram shown?
A= In^2
Write and graph linear equations
The equation of linear equation is y = -5x +3.
What is equation of linear equation?
A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.
The slope intercept form of linear equation is
y = mx + b
where m is the slope.
Given,
The slope = -5
and the points are (4, -17)
y = -17, x = 4, m = -5
-17 = -5(4) + b
-17 = -20 + b
-17 + 20 = b
b =3
The equation of linear equation is y = -5x + b
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Can write the equation to this problem?
The equation, in vertex form, of the graph in the diagram is determined as: y = 1|x - 3| + 5.
What is the Equation of a Graph that Represents an Absolute Value Function?The formula that represents the equation in vertex form of an absolute value function is y = a|x - h| + k, where:
Vertex = (h, k).
Therefore, we will need to determine what the values of a, h, and k is using the information derived from the graph.
Thus:
(h, k) = (3, 5)
a = 1 (this is because the graph opens upward)
To write the equation of the graph, substitute a = 1, h = 3, and k = 5 into:
y = 1|x - 3| + 5
The equation is, y = 1|x - 3| + 5.
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what is the measure of EAC?
The measure of angle EAC IS 50°
What is an angle bisector?The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.
∠BAE = x + 30, ∠EAC = 3x - 10
If AE is a line that bisects BAC,
then ∠BAE = ∠EAC
which becomes,
x + 30 = 3x - 10
collecting like terms,
x - 3x = -10 - 30
-2x = -40
x = -40/-2
x = 20°
But m ∠EAC = 3x - 10
substituting x = 20°
we have ∠EAC = 3(20) - 10
= 60 - 10
∠EAC = 50°
In conclusion, the value of ∠EAC = 50°
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Two parallel lines are cut by a transversal as shown below.
Suppose m4=124°.
Answer:
156°
Step-by-step explanation:
m5 = m7 (vertical angles)
m4 + m5 = 180 (supplementary)
m5 = 180 - 124 = 156
So measure of both angle 5 and 7 is 156
In the figure, m<7=100 degrees. Find the measure of each angle.
22.) <6
23.) <8
24.) <2
25.) <5
26.) <11
The corresponding measure of each angle is 80, 80, 80, 100 and 100 degrees
How to determine the measure of each angle?
Given: m<7=100 degrees
To find <6, <8, <2, <5 and <11
In the <7 is vertically opposite <5. Since vertically opposite angles are equal.
Thus, <5 = <7 = 100 degrees
Also, <5 and <6 are angles on a straight, and the sum of angles on a straight line is 180 degrees. Thus:
<5 + <6 = 180
100 + <6 = 180
<6 = 180 -100 = 80 degrees
Also, <6 and <8 are vertically opposite.
Thus, <8 = <6 = 80 degrees
<2 and <6 are corresponding angles, and corresponding angles are equal. Thus, <2 = <6 = 80 degrees
Likewise, <11 and <7 are corresponding angles
Thus, <11 = <7 = 100 degrees
Therefore, the measure of angle <6, <8, <2, <5 and <11 are 80, 80, 80, 100 and 100 degrees respectively
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The table shows a set of values for x and y
y is inversely proportional to the square x.
a) Find an equation for y in terms of x. (2)
b) Find the positive value of x when y = 25 (2)
Answer:
see explanation
Step-by-step explanation:
(a)
given y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use any ordered pair from the table
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , that is
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is then [tex]\frac{4}{5}[/tex]
Help asap please and I will give brainliest!
Write
y − 2 = (x + 6) in
standard form.
Evaluate the expression:
6² x (16 +19) — 10³
36×(35)-1000=1260-1000=260
Estimate 29.25 + 41.06
And Exact answer
Step-by-step explanation:
70.31
hope it's helpful
Answer:
Step-by-step explanation:
no
What is the area of the figure at the right?
The area of the figure is 21. 25 m². Option D
How to determine the areaIt is important to note that the figure is a kite.
The formula for calculating the area of a kite is expressed as;
A= pq/2
Where;
A is the area of the kitep is the diagonal of the kiteq is the diagonal of the kiteUsing tangent identity
tan 45 = x/ 2. 5
1(2. 5) = x
x = 2. 5
p = 2. 5 + 2. 5 = 5
q = 2. 5 + 6 = 8. 5
Now, substitute the values into the formula
Area = 5(8. 5)/ 2
Area = 42. 5/ 2
divide the values
Area = 21. 25 m²
Hence, the value is 21. 25m²
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Carlos took a total of 8 quizzes over the curse of 4 weeks. What is his unit rate?
The table below shows the energy of a 10 kg ball as a function of velocity. How much energy will the ball have at 10 m/s? velocity 0,2,3,6,10 energy 0,20,45,180,?
The amount of energy that the ball will have at 10 m/s is; 600 J
How to find the energy from velocity?From the given table, we see that when the velocity is 2 m/s, then the energy is 20 J.
If we take the square of the velocity, we get 2² = 4.
Thus, we need to multiply 4 by 6 to get the energy that is equal to 24 as 4 * 6 = 24.
Similarly;
For velocity equal to 3 m/s, the energy is given as:
E = 6 * 3²
E = 54 J
Thus, the general formula to find the energy is given as:
E = 6 * v²
where;
E is the energy
v is the velocity
Now, for velocity equal to 10 m/s, energy is given as;
E = 6 * 10
E = 60 J
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