The possible values of k are -0.56, -3.56, -2 and -1.
Find all possible values of k ?We have the equation of the parabola, y = 0.5 (x- 3 ) ( x+ k)
Substituting x=0, we get that i.e. y =0.5 * (-3) * k -1.5k
So, the y-intercept is (0,-1.5k).
Thus, the height of the triangle becomes |-1.5k| = 1.5k
Again, substituting y=0, 0 = 0.5 (x-3) (x+k) i.e. i.e. x0=(x-3) (x+k)=3 and x=-k
So, the x-intercepts are (3,0) and (-k,0).
Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.
As, area of a triangle = 1/2 * (base )* (height )
Substituting the values, we get,
1.5=1/2 *(3+k)*(1.5k)
i.e.3= 4.5 k + 1.5k ²
i.e. k = -0.56 and k = -3.56
or
1.5=1/2* (-3-k )*(1.5k)
i.e.
3 = -4.5 k - 1.5²
i.e. k = -2 and k = -1.
Thus, the possible values of k are -0.56, -3.56, -2 and -1.
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If f(x) is a polynomial of degree four with leading coefficient 1 such that f(1) = 1, f(2) = 8 , f(3) = 27 and f(4) = 64 , then the value of f(5) is
The required value of the function at f(5) = 125, as of the given conditions.
Given that,
f(x) is a polynomial of degree four with a leading coefficient 1 such that f(1) = 1, f(2) = 8 , f(3) = 27, and f(4) = 64, then the value of f(5) is ot be determined.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
f(x) = x⁴/x
Put x = 5
f(x) = 5⁴ / 5 = 125
Thus, the required value of the function at f(5) = 125, as of the given conditions.
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D Each figure in the sequence shown
is composed entirely of 1 x 1 shaded
squares. If the pattern is continued,
how many 1 x 1 shaded squares will
there be altogether in the first 21
figures?
+000
The total number of 1 x 1 shaded squares that there will be in the first 21 figures is of:
924.
How to obtain the total number of squares?The number of squares for each figure is given as follows:
(4, 8, 12, 16).
As the difference between consecutive terms of the sequence is constant, this sequence is an arithmetic sequence, with first term of 4 and common difference of 4.
The sum of the first n terms of an arithmetic sequence is given as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
The parameters of the equation are given as follows:
n is the number of terms.[tex]a_1[/tex] is the first term.[tex]a_n[/tex] is the nth term.Applying the explicit form, the 21st term of the arithmetic sequence in this problem is given as follows:
[tex]a_{21} = 4 + 20 \times 4 = 84[/tex]
Hence the total number of squares in the first 21 figures is obtained as follows:
[tex]S_{21} = 10.5 \times (4 + 84) = 924[/tex]
Missing InformationThe figures are given by the image shown at the end of the answer.
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Cara wants to build an 80 foot long rectangular sheep pen in back of her barn. If she bought 180 feet of fencing and used her barn wall as one side of the pen equaling the width, what would be the area of the sheep pen?.
If cara wants to build an 80 foot long rectangular sheep pen in back of her barn then the area of the sheep pen will be 1600 square feet.
What shape is a rectangle?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 form.
What is the formula for area of rectangles?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle as Area = length x width
Length of the sheep pen =80 ft
bought fencing = 180 ft
One side of rectangular sheep pen is covered with barn which is equaling the width
perimeter of rectangular sheep pen = 2(length +width)
length need to covered is 2 Length+ width
180 =2 length+width
180 = 2 x80 +width
180-160= width
20= width
Area of rectangle = 80 x 20
=1600 square feet
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Question 15 of 25
The table below shows last year's gross income, standard deduction, and
number of exemptions for four different workers.
Gross
Income
Delaney $77,568
Jamie $71,234
Oliver $74,872
Thomas $77,623
Standard
Deduction
$8350
$5700
$8350
$5700
2
1
1
3
Number of Exemptions at
$3650 Each
Assuming that each worker used the standard deduction and that none of the
workers had any additional adjustments, which worker had the lowest taxable
income last year?
If each worker used the standard deduction and no worker had any additional adjustments, the worker with the lowest taxable income last year was A. Jamie.
What is taxable income?
The taxable income is the difference between a worker's gross income and the total deductions (standard or itemized).
Data and Calculations:
Gross Income Standard Number of Taxable
Deduction Exemptions at Income
$3,650 Each
Delaney $77,568 $8,350 $69,218 ($77,568 - $8,350)
Jamie $71,234 $5,700 $65,534 ($71,234 - $5,700)
Oliver $74,872 $8,350 $66,522 ($74,872 - $8,350)
Thomas $77,623 $5,700 $71,923 ($77,623 - $5,700)
Hence, if each worker used the standard deduction and no worker had any additional adjustments, the worker with the lowest taxable income last year was A. Jamie.
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Through a given point not contained in a given line, there exists ___ ___ line parallel to the given line. (two words)
Through a given point not contained in a given line, there exists exactly one line parallel to the given line.
What are parallel lines?In Mathematics, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and they can never meet. In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m represents the slope.
This ultimately implies that, two (2) lines would be parallel to each other when the slope (m₁) of the first line is equal to the slope (m₂) of the second line.
According to the Parallel postulate, there is always exactly one line that is parallel to a given line in the same plane when a point and a line are given, provided that the point is not on that line.
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Consider AXYZ in the figure below.
The perpendicular bisectors of its sides are TS, US, and VS. They meet at a single point S.
(In other words, S is the circumcenter of AXYZ.)
Suppose VS 80, YZ=86, and ZS=116.
Find XS, UZ, and VY.
Note that the figure is not drawn to scale.
X
T
Z
XS = []
UZ = 0
VY = 0
X
S
The value of XS = 116, UZ = 43, and VY = 84.
What are perpendicular bisectors?
A line or line segment that divides a given line segment into two equal portions is known as a perpendicular bisector.
Here, we have
Given
The perpendicular bisectors of its sides are TS, US, and VS. They meet at a single point S.
VS 80, YZ=86, and ZS=116 and we have to find XS, UZ, and VY.
TS, US, and VS are perpendicular bisectors
So, XV = VY, YU = UZ, XT = TZ
Then, ΔYST ≅ ΔZST
ΔYSV ≅ ΔXSV
ΔYUS ≅ ΔZUS
So, XS = ZS = 116
UZ = 1/2YZ = 1/2×86 = 43
VY = VX
VX² + VS² = XS²
VX = √XS² -VS²
VX = √116² - 80²
VX = 84
Hence, the value of XS = 116, UZ = 43, and VY = 84.
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Your store is 150 ft. X 70 ft. The security cameras you are planning to purchase each cover 400 square feet. You want to cover the whole store. How many cameras do you need?.
There should be 27 cameras.
What is area?The amount of space filled by a flat (2-D) surface or an object's form is known as its area. Draw a square on a sheet of paper with a pencil. A 2-D figure, that is. The term "Area" refers to the area that a form occupies on paper. Now picture that your square is composed of smaller unit squares.
It is 150 feet by 70 feet.
The size of the store will be 150 x 70 feet, or 10,500 square feet. The security cameras now each have 400 square feet.
The area of the shop / each camera's area will determine how many cameras are needed, which is 10500/400.
which is 27
27 cameras are therefore required.
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A triangle has angle measurements of 2x,4x+6,and x-15.what is the value of x
The required value of x of a triangle is 27°.
What is a triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Given, angle measurements of 2x, 4x+6, and x-15
Based on the definition of a triangle, the sum of all angles will be 180 degrees.
So, 2x + 4x+6 + x-15 = 180°
or, 7x - 9 = 180°
or, 7x = 189°
or, x = 189/7 = 27°
Hence, the required value of x of a triangle is 27°.
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what is 210/945 simplified
Answer:
The simplest form of 210/945 is 2/9
Step-by-step explanation:
If two-thirds of a women’s age is 42, how old is she
Answer: 63
Step-by-step explanation:
You can put this solution on YOUR website! Hi there, 2/3 = 42. Multiply 42 by 3 = 126. Divide 126 by 2 = 63. The lady's age. 63yrs old. Proof: 2/3 x 63
Answer:
63
Step-by-step explanation:
42 / 2 = 21
21 * 3 = 63
If 42 is two thirds, then one third is 21 because (2/3) / 2 = 1/3.
If 21 is one third, then the whole is 63 because (1/3) * 3 = 1.
(05.01)
The graph below shows a system of equations:
The x-coordinate of the solution to the system of equations is
The x-coordinate of the solution to the system of equations plotted is -2
How to find the x-coordinate of the solution to the system of equationsThe x-coordinate of the solution to the system of equations is sought by examining the attached graph
The point where the two lines plotted intersect is the solution. At this point, like any other point in a coordinate system will have x coordinate and y coordinate
The x coordinate is solved by tracing the from the point to the x axis, The value where the imaginary trace line drawn intersects the x coordinate is the solution at the x coordinate
This point has the values of -2 in the x axis
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add -1[tex]\frac{1}{4}[/tex] 0.75 +0.45. Write your answer as a decimal to the nearest hundredth.
Answer:
Step-by-step explanation:
-0.05
Answer: -1/20, or -0.05
Step-by-step explanation:
rewrite -1 1/4 as -5/4
rewrite 0.75 as 75/100 and simplify = 3/4
rewrite 0.45 as 45/100 and simplify = 9/20
-5/4+3/4 = -2/4 = -1/2
-1/2+9/20 find LCD
LCD = 20
-1/2 * 10/10
-10/20+9/20= -1/20
PLASE HURRY
Given an equilateral triangle with side length of 2x+4 what is the perimeter of the triangle? To earn full credit, show your work using a method explained in the Orientation.
Perimeter is 30.A triangle's perimeter is measured in the same unit as its side lengths.
What is the perimeter of the triangle?Additionally, a triangle's perimeter and side lengths are measured in the same unit.If the lengths of its sides are measured in a different unit, first convert them to that unit.
Perimeter of a triangle = sum of all three sides.
Since it's equilateral, just solve for x with any of the 2 sides being equal
2x + 4 = 3x + 1
Subtract 1 from both sides
2x + 3 = 3x
Subtract 2x from both sides
3 = x
Perimeter is 10 + 10 + 10 = 30
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Jesse the beetle crawls at a rate of 9 inches per minute, as modeled by the equation y=9x. His rate decreases by -8 inches per minute. Create two ordered pairs showing the distances he will crawl at 2 minutes and 7 minutes, respectively, at his new rate.
Sometimes, he may move backwards.
The two ordered pairs from the proportional relationship are given as follows:
2 minutes: (2,2).7 minutes: (7,7).What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
Initially, Jesse's rate was of 9 inches per minute, however, the rate decreased 8 inches per minute, then the constant of proportionality is obtained as follows:
k = 9 - 8 = 1.
Thus the proportional relationship that gives the distance that Jesse has crawled in x minutes is given as follows:
y = x.
Then the two ordered pairs are defined as follows:
2 minutes: (2,2), as when x = 2, y = x = 2.7 minutes: (7,7), as when x = 7, y = x = 7.More can be learned about proportional relationships at https://brainly.com/question/10424180
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Mr frohock bought a watermelon that weighed 10. 25 pound. If ahe cut it inyo 5 piece of equal weight, jow many pound did each piece weigh?
In linear equation, 2.05 pound did each piece weight .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Describe a linear example?
Any function that depicts a straight line on the coordinate plane is said to be linear. For instance, the equation y = 3x – 2 represents a straight line on a coordinate plane, indicating that it is a linear function.
This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).
Mr frohock bought a watermelon that weighed 10. 25 pound..
10.25/5
= 2.05.
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A figure is translated six units to the left and two units down. Which rule represents this translation?
(x,y) → (x+6, y + 2)
(x,y) → (x+6,y 2)
(x, y) → (x-6, y + 2)
(x, y) → (x-6, y-2)
Answer:
(x, y) → (x-6, y-2)
Step-by-step explanation:
When you translate to the left, you are subtracting.
When you translate downwards, you are also subtracting.
The same thing goes for the other way around!!
When you translate to the right, you are adding.
When you translate upwards, you are also adding.
Hope this helps!! :)
This year's soybean crop of 224000 t represents an increase of 40% over last year's crop. How many tons of soybeans were produced last year?
well, last year it was "x", which oddly enough is the 100%.
now, this year is 224000 tons, and that's an increase of 40%, so that's really the 100% + 40% = 140%, so if 224000 is the 140%, what's "x"?
[tex]\begin{array}{ccll} tons&\%\\ \cline{1-2} x & 100\\ 224000& 140 \end{array} \implies \cfrac{x}{224000}~~=~~\cfrac{100}{140} \implies \cfrac{ x }{ 224000 } ~~=~~ \cfrac{ 5 }{ 7 } \\\\\\ 7x=(5)(224000)\implies x=\cfrac{(5)(224000)}{7}\implies x=160000[/tex]
The ratio of yellow marbles to purple marbles was 13 to 4. If there were 102 marbles in the bag, how many were yellow marbles?
The number of yellow marbles based on the given ratio will be 78.
What are the ratio and proportion?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
A ratio is a comparison of two quantities. A proportion is an equality of two ratios.
Suppose, the number of yellow marbles is Y while purple marbles are P.
As per the given,
The ratio Y/P = 13/4
Total Y + P = 102
(13/4)P + P = 102
13P + 4P = 408
17P = 408
P = 24
And, Y = 102 - 24 = 78
Hence , The number of yellow marbles based on the given ratio will be 78.
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meal A has 170 calories in 3 servings. Meal B has 160 calories in 4 servings. Which meal has more calories per serving
Answer: Meal B
Step-by-step explanation:
Let's find Meal A
170 divided by three = 56.7 Calories per serving
Find Meal B
160 divided by 4 = 60 Calories per serving
Meal B has more Calories per serving!
49x3x7x1 = show your work
Answer:
1,029
Step-by-step explanation:
What is the slope of the line that passes through the points (-6, 5) and (-3, 20)?
Write your answer
in simplest form.
Answer:
5
Step-by-step explanation:
Slope=y2-y1/x2-x1
20-5/-3-(-6)
20-5/-3+6
15/3
=5
Write an equation of the line that passes through $\left(1,2\right)$ and is parallel to the line $y=-5x+4$.
2 = -5(1) + b is equation of the slope-intercept form of line .
What does math's slope intercept form mean?
A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible.
This form is frequently known as the y = mx + b form.
y = mx + b
Parallel lines have the same slope, so
m = -5
y = -5x + b
Use the given point to find b.
2 = -5(1) + b
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Which recursive sequence would produce the sequence
10,35,135,...?
Answer:
10, 35, 135, 410, 1235, ...
Step-by-step explanation:
a(1) = 10
a(n) = 3 * a(n-1) + 5
This recursive sequence starts with the initial value of a(1) = 10, and each subsequent term is calculated by applying the formula a(n) = 3 * a(n-1) + 5. The resulting sequence would be:
a(1) = 10
a(2) = 3 * a(1) + 5 = 3 * 10 + 5 = 35
a(3) = 3 * a(2) + 5 = 3 * 35 + 5 = 135
a(4) = 3 * a(3) + 5 = 3 * 135 + 5 = 410
a(5) = 3 * a(4) + 5 = 3 * 410 + 5 = 1235
And so on. This recursive sequence generates the following sequence: 10, 35, 135, 410, 1235, ...
How do I solve for x?
Answer:
x = 5
Step-by-step explanation:
Since this is an isosceles triangle, the two angles opposite the congruent sides are also congruent. That means that ∠A and ∠C both equal 73°, you don't even need to solve the equation with y in it. Since all the angles in a triangle add up to 180°, we know that ∠B is equal to [tex]180-(73*2)[/tex], which is 34. So if [tex]34=6x+4[/tex], then you can solve to get [tex]x=5[/tex].
Each X=.........student
Answer:
x = 1 student.
Step-by-step explanation:
Are these triangles similar
Answer: No
Step-by-step explanation:
The ratio of the lengths of the shortest sides is [tex]\frac{6}{4}=\frac{3}{2}[/tex].
The ratio of the lengths of the longest sides is [tex]\frac{10}{7}[/tex].
Since these ratios are not equal, the triangles are not similar.
313,307,301,...
Find the 42nd term.
Answer:
ANS:- 67
Step-by-step explanation:
d = a2 - a1
a2 = 307, a1 = 313
d = 307 -313 = -6
an = a1 + (n - 1)d
a1 = 313, n = 42, d = -6
a42 = 313 + (42 -1)(-6)
a42 = 313 + (41)(-6)
a42 = 313 - 246
a42 = 67
a lemonade can have a radius of 1.5 in and a height of 9 in the can is made from a sheet of aluminum that weighs 0.02 Oz per square inch you received $0.35 per pound of aluminum that you recycle how much do you earn recycling 38 cans
Answer:
1. 24 cans/lb x 15,000 lb/trailer = 360,000 cans/trailer
2. Answer will depend on your price per can or per pound. For example, if price is 60 cents per pound: $0.60/lb x 15,000 lb = $9,000
3. 15,000 lbs/trailer / 30 lbs/collector = 500 can collectors/trailer
4. 15,000 lbs/trailer / 800 lbs/bale = 18 complete bales (and 3/4 of another bale)/trailer
5. 24 cans/lb x 800 lb/bale = 19,200 cans / bale
6. 100 bales/boxcar x 800 lbs/bale = 80,000 lb. cans / boxcar
7. 100 bales/boxcar x 19,200 cans/bale = 1,920,000 cans / boxcar
8. Answer will depend on your price per can or per pound. For example, if price is 60 cents per pound: $0.60/lb x 80,000 lb/boxcar = $48,000/boxcar
3)In the figure below
segments PM and AD are medians.
What is the length of segment AD?
A. 22.5
B. 10
C. 9
D. 7
Answer:
i think they are similar figures therefore AD/PM=AC/PR,16/24=x/15,AD=22.5
A car is traveling at a rate of miles per hour. What is the car's rate in miles per minute? How many miles will the car travel in minutes? Do not round your answers.
Rate blank mi/min
Distance traveled in five minutes blank mi
Image provided
Answers to both the subparts using mathematical operations are shown:
(A) Rate of the car in miles/min: 0.95 miles/min
(B) Distance traveled in 5 min: 4.8 miles
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."
The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, we know that the rate of the car is 57 miles/hour.
(A) Car rate in miles/min
We know that 1 hour has 60 minutes. Then,
57/60
0.95 miles/min
(B) Distance traveled in 5 min:
0.95 * 5
4.75
Rounding off: 4.8 miles
Therefore, answers to both the subparts using mathematical operations are shown:
(A) Rate of the car in miles/min: 0.95 miles/min
(B) Distance traveled in 5 min: 4.8 miles
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