Which graph represents StartFraction (x minus 2) squared Over 16 EndFraction minus StartFraction (y + 1) squared Over 9 EndFraction less-than-or-equal-to 1?
The attached graph represents the graph of [tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]
How to determine the graph?The inequality is given as:
[tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]
The above inequality represents a conic section.
The inequality symbol <= implies that, we make use of a closed line on the graph.
Next, we plot the graph using a graphing tool
See attachment for the graph of [tex]\frac{(x - 2)^2}{16} - \frac{(y + 1)^2}{9} \le 1[/tex]
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Complete question
Which graph represents [tex]\frac{(x - 2)^2}{16} = \frac{(y + 1)^2}{9}[/tex]?
Answer:
C
Step-by-step explanation:
Got it right on Edge
Paladin furnishings generated $4 million in sales during 2021, and its year end total assets were $3.2 million. also, at year end 2021 current liabilities were $500,000, consisting of $200,000 of notes payable, $200,000 of accounts payable, and $100,000 of accrued liabilities. looking ahead to 2022 the company estimates taht its assets must increase by $.80 for every $1.00 increase in sales. paladin's profit margin is 3% and its retention ratio is 50%. how large of a sales increase can the company achieve without having to raise funds externally?
Without having to raise funds externally sales could increase by $84,507.04.
Given that $4 million sales in 2021 and in end of the year total assets are $3.2, current liabilities are $500,000, payable notes are $200,000, accounts payable is $200,000 and accrued liabilities are $100,000 and in 2022 assets must increase by $.80 for every $1.00 increase in sales.
The amount of sales increase that the company can achieve without having to raise funds externally is calculated by multiplying the current year sales with the self-supporting growth rate.
Current Year Sales = $4,000,000
Profit Margin = 3.00%
Dividend Payout Ratio = 50%
Therefore, the Retention Ratio = 50%
Total Spontaneous Liabilities is, $200,000 + $100,000=$300,000
Last Year Total Assets = $3,200,000
Therefore, the Self-supporting Growth Rate=Addition to Retained Earnings÷[Total Assets–Total Spontaneous Liabilities-Addition to Retained Earnings]
= [Last year sales×Profit Margin×(1-Dividend Payout Ratio)]÷[Total Assets-Total Spontaneous Liabilities-Addition to Retained Earnings]
= [$4,000,000×0.03×(1–0.50)]÷[$3,200,000-$300,000–{[$4,000,000×0.04×(1–0.050)}]
= $60,000÷[$3,200,000-$300,000-$60,000]
= $80,000÷$2,840,000
= 0.02112676 or 2.112676%
Therefore, the increase in sales that the company can achieve without having to raise funds externally = Last Year Sales×Self-supporting Growth Rate
= $4,000,000×2.112676%
= $84,507.04
Hence, the Increase in Sales so the company achieve without having to raise funds externally $84,507.04”
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The graph shows the cube root parent function.
Which statement is true?
A. (0, 0) is the x- and y-intercept of the function.
B. The function has no intercepts.
C. (0, 1) is the x- and y-intercept of the function.
D. (1, 1) is the x- and y-intercept of the function.
Answer:
A)
Step-by-step explanation:
The cube root parent function is [tex]y=x^3[/tex]
When y=0, x=0, hence (0,0) is the x and y-intercept of the function.
Hope I helped!
On a 8.5 x 11 inches (or larger) paper, create a carnival game (for example it could be: throwing a dart at a target, ball through a hoop, ball in cup, etc).
Provide a written description of your game.
Your game must use at least two different geometric shapes.
Label the dimensions of the shapes with the measurements in real life. Draw on the paper using a scale factor.
For example, if the game has a 3 feet diameter, label 3 feet on the image, but draw it to scale, so that the model game is similar to the actual dimensions. If the scale is 1 foot = 2 inches, then 3 feet = 6 inches.
Find the probability of winning your game. Include the calculations to show the probability.
Determine the type of prize a winner would deserve and the cost of playing your game.
The probability of winning the game is 0.065
The description of the gameThe game involves throwing two darts at two targets.
To win the game, the darts must hit anywhere in the following shapes
Rectangle: 5 by 4 inchesCircle: Radius, r = 3 inchesThe probability of winningThe area of the paper is:
Area = 8.5 inches * 11 inches
Area = 93.5 square inches
The area of the rectangle on the paper is:
Area = 5 inches * 4 inches
Area = 20 square inches
The area of the circle on the paper is:
Area = π * (3 inches)²
Area = 28.3 square inches
The probability of landing on both shapes is
P(Both) = 20/93.5 * 28.3/93.5
Evaluate
P(Both) = 0.065
Hence, the probability of winning the game is 0.065
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Find the gradients of lines A and B.
B
141
12
Hol
8
NO 9 go
6
41
2
-3-2-10
-2
-4
-6
A
2 3 4 5
7x
Let's see
For line A
(2,2)(3,6)Slope
m=6-2/3-2m=4/1m=4For line B
(1,6)(2,4)Slope
m=4-6/2-1m=-2/1m=-2David buys a beanie baby. he later sells it to jessica and loses $3 on the deal. jessica makes a profit of $6 by selling it to bryan for $25. how much did david pay for the beanie baby?
David paid $22 for the beanie baby.
Profit and loss formulas are used to calculate the profit or loss that has been incurred by selling a particular product. They are mainly used in business and financial transactions to depict how much profit or loss a trader has incurred from any particular deal.
Let the cost which David pay for the beanie baby be x and y be the price at which Jessica bought the beanie baby
Profit formula :
Profit = Selling price (S.P.) - Cost price (C.P.)
So using the profit formula
$6 = $25 - y
$19 = y
Now using the same equation for David
-$3 = $19 - x
$22 = x.
Thus David paid $22 for the beanie baby.
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The final exam test scores were: 62, 66, 71, 75, 75, 78, 81, 83, 84, 85, 85, 87, 89, 89, 91, 92, 93, 94, 95, 99. Find the percentile rank for a score of 85 on this test.
Using it's concept, the percentile rank for a score of 85 on this test is the 50th percentile.
What is the percentile of a measure?When a measure is in the xth percentile of a data-set, it is greater or equal than x% of the measures and lesser than (100 - x)%.
In this problem, there are 20 scores, and 85 corresponds to the 10th highest score, hence the percentile is given by:
p = 10/20 = 0.5 x 100% = 50th percentile.
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Find the equation of a line in slope intercept form that is perpendicular to the line y = 2x + 6 through the point (10,4)
The equation of the straight line is y = -1/6(x - 10) + 4
How to determine the line equation?The equation is given as:
y = 2x + 6
Linear equations are represented as:
y = mx + c
Where:
Slope = m
So, we have:
m = 6
The slopes of perpendicular lines are represented as:
n = -1/m
So, we have:
n = -1/6
The equation is then represented as:
y = n(x - x1) + y1
This gives
y = -1/6(x - 10) + 4
Hence, the equation of the straight line is y = -1/6(x - 10) + 4
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end behavior of f(x)= 10/x^2-7x-30
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
What is the end behavior of a rational function
The end behavior of a rational functions is the horizontal asymptote of the rational function when x tends to ± ∞. Then, we find the end behavior by applying limits:
[tex]\lim_{x \to \pm \infty} \frac{10}{x^{2}-7\cdot x - 30}[/tex]
[tex]\lim_{n \to \infty} \frac{10}{x^{2}-7\cdot x - 30}\cdot \frac{x^{2}}{x^{2}}[/tex]
[tex]\lim_{x \to \pm \infty} \frac{\frac{10}{x^{2}} }{1 - \frac{7}{x}-\frac{30}{x^{2}}}[/tex]
[tex]\lim_{x \to \pm \infty} 0[/tex]
0
By applying definition of limits, the end behavior of the rational function f(x) = 10/(x² - 7 · x - 30) is represented for the horizontal asymptote x = 0.
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y ( x + w ) = c ( x + z )
The formula for x in terms of other terms in the equation is; x = (cz-yw)/(y-c).
What is the formular for x in term of other terms in the equation?According to the task content, it follows that the variable X is to be made the subject of the formula;
Hence, it follows that;
y ( x + w ) = c ( x + z )
yx +yw = cx +cz
x(y-c) = (cz-yw)
x = (cz-yw)/(y-c)
Remarks: The complete question requires that x be made the subject of the formula.
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What is the area of the given figure?
10 in.
O 192 units²
O
92.9 units²
O 101.8 units²
O167.2 units2
O
176.7 units2
6 in.
10 in.
9 in.
[tex]\huge\boxed{192\ \text{in}^2}[/tex]
There are three parts to this figure: a rectangle and two triangles that are congruent.
We'll add together the area for each to get the total area.
We'll start by finding the area of the rectangle. We don't know its length, so we need to find the bases of the triangles and add them together.
We know that [tex]a^2+b^2=c^2[/tex]. Substitute and solve for [tex]a[/tex]:
[tex]\begin{aligned}a^2+6^2&=10^2\\a^2+36&=100\\a^2+36-36&=100-36\\a^2&=64\\\sqrt{a^2}&=\sqrt{64}\\a&=8\end{aligned}[/tex]
Now, double this to get the total length of the rectangle, which is [tex]16[/tex] inches.
The area of the rectangle is equal to its length times its height:
[tex]16\cdot9=\underline{144}[/tex]
Now, we'll find the area of one of the triangles and double it since they're congruent.
The area of a triangle is one-half of its base times its height, which we then double.
[tex]2\left(\frac{1}{2}\cdot b\cdot h\right)[/tex]
The [tex]2[/tex] and the [tex]\frac{1}{2}[/tex] cancel each other out.
[tex]b\cdot h[/tex]
Substitute and solve:
[tex]8\cdot6=\underline{48}[/tex]
Finally, add the rectangle's area to the two triangles' area.
[tex]144+48=\boxed{192}[/tex]
Express each ratio as a unit rate. Round to the nearest tenth, if necessary.
140 miles on 6 gallons
a.
23.3 mi/gal
c.
0.042 mi/gal
b.
840 mi/gal
d.
13.6 mi/gal
Please select the best answer from the choices provided
A
B
C
D
Answer:
23.3 mpg
Step-by-step explanation:
For the unit rate of miles per gallon (mpg)
140 miles / 6 gallons = 23 1/3 mpg = 23.3 mpg
The required ratio as a unit rate is 23.3 mi/gal, which is determined by dividing the number of miles by the number of gallons.. The correct answer is option (a).
To express each ratio as a unit rate (mi/gal), we need to divide the number of miles by the number of gallons.
The units rate can be calculated as:
Units rate = number of miles / the number of gallons.
Unit rate = 140 miles / 6 gallons
Apply the division operation to get:
Unit rate = 23.3 mi/gal
Thus, the required ratio as a unit rate is 23.3 mi/gal.
Hence, the correct answer is option (a).
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Solve for the remaining angles
By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.
How to find the missing angles of a triangle
In this question we know the length of the three sides of a triangle, we can find the measure of all angles by using the law of the cosine. So, we know that:
a = 270, b = 442.85, c = 255
Then, by the law of the cosine:
[tex]\cos A = \frac{270^{2}-255^{2}-442.85^{2}}{-2\cdot (442.85)\cdot (255)}[/tex]
A ≈ 33.544°
[tex]\cos B = \frac{442.85^{2}-270^{2}-255^{2}}{-2\cdot (270)\cdot (255)}[/tex]
B ≈ 114.998°
[tex]\cos C = \frac{255^{2}-270^{2}-442.85^{2}}{-2\cdot (270)\cdot (442.85)}[/tex]
C ≈ 31.458°
By knowing the length of the three sides of the triangle and applying the law of the cosine, we find that the measure of the three angles are 33.544°, 114.998° and 31.458°.
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Which answer shows y+2x<4x-3, rewritten to isolate y, and its graph
The answer choice which shows y+2x<4x-3, rewritten to isolate y is; y < 2x -3.
What is the rewritten form of the equation in which case y is isolated?From the task content, it follows that the inequality given in the task content is; y+2x<4x-3.
Hence, the variable y can be isolated from the inequality as follows;
y+2x<4x-3
y < 4x -2x -3
y < 2x -3.
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HELP please, last question!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Fig. D is correct[tex]\textsf{ \underline{\underline{Explanation } }:}[/tex]
" when rays parallel to optical axis/ principal axis fall on a concave mirror it passes through focus of mirror after reflection "
[tex] \qquad \large \sf {Conclusion} : [/tex]
Fig. D is correctTriangle FIT has been reflected over the y-axis. Which of the following best describes the relationship between the y-axis and the line connecting F to F′?
They share the same midpoints.
They are diameters of concentric circles.
They are perpendicular to each other.
They are parallel and congruent.
The relationship between the y-axis and the line connecting F to F′ is (c) They are perpendicular to each other.
How to determine the relationship?When a triangle FIT is reflected over the y-axis, the image and the pre-image of the triangle would be at either sides of the y-axis.
This means that the points on the image and the pre-image of the triangle are perpendicular to each other
Hence, the relationship between the y-axis and the line connecting F to F′ is (c) They are perpendicular to each other.
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Determine the intercepts of the line.
Do not round your answers.
-4x + 7y = 3
The x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively
How to determine the intercepts of a lineThe y-intercept is the point where the value of x is zero while the x-intercept is the point where the value of y is zero
Given the function below;
-4x + 7y = 3
For the x-intercept
-4x = 3
x = -3/4
The x-intercept is (-3/4, 0)
For the y-intercept
7y = 3
y = 3/7
The y-intercept is (0, 7/3)
Hence the x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively
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HELP HELO
HELP GELP GELP GELP HLEP
Answer:
A. <T=17, RS= 10
Step-by-step explanation:
These triangles are congruent by AAS congruency. This means that RS and UV will have the same measure and so will <Q and <T. Simply use that info with the measurements given.
Solving for <T:
8y-44 = 5y+7
3y = 51
y = 17
Solving for RS:
7x-2 = 5x+18
2x = 20
x = 10
Please help! Which of the following is a solution to the system of two equations y = 3x - 7 and 4x - 5y = -20?
a.) (5,8)
b.) (10,12)
c.) 2,-1)
d.) 9,20)
Answer:
a
Step-by-step explanation:
y = 3x - 7 → (1)
4x - 5y = - 20 → (2)
substitute y = 3x - 7 into (2)
4x - 5(3x - 7) = - 20
4x - 15x + 35 = - 20
- 11x + 35 = - 20 ( subtract 35 from both sides )
- 11x = - 55 ( divide both sides by - 11 )
x = 5
substitute x = 5 into (1)
y = 3(5) - 7 = 15 - 7 = 8
solution is (5, 8 )
A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.
Isosceles triangle A B C is shown. The length of A C is 8 centimeters and the lengths of sides A B and B C are congruent. Side A B has length c and side B C has length a. Angle A B C is 30 degrees.
Trigonometric area formula: Area = One-half a b sine (C)
To the nearest square centimeter, how many square centimeters of the plate are covered by the napkin?
16 square centimeters
30 square centimeters
56 square centimeters
60 square centimeters
The napkin covered approximately 56 square centimeters of the plate. The third option is correct.
What is the area of an isosceles triangle?The area of an isosceles triangle can be estimated by using the trigonometric function:
[tex]\mathbf{=\dfrac{1}{2} \times a \times b\times sin (C)}[/tex]
From the given information:
The base angle and sides of an Isosceles triangle are equal.The perimeter of the triangle:
P = a + b + c
38 = a + 8 + c
where;
a = c (base sides)So;
38 = 8 + 2a
38 - 8 = 2a
2a = 30
a = c = 15
Similarly, ∠ABC = 30
∠A + ∠B + ∠C = 180 (sum of angles in a triangle)
∠A + 30 + ∠C = 180
∠A = ∠C = x
2x = 180 - 30
2x = 150
x = 150/2
∠A = ∠C = x = 75°
Using the trigonometric function:
[tex]\mathbf{=\dfrac{1}{2} \times (15) \times (8) \times sin (75)}[/tex]
= 56 square centimeters.
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Answer: Option C
Step-by-step explanation:
Edge 2020
Geometric probability
Answer:
71.4%
Step-by-step explanation:
7+3+8+3=21 total fish
7+8=15 healthy fish
15÷21=0.7142=71.4%
Devin Gallagher purchased home entertainment equipment for $4,020.19 using the store's credit plan. He made
a 20% down payment.
Answer:
The answer will be $3216.152
Step-by-step explanation:
If you do the 20% of $4020.19 then the answer will came $804.038 and then subtract the result from $4020.19 then it will came $3216.152 and it is the result only.
help me please!!!!!!!! 20 points
Answer:
14 in^2
Step-by-step explanation:
Break the figure up into two rectangles (vertical line down the middle). Use the formula area = length x width for the Rectangle A (2 in x 4 in = 8 in^2) and Rectangle B (3 in x 2 in = 6 in^2) Add 8 in^2 and 6 in^2 for a total area of 14 in^2
Isaiah sketches a model of a skateboard ramp. The model has two surfaces on which to skate, represented by sides AB and AD in the diagram.
Triangle A B D is shown. A perpendicular bisector cuts angle B A D to form triangle A B C. Triangle A B C has angle measures 45, 45, and 90 degrees. Triangle A C D has angle measures 60, 30, and 90 degrees.
The steepest side of the model, AB, measures 4 inches. What is the length of the other skating surface, AD?
2 StartRoot 2 EndRoot in.
2 StartRoot 3 EndRoot in.
4 StartRoot 2 EndRoot in.
4 StartRoot 3 EndRoot in.
The length of the other skating surface AD of the ramp is 4√2 inches
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sine rule shows the relationship between the sides and angles of a triangle.
Using sine rule:
AB / sinD = AD / sinB
4/sin(30) = AD / sin(45)
AD = 4√2 inches
The length of the other skating surface AD of the ramp is 4√2 inches
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(C.) 4√2
________
I got it wrong, the correct answer was revealed <3
Is xxx greater than, less than, or equal to 110^\circ110
∘
110, degrees?
The angle z is equal to 110° by vertically opposite angles. Hence, the correct option will be C. z = 110°.
What is vertically opposite angles?The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Given;
The one angle is given as 110°.
So, angle z will be equal to 110° by vertically opposite angles.
Hence, the correct option will be C. z = 110°.
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I need help fast please
Answer:
3.4
Step-by-step explanation:
[tex]Interval=\frac{4-2.2}{9}\\Interval=0.2\\therefore :\\ 6 intervals =6(0.2)\\ 6 intervals =1.2\\x=2.2+1.2\\x=3.4[/tex]
Jane wants to buys some lollipops. If she buys 2 lollipops, she will have 3 dollars left. If she wants to buy 3 lollipops, she will need 2 more dollars. Jane has ___ dollars.
Since Jane wants to buys some lollipops, Jane has $13 dollars.
To answer the question, we need to solve simultaneous equations
What are simultaneous equations?Simultaneous equations are pairs of equations that contain two unknowns
How to calculate how much Jane has using simultaneous equationsLet
x = price per lollipop and y = total amount Jane hasWe know that If she buys 2 lollipops, she will have 3 dollars left, so we have that
y - 2x = 3 (1)
Also, If she wants to buy 3 lollipops, she will need 2 more dollars. So, we have that
y + 2 = 3x (2)
The required simultaneous equationsSo, the required simultaneous equations are
y - 2x = 3 (1)
y + 2 = 3x (2)
From (1), x = (y - 3)/2
Substituting x into (2), we have
y + 2 = 3x (2)
y + 2 = 3(y - 3)/2
2(y + 2) = 3(y - 3)
2y + 4 = 3y - 9
2y - 3y = -9 - 4
-y = -13
y = -13/-1
y = 13
So, Jane has $13 dollars.
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What kind of function is
5x + 19y = 84 ? Thanks
Linear, slope-Intercept form Quadratic
exponential
linear, standard form
Answer:
It's a linear function.
A school survey asked students which candidate they supported for class president. The survey data are shown in the relative frequency table. What percentage of females polled supported Martinez?
A:30%
B:58%
C: about 56%
D:about 54%
Answer:
About 56%
Step-by-step explanation:
A local school district requires all fourth graders to complete a 20-minute test containing 200 multiple-choice mathematics problems. Students are not expected to complete all of the questions, but are graded on the number they are able to get correct in the time limit. What component of mathematics fluency is most likely the goal of this type of assessment
The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
GIven,
A local school district requires all fourth graders to complete a 20-minute test containing 200 multiple-choice mathematics problems.
The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
The school district is assessing the rate because they are seeing how many questions students can answer in a given time frame.
Hence, The component of mathematics fluency is most likely the goal of this type of assessment is Rate.
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