Two unit squares share the same center. the overlapping region of the two squares is an octagon with perimeter 10/3. The area of the octagon is 0.833 square unit.
Let the octagon's eight successive vertices be A, B, C, D, E, F, G, and H.
Connect the squares' vertices to the shared center O by drawing the segments OA, OB, OC, OD, OE, OF, OG, and OH.
The octagon is divided into 8 triangles by the segments.
The bases of these triangles are AB, BC, CD, DE, EF, FG, GH, and HA; each triangle's height equals 1/2 of a unit.
Consequently, the octagon's surface area is
Area = (1/2) × (1/2) × (AB + BC + CD + DE + EF + FG + GH + HA)
Area = (1/4) × Perimeter of the octagon
Perimeter of the octagon = 10/3
Area = (1/4) × (10/3)
Area = 10/12
Area = 0.833 square unit.
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the line through (2, 4, 5) perpendicular to the plane 3x 7y - 5z = 21
Line through (2,4,5) perpendicular to plane 3x-7y+5z=21 found by finding normal vector <3,-7,5> and direction vector <0,5,-3> from cross product. Parametric equation is r(t)=<2,4,5>+t<0,5,-3>.
What is plane ?
A plane is a Euclidean, two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point, a line and three-dimensional space.
The normal vector is given by the coefficients of x, y, and z in the equation of the plane:
n = <3, -7, 5>
Next, we need to find a point on the line and a direction vector for the line. The point on the line is (2, 4, 5) and the direction vector can be found by taking the cross product of the normal vector and an arbitrary vector not parallel to the normal vector.
An arbitrary vector not parallel to the normal vector could be <1, 0, 0>. Taking the cross product, we get:
d = n x <1, 0, 0> = <0, 5, -3>
So, the line through (2, 4, 5) perpendicular to the plane 3x - 7y + 5z = 21 is given by:
r(t) = <2, 4, 5> + t<0, 5, -3> = <2 + 0t, 4 + 5t, 5 - 3t>
Line through (2,4,5) perpendicular to plane 3x-7y+5z=21 found by finding normal vector <3,-7,5> and direction vector <0,5,-3> from cross product. Parametric equation is r(t)=<2,4,5>+t<0,5,-3>.
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the average weight of a honeycrisp apple is 110 grams and the standard deviation is 20 grams. what is the z-value for an apple that weighs 140 grams?
the z-value for an apple that weighs 140 grams is 1.5.
The z-value is used to determine how many standard deviations an observation is from the mean of a normal distribution. To find the z-value for an apple that weighs 140 grams, we need to calculate the difference between the apple's weight and the mean weight, and divide by the standard deviation.
Given that the average weight of a honeycrisp apple is 110 grams and the standard deviation is 20 grams, we can calculate the z-value as follows:
(140 - 110) / 20 = 1.5
This means that the apple that weighs 140 grams is 1.5 standard deviations above the mean weight of 110 grams. This information can be used to calculate the probability of finding an apple with a weight of 140 grams. For example, if we use a standard normal distribution table, we can find that the probability of finding an apple with a weight greater than 140 grams is 0.0668, or 6.68%.
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Which number is closest to total deaths resulting from ladder misuse each year?
Select the best answer:
a. More than 1,000
b. More than 300
c. Less than 100
d. More than 600
Option C is correct. Less than 100 is closest to total deaths resulting from ladder misuse each year.
According to the Consumer Product Safety Commission (CPSC), on average, approximately 300 people die each year in the United States from falls involving ladders.
However, not all of these deaths are due to ladder misuse. In fact, the number of deaths resulting specifically from ladder misuse is likely to be lower. It is estimated that a significant portion of ladder-related fatalities are caused by factors such as overreaching, misusing the ladder, or failing to follow proper safety guidelines.
To reduce the number of deaths and injuries resulting from ladder misuse, it is important to follow safety guidelines and to choose the right ladder for the job, taking into consideration factors such as height, weight, and stability.
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The difference of a number (n) and 8 is no less than 10.
For given expression n-8>=10 to be true, n>=18.
Describe expressions.Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.
e.g. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the expression x/2 + 6. Complex riddles are solved using mathematical expressions.
Now
Given
The difference of a number (n) and 8 is no less than 10.
We can write this as expression n-8>=10,
and for this to be true n>=18.
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according to chebyshev's theorem, at least what percent of any set of observations will be within 1.8 standard deviations of the mean? (round your answer to the nearest whole percent.)
According to Chebyshev's theorem, at least 69 percent of any set of observations will be within 1.8 standard deviations of the mean.
Standard deviations of the mean = 1.8 s
According to Chebyshev's theorem at least (1 - 1/k^2)×100% observations will lie within k standard deviation from the mean.
The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 1/(1.8)^2)×100%
The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 1/3.24)×100%
The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 0.31)×100%
The proportion of observations that will be within 1.8 standard deviations of the mean = 0.69 × 100%
The proportion of observations that will be within 1.8 standard deviations of the mean = 69%
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the admissions office wants to estimate the cost of textbooks for students at our college. let the variable x be the total cost of all textbooks purchased by a student this semester. the plan is to randomly identify 100 students and obtain their total textbook costs. the average cost for the 100 students will be used to estimate the average cost for all students. (a) describe the parameter the admissions office wishes to estimate.
The admissions office wishes to estimate the average cost of textbooks for all students, represented by the parameter μ (the population mean).
The parameter of the admissions officeThere are steps followed to determine the parameter the admissions office wishes to estimate:
Define the population: In this case, the population is all students at the college.Define the variable of interest: The variable of interest is the cost of textbooks for each student, represented by the variable x.Determine the parameter of interest: The parameter of interest is the average cost of textbooks for all students, represented by the population mean μ.Choose a sample: The admissions office plans to randomly select 100 students and obtain their total textbook costs.Use the sample to estimate the population parameter: The average cost for the 100 students will be used to estimate the average cost of textbooks for all students, represented by the population mean μ.Learn more about The parameter of the admissions office here:
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if a man casts a 3 ft shadow at noon, and a 9 ft shadow at 6pm, then what length of shadow does his dog cast at 6pm, if it casts an 2ft shadow at noon?
His dog casts a shadow of 6ft at 6 pm if it casts a 2ft shadow at noon.
A man casts a 3 ft shadow at noon and a 9 ft shadow at 6 pm.
His dog casts a 2 ft shadow at noon.
Therefore we can find the length of shadow casts by his dog at 6 pm as follows:
Length of the shadow of a man at noon/length of the shadow of a man at 6 pm = length of the shadow of his dog at noon/length of the shadow of his dog at 6 pm
⇒3/9 = 2/length of the shadow of his dog at 6 pm
⇒length of the shadow of his dog at 6 pm = (2 × 9)/3
⇒length of the shadow of his dog at 6 pm = 6 ft
Hence, the shadow cast by his dog at 6 pm will be 6 ft.
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A veterinarian knows that the supplement glucosamine is beneficial for dogs’ joints. He wants to determine if a supplement with both glucosamine and chondroitin would be more beneficial than glucosamine alone for dogs’ joint health. The veterinarian asks the owners of dogs with known joint issues if they would be willing to have their dog participate in his study, and 32 owners agree to the study. The veterinarian also knows that breed and age may affect the results of the experiment.
Which of the following designs would be most appropriate for this experiment?
A) Completely randomized design: Randomly assign the treatments to the dogs.
B) Matched pairs design: Block the dogs based on breed. Then, within each block, pair the dogs based on age. Randomly assign the treatments to each dog in the pairs.
C) Randomized block design: Block the dogs based on breed. Then, randomly assign half of the dogs in each block to receive glucosamine only and the other half to receive glucosamine with chondroitin.
D) Observational study: The veterinarian should randomly select patient records. Then, use the joint health of dogs that use glucosamine only and those that use glucosamine with chondroitin.
The correct option: A) Completely randomized design: Randomly assign the treatments to the dogs.
How does randomized design work?"Any randomized design is regarded as a form of experiment that is assigned to various treatments by carrying out various experiments on various groups.
The answer to the query is
A veterinarian performs an experiment to see if glucosamine on its own or glucosamine + chondroitin is more useful.By randomly splitting the canines into 2 groups of sixteen each, a veterinarian experimented on 32 dogs. 16 dogs receive glucosamine therapy, and the remaining 16 receive glucosamine and chondroitin therapy.Each dog's health is assessed and compared after six months.Therefore, we get to the conclusion that the treatment given to the dogs at random is the best course of action.
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14. there are two bags. bag a contains 1 red ball and 9 blue balls. bag b contains 10 blue balls. you choose a ball at random from bag a and place it into bag b. you then choose a ball at random from bag b and place it into bag a. if after this process the red ball is in bag a, what is the probability that it was moved?
The probability the that red ball was moved is 1/100
Given that there are two bags. Bag A contains 1 red ball and 9 blue balls. Bag B contains 10 blue balls. A ball is chosen at random from bag A and placed into bag B. Then a ball is chosen at random from bag B and placed into bag A. After this process, the red ball is in bag A and we are asked to find the probability that it was moved.
Probability of the red ball chosen from bag A = 1/10
Probability of the red ball chosen from bag B = 1/10
After this process, the red ball is in bag A, the probability that it was moved.
1/10 × 1/10 = 1/100
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how do you calculate hire purchase
Hire purchase is a method of purchasing goods in which the retailer arranges for a lending firm to collect a down payment from you and you pay the remaining balance in monthly instalments.
What is hire purchase?A hire purchase, often referred to as an instalment plan, is a deal where a client accepts a contract to buy an item by making a down payment and paying the remaining amount of the asset's price plus interest over time.
Hire purchase is a method of purchasing goods in which the retailer arranges for a lending firm to collect a down payment from you and you pay the remaining balance in monthly instalments.
Deposit + the sum of the monthly payments = a hire buy.Deposit + the sum of the monthly payments a= hire purchase.To learn more about Deposit refer to:
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calculate the iterated integral. 1 0 3 1 (12x3 − 9x2y2) dy dx
The double integral is used to calculate the area of a region enclosed by two curves.
The region is bounded by the curves x = 1, y = 0, x = 3 and y = [tex]3x2 - 9x2y2[/tex]. In this case, the double integral is given by the expression [tex]∫10∫312x3 - 9x2y2 dy dx.[/tex]
In order to calculate the double integral, the iterated integral method is used. This involves integrating the inner integral with respect to y first, and then integrating the outer integral with respect to x.
The first step is to integrate the inner integral with respect to y. This gives us the expression [tex]∫0 3 (12x3 - 9x2y2) dy[/tex]. After integrating with respect to y, we then integrate the outer integral with respect to x. This gives us the expression [tex]∫10 ∫0 3 (12x3 - 9x2y2) dy dx.[/tex]
The result of this double integral is the area of the region bounded by the two curves. The result of the double integral is therefore the area of the region bounded by the two curves. The result of the double integral is therefore the area of the region enclosed by the two curves. The result of this double integral is the area of the region bounded by the two curves.
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which derivative is approximated by tan(pi/4 + 0.0001) - 1 / 0,0001 ?
The value of derivative is approximated by tan(pi/4 + 0.0001) - 1 / 0,0001 is pi / 4 by limits and continuity.
Let the given expression be some I (say)
then , I = tan(pi/4 + 0.0001) - 1 / 0,0001
we know that tan(pi/4) = 1
hence replace 1 by tan(pi/4) in the above expression,
I = tan(pi/4 + 0.0001) - tan(pi/4) / 0,0001
Now, tan (I) = limx→0 tan(I+x) - tan(I) / x
in this case , x = 0.0001 and I = pi/4
Therefore , the derivative is approximated by tan(pi/4 + 0.0001) - 1 / 0,0001 is at pi/4.
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In the mesosphere, the atmospheric layer
between 50 km and 80 km in altitude, the average
atmospheric temperature varies linearly with
altitude. If the average temperature at 50 km
altitude is 10°C and the average temperature at
80 km is-80°C, then at what altitude is the average
temperature -50°C?
For the slope of -3, the altitude where the average temperature is -50°C is 70 km.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
At 50 kilometer from earth's surface, the temperature is 10°C.
At 80 kilometer from earth's surface, the temperature is -80°C.
The given temperature for unknown altitude is -50°C.
We are told that the temperature varies linearly with altitude, so if y represents the temperature (in °C) and x represents altitude (in km), these variables are related by the equation y = mx + b, where m (the slope) and b (the y-intercept) are constants.
The two points on this line are (50 km , 10°C) and (80 km , -80°C).
Use these points to find the slope m -
m = (y2 - y1)/(x2 - x1)
m = (-80 - 10)/(80 - 50)
m = -90/30
m = -3
Recall that the slope of a linear relationship is the "unit rate of change". In other words, the slope of -3 means that the temperature declines by 3°C for every 1 km of additional altitude.
Since the altitude at which the temperature is -50°C is needed, the value of x such that (x, -50°C) is on this line is needed. To find x, simply use the slope formula again, using either of the other two points:
Slope formula using (50,10) and (x,-50) -
m = (y2 - y1)/(x2 - x1)
-3 = (-50 - 10)/(x - 50)
-3(x - 50) = -60
-3x + 150 = -60
-3x = -60 - 150
-3x = -210
x = -210/-3
x = 70
Therefore, the altitude will be 70 km.
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calculate the area of trapezium whose parallel sides are of length 19 cm and 21 cm while the distance between them is 14 cm.
Answer:
The area of a trapezium with parallel sides of length 19 cm and 21 cm, and a distance of 14 cm between them, is 280 square cm.
Step-by-step explanation:
Solve for x pleaseeee
The values of x = 10√3 derived using the trigonometric ratio of cosine.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent x and hypotenuse 30;
cosθ = x/30
for the smaller right triangle with adjacent 30 - 20 = 10 and hypotenuse x
cosθ = 10/x
x/30 = 10/x
x² = 300 {cross multiplication}
x = √300 {take square root of both sides}
x = √100 × √3
x = 10√3.
Therefore, the values of x = 10√3 derived using the trigonometric ratio of cosine.
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research findings from a human clinical trial study on high blood pressure treatments in older adults were just published in a research journal. figure 1, a box-whisker plot, reports the mean blood pressure levels of the subjects after six weeks of treatment on placebo medication, treatment a, or treatment b. what information is important to include on the box-whisker plot?
P-values that are precise serve as a measure of statistical significance is important to include on the box-whisker plot.
In a clinical trial, research is conducted on human participants (sometimes known as volunteers) with the goal of advancing medical knowledge.
Clinical trials also known as interventional studies and observational studies are the two primary categories of clinical research. Medical products, such as medications or gadgets, surgeries, or adjustments to participants' behavior, including dietary changes, can all be considered treatments.
The null hypothesis should be rejected if the p-value is less than 0.05, which is commonly regarded as statistically significant. The null hypothesis is not rejected if the p-value is greater than 0.05 since it indicates that the divergence from the null hypothesis is not statistically significant.
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find the value of for which the area enclosed by the curves =−2 and =2− is equal to 128.
At the value of c = 21 (approx) for which the area enclosed by the curves y = c - x^2 and y = x^2 - c is equal to 128.
The curves are y = c - x^2 and y = x^2 - c
The area enclosed by these curves is 128.
We must determine the x-coordinates of the places of intersection in order to determine the bounds of integration:
c - x^2 = x^2 - c
Subtract c on both side, we get
-x^2 = x^2 - 2c
Subtract x^2 on both side, we get
-2x^2 = -2c
Divide by -2 on both side, we get
x^2 = c
Taking square root on both side, we get
x = ±√c
The between the curve is given by
[tex]\int\limits^{\sqrt{c}}_{-\sqrt{c}}{[(c-x^2)-(x^2-c)]} \, dx[/tex] = 128
Simplify
[tex]\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(c-x^2-x^2+c)} \, dx[/tex] = 128
[tex]\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(2c-2x^2)} \, dx[/tex] = 128
[tex]2\int\limits^{\sqrt{c}}_{-\sqrt{c}}{(c-x^2)} \, dx[/tex] = 128
Now integrating with respect to x
[tex]2\left(cx-\frac{x^3}{3}\right)^{\sqrt{c}}_{-\sqrt{c}}[/tex] = 128
[tex]2\left[\left(c(\sqrt{c})-\frac{(\sqrt{c})^3}{3}\right)-\left(c(-\sqrt{c})-\frac{(-\sqrt{c})^3}{3}\right)\right][/tex] = 128
[tex]2\left[\left(c(\sqrt{c})-\frac{(\sqrt{c})^3}{3}\right)-\left(-c\sqrt{c}+\frac{(\sqrt{c})^3}{3}\right)\right][/tex] = 128
[tex]2\left[c\sqrt{c}-\frac{(\sqrt{c})^3}{3}-c\sqrt{c}-\frac{(\sqrt{c})^3}{3}\right][/tex] = 128
[tex]2\left[-\frac{2(\sqrt{c})^3}{3}\right][/tex] = 128
[tex]-\frac{4}{3}(\sqrt{c})^3[/tex] = 128
[tex]-\frac{4}{3}(c\sqrt{c})[/tex] = 128
Multiply by -3/4 on both side, we get
c(√c) = -96
Square on both side, we get
c^2(c) = 9216
c^3 = 9216
Taking cube root on both side, we get
c = 20.97
c = 21 (approx)
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The complete question is:
Find the value of c for which the area enclosed by the curves y = c - x^2 and y = x^2 - c is equal to 128.
03
!!!
!!!
In the figure below, m/LJK= 38° and m/KLJ= 71°.
What is m/JKH?
OA. 19°
OB. 90°
OC. 9°
OD. 39°
H
L
K
Note: picture not drawn to scale
The measure of the angle JKH is 19 degrees
How to determine the measure of JKHThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
m/LJK= 38° and m/KLJ= 71°.
Start by calculating the external angle of JKL
So, we have
External = LJK + KLJ
External = 38 + 71
External = 109
The measure of angle JKH is then calculated using:
JKH + 90 = External
This gives
JKH + 90 = 109
Evaluatet the like terms
JKH = 19
Hence, the angle has a value of 19 degrees
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Describe the transformations from shape A to B
Answer:
Therefore the transformation is a dilation of Figure a by a scale factor of -2
Step-by-step explanation:
Take any point on figure A and see what its coordinates are
Take the corresponding point on figure B and see what its coordinates are
This will give you an idea of what transformation has taken place
In figure A, take point (1, 3)
The corresponding point in Figure B is (-2, -6)
This is a dilation of the point (1, 3) by a scale factor of -2 since -2 x (1, 2) = (-2, -6)
The other points are similarly dilated
(3, 3) ==> (-6, -6)
(3, 4) ==> (-6, -8)
Therefore the transformation is a dilation of Figure a by a scale factor of -2
A rectangle ha an area of 24 quare meter. The width of the rectangle i 4 meter. What i the length of the rectangle? meter
Expected length = 6 meter.
Using the formula,
A = W × L
where,
Area (A) = 24
Width (W) = 4
Length (L) = ?
so, A/W = 24/4 = 6
Hence, length of the rectangle is 6 meter.
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A cyclit leave home and ride due eat for a ditance of 45 km. She return home on the ame bike path, if the entire trip take 4 hr , what i her diplacement
The displacement made by the cyclist is 0, this is caused by the same path traveled by the cyclist.
DisplacementDisplacement is the change in position of a moving object relative to a frame of reference. That is, locking is a change in the initial position of the object to the final position of the object.
The displacement in this case is calculated by the Pythagorean theorem.
Displacement² = S₁² + S₂²
The displacement will be zero when the start and end points are the same, that's what makes the problem zero. In the question, the distance traveled by the rider is 45 km, but because there is no position lock because the rider is traveling the same path, the closing done by the cyclist is 0.
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Part A Joseph runs 4 miles on Monday. Each day after that he runs the same 2 mile route every morning. His goal is to run at least 10 miles by the end of the week. What inequality represents the least number of days after Monday that Joseph needs to run to reach his goal
Part B what is the least number of days after Monday that Joseph needs to run to reach his goal
Answer: 2x + 4mi >=10 , 3
Step-by-step explanation:
x=days after monday
Since Joseph ran 4 miles the first day, that number stays constant. The 2miles depends on the amount of days he runs for so that is the coefficient. Atleast means greater than or equal to. Using the inequality, we can solve that x >= 3.
2x+4>=10
-4 -4
2x>=6
/2 /2
x>=3
Describe each x-intercept as "crosses" or "touches" the x-axis
Answer:
Third option
touches at x = 1crosses at x = -3crosses at x = -5Step-by-step explanation:
If the polynomial has a factor of the form [tex](x - h)^p,[/tex] the behavior of its graph is determined by the value of p. p .
One zero of the polynomial is x = h
x - h is a zero of multiplicity p
The following is a summary of rules regarding multiplicities and x-intercepts.
For even multiplicities, i.e. p = 2, 4, 6, 8,... the graph will touch the x-axis for the zerosFor odd multiplicities, i.e. p = 1, 3, 5, 7,... the graph will cross the x-axis for the zerosThe given polynomial is:
[tex]\mbox {\large \textsf(x - 1)^2(x+3)(x + 5)^5}}[/tex]
The zeros can be found by setting each of these factors to 0 and solving for x
x - 1 = 0 ==> x = 1
x + 3 = 0 ==> x == -3
x + 5 = 0 ==> x = -5
Hence, the zeros of this polynomial are
x = 1 with a multiplicity of 2x = -3 with a multiplicity of -3x = -5 with a multiplicity of -5Using the rules provided we see that the graph
touches at x = 1crosses at x = -3crosses at x = -5This corresponds to
Third option
the freshmen want to plan a party for June to celebrate the big accomplishment of surviving their first year. they have to decide if they are going to order pizza from pizza hut or Hungry Howies. pizza hut charges a 10 delivery fee, plus 5 for each large pizza. alternately hungry Howies charges a 15 delivery fee plush 4.50 for each large pizza
The two equations representing the costs are 10 + 5x and 15 + 4.5x.
What are the three types of solutions for a system of linear equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Let, 'x' be the number of pizzas.
Therefore, From the given information the two linear equations we can form is, 10 + 5x and 15 + 4.5x.
As the delivery charges for both the stores is a constant.
We can determine the number of pizzas when the cost for both options would be the same by equating these two equations.
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HELP ASAP PLS WILL GIVE BRAINLIEST
Answer:
SAS because you have two congruent sides surrounding one congruent angle
Help me I really need help
All of the y-values are not a constant multiple of the corresponding x-values, so the relationship is not a proportional relationship.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Next, we would determine the constant of proportionality (k) for the relationship between the x-values and y-values in this table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/1 ≠ 5/2 ≠ 6/3
Since the constant of proportionality (k) for the relationship between the x-values and y-values are different, we can logically deduce that this is not a proportional relationship.
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What is the image point of (-3, 4) after the transformation D5 o R270-?
I
Submit Answer
attemp
The new coordinates of the point will be (2, -3).
What is coordinate?Coordinate is a system used to determine the exact location of a point on a 2-dimensional plane or 3-dimensional space. It is typically used to pinpoint a specific spot on a map or graph. Coordinate systems are usually written in two or three numbers, representing the x, y and z positions of the point. These coordinates can then be used to calculate distances, angles and other measurements.
After the transformation D5 o R270-, the image point of (-3, 4) will be (2, -3). The transformation D5 is a dilation, which changes the distance between the origin and the point by a factor of 5. The transformation R270- is a rotation by 270 degrees counter-clockwise, which moves the point to the left and up by the same distance. Therefore, the new coordinates of the point will be (2, -3).
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how much mewtal is needed to cast a cubical metal box with 12 inch long exterior edges if the thickness of its walls should be exactly 3 inches?
Total metal needed to cast a cubical metal box with exterior edge length 12 inches and thickness 3 inches is equal to 999cubic inches.
Length of the exterior edge of the cubical metal box = 12 inches
Thickness of the wall of cubical metal box = 3 inches
Length of the interior edge of the cubical metal box
= 12 inches - 3 inches
= 9 inches
Volume of the exterior cubical metal box = 12³
= 1728 cubic inches
Volume of the interior cubical metal box = 9³
= 729cubic inches
Total metal required to cast a cubical metal box
= (Volume of the exterior - Volume of the interior )cubical metal box
= (1728 - 729 )cubic inches
= 999 cubic inches
Therefore, the total metal required to cast a cubical metal box is equal to 999 cubic inches.
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in response to recent unusual earthquake activity, a large city has enacted an ordinance requiring the permanent placement of seismographic equipment in the basements of 20 randomly selected commercial buildings throughout the city as part of the creation of an early-warning network. although the owners of the buildings will not be compensated, the cost of the purchase and installation of the equipment is to be borne by a private university that will operate the early-warning network. the owner of one building that has been randomly selected as a site for this equipment has challenged this law as unconstitutional, though the actual impact on him would be negligible. should the court rule in favor of the owner?
The court should not rule in favor of the owner, as the ordinance is likely constitutional. The ordinance is likely to be upheld as an exercise of the city's police power, which grants local governments the authority to pass laws and regulations in the interests of public health, safety, and welfare.
Furthermore, the ordinance does not appear to be an unreasonable exercise of the city's police power, as the installation of seismographic equipment is likely to benefit the public interest by providing early warning in the event of an earthquake. Moreover, the ordinance does not appear to be overly burdensome on the owner, as the cost of the purchase and installation of the equipment is to be borne by a private university, and the owner will not be compensated.
In short, the ordinance does not appear to be an unconstitutional taking of private property, as the owner's burden is minimal and the public benefit is substantial.
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Select all expressions equivalent to -62 + (-5.5) + 3.52 + 5y - 2.5.
Answer:
I think the answer is 5y-8-2.5z
