Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the systems of equations with their solution sets. y + 12 = x2 + x x + y = 3 y − 15 = x2 + 4x x − y = 1 y + 5 = x2 − 3x 2x + y = 1 y − 6 = x2 − 3x x + 2y = 2 y − 17 = x2 − 9x -x + y = 1 y − 15 = -x2 + 4x x + y = 1 Solution Set Linear-Quadratic System of Equations {(-2, 3), (7, -6)} arrowRight {(-5, 8), (3, 0)} arrowRight {(-2, 5), (3, -5)} arrowRight {(2, 3), (8, 9)} arrowRight
Answers
Answer:
Step-by-step explanation:
The solution of this systems of equations is the intersection of both graphs
Let's kick start with a:
a)
[tex]y+12 = x^2+x \\ \\ x+3 = y[/tex]
From the first attached diagram by using graph:
the solution is the set {(-5, 8), (3, 0)}
b)
[tex]y-15=x^3+4x \\ \\ x-y =1[/tex]
Using the graph tool from the last diagram below;
the solution is the set⇒( there is no solution)
c)
[tex]y+5 =x^2-3x \\ \\ 2x+y =1[/tex]
From the second attached diagram by using graph:
the solution is the set {(-2, 5), (3, -5)}
d)
[tex]y-6=x^2-3x \\ \\ x+2y =2[/tex]
the solution is the set ⇒ there is no solution (shown in the last diagram below)
e)
[tex]y-17=x^2-9x \\ \\ -x+y =1[/tex]
the solution is the set {(2, 3), (8, 9)} as shown in the third diagram
f) Lastly:
[tex]y-15=-x^2+4x \\ \\ x+y =1[/tex]
Using the graph tool from the fourth diagram below;
the solution is the set {(-2, 3), (7, -6)}
The solution to the system of equations are the truth values of the system of equations
[tex]\mathbf{(a)\ y + 12 = x^2 + x,\ x + 3 = y}[/tex]
The graphs of the equations intersect at (-5,8) and (3,0).
So, the solution set is {(-5,8), (3,0)}
[tex]\mathbf{(b)\ y - 15 = x^3 + 4x,\ x - y = 1}[/tex]
The graphs of the equations do not intersect
So, the system has no solution
[tex]\mathbf{(c)\ y + 5 = x^2 - 3x,\ 2x + y = 1}[/tex]
The graphs of the equations intersect at (-2,5) and (3, -5).
So, the solution set is {(-2, 5), (3, -5)}
[tex]\mathbf{(d)\ y - 6 = x^2 - 3x,\ x + 2y = 2}[/tex]
The graphs of the equations do not intersect
So, the system has no solution
[tex]\mathbf{(e)\ y - 17 = x^2 - 9x,\ -x + y = 1}[/tex]
The graphs of the equations intersect at (2,3) and (8,9).
So, the solution set is {(2, 3), (8, 9)}
[tex]\mathbf{(f)\ y - 15 = -x^2 + 4x,\ x + y = 1}[/tex]
The graphs of the equations intersect at (-2,3) and (7,-6).
So, the solution set is {(-2, 3), (7, -6)}
Read more about system of equations at:
https://brainly.com/question/12895249
Related Questions
Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below.
Answers
Answer:
The question is incomplete, here is the complete question.
Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below. Children in 50 Households Number of Children Number of Households 0 5 1 11 2 13 3 10 4 9 5 2 Using a proportion, what can you infer about the number of households in her town that have more than three children?
A) About 242 households have more than three children.
B) About 269 households have more than three children.
C) About 296 households have more than three children.
D) About 565 households have more than three children.
Step-by-step explanation:
The given sample size is 50
The number of households with more than three children = 9+2
= 11
The proportion of household where more than three children are present is calculated by:
Household with a greater number of children/sample size
= 11/50
The original household size= 1,346
Therefore, the amount of household with children greater than 3 is:
= 1346×11/50
= 1346× 0.22
= 296.12
= 296
Thus, about 296 households have more than three children.
5. What is the height of a pyramid (with a square base) whose side length is 12 cm and its slant
height is 10 cm?
a.) 22 cm
b.) 8 cm
d.) None of these
c.) 2 cm
Answers
Answer:
384
Step-by-step explanation:
The formula for the volume is Area of Base * H / 3
The area of the base is 144
If you draw the height from the peak, you will get a right triangle with side length 6 and hypotenuse 10
Pythagorean Theorem, and the height is 8
144 * 8 / 3 = 384
Hope this helps.
A prism has an isosceles triangle bases with leg lengths of 5 inches 5 in and 8 inches and a height of 3 in the distance between the bases is 12 in find the surface area show your work
Answers
Answer:
240 Square Inches
Step-by-step explanation:
See the attached diagram
The Isosceles Triangle based prism consists of two triangles of equal area, to rectangles of equal area and the rectangle at the base.
Therefore:
Surface Area of the Prism =Surface Area of Two Triangular Base+Area of three Rectangles
Area of one Triangular Base=0.5 X 8 x 3 =12 Square inches
Area of Rectangle 1=5 x 12 =60 Square Inch
Area of Rectangle 2=5 x 12 =60 Square Inch
Area of Rectangle 3=8 x 12 =96 Square Inch
Therefore:
Surface Area of the Prism=2(12)+2(60)+96
=240 Square Inches
Answer:
240 in²
Step-by-step explanation:
The prism has an isosceles triangle with the following data:
- Two lengths = 5 inches
- Other length = 8 inches
- Height = 12 inches
Since the prism consist of 2 triangle bases and three rectangular faces, the surface area (SA) of the prism can be calculated as follows:
[tex] SA = SA_{b1} + SA_{b2} + SA_{f1} + SA_{f2} + SA_{f3} [/tex]
Where:
[tex]SA_{b1}[/tex] and [tex]SA_{b2}[/tex] are the surface areas of the two triangle bases.
[tex]SA_{f1}[/tex], [tex]SA_{f2}[/tex] and [tex]SA_{f3}[/tex]: are the surface areas of the three rectangular faces.
The surface area of the triangle bases can be calculated as follows:
[tex] SA_{b1} = SA_{b2} = \frac{b*h}{2} [/tex]
Where:
b: is the base = lenght of 8 inches
h: is the height = 3 inches
[tex] SA_{b1} = SA_{b2} = \frac{8*3}{2} = 12 in^{2} [/tex]
Now, we need to find the surface area of the rectangular faces using the following data:
Rectangular face 1 = rectangular face 2:
- One side = 12 inches
- Other side = 5 inches
Rectangular face 3:
- One side = 12 inches
- Other side = 8 inches
Hence, the SA of the rectangular face 1 and rectangular face 2 is:
[tex] SA_{f1} = SA_{f2} = 12*5 = 60 in^{2} [/tex]
And the SA of the rectangular face 3 is:
[tex] SA_{f3} = 12*8 = 96 in^{2} [/tex]
Finally, the SA of the prism is:
[tex] SA = SA_{b1} + SA_{b2} + SA_{f1} + SA_{f2} + SA_{f3} [/tex]
[tex] SA = 2*12 + 2*60 + 96 = 240 in^{2} [/tex]
Therefore, the surface area of the prism is 240 in².
I hope it helps you!
An insurance agent research suggested that first year drivers had roughly an 13% chance of being involved in an automobile accident while driving. The insurance agent provided insurance to 152 first year drivers last year. What is the probability (based on the statistics) that 24 or more of those drivers were involved in accidents?
Answers
Answer:
Probability that 24 or more of those drivers were involved in accidents is 0.15625.
Step-by-step explanation:
We are given that an insurance agent research suggested that first year drivers had roughly an 13% chance of being involved in an automobile accident while driving.
The insurance agent provided insurance to 152 first year drivers last year.
Let [tex]\hat p[/tex] = sample proportion of drivers who were involved in accidents
The z score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt\frac{\hat p(1-\hat p)}{n} {} }[/tex] ~ N(0,1)
where, p = population proportion of first year drivers involved in an automobile accident while driving = 13%
n = sample of first year drivers = 152
Now, probability that 24 or more of those drivers were involved in accidents is given by = P([tex]\hat p[/tex] [tex]\geq[/tex] [tex]\frac{24}{152}[/tex])
P([tex]\hat p[/tex] [tex]\geq[/tex] 0.16) = P( [tex]\frac{\hat p-p}{\sqrt\frac{\hat p(1-\hat p)}{n} {} }[/tex] [tex]\geq[/tex] [tex]\frac{0.16-0.13}{\sqrt\frac{0.16(1-0.16)}{152} {} }[/tex] ) = P(Z [tex]\geq[/tex] 1.01) = 1 - P(Z < 1.01)
= 1 - 0.84375 = 0.15625
The above probability is calculated by looking at the value of x = 1.01 in the z table which has an area of 0.84375.
Hence, the required probability is 0.15625.
The lines shown below are perpendicular. If the green line has a slope of -1/4, what is the slope of the red line
Answers
Answer:
4
Step-by-step explanation:
The slope of the green line is the negative reciprocal of that of the red line:
-1 / (-1/4), or just 4
Answer:
+4
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals of one another.
Here, with one slope being -1/4, the slope of a perpendicular line would be +4.
Can anyone please help?
(sorry for low quality...)
Answers
Answer:
see below
Step-by-step explanation:
The age is not a proportional relationship because it does not go through the point (0,0)
The hours is a proportional relationship. It goes through the point (0,) and has a constant slope
Answer:
3. NO
4. YES
Step-by-step explanation:
A proportional relation is of the form:
y = kx
Note that the y-intercept has to be 0, and slope should be constant
First one (Height against age) is not proportional because the intercept is 30, not 0
Second one (Time against distance) is proportional because the slope is constant and the y-intercept is 0
Which equation has roots -2 and 3? A. y=x2+x−6 B. y=x2−x−6 C. y=x2−5x−6 D. y=x2+5x−6
Answers
Answer:
The answer is B.
Step-by-step explanation:
You have make y equals to 0 and solve each and every equation one by one :
Option A,
[tex] {x}^{2} + x - 6 = 0 \\ {x}^{2} + 3x - 2x - 6 = 0 \\ x(x + 3) - 2(x + 3) = 0 \\ (x - 2)(x + 3) = 0 \\ x = 2 \: or \: - 3[/tex]
Option B,
[tex] {x}^{2} - x - 6 = 0 \\ {x}^{2} - 3x + 2x - 6 = 0 \\ x(x - 3) + 2(x - 3) = 0 \\ (x + 2)(x - 3) = 0 \\ x = - 2 \: or \: 3[/tex]
Option C,
[tex] {x}^{2} - 5x - 6 = 0 \\ {x}^{2} + x - 6x - 6 = 0 \\ x(x + 1) - 6(x + 1) = 0 \\ (x - 6)(x + 1) = 0 \\ x = 6 \: or \: - 1[/tex]
Option D,
[tex] {x}^{2} + 5x - 6 = 0 \\ {x}^{2} - x + 6x - 6 = 0 \\ x(x - 1) + 6(x - 1) = 0 \\ (x + 6)(x - 1) = 0 \\ x = - 6 \: or \: 1[/tex]
Laura has let out 60 m of her kite string, which makes an angle of 68º with the ground. What is the height of the kite?
Answers
Answer:
55.6mStep-by-step explanation:
The set up will form a right angled triangle. The distance that Laura let out her kite string will be the hypotenuse of the triangle, the angle that the kite makes with the ground will be the angle of elevation, facing the height of the kite.
The height of the kite H, will be the opposite side of the triangle since it is facing the angle directly. based on the trig identity SOH;
sintheta = opposite/hyp
sin68° = H/60
H = 60sin68°
H = 55.6m
The height of the kite is 55.6m
The algebraic expression 4x2 + 3Vx+5 is a polynomial
Please select the best answer from the choices provided
T
F
Answers
Answer:
In this problem, I can not tell what is V, so I will answer it in a general way.
A polynomial is something of the form:
a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f
a, b, c, d, e, and f are real numbers and constant.
Where the degree of the polynomial is equal to the greatest power (in this case 5).
You write:
4x^2 + 3Vx + 5
Now, if V is a real number, then we have that this is a polynomial of degree 2.
Because we can write this as:
4*x^2 + (3V)*x + 5
So the answer is true.
Now, if V is a variable or an operation, the answer will be false.
He triangular pyramid shown is made up of four congruent triangles. The length of the base is 8 inches, and the height of the base is 6.9 inches. A triangular pyramid. Talia is finding the lateral area of the pyramid. She says that the expression 4 (one-half (8) (6.9)) represents the lateral area. Which explains whether Talia is correct and why? Talia is correct. The three faces have the same area as the base, and the area of the base is One-half (8) (6.9). Talia is correct. The lateral area can be found by approximating one large triangle, which can be found using the expression 4 (one-half (8) (6.9)). Talia is not correct. Only the base has an area of One-half (8) (6.9), and three other faces have a different area. Talia is not correct. The lateral area has three faces, so the expression should be 3 (one-half (8) (6.9)).
Answers
Answer:
Talia is not correct. The lateral area has three faces, so the expression should be 3 (one-half (8) (6.9)).
Step-by-step explanation:
A triangular prism has four triangles, three at the sides and one at the base.
A congruent shape has the same feature (side dimensions and angles), therefore all three sides of the prism, and the basal triangle have the same area (since they are congruent).
The area of the base will be One-half (8) (6.9), therefore each of the three sides too will have that same area.
Lateral area means only the areas of the sides excluding the base, therefore, the lateral area will be 3 (one-half (8) (6.9))
Answer:
Its D
Step-by-step explanation:
help me ASAP
factorise; a=b-bx
10 points to whoever answers this
Answers
Answer:
a=-b(x-1)
Step-by-step explanation:
Is it factored, but that question doesn't have too much helpful in it
Answer:
a=-b(x-1)
Step-by-step explanation:
Find x,
45x - 15x = 300
Answers
Answer:
x = 10
Step-by-step explanation:
45x - 15x = 300
Combine like terms
30x = 300
Divide each side by 30
30x/30 = 300/30
x = 10
Solve the system of equations.
Answers
Step-by-step explanation:
use substitution method so it will now look like
8x + 5(-4x) = 24
8x + (-20x) = 24
-12x = 24 (divide both sides by 12)
-x = 2 (multiply both sides by negative 1)
x = -2
substitute to find y
y= -4(-2)
=8
Answer:
[tex]x=-2\\y=8[/tex]
Step-by-step explanation:
[tex]8x+5y=24\\y=-4x[/tex]
We already have y in terms of, so the easiest way to do is by plugging that value in the first equation.
[tex]8x+5y=24\\8x+5(-4x)=24\\8x-20x=24\\-12x=24\\x=\frac{24}{-12} \\x=-2[/tex]
After having found the value of x, replace it in the second equation to find y.
[tex]y=-4(-2)\\y=8[/tex]
How do you simplify the expression q(x) = (x² + x - 1) × (x² - x - 1)?
Answers
Answer:
q=−3x3+4x2−x
hope this helped :)
Step-by-step explanation:
During a middle school basketball game, every spectator placed his or her ticket stub into one of several containers. After the game, the coach chose eleven people to march in the sportsmanship parade. Who are the samples and populations?
Answers
Answer:
The eight people to march in a sportsmanship parade.
Step-by-step explanation:
Round the following number as a indicated 106,513 down to a hundred thousand start with a hundred thousand first
Answers
Answer:
100,000
Step-by-step explanation:
Type the integer that makes the following subtraction sentence true:
8 − ?= –1
Answers
Answer:
9
Step-by-step explanation:
Since the value is negative, that means that missing integer has to be 1 greater than 8 to make -1. 1 more than 8 is 9. Hope this helps! If you are still confused, please comment!
NEED THIS ASAP!!
20% of the students in Mr. MacGregor’s class earned As on their final projects. 5% of the students who received As on their final projects also received As on their final exams. Find the probability that a student chosen at random received an A on both the final exam and the final project.
A.
0.01
B.
0.05
C.
0.10
D.
0.50
Answers
Answer:
its B
Step-by-step explanation:
the first part of the question was unnecessary information its just 5% move the decimal two to the right to find the actual number
The perimeter of a rectangle is 16 inches. The equation that represents the length of the rectangle and a represents the width of the rectangle.which means is possible for the length of the rectangle?
Answers
Answer and Step-by-step explanation:
As we know that
[tex]Perimeter\ of\ rectangle = 2\times (length + breadth)[/tex]
Given that
The perimeter of a rectangle is 16 inches i.e length and breadth should be measured by that way in which the perimeter of rectangle comes 16 inches
We considered four way of measuring the perimeter
Length Width Perimeter
1 7 16
2 6 16
3 5 16
4 4 16
Simple it is as we multiply the 8 by 2 it gives 16 inches and the same is displayed above
So there are four combinations of 8 how it came.
Answer:
A
Step-by-step explanation:
Edgenuity
Samantha and Luis are attempting to determine the average number of library books that seventh-grade students check out at
one time. Samantha surveys every other seventh grade student leaving the library. She samples a total of 40 of the 200
seventh graders. Luis samples 30 of the 200 seventh grade students at random in the school cafeteria, Whose sample is the
most random?
Answers
Answer:
Luis because the sample is taken from the population of all seventh graders.
Step-by-step explanation:
What solid 3D object is produced by rotating the semicircle about line \blue mmstart color #6495ed, m, end color #6495ed?
Answers
Answer:
Sphere
Step-by-step explanation:
its a sphere with a radius of 5
The solid three dimensional image that is produced from the rotation of the semicircle is called a sphere.
What is rotation of a plane?
This is used to define the movement of an object in a three dimensional plane around a fixed point.
This transformation os known to occur in a given point of the figure. The roataion is done at a certain degree.
Read more on rotation here: https://brainly.com/question/15624908 #SPJ2
students deliver catalogues and leaflets to houses. one day they have to deliver 384 catalogues and 1890 leaflets. each student can deliver either 16 catalogues or 90 leaflets in 1 hour. each student can only work for 8 hours. all students hired are paid 51.30 per day, even if they dont work a full day. If the minium number of students are hired, how much will the wage bill be?
Answers
Answer:
£352.80
Step-by-step explanation:
Divide the total number of catalogues by the per hours and hours.
15 per hour x 8 hours= 90 catalogues
360 catalogues ÷ 90 catalogues = 4 students.
Divide the total number of leaflets by the per hours and hours.
80 per hour x 8 hours= 640 leaflets
1440 leaflets ÷ 640 leaflets = 3 students
4 students + 3 students=7 students.
7 students x £51.30 per day = £352.80
The wage will be £352.80
Answer:
hi
Step-by-step explanation:
hi
Consider the function represented by the following table.
The function is increasing
linear
quadratically
exponentially
Answers
Answer:
The answer is exponentially.
Step-by-step explanation:
Because your X goes up by one while your f(x) goes up by three for every X, which makes it exponential.
Answer:
exponentially
Step-by-step explanation:
PLEASE HELP ASAP 5TH GRADE
Answers
Answer:
Your answer is C.
Step-by-step explanation:
take 2/5 x 240 = 96 which is two fifths of 240
Hope this helps. :)
Have a good day!
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Answers
Answer:
3xy2 + 3xy
Step-by-step explanation:
0,0
Juanita has 30 beads. 90% of the beads are white.
How many beads are white?
18
25
27
21
Answers
Answer is 27
Vincent bought a 25-pound bag of rice. He cooked 6.25 pounds of the rice. He stored the rest of the rice in 334 - pound portions. What is the maximum number of 334 - pound portions he stored?
Answers
Question:
Vincent bought a 25-pound bag of rice. He cooked 6.25 pounds of the rice. He stored the rest of the rice in [tex]3\frac{3}{4}[/tex] - pound portions. What is the maximum number of [tex]3\frac{3}{4}[/tex] - pound portions he stored?
Answer:
The maximum number of portion he stored is 5 portion
Step-by-step explanation:
Given
Size of Rice = 25 lb
Size of Cooked Rice = 6.25 lb
Portions saved = [tex]3\frac{3}{4}[/tex] lb
Required
Number of portion saved;
First, the size of rice after cooking needs to be calculated;
If 6.25lb of rice was cooked from a total of 25lb;
Then, the size of rice left is
[tex]Size = 25lb - 6.25lb[/tex]
[tex]Size = 18.75lb[/tex]
Now that we have the amount left after cooking; we can simply calculate the maximum number of portions;
This is calculated by dividing size of rice left by portions of saved rice;
i.e.
Maximum number of portion = Size of rice left / Portions of saved rice
Maximum number of portion = [tex]\frac{18.75lb}{3\frac{3}{4}lb}[/tex]
Convert [tex]3\frac{3}{4}[/tex] to mixed fraction
Maximum number of portion = [tex]\frac{18.75lb}{\frac{15}{4}lb}[/tex]
Maximum number of portion = [tex]\frac{18.75}{\frac{15}{4}}[/tex]
Rewrite expression
Maximum number of portion = [tex]18.75 / \frac{15}{4}[/tex]
Change divide (/) sign to multiplication (*)
Maximum number of portion = [tex]18.75 * \frac{4}{15}[/tex]
Maximum number of portion = [tex]\frac{75}{15}[/tex]
Maximum number of portion = 5
Hence, the maximum number of portion he stored is 5 portions
What percent is 60 is 42
Answers
Answer:
The percentage is 70%
Answer:
the answer is 70%
Step-by-step explanation:
Let's consider 42 as x% of 60.
x% of 60 = 42 (x% means x/100)
(x/100) * 60 = 42
60x/100 = 42
60x = 42 * 100 = 4200
x = 4200
Allen needs to prepare a compound for the patient to pick up tomorrow. He needs to mix of drug A, with of drug B and of drug C. What is the total amount of the drugs mixed together? 2/5+5/3+9/3
Answers
Answer:
76/15
Step-by-step explanation:
Drug A=2/5
Drug B=5/3
Drug C=9/3
Add the drug combinations together
Drug A + B + C=2/5 + 5/3 + 9/3
The L.C.M of the denominators is 15
=6+25+45/15
=76/15
Or
=5 1/15
Allen needs to prepare 76/15 compound for the patient
Ethan drew a scale drawing of a house. He used the scale 1 millimeter : 5 meters. The actual
length of the garage is 10 meters. How long is the garage in the drawing?
millimeters
Answers
Answer:
2 millimeters
Step-by-step explanation:
Ethan used the scale 1 millimeter : 5 meters.
This means that 1 millimeter in the drawing represents 5 meters in actual life.
The actual length of the garage is 10 meters. Therefore:
5 meters = 1 millimeter
=> 10 meters = (10 * 1) / 5 = 2 millimeters
The garage is 2 millimeters long in the drawing.