Answer:
The solution is (-1, 0)-----------------------------------
Given lines:
y = - 2x - 2 and y = x + 1Plot both of the lines using the graphing calculator by adding the equations, then find the graphical solution as the intersection of the lines.
See attached.
The solution is (-1, 0).
is 3/16 greater than 1/16
3 3/10 minus 2 1/5 as improper fraction
Answer:
11/10
Step-by-step explanation:
33/10 - 22/10
A pack of paper costs $3.79, including tax. Mr. Valentino wants to purchase packs of paper for his class and has a $15 budget. Write and solve an inequality to solve for the number of packs of paper Mr. Valentino can purchase, and describe the graph of the solution.
Answer:
3 stacks of paper can be purchased.
Step-by-step explanation:
Start by setting up the inequality:
15 = 3.79x
Now that you have set up the inequality, go to solve the inequality.
You should get the answer 3.958 (rounded). Since Mr. Valentino can not by a half stack of paper, drop the decimal so we are left with 3.
I would describe the graph as a straight line increasing, with money on y and stacks of paper on the x axis
Simplify (3x^2y^5)^3
Work Shown:
[tex]\left(3\text{x}^2\text{y}^5\right)^3\\\\\left(3\right)^3\left(\text{x}^2\right)^3\left(\text{y}^5\right)^3\\\\27\text{x}^{2*3}\text{y}^{5*3}\\\\27\text{x}^{6}\text{y}^{15}\\\\[/tex]
Explanation:
The outer exponent 3 is "distributed", so to speak, to each term inside the parenthesis. This isn't the actual distribution rule. But we can think of it as such. This is what's happening in the second step.
So we'll cube the coefficient 3 to get 3^3 = 27, and we'll cube x^2 to get x^6, and finally cube y^5 to get y^15.
I used the rule [tex](a^b)^c = a^{b*c}[/tex] for the third step.
i’m not sure if the first one right but i need help
The formula is written as (3x+9)(x+9) of + 36x + 81 = 0. A second-degree polynomial equation can be used to define quadratics.
A quadratic equation is defined.Multiplying a variable by itself is the mathematical operation known as "squaring," which is frequently used to refer to a quadratic issue. This vocabulary is based on the notion that a square's area is equal to the sum of its side lengths. The word "quadratic" derives from the Latin quadratum, which meaning square.
here ,
[tex]= + 36x + 81 = 0\\= 3x^2 + 27x + 9x + 81\\= 3x(x+9) + 9(x+9)\\= (3x+9)(x+9)\\= 3(x+3)(x+9)[/tex]
factorized form is [tex](3x+9)(x+9) of + 36x + 81 = 0 .[/tex]
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if the slope of a line is 3 ,then the slope of a parallel line is 4
4 3
true or false?
The given statement “if the slope of a line is 3, then the slope of a parallel line is 4” is false because parallel lines have equal slopes
How to determine the true statement of the parallel line?From the question, we have the following parameters that can be used in our computation:
Slope of a line = 3
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 3
This means that the slope is 3
The slopes of parallel lines are equal
This means that the slope of the other line is 3
Hence, the statement is false
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10. What is a composition of rigid motions and a dilation that maps APZY onto ARST
I’m confused on this subject please explain to me how you got an answer thank you
Answer:
dilation by a factor of 1/2reflection over the line y = -xStep-by-step explanation:
You want to find a sequence of transformations that will map ∆PZY to ∆RST as shown in the figure.
DilationFirst of all, we notice the triangles are not the same size. We can find the required dilation factor by finding the ratio of corresponding side lengths.
The first two letters in the triangle designators in the similarity statement are PZ and RS. Since RS is the target size, the dilation factor needs to be ...
k = RS/PZ
Counting grid squares in the figure, we see this ratio is ...
k = 2/4 = 1/2
Dilation by a factor of 1/2 will make triangle PZY the same size as ∆RST.
Using the origin as the center of the dilation, all of the points of ∆PZY move to a position that is half their original distance from the origin. The dilated triangle is purple triangle P'Z'Y' in the attached figure.
ReflectionWhen we name the vertices of ∆PZY or ∆P'Z'Y', we are naming them in counterclockwise order. The vertices of ∆RST are being named in clockwise order. This reversal of the sequence of vertices is caused by a reflection over a line.
The line of reflection will be halfway between a vertex and its reflected image. For example, reflecting ∆P'Z'Y' across the y-axis give ∆P"Z"Y", as shown in the attached figure. This reflection requires an additional transformation to map P"Z"Y" to RST.
We want to map P' to R, Z' to S, and Y' to T. As it happens the line halfway between these pairs of points is the line y=-x, the dashed line shown in the attachment.
Reflection across the line y = -x will map ∆P'Z'Y' to ∆RST.
This transformation, together with the dilation above, will map the ∆PZY to ∆RST as required.
__
RotationIf we use the reflection over the y-axis described above, we are faced with mapping ∆P"Z"Y" to ∆RST. We notice that segment P"Z" points "east" (in the +x direction). We want to map this segment to RS, which points "north" (in the +y direction). That can be accomplished by rotating ∆P"Z"Y" 90° counterclockwise about the origin.
So, another sequence of transformation that will make the required mapping is ...
dilation by a factor of 1/2reflection across the y-axisrotation 90° CCWThe order of reflection and rotation is important. The dilation can occur anywhere in the sequence.
Alternate solutionPerhaps you realize that we could reflect the figure across the x-axis instead of the y-axis. In that case, the rotation needs to be 90° CW to complete the mapping. That is, yet another sequence could be ...
dilation by a factor of 1/2reflection across the x-axisrotation 90° CWIf you decide you want to do the rotation before the reflection, then the direction of rotation is reversed.
__
Additional comment
Figuring the answer to these mapping problems requires a certain amount of spatial sense. It can help to cut a figure from paper or cardboard and label the vertices. Then you can translate it, rotate it, flip it over, to see what works to get it to the right position. If you have a little trouble with the rotation, you can stick a pin through the center of rotation so your figure keeps its appropriate distance and orientation relative to that center.
Tracing paper and/or transparencies can be helpful for these exercises.
A system of linear equations with an infinite number of solutions is a(n) __________ system.
A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
When a system of linear equations consists of an infinite number of solutions then this equation should be dependent and consistent as well, and this system is said to be a system of equivalent equations.
Thus, A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.
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Lin solved the equation incorrectly. Find the errors in her solution.
x = 3/4 is the correct solution of the given expression.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
The expression Lin tried to solve
8(x-3)+7=2x(4-17)
Simplifying the expression,
8x - 24 = 2x(-13)
8x - 24 = -26x
8x+26x = 24
32x = 24
x = 24/32
x = 3/4
Thus, x = 3/4 is the correct solution of the given expression.
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The patient’s weight is 245 lbs. If the patient loses 1 kg every week for 5 weeks:
a. How much will the patient weight in pounds?
b. How much will the patient weight in kilograms?
a) The patient weight in pounds is 234 lbs.
b) The patient weight in kilograms is 106.36 Kg.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
The patient’s weight is 245 lbs.
Each week patient loses = 1 Kg
So, In 5 week patient loses = 5 Kg
As, 1 kg = 2.2 lbs
In 5 week patient loses = 11 lbs
a) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs.
= 234 lbs.
b) The weight of the patient after 5 weeks = 234 lbs.
The weight of the patient after 5 weeks in Kg
= 234 lbs x 1 kg per 2.2 lbs.
= 106.36 kg
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noah has a part-time job at a coffee shop. last month he earned 160$. Noah pays an income tax rate of 10%. how much does Noah earn after tax?
Step-by-step explanation:
first of all, if he continuously earns only $160 per month (or at least in that dimension), then he will not have to pay any income tax.
but to do the exercise :
100% = $160
1% = 100%/100 = 160/100 = $1.60
10% = 1% × 10 = 1.6 × 10 = $16
he earns after tax
160 - 16 = $144
FYI :
when we combine all the calculations above into one sequence, then we know
100% - 10% = 90%
and 90% of 100% is 100% × 0.9
and so he earns after tax
160 × 0.9 = $144
PLEASE FAST WILL GIVE BRANILY
A 12-foot tall tent pole is secured to the ground using a piece of rope 15 feet long from the top of the tent pole to the ground. If the tent pole makes a 90-degree angle with the ground, determine the number of feet along the ground from the tent pole to the rope.
3 feet
9 feet
19 feet
81 feet
Answer:
3 feet
Step-by-step explanation:
To solve this problem, we can use the Pythagorean theorem. Let's call the distance from the tent pole to the rope x. We can set up the following equation:
x^2 + 12^2 = 15^2
Solving for x, we get:
x = sqrt(15^2 - 12^2)
x = sqrt(9)
x = 3
Therefore, the distance from the tent pole to the rope is 3 feet.
Red city rockets connections academy
Answer: what
Step-by-step explanation:
PLEASE HELP FRACTION S EASY!! A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses pounds of gravel. For each pound of gravel, he uses pound of cement. He is making enough concrete that he needs to use 3 pounds of sand.
How many pounds of cement does he use?
The pound of cement used based on the information will be C. 2 pounds.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.
The pound of cement used will be:
Gravel = 1 2/3 × 3
= 5 pounds
Cement used will be:
= 2/5 × 5.
= 2 pounds.
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Which of the following is most likely the next step in the series?
ООО
О А.
B.
О с.
O D.
The next step in the series is, shown in Option C.
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
There are three steps are shown.
Now, In first step, only one line shown.
In second line the line is left to first line.
And, So on.
Hence, The next step in the series is, shown in Option C.
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What is an equation of the line that passes through the points (4,7) and (-3,7)
Answer:y=
Step-by-step explanation:Firstly let's find the slope which is (7-7)/(4-(-3))=0. Using the point slope formula y-y1=m(x-x1) we plug in one of the points and simplify y-7=0(x-4). Simplifying and solving for y gives us y=
A survey asks 50 students how many people live i their home and whether they love with a grandparent. A total of 10 students live with a grandparent. Of the 16 students with more than four people living in their home, 6 live with a grandparent. Which two-way table represents the results of the survey?
Answer:A two-way table, also known as a contingency table, is a way to organize and present categorical data in a tabular format. It can be used to show the relationship between two categorical variables, such as whether a student lives with a grandparent and the number of people who live in their home.
Based on the information you provided, the two-way table would look like this:
More than 4 people | 6 | 10
4 or fewer people | 4 | 30
It should be noted that the information you provided does not add up to 50 students.
Total for students living with grandparents: 10,
Total for students with more than 4 people: 6+10 =16.
Let me know if this table is incorrect and I'll provide you with more information
Step-by-step explanation:
Yoga Common Core Performance Assessment_ Regina takes yoga classes 2 days a week at the community center. The cost for the classes is $72, and Regina pays an additional one-time fee of $12 to rent the yoga equipment used in class. The classes run for 6 weeks. The local gym offers the same yoga program, including equipment, for $8 a class. Is Regina paying more or less than what the local gym charges for yoga classes?
On solving the provided question, we can say that - by the help of unitary method the value of 9 units will be
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
cost for the 12 classes = $72
cost of 1 unit = $6
cost of 9 units = $54
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find the values of the variable in the following, giving brief reasons:
Therefore , as a result, we may state that the stated trapezoid angles x = 110°, which is the solution to the problem.
Explain the trapezoid.A trapezoid is a quadrilateral that has at least one connected pair of sides. It has the name trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. The trapezoid's base is made up of its parallel sides. A closed, flat shape having two neighboring sides and four successive sides is called a trapezoid. The parallel walls and base of the trapezoid are commonly referred as as the parallel sides and the legs, respectively.
Here,
Given : 110°
and 90°
To find the value of x ,
Thus,
The value of angle opposite to x :
=> 110° + y =180°
=>y =180°-110°
=>y = 70°
thus, x value is
=> x + 70° =180°
=> x =110°
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B. Higher Order Thinking For keeping business records, every three months of a year is called a quarter. How many months are equal to three-quarters of a year? Explain how you found your answer.
Answer:
9 months
Step-by-step explanation:
1 quarter is 3 months
3 quarters is 3 times 1 quarter, so it is 3 times 3 months.
3 x 3 months = 9 months
Answer: 9 months
Question 9 of 10
Which is the largest number?
OA. 5.8 x 10-3
B. 2.5 x 105
о C. 1.9 × 106
OD. 8.7 x 10²
On solving the provided question, we can say that F= The lifting force is 27135 0.003357*250*180*180 = F=27135, surface area
What is surface area and an illustration?The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.
The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.
F= k*a*v^2
a= 250
v=190
30300=k*250*{190^2}
k= 0.03357
F= 0.003357*250*180*180
F=27135
The lifting force is 27135
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Given:m<1+m<2=90 and m<3+m<4=90,prove m<1=m<4
The proof that the angles m<1 = m<4 is shown below
How to prove the measure of the anglesFrom the question, we have the following parameters that can be used in our computation:
Measure of angles
The angle measurements are then given as
m<1 + m<2 = 90 and m<3 + m<4 = 90
The relationship to prove is also given as
m<1 = m<4
Using the above as a guide, we have the following:
Subtract the equations m<1 + m<2 = 90 and m<3 + m<4 = 90
This gives
m<1 + m<2 = 90
-(m<3 + m<4 = 90)
Evaluate the difference
m<1 + m<2 = m<3 + m<4
When both sides of the angle equations are compared, we have:
m<1 = m<4
m<2 = m<3
Ignoring the second equation, we have
m<1 = m<4
Hence, the measure of the angles has been proved
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NTP2PS
Write 3 equivalent ratios.
For the given ratio.
12/14
Answer:
4 7
Step-by-step explanation:
Solve for x
Select the correct response:
A: 14
B: 19.25
C: 10
D: 6.5
The value of the x is 10.
What is the exterior angle theorem?
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.
We have given,
angles of the triangle:
Interior angles :
∠D = 2x + 7,
∠E = 26°,
Exterior angle:
∠C = 6x - 7
To find x = ?
few common properties about the angles of a triangle:
A triangle has 3 internal angles which always sum up to 180 degrees.
It has 6 exterior angles and this theorem gets applied to each of the exterior angles.
Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.
Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.
So,
∠C = ∠D + ∠E
6x - 7 = 2x + 7 + 26,
6x - 7 - 2x - 7 = 26,
4x - 14 = 26,
4x = 40
x = 40/4
x = 10,
Hence, the value of the x is 10.
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Find the range of the relation. x y –3 4 –2 2 –1 0 0 –2 1 –4 Responses {–4, 4} {–4, 4} {–3, –2, –1, 0, 1} {–3, –2, –1, 0, 1} {–4, –3, –2, –1, 0, 1, 2, 4} {–4, –3, –2, –1, 0, 1, 2, 4} {–4, –2, 0, 2, 4}
The range of the function will be;
⇒ { 4, 2, 0, - 2, - 4 }
or, { - 4, - 2, 0, 2, 4 }
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The relation is,
⇒ (x, y) = (- 3, 4) , (- 2, 2), (- 1, 0), (0, - 2), (1, - 4)
Now,
Since, The relation is,
⇒ (x, y) = (- 3, 4) , (- 2, 2), (- 1, 0), (0, - 2), (1, - 4)
We know that;
The range of relation is the value of y.
Hence, The range of relation = { 4, 2, 0, - 2, - 4 }
Thus, The range of the function will be;
⇒ { - 4, - 2, 0, 2, 4 }
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Which is the graph of the equation y-1=(x-3)?
O
(-31).
10
CO
8
fi
Q
4.
y
Answer:
The graph of the equation "y - 1 = (x - 3)" is a straight line.
To graph this equation, we can start by rearranging the equation to get "y = x - 3 + 1". This simplifies to "y = x - 2".
This equation is in slope-intercept form, which means that the slope of the line is given by the coefficient of the x term, and the y-intercept (the point where the line crosses the y-axis) is given by the constant term. In this case, the slope is 1 and the y-intercept is (-2, 0).
To graph the line, we can start by plotting the y-intercept at the point (0, -2). Then, we can use the slope of 1 to find a second point on the line and draw a straight line through these two points. The graph of the equation "y = x - 2" is shown below:
[asy]
unitsize(1.5cm);
draw((-1.5,0)--(1.5,0));
draw((0,-2.5)--(0,2.5));
draw((-1.5,-2)--(1.5,2),dashed);
label("$x$", (1.5,0), E);
label("$y$", (0,2.5), N);
[/asy]
The graph of the equation "y - 1 = (x - 3)" is the same as the graph of the equation "y = x - 2", except that all the y-values on the graph are increased by 1. This means that the graph of the equation "y - 1 = (x - 3)" is obtained by shifting the graph of "y = x - 2" upward by 1 unit. The graph of the equation "y - 1 = (x - 3)" is shown below:
[asy]
unitsize(1.5cm);
draw((-1.5,0)--(1.5,0));
draw((0,-2.5)--(0,2.5));
draw((-1.5,-1)--(1.5,3),dashed);
label("$x$", (1.5,0), E);
label("$y$", (0,2.5), N);
[/asy]
The answer choices given in the question do not match the description of the graph of the equation "y - 1 = (x - 3)". "O" does not match the description of the graph, as it is not a graph of a straight line. "(-31)" and "10" do not match the description of the graph, as they are not graphs at all. "CO" does not match the description of the graph, as it is the graph of a circle, not a straight line. "8" does not match the description of the graph, as it is the graph of an exponential function, not a straight line. "fi" does not match the description of the graph, as it is not a graph of a function. "Q" does not match the description of the graph, as it is not a graph at all. "4." does not match the description of the graph, as it is not a graph of a function. "y" does not match the description of the graph, as it is not a graph at all.
Rewrite (2x+v)^2 without parentheses and simplify
Answer:
[tex]4x^2+4vx + v^2[/tex]
Step-by-step explanation:
[tex](2x+v)^2 \\(2x)^2+2(2x)(v)+(v)^2\\4x^2+4vx + v^2[/tex]
What constant term should be used to complete the square?
x2.5x+_ _ _ =7
4/25
49/25
-49/25
25/4
The constant term that should be used to complete the square? x2 - 5x + _____ = 7 is 25/4
What is quadratic equation ?
A quadratic equation in the variable x is of the form. ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. • Roots of a quadratic equation : A real number α is said to be a root of the. quadratic equation ax2 + bx + c = 0, if aα2 + bα + c = 0.
Given:
x^2-5x+c=7, the constant term c will be obtained using the formula:
c=(-b/2a)²
The quadratic equation in its generic form is:
ax^2 + bx + c
To complete squares we must add the following term:
(b / 2) ^ 2
The equation is:
ax^ 2 - 5x + k = 7
By completing squares we have:
x ^ 2 - 5x + (-5/2) ^ 2 = 7 + (-5/2) ^ 2
Rewriting:
x ^ 2 - 5x + 6.25 = 7 + 6.25
Hence, A constant term should be used to complete the square is 25/4 or 6.25.
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Need to find the x and y
Need to find the x and y: The Graph asking in question is attached below:
What is Graph?A graph is a type of data structure used to represent relationships between different objects. It consists of nodes, which are connected by edges. The nodes represent the objects, while the edges represent the relationships between them. Graphs can be used to represent many different types of information, such as road networks, social networks, and even computer networks. Graphs can be used to solve a variety of problems, such as finding the shortest path between two nodes, or finding the most efficient way to route data throughout a network. Graphs can be represented in a variety of ways, such as in the form of a table, a map, or a diagram. In addition, graphs can be used to represent abstract concepts such as relationships between individuals.
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Find the sum or difference (I will give you brainlist :D)
To find the sum or difference we must know what k is however you can simplify the expression by rewriting and removing the parenthesis furthermore collecting the like terms to get the solution.
Attached photo shows the steps to the solution :P