The goal of elimination is to remove one of the variables by combining the equations together.
Let's say we have an equation with 3 variables:
a + b + c = 0
The goal of elimination is to remove one of the variables by combining the equations together.
Multiply the first equation by a number, n, such that nb + nc = 0
For example:
Let n = -2
-2b + -2c = 0
Add the two equations:
a + b + c = 0
-2b + -2c = 0
a - b = 0
Solve for b:
a - b = 0
b = a
Therefore, the final equation is:
a + a + c = 0
2a + c = 0
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2. Tell whether the segment lengths form an acute, right, or obtuse? 9, 12, 17
Answer:
obtuse angled triangle
Step-by-step explanation:
Given 3 segments , say a, b and c , with c the longest then
• If a² + b² = c² ⇒ right triangle
• If a² + b² > c² ⇒ acute triangle
• If a² + b² < c² ⇒ obtuse triangle
Here c = 17 and 17² = 289
9² + 12² = 81 + 144 = 225
Since 225 < 289 , then triangle is obtuse
PLZ I NEED HELP NOW THANKS
Answer:
1240.4 mm²
Step-by-step explanation:
SA of Pentagonal pyramid:
(as)(5/2) + (sl)(5/2)
↑ ↑
base area lateral area
_____________________
a: apothem (in-radius) length, s: side length.
l: slant height.
______________________
Since we are already given the base area which is 440.4 mm². All we need to do is find the lateral area and add both areas together.
Given that the triangular face of the lateral part has a side/base length of 16mm, and a 20mm slant height.
A triangle has an area of ½bh and since there are 5 of these faces total, (5)(½bh) = (5/2)(bh). In a three dimensional perspective, b will be s and h will be l so (sl)(5/2).
With this information the surface area is:
(16)(20)(5/2)mm + (440.4 mm²) →
800 mm² + 440.4 mm² =
1240.4 mm²
Select the correct answer.
How many solutions does this system of equations have?
y = 2x + 5
y = x^3 + 4x^2 + x + 2
A. No solution
B. 1 solution
C. 2 Solutions
D. 3 Solutions
An equation is formed of two equal expressions. The number of solutions that the given system of equation will give is 3. Thus, the correct option is D.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The number of solutions that the system of equations will have can be found by plotting both the equation on the graph.
Since the point at which the graph intersects is the solution of the system of equations.
Hence, the number of solutions that the given system of equation will give is 3. Thus, the correct option is D.
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Solve the inequality x-4 < - 3.Then graph the solution set.show your work.
Answer:
x < 1
Step-by-step explanation:
x - 4 < - 3
+ 4 +4 Do inverse operations by adding 4 on both sides
x < 1
Therefore, the answer is x < 1.
(It isn't allowing me to attach a photo but I am just going to try make a visual of the graph below)
<------------------------------o------------------>
-4 -3 -2 -1 0 1 2 3 4
The circle is open because based on the concept that in inequalities, less/greater than and/or equal to (such as these ≥ ≤ ) signs are graphed with closed circles, while less/greater than (like these > <) signs are graphed with open circles. The direction of the arrow is moving to the left on the number line because all possible values for x would be less than 1. When graphing the inequality you would use a solid line rather than a dashed line (I had to improvise since I could not attach an image).
Solve the following equation by first writing the equation in the form a x squared = c: t squared minus 49 = 0 a. t = 49 b. t = plus-or-minus 49 c. t = 7 d. t = plus-or-minus 7 Please select the best answer from the choices provided A B C D
The best answer is t = 7. Option C
What is a quadratic equation?A quadratic equation is simply defined as an equation that could be rearranged in standard form.
It is also described as an algebraic equation having the highest exponent of as 2.
It is so arranged such that;
x represents an unknown valueVariables, a, b, and c represent known numbersAlso, a is not equal to 0, a ≠ 0It is important to note that the three methods of solving quadratic equation are;
FactorizationUsing the quadratic formulaUsing completing the square methodFrom the information given, we have that the form is;
x² = c
Given t squared minus 49 = 0
First, represent mathematically
t² - 49 = 0
Now, collect like terms, we have;
t² = 49
Take square root of both sides
t = √49
t = 7
Hence, the equation is t = 7
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Seven netball teams played in a school's competition. Each team had 7 players. If 3/7 of the number of players were disqualified for poor conduct, how many pupils were qualified?
Carly is telling Stephanie about her parents' divorce. Which body language would best display that Stephanie is actively listening to Carly?
Returning text messages as Carly speaks.
Turning her body toward Carly.
Stopping Carly's story to ask questions.
Focusing on people in the background.
Answer:
Turning her body toward Carly.
Step-by-step explanation:
Since turning someone's body towards the speaker means that they are actively paying attention. If she would return text messages, it would make it look like Stephanie doesn't care at all, same thing for focusing on people in the background. If she were to stop Carly's story to ask off-topic questions, it would also make Stephanie seem ignorant.
Please help! Due Soon - You will get 30 points and brainliest! - 4 pictures in total - links=reported - thanks!
Answer:
(the last one) i think its B
Step-by-step explanation:
If { 4x+y=13
x−y=2
, then y=
Answer:
2.5
Step-by-step explanation:
Taking eguation i
4x+y=13
x= 13-y/4
Taking equation ii
x-y = 2
Substituting the value of x in eq i from ii
x- y =2
13-y/4- y=2
13-y-y=2×4
13-2y =8
-2y=8-13
y=-5/-2
Therefore y=2.5
A scientist studies the population of an insect colony. She begins her study with 10,000 insects in the colony and measures the population of the colony
each year. She uses the given formula to model the insect population, P, é years since the beginning of the study.
P= 10,000(1.08)
By what percent does the Insect population grow each year?
%
PLEASE HELP! WILL GIVE BRAINLIEST!
Khan Academy - Solve Similar Triangles (advanced)
Solve for X.
Answer:
x = 3[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
4 + 6 = 10
[tex]\frac{2}{6}[/tex] = [tex]\frac{x}{10}[/tex]
6x = 20
x = 3[tex]\frac{1}{3}[/tex]
y = -11x - 25 ...........(i)
y = 5x - 7 ...............(ii)
Answer:
3/2
Step-by-step explanation:
5x-7=-11x-25
5x+11x=-25+7
16x=18
x=18/16
x=3/2
cans someone please help me
Answer:
8 x 16 = 128 (area of rectangle)
Area of triangle:
16 - 12 = 4
6 x 4 = 24
24 divided by 2 = 12 (area of triangle)
Now lets add both areas:
128 + 12 = 140 ft2 is your answer.
Add: 2y+1/y-3+y+2/6y 1.Find the LCD. LCD= (y-3)(6y) 2. Multiply to create common denominators. 2y+1/y-3 (6y/6y)= 12y^2+6y/(y-3)(6y)
Answer:
C
Step-by-step explanation:
edge 2020
C 12y^2+5y-6/(y-3)(6y)
Please help me with this question:
What is 2x-2?
Answer:
as a factor 2(x-1) this should help or be the correcr answer
HELP!!! NO LINKS PLEASE!!!
a) A designer has a circular tablecloth with radius 0.5 m. He wants to sew a fringe around the cloth. The fringe is sold by the tenth of a meter.
(i) What length of fringe is needed?
(ii) One meter of fringe costs $4.70. How much will the fringe cost?
b) A semicircular mat has a diameter of 18 m. What is the area of the mat?
Step-by-step explanation:
a) (i) length = 2(pi)r = 2(3.14)(.5 m) = 3.14 m
(ii)3.14 m × ($4.70/m) = $14.76
b) A = (pi)r^2 = (3.14)(18 m)^2 = 1017.9 m^2
1. True or False: The solution you get from substitution is the same as the solution you would get
from graphing. *
False
True
2. For substitution, we want *
(1 Point)
a. both equations to be in standard form Ax + By = C
b. equations with negative numbers
C. at least one equation to be y= or x=
d. equations with positive numbers
answer:
my answer to the first one would be false
my answer to the second would be a
Solve for x. *they are similar* NO BOTS OR ELSE U WILL BE REPORTED
Answer:
x = 5
Step-by-step explanation:
i will insert an image of my work below
How many 1/3 cup servings are there in 10 cups of cereal?
Answers:
30
1/10
1/3
9
Answer:
30
Step-by-step explanation:
To the nearest square centimeter, what is the area of the shaded sector in he circle shown below? Radius= 12 cm, angel = 110 degrees
Answer:
138.23 cm²
Step-by-step explanation:
The formula for the area of a sector is given as:
θ/360 × πr²
θ = 110°
Radius = r = 12 cm
Hence
Area of a sector = 110/360 × π × 12²
= 138.23007676 cm²
Approximately, Area of a sector = 138.23 cm²
A botany student drew a sketch of a birch tree using a scale of 1 inch:2 meters. Find the
actual height of the tree, if it measures 3 inches in the sketch.
Answer:
6 meters
Step-by-step explanation:
^_^
How do you find the difference between two different numbers?
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.
Subtracting two integers from each other is a type of subtraction.
The process for determining the difference between two decimals and two whole numbers is the same.
We only add a new step.
Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.
To give them all the same amount of decimal places, we must first convert each decimal.
7.2 becomes 7.200 as a result.
The computation may now be done as before:
8.967 - 7.200 = 1.767
Therefore, there is a 1.767 discrepancy between these figures.
In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.
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Taylor drives 7.5 miles in 10 minutes. If she drove two hours in total at the same rate,
how far did she go?
Before you try that problem, answer the question below.
How many minutes did Taylor drive in total?
Answer:
200 is your answer. (insert more text to be helpful here)
Calculate the slope of the following line:
m=
Answer:
m= -1/3
Step-by-step explanation:
slope is rise/run or change in y/change in x
i pick out point (9,0) to (6,1)
the increase in y of this triangle is 1 and increase in x is 3
note that this line will have a negative slope as it goes downwards from left to right instead of upwards
hence m= rise/run= -1/3
m(x)=−2(x−3)(x−9) solve for y-intercept
Answer:
(0, -54)
Step-by-step explanation:
We find the y-intercept by plugging in 0 for x:
[tex]y=-2(x-3)(x-9)\\y=-2(0-3)(0-9)\\y=-2*-3*-9\\y=6*-9\\y=-54[/tex]
Find the mean, variance and standard deviation for the probability distribution given below:
X -1 3 9 12
P(X) 0.587 0.115 0.21 0.088
A. Mean = B. Variance = C. Standard Deviation =
The mean, variance, and standard deviation for the probability distribution given are A. Mean = 5.5; B. Variance = 13.875; C. Standard Deviation = 3.722.
The mean, variance and standard deviation of the probability distribution can be calculated using the formula. The mean is calculated by summing up the product of all the values and their respective probabilities and then dividing it by the total probability. In this case, the mean is calculated as:
(1*0.587 + 3*0.115 + 9*0.21 + 12*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 5.5.
The variance is calculated by summing up the product of the squares of the values and their respective probabilities and then dividing it by the total probability. In this case, the variance is calculated as:
(1^2*0.587 + 3^2*0.115 + 9^2*0.21 + 12^2*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 13.875.
The standard deviation is the square root of the variance and it is calculated as √13.875 = 3.722.
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Why are the acute angles of an isosceles right triangle always 45?
An isosceles right triangle has two sides that are equal in length; this means that the angles opposite the sides must also be equal. Since the triangle is a right triangle and the sum of angles of a triangle is 180 degrees, the angles must each be 45 degrees.
The acute angles of an isosceles right triangle are always 45 because of the Pythagorean Theorem. This theorem states that in a right triangle the sum of the squares of the two sides adjacent to the right angle (the legs) is equal to the square of the hypotenuse. Since an isosceles right triangle has two equal legs, and the hypotenuse is the longest side, the two legs must both have the same length, and the angles opposite from these sides must also be the same. This means that the two acute angles in an isosceles right triangle must both be 45 degrees.
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In the diagram, two circles, each with center $D$, have radii of $1$ and $2$. The total area of the shaded region is $\frac5{12}$ of the area of the larger circle. How many degrees are in the measure of (the smaller) $\angle ADC$
Angle ADC = 120 degrees.
What is area of sector?A certain portion of a circle that is created based on two radius of the same circle and one arc. Area of sector for a circle with radius r is given by π r²Ф/ 360°
What is the angle of ADC in the smaller circle?
Given, two circles of radius 1 unit and 2 unit which have same center D.
We know area of a circle = π r²
Area of larger circle = π 2² = 4π
it is said that the total area of the shaded region that means area of a particular sector is 1/12 of the area of the larger circle.
area of sector, ACD = 1/12 ×4π
as per the question, the ACD sector is located in the smaller circle that has radius 1 unit.
formula for area of sector ACD = π r² ×Ф/360°
where,Фis the central angle of ACD sector
and Ф = ADC
from the above statement, 4π/12 = π r² ADC/360
ADC = 1/3×360°
ADC = 120 degrees
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Calculate the slope of the line.
m=
Answer:
m=4
Step-by-step explanation:
look at the traingle formed with line with points (6,5) and (4, -3)
look at change in y (how tall the triangle is) and change in x (the base of triangle)
change in y=8
change in x=2
m=rise/run also known as change in y/change in x
=8/2
=4
note that this is a positive gradeint line
How many solutions does y 2x 5 and 8x 4y =- 20 have?
A system of linear equations: y + 2x = -5 and 8x + 4y = -20 has infinitely many solutions.
The 3 possible solutions of a linear system are:
- Unique or one solution
- Infinite solutions
- No solution
If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
The given linear system is:
y + 2x = -5 ....... (equation 1)
8x + 4y = -20 ..........(equation 2)
Rearrange equation 1 to:
2x + y = -5
Multiply both sides by 4:
8x + y4 = -20
Hence, equation 1 is equivalent to equation 2. Hence, the given linear system has infinitely many solutions.
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