Answer:
The solution to the given system of linear equation is;
[tex]\begin{gathered} x=16 \\ y=-41 \end{gathered}[/tex]Explanation:
Given the linear system of equation;
[tex]\begin{gathered} 3x+y=7\text{ ---------------1} \\ -2x-y=9\text{ --------------2} \end{gathered}[/tex]We want to solve the simultaneous equation by elimination.
We need to eliminate either x or y. from the given equation, we can see that by adding equation 1 and 2 together we can eiminate y;
So, let's add equation 1 and 2 together;
[tex]\begin{gathered} 3x-2x+y-y=7+9 \\ x=16 \end{gathered}[/tex]Since we have the value of x, we can use it to get y by substituting into equation 1;
[tex]\begin{gathered} 3x+y=7 \\ 3(16)+y=7 \\ 48+y=7 \\ y=7-48 \\ y=-41 \end{gathered}[/tex]Therefore, the solution to the given system of linear equation is;
[tex]\begin{gathered} x=16 \\ y=-41 \end{gathered}[/tex]There are 128 teams entered in a basketball tournament. Half of the teams are eliminated each round. How many teams are left after 4 rounds?
We have 128 teams.
In each round, half of the teams remain, so if T is the number of teams and n is the number of rounds, we have:
[tex]T(n)=0.5\cdot T(n-1)[/tex]and we start with n=0 so T(0)=128.
Then, we can use this recursive expression to find T after four rounds (n=4), but it is better if we derive an explicit formula for T in function of n (and not in function of the past terms of the sequence):
[tex]\begin{gathered} T(1)=0.5\cdot T(0) \\ T(2)=0.5\cdot T(1)=0.5\cdot0.5\cdot T(0)=0.5^2\cdot T(0) \\ T(n)=0.5^n\cdot T(0)=0.5^n\cdot128 \end{gathered}[/tex]With the last expression we can calculate T for any value of n. Then, for n=4, we have:
[tex]T(4)=0.5^4\cdot128=(\frac{1}{2})^4\cdot128=\frac{1}{2^4}\cdot128=\frac{1}{16}\cdot128=8[/tex]NOTE: in this case, its better to express the factor 0.5 as a fraction instead of a decimal.
Answer: after 4 rounds there will be 8 teams left.
If Miss. lora has 4 people in her class and she has 28 more. How many people are in her class.
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
sorry no Step-by-step explanation
What is an equation of the line that passes through the point (2,-5)(2,−5) and is parallel to the line x-2y=16x−2y=16?
The slope intercept form of the required line is x -2y = 12
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The given line is
[tex]x - 2y = 16\\2y = x - 16\\y = \frac{1}{2}x - \frac{16}{2}\\[/tex]
Slope of the line = [tex]\frac{1}{2}[/tex]
Slope of the line parallel to this line = [tex]\frac{1}{2}[/tex]
The line passes through (2, -5).
Equation of the required line-
[tex]y - (-5)= \frac{1}{2}(x - 2)\\2y + 10 = x - 2\\ x - 2y = 10 + 2\\x-2y = 12[/tex]
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Which is the domain and range of the parabola with the equation y = 0.5(x²-10x-5)?
The domain of the given function is the set of all real numbers that is represented as x ∈ (-∝,∝ ) and range of the function is [-15,∝).
What is domain and range of a function?The set of values that can be plugged into a function is known as its domain. The range of a function is the collection of all potential values that can result from the dependent variable, or the collection of all possible values after substituting the domain.
Domain of a polynomial function is the set of all real numbers which is given by x ∈ (-∝,∝ ).
Since the given function y = 0.5(x^2 - 10x - 5) is a polynomial function, it's domain is x ∈ (-∝,∝ ).
To obtain the range of the function, plot the graph of the parabola which is shown in the figure.
The vertex of the parabola is at (5,15). Value of y does not go below 15. Therefore the set of all possible values that the function takes is given by [-15,∝).
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On a snow day, Robert created two snowmen in his backyard. Snowman A was built to a height of 33 inches and Snowman B was built to a height of 45 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 6 inches per hour and Snowman B's height decreased by 9 inches per hour. Let AA represent the height of Snowman A tt hours after sunrise and let BB represent the height of Snowman B tt hours after sunrise. Graph each function and determine which Snowman is taller after 3 hours.
What is the measure of n?
5
15
m
n= [?l
The measure of the hypotenuse n is 5√3
Hypotenuse
Hypotenuse refers the longest side of a right-angled triangle, the side opposite the right angle. And the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
Given,
Here we have the triangle with some measures on it.
Here we need to find the value of n.
While we looking into the diagram, we have identified that, n is the hypotenuse of the triangle,
So, the value of n is the root of the product of the two hypotenuse segments it touches:
=> n = √(5·15)
=> n = √75
It can be simplified as,
=> n = √(3 x 25)
=> n = 5√3
Therefore, the value of n is 5√3.
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Which describes how to find all rotation angles less that 360° that will map a regular polygon onto itself?
This question is about rotations of polygons.
To rotate a polygon onto itself, we need to know the exact rotation we have to do. This rotation depends on the type of polygons, specifically, the number of sides.
To know the exact angle rotation to map the polygon onto itself, we just have to divide 360° by the number of sides.
Therefore, the right answer is the third choice.Answer:
This question is about rotations of polygons.
To rotate a polygon onto itself, we need to know the exact rotation we have to do. This rotation depends on the type of polygons, specifically, the number of sides.
To know the exact angle rotation to map the polygon onto itself, we have to divide 360° by the number of sides.
Therefore, the right answer is the third choice.
Step-by-step explanation:
The track team has 11 distance runners but can only enter five in the meet. How many combinations of five runners can the coach create?.
Answer:
55
Step-by-step explanation:
11 x 5 = total combinations
11 x 5 = 55
PLEASEEE HELP I REALLY NEED HELP ITS MENTAL MATH!!!!!!!!!!!!
Answer:
6y+12
Step-by-step explanation:
4(y+3)+2y
= 4y+12+2y
=6y+12
Answer:
[tex]\sf 6y+12[/tex]Step-by-step explanation:
[tex]\sf 4(y+3)+2y[/tex]
Expand (Distributive property):-
[tex]\sf 4y+12+2y[/tex]
Combine like terms:-
[tex]\sf 4y+2y+12[/tex]
[tex]\sf (4y+2y)=6y[/tex]
[tex]\sf 6y+12[/tex]
__________________
Hope this helps!
Have a great day! :)
Where is the center of dilation located?
inside figure A
outside figure A
on a vertex of figure A
B
A
The center of dilation is outside figure A
In this question, rectangle A is dilated to rectangle B.
We know that, the center of a dilation is nothing but a fixed point about which all points are expanded or contracted.
We can observe that B = 1/2 * A
This means, the scaling factor is k = 1/2
Let's determine the center of dilation:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.
k - Scale factor
P(x, y) - Original point
P'(x, y) - Resulting point
(3, 1) = O(x, y) + 1/2 [(6, 2) - O(x, y)]
(3, 1) = O(x, y) - 1/2 O(x, y) + (3, 1)
1/2O(x, y) = (0, 0)
so, the center of dilation is the origin (0, 0)
So, in this case the center of dilation is outside figure A.
Therefore, the center of dilation is outside figure A
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Connor filled his 108 gallon pool with water in 8 hours. How many gallons per
hour did he use?
Answer:
I'm pretty sure it's 13.5.
Step-by-step explanation:
Boom first let's do 108 ÷ 8
After that you should get 13.5.
13 and a half gallons per hour.
One popular smoothie recipe uses 2/3 oz of acai juice to make one smoothie. Acai juice typically comes in a 5-oz container, and you want to know how many smoothies can be made from one container. (Write both a multiplication equation and division equation that represents this scenario) (Determine the number of smoothies can be made from one oz of acai)
You can make one and a half smoothies from one oz of acai juice
How to write multiplication equation and division equation?
Given that:
smoothie recipe uses 2/3 oz of acai juice to make one smoothie and
Acai juice comes in a 5-oz container
In order to know how many smoothies can be made from one container, you divide the volume of the Acai juice container by the volume needed to make one smoothie. Thus the equation is:
No. of smoothies = volume of container/volume needed for one smoothie
The number of smoothies that can be made from one oz of acai is:
No. of smoothie = 1/(2/3) = 1 1/2 smoothies
Therefore, the number that can be made from one oz is one and half smoothies
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An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 27 feet up. The ladder makes an angle of 62° with the ground.
Find the length of the ladder. Round your answer to the nearest tenth of a foot if
necessary?
Answer: 59.5 ft
Step-by-step explanation:
When the ladder lay on the wall it makes a triangle. And for this equation, we have to use the sin to find the length.
Sin = opposite / hypotenuse
Sin 62 = 27 / h
27 / 0.4539
h= 59.48
h=59.5 feet
Answer:
30.6
Step-by-step explanation:
I AM HIM
Which of the following relations is NOT a function?
OA. (-6, 4), (1, 3), (-2, 1), (6, 2)
• B. (1, 4), (-2, 2), (1, 1), (-6, 2)
• C.
(-2, 4), (1, 2), (6, 1), (-6, 5)
O D.
(6, 4), (-2, 2), (1, 1), (-6, 2)
Answer:
B
Step-by-step explanation:
2 x values must be the same to not be a function, therefore b must be the answer.
Question 3(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In AJKL, mZJ = 67° and mL = 90°. Determine the measure of the exterior angle to ZK.
23°
113°
O 157°
O 78.5°
By applying the exterior angle theorem, the measure of the exterior angle to angle ZK in triangle JKL is equal to 157°
What is the exterior angle theorem?In Mathematics, the exterior angle theorem can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
How to determine the value of angle ZK?In order to determine the value of ∠G in triangle JKL (ΔJKL), we would have to apply exterior angle theorem. Mathematically, the exterior angle theorem can be used to model the angles in triangle JKL (ΔJKL) and this is given by:
m<G = m<ZJ + m<L
Substituting the given parameters into the formula above, we have;
m<ZK = 67° + 90°.
m<ZK = 157°.
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What is the slope of the line that contains the points (-3, -4) and (-6, 2)?
The slope of the line that contains the (-3, -4) and (-6, 2) is -2.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variables.
The slope is refer to as rise over run.
Therefore, the slope of the line that contains the points (-3, -4) and (-6, 2) can be found as follows:
slope = y₂ - y₁ / x₂ - x₁
where
x₁ = - 3
x₂ = - 6
y₁ = - 4
y₂ = 2
Therefore,
slope = m = 2 + 4 / -6 + 3
slope = 6/ -3
Therefore,
slope = - 2
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Area of the base of a rectangular box is 205 cm² and its height is 3 cm. Find the volume of the box
Answer:
V= 615 cm³
Step-by-step explanation:
the volume (V) of a rectangular box is calculated as
V = Ah ( A is the area of the base and h the height ) , then
V = 205 × 3 = 615 cm³
Answer:
Step-by-step explanation: In order to find the volume of box, we need to know the formula
The formula is
volume= LxBxH where L=length, B= breadth and H= height
SO, area= L x B
we can say,
Volume= area x height= 205 x 3= 615 cm^3
Hence, the volume of the box= 615 cm^3
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How to convert 1 million seconds to hours
Solution
Step 1
To convert seconds to hours, divide the seconds by 3600.
Step 2
1 million seconds = 1000000 seconds
[tex]\begin{gathered} To\text{ hours} \\ \\ \text{= }\frac{1000000}{3600} \\ \\ =\text{ }277\frac{7}{9}\text{ hours} \end{gathered}[/tex]Parallel line of y=-1/2x-2
The parallel line of y=-1/2x-2 is y=-1/2x
Slope-intercept form y=mx+b of linear equations the slope-m and the y-intercept -b of a line,
here y=-1/2x-2 slope of the linear equation is m=-1/2,
whereas the y-intercept is b=-2,
Parallel lines are those lines that are equidistant from each other, the condition for representing two lines is parallel their slopes should be equal or the same.
here slope of the line is -1/2, and the fundamental equation of a line in slope intercept form is y=mx+b, taking the assumption the parallel line is passing through the origin hence the y-intercept of the parallel line is 0, b=0.
therefore, the parallel line of y=-1/2x-2 is y=-1/2x
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Identify the maximum or minimum point from the graph:f(x)=|x-3|Answer as an ordered pair (x,y)
we have
f(x)=|x-3|
the vertex of the function is the point (3,0)
the function has a minimum
the vertex is the minimum
so the answer is
the minimum is the point (3,0)Write all integers that belong to the intervals:[-1, 1]
Okay, here we have this:
Considering that the intervals are closed, we have the following integers in this interval: -1,0,1.
help me please, correct answer gets brainliest
Answer:
Only D and B
Step-by-step explanation:
True or False? Every quadrilateral is a rhombus. Every parallelogram is a quadrilateral. Every square is a quadrilateral. Every rhombus with four right angles is a square. X Ś True False O True False O True False True False ?
First of all it's important to note that all parallelograms, rhombuses and squares are quadrilateral and they meet the following properties:
- Rhombus: quadrilateral whose four sides have the same length.
- Parallelogram: quadrilateral that has two pairs of parallel sides.
- Square: quadrilateral whose four sides and internal angles have the same length/measure.
With these definitions in mind we can solve the True or False table in the picture.
The first statement is false not every quadrilateral is a rhombus. For example rectangles that are not squares are not rhombuses since their four sides aren't all equal.
The second is true, as we saw before parallelograms are quadrilaterals. The same reason applies to the third statement, squares are qudrilaterals.
Now let's see the last statement. A rhombus with four right angles is a quadrilateral that has four equal sides (because it's a rhombus) and four equal angles (all measuring 90°). These are the conditions required for a quadrilateral to be considered a square so this last statement is true.
AnswersThen the answers are:
F
PLEASE HELP ME I WILL MARK YOU BRANLYEST
Solve the inequality and graph the solution.
−0.8b + 2.3 > 8.7
number line with an open circle plotted at negative eight and arrow pointing right
number line with a closed circle plotted at negative eight and arrow pointing right
number line with an open circle plotted at negative eight and arrow pointing left
number line with a closed circle plotted at negative eight and arrow pointing left
The solution of the inequality:
-8 > b
And the graph can be seen below.
How to solve the inequality?Here we start with the inequality:
-0.8*b + 2.3 > 8.7
To solve this we need to isolate the variable b.
Let's do that in the right side:
-8.7 + 2.3 > 0.8*b
-6.4 > 0.8*b
-6.4/0.8 > b
-8 > b
So b is smaller than -8. then the correct graph is:
"number line with an open circle plotted at negative eight and arrow pointing left"
.
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Simplify 9/16 + 1/16 • (2_3)-1
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
9/16 + 1/16 * (2/3)^(-1)
Step 02:
we must apply the algebraic rules to find the solution
[tex]\frac{9}{16}+\frac{1}{16}\cdot(\frac{2}{3})^{-1}=\frac{9}{16}+\frac{1}{16}\cdot\frac{3}{2}=\frac{9}{16}+\frac{3}{32}[/tex][tex]\frac{9\cdot2+3\cdot1}{32}=\frac{21}{32}[/tex]The answer is:
21 / 32
Suppose the cost per ton y to build an oil platform of x thousand tons is approximately by:What is the cost per ton for x=300?
The cost per ton of x = 300 is 318.18
To solve this, we need to reaplce x in the function:
[tex]\begin{gathered} \begin{cases}f(x)=\frac{262,500}{x+525} \\ x=300\end{cases} \\ f(300)=\frac{262,500}{300+525}=\frac{262,500}{825} \\ f(300)\approx318.18 \end{gathered}[/tex]And then we get the anser
The equation for line j can be written as y =
= -5/7x-10. Line k, which is parallel to line j,
includes the point (-9, 5). What is the equation of line k?
The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].
What is the Relation between two Parallel Lines?
To determine whether two lines are parallel or not, apply the parallel line's formula. When we have the slope of two lines that we want to compare, the parallel line formula can be used. The separation between the parallel lines remains constant. Parallel lines are those that never cross each other. Since the two lines are equal in this situation and the angle is 180 degrees, they will never intersect.
In the given equation, we have:
The equation of the line is y = -5/7x-10.
and, Line k, which is parallel to the line of the equation :
[tex]y = \frac{-5x}{7} -10.[/tex]
[tex]y + \frac{5x}{7} +10. =0[/tex]
So, the equation of the line which is parallel to the line of the equation is:
[tex]y + \frac{5x}{7} +k. =0[/tex]
and since the two lines are parallels
So, the slope of equation 1 and the slope of equation two will be the same;
Also, It is given that the line includes the point (-9, 5).
So,
[tex]5 + \frac{5 \times -9}{7} +k. =0[/tex]
⇒[tex]k = -\frac{5 \times -9}{7} -5[/tex]
⇒[tex]k = \frac{10}{7}[/tex]
So, The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].
Hence,
The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex]..
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Consider a set of data in which the sample mean is 23.8 and the sample standard deviation is 6.6. Calculate the z score given that x= 26.7 round your answer two decimal places.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\begin{gathered} mean(\mu)=23.8 \\ standard\text{ }deviation(\sigma)=6.6 \\ x=26.7 \end{gathered}[/tex]STEP 2: Write the formula for calculating z-scores
[tex]z=\frac{x-\mu}{\sigma}[/tex]By substitution,
[tex]\begin{gathered} z=\frac{26.7-23.8}{6.6}=\frac{2.9}{6.6}=0.43939393939 \\ \\ z\approx0.44 \end{gathered}[/tex]Hence, the z score is approximately 0.44 to 2 decimal places
Carlos had 194 seeds and 11 flower pots. He put the same number of seeds in each flower pot. Which is the best estimate for the number of seeds in each flower pot?
a:10
b:20
c:30
d:40
Answer: B
Step-by-step explanation: The question says estimate, meaning you'll have to round the numbers. 194 gets rounded up to 200, while 11 gets rounded down to 10.
200 / 10 = 20, thus the answer is B
Given the inequality 4(n-5) <3(n + 11), determine which integer makes the inequality false.
S:{4}
S:{11}
S:{53}
S:{-8}
The integer n = 53 will make the inequality 4(n - 5) < 3(n + 11) false
InequalityIn mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
In this expression, we can solve and find what makes it's true and take the odd one out.
4(n - 5) < 3(n + 11)
4n - 20 < 3n + 33
n < 53
From the options given, the value of n that will make the inequality true is less than 53 and that makes the integer 53 to be false.
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