Answer:
[tex]x = - 4[/tex]
[tex]y = - 4[/tex]
Step-by-step explanation:
Looking at these equations, we can see neither x or y have the same coefficient. Therefore, we need to multiply or divide, to make either the x or the y the same. It's less of a hassle to make the Xs the same, so let's do that. Taking the top equation and multiplying it by 4, we get:
[tex]4x - 20y = 64[/tex]
Now let's subtract the top equation from the bottom equation, leaving us with a third equation:
[tex] - 18y = 72[/tex]
Divide 72 by -18 to get
[tex]y = - 4[/tex]
Now let's substitute into our first equation to find X:
[tex]x + 20 = 16[/tex]
Leaving us with:
[tex]x = - 4[/tex]
Now let's substitute into the second equation to check our solution is correct:
[tex] - 16 + 8 = - 8[/tex]
This is correct, so the answer is X and Y are both equal to -4
Which of the following is NOT a solution to the system of inequalities? Please help
A) (1, 5)
B) (2, 1)
C) (1, 2)
D) (0, 4)
Answer:
B (It isn't in the shaded region)
Find the discriminant of the quadratic equation x2 14x 8 = 0 and use it to determine the number and types of solutions. b2 − 4ac
The discriminant is 164 and there are two real solutions.
What is Quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax^2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
We can find the discriminant as shown below:
x^2+14x+8=0
a=1, b=14, c=8
Discriminant=b^2-4ac
=(14)^2-4*1*8
=196-32
=164>0
As the discriminant is positive and greater than zero. So, there are two real and distinct solution.
Hence, discriminant is 164 and two real solution.
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Select the correct answer. the data set shows the ages of the members of a book club. what is the shape of the distribution of this data set? 19, 21, 18, 19, 16, 21, 20, 17, 16, 17, 20, 18
These trapezoids are similar. Which of the following is the correct similarity statement?
Answer:
ABCD-DEFG
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Suppose that the waiting time for a license plate renewal at a local office of a state motorvehicle department has been found to be normally distributed with a mean of 30 minutes anda standard deviation of 7.5 minutes. What is the probability that a randomly selected individual will have a waiting time between 16 and 44 minutes
The probability that a randomly selected individual will have a waiting time between 16 and 44 minutes is 93.72%.
Given mean of 30 minutes and standard deviation of 7.5 minutes.
In a set with mean d and standard deviation d. , the z score is given as:
Z=(X-d)/s.
where d is sample mean and s is standard deviation.
We have to calculate z score and then p value from normal distribution table.
We have been given d=30, s=7.5
p value of Z when X=44 subtracted by the p value of Z when X=16.
When X=44,
Z=(44-30)/7.5
=14/7.5
=1.87
P value=0.9686
When X=16
Z=(16-30)/7.5
=-1.87
P Value=0.0314.
Required probability is =0.9686-0.0314
=0.9372
=93.72%
Hence the probability that a randomly selected individual will have a waiting time between 16 and 44 minutes is 93.72%.
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At the flower store they told her that the vase should be filled for the flowers to last the longest. her cylinder vase has a radius of 3in and a height of 8in. how much water should mary pour into the vase?
Mary should pour around 3.7 liters or 226.08 in³ volume of water in the vase.
Given Information and Formula Used
Radius of the cylindrical vase, r = 3 inches
Height of the cylindrical vase, h = 8 inches
The formula for the volume, V of a cylinder is given as,
V = πr²h
Here, r is the radius of the cylinder and h is the height of the cylinder.
Calculating the Volume
Substituting the given values of r and h in the formula for the volume of cylinder, we get
Volume, V = π(3)²(8)
Using π = 3.14, we have,
V = 3.14(9)(8)
V = 226.08 cubic inches
Volume in Liters
Since, 1 Liter = 61.0237 cubic inches,
1 cubic inch = 1/61.0237 liters
⇒ 226.08 cubic inches = 226.08/61.0237 liters
⇒ 226.08 cubic inches ≈ 3.07 liters
Thus, Mary needs to pour approximately 3.07 liters volume of water in the vase.
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3
Identify the correct property of equality to solve each equation.
3+x=27
XI
= 5
The correct property of equality to solve each equation is x=24.
We have given that,
Identify the correct property of equality to solve each equation.
3+x=27
What is the property of equality?
The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.
For this case, we must solve the following equation
3+x=27
Subtracting 3 on both sides of the equation we have
3+x-3=27-3
x=24
We observe the property of equality of subtraction.
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Determine the equation of the circle with centre (-3;5) and passing through a point (2;-9)
Therefore, the equation of circle is: [tex](x+3)^{2}+(y+5)^{2} = 100[/tex]
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its center. The radius must typically be a positive integer. Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane. A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.Here we know that[tex](h,k) = (-3,5)[/tex]but we are not given the radius.
However, we can find the radius by using the distance formula.
[tex]\sqrt{x^{2} +y^{2} }[/tex], where [tex]x=x_{1} -x_{2}[/tex] and [tex]y=y_{1} -y_{2}[/tex]
Putting the values, we get:
[tex]\sqrt{8^{2} +6^{2} }[/tex]
The radius comes out to be:
[tex]r=10[/tex]
An equation of the circle with center [tex](h,k)[/tex] and radius r is
[tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex]
Now, substituting the values, we get:
[tex](x--3)^{2} +(y-5)^{2} = 10^{2}[/tex]
Therefore, the equation of circle is:
[tex](x+3)^{2}+(y+5)^{2} = 100[/tex]
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Please help! If the current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms, what is the voltage?
The value of the voltage is 18 - j volts if the current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms option (c) is correct.
What is a complex number?
It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have:
The current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms.
As we know,
V = IR
V = (3 + j2)(4 - j3)
[tex]\rm V=\left(3\cdot \:4-2\left(-3\right)\right)+\left(3\left(-3\right)+2\cdot \:4\right)j[/tex]
j² = -1 (complex part)
After simplification:
V = 18 - j volts
Thus, the value of the voltage is 18 - j volts if the current in a circuit is 3 + j2 amps and the resistance is 4 - j3 ohms option (c) is correct.
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Triangles J K L and M N R are shown.
In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?
∠J ≅ ∠M
∠L ≅ ∠R
∠K ≅ ∠N
∠R ≅ ∠K
The correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.
Here we are given that
KL = NR
JL = MR
Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.
So for the triangles to be congruent by SAS, angle L must be congruent to angle R.
∠L=∠R
Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
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Answer: option b
Step-by-step explanation:
Find the solutions to the equation below.
Check all that apply.
2x² +9x+4=0
A. x = -4
B. X= 4
C. X=-3
D. X= 7
0 E. x= -1/2
F. X=2
SUBMIT
Answer-
-1/2, -4
Step-by-step explanation:
A, E
Did the math to find the solution earlier, got right xoxo :)
Calculator
Bookwork code: Q86 allowed
Second chance! Review your workings and see if you can correct your mistake.
Bethany rolled a six-sided dice a number of times and recorded the outcomes in
the table below.
< Back to task
Work out the relative frequency of landing on
a) the number 4.
b) a prime number.
Give your answers as decimals.
Outcome
1
2
3
4
5
Frequency
12
6
8
14
3
Watch video
7
Answer >
1) The frequency of landing 4 is 14.
2) The frequency for prime numbers is 8 and 3.
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
Outcome Frequency
1 12
2 6
3 8
4 14
5 3
1) The frequency of landing 4 is 14.
2) The frequency for prime numbers is 8 and 3.
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There are twenty classes at each of two middle schools. The number of students in each class at each school is shown in the dot plots below.
Number of Students in Each Class at Poplar Middle School
A dot plot. A number line going from 20 to 29 labeled Number of Students. There are 3 dots above 20, 5 above 21, 7 above 22, 4 above 23, 1 above 24, and 0 above 25, 26, 27, 28, and 29.
Number of Students in Each Class at Oak Middle School
A dot plot. A number line going from 20 to 29 labeled Number of Students. There is 1 dot above 20, 2 above 21, 2 above 22, 4 above 23, 3 above 24, 2 above 25, 2 above 26, 2 above 27, 1 above 28, and 1 above 29.
Which statement correctly compares the mean number of students for the data in the plots?
The correct answer is option B: there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.
What are statistics?The practice or science of organizing and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.
From the dot plot attached, we can find the average number of students per class for each school.
For Poplar Middle School;
Total number of students = (20 × 3) + (21 × 5) + (22 × 7) + (23 × 4) + (24 × 1) = 435 students.
There are 20 classes.
Thus;
Average number of students per class = 435/20 = 21.75
For Oak Middle School;
Total number of students = (20 × 1) + (21 × 2) + (22 × 2) + (23 × 4) + (24 × 3) + (25 × 2) + (26 × 2) + (27 × 2) + (28 × 1) + (29 × 1) = 483
The average number of students per class; 483/20 = 24.15
Difference in average = 24.15 - 21.75 = 2.40
This implies that there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.
Therefore the correct answer is option B: there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.
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In the following exercises, multiply the binomials. Use any method.
243. (y − 6)(y − 2)
Answer:
Hence the expression. [tex](y-6)(y-2)=y^{2} -8x-12[/tex]
Step-by-step explanation:
The given expression is (y-6)(y-2).We have to multiply the given expression.Multiply the (y-6) by -2, multiply the (y-6) by y then add like terms.[tex]$$\begin{array}{r}y-6 \\\times \quad \underline{y-2} \\-2 y-12 \\\underline{y^{2}-6 y} \\y^{2}-8 y-12\end{array}$$[/tex]
What line segment is equal to AC - BC?
(Picture included)
Answer:
A_____BStep-by-step explanation:
What line segment is equal to AC - BC?
A_____B_____C -
B_____C =
A_____B
Need some help please?
The value of the unknown length is 24
How to determine the unknown length?Represent the unknown length with x.
So, we have the following equivalent ratio:
30 : 30 + x = 25 : 45
Express as fraction
30/30 + x = 25/45
Simplify the fraction
30/30 + x = 5/9
Cross multiply
150 + 5x = 270
Evaluate the like terms
5x = 120
Divide by 5
x = 24
Hence, the value of the unknown length is 24
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Please help. Prove quadrilateral WXYZ, having vertices W(-5, 6), X(-1, 10), Y(1, 4), and Z(-2, -3) is a trapezoid.
I need help writing a 2 column proof
The proof that quadrilateral WXYZ, having vertices W(-5, 6), X(-1, 10), Y(1, 4), and Z(-2, -3) is a trapezoid is given below.
What is a mathematical proof?Mathematical proof is a set of logical statements that are sequentially indicated to guaranty that a stated position is indeed accurate.
What is the proof for the quadrilateral above?It is to be noted that with parallelograms, the diagonals intersect at the midpoints. (See the attached image).
The Diagonals are WY and XZ; Where
WY : (-4, -3) to (6, -2); and
Midpoint is [ (0 + 2)/2 , (-1 + -4)/2 ]
= (1, -5/2)
The diagonals are bisectors of each other.
It is to be noted that the diagonals are not congruent. For if they were congruent, then the above would not be a trapezoid.
The Length of WY = √((-4 - 6)² + (-3 - (-2))²)
WY = √(100 + 1)
WY = √101
The Length of XZ = √((0 - 2)² + ( -1 - -4)²)
XZ = √(4+9)
XZ = √13
From the above, it is clear that both diagonals are unequal. Hence, given the first and second proof, we can state that quadrilateral WXYZ is a Trapezoid.
QED
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Given an expression such as 3x + 2y, find the value of the expression when x is equal to 4 and y is equal to 2.4 Given an expression such as 3x + 2y , find the value of the expression when x is equal to 4 and y is equal to 2.4
Answer:
16.8
Step-by-step explanation:
3x+2y
3(4)+2(2.4)
12+4.8
16.8
25/3 ÷ x = 7/3 ÷8.1
I don't get it, what's the answer??
Answer:
x=28.93(rounded) x=28.929(not rounded)
Step-by-step explanation:
Step-by-step explanation:
25/3÷x=7/3÷8.1
25/3×8.1=7/3×x
135/2=7/3×x
x=135/2×3/7
x=405/14=28.929
2 six-sided dice, one green and one red, are released. What is the probability that : The number on the red die is 3
18
Select the correct answer.
Exponential function fis represented by the table.
X
f(x)
=
-2
-46
OA
O B.
OC.
O D.
-1
-22
0
-10
1
-4
Function g is represented by the equation.
g(x)
- 18(3)² + 2
Which statement correctly compares the two functions on the interval [-1, 2]?
2
-1
ہے
Only function fis increasing, and only function fis negative.
Only function fis increasing, but both functions are negative.
Both functions are increasing, but function g increases at a faster average rate.
Both functions are increasing, but function fincreases at a faster average rate.
A statement which correctly compares the two functions on the given interval [-1, 2] is: C. Both functions are increasing, but function g increases at a faster average rate.
How to compares the two functions?First of all, we would determine the values of function g(x) on the given interval [-1, 2] as follows:
g(x) = -18(⅓)^x + 2
At x = -1, we have:
g(-1) = -18(⅓)^(-1) + 2
g(-1) = -52.
At x = 0, we have:
g(0) = -18(⅓)^(0) + 2
g(0) = -16.
At x = 1, we have:
g(1) = -18(⅓)^(1) + 2
g(1) = -4.
At x = 2, we have:
g(2) = -18(⅓)^(0) + 2
g(2) = 0.
By critically observing the values of each functions, we can logically deduce that both functions are increasing but function g(x) increases at a faster average rate because it started with a lower value and ended with a higher value.
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Is it necessary to perform the horizontal line test when finding the inverse of every function?
Yes, the horizontal line test is important when finding the inverse of a function because without the intersection of the line, they would be no inverse.
Steps in finding inverse of a functionThe steps include;
Replace f(x)with y in the equation of the functionInterchange x and y in the functionThen solve for yReplace y with f-1(x) in the functionA property of horizontal line is that if it intersects the graph of a function more that on way, then 'f' does not have an inverse.
If no horizontal line intersects the graph , 'then f' does have an inverse.
Thus, the horizontal line test is important when finding the inverse of a function because without the intersection of the line, they would be no inverse.
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A sample of carbon dioxide occupies a volume of 3.50 l at 125 kpa pressure. what pressure would the gas exert if the volume was decreased to 2.00 l? use the formula: p1v1 = p2v2 2.19 kpa 18.8 kpa 21.9 kpa 219 kpa
The gas exerts a pressure of 218.75 kPa when its volume is reduced to 2.0 L, following the behavior of an ideal gas.
Ideal gas behavior:
Suppose the initial volume of carbon dioxide gas is V = 3.5l
Initial pressure is P = 125 kPa
Since the volume is reduced to 2.0l, the final volume is shown as V'= Will be done. 2L
The final pressure of the gas is P'.
We consider the behavior of gas to be ideal. From the ideal gas equation, it becomes as follows.
PV = P'V'
125 × 3.5 = P'× 2
P'= 218.75 kPa
Therefore, the final pressure is 218.5 kPa.
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Answer:
First part: 219 kPa (option D)
Second part: 2.3 L (option A)
Step-by-step explanation: just got asked the question
Find the value of d.
d
0.
e
75°
194°
Answer: C
Step-by-step explanation:
[tex]75=\frac{d+94}{2}\\ \\ 150=d+94 \\ \\ d=56[/tex]
The Marcos family consists of 2 adults and 4 children. They spent a total of $40 on circus tickets. Let x represent the cost of an adult ticket, and let y represent the cost of a child’s ticket. Which graph represents the possible costs of the tickets?
On a coordinate plane, a line goes through points (0, 10) and (20, 0).
On a coordinate plane, a line goes through points (0, 20) and (10, 0).
On a coordinate plane, a line goes through points (negative 10, 0) and (0, 20).
On a coordinate plane, a line goes through points (negative 20, 0) and (0, 10).
Answer:
First Option
Step-by-step explanation:
First, we will find the equation for the total cost of the tickets.
Given x = Cost of 1 adult ticket
y = Cost of 1 Child ticket
Total Cost of tickets at $40:
2x + 4y = 40
To find which graph represent the cost of the tickets,
we can substitute x = 0 to find y and vice-versa.
If x = 0 ,
[tex]2(0) + 4y = 40\\4y = 40\\y = \frac{40}{4} \\= 10[/tex]
So when x = 0 , y = 10 which gives the coordinates (0,10).
Now if y = 0,
[tex]2x+4(0) = 40\\2x = 40\\x = \frac{40}{2} \\= 20[/tex]
So when y = 0 , x = 20 which gives the coordinates (20,0)
This shows that this particular line passes through these 2 points and therefore the answer is the first option.
Answer: A i just took the test
Step-by-step explanation:
$10.14 is what percent of $8.45?
Write your answer using a percent sign (%). For example, 0.5%, 12.7%, or 56%.
Answer:
120%
Step-by-step explanation:
10.14 is more than all of 8.45.
8.45 is 100% of 8.45.
So 10.14 will be more than 100%.
10.14 ÷ 8.45 = 1.2
This is the decimal value.
To change to %, multiply by 100.
1.2 × 100 = 120
10.14 is 120% of 8.45
Solve the system of equations using elimination: -x-2y=19 and -x-y=12.
Answer:
[tex]\begin{cases}x=-5\\y=-7\end[/tex]
Step-by-step explanation:
[tex]\begin{cases}-x-2y=19\left(1)\right\\-x-y=12\left(2)\right\end[/tex]
(2)-(1)
[tex]y=-7[/tex]
Sub into (2)
[tex]-x+7=12\\x=-5[/tex]
Solutions:
[tex]\begin{cases}x=-5\\y=-7\end[/tex]
Water freezes at 0^\circ0
∘
0, degrees Celsius.
Manoj's water is 3^\circ3
∘
3, degrees Celsius.
Leo's water is 7^\circ7
∘
7, degrees Celsius.
Whose water matches each description?
Manoj's water
Leo's water
Is at a greater temperature
Is closer to freezing
\quad
Leo's water is at a greater temperature. And Manoj's water is closer to freezing.
What is the temperature?The temperature refers to the degree of hotness ant coldness of the substance.
Water freezes at 0 °C.
Manoj's water is 3 °C.
Leo's water is 7 °C.
Leo's water is at a greater temperature.
Manoj's water is closer to freezing.
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A passenger car weighs 4.5 times 10 superscript 3 units. which unit of measure was used? grams ounces pounds tons
Pound is the unit of measure of passengers car weight
According the statement
The weight of passengers car is 4.5 times 10 superscript 3 units.
from this it is clear that the in simple terms the weight become 4.5 * 10^3
AND
the term 10^3 is used when we measure the weight in pounds.
So, Pound is the unit of measure of passengers car weight.
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Which term describes the slope of the line below?
Answer:
B. Zero
Step-by-step explanation:
The slope of the line is in the the first two quadrants and is horizontal, meaning it has zero slope.
Answer:
Zero slope :)
Step-by-step explanation:
A zero slope is a horizontal line. When there is a zero slope, y will be equal to a constant. :)
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