Put y = -4 into the expression below:
[tex]y^2-7y+2[/tex]Hence,
[tex]\begin{gathered} y^2-7y+2=(-4)^2-7(-4)+2 \\ =16+28+2 \\ =46 \end{gathered}[/tex]Therefore, the value of the expression when y = -4 is 46
1. Type the number only, no variables. 5 10 8 Your answer
given expression :
[tex]\begin{gathered} \frac{5}{8}=\frac{10}{x} \\ \text{Apply cross multiplication} \\ 5x=10\times8 \\ x=\frac{80}{5} \\ x=16 \end{gathered}[/tex]Answer : 16
Laura is playing a game of chance in which she tosses a dart into a rotating dart board with 8 equal-size slices numbered 1 through 8. The dart lands on a numbered slice at random
Solution:
Given that;
Laura is playing a game of chance in which she tosses a dart into a rotating dart board with 8 equal-size slices numbered 1 through 8
a) For the expected value;
If Laura tosses the dart once, and she wins $1 if the dart lands in slice 1, $3 if the dart lands in slice 2, $5 if the dart lands in slice 3, $8 if the dart lands in slice 4, and $10 if the dart lands in slice 5 and loses she loses $9 if the dart lands in slices 6, 7, or 8
The expected value will be
[tex]Expected\text{ value}=\frac{1(1)+3(1)+5(1)+8(1)+10(1)+9(3)}{8}=\frac{27-27}{8}=\frac{0}{8}=0[/tex]Hence, the expected value is $0
b) If Laura plays many games, she is expected to neither gain nor lose money.
This is because she has 5 out of 8 chances to win some money and the expected value is $0t
Hence, Laura can expect to break even (neither gain nor lose money)
Please just give me answer checking my answers to make sure my answers ok. I don't need the steps
Given:
The explicit formula for a geometrc sequence is given:
[tex]a_n=500\times(0.5)^{n-1}[/tex]To find the 6th term put n=6 here,
[tex]\begin{gathered} a_6=500\times(0.5)^{6-1} \\ =500\times(0.5)^5 \\ =500\times0.03125 \\ =15.625 \end{gathered}[/tex]Hence, option B is correct.
How to find the inverse of a matrix of it exists Question number 15
2x2 matrix's inverse:
[tex]\begin{gathered} A^{(-1)}=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}\end{bmatrix}^{(-1)}=\frac{1}{ad-bc}\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & \end{bmatrix} \\ \\ \\ It\text{ exists only if: } \\ ad-bc\ne0 \end{gathered}[/tex]For the given matrix:
[tex]\begin{gathered} \begin{bmatrix}{6} & {-3} & \\ {-8} & {4} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{6\times4-(-3)\times(-8)}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{24-24}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{0}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ \end{gathered}[/tex]As the determinat (ad-bc) is 0 the matrix isn't a invertible matrix. The inverse of the given matrix doesn't existFor questions 8 - 10, find all the solutions for x.8. 2x 4+14= 229. 8x +19 -54 +3x?10. 7x² + 12 =51- 4x?
x = 2 or x = -2
Explanation:8) 2x² + 14 = 22
collect like terms by subtracting14 from both sides of the equation:
2x² + 14 - 14 = 22 - 14
2x² + 0 = 8
2x² = 8
DIvide both sides by 2:
2x²/2 = 8/2
x² = 4
Square root both sides of the equation:
[tex]\begin{gathered} \sqrt[]{x^2}\text{ = }\pm\sqrt[]{4} \\ x\text{ =}\pm2 \\ \pm2\text{ = +2 or -2} \\ x\text{ =2 or x = -2} \end{gathered}[/tex]hey, can someone please help me solve this equation? i really need help
Solution
For this case we can use the following definition:
[tex]\cot N=\frac{\cos N}{\sin N}[/tex]And from the figure given we have:
[tex]\cos N=\frac{12}{37},\sin N=\frac{35}{37}[/tex]And replacing we got:
[tex]\cot N=\frac{12}{35}[/tex]Hello! I need some assistance with this homework question, pleaseQ19
We start with the parent function:
[tex]y=\sqrt[]{x}[/tex]The transformations are:
• Shift up 6 units
,• Reflect about the x-axis
,• Reflect about the y-axis
The first transformation is equal to add 6 units to y:
[tex]\begin{gathered} y_2=y+6 \\ y_2=\sqrt[]{x}+6 \end{gathered}[/tex]Then, a reflection across the x-axis makes y change sign, so we will have:
[tex]\begin{gathered} y_3=-y_2 \\ y_3=-\sqrt[]{x}-6 \end{gathered}[/tex]Finally, a reflection across the y-axis makes the argument x change sign, so we will have:
[tex]\begin{gathered} y_4=y_3(-x) \\ y_4=-\sqrt[]{-x}-6 \end{gathered}[/tex]This is the final function.
We can graph this function, and the intermediate steps, as:
Answer: y = -√-x - 6
plot on a number line . 3| y+4 | >12
3 |y + 4| > 12
| y + 4 | > 12/3 = 4
| y + 4 | > 4
Two solutions:
y + 4 > 4 ==> y > 0
y + 4 < -4 ==> y < -8
Cooper wrote checks on his checking account for $20 and $35. he also deposited $63 in the account. witch number describes the change in the balance of his account
The checks he wrote are withdraw from his account, so the amounts will be substracted from its balance.
The deposit, on the contrary, will add to the balance of his account.
Then, the net change in his account will be:
[tex]\Delta=-20-35+63=8[/tex]The net change in the balance of his account is $8, increasing the original balance.
A room is measured to be 10.0m long, 5.6m wide and 155 m high.What is the volume of the room?What is the mass in kilograms of smoke inside the room if it’s density is 1.506kg/m^3?
The rule of the volume of the solid shaped a rectangular solid is
[tex]V=L\times W\times H[/tex]L is the length
W is the width
H is the height
Since the dimensions of the room are
10 m long
5.6 m wide
155 m high
Then
L = 10
W = 5.6
H = 155
Substitute them in the rule above
[tex]\begin{gathered} V=10\times5.6\times155 \\ V=8680m^3 \end{gathered}[/tex]The volume of the room is 8680 cubic meters
The rule of the mass is
[tex]m=d\times V[/tex]m is the mass
d is the density
V is the volume
Since the density is 1.506 kg/m^3
Then d = 1.506
Since the volume is 8680 m^3
Then
[tex]\begin{gathered} m=1.506\times8680 \\ m=13072.08\operatorname{kg} \end{gathered}[/tex]The mass of the smoke inside the room is 13072.08 kg
15
Be sure to read the directions carefully and write what is asked for.
Part A: Multiply (without simplifying your answer): 5√12 2√/6 =
Part B: What perfect square can you take out of the radicand from Part A's answer?
Part C: After simplifying, what is the final answer to Part A?
The product of radical numbers is 10√72. The simplest form of the radical part is 60√2.
What is the meaning of radical?
The square root or nth root is represented by the symbol √. Expression with a square root is referred to as a radical expression. Radicand: A value or phrase included within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.
Given numbers are 5√12 and 2√6.
Now multiply the given numbers:
5√12 × 2√12
Multiply whole number with whole number and radical part with radical part:
=(5 × 2) × (√12 ×√6)
= 10 × √72
= 10√72
= 10 √(6 × 6 × 2)
Take out perfect square of the radicand:
= 10 × 6 √( 2)
= 60√2
To learn more about radicand, click on below link:
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true or false : the equation below is too complicated to use the isolate the radical then square both sides
The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex] is not true.
Given that,
The radical must first be isolated before both sides of the following equation may be squared.
The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex]
We have to say the equation is true or false.
The result of multiplying an integer by itself is known as the square root of the number. The radical sign represents the square root. As an illustration, √16 = 4. The radical symbol is also known as the root symbol or surds.
Take Left hand side.
[tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }[/tex]
Root is
[tex]\sqrt{\frac{x+3}{x+1}}[/tex]
The right hand side is 3
The left hand side ≠ right hand side.
Therefore, The equation is [tex]\frac{\sqrt{x+3} }{\sqrt{x+1} }=3[/tex] is not true.
To learn more about equation visit: https://brainly.com/question/10413253
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please help. i just need to know how to complete this
1. Given:
[tex]\bar{TO}\cong\bar{AN}[/tex]Conclusion: Definition of congruence
Reason:
The line segment TO and AN are equal in length.
2. Given:
E is the midpoint of the line segment BD.
Conclusion: Definition of midpoint
Reason:
Since, E is in equidistant from the proint B and D on the line segment BD.
Therefore, using using the Definition of midpoint, E is the midpoint of the line segment BD.
If the area of a rectangle is 60 cm and the length is 5cm and the width is (x+4) find x
Answer:
8
Step-by-step explanation:
A=length*width
60=5*(x+4)
60=5x+20
40=5x subtract 20 from both sides
8=x divide by 5 on both sides
x=8
The points represented by the table lie on a line. How can you find the slope of the line from the table? What is the slope of the line? Х 2 4 6 8 y 5 1 -3 -7
The given table is
x 2 4 6 8
y 5 1 -3 -7
The formula for determining the slope of a line is expressed as
slope = (y2 - y1)/(x2 - x1)
From the table,
x1 = 2, x2 = 4
y1 = 5, y2 = 1
Slope = (1 - 5)/(4 - 2)
Slope = - 4/2
Slope = - 2
The functions f(x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 2−2≤x≤2 goes from least to greatest.
SOLUTION:
The formula for the average rate of change of a function is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For f(x);
[tex]\begin{gathered} m=\frac{30-(-10)}{2-(-2)} \\ m=10 \end{gathered}[/tex]For (x):
[tex]\begin{gathered} m=\frac{10-46}{2-(-2)}= \\ m=-9 \end{gathered}[/tex]For h(x):
[tex]\begin{gathered} m=\frac{h(2)-h(-2)}{2-(-2)} \\ m=\frac{(-2^2-5(2)+25)-(-(-2)^2-5(-2)+25)}{2-(-2)} \\ m=-5 \end{gathered}[/tex]From this calculation, ranking the average rateof change from least to greatest, swe have;
[tex]g(x),h(x),f(x)[/tex]I need help please give me an answer for this.
surface area of the net pyramid is 125 in²
Explanation:Surface area of a net pyamid is calculated as:
[tex]S\mathrm{}A\text{ = area of base + }\frac{1}{2}perimeter\text{ of base }\times slant\text{ height}[/tex]side of the base = 5 in
Area of the base = area of square
Area of the base = (side of the base)² = 5²
Area of base = 25 in²
Perimeter of base = perimeter of square
Perimeter of base = 4(side of the base) = 4(5)
Perimeter of base = 20 in
slant height = 10 in
Inserting the values into the formula for surface area:
[tex]\begin{gathered} S.A\text{ = }25\text{ + }\frac{1}{2}(20)(10) \\ S.A\text{ = }25\text{ + 100} \\ S\mathrm{}A\text{ = 125 in}^{2} \end{gathered}[/tex]If $2000 is invested at 7% compounded continuously, what is the amount after 3 years?
Given:
Amount = $2000
rate = 7%
time = 3 year
Amount after 3 year is:
[tex]A=Pe^{rt}^{}[/tex]Where:
[tex]\begin{gathered} P\text{ = initial amount} \\ r=\text{rate} \\ t=\text{ time} \\ A=\text{ amount after t time } \end{gathered}[/tex][tex]\begin{gathered} rate=\frac{7}{100}^{} \\ =0.07 \end{gathered}[/tex][tex]\begin{gathered} A=2000e^{0.07\times3} \\ =2000e^{0.21} \\ =2000\times1.233 \\ =2467.35 \end{gathered}[/tex]After 3 year amount is 2467.35
Use the tests for divisibility to determine which numbers divide evenly into the given number,766
Step 1: Concept
The rule for 2: 2 can divide any number that ends with even numbers 0, 2, 4, 6, 8.
The rule for 3: For a number to be divide by 3, its sum must be divided by 3.
The rule for 4: For a number to be divide by 4, the last two digits must be divided by 4
The rule for 5: For a number to be divided by 5, it must end with 0 or 5.
The rule for 6: A number is divisible by 6 if it is divisible by 2 and 3.
The rule for 8: A number is divisible by 8 if its last three digits are divisible by 8.
The rule for 9: For a number to be divisible by 9, its sum must be divisible by 9.
The rule for 10: For a number to be divided by 10, it must end with 0.
Step 2: Test for 766
766 can be divided by 2 because it ends with the even number 6.
766 cannot be divided by 3 because it sum (7+6+6 = 19) cannot be divide by 3.
766 cannot be divided by 4 because it last two digits cannot be divide by 4.
766 cannot be divided by 5 because it does not end with 0 or 5.
766 cannot be divided by 6 because it cannot be divide by 3
766 cannot be divided by 8 because the last three digits cannot be divided by 8.
766 cannot be divided by 9 because the sum of its digits cannot be divided by 9.
766 cannot be divided by 10 because the number did not end with 0.
Step 3: Final answer
2
Claim: Most adults erase all of their personal information online if they could. A software firm survey of randomly selected adults showed that % of them would erase all of their personal information online if they could. Make a subjective estimate to decide whether the results are significantly low or significantly high, then state a conclusion about the original claim.
Claim: Most adults would erase all of their personal information online if they could
Sample size: 625
Yes: 50.3%
The null hypothesis, due to randomness, is p = 0.5. From the results, the claim states that p > 0.5, and the result of the survey is p = 0.503.
The result is close to the null hypothesis, so we can conclude that there is no significant evidence for the claim.
Answer:
The results are not significantly high so there is not sufficient evidence to support the claim.
I have a question where I need to graph a hyperbola equation and all I am given is the equation Picture included
Given
The equation of the hyperbola is:
[tex]\frac{y^2}{9}\text{ -x}^2\text{ = 1}[/tex]We can see that this is a vertical hyperbola since y is positive.
The general equation of a vertical hyperbola is:
[tex]\begin{gathered} \frac{(y-k)^2}{a^2}\text{ -}\frac{(x\text{ -h})^2}{b^2}=\text{ 1} \\ Where\text{ }(h,k)\text{ is the center} \end{gathered}[/tex]The steps to graph a hyperbola are:
1. Determine if it is horizontal or vertical. Find the center point, a, and b.
2. Graph the center point.
3. Use the a value to find the two vertices.
4. Use the b value to draw the guiding box and asymptotes.
5. Draw the hyperbola.
Step 1: This hyperbola is vertical
center point = (0,0)
Step 2: The values of a and b
[tex]\begin{gathered} a^2=\text{ 9} \\ a\text{ = 3} \\ b^2\text{ = 1} \\ b\text{ = 1} \end{gathered}[/tex]Step 3: Draw the guiding box:
Step 4: Draw the asymptotes
The asymptotes are diagonal lines through the corners of the box
Step 5: Finally, we draw in our hyperbola. Each half starts at the vertex and continues towards the asymptotes but never actually reaches them.
Step 6:
The center point, guiding box, and asymptotes are not technically part of the answer, so a clean version of the graph would look like this:
The graph of the hyperbola is shown below:
In the equation 3x2 + 6x = 12, the value of c is
Explanation:
The general quadratic equation is given below as
[tex]ax^2+bx+c=0[/tex]The equation given in the question is given below as
[tex]3x^2+6x=12[/tex]By reaaranging the equation into the standard form, we will have
[tex]3x^2+6x-12=0[/tex]Hence,
The value of c is
[tex]c=-12[/tex]20x -y= 250 solve for y
y = 20x - 250
What is the solution to the equation below? Round your answer to two decimal places.5x = 55A.x = 1.04B.x = 0.40C.x = 2.49D.x = 2.40
For this problem, we are given a certain equation and we need to solve it for x.
The expression:
[tex]5^x=55[/tex]We need to apply a logarithm to both sides:
[tex]\log5^x=\log55[/tex]We can now use the properties of the logarithm to isolate the x variable.
[tex]\begin{gathered} x\log5=\log55\\ \\ x=\frac{\log55}{\log5}=2.49 \end{gathered}[/tex]The correct answer is C. x = 2.49
Could you tell me the empty box table what do I put in
We can see that for x = 0 that implies y = 10.
We can also see that for each x , y decreases 2 units, so the rate of change is -2.
The relation between x and y is a linear function:
y = 10 - 2x
Let's see if it is right.
For x = 0, we get
y = 10 - 2 . 0
y = 10
Ok!
For x = 1
y = 10 - 2 . 1
y = 10 - 2
y = 8
Ok!
For x = 2
y = 10 - 2 . 2
y = 6
Ok!
For x = 15
y = 10 - 2 . 15
y = 10 - 30
y = -20
Answer: start value: 0 ;
rate of change: -2,
relation between x and y: y = 10 -2x
Please help:y = x + 4y = x^4Graph your system of equations and show the solution graphically to verify your solution.
Given:
[tex]\begin{gathered} y=x+4 \\ y=x^4 \end{gathered}[/tex]Graphing:
green line is y = x + 4
blue line is y = x^4
The solutions are:
(-1.28, 2.72) and (1.53, 5.53)
Answer: (-1.28, 2.72) and (1.53, 5.53)
East High School has 540 students. There are 220 girls in the school. What is the ratio of girls to boys at East High School?
11/16
1) Gathering the data
540 students
220 girls
540-220= 320
320 boys
2) Let's find out the ratio of girls to boys
Placing the number of girls in the numerator, and subsequently the number of boys as the denominator
Then simplify :
So we can state there's a ration of 11/16
There are 11 girls to 16 boys in that school
Solve the equation using the order of operations 4(x-8)+14=-24
SOLUTION
Using the order of operations we have
[tex]\text{PEMDAS}[/tex]where
[tex]\begin{gathered} P=\text{parenthesis} \\ E=\text{Exponential } \\ M=\text{ Multiplication } \\ D=\text{Division } \\ A=\text{Addition } \\ S=\text{Subtraction } \end{gathered}[/tex]Note: Multiplication and Division operate at the same level but we consider the operation that appears first from the left hand sides of the equation given the same as Addition and subtraction.
Given the equation.
[tex]4(x-8)+14=-24[/tex]Expand the parenthesis
[tex]4x-32+14=-24[/tex]Add the like terms
[tex]4x-18=-24[/tex]Add 18 to both sides of the equation
[tex]\begin{gathered} 4x-18+18=-24+18 \\ 4x=-6 \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} \frac{4x}{4}=\frac{-6}{4} \\ \\ x=\frac{-3}{2} \end{gathered}[/tex]Therefore
x= -3/2
The figure shows two parallel lines AB and De cut by the transversals AE and BD ( in the picture ) Which statement best explains the relationship between ABC and EDC? A) ABC - EDC because m<3 = m<6 and m<1 = m<4B) ABC - EDC because m<3 = m<4 and m<1 = m<5 C) ABC = EDC because m<3 = m<4 and m<1 = m<5D) ABC = EDC because m<3 = m<6 and m<61 = m<4
ANSWER:
2nd option: ΔABC ~ ΔEDC, because m<3 = m<4 and m<1 = m<5
STEP-BY-STEP EXPLANATION:
In order to answer the question we must take into account the difference between similarity and congruence.
We can see it in the following image:
That is, similar have the same figure but not the same size, while congruent have the same size and the same figure.
We can see that in this case the triangles are similar, we know this since angles 3 and 4 are equal because they share a vertex.
So the correct answer is the 2nd option: ΔABC ~ ΔEDC, because m<3 = m<4 and m<1 = m<5
A GPA is usually an example of a a. b. mean bimodal distribution trimodal distribution weighted average C. d. 48
I find the following data for the concept GPA:
Your GPA is calculated in two steps:
The grade awarded for each course is multiplied by the credit value for each course.
The aggregate score is divided by the total number of credits for all courses completed in the defined period of study.
So, the weighted average reflects the relative contribution made by all the courses you have undertaken based on their credit value.
From the above data, the correct option for the answer is d. weighted average.