step 6
(11 - 4)x + 2
the answer is option D.
distributive
what is the distance between points (5,2) and (1,-3) on a coordinate plane?A 3B 4.1C 8.5D 6.4
We are asked to find the distance between the following two points
[tex](5,2)\: and\: (1,-3)[/tex]Recall that the distance formula is given by
[tex]d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}[/tex][tex]\begin{gathered} \mleft(x_1,y_1\mright)=\mleft(5,2\mright) \\ (x_2,y_2_{})=(1,-3) \end{gathered}[/tex]Let us substitute the given points into the above distance formula
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1_{}-5_{}})^2+({-3_{}-2})^2} \\ d=\sqrt[]{({-4})^2+({-5})^2} \\ d=\sqrt[]{16^{}+25^{}} \\ d=\sqrt[]{41} \\ d=6.4 \end{gathered}[/tex]Therefore, the distance between the given two points is 6.4
Option D is the correct answer.
(1/4) raised to the power of (x-2)=16I'll upload a picture
Answer
x = 0
Explanation
[tex]\begin{gathered} (\frac{1}{4})^{x-2}=16 \\ 4^{-1(x-2)}=4^2 \\ 4^{-x-2}=4^2 \\ \text{Equate both sides of the equation} \\ -x+2=2 \\ -x=2-2 \\ -x=0 \\ x=0 \end{gathered}[/tex]A researcher wants to know if eating a mint affects whether people can distinguish between two popular orange juice brands. To conduct an experiment, the researcher places 50 participants in two groups. The treatment group will eat a mint before drinking a juice, while the control group will not eat a mint before drinking. Then the participants will guess the juice brand. To select the groups, the researcher labels each participant with a number and selects slips of paper labeled 1–50 from a bowl at random. The first 25 participants whose numbers are selected will be the treatment group, while the other 25 will be the control group.
The characteristics of the two groups
should be roughly equivalent because both groups will have 25 participants.
should be roughly equivalent because the participants were labeled and then randomly selected for the groups.
might not be roughly equivalent because one group may contain people that drink more juice than the other group.
might not be roughly equivalent because one group may contain more people that prefer a particular juice brand.
By the concept of probability D might not be roughly equivalent because one group may contain more people that prefer a particular juice brand.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty. A probability is a number that expresses the likelihood or chance that a specific event will take place. Probabilities can be stated as proportions between 0 and 1, or as percentages between 0% and 100%. The likelihood that something will happen is called the probability. the total number of conceivable outcomes. For instance, there is a 1 in 2 chance of tossing a coin and getting heads.
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Round .00000572. Using single digit and power of 10
Given that
There is a number and we have to round it using the single digit and in powers of 10.
Explanation -
Whenever we convert a decimal number into powers of 10.
The power of 10 is always equal to the negative number of digits after the decimal.
Then, the number 0.00000572 can be written as0
[tex]0.00000572=5.72\times10^{-6}[/tex]Now we have to round off it to a single digit.
Then,
[tex]5.72\times10^{-6}\approx6\times10^{-6}[/tex]Final answer -
Therefore the final answer is 6 x 10^(-6)The hypotenuse of an isosceles right triangle is 6cm longer than either of its legs. Note that an Isosceles right triangle is a right triangle whose legs are the same length, find the exact length of its legs and it’s hypotenuse
We know by the pythagorean theorem that
We know that the length of the hypotenuse squared will be equal to the sum of the legs squared. The problem says that the legs have the exact same length and the hypotenuse is 6cm longer, so we can write
Where "a" is the leg length, see that we can apply the pythagorean theorem here, and it will be
[tex]a^2+a^2=(a+6)^2[/tex]See that now c = a + 6, and b = a.
We can simplify that expression
[tex]2a^2=(a+6)^2[/tex]We know that
[tex](a+6)^2=a^2+12a+36[/tex]Therefore our equation will be
[tex]2a^2=a^2+12a+36[/tex]Now we pass all the terms for one side and we will have a quadratic equation
[tex]-a^2+12a+36=0[/tex]We can use the formula for the quadratic equation and find out the solutions
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Using it
[tex]\frac{-12\pm\sqrt[]{12^2-4\cdot(-1)\cdot36}}{2\cdot(-1)_{}}[/tex]Now we can just do all the calculus
[tex]\frac{-12\pm\sqrt[]{144^{}+144}}{-2_{}}=\frac{12\pm\sqrt[]{2\cdot12^2}}{2}=\frac{12\pm12\sqrt[]{2}}{2}[/tex]Then the solution are
[tex]\begin{cases}a_1=6+6\sqrt[]{2} \\ a_2=6-6\sqrt[]{6}\end{cases}[/tex]Even though we have two solution, see that the second one is negative, and we can't have negative length! Then the length of its legs will be
[tex]a=6+6\sqrt[]{6}[/tex]And the hypotenuse will be a + 6, then
[tex]h=6+6+6\sqrt[]{6}=12+\sqrt[]{6}[/tex]Therefore, the legs and the hypotenuse length is
[tex]\begin{gathered} l=6+\sqrt[]{6} \\ h=12+6\sqrt[]{6} \end{gathered}[/tex]We can write it approximately as
[tex]\begin{gathered} l=14.485\text{ cm} \\ h=20.485\text{ cm} \end{gathered}[/tex]If we want a more rough approximation we can say it's
[tex]\begin{gathered} l=14.5\text{ cm} \\ h=20.5\text{ cm} \end{gathered}[/tex]-5ln+4l<15 true or false
So, for values lesser than -1 and greater than -7 this inequality is true.
In this inequality let's work applying the Absolute Value properties
1) -5ln+4l<15 Dividing both sides by 5
-|n+4|<3
|n+4|>-3
2) Applying Absolute value properties
|n+4|>-3
|n+4|>-3
n+4-4>-4-3
n>-4-3
n>-7
|n+4|>3
n+4>3
n+4-4>3-4
n>-1
3) So n < -1 and >-7
So for values lesser than -1 and greater than -7 this inequality is true.
There are 8 roses in a vase of 11 flowers. The rest are daisies.(a) What is the ratio of roses to daisies?0(b) What is the ratio of daisies to all flowers in the vase?0$ P
Let
x -----> number of roses
y-----> number of daisies
we have that
x=8
y=11-8=3
so
Part A
What is the ratio of roses to daisies?
ratio=x/y --------> ratio=8/3 or 8:3
Part B
What is the ratio of daisies to all flowers in the vase?
ratio=y/(x+y) -------> ratio=3/11 or 3:11
Does the quadratic functionf(x) = 4x2 – 12x + 9 have one,two, or no real zeros? Utilize thequadratic formula to determinethe answer[?] real zero(s)-b Vb2 - 4acRemember the quadratic formula: x =
SOLUTION
Step1: Write out the equation
[tex]y=-2x^2-4x+2[/tex]Compare the equation with the general form of a quadratic equation
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{then } \\ a=-2,b=-4,c=2 \end{gathered}[/tex]Step2 Write out the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Step3: Substitute the parameters in step1
ASAP Please help and ThankyouThis graph shows how the total distance jack has walked depends on the number of trips he has made to school. What is the rate of change?
we will take two points on the line,
first is (0,2) and other is (1, 4)
the rate of change will be the slope of the line,
[tex]\begin{gathered} m=\frac{4-2}{1-0} \\ m=\frac{2}{1}=2 \end{gathered}[/tex]so the rate of the change is 2 km per trip
so the answer is 2
55 pointsWhen the equation log. ( VnUn = 3 is solved for n in terms of a, where a > 0,a # 1, the resulting equation isn=adn = 03ооооn = 9n = 26Previous
please wait the question is downloading
the answer is
n=a^69000 Employees 24 hours a day 365 days a week how many man hours a year
Answer: 2096 work hours per year
Evaluate the function for the given value of x.p(x) = x2-9x, q(X) = VX-6,(p. q)(x) = ?
The functions are:
[tex]\begin{gathered} p(x)=x^2-9x \\ q(x)=\sqrt[]{x-6} \end{gathered}[/tex]So the product (p*q) is
[tex](p\cdot q)(x)=(x^2-9x)(\sqrt[]{x-6})[/tex]So the solution is is B)
The dancer at (4,1) needs hair gel. She moved to the right on a slope of 8. Where can you deliver her hair gel? Will you please provide a graph and a written detailed explanation? Thank you!
It is given that the dancer is at the point (4,1), and then moved to the right on a slope of 8.
It is required to find the point she can be located by showing a graph with a detailed explanation.
Recall that the slope is the measure of the steepness of a line calculated by dividing the vertical change by the horizontal change.
Since the slope is given as 8, and this can be written as 8/1. It follows that the vertical change is 8 and the horizontal change is 1.
To find the new point add 1 to the x-coordinate (which represents the horizontal) and 8 to the y-coordinate (which represents the vertical):
[tex](4,1)\rightarrow(4+1,1+8)=(5,9)[/tex]Hence, the new position is at the point (5,9).
This is illustrated in the graph below:
The gel can be delivered at (5,9) as shown above.
Leann determines the volume of the cylinder shown using the formula V=Bh.
We have that the base of the cylinder is a circle, and the area of a circle can be calculated with the following equation:
[tex]B=\pi\cdot r^2[/tex]In this case, we have the following:
[tex]\begin{gathered} \pi=3.14 \\ r=\frac{d}{2}=\frac{6}{2}=3 \\ \Rightarrow B=(3.14)(3)^2=(3.14)(3)(3) \end{gathered}[/tex]therefore, the area of the base is B=(3.14)(3)(3) = 28.26 cm^2
2. Ifa 28% tip is left on a restaurant bill of $80, find the total amount of the bill including
To find 28% of $80, we have to first convert 28% to decimal, then multiply $80 with it.
28% = 28/100 = 0.28
Now,
[tex]0.28\times80=\$22.4[/tex]The total amount of bill INCLUDING the tip is the total bill added to the tip amount. That is:
[tex]80+22.4=\$102.40[/tex]Total Amount:$102.40
You and a friend go to Efren’s Tacos and Burritos for lunch. You order 2 tacos and 2 burritos for a total of $9.00. Your friend orders 1 taco and 3 burritos for a total of $10.50. Create a system of equations and solve for how much each burrito costs and how much each taco costs.
Use b as your variable for burritos and t as your variable for tacos.
PLEASE SOMEONE ANSWER THIS FAST
Each burrito costs $3 and each taco costs $1.50.
How to calculate the equation?Let b = variable for burrito
Let t = variable for tacos.
The equation based on the information will be illustrated as:
t + 3b = 10.50 .... i
2b + 2t = 9 ..... ii
From equation i, t = 10.50 - 3b. Put this into equation ii
2b + 2t = 9 .
2b + 2(10.50 - 3b) = 9
2b + 21 - 6b = 9
Collect like terms
4b = 12
b = 12/4
b = 3
Burrito = $3
Since t + 3b = 10.50
t + 3(3) = 10.50
t + 9 = 10.50
t = 10.50 - 9
t = 1.50
Taco= $1.50
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Econ The area of a square is 36 square meters. What is the length (in meters) of one side of the square
We have the following equation of the area of a square:
[tex]A=s^2[/tex]where s is the length of the side.
In this case, we have that the area is 36 square meters, then:
[tex]\begin{gathered} A=36m^2=s^2 \\ \Rightarrow s^2=36 \end{gathered}[/tex]if we apply the square root on both sides we get:
[tex]\begin{gathered} \sqrt[]{s^2}=\sqrt[]{36}=6 \\ \Rightarrow s=6 \end{gathered}[/tex]therefore, the measure of the side of the square is 6 meters
Instructions: Create a table of values for the given function.
Given the function:
f(x) = 4x - 4
We re asked to create a table of values for thhe above function.
In order to create the tabe of value, we will use the x values give n in the table to replace the value of x in the function.
When x = -2
f(x) = 4(-2) - 4
= -8 - 4
= -12
When x = -1
f(x) 4(-1() - 4
= -4 - 4
= -8
When x = 0
f(x) = 4(0) - 4
= 0 - 4
= -4
When x = 1
f(x) = 4(1) - 4
= 4 - 4
= 0
When x = 2
f(x) = 4(2) - 4
= 8 - 4
= 4
So, let's complete the table:
x y
-2 -12
-1 -8
0 -4
1 0
2 4
Solve for x. x - 4= -12 A. -8 B. -16C. 16 D. 8
Given that;
[tex]x-4=-12[/tex]STEP 1: Add 4 to both sides of the equation;
[tex]x-4+4=-12+4[/tex]STEP 2: Simplify further;
[tex]x=-8[/tex]CORRECT OPTION: A
How many baseballs with a diameter of 2.90inches, can fit into a box that is 48in x 40in x36in?
Answer:
5413 baseballs
Explanation:
Dimensions of the box = 48in x 40in x 36in.
The diameter of one baseball = 2.90 inches
Radius = Diameter ÷ 2 = 2.90 ÷ 2 =1.45 Inches
First, we find the volume of one of the baseball.
The baseball is in the shape of a sphere and:
[tex]\text{Volume of a Sphere}=\frac{4}{3}\pi r^3[/tex]Therefore, the volume of one baseball will be:
[tex]\begin{gathered} =\frac{4}{3}\times\pi\times1.45^3 \\ =12.77in^3 \end{gathered}[/tex]Next, we find the volume of the box.
[tex]\begin{gathered} \text{Volume of the box}=48\times40\times36 \\ =69120in\text{.}^3 \end{gathered}[/tex]Therefore, the number of baseballs that will fit into the box will be:
[tex]\begin{gathered} \frac{\text{Volume of the box}}{Volume\text{ of one baseball}}=\frac{69120}{12.77}=5412.7 \\ \approx5413 \end{gathered}[/tex]find the solution of this system of equations2x-2y=149x+4y=37
2x-2y=14
9x+4y=37
Multiply the first equation by 2, and then add both :
4x-4y=28
+
9x+4y=37
_______
13x = 65
Divide both sides of the equation by 13
13x/13 = 65/13
x= 5
Replace x on any equation and solve for y:
2x-2y=14
2(5)-2y=14
10-2y= 14
Subtract 10 from both sides:
10-10-2y= 14-10
-2y= 4
Divide both sides by -2
-2y/-2 =4/-2
y= -2
Solution:
x=5
y= -2
35 06286 rounded to the nearest ten thousandth is
35. 06 286 = 35.0629
Find the total value of the investment after the time given: $36,000 at 13.7% compounded semiannually for 2 years
A = P ( 1 + r/n ) ^ nt
P is the principle which is 36000
r is the rate which is 13.7 % or .137 in decimal form
n is the number of time per year, semi annual means 2 times per year
t is the time = 2
A = 36000( 1 + .137/2) ^ (2*2)
36000( 1 + .137/2) ^ (4)
Choose all properties that were used to simplify the following problem:
[38 + 677] + (-38)
[677 + 38] + (-38)
677 + [38 + (-38)]
677 + 0
677
additive identity
additive inverse
commutative property of addition
associative property of addition
distributive property
The property used in this problem are
commutative property of additionassociative property of additionadditive inverseadditive identityProperty of numbers.
We know that, there are four basic properties of numbers.
They are commutative, associative, distributive, and identity.
Given,
Here we have the problem
[38 + 677] + (-38)
[677 + 38] + (-38)
677 + [38 + (-38)]
677 + 0
677
Now, we need to identify all properties that were used to simplify the problem.
In the first step of the problem is,
[38 + 677] + (-38)
We have used the commutative property of addition to interchange the given numbers in the brackets,
[677 + 38] + (-38)
Now, we have to use the associative property of addition to group the numbers,
677 + [38 + (-38)]
Then we have to use the additive inverse, to get the value of brackets,
677 + 0
Finally we have to use the additive identity to get the result.
677
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In the quadratic formula the expression b^2-4ac is called the _____1 maximum value 2 discriminant3 minimum value
ANSWER :
Discriminant
EXPLANATION :
b^2 - 4ac in quadratic formula determines if the roots are real or imaginary.
It is called discriminant.
to a certain meeting room a college charge a reservation fee of $37 and a ln additional fee of $9.40 per hour. the math club wants to spend less than $ 93.40 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room. use t for the number of hours the meeting room is rented and solve your inequality for t
For the information given in the statement, you have the inequality:
[tex]\text{ \$37+\$9.40t < \$93.40}[/tex]Now, to solve the inequality, subtract $37 from both sides of the inequality.
[tex]\begin{gathered} \text{ \$37+\$9.40t -\$37< \$93.40 - \$37} \\ \text{ \$9.40t < \$}56.4 \end{gathered}[/tex]Now, divide by $9.40 into both sides of the inequality
[tex]\begin{gathered} \text{ \$9.40t < \$}56.4 \\ \frac{\text{ \$9.40t }}{\text{ \$9.40}}\text{< }\frac{\text{\$}56.4}{\text{ \$9.40}} \\ t<6 \end{gathered}[/tex]Therefore, the math club could rent the meeting room for a maximum of 6 hours.
4. Which of the following expressions will have the same value as the expression below? -7-(-5)A. -7+(-5)B. -7-5C. 7+(-5)D. -7+5
1) Let's operate this expression -7 -( -5)
-7 -( -5) The minus before the parentheses work as -1 x (-5)
-7 +5
-2
2) Examining each expression
a) -7+(-5) = -7 -5 = -12
b) -7-5= -12
c) 7-5 = 2
d) -7+5 = -2
3) So according to the options, the answer is D
What is 505 divided by 2, if there is a remainder, please say it in your answer or explanation.
Answer:
252,5 or 2,525 rounded.
Step-by-step explanation:
Rounding explanation:
2525_
You rounded to the nearest one's place. The 5 in the ones place rounds down to 5, or stays the same because the digit to the right in the tenth place is _.
2,525
When the digit to the right is less than 5 we round toward 0.2525 was rounded down toward zero to 2,525
what is the dependent variable to the following equationy=3x+9
hello
to solve this question, let's identify the independent an dependent variable.
*independent variable: this is the variable that can stand alone on it own. It is usually equated with the rest of the equation.
in this question, the independent variable is y
*dependent variable: this is the variable that can't stand on it's own and also depends on the other side of the equation.
in this question, the dependent variable is x
One serving of mikes crackers has 150 calories and a mass of 30 grams. how many calories are in y of the crackers
one serving has 150 calories and a mass of 30 g
1 gram= 150/30 = 5 calories
so y grams = y x 5 calories = 5y calories