Answer:
x=8/21
Step-by-step explanation:
(3/4)/(2/7) = 1/x
(3/4)x = (2/7)
x = (2/7) / (3/4)
x = (2/7) * (4/3)
x = 8/21
Use the distributive property to multiply (2w+ 7)(2w-7).
Here are the steps in multiplying binomials using the distributive property:
1. Multiply the first 2w and first 7 by the terms inside the second parenthesis/binomial. Add the products.
[tex](2w)(2w)+(2w)(-7)+(7)(2w)+(7)(-7)[/tex]2. Simplify.
[tex]4w^2-14w+14w-49[/tex]3. Combine similar terms like -14w and 14w and the result is 0.
[tex]4w^2+0-49[/tex][tex]4w^2-49[/tex]Hence, the product of the two binomials is 4w² - 49.
Can you help me understand how to do this please?
The given equation is
- 26 = 2(u - 7) - 8u
The first step is to expand the parentheses on the right side of the equation by multiplying the terms inside by the term outside. We have
- 26 = 2u - 14 - 8u
The next step is to collect like terms. The terms containing u will be on one side of the equation while the constant terms would be on the other side.
By adding 14 to both sides of the equation, we have
- 26 + 14 = 2u - 14 + 14 - 8u
- 12 = 2u - 8u
- 12 = - 6u
- 6u = - 12
Dividing both sides of the equation by - 6, we have
- 6u/- 6 = - 12/- 6
u = 2
The equation 4.05p + 14.40 = 4.50(p +3) represents the number p of pounds of peanuts you need to make trail mix. How many pounds of peanuts do you need for the trail mix?
The equation given is a one variable equation, "p".
The question asks to find the value of "p", which is the pounds of peanuts.
So, we need to solve the euqation for "p".
[tex]4.05p+14.40=4.50(p+3)[/tex]First, we need to put all the terms that have "p" in one side. For this, we will have to use the distributive property in the parenthesys first:
[tex]\begin{gathered} 4.05p+14.40=4.50p+4.50\cdot3 \\ 4.05p+14.40=4.50p+13.50 \end{gathered}[/tex]Now, we can substract 4.05p in both sides to get the "p" term of the left to the right:
[tex]\begin{gathered} -4.05p+4.05p+14.40=-4.05p+4.50p+13.50 \\ 14.40=(4.50-4.05)p+13.50 \\ 14.40=0.45p+13.50 \end{gathered}[/tex]Now, we do the same for the 13.50, substract it in both sides:
[tex]\begin{gathered} 14.40-13.50=0.45p+13.50-13.50 \\ 0.9=0.45p \\ 0.45p=0.9 \end{gathered}[/tex]Now, we can divide both sides by 0.45:
[tex]\begin{gathered} \frac{0.45p}{0.45}=\frac{0.9}{0.45} \\ p=2 \end{gathered}[/tex]So, the answer is p = 2, thus, you need 2 pounds of peanuts for the trail mix.
What is the ratio of all the apples in the bag to red and green ?
There are 11 apples on the basket, if 5 of them are green and the rest are red, to determine the number of red apples, you have to calculate the difference between the total and the number of green apples:
[tex]11-5=6[/tex]a) There are 6 red apples on the basket, the ratio of all apples to red apples can be expressed as follows:
First, write the total number of apple and then write the number of red apples, separate both values by a colon
[tex]11\colon6[/tex]b) To write the ratio of red apples to green apples you have to write the number of red apples on the basket and the number of green apples, both values separated by a colon:
[tex]6\colon5[/tex]Which graph correctly shows the solution to the inequality
explain your reasoning.
The solution for the given inequality is x≥3. Therefore, option C is the correct answer.
The given inequality is (7x-3)/9 ≥ 8-2x.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Inequality can be solved as follows:
(7x-3)/9 ≥ 8-2x
Multiply 9 on both the sides of an inequality, we get
7x-3 ≥ 9(8-2x)
⇒ 7x-3≥72-18x
Add 3 on both the sides of an inequality, we get
7x≥75-18x
Add 18x on both the sides of an inequality, we get
25x≥75
⇒ x≥3
The solution for the given inequality is x≥3. Therefore, option C is the correct answer.
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Suppose that among the 5000 students at a high school, 1200 are taking an online class and1700 prefer watching basketball to watching football. Taking an online class and preferringbasketball are independent. How many students are taking an online course and preferbasketball to football?
Solution:
Given:
[tex]\begin{gathered} total=5000 \\ n_{online\text{ class}}=1200 \\ n_{basketball}=1700 \end{gathered}[/tex]Since both events are independent, then;
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence,
[tex]\begin{gathered} P(online)=\frac{1200}{5000} \\ P(basketball)=\frac{1700}{5000} \\ Hence,\text{ } \\ P(online\cap basketball)=\frac{1200}{5000}\times\frac{1700}{5000} \\ P(online\cap basketball)=\frac{51}{625} \\ P(online\cap basketball)=0.0816 \end{gathered}[/tex]The number of students taking an online course and prefer basketball to football is;
[tex]\begin{gathered} n(online\cap basketball)=0.0816\times5000 \\ n(online\cap basketball)=408 \end{gathered}[/tex]Therefore, the number of students taking an online course and prefer basketball to football is 408
Select the correct answer from each drop-down menu.Veronica wants to cut a sheet of paper into squares with an area of 12 square inches. For the best approximation, the length of each sideof the square pleces of paper must be approximately equal to 3.46 v Inches. If each side were exactly this length, the area of eachsquare would bev square Inches.1. 11.97162. 12.04093. 16
Note that the area of a square is the square of its side.
[tex]A=s^2[/tex]If the area is 12 square inches, the side is approximately :
[tex]\begin{gathered} 12=s^2 \\ s=\sqrt[]{12} \\ s=3.46 \end{gathered}[/tex]And the area will be :
[tex]\begin{gathered} A=3.46^2 \\ A=11.9716 \end{gathered}[/tex]The answers are :
3.46 inches
and
11.9716 square inches
Four students tried to create factor rainbows for the number 81. Complete the statements below about the number 81.
3⁴ is factor rainbows for the number 81.
What does a math factor mean?
A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them.81 is a perfect square number.
Hence, we can express it as 9 × 9 = 81.
9 can further be factored as 3 × 3 = 9.
Factor of 81 = 1,3,9,27,81
negative factor of 81 = -1,-3,-9,-27,-81
prime factors of 81 = 3 * 3 * 3 * 3 = 3⁴
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Solve the following system of equations by using elimination: x + 2y = 8 -x - 3y = 2
Solve the following system of equations by using elimination:
[tex]\begin{cases}x+2y=8\ldots\ldots\text{.}(1) \\ -x-3y=2\ldots\ldots(11)\end{cases}[/tex]Using Elimination method:
[tex]\begin{gathered} \begin{cases}x+2y=8 \\ \frac{-x-3y=2}{-y=10}\end{cases}\text{+} \\ \text{divide both side by -1} \\ -\frac{y}{-1}=\frac{10}{-1} \\ y=-10 \end{gathered}[/tex]Substitute the value of y in equation (1):
[tex]\begin{gathered} x_{}+2y=8 \\ x+2(-10)=8 \\ x-20=8 \\ x=8+20 \\ x=28 \end{gathered}[/tex]Therefore the value of x = 28 and y = -10
Hence the correct answer is (x,y) = (28,-10)
which of the following is not a way to represent the solution of the inequality 2(x+1) >or equal to 20?
The only incorrect choice in the options is B.
A number line with a closed circle on 9 and shading to the left
Explanations:The given inequality is expressed as:
[tex]2\text{ (x + 1) }\ge\text{ 20}[/tex]Step 1: Open up the brackets[tex]2x\text{ + 2 }\ge\text{ 20}[/tex]Step 2: Collect like terms[tex]\begin{gathered} 2x\text{ }\ge\text{ 20 - 2} \\ 2x\text{ }\ge\text{ 18} \end{gathered}[/tex]Step 3: Divide both sides by 2[tex]\begin{gathered} \frac{2x}{2}\ge\frac{18}{2} \\ x\text{ }\ge\text{ 9} \end{gathered}[/tex]This can also be written as:[tex]9\text{ }\leq\text{ x}[/tex]Drawing this on a number line:This means that x is includes 9 and all the numbers above 9.
From the number line drawn above. A number line with a close circle on 9 and shading to the right is drawn.
John needs to wrap the edge of his rectangular desk with duct tape He knows the width is 10/8 of a meter and the length of a meter How much duct tape does he need to wrap the desks perimeter
13/4 m or 3.25 meters
1) Given the width is 10/8 meter
The length is 3/8 meter
2) To wrap the rectangular desk let's use this formula, for the Perimeter (2p):
2p= 2(w+l) Plug into w and l the measures
2p = 2(3/8 +10/8) Proceed with the sum within the parentheses
2p = 2(13/8) Distribute the factor
2p =13/4
3) Hence, the perimeter is 13/4 or 3.25 meters
Consider the following data:x-2-1 0 1P(X=x) 0.10.10.20.2Step 4 of 5: Find the value of P(X < 2). Round your answer to one decimal place.20.4
STEP - BY - STEP EXPLANATION
What to find?
P(X < 2)
Given:
[tex]P(X<2)=P(X=-2)+P(X=-1)+P(X=0)+P(X=1)[/tex]From the given table;
P(X=-2) = 0.1
P(X=-1)=0.1
P(X=0)=0.2
P(X=1)=0.2
Substitute the values into the formula above and simplify.
[tex]P(X<2)=0.1+0.1+0.2+0.2[/tex][tex]=0.6[/tex]Hence, P(X < 2)=0.6
ANSWER
0.6
the product in simplest form.
5/6 2/5
Answer:
1/3
Step-by-step explanation:
[tex]\frac{5}{6}*\frac{2}{5} = \frac{5*2}{6*5} =\frac{10}{30} = \frac{1}{3}[/tex]
5 and 5 cancel out, 2 becomes 1, and 6 simplifies to 3.
Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x))f(x) = 2x2 + 16g(x) = /5x^3
Given the functions
[tex]\begin{gathered} f(x)=2x^2+16 \\ g(x)=\sqrt[]{5x^3} \end{gathered}[/tex]First, we get the composite function
[tex]f(g(x))=f(\sqrt[]{5x^3})[/tex]To get f(√5x³), we will substitute x in f(x) with √5x³ as shown:
[tex]f(g(x))=2(\sqrt[]{5x^3})^2+16[/tex]The square root and power 2 cancel each other
[tex]\begin{gathered} f(g(x))=2(5x^3)+16 \\ \text{Simplify} \\ f(g(x))=10x^3+16 \end{gathered}[/tex]Answer:
[tex]f(g(x))=10x^3+16[/tex]Solve 5x + 6 = 7 for x.
x = 1/5
Explanations:The given equation is:
5x + 6 = 7
Step 1: Collect like terms
Note that 6 becomes -6 when it crosses to the right side of the equality sign
5x = 7 - 6
5x = 1
Step 2: Divide both sides by 5
5x / 5 = 1 / 5
x = 1 / 5
Find the opposite of the given number 18/19
The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0, then we have to invert the sign of the original number, if we have a positive one and we are told to find its opposite we just put it a negative sign, if the original number is negative then we rewrite it as a positive number.
In this case, we have 18/19, then the opposite number of it is -18/19
1. What value of x=? makes therelation not a function?2 12HRUL00-A) -5B) 0C) 4D) 6(MGSE9-12.F.IF.1) Understand Functions
In functions, for any value of x, there's a unique value for y.
On the table, in the x column, having 6 yielding two different values of y in rows 2 and 3 will mean that it's not a function because the y values must be unique.
Therefore, the answer is 6
What is the solution set of y=-1/6x+4
Convert to find the equivalent rate. 300 fluid ounces minute fluid ounces second
Answer
Explanation
We want to convert 300 fluid ounces per minute into fluid ounces per second.
Note that
1 minute = 60 seconds
We then do the conversion thus
[tex]undefined[/tex]A square window has an area of x² + 12x + 36 square feet. Find the length of oneside of the square
Solution
Given that a square window has an area of x² + 12x + 36
[tex]\begin{gathered} Area\text{ of square = l}^2 \\ Where\text{ l = length of the square} \\ Thus,\text{ length of the square= }\sqrt{Area}\text{ of the square} \end{gathered}[/tex][tex]\begin{gathered} l=\sqrt{x²+12x+36} \\ l=\sqrt{(x^2+6x+6x+36}) \\ l=\sqrt{x(x+6)+6(x+6)} \\ l=\sqrt{(x+6)(x+6)} \\ l=\sqrt{(x+6)^2} \\ l=x+6 \end{gathered}[/tex]The length of one side of the square = x+6
10. Sarah wants to buy a blouse that costs $28. Her mom said she can buy this when it goes on sale for of the original price. What will the sale price be? 18 11. A class has eighteen students. The teacher asks how many students in the class have pets and finds of 18 the students have pets. How many students do not have pets? 12. Mrs. Bennett asked each of her 30 math students to select their favorite type of pizza. 30 of the students chose cheese pizza of the students chose pepperoni pizza 3 The remaining chose sausage pizza, How many students chose sausage pizza?
Sarah wants to buy a blouse that costs $28. Her mom said she can buy this when it goes on sale for 2/7 of the original price.
2/7 part of 28 is
[tex]28\times\frac{2}{7}=8[/tex]So, the selling price will be $8.
Fernando picks a marble at random. without putting the first marble back he picks second marble at random are thertwo events dependent or independent
Given the word problem, we can deduce the following information:
1. Fernando picks a marble at random.
2. Without putting the first marble back, he picks a second marble at random.
To determine if the events are dependent or independent, we first note that dependent events influence the probability of other events, while independent events do not affect one another.
Since Fernando picks a marble without putting the first marble back, the probability of the second pick is affected.
Therefore, the answer is dependent.
A value and a sequence is times the previous value like this 8 16 32 64. How would the sequence be represented as a recursive equation?
Given:
The sequence is 8, 16, 32, 64.
The first term is 8.
[tex]undefined[/tex]What is the first step to solve 1/4x- 5=8
Given the equation :
[tex]\frac{1}{4}x-5=8[/tex]The first step is to add 5 to both sides
so,
[tex]\frac{1}{4}x-5+5=8+5[/tex]evaluate the expression 4-2i/3i
and write the result in the form a+bi
The given expression in the form of (a + ib) can be written as -
-2/3 + i(4/3).
What is a expression? What is a mathematical equation? What is Equation Modelling? What are complex numbers?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -
[tex]{\displaystyle i^{2}=-1}[/tex]
Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers
We have the following expression -
(4 - 2i)/3i
We have -
(4 - 2i)/3i
4/3i - 2i/3i
- 2/3 + i(4/3)
Therefore, the given expression in the form of (a + ib) can be written as -
-2/3 + i(4/3).
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What’s does “solve for x in terms of y” mean?
When you have a function written in explicit form with two variables(let's call them 'x' and 'y'), it is written as a combination of 'x' and 'y' equal to some constant.
[tex]\begin{gathered} F(x,y)=k \\ k\in\mathfrak{\Re } \end{gathered}[/tex]To "solve for x in terms of y", is the same as rewritting this function as an equality in the following form:
[tex]x=f(y)[/tex]Let's try an example to show how this works.
Given the following function:
[tex]y^2+x^{}=2[/tex]Now, solving for x in terms of y, is the same as rewriting x as a function of y.
[tex]x=2-y^2[/tex]Rhombus STAR has vertices S(-1,2), T(2,3), A(3,0), and R(0,-1).What is the perimeter of rhombus STAR?ABCD√344√34√104√10
INFORMATION:
We know that:
- Rhombus STAR has vertices S(-1,2), T(2,3), A(3,0), and R(0,-1)
And we must calculate the perimeter of the rhombus
STEP BY STEP EXPLANATION:
To calculate it, we must find first the measure of one of the sides.
We can find one of the sides calculating the distance between two consecutive vertices.
So, calculating the distance between vertices S and T
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(2-(-1))^2+(3-2)^2} \\ d=\sqrt{3^2+1^2} \\ d=\sqrt{10} \end{gathered}[/tex]Finally, to find the perimeter, we need to use that the rhombus has 4 equal sides. So, we the perimeter would be
[tex]\begin{gathered} perimeter=4\times\sqrt{10} \\ perimeter=4\sqrt{10} \end{gathered}[/tex]ANSWER:
D. 4√10
Find the area of the shape shown below. 7TH As 6 Asy TATUS 2 Col units? Stuck? Watch a video or use a hint. Pro Raport a problem
Answer:
Step-by-step explanation:
Hello could you please help me with this problem. Write and equation in standard form of the line that passes through (2,-3) and (-3,7).
Given:
point (2,-3) and (-3,7)
First, solve for the slope of the line
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{substitute} \\ (x_1,y_1)=(2,-3) \\ (x_2,y_2)=(-3,7) \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-(-3)}{-3-2} \\ m=\frac{7+3}{-5} \\ m=\frac{10}{-5} \\ m=-2 \end{gathered}[/tex]Now that we have solved for the slope, substitute it to the slope-intercept form y = mx + b to find the y-intercept. Use the point (2,-3) but using (-3,7) works just as well.
[tex]\begin{gathered} y=mx+b \\ -3=(-2)(2)+b \\ -3=-4+b \\ -3+4=b \\ b=1 \end{gathered}[/tex]The slope intercept form of the line is
[tex]y=-2x+1[/tex]Rearrange it to follow the standard form Ax + By = C, and we have
[tex]\begin{gathered} y=-2x+1 \\ y+2x=-2x+2x+1 \\ 2x+y=\cancel{-2x+2x}+1 \\ \\ \text{The equation of the line that passes through (2,-3) and (-3,7) in standard form is} \\ 2x+y=1 \end{gathered}[/tex]You have a bank account in which your balance increases annually at a rate of 4%. If your initial investment was $100. Write an equation that represents your balance.
Initial investment = $100
The balance increases annually at a rate = 4%
The increased amount = 4% of $100
This gives
[tex]\frac{4}{100}\times\text{\$}100=\text{\$}4[/tex]Hence the investment increase annually by $4 yearly
In the second year the investment will increase by 2 x $4 = $8
In the third year the investment will increase by 3 x $4 = $$12
This implies that
In n years
The investment will increase by n × $4 = $4n
The balance at n years is given as
Balance = Investment + year increment
This is as shown below
[tex]\text{Balnace }=\text{ \$100 }+\text{ \$4n}[/tex]