To determine if what Braden says is correct or not, we will remember how to determine equivalent ratios. It comes from the different ways to write the same ratio, or the same proportion, as a fraction. If we are able to show that a fraction is just a simplification of the other, than they are equivalent.
From this, let's simplify the fraction which is eq
A quantity with only magnitude is called a what?can you please explain it.
A quantity with only magnitude is called an scalar.
Hence, the answer is B.
Ordered the sides in the triangle from shortest to longest?
The sine rule states that
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]Where a is the opposite side to angle A, b is the opposite side to angle B, and c is the opposite side to angle C
In our problem:
[tex]\frac{\sin(40degree)}{EF}=\frac{\sin(55degree)}{FG}=\frac{\sin(85degree)}{EG}[/tex]Remember that the function sine is growing in the interval [0,90°]; therefore, from the first 2 equalities
[tex]undefined[/tex]Our family has a small pool for relaxing in the summer that holds 1500 gallons of water. I decided to fill the pool for the summer. When I had 5 gallons of water in the pool, I decided that I didn't want to stand outside and watch the poik fill, so I had to figure out how long it would take so that I could leave, but come back to turn off the water at the right time. I checked the flow on the hose and found that it was filling the pool at a rate of 2 gallons every minute. Use a table, a graph, and a equation to create a mathematical model for the number of gallons of water in the pool ar minutes?
Let the volume, as a function of time t, be v:
v(t) = 5 + 2t
v(t) = 5 + 2t
The mathematical model is v(t) = 5 + 2t
1/4x+1/2=5(5/6x+5)x= ?
For this problem, we need to solve the following expression:
[tex]\frac{1}{4}x+\frac{1}{2}=5(\frac{5}{6}x+5)[/tex]For that, we need to isolate the x variable on the left side:
[tex]\begin{gathered} \frac{1}{4}x+\frac{1}{2}=\frac{25}{6}x+25\\ \\ \frac{25}{6}x-\frac{1}{4}x=\frac{1}{2}-25\\ \\ \frac{2\cdot25x-3x}{12}=\frac{1-50}{2}\\ \\ \frac{47x}{12}=-\frac{49}{2}\\ \\ x=-\frac{12\cdot49}{2\cdot47}\\ \\ x=-\frac{588}{94}=-\frac{294}{47} \end{gathered}[/tex]The value for x is equal to -294/47.
Real Life Application: Page 30 Q 102 An open box of maximum volume is to be made from a square piece of material 24 cm on a side by cutting equal squares from the corners and turning up the sides (see figure). a. Write volume V as a function of x, the length of the corner squares. a. What is the domain of the function?
The image below will be needed to find the volume function
From the image above, we can see that the dimensions of the open box are
[tex](24-2x)\times x\times(24-2x)[/tex]Therefore, the volume function V is given as
[tex]V(x)=(24-2x)\times x\times(24-2x)[/tex]Thus,
[tex]\begin{gathered} V(x)=x(4x^2-96x+576) \\ V(x)=4x^3-96x^2+576x \end{gathered}[/tex]The volume function V is given by V(x) = 4x³ - 96x² + 576x
The domain of V is the values of x for which V is defined for this problem.
What is the value of the expression below? 25614 O A. 4 OB. 16 O C. 64 OD. 8
Step 1: Problem
[tex]256^{\frac{1}{4}}[/tex]Step 2: Concept
Apply theorem of exponent
Step 3: Method
[tex]\begin{gathered} 256=4^4 \\ 256^{\frac{1}{4}\text{ }}=(4^4)^{\frac{1}{4}} \\ =4^{\frac{4}{4}} \\ =4^1 \\ =\text{ 4} \end{gathered}[/tex]Step 4: Final answer
4
1 A customer in Kentucky orders a box of 25 small bags of Zollipops for $56.00. Kentucky's sales tax is 6%. What's the total cost?
A fast boat to Japan travels at a constant speed of 18.95 miles per hour for 350 hours. How far was the voyage?
we have the following:
[tex]\begin{gathered} v=\frac{d}{t} \\ d=v\cdot t \end{gathered}[/tex]replacing:
[tex]\begin{gathered} d=18.95\cdot350 \\ d=6632.5 \end{gathered}[/tex]The answer is 6632.5 miles
Find the slope of the line graphed below. 4- 3 3- 2-+ + 3 - 3 -5 - 2 2 4 5 -1 -27 - 3. 5
We are going to find the slope with the slope formula and the points (-2,1) and (2,4) (taken from the graph)
[tex]m=\frac{y2-y1}{x2-x1}=\frac{4-1}{2-(-2)}=\frac{3}{4}[/tex]The answer is equal to 3/4
A triangle has two sides of length 13 and 7. What is the smallest possible whole-numberlength for the third side?
ANSWER
6
EXPLANATION
We want to find the smallest possible length of the third side.
To do this, we apply the Triangle Inequality Rule.
It states that the sum of the two sides of a triangle must be greater than or equal to the length of the third side.
Let the length of the third side of the triangle be x.
This could then mean 3 things:
[tex]\begin{gathered} 13+7\ge x \\ 13+x\ge7 \\ x+7\ge13 \end{gathered}[/tex]Now, we have to solve each of them to find the least possible value of x:
[tex]\begin{gathered} \cdot20\ge x\Rightarrow x\le20 \\ \cdot x\ge7-13\Rightarrow x\ge-6 \\ \cdot x\ge13-7\Rightarrow x\ge6 \end{gathered}[/tex]The first option cannot work because then we are dealing with the greatest possible value of x as 20.
The second option cannot work because x cannot be a negative value.
The third option is valid.
Therefore, the smallest possible value of the length of the third side of the triangle is 6.
in the figure below, two seconds are drawn to a circle from exterior point H. Suppose that HW=72, HZ=9, and HX=14.4. Find HY.
When two secants are arranged in the form of the picture the segments must obey the following rule:
[tex]HX\cdot HY=HZ\cdot HW[/tex]Applying the data from the problem we have:
[tex]\begin{gathered} 14.4\cdot HY=9\cdot72 \\ HY=\frac{9\cdot72}{14.4} \\ HY=45 \end{gathered}[/tex]The length of HY is 45.
Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you place the card back in the deck, shuffle the deck, and draw another card. You repeat this process until you have drawn 15 cards in all. What is the probability of drawing at least 6 clubs?
The probability of drawing at least 6 clubs is 0.1484
The variable X follows a binomial distribution, because we have n identical and independent events (15 cards) with a probability p of success and 1-p of fail (there is a probability of 1/4 to be club and 3/4 to be diamond, heart or spade). Then, the probability that x of the n cards are club is:
P(x) = (^nC_x) * (p^x) * (1 - p)^n - x
P(x) = 15!/(15 - x)! * (0.25)^x * (0.75)^15 - x
So, the probability P of drawing at least 6 clubs is:
P = P(6) + P(7) + . . . + P(15)
P(6) = 15!/(15 - 6)! * (0.25)^6 * (0.75)^15 - 6
P(6) = 0.0917
P(7) = 15!/(15 - 7)! * (0.25)^7 * (0.75)^(15 - 7)
P(7) = 0.03932
P(8) = 15!/(15 - 8)! * (0.25)^8 * (0.75)^15 - 8
P(8) = 0.0131
P(9) = 15!/(15 - 9)! * (0.25)^9 * (0.75)^15 - 9
P(9) = 0.003398
P(10) = 15!/(15 - 10)! * (0.25)^10 * (0.75)^15 - 10
P(10) = 0.00068
P(11) = 15!/(15 - 11)! * (0.25)^11 * (0.75)^15 - 11
P(11) = 0.000103
P(12) = 15!/(15 - 12)! * (0.25)^12 * (0.75)^15 - 12
P(12) = 0.000102
P(13) = 15!/(15 - 13)! * (0.25)^13 * (0.75)^15 - 13
P(13) = 8.80099833e-7
P(14) = 15!/(15 - 14)! * (0.25)^14 * (0.75)^15 - 14
P(14) = 4.19095159e-8
P(x15) = 15!/(15 - 15)! * (0.25)^15 * (0.75)^15 - 15
P(15) = 9.3132257e-10
So, the probability would be,
P = P(6) + P(7) + . . . + P(15)
P = 9.3132257e-10 + 4.19095159e-8 + 8.80099833e-7 + 0.000102 + 0.000103 + 0.00068 + 0.003398 + 0.0131 + 0.03932 + 0.0917
P = 0.1484
Therefore, the probability of drawing at least 6 clubs is 0.1484
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Level 5 escape room 7th grade Regions in the shade is how the code is made
Start with the operation:
[tex]\frac{7}{9}-\frac{3}{6}=\frac{5}{18}[/tex]The denominator of this fraction is the first number of the code: 5
Now we use the last result to operate:
[tex]-\frac{8}{9}-1\text{ }\frac{5}{18}=-\frac{8}{9}-\frac{23}{18}=-\frac{13}{6}=-2\text{ }\frac{1}{6}[/tex]The denominator of this fraction is the second number of the code: 6
Now we have the horizontal rational operation: 4.7 - 2.8 = 1.9
The integer part of this number is the third number of the code: 1
Finally, we operate:
-5.8 - 2.9 = -8.7
We get the last part of the code: 7
Code: 5617
NEED HELP ASAP!!!!!!!!
The values of y/x when y is -6 and x is -1 is 6, when y is 0 and x is 1 is 0 and when y is 6 and x is 3 is 2.
According to the question,
We have the following information:
y = 3x-3
Now, in order to solve this equation we have to fill the given table with the values of x and y:
So, we have x = -1 and y = -6:
y/x = -6/-1
6
We have x = 1 and y = 0:
y/x = 0/1
0
We have x = 3 and y = 6:
y/x = 6/3
2
Hence, the values of y/x when y is -6 and x is -1 is 6, when y is 0 and x is 1 is 0 and when y is 6 and x is 3 is 2.
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The allowable shear stress of a weld is 35% of the nominal tensile strenath of the weld metal. If the nominal tensile strength is 66,000 psi, what is the allowable shear stress?
Answer:
[tex]23,100\text{ psi}[/tex]Explanation:
Here, we want to calculate the allowable shear stress
From the given question:
Allowable shear stress = 35 % of normal tensile strength
Given the normal tensile strength, we want to calculate the allowable shear stress
Mathematically:
[tex]Allowable\text{ shear stress = }\frac{35}{100}\times\text{ 66,000 psi = 23,100 psi}[/tex]Type your response in the box.Go to the graphing tool and graph these equations in the same coordinate plane. Then use the graphs you created to answer the questions.y= 3x - 2y=x+ 2What do the graphs have in common? What's different about the graphs?
Answer:
• Similarity: Point (2,4)
• Differences: y-intercepts and slopes.
Explanation:
Given the equations:
[tex]\begin{gathered} y=3x-2 \\ y=x+2 \end{gathered}[/tex]The two equations are graphed on the same coordinate plane and the graph attached below.
Similarity: The two graphs have point (2,4) in common.
Differences: The two graphs have different y-intercepts and slopes.
Note that if the slope were to be the same with different y-intercepts, they will not have any point in common.
Answer: Similarity: Both graphs are increasing as x increases.
Differences:
The graph of the equation y = x + 2 shows linear growth, and the graph of the equation y = 3x – 2 shows exponential growth.
The graph of the equation y = 3x – 2 increases faster than the graph of the equation y = x + 2.
Step-by-step explanation: Edmentum Answer
Type the correct answer in each box. Use numerals instead of words. Consider the systems of equations below. System A System B System C I2 + y2 = 17 y = 12 - 70 + 10 = y = – 2229 - 1 2 3 - y = -65 + 5 &r - y = -17 Determine the number of real solutions for each system of equations. System A has real solutions. System B has real solutions. System C has real solutions.
A) Given:
[tex]\begin{gathered} x^2+y^2=17\ldots\ldots\ldots\text{.}(1) \\ y=-\frac{1}{2}x\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]To find: The number of real solutions
Explanation:
Substitute equation (2) in (1), we get
[tex]\begin{gathered} x^2+(-\frac{1}{2}x)^2=17 \\ x^2+\frac{x^2}{4}=17 \\ \frac{5x^2}{4}=17^{} \\ x^2=\frac{68}{5} \\ x^2-\frac{68}{5}=0\ldots\ldots.(3) \end{gathered}[/tex]Here,
[tex]a=1,b=0,\text{ and c=-}\frac{68}{5}[/tex]So, the discriminant is,
[tex]\begin{gathered} \Delta=b^2-4ac \\ =0-4(1)(-\frac{68}{5}) \\ =54.4 \\ >0 \end{gathered}[/tex]Since the discriminant is greater than zero.
Hence, it has two real solutions
Final answer:
System A has two real solutions.
IV. Find the Slope of the line segment whose endpoints are given Ang (-1,-6). (-6,5) and (-4, 4), (-2, 2) and (-1,1). (5.-5) and (-3.1.-2.8). (–4.92. -3.3) and (4.9.-1.3), (-5.2,-0.6) and (3.1. -2.1), (-0.52, -0.6)
Slope of two points: (-6,5) and (4,4)
Slope of two points: (-2,2) and (-1,1)
Slope of two points: (5,-5) and (-3.1,-2.8)
Slope of two points: (-4.92,-3) and (4,4)
Solve for x
5/7(x+2)-3/7x=2/7(x+5)
Infinite
No solution
x=1
x=3
Answer:
infinite
Step-by-step explanation:
[tex]\frac{5}{7}(x+2)-\frac{3}{7}x=\frac{2}{7}(x+5) \\ \\ 5(x+2)-3x=2(x+5) \\ \\ 5x+10-3x=2x+10 \\ \\ 2x+10=2x+10[/tex]
Since we get an identity, there are infinitely many solutions.
Explain what a chord is and determine if a diameter is or is not a chord. Explain in 5-7 sentences.
Solution:
A chord is a line segment in a circle with both endpoints on the circle. It is a line whose both ends touch the circumference of a circle.
The diameter is a line that touches both ends of a circle and passes through the center of the circle. Hence, a diameter is a special chord that passes through the center of the circle and it is the longest chord in the circle.
Further explanation:
From the image shown, image 1 has a line that is not a chord because its ends do not touch the circle. Image 2 is a chord because its ends touch the circle. That is what differentiates a line from a chord. Its ends must touch the circumference of a circle.
A diameter is also a chord because it meets the condition of a chord. Its ends touch the circle.
What differentiates both is that a chord does not pass through the centre of the circle, while a diameter passes through the centre.
Therefore, a diameter is a chord.
SHOW THE EQUATION YOU SET UP10% of what number is 90?
Recall that the x% of y can be computed using the following expression:
[tex]y\cdot\frac{x}{100}\text{.}[/tex]Now, let n be the number such that its 10% is 90, then we can set the following equation:
[tex]90=n\cdot\frac{10}{100}\text{.}[/tex]Simplifying the above equation we get:
[tex]90=\frac{1}{10}n\text{.}[/tex]Multiplying the above equation by 10 we get:
[tex]\begin{gathered} 90\times10=\frac{1}{10}n\times10, \\ n=900. \end{gathered}[/tex]Answer:
Equation:
[tex]\frac{1}{10}n=90.[/tex]Number: 900.
1 Expandts implify:(X+2)(-x +3X-7 +x)
Given the following expression:
[tex]\mleft(x+2\mright)(-4x^2+3x-9+x^4)[/tex]Let's simplify;
Applying the PEMDAS Rule (Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction).
Step 1: Simplify first the equation within the parenthesis.
[tex](x+2)(-4x^2+3x-9+x^4)[/tex][tex](x+2)\text{ = (x + 2) ; already in simplified form}[/tex][tex](-4x^2+3x-9+x^4)\text{ = }(x^4-4x^2+3x-9)\text{ ; already in simplified form}[/tex]Step 2: Proceed with the multiplication.
[tex](x+2)(x^4-4x^2+3x-9)\text{ }[/tex][tex](x)(x^4-4x^2+3x-9)\text{ = }\mleft(x^4\mright)\mleft(x\mright)-(4x^2)(x)+(3x)(x)-(9)(x)=x^5-4x^3+3x^2\text{ - 9x}[/tex][tex](2)(x^4-4x^2+3x-9)\text{ = }(x^4)(2)-(4x^2)(2)+(3x)(2)-(9)(2)=2x^4-8x^2+6x-18[/tex]Step 3: Let's add the product of x and 2 being multiplied to -4x^2+3x-9+x^4.
[tex](x+2)(x^4-4x^2+3x-9)\text{ }[/tex][tex](x)(x^4-4x^2+3x-9)\text{ + }(2)(x^4-4x^2+3x-9)[/tex][tex](x^5-4x^3+3x^2\text{ - 9x) + }(2x^4-8x^2+6x-18)[/tex][tex]x^5-4x^3+3x^2\text{ - 9x + }2x^4-8x^2+6x-18[/tex][tex]x^5\text{+ }2x^4-4x^3+3x^2\text{ }-8x^2\text{- 9x }+6x-18[/tex][tex]x^5\text{+ }2x^4-4x^3-5x^2\text{-3x}-18[/tex]Therefore, the product of (x+2) (-4x^2+3x-9+x^4) is x^5 + 2x^4 -4x^3 -5x^2 -3x - 18.
Please help w/ logarithms and if you do not know how to solve just let me know and I'll exist the session :)
From the first table, we have;
Given that;
[tex]f(x)=b^x[/tex]But, table II gives;
Given that;
[tex]g(x)=\log _b(x)[/tex]Where b is same positive constant for both equations.
Recall from a law of logarithm that;
[tex]\text{If }\log _ba=c,\Leftrightarrow a=b^c[/tex]Thus;
[tex]\begin{gathered} g(x)=\log _b(x) \\ x=b^{g(x)} \\ \end{gathered}[/tex][tex]f(x)=7,x=1.404[/tex]Also;
from the second table;
[tex]x=10,g(x)=1.661[/tex]Solve for y-5y> -20 PLEASE HURRY
-5y > -20
Absolute value, there are 2 solutions:
-5y>-20 and -5y< 20
-5y>-20
Divide both sides by -5
-5y/-5 < -20/-5
y< 4
-5y < 20
Divide both sides by -5
-5y/-5 > 20/-5
y > -4
A figure has sides of length 8x, 5, 7, 6x, 6.Find the perimeter.Simplify the resulting expression.
The perimeter of any figure is the sum of all its sides. In the figure, we have the following sides:
8x, 5, 7, 6x, 6.
Perimeter is, therefore:
8x + 5 + 7 + 6x + 6
Summing similar terms:
P = (8x + 6x) + (5 + 7 + 6)
Thus, the following is the simplified expression for perimeter:
P = 14x + 18
5. 47 divided by 5 =
9.4
Explanation:47 divided by 5 = 47/5
In fraction:
47/5 = 9 2/5
In decimal, 9 2/5 = 9 + 0.4
47/5 = 9.4
find a polynomial function of lowest degree with rational coefficients
Since -5i is a zero, then its complex conjugate +5i is also a zero of the function.
Therefore,
x + 5i, x - 5i , and x - 3 are factors of the polynomial.
Hence, the polynomial function, P(x), of the lowest degree with rational coefficients is given by
[tex]P(x)=(x+5i)(x-5i)(x-3)[/tex]Which implies that
[tex]\begin{gathered} P(x)=(x^2-(5i)^2)(x-3)=(x^2-25i^2)(x-3) \\ \text{ Since i}^2=-1,\text{ then we have} \\ P(x)=(x-3)((x^2+25)=x^3+25x-3x^2-75 \end{gathered}[/tex]Hence the polynomial is
[tex]P(x)=x^3-3x^2+25x-75[/tex]Find the area of the shape use decomposition
We can divide the figure into two triangles.
As you can observe, both triangles are equal, their base is 3 units long and their height is 5 units long. The height is outside the triangle because it's an obtuse triangle. First, let's use the area formula for triangles.
[tex]A=\frac{bh}{2}[/tex]Where b = 3 and h = 5. Let's find the area of one triangle.
[tex]A=\frac{3\cdot5}{2}=\frac{15}{2}[/tex]Then, we multiply this area by 2 because there are two triangles.
[tex]A_{\text{total}}=2\cdot\frac{15}{2}=15[/tex]Therefore, the area of the shape is 15 square units.The cost to rent a car is $25 plus an additional $0.15 for each mile the car is driven. How many miles was a car driven if it had a bill of $71.80?479645454312Please explain the answer.
Since the form of the linear equation is
[tex]y=mx+b[/tex]m is the rate of change
b is the initial amount
Since the cost of the rental car is $25 and $0.15 for each mile, then
The initial amount is 25 dollars
b = 25
The rate of change is 0.15 dollars per mile
m = 0.15
Then the equation is
[tex]T.C=0.15x+25[/tex]T.C is the total cost
x is the number of miles
Since the given total cost is $71.80
Then T.C = 71.8
[tex]71.8=0.15x+25[/tex]Subtract 25 from both sides
[tex]\begin{gathered} 71.8-25=0.15x+25-25 \\ \\ 46.8=0.15x \end{gathered}[/tex]Divide both sides by 0.15
[tex]\begin{gathered} \frac{46.8}{0.15}=\frac{0.15x}{0.15} \\ \\ 312=x \end{gathered}[/tex]The car was driven for 312 miles
The answer is the last option
Select all the expressions whichrepresent the total number of bookread by Joel, Lucas and Erica.x + (2x + 3) + (5 - 4x)6x + 87x+27X-2x + (2x + 3) + (4x - 5)
Given:
Joel read x books
Lucas read 3 more than twice the number of books Joel read
So,
Lucas read 2x + 3
Erica read 5 less than four times the number of books Joel read
So,
Erica read 4x - 5
So, the total number of books read by Joel , Lucas and Erica :
x + (2x + 3) + (4x - 5)
= 7x - 2
So, the correct options are:
[tex]\begin{gathered} 7x-2 \\ x+(2x+3)+(4x-5) \end{gathered}[/tex]