The distributive property of multiplication states the following:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]So, for the given expression, we have:
[tex]-3(x+3)=(-3)\cdot x+(-3)\cdot3=-3x-9[/tex]Which equation has the same solution as x2 + 8x – 17 = -8? Submit Answer (3-4)2 = -7 O (2+4)2 = 25 O (x – 4)2 = 25 (x - 1)² = -7 problem 3 out of max 6
Given
[tex]x^2+8x-17=-8[/tex]
Procedure
[tex]\begin{gathered} x^2+8x+16-16-17=-8 \\ (x+4)^2=16+17-8 \\ (x+4)^2=25 \end{gathered}[/tex]
The answer would be (x+4)^2 = 25
=GEOMETRYPythagorean TheoremFor the following right triangle, find the side length x. Round your answer to the nearest hundredth.
From the triangle, we have:
c = 13
b = 7
Let's solve for a.
The triangle is a right triangle.
To find the length of the missing sides, apply Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]We are to solve for a.
Rewrite the equation for a:
[tex]a^2=c^2-b^2[/tex]Thus, we have:
[tex]\begin{gathered} a^2=13^2-7^2 \\ \\ a^2=169-49 \\ \\ a^2=120 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{120} \\ \\ a=10.95 \end{gathered}[/tex]ANSWER:
[tex]10.95[/tex]how many liters of 10% salt water do you need to add to 5 liters of 25% salt to make 15% salt?
Answer:
You will need 10 liters of 10% salt water
Step-by-step explanation:
Determine whether each expression can be used to find the length of side RS.
ANSWER:
[tex]\begin{gathered} \sin (R)\rightarrow\text{ Yes} \\ \tan (T)\rightarrow\text{ No} \\ \cos (R)\rightarrow\text{ No} \\ tan(R)\rightarrow\text{ No} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
Since we know a side and the hypotenuse, we can rule out tangent and cotangent, since these are related to the two legs.
Therefore, if we want to know that side we must apply sine or cosine, just like this:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{ hypotenuse}} \\ \text{therefore, in this case:} \\ \sin R=\frac{21}{35} \\ \cos \theta=\frac{\text{adjacent}}{\text{ hypotenuse}} \\ \cos R=\frac{\text{unknown}}{35} \end{gathered}[/tex]Therefore, the way to calculate the value of the missing side is by means of the sine of the angle R
The width of a rectangle measures (4.3q - 3.1) centimeters, and its length
measures (9.6q-3.6) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
The expression that represents the perimeter and the of the rectangle is: 14.6q - 13.4.
What is the Perimeter of a Rectangle?A rectangle's perimeter if the length of its surrounding borders. Thus, the perimeter of a rectangle is the sum of all the length of the sides of the rectangle which can be calculated using the formula below:
Perimeter of a rectangle = 2(length + width).
Given the following:
Width of the rectangle = (4.3q - 3.1) centimetersLength of the rectangle = (9.6q - 3.6) centimetersTherefore, substitute the expression for the width and length of the rectangle into the perimeter of the rectangle formula:
Perimeter of rectangle = 2(9.6q - 3.6 + 4.3q - 3.1)
Combine like terms
Perimeter of rectangle = 2(7.3q - 6.7)
Perimeter of rectangle = 14.6q - 13.4
Learn more about the perimeter of rectangle on:
https://brainly.com/question/24571594
#SPJ1
Hello, can you help me with a Standard deviation question, please?
To now how many had a score under 66, we have to calculate the following probability
[tex]P(X<66)=P(Z<\frac{66-81}{5})=P(Z<-3)=0.0013[/tex]So the amount of people that had a score under 66 is
[tex]4502\cdot0.0013=5.86\approx6[/tex]So 6 people get a score under 66
Find all X values where the tangent line to the graph of the function…
Consider the function,
[tex]f(x)=6\sin x+\frac{9}{8}[/tex]The first derivative gives the slope (m) of the tangent of the curve,
[tex]\begin{gathered} m=f^{\prime}(x) \\ m=\frac{d}{dx}(6\sin x+\frac{9}{8}) \\ m=6\cos x+0 \\ m=6\cos x \end{gathered}[/tex]The equation of the line is given as,
[tex]y-3\sqrt[]{3}x=\frac{7}{3}[/tex]This can be written as,
[tex]y=3\sqrt[]{3}x+\frac{7}{3}[/tex]Comparing with the slope-intercept form of the equation of a line, it can be concluded that the given line has a slope,
[tex]m^{\prime}=3\sqrt[]{3}[/tex]Given that the tangent to the curve is parallel to this line, so their slopes must also be equal,
[tex]\begin{gathered} m=m^{\prime} \\ 6\cos x=3\sqrt[]{3} \\ \cos x=\frac{\sqrt[]{3}}{2} \\ \cos x=\cos (\frac{\pi}{6}) \end{gathered}[/tex]Consider the formula,
[tex]\cos A=\cos B\Rightarrow A=2k\pi\pm B[/tex]Applying the formula,
[tex]x=2k\pi\pm\frac{\pi}{6}[/tex]Thus, the required values of 'x' are,
[tex]x=2k\pi\pm\frac{\pi}{6}[/tex]Therefore, options 1st and 2nd are the correct choices.
5. Prove triangle ABD is congruent to triangle CDB. DC|AB D
Given g=(1+2a)/a, solve for the variable a.
We are given the equality
[tex]g=\frac{1+2a}{a}[/tex]and told to solve for a. That is, we should apply mathematical operations on both sides of the equality so we "isolate" variable a on one side of the equality. We start by multiplying both sides by a, so we get
[tex]a\cdot g=1+2a[/tex]Now, we subtract 2a from both sides. We get
[tex]a\cdot g-2a=1[/tex]We can factor on the left side a as a common factor, so we get
[tex]a\cdot(g-2)=1[/tex]Finally, we divide by (g-2) on both sides, so we get
[tex]a=\frac{1}{g-2}[/tex]Give two examples when you would need to know the perimeter and two examples of when you would need to know the area.
Perimeter is the distance around a figure. The instances where we need to find perimeter include
1) The total length of the boundary of a marked field. This would involve adding the distance around it. Both the curved and straight paths
2) The length of barbed wire to be placed on a fence would require us to find the distance round the fence
The area of a shape is the space enclosed within the perimeter of the shape. The instances where we need to find area include
1) The area of a wall is calculated to determine how much paint is needed to paint it. The paint is used per square unit.
2) The area of a field is calculated to determine the cost of mowing it since the cost is calculated per unit square
Determine an algebraic model of a function that satisfies the following key features.
Solution:
Given the conditions;
[tex]As\text{ }x\rightarrow-\infty,y\rightarrow\infty\text{ and }x\rightarrow\infty,y\rightarrow\infty[/tex]When;
[tex]x\rightarrow-\infty,y\rightarrow\infty[/tex]Then, the degree of the polynomial is even.
Then, given three x-intercepts, it means one of the root could have been repeated.
Thus, the model function is;
[tex]f\lparen x)=\left(x+1\right)\left(x-3\right)\left(x^2\right)[/tex]Please help with the question below (please try to answer in maximum 5/10 minutes).
Given
Joshira can create 1 item in 3/4 of an hour.
To find:
How many items can she create in 8 hours?
Explanation:
It is given that,
Joshira can create 1 item in 3/4 of an hour.
That implies,
[tex]\begin{gathered} Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }\frac{3}{4}\text{ }hour=1 \\ Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }1\text{ }hour=1\div(\frac{3}{4}) \\ =1\times\frac{4}{3} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, number of items created in 8 hours is,
[tex]\begin{gathered} Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }8\text{ }hours=\frac{4}{3}\times8 \\ =\frac{32}{3} \\ =\frac{30+2}{3} \\ =\frac{30}{3}+\frac{2}{3} \\ =10+\frac{2}{3} \\ =10\frac{2}{3}\text{ }items \end{gathered}[/tex]Hence, she can create 10 2/3 items in 8 hours.
9) Professor Elderman has given the same multiple-choice final exam in his Principles ofMicroeconomics class for many years. After examining his records from the past 10 years, hefinds that the scores have a mean of 76 and a standard deviation of 12.Professor Elderman offers his class of 36 a pizza party if the class average is above 80. What isthe probability that he will have to deliver on his promise?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
score:
mean = 76
standard deviation = 12
Step 02:
probability:
normal distribution:
normal distribution diagram:
mean + 1 standard deviation = 76 + 12 = 88
probability (class average score is above 80):
p (score > 80) = 34% + 13.5% + 2.4% + 0.1% = 50% = 0.5
The answer is:
p (score > 80) = 50% = 0.5
Plot the vertex of f(x) = (x − 2)2 + 2.
Take into account that the general function of a parabola in vertex form is given by:
[tex]f(x)=a(x-h)^2+k[/tex]where (h,k) is the vertex of the parabola.
By comparing the previous general function with the given function:
[tex]f(x)=(x-2)^2+2[/tex]you can notice that:
h = 2
k = 2
Hence, you can conclude that the vertex of the given function is (2,2)
if q(x)= int 0 ^ x^ 3 sqrt 4+z^ 6 dz then
Solution:
Given that:
as the x increases by 1, what will the rate of change for y in this equation y=-3x+10
Answer:
Rate of change = -3
Explanation:
Given the equation:
[tex]y=-3x+10[/tex]When x=1
[tex]\begin{gathered} y=-3(1)+10 \\ =-3+10 \\ =7 \end{gathered}[/tex]When x=2
[tex]\begin{gathered} y=-3(2)+10 \\ =-6+10 \\ =4 \end{gathered}[/tex]Observe that the value of y decreases by 3 as the x increases by 1.
Thus, the rate of change is -3.
Alternate Route
Another way is to express and compare the line with the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=-3x+10 \end{gathered}[/tex]The rate of change is the coefficient of x.
Coefficient of x = -3
Thus, the rate of change is -3.
hello, in the picture you can see a graph and my teacher said that the domain and range would be all real numbers possible. could you please help me because I don't understand why.
The domain is all the values of the independent variable (in this case, x) for which the function is defined.
In this case, as it is indicated with the arrows in both ends, the function continues for greater and smaller values of x.
As there is no indication that for some value or interval of x the function is not defined (a discontinuity, for example), then it is assumed that the function domain is all the real values.
Example function:
We have the function y=1/(x-2)
We can look if there is some value of x that makes the function not defined.
The only value of x where f(x) is not defined is x=2. When x approximates to 2, the value of the function gets bigger or smaller whether we are approaching from the right or from the left.
Then, the function is not defined for x=2. So, the domain of f(x) is all the real numbers different from x=2.
The domain is, by default, all the real numbers, but we have to exclude all the values of x (or intervals, in some cases like the square roots) for which f(x) is not defined.
in the figure below, RTS is an isosceles triangle with sides SR=RT, TVU is an equilateral triangle, WT is the bisected of angle STV, points S, T, and U are collinear, and c= 40 degrees.I'm completely lost and have to answer for a, b+c, f, b+f, a+d, e+g
Step 1: Concept
Triangle SRT is an isosceles triangle with equal base angles a = b
Triangle TUV is an equilateral triangle with all angles equal: g = d = h
Step 2: Apply sum of angles in a triangle theorem to find angle a and b.
[tex]\begin{gathered} a+b+c=180^o \\ c=40^o \\ \text{Let a = b = x} \\ \text{Therefore} \\ x\text{ + x + 40 = 180} \\ 2x\text{ = 180 - 40} \\ 2x\text{ = 140} \\ x\text{ = }\frac{140}{2} \\ x\text{ = 70} \\ a\text{ = 70 and b = 70} \end{gathered}[/tex]Step 3:
2) a = 70
3) b + c = 70 + 40 = 110
Step 4:
Since WT is a bisector of angle STV,
Angle f = e = x
b + f + e = 180 sum of angles on a straight line.
b = 70
70 + x + x = 180
2x = 180 - 70
2x = 110
x = 110/2
x = 55
Hence, f = 55
4) f = 55
5) f + b = 55 + 70 = 125
Step 5:
Since triangle TUV is an equilateral triangle, angle g = h = d = 60
g = 60
h = 60
d = 60
6) Angle a + d = 70 + 60 = 130
7) e + g = 55 + 60 = 115
Lawn20 meters-WalkwayGazeboRHQ15 metersA bag of grass seed costs $64.26. If agardener wants to calculate the costofgrass seed required to plant the lawn,what additional information wouldhe need to know?A the location of the walkwayBthe perimeter of the lawnс the weight of one bag of grass seedD the area that can be covered byone bag of seed
He needs option D. Because the perimeter is not the total area (it is only the distance in meters/centimeters that surround the lawn, we need to know how much area a bag of grass seeds covers, for us to know how many to buy. Also, we need the area of the walkway, since it is not covered by grass
The area of a triangle is:
[tex]Area\text{ = }\frac{b(h)}{2}[/tex]But, since there is a walkway that isn't covered in grass, we need to subtract the circle area from the triangle area
Area of circle:
[tex]Area\text{ = }\pi r^2[/tex]Then the total area of the lawn :
[tex]Area\text{ Lawn = }\frac{b(h)}{2}\text{ - \lparen}\pi r^2)[/tex]As a test engineer, you are in charge of maintaining an experimental aircraft . According to the maintence manual, you need to inspect a wing every 10 flight hours. The aircraft flown 3 flights, each lasting 2.75 hours Since the last inspection. How many hours do you need before the wing should be inspected?
EXPLANATION
Let's see the facts:
Inspect period = 10 flight hours
Flown= 3 flights/2.75 hours
Total flights hours = 3x2.75 = 8.25 hours
The difference is 10-8.25 = 1.75 hours.
We need 1.75 hours more before the next wing inspection.
Find two points on the graph of this function other than the origin that fits in the given grid express each coordinate as an integer or simplified fraction or around four decimal places as necessary another coordinates to plot points on
Substitute arbitrary values of x for which -10 < h(x) < 10.
In this instance, we can use x = 1, and x = -1
[tex]\begin{gathered} h(x)=-\frac{5}{8}x^5 \\ h(1)=-\frac{5}{8}(1)^5 \\ h(1)=-\frac{5}{8} \\ h(1)=-0.625 \\ \\ h(x)=-\frac{5}{8}x^{5} \\ h(-1)=-\frac{5}{8}(-1)^5 \\ h(-1)=\frac{5}{8} \\ h(-1)=0.625 \end{gathered}[/tex]Therefore, the points that fits in the grid in the function h(x) are (1, -0.625) and (-1, 0.625).
The rat population in major metropolitan city is given by the formula n(t)=40e^0.015t where t is measured in years since 1991 and n(t) is measured in millions. What does the model predict the rat population was in the year 2008?
To use the model we need to find the value of t. To do this we substract the year we want to know from the year the model began, then:
[tex]t=2008-1991=17[/tex]Now that we have t we plug it in the function:
[tex]n(17)=40e^{0.015\cdot17}=51.618[/tex]Therefore the model predict that there were 51.618 millions of rats in 2008.
State the rational number represented by each letter on the number line as a decimal.
The rational number represented by the letter D is -43/100 and by the letter R is -46/100.
What is rational number?
A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
Here the number line is divided into 10 division with equal distance.
Each division is of the distance 0.01
So, the decimal number represented by letter D is -0.43 and by the letter R is -0.46.
To convert decimal number into rational number,
-0.43 = -43/100
-0.46 = -46/100
Therefore, the rational number represented by each letter on the number line as a decimal are D = -43/100 and R = -46/100.
To know more about the rational number, click on the link
https://brainly.com/question/12088221
#SPJ13
Copper has a density of 4.44 g/cm3. What is the volume of 2.78 g of copper?
60 points please help
The volume of 2.78 g of copper is 0.626 [tex]cm^{3}[/tex].
According to the question,
We have the following information:
Density of cooper = 4.44 [tex]g/cm^{3}[/tex]
Mass of copper = 2.78 g
We know that the following formula is used to find the density of any material:
Density = Mass/volume
Let's denote the volume of copper be V.
Now, putting the values of mass and density here:
4.44 = 2.78/V
V = 2.78/4.44
V = 0.626 [tex]cm^{3}[/tex]
(Note that the units if mass, volume and density are written with the numbers. For example, in this case, the unit of mass is grams, the unit of volume is [tex]cm^{3}[/tex].)
Hence, the volume of the copper is 0.626 [tex]cm^{3}[/tex].
To know more about volume here
https://brainly.com/question/1578538
#SPJ1
1. Which of the following is NOT a linear function? (1 point ) Oy=* -2 x x Оy - 5 ya 0 2. 3*- y = 4 3.
hello
to solve this question we need to know or understand the standard form of a linear equation
the standard form of a linear equation is given as
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]from the options given in the question, only option D does not corresponds with the standard form of a linear equation
[tex]undefined[/tex]Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
To find out the slope, we need two points
so
looking at the graph
we take
(-4,5) and (0,-3)
m=(-3-5)/(0+4)
m=-8/4
m=-2the y-intercept (value of y when the value of x is zero) is the point (0,-3)
the equation of the line in slope-intercept form is
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
so
m=-2
b=-3
substitute
y=-2x-3A net of arectangular pyramidis shown. Therectangular base haslength 24 cm andwidth 21 cm. Thenet of the pyramidhas length 69.2 cmand width 64.6 cm.Find the surfacearea of the pyramid.
Solution
The Image will be of help
To find x
[tex]\begin{gathered} x+24+x=69.2 \\ 2x+24=69.2 \\ 2x=69.2-24 \\ 2x=45.2 \\ x=\frac{45.2}{2} \\ x=22.6 \end{gathered}[/tex]To find y
[tex]\begin{gathered} y+21+y=64.6 \\ 2y+21=64.6 \\ 2y=64.6-21 \\ 2y=43.6 \\ y=\frac{43.6}{2} \\ y=21.8 \end{gathered}[/tex]The diagram below will help us to find the Surface Area of the Pyramid
The surface area is
[tex]SurfaceArea=A_1+2A_2+2A_3[/tex]To find A1
[tex]A_1=24\times21=504[/tex]To find A2
[tex]\begin{gathered} A_2=\frac{1}{2}b\times h \\ 2A_2=b\times h \\ 2A_2=21\times22.6 \\ 2A_2=474.6 \end{gathered}[/tex]To find A3
[tex]\begin{gathered} A_3=\frac{1}{2}bh \\ 2A_3=b\times h \\ 2A_3=24\times21.8 \\ 2A_3=523.2 \end{gathered}[/tex]The surface Area
[tex]\begin{gathered} SurfaceArea=A_1+2A_2+2A_3 \\ SurfaceArea=504+474.6+523.2 \\ SurfaceArea=1501.8cm^2 \end{gathered}[/tex]Thus,
[tex]SurfaceArea=1501.8cm^2[/tex]You must show your work as you... determine whether QR and ST are parallel, perpendicular, or neither. Q(9, 10), R(-5, 2), S(-8, -2), T(-1, 2) Parallel Perpendicular Neither
WILL MARK BRAINLIEST
PLS HELP ASAP
Slope of QR = 4/7; Slope of ST = 4/7, therefore, the lines are parallel to each other.
How to Determine if Two Lines are Parallel or Perpendicular?To determine if two given lines are perpendicular to each other or parallel to each other, find their slopes.
Slope, m = change in y / change in x.
If they have the same slope, m, then they are parallel lines. If they have slopes that are negative reciprocal to each other, then they are perpendicular lines.
Given:
Q(9, 10)
R(-5, 2)
S(-8, -2)
T(-1, 2)
Find the slope of QR and ST:
Slope of QR = (10 - 2)/(9 -(-5)) = 8/14 = 4/7
Slope of ST = (-2 - 2)/(-8 -(-1)) = -4/-7 = 4/7
The slope are the same, therefore they are parallel to each other.
Learn more about parallel lines on:
https://brainly.com/question/10790818
#SPJ1
Select the correct answerVector u has its initial point at (15, 22) and its terminal point at (5, 4). Vector v points in a direction opposite that of u, and its magnitude is twicethe magnitude of u. What is the component form of v?OA V=(-20, 36)OB. V=(-20, 52)Ocv = (20, 36)ODV= (20, 52)
Answer
Option C is correct.
v = (20, 36)
Explanation
If the initial and terminal points of a vector are given, the vector itself is obtained, per coordinate, by doing a terminal point coordinate minus initial point coordinate.
u = [(5 - 15), (4 - 22)]
u = (-10, -18)
Then, we are told that vector v points in the opposite direction as that of vector u and its magnitude is twice that of vector u too.
In mathematical terms,
v = -2u
v = -2 (-10, -18)
v = (20, 36)
Hope this Helps!!!
For which equation would x = 12 be a solution?x - 12 = 12x - 24 = 12x - 14 = 2x - 5 = 7
Explanation
We are required to solve each equation till we arrive at the one that satisfies the "x=12" question.
First equation:
[tex]\begin{gathered} x-12=12 \\ Collect\text{ like terms} \\ x=12+12 \\ x=24 \end{gathered}[/tex]Second equation:
[tex]\begin{gathered} x-24=12 \\ Collect\text{ like terms} \\ x=12+24 \\ x=36 \end{gathered}[/tex]Third equation:
[tex]\begin{gathered} x-14=2 \\ Collect\text{ like terms} \\ x=2+14 \\ x=16 \end{gathered}[/tex]Last equation:
[tex]\begin{gathered} x-5=7 \\ Collect\text{ like terms} \\ x=7+5 \\ x=12 \end{gathered}[/tex]Hence, the last equation is the solution.
