The area of the pool that Tanner does not need to cover is
20.125 square meters
Dimensions of the pool:
Length = 5 3/4 m by 3 1/2 m
area of rectangular pool
= product of dimensions
= 23/4 × 7/2
=20.125 square meters
Area is a unit of measurement used to describe a region's size on a flat or curved surface. While the area of a plane region or plan area refers to the area of a shape or planar lamina, surface area refers to the volume of a raised platform or the edge of a three-dimensional object.
Area is the two-dimensional equivalent of the volume of a solid as well as the length of a curve (a one-dimensional term). It can be compared to the amount of material of a certain thickness needed to create a model of the shape or the amount of paint needed to completely cover a surface in one application.
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Lines AB and CD at E. If m∠AEC=x^2+3x and m∠BED=6x+4 ,find m∠CEB.
Explanation
Step 1
when two lines intersect, vertical angles that are equal are formed.Also two angles are Supplementary when they add up to 180 degrees
then
[tex]\begin{gathered} m\measuredangle\text{AEC =}m\measuredangle BED \\ \text{replacing} \\ x^2+3x=6x+4 \end{gathered}[/tex]and
[tex]m\measuredangle\text{AEC}+\text{ m}\measuredangle CEB=180[/tex]Step 2
solve for x,
[tex]\begin{gathered} x^2+3x=6x+4 \\ x^2+3x-6x=+4 \\ x^2+3x-6x-4=0 \\ x^2-3x-4=0 \\ \text{factorize} \\ (x-4)(x+1)=0 \\ it\text{ means} \\ x-4=0 \\ x=4 \\ or \\ x+1=0 \\ x=-1 \end{gathered}[/tex]we just take the positive number, because we are searching for an angle ( angles and distance are always positives)
then
[tex]x=4[/tex]Step 3
replace the value of x in the angle AEC
[tex]\begin{gathered} m\measuredangle AEC=x^2+3x \\ m\measuredangle AEC=4^2+3\cdot4 \\ m\measuredangle AEC=16+12 \\ m\measuredangle AEC=28 \\ \end{gathered}[/tex]replace the value of AEC in equation (2) to find CEB
[tex]\begin{gathered} m\measuredangle\text{AEC}+\text{ m}\measuredangle CEB=180 \\ 28+m\measuredangle CEB=180 \\ \text{subtract 28 in both sides} \\ 28+m\measuredangle CEB-28=180-28 \\ m\measuredangle CEB=152 \end{gathered}[/tex]I hope this helps you.
At the pediatrician's office, patients are able to draw a toy from the toy bin. The toy bin has 12 puzzles, 16boxes of crayons, and 2 bouncy balls. What is the probability of drawing...a box of crayons?a puzzle?anything but a bouncy ball?(write your answer as a fraction in lowest terms)
SOLUTION
Total outcomes = 12 puzzles + 16 boxes of crayons + 2 bouncy balls = 30.
[tex]\begin{gathered} \text{Probability = }\frac{required\text{ outcome}}{\text{total outcome}} \\ \\ \text{probability of drawing a box of crayons = }\frac{16}{30}=\text{ }\frac{8}{15} \end{gathered}[/tex][tex]\text{Probability of drawing a puzzle = }\frac{12}{30}\text{ = }\frac{2}{5}[/tex]Probability of anything but bouncy ball means the probability of drawing out a box of crayons or probability of drawing out a puzzle.
[tex]\begin{gathered} \text{This becomes = }\frac{8}{15}+\frac{2}{5} \\ \\ =\text{ }\frac{8+6}{15}\text{ = }\frac{14}{15} \\ \end{gathered}[/tex]Use the image below to describe at least three different ratios, written In simplest form. Indude at least one part-to-part ratio and one part-to-whole ratio.
Par
In the figure shown we notice that there are 15 blue squares and 10 white squares. The ratio between them is 15 to 10, this is equivalent to a ratio 3 to 2.
Therefore, there are 3 blue squares for each 2 squares, this can be written as:
[tex]3\colon2[/tex]3/8 / 1/4 as a model
The given expression :
[tex]\frac{3}{8}\div\frac{1}{4}[/tex]Simplify :
I need this answered from my prep guide, I will include the picture of the answer options
SOLUTION
(a) The vertex of the parabola
[tex]\begin{gathered} (y+1)^2=12(x-3) \\ so,\text{ } \\ 12(x-3)=(y+1)^2 \end{gathered}[/tex]Now,
[tex]\begin{gathered} 4p\mleft(x-h\mright)=\mleft(y-k\mright)^2 \\ \mathrm{\: is\: the\: standard\: equation\: for\: a\: right-left\: facing\: parabola\: with\: vertex\: at}\: \: \\ \mleft(h,\: k\mright),\: \\ \mathrm{and\: a\: focal\: length\: }\: |p| \end{gathered}[/tex]From the initial equation we have
[tex]\begin{gathered} 12(x-3)=(y+1)^2 \\ 4\times3(x-3)=(y-(-1)^2) \\ \text{comparing to }4p(x-h)=(y-k)^2 \\ \text{vertex (h, k) = (-3, -1)} \end{gathered}[/tex]Therefore, the vertex of the parabola is (-3, -1)
(b) The parabola opens at?
Let us see the graph of the parabola
From the image, we can see that the Parabola opens right
(c) The focus
This can be determined using the formula
[tex]\begin{gathered} (h+p,-1) \\ \text{note from above that h = 3 and p = 3} \\ \text{the focus becomes } \\ (3+3,-1) \\ (6,-1) \end{gathered}[/tex]Now, the focus has coordinates (6, -1). Looking at the graph, we can see that from the point x = 6, the focus is 3 units away from the vertex.
(d) The directrix is read from point x = 0.
So, reading from x = 0, from the graph we can see that directrix is 6 units away from thr focus
From our explanation above, we can see that
(e) The focus is the point (6, -1)
(f) And the directrix is
[tex]x=0[/tex]Write the equation in slope-intercept form and then graph the equation that passes through (5, -7) and is parallel to to y = −4x + 3
The slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept.
For two lines to be parallel they have to have the same slope. So a line parallel to
[tex]y=-4x+3[/tex]Has m = -4. So until now we have this equation:
[tex]y=-4x+b[/tex]To find the intercept b we use the given point (5,-7). We just have to replace these values of x and y into the equation above and solve for b:
[tex]\begin{gathered} -7=-4\cdot5+b \\ -7+20=b \\ 13=b \end{gathered}[/tex]So there we have the complete equation of the asked line:
[tex]y=-4x+13[/tex]And the graph is:
Jeans are marked up 150% at Antoinette's Boutique. Today they are all on sale, 20% off the usual retail. If the wholesale price of jeans is $20, how much do they sell for today?
To solve the exercise you can use a rule of three.
Let us first find the usual price of jeans:
[tex]\begin{gathered} \text{ \$20}\rightarrow100\text{\%}\Rightarrow\text{ wholesale price of jeans} \\ \text{ \$x}\rightarrow150\text{\%}\Rightarrow\text{ usual sale price of jeans} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{150\text{\%}\cdot\text{ \$20}}{100\text{ \%}} \\ x=\frac{150\cdot\text{\$20}}{100} \\ x=\text{\$}\frac{150\cdot\text{20}}{100} \\ x=\text{\$}\frac{3000}{100} \\ x=\text{\$}30 \end{gathered}[/tex]Then, the usual price of the jeans is $30.
Now, let us find the discounted price of the jeans
[tex]\begin{gathered} \text{ \$30}\rightarrow100\text{\%} \\ \text{ \$x}\rightarrow80\text{\%} \\ \text{ Because now the jeans have a 20\% discount, that is} \\ 100\text{\%}-20\text{\%}=80\text{\%} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{80\text{\%}\cdot\text{ \$30}}{100\text{ \%}} \\ x=\frac{80\cdot\text{ \$30}}{100} \\ x=\text{ \$}\frac{80\cdot\text{30}}{100} \\ x=\text{ \$}\frac{240\text{0}}{100} \\ x=\text{\$}24 \end{gathered}[/tex]Therefore, today the jeans sell for $24.
Sarah spends of her monthly take-home pay on rent, food, and clothing. If she earns $1,830 in take-home pay each month, how much does she spend on rent, food, and clothing? A$610 B $915 C $990 D $1,220 E $2,745
We have that Sarah spends 2/3 of $1,830 in rent food and clothing
In order to find the money she spends, we just have to divide $1,830 in 3 and multiply the result by 2:
[tex]\begin{gathered} \frac{1830}{3}=610 \\ 610\cdot2=1220 \end{gathered}[/tex]Answer - D. $1,220The shorter sides of a rectangle measure 4 inches eachand one of its diagonals measures 8 inches. Which ofthe following is the measure of one of its longer sides?
Lets draw a picture of the rectangle:
From our figure, we can note that triangle ABC is a right triangle, so we can apply Pythagorean theorem, that is
[tex]4^2+x^2=8^2[/tex]which gives
[tex]16+x^2=64[/tex]If we move 16 to the right hand side, we get
[tex]\begin{gathered} x^2=64-16 \\ x^2=48 \end{gathered}[/tex]Then, x is given by
[tex]x=\sqrt[]{48}[/tex]since 48 = 16 x 3, we get
[tex]\begin{gathered} x=\sqrt[]{16\times3} \\ x=\sqrt[]{16}\times\sqrt[]{3} \\ x=4\sqrt[]{3} \end{gathered}[/tex]therefore, the answer is
[tex]x=4\sqrt[]{3}[/tex]which is the measure of the longer side.
1. Rectangular Prism: a. The measures: 1 =5, w = 7, h = 8 .. b. The measures: h =7, w = 7,1 = 7. C. W = 3.6, I = 4.2, h = 8.3
Volume of rectangular prism = Length x width x height = lwh
Part a
l=5, w=7, h=8
Volume = 5 x 7 x 8
=280 cm^3
Part b
l=7, w=7, h=7
Volume = 7 x 7 x 7
Volume = 343cm^3
Part c
l=4.2, w=3.6, h=8.3
Volume= 125.496 cm^3
Use the graph to answer the questionWhat is the average rate of change of f(x) between P and Q?
The average rate of change of a function over a interval [a,b] is given by:
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where, in this case:
[tex]\begin{gathered} a=1 \\ b=2 \\ f(a)=0 \\ f(b)=3 \\ so: \\ r=\frac{3-0}{2-1}=\frac{3}{1}=3 \end{gathered}[/tex]Answer:
D. 3
(6x 2 +3x 3 +7x)−(x+3× 2 +2x 3
Given
[tex](6x^2+3x^3+7x)-(x+3x^2+2x^3\text{)}[/tex]To solve this question, let's observe the following steps
Step 1: Remove the parentheses (Brackets). So that we will obtain=>
[tex]6x^2+3x^3+7x-x-3x^2-2x^3[/tex]The next step is to collect like terms
[tex]3x^3\text{ }-2x^3\text{ + }6x^2-3x^2\text{ +}7x\text{ - x}[/tex]Then we will proceed to simplify further
[tex]x^3+3x^2\text{ + 6x}[/tex]Rewrite the following expression in exponential form. log, 0.04 = -2 O A. - 25 = 0.04 O B. 5-2=0.04 O c. 50.04 = -2 O D. 0.04 -² = 5 5 SUE PREVIOUS
Answer:
B
graph the system of inequalties make sure your solution area is clear in your graph. then name a solution point & and a non soultion point
the red line indicates
[tex]y\ge2x-1[/tex]green line indicates
[tex]y<-x+2[/tex]the blue line indicates
[tex]y\ge-4[/tex]to find the solution point in the graph, we need to find the point at which they intersect and this graph, it doesn't have a solution point because all the three points didn't intersect
14. (04.06 LC)The first four terms of a sequence are shown below:8, 5, 2, -1Which of the following functions best defines this sequence? (5 points)f(1) = 8, f(n + 1) = f(n) + 5; forn 21f(1) = 8, f(n + 1) = f(n) - 5; for n 2 1f(1) = 8, f(n + 1) = f(n) - 3; for n 2 1f(1) = 8, f(n + 1) = f(n) + 3; forna 1
Given
The sequence, 8, 5, 2, -1.
To find: Which of the following functions best defines this sequence?
a) f(1) = 8, f(n + 1) = f(n) + 5; for n=1,2,3,4,...
b) f(1) = 8, f(n + 1) = f(n) - 5; for n=1,2,3,4,...
c) f(1) = 8, f(n + 1) = f(n) - 3; for n=1,2,3,4,...
d) f(1) = 8, f(n + 1) = f(n) + 3; for n=1,2,3,4,...
Explanation:
It is given that,
The first four terms of a sequence is, 8, 5, 2, -1.
Since,
[tex]\begin{gathered} 5-8=-3 \\ 2-5=-3 \end{gathered}[/tex]Then, the above sequence is an arithmetic sequence.
That implies,
[tex]\begin{gathered} f(n)=f(1)+(n-1)d \\ =8+(n-1)(-3) \end{gathered}[/tex]Therefore, for n=1,2.
[tex]\begin{gathered} f(1)=8 \\ f(2)=8+(2-1)(-3) \\ =8-3 \\ =f(1)-3 \end{gathered}[/tex]Then,
[tex]f(n+1)=f(n)-3[/tex]Final result: Hence, the answer is option c).
-11b+7=40 how do we solve for b?
We want to find the unknown value b in the following equation
-11b + 7 = 40
Since both sides are the same we can substract 7 both sides and it will be true
-11b + 7 - 7 = 40 - 7
-11b + 0 = 33
-11b = 33
We want to have just b in one side of the equation, we can divide both sides by -11, since they are equal:
-11b = 33
[tex]\begin{gathered} \frac{-11b}{-11}=\frac{33}{-11} \\ 1\cdot b=-3 \\ b=-3 \end{gathered}[/tex]Answer: b = -3What is the missing length? y 16 km area = 144 km y = kilometers
Area = length x width
Area = 144km^2
length = 16km
width = y
144 = 16 x y
y = 144/6 = 26 km
y = 24km
Further analysis finds that the correlation coefficient for this data is negative 0.792 which they may is a good description of what the scatter plot and correlation coefficient indicate
Jc, this is the correct answer:
As you can see in the scatter plot, the more time one of the physical trainer's client exercises, the less weight he or she has. However, we don't have any evidence that the cause of this is exclusively the time of exercise, more likely there would be other reasons or factors involved.
In consequence, the right answer is D.
valuate the expression when x = 10. Show your work, and explain each step you take 5x = 152.Evaluate the expression when b = 5 and h = 6. Show your work and explain each step you take 1/2b*h
In the first part, we have the followed expression:
[tex]5x\text{ - 15}[/tex]Wants to know the value of it when x=10, so we just need to substitute the value in the expression, wich gives us:
[tex]5\times(10)\text{ - 15, wich give us the expression: 50 - 15 = 35}[/tex]In the second part, we have the expression:
[tex]\frac{1}{2}b\times h[/tex]And we want to know the value of it when b=5 and h=6, so lets substitute those values in our expression:
[tex]\frac{1}{2}(5)\times(6),\text{ wich gives us, }\frac{1}{2}30\text{ = }\frac{30}{2}\text{ = 15}[/tex]Simplify: 8z + 5y + 6z + Зу * O 14z + 8y 13y + 9z O 22y 22z
Answer:
14z + 8y
Explanation:
Given the equation 8z + 5y + 6z + Зу
first is to collect the like terms;
8z + 5y + 6z + Зу
= (8z + 6z) + (5y + 3y)
= 14z + 8y
Hence the simplified form is 14z + 8y
½(10p-7q) if p=9 and q=2
Evaluate the expression for p = 9 and q = 2:
[tex]\begin{gathered} \frac{1}{2}(10(9)-7(2)) \\ \frac{1}{2}(90-14) \\ \frac{1}{2}(76)=38 \\ \end{gathered}[/tex]Select ALL the correct answers.Consider the geometric sequence below.Select all functions that define the given sequence-4, -6, -9, -27/2, -81/2
Given:
The geometric series
-4, -6, -9, -27/2, -81/2
Required:
Choose the correct option.
Explanation:
The given series is:
-4, -6, -9, -27/2, -81/2
The nth term of the geometric series is given by the formula:
[tex]a_n=ar^{n-1}[/tex]Where a = first term and r = common ratio
From the given series
a = -4
[tex]\begin{gathered} r=\frac{-6}{-4} \\ r=\frac{3}{2} \end{gathered}[/tex]Thus the nth term is:
[tex]f(n)=-4(\frac{3}{2})^{n-1}\text{ where n =2,3,4,.....}[/tex]Final Answer:
[tex][/tex]Instructions: Given the coordinate points of the preimage, use the transformation given to provide the points of the image. V(-5,-2) W(-2,1) X(-3,-3) Rotation: 90º about the origin v' W'( X'(3 -3 > Check
The rotation is 90 degree about the origin. The rule can be express below
[tex](x,y)\rightarrow(y,-x)[/tex]Therefore,
[tex]\begin{gathered} V(-5,-2)\rightarrow V^{\prime}^{}(-2,5) \\ W(-2,1)\rightarrow W^{\prime}(1,2) \\ X(-3,-3)\rightarrow X^{\prime}(-3,3) \end{gathered}[/tex]Note this is a clockwise 90 degree rotation.
Part A: Write g(x) as a transformation of f(x).Part B: Write h(x) as a transformation of f(x).Part C: Write m(x) as a transformation of f(x)
ANSWERS
• g(x) = f(x) - 2
,• h(x) = -f(x)
,• m(x) = f(x) + 7
EXPLANATION
The values on the table of function g(x) are all 2 less than the values of f(x). Therefore g(x) = f(x) - 2.
The values of function h(x) are all the opposite of the values of f(x). Therefore h(x) = -f(x).
The values of function m(x) are all 7 more than the values of f(x). Therefore m(x) = f(x) + 7.
Can you help me with this?
Ryan is trying to earn $350 to purchase a new pair of Jordan 1 sneakers. He already has $75 in his bank account and will mow lawns to earn the remainder of the money. If he earns $25 for each lawn mowed, create an equation to determine how many lawns he will need to mow. Let m represent the number of lawns mowed.
A biologist just discovered a new strain of bacteria that helps defend thehuman body against the flu virus. He puts 75 cells in a petri dish, theygrow at rate of 20% per hour. How many hours will it take to create aneffective dosage of 1,750 cells? *O About 17 hoursAbout 14 hoursO About 28 hoursAbout 20 hours
Given:
Rate = 20%
Here let's use the exponential growth function to find the number of hours.
Hello i am a senior graduating May i am struggling on algebra on .. if you can please help me with this problem
Answer:
Explanation:
Here, we want to complete the remainder of the table for the given function rule
What this means is that we need to fill in the given y values
To do this, we simply substitute the x values at each point, to get the corresponding y-value
We proceed as follows:
A) At this point , x is-3 , so we substitute -3 for x
Mathematically:
[tex]\begin{gathered} y\text{ = -}\frac{(-3)}{3}\text{ + 2} \\ y\text{ = }\frac{3}{3}\text{ + 2} \\ \\ y\text{ = 1 + 2} \\ y\text{ = 3} \end{gathered}[/tex]B) Here, x is 0
[tex]\begin{gathered} y\text{ = -}\frac{0}{3}\text{ + 2} \\ y\text{ = 0 + 2} \\ y\text{ = 2} \end{gathered}[/tex]C) Here, x is 3
[tex]\begin{gathered} y\text{ = -}\frac{3}{3}\text{ + 2} \\ y\text{ = -1 + 2} \\ y\text{ = 1} \end{gathered}[/tex]D) Here, x is 6
[tex]\begin{gathered} y\text{ = -}\frac{6}{3}\text{ + 2} \\ y\text{ = -2 + 2} \\ y\text{ = 0} \end{gathered}[/tex]Which of the expressions are equivalent to the one below? Check all thatapply.3. (2 + 6) + 4.5A. (6+2): 3+ 4.5B. 3.2 + 3.6+4.5O C.3.2 + (6 + 4): 5D. 5·4+3.(6+2
We have
[tex]3\cdot(2+6)+4\cdot5=44[/tex]For the other expressions
[tex](6+2)\cdot3+4\cdot5=44[/tex][tex]3\cdot2+3\cdot6+4\cdot5=44[/tex][tex]3\cdot2+(6+4)\cdot5=56[/tex][tex]5\cdot4+3\cdot(6+2)=44[/tex]As we can see the expressions that are equivalent are A, B, and D.
ANSWER
A, B, and D.
Which sequence of transformations maps polygon ABCD onto polygon WXYZ?
We have to find the transformations that led from polygon ABCD to WXYZ.
As the shapes are not equally oriented, we have to find if one of the transformation is a rotation or a reflection.
We can fin this by looking at the position of corresponding sides. So first, we have to find corresponding sides of the two polygons. The polygon WXYZ has also a scale transformation, so its size is proportional, with a proportion greater than 1 as it is bigger, to the size of ABCD.
Each side in the pre-image has a corresponding side in the image. Each corresponding side in the image will be k times bigger than the side in the pre-image, and this k is the same for the four sides.
We can look at the sides that are parallel to the axis, BC and CD, and see that CD is longer than BC. If we look at WXYZ, YZ is longer than YX.
Then, we can conclude that YZ and CD are corresponding sides as BC and YX.
The scale factor is k = 2 as YZ is twice as long as CD.
Then we can see, by the position of BC and CD respect to YX and YZ that no rotation can convert the pre-image into the image, so the orientation of the image is due to a reflection with axis of symmetry at x = 7.
Then, after the reflection, the image is dilated with a factor k = 2.
Answer:
B. A reflection of polygon ABCD followed by a dilation of the image with a scale factor of 2.
Answer:
B
Step-by-step explanation:
plato
Solve the y system of inequalities by choosing the correct graph.y> 3y< |x-2|
The solution graph of the system of inequalities : y> 3 and y< |x-2| is attached below.
The given inequalities are:
y>3 and y< |x-2|
Now we will solve y< |x-2|
applying absolute value we get
x - 2 < -y or x - 2 > y
Now we will solve the two equations graphically.
Using the graph we can clearly see that the red part represents the inequality y< | x - 2 | while the blue part denotes the inequality y > 3
Hence the solution of the two inequalities will be the region shaded by both the graphs.
Any monotonically increasing function can, by definition , be applied both for sides of just an inequality without distorting their relationship as long as both expressions fall inside the scope of the function. If a monotonically falling function are applied to both sides of an inequality, the inequality relation might be reversed.
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