Solution
We want to get why
[tex]\frac{3}{\text{ \lparen1/5\rparen}}\text{ is different from }\frac{\text{ \lparen1/5\rparen}}{3}[/tex]Reason 1: Commutation Law Does Not Hold For Division (or quotient)
Generally,
[tex]\frac{a}{b}\ne\frac{b}{a}[/tex]Reason 2: Actual Computation
First
[tex]\begin{gathered} \frac{3}{\text{ \lparen1/5\rparen}}=3\div\frac{1}{5} \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=3\times\frac{5}{1} \\ \\ \frac{3}{\text{ \lparen1/5\rparen}}=15 \end{gathered}[/tex]Secondly
[tex]\begin{gathered} \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{5}\div3 \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{5}\times\frac{1}{3} \\ \\ \frac{\text{ \lparen1/5\rparen}}{3}=\frac{1}{15} \end{gathered}[/tex]It is now obvious that
[tex]\frac{3}{\text{ \lparen1/5\rparen}}\ne\frac{\text{ \lparen1/5\rparen}}{3}[/tex]2.2.18Find the vertex of the graph of the quadratic function. Determine whether thegraph opens upward or downward, find the y-intercept, and sketch the graph.f(x) = - x2 - 2x+3The vertex is(Simplify your answer. Type an ordered pair.)
The quadratic function is given by the following expression:
[tex]f(x)=-x^2-2x+3[/tex]The direction at which the graph opens is determined by the signal of the number multiplying x². If the number is positive then the graph opens upwards, if it is negative it opens downward. In this case it is negative so it opens donward.
The vertex of a quadratic expression can be found by the following expression:
[tex]x=\frac{-b}{2a}[/tex]Where a is the number multiplying "x²", while b is the number multiplying "x". Applying the data from the problem we have:
[tex]x=\frac{-(-2)}{2\cdot(-1)}=\frac{2}{-2}=-1[/tex]To find the value of "y" for the vertex we need to apply the coordinate for x on the expression. We have:
[tex]\begin{gathered} f(-1)=-(-1)^2-2\cdot(-1)+3 \\ f(-1)=-1+2+3=4 \end{gathered}[/tex]The coordinates of the vertex are (-1,4).
To sketch a graph we need to find the x-intercept and y-intercept of the function. These are given when f(x) = 0 and x=0 respectively. Let's find these points.
[tex]\begin{gathered} 0=-x^2-2x+3 \\ -x^2-2x+3=0 \\ x_{1,2}=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(-1)(3)}}{2\cdot1} \\ x_1=-3 \\ x_2=1 \end{gathered}[/tex][tex]f(x)=-0^2-2\cdot0+3=3[/tex]The x intercept happens in two points -3 and 1, while the y intercept happens in the point 3. With this and the vertex we can sketch the function.
What is the probability of choosing a recheck at first and then choosing a red card with a replacement
Since there are 25 cards in the deck
Since there are 4 jacks on it 2 red and 2 black
Since the probability of an event = outcomes of events/total outcomes
Then for the first card
There are 2 red jacks for a total of 52 cards
[tex]P(r.j)=\frac{2}{52}=\frac{1}{26}[/tex]For the second card with NO replacement
Since there are 26 red cards in the deck
Since we took out one of them for the first card, then
There are 25 red cards
Since the total is less by 1 because of the first card, then
There are 51 cards
[tex]P(r)=\frac{25}{51}[/tex]Since and in probability means multiply, then
[tex]P(r.j&r)=\frac{1}{26}\times\frac{25}{51}=\frac{25}{1326}[/tex]The answer is the 3rd choice 25/1326
Hi, could you please help me understand why I got some of the answers wrong?
For the figure in the right up
The two triangles have 2 equal angles and one equal side
Then it should be AAS
Triangle AOC is congruent to triangle BOC
You must write the name of the triangles with equal angles
Since < AOC = < BOC ------- Given
Since Since OC = OC ------- common side
By using the AAS theorem of congruency
Then triangle AOC is congruent to triangle BOC
For the figure in the right down
Since OX // YC, then
Since
Since OC = CB ------- Given
Then by using the AAS theorem of congruency
Triangle XCO is congruent to triangle YBC
Use the number line to answer the question. Each tick represents 1.Which point is located at 2?PQSnone of the above
Given that each tick represents 1. The numbers on the right of 0 are positiv and on the left of 0 are negative. SInce 2 is positive, 2 lies on the right side of 0.
Since each tick represents 1, the first tick represents 0+1 = 1.
Now, the second tick represents 0 + 2 = 2. The second tick on the right of 0 denoted as S.
The correct option is S.
Need to find out how to solve 4/p=11/2
To solve the equation for p, we can first apply the cross product method, that is, we multiply the numerator and denominator that each line of the "X" connects.
Then, we have:
[tex]\begin{gathered} \frac{4}{p}=\frac{11}{2} \\ 4\cdot2=11\cdot p \\ 8=11p \end{gathered}[/tex]Now, we divide by 11 from both sides of the equation:
[tex]\begin{gathered} \frac{8}{11}=\frac{11p}{11} \\ \boldsymbol{\frac{8}{11}=p} \\ \text{ or} \\ 0.72=p \end{gathered}[/tex]Therefore, the value of p that satisfies the given equation is 8/11 or 0.72.
Can you help me with this? The approximate area of the circle is (Blank) square feet. (Use 22/7 as an approximation for pi) The approximate circumference of the circle is (Blank) feet. Use 22/7 as an approximation for pi
Let's begin by listing out the given information:
Could someone help me out please I don’t know how to
As per given by the question,
There are given that ,
[tex]4y^2+y-9,\text{ when y=-3}[/tex]Now,
There are given y=-3.
So,
Substitute the value -3 instead of y in given equation,
Then,
From the equation,
[tex]4y^2+y-9[/tex]Put the value of y in given equation,
[tex]4y^2+y-9=4(-3)^2+(-3)-9[/tex]Now, solve the above equation,
[tex]\begin{gathered} 4y^2+y-9=4(-3)^2+(-3)-9 \\ =4(9)-3-9 \\ =36-3-9 \\ =36-12 \\ =24 \end{gathered}[/tex]Hence, the value of given equation is 24.
what digit is in the
EXPLANATION
Rounding 9177 to the nearest hundred give us the following number:
9,200
10x-76=754 how do I solve this
Answer:
x=83
Step-by-step explanation:
10x-76=754
Move 76 to the other side and it becomes positive
10x=754+76
Add 754 and 76
10x=830
divide both sides by 10
10x/10=830/10
x=83
Can you tell me what would make something a function vs. what is not a function?
Answer:
fails the vertical line test: not a function
Step-by-step explanation:
You want to know how to tell if a relation is a function or not.
RelationA relation is a map between values of the independent variable (input, x) and values of the dependent variable (output, y). Such a map can be represented many ways, including a table, graph, set of ordered pairs, dual number lines, or even a diagram showing inputs and outputs. The attachment shows such a diagram.
A relation does not need to be between numbers. Tokens of any kind can be used for input and output identifiers.
FunctionA function is a relation in which each input corresponds (maps) to exactly one output.
The relation shown on the left of the attachment is not a function because the first (top) input item (A) maps to more than one output item (B).
When a relation is expressed as ordered pairs (x, y) or a table, it will be a function if and only if no x-value is repeated.
When a relation is expressed as a graph, it will be a function if and only if no vertical line intersects more than one point on the graph. (This is the "vertical line test.")
3. A doctor sees between 7 and 12 patients each day. On Mondays and Tuesdays.the appointment times are 15 minutes. On Wednesdays and Thursdays, they are30 minutes. On Fridays, they are one hour long. The doctor works for no morethan 8 hours a day. Here are some inequalities that represent this situation,0.25 Sy 51YS0S 12Y S83a. What does each variable represent?Your anowar3b. What does the expression xy in the last inequality mean in thissituation?
Solution
We have the following inequalities:
0.25 <= y<= 1, 7 <= x<= 12, xy <= 8
And we can conclude this:
Part a
the variable y represents the appointment time in hours and x the number of patients by the doctor
Part b
the expression xy is the time in hours that spends with a patient
There’s a few more questions like this I been stuck on
Problem N 9
we have that
m by addition angles postulate
substitute given values
164=(13x+4)+(10x-1)
solve for x
164=23x+3
23x=164-3
23x=161
x=7
Find out the measure of angle SQR
msubstitute the value of x
mm
Rhianna is baking a cake and some cookies for a party. She used 4 1/2 cups of flour for the cake. For each tray of cookies, she needs 2 1/2 cups of flour. She decides to use at least 15 cups of flour for the cake and the cookies.Assuming she can make fractional trays of cookies, how many trays, x, can she make?
The first step is to find how many cups of flour she has left to bake the cookies after baking the cake. To do it, substract the amount of flour she needs for the cake to the total amount of flour she decided to use.
[tex]15-(4+\frac{1}{2})=15-4.5=10.5[/tex]She has 10.5 cups of flour to bake the cookies. To find how many tray of cookies, solve the following equation for x:
[tex]\begin{gathered} (2+\frac{1}{2})x=10.5 \\ (2.5)x=10.5 \\ x=\frac{10.5}{2.5} \\ x=\frac{21}{5} \end{gathered}[/tex]She can make 21/5 trays of cookies. Written as a mixed number it is 4 1/5, it means she can make 4 1/5 or less trays of cookies.
Solve the system of equations by any method. 6x+11y =16x+2y =4
Hello! I'll draw the solution of this system of equations:
Now, let's go back to the second equation and replace where's y by 8:
So, the solution will be: (-12, 8) or x= -12 and y= 8.
compare the elevation of death valley and westmorland using< or >
Answer:
If D represent the elevation of Death valley , California and W represent the elevation of Westmorland, California.
So, we would have;
[tex]DWhich means that;the elevation of Death valley < the elevation of Westmorland
Explanation:
Given that the elevation of Death valley , California is -282 feet
[tex]D=-282[/tex]And the elevation of Westmorland, California is -157 feet;
[tex]W=-157[/tex]And we know that -282 ft is less than -157 ft.
[tex]-282<-157[/tex]Therefore, the elevation of Death valley , California is less than the elevation of Westmorland, California.
So, if D represent the elevation of Death valley , California and W represent the elevation of Westmorland, California.
So, we would have;
[tex]DWhich means that;the elevation of Death valley < the elevation of Westmorland
what will the deposit have to be if you want to have 12000 in an account that will earn 8.55% compounded weekly at the end of 5 years
Given:
The expected deposit =?
This is also referred to the principal
r = rate = 8.55%
t = time = 5years
n = we
What is the surface area of the following figure?
Answer:
surface area of cube = 37.5 units
Step-by-step explanation:
Find the area of one side of the cube with the formula sidexside:
2.5 x 2.5 = 6.25 units
now multiple the area of one side by the number of sides of the cube which is 6 sides:
6.25 x 6 = 37.5 units
What is the volume of this cone? Use 3.14 and round your answer to the nearest hundredth. 38 mm cubic millimeters
ANSWER
[tex]V=7179.09\operatorname{mm}[/tex]EXPLANATION
We are given the height of the cone as 19 mm and the diameter of its base as 38 mm.
The volume of a cone is given as:
[tex]V=\frac{1}{3}\pi\cdot r^2h[/tex]where r =radius; h = height
The diameter of a circle (the base of a cone) is twice the radius. Therefore:
[tex]\begin{gathered} D=2r \\ r=\frac{D}{2} \\ r=\frac{38}{2} \\ r=19\operatorname{mm} \end{gathered}[/tex]Therefore, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot19^2\cdot19 \\ V=7179.09\operatorname{mm}^3 \end{gathered}[/tex]The stem-and-leaf plot above shows house sale prices over the last
Stem (hundred thousands)
Leaf (ten thousands)
0
224667889
1
2
3
2344566678899
0122344567799
001122344566688
What was the less expensive house sold in 100,000 range? Give your
$
The least expensive house in the 100,000 range, given the stem and lead plot on house sale prices, is $120, 000.
How to find the house sale price?The stem and leaf plot on the house sale prices is given such that the stem is in hundreds of thousands and the leaf is in ten thousands.
This means that if you have a stem of 0 and a leaf of 2, the house price is:
= 0 + 20,000
= $20,000
A stem of 3 and a leaf of 4 means the house price is:
= 300,000 + 40,000
= $340,000
The cheapest house in the 100,000 range is the leaf value of 2 which means the least expensive house is:
= 100,000 + 20,000
= $120,000
Find out more on stem and leaf plots at https://brainly.com/question/23450543
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I need help with my math
Answer: Graph the value of b first on the Y - axis
The slope - intercept form of equation is
y = mx + b
where m = slope , and b = intercept
You graph the value of b on the Y - axis
check the photo please. this is my homework by the way.
m∠D = 28º , m∠C= 109º
1) Given that these triangles are congruent, we can state that the angles of both are equal, and their sides as well.
2) Let's check on the picture:
Since the triangles are congruent, we can state that m∠D = m∠A, and m∠C = m∠F
So m∠D = 28º Since 62 and 28 are complementary angles
And
m∠C = 109º Since m∠EFM and ∠EFD are supplementary
A pendant has a 5/8 inch by 1/2 inch rectangular shape with a 1/3 inch silver border. What are the dimensions of the pendant, including the silver border? (Use the larger value for length and the smaller value for width.)
Length of pendant including silver border is = 23/24 inch
The width of the pendant including the silver border is = 5/6 inch
What is the sum of fractions?When adding two fractions with the same denominator (lower number), just add the numerator (upper number) and leave the denominator unchanged if the fractions are like. To add fractions with different denominators, you must rewrite the fractions so that they have a common denominator before computing the sum.
The first step is to find the least common multiple (LCM) of the denominators.This LCM will become the lowest common denominator (LCD) for the fractions.Then, rewrite each fraction by multiplying both the numerator and denominator to a number so you can get LCM as the denominator.Now add the numerators leaving denominators unchanged.For the given case,
The length of the pendant including the silver border is
(5/8)+ (1/3) = (15+8)/24
= 23/24 inch
The width of the pendant including the silver border is
(1/2) + (1/3) = (3 + 2)/6
= 5/6 inch
To know more about the sum of fractions, visit:
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A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated usi Xthe origin as the center of dilation.Which rule could represent this dilation?
The rule for a dilation by a factor of k using the origin as the center of dilation, is:
[tex](x,y)\rightarrow(kx,ky)[/tex]In the options A and B, additions and substractions are involved. Then, they cannot be the rule of a dilation about the origin.
In the options C and D, we can see that both are dilations about the origin. The factor used in the option C is 5/4, while the factor used in the option D is 0.9.
Nevertheless, notice that 5/4 is greater than 1 and 0.9 is smaller than 1.
Then, the dilation from option C would produce a bigger polygon, while the dilation from option D will produce a smaller polygon.
Since the polygon must be a smaller one, then the rule that could represent this dilation is:
[tex](x,y)\rightarrow(0.9x,0.9y)[/tex]Which corresponds to option D.
What percent of 40 is 17?
In general, we can calculate what percent of y is x using the equation:
[tex]P=\frac{x}{y}\cdot100\text{\%}[/tex]In our problem, we identify:
[tex]\begin{gathered} x=17 \\ y=40 \end{gathered}[/tex]The percentage is:
[tex]\begin{gathered} P=\frac{17}{40}\cdot100\text{\%}=\frac{17\cdot5}{2}\text{ \%} \\ \Rightarrow P=42.5\text{\%} \end{gathered}[/tex]Consider the triangle shown below where m∠C=50∘, b=11 cm, and a=23 cm.Use the Law of Cosines to determine the value of x (the length of AB in cm).x=
The Law of Cosines is:
[tex]c^2=a^2+b^2-2ab\cdot\cos C[/tex]Where "a", "b" and "c" are sides of the triangle and "C" is the angle opposite side "c".
In this case you know that:
[tex]\begin{gathered} m\angle C=50\degree \\ b=11\operatorname{cm} \\ a=23\operatorname{cm} \\ c=x \end{gathered}[/tex]Then, you can substitute values as following:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cdot\cos C \\ x^2=(23\operatorname{cm})^2+(11\operatorname{cm})^2-2(23\operatorname{cm})(11\operatorname{cm})\cdot\cos (50\degree) \end{gathered}[/tex]Finally, evaluating, you get that the answer is:
[tex]\begin{gathered} \\ x\approx18.02\operatorname{cm} \end{gathered}[/tex]The midpoint of AB is M(6,1). If the coordinates of A are (4,8), what are the coordinates of B?
Midpoint : (6,1)
Point A : (4,8)
Point B (xb,by)
Midpoint (xm, my)=( x1+x2) /2 , ( y1+y2)/2
So:
xm= 6 = (4+xb) /2
6 = (4+xb) /2
Solve for xb
6 x 2 = 4+ xb
12 = 4+xb
12-4 = xb
8 = xb
For Yb:
my= 1 = (8+yb) /2
1 = (8+yb) /2
Solve for yb
1(2) = 8+yb
2 = 8+ yb
2-8 = yb
-6 = yb
Coordinate of B = (xb,yb) = (8,-6)
Write the phrase as an algebraic expression: a number divided by 2
Answer:
x/2
Explanation:
Let the number = x
If the number is divided by 2, then an algebraic expression to represent the phrase is:
[tex]\frac{x}{2}[/tex]It can also be written in the form:
[tex]x\div2[/tex]According to psychologist IQs are normally distributed with a mean of 100 and a standard deviation of 19. What’s the percentage of the population has IQs above 154?
In order to solve this problem, we will calculate the z-score of the given data.
To do this, we use the formula,
[tex]z=\frac{x-\mu}{\sigma}[/tex]We plug in the given data:
[tex]z=\frac{154-100}{19}\approx2.8421[/tex]With this z-score, we can consult a z-score probability table or use an online resource. However, this will give us
[tex]P(z<2.8421)[/tex]but we are interested in itbeing greater than it, so we must calculate
[tex]1-P(z<2.8421)=1-0.99776=0.00224[/tex]So, the percentage of the population that has an IQ above 154 is 0.224%.
Which represents the inverse of the function f(x) = 4x?h(x) = x + 4Oh(x) = X-4Oh(x) = 2xh(x) =17 1x
f(x) = 4x
To find the inverse of a function, you have to replace every x with an y, as follows:
f(x) = 4y
then, replace f(x) with an x,
x = 4y
and now, isolate y,
x/4 = y
Finally, replace y whit h(x),
h(x) = 1/4x
Question 4 If the vertices of ABC are A(-3,5), B(2,4). and C(-1,2), then ABC is classified as
To be able to classify the triangle you have to plot it
You can calculate the length of the sides as follows:
[tex]\begin{gathered} AC=\sqrt[]{(-1+3)^2+(5-2)^2} \\ AC=\sqrt[]{13} \end{gathered}[/tex][tex]\begin{gathered} AB=\sqrt[]{(5-4)^2+(2+3)^2} \\ AB=\sqrt[]{26} \end{gathered}[/tex][tex]\begin{gathered} BC=\sqrt[]{(2+1)^2+(4-2)^2} \\ BC=\sqrt[]{13} \end{gathered}[/tex]Sides AC and BC are equal.
You can classify this triangle as an isosceles triangle