1 cup will fills double than 1/2 cup, so:
[tex]\frac{2}{3}\cdot2=\frac{4}{3}[/tex]With 1 cup you will be able to fills 4/3, in other words 1 full container and 1/3 of another.
Alice likes to have wine with her dinner on Friday and Saturday night. She usuallybuys two bottles of wine for the weekend. She really needs to cut back on spending.She decides to buy only one bottle per week. On average a bottle of wine costs $15.How much does she save in one year?
Alice decides to buy only one bottle per week, instead of two. That means that she is saving half of her last expenses. There are 52 weeks in one year, so the savings can be calculated as:
Savings = (# of weeks) * (average cost of a bottle of wine)
We know that a bottle of wine costs $15 on average, so:
Savings = 52*15
Savings = $780
in the figure below, points J, K, and L are the midpoints of the sides of XYZ. suppose YZ =76, JK =12, and XY =68. find the following lengths. JL, XZ, and LZ
Given data:
The first length given is YZ =76.
The second length given is JK =12.
The third length given is XY=68.
The JL length is,
[tex]\begin{gathered} JL=\frac{1}{2}(YZ) \\ =\frac{1}{2}(76) \\ =38 \end{gathered}[/tex]The XZ length is,
[tex]\begin{gathered} XZ=2(JK) \\ =2(12) \\ =24 \end{gathered}[/tex]The LZ length is,
[tex]\begin{gathered} LZ=\frac{1}{2}(XZ) \\ =\frac{1}{2}(24) \\ =12 \end{gathered}[/tex]Thus, JL=38, XZ=24, and LZ=12.
✓ 1234Graph the set {xx2-1) on the number line.Then, write the set using interval notation.-7-6-5-4-3-2-11 2 3{x|x ≥-1}=045 6(0,0)
Given set: x greater than or equal to -1
The interval includes -1 and all the values greater than -1, to graph it put a full point in the -1 and draw an arrow to the the right of -1:
Interval notation:[tex]\lbrack-1,\infty)[/tex]The triangles shown below are similar.24Similar Help30Solve for x.X=
Here, we are given two similar triangles.
Let's find the value of x.
The corresponding sides of similar triangles are proportional.
To find the value of x, apply the ratio for simlilar triangles.
Thus, we have:
[tex]\frac{24}{8}=\frac{30}{x}[/tex]Cross multiply:
[tex]\begin{gathered} 24x=30(8) \\ \\ 24x=240 \end{gathered}[/tex]Divide both sides by 24:
[tex]\begin{gathered} \frac{24x}{24}=\frac{240}{24} \\ \\ x=10 \end{gathered}[/tex]Therefore, the value of x is 10
ANSWER:
10
Find all possible inflection points of f(x) = -x^4 + 24x^2. Are there any actual inflection points of f(x)?
Given the function:
[tex]f(x)=-x^4+24x^2[/tex]You need to remember that the Inflection Points of a function are where it changes its concavity.
By definition, a function can have more than one inflection point:
1. You need to find:
[tex]f^{\prime}(x)[/tex]Remember the following Derivatives Power Rule:
[tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]You get:
[tex]f^{\prime}(x)=-4(x^{4-1})+(2)(24)(x^{2-1})[/tex][tex]f^{\prime}(x)=-4x^3+48x[/tex]2. Find the second derivative by derivating the first derivative. This is:
[tex]f^{^{\prime}^{\prime}}(x)=(-4)(3)x^{3-1}+48[/tex][tex]f^{^{\prime\prime}}(x)=-12x^2+48[/tex]3. Find the third derivative by derivating the second derivative:
[tex]f^{^{\prime^{\prime}^{\prime}}}(x)=(-12)(2)x^[/tex][tex]f^{^{\prime^{\prime}^{\prime}}}(x)=-24x[/tex]4.Find the roots of the second derivative:
- Set up that:
[tex]-12x^2+48=0[/tex]- And solve for "x":
[tex]\begin{gathered} -12x^2=-48 \\ \\ x=\sqrt{\frac{-48}{-12}} \\ \\ x_1=2 \\ x_2=-2 \end{gathered}[/tex]5. Substitute each root into the third derivative and evaluate:
[tex]f^{^{\prime^{\prime}^{\prime}}}(2)=-24(2)=-48[/tex]It is less than zero, therefore there is an inflection point in that x-value.
[tex]f^{^{\prime^{\prime\prime}}}(-2)=-24(-2)=48[/tex]It is positive output value, therefore there is an inflection point in that x-value.
6. Substitute those x-values into the original function and evaluate:
[tex]f(2)=-(2)^4+24(2)^2=80[/tex][tex]f(-2)=-(-2)^4+24(-2)^2=80[/tex]Therefore, the inflections points are:
[tex]\begin{gathered} (-2,80) \\ (2,80) \end{gathered}[/tex]Hence, the answer is:
There are two inflection points:
[tex]\begin{gathered} (-2,80) \\ (2,80) \end{gathered}[/tex]I will show you the question
a.)
[tex]\begin{cases}y_1=1+3x \\ y_2=3+2x\end{cases}[/tex]b.)
[tex]1+3x=3+2x\rightarrow3x-2x=3-1\rightarrow x=2[/tex]so for a ride of 2 miles the cost will be the same for both companies
c.)for a ride of 10 miles we get that the cost for each company is
[tex]\begin{gathered} y_1=1+3\cdot10=31 \\ y_2=3+2\cdot10=23 \end{gathered}[/tex]So Madeline's is cheaper
Lilly likes to collect records. Last year she had 10 records in her collection. Now she has 13 records. What is the percent increase in her collection?
The percentage increase is 30%
Here, we want to calculate percentage increase
Mathematicall, this is;
[tex]\text{percentage increase = }\frac{new\text{ value -old value}}{\text{old value}}\text{ }\times\text{ 100}[/tex]From the question, the old value is 10 and the new value is 13
Substituting these values, we have that;
[tex]\text{Percentage increase = }\frac{13-10}{10}\text{ }\times\text{ 100 = }\frac{3}{10}\text{ }\times\text{ 100 = 30\%}[/tex]Janelle bought a beach chair on sale at 60% off. The original price was $43.95.Find the amount of discount in dollars.Find the sale price in dollars.
Given:
Percentage off on beach chair = 60%
Original price = $43.95
Required: Amount of discount and selling price
Explanation:
Amount of discount = Percentage of discount x Original Price=
[tex]\begin{gathered} =\frac{60}{100}(43.95) \\ =26.37 \end{gathered}[/tex]Amount of discount = $26.37
Selling price = Original Price - Discount amount
[tex]\begin{gathered} =43.95-26.37 \\ =17.58 \end{gathered}[/tex]The beach chair sells at $17.58.
Final Answer: Amount of discount = $26.37
Selling Price = $17.58
The following table represents the highest educational attainment of all adultresidents in a certain town. If a resident who has completed only a bachelor's degreeis chosen at/random, what is the probability that they are aged 50 or over? Roundyour answer to the nearest thousandth.Age 20-29 Age 30-39 Age 40-49 Age 50 & overTotalHigh school only144394155416144552Some college127813528612092558397759163819334139Bachelor's degreeMaster's degree11176833375522689Total481535672390619116963Answer:Submit Answer
Given that, a resident who has completed only a bachelor's degree
is chosen at random.
To find the probability that a resident who has completed only a bachelor's degree are aged 50 and above.
Number of students who has completed only a bachelor's degree and are aged 50 and above =1933
Total number of students who have completed bachelor's degree is 4139.
Probability is defined as,
[tex]P=\frac{\text{Desired outcomes}}{\text{total outcomes}}[/tex][tex]\begin{gathered} P=\frac{1933}{4139} \\ =0.4670 \end{gathered}[/tex]So, the probability that a resident who has completed only a bachelor's degree are aged 50 and above is 0.4670
if y is directly proportional to x when x = 6 and y = 12, write an equation to model the given relationship. Find the value of y if x = -30?
Since we have that y is directly proportional to x, then the relationship can be written like this:
[tex]y=kx[/tex]Now, since y=12 when x=6, we have the following:
[tex]\begin{gathered} 12=k(6) \\ \Rightarrow k=\frac{12}{6}=2 \\ k=2 \end{gathered}[/tex]Therefore, the equation would be y = 2x.
Finally, if x=-30, then:
[tex]y=2(-30)=-60[/tex]What is the answer to 14 - 6t=t
Statement Problem: What is the answer to;
[tex]14-6t=t[/tex]Solution:
Add 6t to both sides of the equation;
[tex]\begin{gathered} 14-6t+6t=t+6t \\ 14=7t \end{gathered}[/tex]Divide both sides by 7;
[tex]\begin{gathered} \frac{14}{7}=\frac{7t}{7} \\ t=2 \end{gathered}[/tex][tex]14-6t=t[/tex]
Simplify the equation:
[tex]14+-6t=t[/tex]
[tex]-6t+14=t[/tex]
Subtract t from both sides:
[tex]-6t+14-t=t-t[/tex]
[tex]-7t+14=0[/tex]
Subtract 14 from both sides:
[tex]-7t+14-14=0-14[/tex]
[tex]-7t=-14[/tex]
Divide both sides by -7:
[tex]\frac{-7t}{-7} =\frac{-14}{-7}[/tex]
[tex]\fbox{t=2}[/tex]
Hope this helps!
A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB = 20 feet. What is the length of arc AC, in feet?
Answer:
The length of the arc AC is;
[tex]AC=20ft[/tex]Explanation:
Given the radius AB as 20ft.
[tex]AB=20\text{ ft}[/tex]And angle ABC measures 1 radian.
Using the Method 1;
Length of Arc AC is;
[tex]AC=\omega r[/tex]Substituting the angle in radian and the radius;
[tex]\begin{gathered} AC=1\times20\text{ ft} \\ AC=20\text{ ft} \end{gathered}[/tex]The length of Arc AC is 20 ft
Method 2;
We will firstly convert the angle from radian to degree.
As shown below;
[tex]\begin{gathered} \theta=1\text{ rad}\times\frac{180}{\pi} \\ \theta=57.3^0 \end{gathered}[/tex]Then we will apply the formula for calculating the length of an arc;
[tex]C=\frac{\theta}{360}\times2\pi r[/tex]Substituting the value of the angle and the radius.
[tex]\begin{gathered} C=\frac{57.3}{360}\times2\pi\times20ft \\ C=\frac{57.3}{360}\times40\pi ft \\ C=20ft \end{gathered}[/tex]Therefore, the length of the arc AC is;
[tex]AC=20ft[/tex]Solve and graph the following inequality: - 2x + 4 > - 6
From the question,
-2 x + 4 > -6
- 2x > -6 - 4
-2 x > -10
Divide both sides by -2
x < 5
Graph the line with the points (2,3) with the slope =1/2
To solve this problem, first, we compute the equation of the line that passes through the point (2,3) and has slope 1/2 using the slope-point formula for the equation of a line:
[tex]y-3=\frac{1}{2}(x-2)\text{.}[/tex]Answer:
1. Determine the missing length in the following right triangle. Round to thenearest tenth.
We can apply Pythagorean theorem to the given right triangle:
[tex]x^2+16^2=20^2[/tex]which gives
[tex]x^2+256=400[/tex]If we move +256 to the right hand side, we get
[tex]\begin{gathered} x^2=400-256 \\ \text{then} \\ x^2=144 \end{gathered}[/tex]Finally, x is given by
[tex]x=\sqrt[]{144}[/tex]then, the answer is x= 12
Weatha rides her bike to the park. The park is 5 3/4miles from her house, and she's already ridden 1.4 miles. How many more miles does weatha still need to travel?
then
5.75 miles - 1.4 miles = 4.35 miles
answer 4.35 miles
If angle TUV = 35°, and angle TUW = 14º, what is the measure of angle VUW?
You have the measurements of angles TUV and TUW, these two angles share the vertex U and one side T, so we can assume they are adjacent:
Angle VUW has its vertex on U and its sides are W and V, this means that angles TUW and TUV are included in angle VUW.
According to the angle addition postulate you can determine that:
VUW= TUV + TUW
VUW= 35º+14º
VUW= 49º
Can I have some help?
If A is ( - 1, 5)
and the transformation rule is; (x+3, y - 6)
To find A'
add 3 to the x-cordinate and subtract 6 from the y-coordinate of A
That is;
A' = ( -1+ 3 , 5 -6) = (2, -1)
Therefore;
A' = (2, -1)
100gal =_qtClick the icon to view the customary units.185 gal = qt2(Type an integer, fraction, or mixed number.)를Enter your answer in the answer box and then click Check Answer
Answer:
8 1/2 gallons is equivalent to 34 qt
Explanation:
The conversion standard is
1 gallon --------------- 4 qt
8 1/2 gallons ----------- x qt
Step 1: convert mixed fractions into improper fraction
8 1/2 = (2 x 8) + 1 / 2
8 1/2 = 16 + 1 / 2
8 1/2 = 17 /2 gallons
Since, 1 gallon -------- 4 qt
17/2 gallons -------x qt
Cross multiply
1 * x = 17/2 x 4
x = 17 x 4 / 2
x = 68 / 2
x = 34 qt
Last one then I finish my answer any help will be appreciated
Answer:
x-axis?? I HATE IXL it is the worst thing on earth
Step-by-step explanation:
m(x) =2-x and n(x) =1+x^2Given:minimum x and Maximum x: -9.4 and 9.4minimum y and maximum y: -6.2 and 6.2Use m(x)/n(x)a) what are the zeroes?b) are there any asymptotes? c) what is the domain and range for this function?d) it it a continuous function?e) are there any values of y= m(x)/n(x) that are undefined? Explain
Given m(x) and n(x), the rational function m(x)/n(x) is
[tex]f(x)=\frac{m(x)}{n(x)}=\frac{2-x}{1+x^2}[/tex]a) The zeroes of the function are the values of x such that f(x)=0; then,
[tex]\begin{gathered} f(x)=0 \\ \Rightarrow\frac{2-x}{1+x^2}=0 \\ \Rightarrow2-x=0 \\ \Rightarrow x=2 \end{gathered}[/tex]The zero of the function is at x=2.
b) Notice that the limits when x->+/- infinite are
[tex]\begin{gathered} \lim _{x\to-\infty}f(x)=\lim _{x\to-\infty}-\frac{x}{x^2}=-\lim _{x\to-\infty}\frac{1}{x^{}}=-(\frac{1}{-\infty})=\frac{1}{\infty}=0 \\ \text{and} \\ \lim _{x\to\infty}f(x)=\lim _{x\to\infty}-\frac{x}{x^2}=-\lim _{x\to\infty}\frac{1}{x^{}}=-(\frac{1}{\infty})=-\frac{1}{\infty}=0 \end{gathered}[/tex]This implies that there is an asymptote at y=0; however, notice that
[tex]\begin{gathered} f(x)=-0.1 \\ \Rightarrow x=3,7 \end{gathered}[/tex]Thus, the graph of f(x) crosses y=0; thus, there are no asymptotes even if the behavior of the function tends to zero.
c) The function's domain consists of every value of x such that the denominator of f(x) is different than zero. Notice that 1+x^2>=1 since x^2>=0; thus
[tex]\text{domain(f(x))}=\mleft\lbrace x\in\R\mright\rbrace=(-\infty,\infty)[/tex]d) n(x) and m(x) are polynomial function; thus both functions are continuous. Then,
[tex]\begin{gathered} f(x)=\frac{m(x)}{n(x)}\to\text{ is continuous for every x such that }n(x)\ne0 \\ \text{and} \\ n(x)\ne0,\text{ always} \\ \Rightarrow f(x)\to\text{continuous for every x} \end{gathered}[/tex]Therefore, the rational function is indeed continuous for any value of x.
e) As we stated before, f(x) is defined for every value of x such that n(x) is different than zero, and n(x)>1 for every x. Thus, there are no values of x such that m(x)/n(x) is undefined.
f) As for the end behavior of the function, we found that the limits when x approaches +/- infinite are equal to zero. Therefore, the end behavior of the function is not positive nor negative since 0=-0
The area of an 19-cm-wide rectangle is 437 cm. What is its length?
The area of a rectangle is equal to:
[tex]\text{Area = Width }\cdot\text{ length}[/tex]In this case, we know that the area is equal to 437 cm^2 and the width is 19 cm, so we can replace the values and get:
[tex]437cm^2=(19\operatorname{cm})\cdot(length)[/tex]So, we can solve for length dividing both sides by 19 cm as:
[tex]\begin{gathered} \frac{437cm^2}{19\text{ cm}}=\frac{(19\operatorname{cm})}{19\operatorname{cm}}\cdot(length) \\ 23\text{ cm = length} \end{gathered}[/tex]Therefore, the length of the rectangle is 23 cm
Answer: 23 cm
The length of a rectangle is 23 cm.
To find the length of a rectangle, we will use the formula of the area of a rectangle,
Area = L × B
Where,
L = length
B = breadth
Given in the question,
Area = 473 cm
breadth = 19 cm
length =?
Now, we will put values in the above formula,
Area = L × B
437 = L × 19
L = 437/19
L = 23 cm
Therefore, the length of a rectangle is 23 cm.
To learn about the area of a rectangle:
https://brainly.com/question/15225905
https://brainly.com/question/20693059
Graph the following: 4x-3y=21
Pls show your work!!! I will give brainly
The graph of the equation shows the slope of 4/3 and the intercept is -7
Graph of a Linear EquationThe graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.
In the given equation, 4x - 3y =21. We can rewrite this into the standard form of y = mx + c and determine the slope of the line.
This becomes; 4x - 3y = 31, y = 4/3 x - 7
The slope of the line is 4/3 and the intercept is -7
The graph of this line is attached below;
learn more on graph of linear equation here;
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I need help with this math question it would be greatly appreciated.
Answer
equation of L₁ is y = 2x - 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given L₂
x + 2y = 3 ( subtract x from both sides )
2y = - x + 3 ( divide through by 2 )
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2
slope of L₁ = 2 and passes through (3, - 1 ) , then
y = 2x + c ← is the partial equation of L₁
to find c substitute (3, - 1 ) into the partial equation
- 1 = 6 + c ⇒ c = - 1 - 6 = - 7
y = 2x - 7 ← equation of L₁
for each expression combine like terms and write an equivalent expression with fewer terms a. 5 + 2x + 7 + 4x b. 4 - 2x+5xc. 10x - 5 + 3 x - 2
a) 5 + 2x + 7 + 4x
By combining like terms, we would add the terms containing the variable, x together. We would als add the constant terms(not containing the variable, x) together. It becomes
2x + 4x + 5 + 7
= 6x + 12
What equation would you use to find the measure of
SOLUTION
The shape is a parallelogram
The consecutive angle of a parallelogram is supplementary that is added up to 180 degree
[tex]\angle M+\angle L=180^0[/tex]Hence we have
[tex]\begin{gathered} \angle L=(2z-3)^0 \\ \angle M=(5z-6)^0 \\ (2z-3)^0+(5z-6)^0=180^0 \end{gathered}[/tex]Therefore the right option is D
What is the slope of the following points? (11,9) and (12,9)
the equation to find the slope between 2 points is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]name the points
1=(11,9)
2=(12,9)
apply the formula
[tex]\begin{gathered} m=\frac{9-9}{12-11} \\ m=\frac{0}{1} \\ m=0 \end{gathered}[/tex]the slope between the points is 0.
Chole always brings her own shopping bags to buy fruits. A bag with 65 cucumbers in it has a mass of 7.23 kg. The same bag with 56 cucumbers in it has a mass of 6.24 kg. Find the mass of the bag when it is empty in grams.
Please help me. ( =___ ) below the last fill in space
Explanation:
We are asked to get the slope of the graph
To do so, we have to make use of the relationship:
[tex]\text{slope}=\frac{\text{rise}}{\text{fall}}=\frac{\text{change in y}}{change\text{ in x}}[/tex]From the graph given
We have the following points:
[tex](1,8)\text{ and (2,4)}[/tex]So we can obtain the slope as follow
[tex]\text{slope}=\frac{4-8}{2-1}[/tex]Thus, the slope
[tex]\text{slope}=\frac{-4}{1}[/tex]Use this information for questions
5 and 6.
It costs $7.50 per person to ice skate at Chea
Skate Rink. Five friends went to Cheap Skat
for the afternoon.
5. Which equation can be used to find th
total cost?
Answer:
7.5x = total cost
As the cost is 7.5 dollars for each person, multiple the cost by the amount of people for the total cost of the whole party.