show all supporting calculations .write an explanation of your conclusion in a complete sentence
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Related Questions
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?
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then
5.75 miles - 1.4 miles = 4.35 miles
answer 4.35 miles
Don Swiffer earns $9.75 per hour as a clerk. He starts work Mondaythrough Friday morning at 8:00 AM. He takes a half hour lunch break everyday. If he finishes work at 3:00 PM Monday through Thursday and leaveswork at 4:00 PM on Friday. What was his total pay for the week?
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Answer: $326.625
Explanation:
The infromation that we have is:
Payment per hour: p = $9.75 (I will identify the payment per hour as "p").
He worls from 8:00 am until 3 pm from monday through thursday, this means that he works 7 hours on those days. But since he takes a half hour lunch break, we take half an hour from the 7 hours:
[tex]7-0.5=6.5[/tex]Each from monday trough thursday that he works, he does it for 6.5 hours.
Thus, the total amount of hours for this four days of the week is:
[tex]4\times6.5=26[/tex]On Friday he works from 8:00 am to 4:00pm, that is 8 hours, as in the previus days, we substract half hour for his break:
[tex]8-0.5=7.5[/tex]So the total amount of hours that he works in the week is the sum of the 26 hours that he works from monday through thursday, plus the 7.5 hours that he works on friday:
[tex]h=26+7.5=33.5[/tex]h represents the amount of hours that he works in a week.
His total pay for the week "T" is:
[tex]T=h\times p[/tex]The product between the number of hours and the payment per hour:
[tex]T=33.5\times9.75=326.625[/tex]Answer: $326.625
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
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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
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?
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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]Which of the following describes the transformation f(x)−5?
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The translation that describes the transformation f(x) - 5 is:
A shift down of five units.
What is a translation?Among the many transformations that a function or a figure can undergo is a translation, along with reflections, rotations and dilation.
In a translation, only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are represented as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.In this problem, the translation rule is given as follows:
f(x) - 5.
Hence the meaning is given by:
A shift down of 5 units of the function f(x).
More can be learned about translations at https://brainly.com/question/28174785
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1. Determine the missing length in the following right triangle. Round to thenearest tenth.
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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
The length of a new rectangular playing field is 8 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 576 yards, what are its dimensions?
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Answer:
• Width: 56 yards.
,• Length: 232 yards.
Explanation:
Let the width of the rectangular field = w
Quadruple the width = 4w
The length is 8 yards longer than quadruple the width. Therefore:
[tex]\text{Length}=(4w+8)\text{ yards}[/tex]The perimeter of the field is 576 yards.
[tex]\begin{gathered} \text{Perimeter of a rectangle = 2(Length+Width)} \\ 576=2(4w+8+w) \end{gathered}[/tex]We solve the equation for w.
[tex]\begin{gathered} \text{Divide both sides by 2} \\ \frac{576}{2}=\frac{2(4w+8+w)}{2} \\ 288=5w+8 \\ \text{Subtract }8\text{ from both sides} \\ 288-8=5w \\ 280=5w \\ \text{Divide both sides by }5 \\ \frac{280}{5}=\frac{5w}{5} \\ w=56\text{ yards} \end{gathered}[/tex]The width of the rectangular playing field is 56 yards.
Next, we find the length.
[tex]\begin{gathered} \text{Length}=(4w+8)\text{ yards} \\ =4(56)+8 \\ =224+8 \\ =232\text{ yards.} \end{gathered}[/tex]The length of the rectangular playing field is 232 yards.
Please help me. ( =___ ) below the last fill in space
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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]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?
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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
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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.
If angle TUV = 35°, and angle TUW = 14º, what is the measure of angle VUW?
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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
What equation would you use to find the measure of
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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
Draw the following lines and label them with the matching letter. Then write an equation for each. Slope is 0, y-intercept is 5 Slope is 2, y-intercept is -1 Slope is -2, y-intercept is 1 Slope is -12, y-intercept is -1(Use a graph)
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Slope 0, y intercept is 5. If the slope is 0 it means it is a horizontal line.
Slope 2, y intercept -1. The line cuts y axis in -1 and the rate is 2
Slope -2, y intercept 1. The line cuts y axis in 1 and the rate is -2
Slope -12, y intercept -1. The line cuts y axis in -1 and the rate is -12
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.
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The first term is, 3x2 its coefficient is 3 .
The middle term is, -18x its coefficient is -18 .
The last term, "the constant", is -22
Step-1 : Multiply the coefficient of the first term by the constant 3 • -22 = -66
Step-2 : Find two factors of -66 whose sum equals the coefficient of the middle term, which is -18 .
-66 + 1 = -65
-33 + 2 = -31
-22 + 3 = -19
-11 + 6 = -5
-6 + 11 = 5
-3 + 22 = 19
-2 + 33 = 31
-1 + 66 = 65
Jack is mixing a cleaning solution that is 12% bleach. After mixing the solution, jack has 150 ounces of cleaning solution. How many ounces of bleach did Jack use?
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Answer:
8
Step-by-step explanation:
12 is 8% of 150 hope this helps
Addition and subtraction of algebraic expressions(9x - 1)/6 + (2x -10)/5
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To solve this question, follow the steps below.
Step 01: Find the LCM of 5 and 6 (denomitators).
5, 6 | 2
5, 3 | 3
5, 1 | 5
1, 1
The LCM is 2*3*5 = 30
Step 02: Rewrite the fractions using 30 as the denominator.
To do it, divide 30 by the original denominator and multiply the result by the numerator.
[tex]\frac{5\cdot(9x-1)}{30}+\frac{6\cdot(2x-10)}{30}[/tex]Step 03: Solve the expression.
First, since the fractions have the same denominator, you can write them using only one denominator:
[tex]\frac{5\cdot(9x-1)+6\cdot(2x-10)}{30}[/tex]Now, remove the parentheses by solving the multiplications.
[tex]\begin{gathered} \frac{5\cdot9x+5\cdot(-1)+6\cdot2x+6\cdot(-10)}{30} \\ \frac{45x-5+12x-60}{30} \end{gathered}[/tex]Adding like terms:
[tex]\begin{gathered} \frac{45x+12x-5-60}{30} \\ \frac{57x-65}{30} \end{gathered}[/tex]Answer:
[tex]\frac{57x-65}{30}[/tex]What is the answer to 14 - 6t=t
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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!
I will show you the question
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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
Can I have some help?
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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)
How many solutions does this equation have?
6 +9q = -3 +8q
.no solution
.one solution
.infinitely many
solutions
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-6. -6
9q=-9+8q
-8q -8q
q= -9
Answer: one solution
✓ 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)
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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=
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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
What is the slope of the following points? (11,9) and (12,9)
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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.
the squre if certian number is 22 less than 13 times the original number find the number
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⇒Let that number unknown number be represented by letter x.
⇒ Mathematically this can be written as
⇒[tex]x^{2} =13x-22\\[/tex]
Note that this can help you find the unknown value by solving for x
[tex]x^{2} -13x+22=0\\\\(x-11)(x-2)=0\\x-11=0\\or \\x-2=0\\\\x=11\\\\or\\x=2[/tex]
Note there are two solutions for this question. the answer is 11 and 2
GOODLUCK!!
58.Arrange this set of tools from the smallest of a largest size
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let convert to decimal
[tex]\begin{gathered} \frac{3}{8}=0.375 \\ \frac{3}{4}=0.75 \\ \frac{5}{8}=0.625 \\ \frac{7}{16}=0.4375 \\ \frac{1}{2}=0.5 \\ \frac{5}{16}=0.3125 \end{gathered}[/tex]From the smallest ot the largest
[tex]\frac{5}{16},\frac{3}{8},\frac{7}{16},\frac{1}{2},\frac{5}{8},\frac{3}{4}[/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.
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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
A pool initially contains 1,385 cubic feet of water. Apump begins emptying the water at a constant rate of20 cubic feet per minute. Which of the followingfunctions best approximates the volume v(t), incubic feet, of water in the pool t minutes afterpumping begins, for 0 st s 69 ?A) y(t) = 1,385 - 200B) v(t) = 1,385 – 69tC) v(t) = 1,385 + 20tD) v(t) = 1,385 +691
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Since the tank has an initial volume we can initiate the equation like this
[tex]V(t)=1385[/tex]then since the pool is emptying, it means that the volume is decreasing
[tex]V(t)=1385-[/tex]then the rate at which it is decreasing is 20 cubic feet per minute, meaning that the final equation should be
[tex]V(t)=1385-20t[/tex]Hi there. I think I have this right but I feel unsure
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1) Since a carton resembles a rectangular prism, we can solve it for the volume once we have 3 measurements and the volume of a rectangular prism is found by the product of those three dimensions (width, height, and length).
2) So, we can write out the following (setting a proportion):
[tex]\begin{gathered} V=3\times2\times2=12\:ft^3 \\ V=4\times5\times6=120\:ft^3 \\ 12----3\:seconds \\ 120----x \\ \\ \frac{12}{120}=\frac{3}{x} \\ \frac{1}{10}=\frac{3}{x} \\ x=3\cdot10 \\ x=30\:sec \\ \end{gathered}[/tex]Find all possible inflection points of f(x) = -x^4 + 24x^2. Are there any actual inflection points of f(x)?
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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]Graph the line with the points (2,3) with the slope =1/2
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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: