Because we know one point and an axis of symmetry, we know that the point (2, -7) must lie on the graph.
Which other point must lie on the graph?If a function has a line of symmetry at x = x₀, then we know that:
f(x₀ + x) = f(x₀ - x).
So we have symmetry around that line.
Then, if the line of symmetry is at x = 5 and we know that:
f(8) = f(5 + 3) = -7
We also must have:
f(2) = f(5 - 3) = -7
Then the point (2, - 7) must be on the graph.
If you want to learn more about symmetry you can read:
https://brainly.com/question/11408596
The ratio of the number of dolls Jacky had to the number of dolls Peter had was 5:2 but, after Jacky gave 15 dolls to Peter, they have an equal number of dolls. How many dolls did they have altogether?
Answer:
70 dolls
Step-by-step explanation:
Hello!
The ratio is 5:2, which are division of a whole. They can be represented as 5x and 2x.
Jacky has 5x dolls, and Peter has 2x dolls. They were equal after subtracting 15 dolls from 5x and adding them to 2x.
Equation:
5x - 15 = 2x + 15Solve:
5x - 15 = 2x + 155x - 30 = 2x5x = 2x + 303x = 30x = 10So Jacky has 5(10) dolls, or 50 dolls, and Peter has 2(10) or 20 dolls.
The total sum is 70 dolls.
Jin's family took a road trip to Niagara Falls. Jin slept for the last 24 miles of the trip. If the total length of the trip was 400 miles, what percentage of the total trip had they travelled when Jin fell asleep?
Answer:
94%
Step-by-step explanation:
400-24=376
Find 376 out of 400 as a decimal:
376/400 = 0.94
0.94x100 = 94%
PLEASE HELP!! Need by 3/29/22!
Find the area of these shapes
Answer:
Step-by-step explanation:
area of A=15*18=270 cm^2
area of B=15*18=270 cm^2
area of C=1/2 ×x×18=9x cm²
area of D=1/2×15×18=135 cm²
Helpppppp!!!
(Show work)
Answer:
Step-by-step explanation:
Find ℒ{f(t)} by first using a trigonometric identity. (write your answer as a function of s. ) f(t) = cos2(t)
The Laplace transform of f(t) = cos² t is equal to the following expression: [tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex].
How to determine the Laplace transform of a non-simple trigonometric expression
In this we need to rewrite the given function in terms of sines and cosines, whose Laplace transforms are well known. There is the following trigonometric formula:
[tex]\cos ^{2} t = \frac{1-\cos 2t}{2}[/tex] (1)
Now we proceed to apply the Laplace transforms:
[tex]\mathcal {L} \{f(t)\} = \frac{1}{2}\cdot \mathcal {L} \left\{1 \right\}-\frac{1}{2}\cdot \mathcal {L}\left\{\cos 2t\right\}[/tex]
[tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex]
The Laplace transform of f(t) = cos² t is equal to the following expression: [tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex]. [tex]\blacksquare[/tex]
Remark
The statement is poorly formatted, the correct form is shown below:
Find [tex]\mathcal {L}\{f(t)\}[/tex] by first using a trigonometric expression. (Write your answer as a function of s). f(t) = cos² t
To learn more on Laplace transforms, we kindly invite to check this verified question: https://brainly.com/question/2088771
Determine the length of a chord whose central angle is 90 degrees in a circle with a radius of 15 inches
Answer:
14.6
Step-by-step explanation:
Charmaine got a prepaid debit card with $15 on it. for her first purchase with the card, she bought some bulk ribbon at a craft store. the price of the ribbon was 21 cents per yard. if after that purchase there was $12.27 left on the card, how many yards of ribbon did charmaine buy?
Answer:
15- 12.27 = 2.73
2.73 is how much she spent on the ribbon.
2.73/ 0.21 = 13
She purchased 13 yards.
Bobby has 58 of a pepperoni pizza in his refrigerator. He eats 14 of this for his lunch. Of the following, which is the best estimate of the fraction of the original pizza left after Bob's lunch?
Answer:
5/32
Step-by-step explanation:
Dont undersrand this at allll...
Answer:
2.3 2 1/3
Step-by-step explanation: you add up all the bikes then divide them by 3 because that's the number of people
Describe the correlation you would expect with these data sets.
(i) The height of a person and the speed at which they can run.
(ii) The age of a second car and its value.
(iii) Time spend watching TV and exam score
(iv) Height and income
(v) Sale of the apartment and high cost
Answer:
(i) no correlation as one variable is not dependent on the other.
(ii) The age of a car does affects its value. Therefore, the age will be the independent variable (x-axis) and the value will be the dependent variable (y-axis). Unless the car is a classic, sought-after car, as the age increases, its value decreases, so this will be a negative correlation.
(iii) The time spent watching TV may affect exam score (since the more time spent watching TV equals less available time to spend studying). Therefore, the time spent watching TV will be the independent variable (x-axis) and the exam score will be the dependent variable (y-axis). As time spent watching TV increases, the exam score could potentially decrease, so this will be a negative correlation.
(iv) no correlation, since one variable is not dependent on the other.
(v) The cost of an apartment may affect its sale, but there are many factors that can affect this such as location of the apartment and the buyers it appeals to. The cost will be the independent variable (x-axis) and the sale will be the dependent variable (y-axis). In usual circumstances, we would expect to see as the cost of an apartment increases, the sale may decrease, as less and less buyers can afford to buy it, so this will be a negative correlation.
Keisha received a $90 gift card for a coffee store. She used it in buying some coffee that costs $8.47 per pound. After buying the coffee, she had $47.65 left on her card. How many pounds of coffee did she buy?
Answer: 4
Step-by-step explanation:
It sounds like you want to know how many pounds of coffee Latoya bought. First, let's figure out how much she spent. Subtract the amount she has left from the amount she started out with:
90 - 57.68 = 32.32
Latoya spent $32.32 on coffee. Since it cost $8.08 per pound, we can divide the total cost by 8.08 to figure out how many pounds she bought:
32.32/8.08 = 4
The box-and-whisker plot below represents some data set. What is the minimum value of the data?
Answer:
minimum value is: the left whisker
Step-by-step explanation:
box an whisker plot: left line is the minimum, first part of the box is Q1, where the box has a middle line it is called Median, the other end of the box is Q3, the right line is called the maximum whisker.
Hope this helps
If 1/10 of a scarf is knit in 48 minutes.what fraction of a scarf is knit in 1 hour
Answer:
1/8
Step-by-step explanation:
i believe this is the answer
Simplify: 14-30/ 2 (- 4)
Thanks! :)
Answer:
The answer is 2
-16/-8=2
Please help extremely confused
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale. (picture of diagram included)
Answer:
basic geometry and trig ratios
Step-by-step explanation:
sin 10 = 500/x
x = 500/sin 10
x = 2 879,4 m
What information is included in this loan agreement that would NOT be included if Ron had gotten a loan from a bank or credit union?
Write an equivalent expression to 16x + 20 using factoring.
Answer:
4(4x + 5)
Step-by-step explanation:
4 goes into both 16 and 20.
4×4 is 16 and
4×5 is 20.
When factoring you put the nunber you factored out typically, in front. Then the remaining factor goes in a set of parenthesis.
This is like undoing distributive property.
16x + 20
= 4(4x+5)
Take 2 common
2(8x+10)Again take two common
2(2(4x+5)Simplify
4(4x+5)Done
Help solve this circle
You're basically using the supplement angle to find the missing number.
Write the word sentence as an equation.
5 is one-fourth of a number c. PLEASE HELP
Tile the rectangle shown using square inches to find the area, and then use multiplication to confirm the area. Use paper to show your work.
Answer:
19 11/16
Step-by-step explanation:
5 1/4 x 3 3/4
Area = width x length
Complete the table.
Milkshakes Cost
Answer:
811
Step-by-step explanation:
i d k
You have a cup of lemonade. Each ice cube has a length of 2 cm, a width of 1 1/4 cm and a height of 3 cm. What is the volume of one of the ice cubes? Show your steps and Explain how you used math to come to your decision.
volume : 7.5 cm²
volume of cube : length * width * height[tex]\hookrightarrow \sf Length \ * Width \ * \ Height[/tex]
[tex]\hookrightarrow \sf 2 \ * 1\dfrac{1}{4} \ * \ 3[/tex]
[tex]\hookrightarrow \sf 2 \ * \dfrac{5}{4} \ * \ 3[/tex]
[tex]\hookrightarrow \sf \dfrac{15}{2}[/tex]
[tex]\hookrightarrow \sf 7.5 \ cm^2[/tex]
Answer:
[tex]\sf volume=7 \frac12 \ cm^3[/tex]
Step-by-step explanation:
Formula
volume of cuboid = length × width × height
Given dimensions of the ice cube:
length = 2 cmwidth = 1 1/4 cmheight = 3cmSubstituting the given values into the formula:
[tex]\sf \implies volume=2\times 1 \frac14 \times 3[/tex]
Converting to improper fractions:
[tex]\sf \implies volume=\dfrac21\times \dfrac54 \times \dfrac31[/tex]
[tex]\sf =\dfrac{ 2\times 5 \times 3}{1 \times 4 \times 1}[/tex]
[tex]\sf =\dfrac{30}{4}[/tex]
Dividing the numerator and denominator by the highest common factor:
[tex]\sf \implies volume=\dfrac{30 \div 2}{4 \div 2}[/tex]
[tex]\sf =\dfrac{15}{2}[/tex]
Converting the improper fraction into a mixed number:
[tex]\sf \implies volume=7 \frac12 \ cm^3[/tex]
let f(x)=3x+4 and g(x)=2x-5 find (f-g)(x)
Step-by-step explanation:
find; (f-g)(x)
(f(x) - g(x))
f(x) = 3x + 4, g(x) = 2x - 5
3x + 4 - 2x + 5
x +9
The first three terms of a geometric sequence are as follows.
-3, 15, -75
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
Here the common ratio is -5
next terms will be 375 and -1875
In the image below, why must triangle A'B'C be similar to ABC?
(Don't mind the chosen answer)
Answer: Option (3)
Step-by-step explanation:
You can get 2 pairs of corresponding angles from the parallel segments, meaning that they are similar by angle-angle.
find the slope of the line that passes through the pints (2,7) and (2,6)
Answer:
Undefined Slope
Step-by-step explanation:
The points (2,6) and (2,7) are on the same vertical line of 2, which results in an undefined slope.
Answer:
m=undefined
Step-by-step explanation:
The formula to find the slope isn't very complicated. The formula is:
y₂-y₁
m= --------
x₂-x₁
You have the points (2,7) and (2,-6). In (2,7) 2 is your x and 7 is your y. Since (2,7) is your first coordinate set, we put 2 as our x₁ . We put 7 as our y₁ .
In (2,-6) 2 is your x and -6 is your y. Since (2,-6) is your second coordinate set, we put 2 as our x₂ . We put -6 as our y₂ .
Let's substitute all of these numbers in:
-6-7 -13
m= ------- = -------
2-2 0
So we have -13/0 .You would think that any number divided by 0 is 0, right?
No. Any number divided by 0 is undefined.
Therefore, you slope, m, would be:
m=undefined .
Solve for area and perimeter in each of the following problems.
Answer:
1. perimeter =2(l+w)
=2(17+10)
= 54 yards
Are of the perimeter=l times b
=17 x 10
=170 yd square
Just follow this concept for all of them. It the same thing. Good Luck!!
Step-by-step explanation:
On May 1, Anna purchased a new condo. She pays a monthly maintenance fee of $230. Her monthly property taxes equal 13.5% of the monthly fee. How much will Anna pay in property taxes for this calendar year?
Answer:
$31.05
Step-by-step explanation:
You can get this answer by changing percent (13.5%) to just 13.5, or in other words, a decimal. you also change 230. to a decimal by by moving the decimal point two times to the left to get 2.30. You can then get your answer by multiplying the values together (2.30 x 13.5)
Jim rented a truck for one day. there was a base fee for $19.95 and there was an additional charge of 91 cents for each mile driven. Jim had to pay $243.81 when he returned the truck. For how many miles did he drive the truck?
Answer:
Jim travelled 246 Miles.
Step-by-step explanation:
The perimeter of a rectangle is 168 m. Its length is five times its width. Find the length and width.
Answer:
Length of rectangle = 63 mWidth of rectangle = 21 mStep-by-step explanation:
Given:
Perimeter of rectangle = 168 mLength of rectangle is five times the widthTo Find:
Length and WidthSolution:
Let's assume width of rectangle x m and length of rectangle be 3x m. To calculate the dimensions of the rectangle we will use the formula of Perimeter of the rectangle
Perimeter of rectangle = 2(L + B)
Substituting the required values:
→ 168 = 2(3x + x)
→ 168 = 2(4x)
→ 168/2 = 4x
→ 84 = 4x
→ 84/4 = x
→ 21 = x
Hence,
Length of the Rectangle = 3x = 3(21) = 63 mWdith of the rectangle = x = 21 mAnswer:
Length = 70 metreWidth = 14 metre⠀
Step-by-step explanation :
⠀
As, it is given that, the perimeter of a rectangle is 168 m and its length is five times its width and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w metre and therefore, the length will be 5w metre .
⠀
Now, According to the Question :
⠀
[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (5 w + w )= 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (6 w )= 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{12 w = 168 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf \: w = \dfrac{168}{12} }}}[/tex]
⠀
[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ w = 14 }}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The width of the rectangle 14 metre .⠀
Now, we are to find the length of the rectangle :
⠀
[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5w }}}}}} \: \: [/tex]
⠀
[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5 \times 14 }}}}}} \: \: [/tex]
⠀
[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ Length = 70 }}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The length of the rectangle is 70 metre