Answer:
[tex]\boxed{f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}}[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-3x[/tex]
[tex]f(x)=y[/tex]
[tex]y=2x^2-3x[/tex]
Switch variables.
[tex]x=2y^2-3y[/tex]
Solve for y.
Multiply both sides by 8.
[tex]8x=16y^2-24y[/tex]
Add 9 on both sides.
[tex]8x+9=16y^2-24y+9[/tex]
Take the square root on both sides.
[tex]\sqrt{8x+9} =\sqrt{16y^2-24y+9}[/tex]
Add 3 on both sides.
[tex]\sqrt{8x+9}+3 =\sqrt{16y^2-24y+9}+3[/tex]
Divide both sides by 4.
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{\sqrt{16y^2-24y+9}+3}{4}[/tex]
Simplify.
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y-3+3}{4}[/tex]
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y}{4}[/tex]
[tex]\frac{\sqrt{8x+9}+3}{4}=y[/tex]
Inverse y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}[/tex]
Answer:
[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Step-by-step explanation:
[tex] f^{-1}(x) = 2x^2 - 3x [/tex]
Change function notation to y.
[tex] y = 2x^2 - 3x [/tex]
Switch x and y.
[tex] x = 2y^2 - 3y [/tex]
Solve for y.
[tex] 2y^2 - 3y = x [/tex]
Complete the square on the left side. We must divide both sides by 2 to have y^2 as the leading term on the left side.
[tex] y^2 - \dfrac{3}{2}y = \dfrac{x}{2} [/tex]
1/2 of 3/2 is 3/4. Square 3/4 to get 9/16.
Add 9/16 to both sides to complete the square.
[tex] y^2 - \dfrac{3}{2}y + \dfrac{9}{16} = \dfrac{x}{2} + \dfrac{9}{16} [/tex]
Find common denominator on right side.
[tex] (y - \dfrac{3}{4})^2 = \dfrac{8x}{16} + \dfrac{9}{16} [/tex]
If X^2 = k, then [tex] X = \pm \sqrt{k} [/tex]
[tex] y - \dfrac{3}{4} = \pm \sqrt{\dfrac{1}{16}(8x + 9)} [/tex]
Simplify.
[tex] y = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Back to function notation.
[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
1. 2² X 5⁵ 2⁴ 2. (6⁵)² 6⁷ 3.(2x7)⁵ 7⁴ toloong
Answer:
1. 2⁶
2. 6⁷
3. 14⁵
Step-by-step explanation:
We assume and apply the laws of logarithms and indices in the problems above.
1. Product Rule Law: which states that
loga (MN) = loga M + loga N
Where 2² X 5⁵ = 2²+⁵ = 2⁷
2. The Power rule: in which (6⁵)² = 6⁵+² = 6⁷
3. (2x7)⁵ = (14)⁵ or 5 log 14
George walks 1 mile to school. He leaves home at the same time each day, walks at a steady speed of 3 miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first 1/2 mile at a speed of only 2 miles per hour. At how many miles per hour must George run the last 1/2 mile in order to arrive just as school begins today?
Answer:
George must run the last half mile at a speed of 6 miles per hour in order to arrive at school just as school begins today
Step-by-step explanation:
Here, we are interested in calculating the number of hours George must walk to arrive at school the normal time he arrives given that his speed is different from what it used to be.
Let’s first start at looking at how many hours he take per day on a normal day, all things being equal.
Mathematically;
time = distance/speed
He walks 1 mile at 3 miles per hour.
Thus, the total amount of time he spend each normal day would be;
time = 1/3 hour or 20 minutes
Now, let’s look at his split journey today. What we know is that by adding the times taken for each side of the journey, he would arrive at the school the normal time he arrives given that he left home at the time he used to.
Let the unknown speed be x miles/hour
Mathematically;
We shall be using the formula for time by dividing the distance by the speed
1/3 = 1/2/(2) + 1/2/x
1/3 = 1/4 + 1/2x
1/2x = 1/3 - 1/4
1/2x = (4-3)/12
1/2x = 1/12
2x = 12
x = 12/2
x = 6 miles per hour
simplify
[tex] {a}^{ - 2} {b}^{3} [/tex]
Answer:
Below
Step-by-step explanation:
● a^(-2) *b^3
●(1/a^2) *b^3
● b^3 / a^2
On a coordinate plane, a line is drawn from point J to point K. Point J is at (negative 6, negative 2) and point K is at point (8, negative 9). What is the x-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:5? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 –4 –2 2 4
Answer:
-2
Step-by-step explanation:
The coordinate of a point that divides a line AB in a ratio a:b from A([tex]x_1,y_1[/tex]) to B([tex]x_2,y_2[/tex]) is given by the formula:
[tex](x,y)=(\frac{bx_1+ax_2}{a+b} ,\frac{by_1+ay_2}{a+b} )=(\frac{a}{a+b}(x_2-x_1)+x_1 ,\frac{a}{a+b}(y_2-y_1)+y_1 )[/tex]
Given that a line JK, with Point J is at ( -6, - 2) and point K is at point (8, - 9) into a ratio of 2:5. The x coordinate is given as:
[tex]x=\frac{2}{2+5} (8-(-6))+(-6)=\frac{2}{7}(14) -6=4-6=-2[/tex]
Line segments can be divided into equal or unequal ratios
The x coordinate of the segment is -2
The coordinates of points J and K are given as:
[tex]J = (-6,-2)[/tex]
[tex]K = (8,-9)[/tex]
The ratio is given as:
[tex]m : n =2 : 5[/tex]
The x-coordinate is then calculated using:
[tex]x = (\frac{m}{m + n }) (x_2 - x_1) + x_1[/tex]
So, we have:
[tex]x = (\frac{2}{2 + 5 }) (8 - -6) -6[/tex]
[tex]x = (\frac{2}{7}) (14) -6[/tex]
Expand
[tex]x = (2) (2) -6[/tex]
Open bracket
[tex]x = 4 -6[/tex]
Subtract 6 from 4
[tex]x = -2[/tex]
Hence, the x coordinate of the segment is -2
Read more about line ratios at:.
brainly.com/question/14382744
Which letter has a line of symmetry?
Answer:
D. all of the above
Step-by-step explanation:
All the letters from the options have a line of symmetry.
please answer this question now
Answer:
≈ 94.9 mi²
Step-by-step explanation:
The area (A) of Δ WXY can be calculated as
A = [tex]\frac{1}{2}[/tex] × WY × WX × sinW
∠ W = 180° - (40 + 21)° = 180° - 61° = 119°
Calculate WX using the Sine rule, that is
[tex]\frac{11}{sin21}[/tex] = [tex]\frac{WX}{sin40}[/tex] ( cross- multiply )
WX sin21° = 11 sin40° ( divide both sides by sin21° )
WX = [tex]\frac{11sin40}{sin21}[/tex] ≈ 19.73 mi , thus
A = 0.5 × 11 × 19.73 × sin119° ≈ 49.9 mi² ( to the nearest tenth )
I Shall Name Thee Brainliest! (:
What is -7Q + 6 + 5Q = 15 - 7 solve and check
3 (P+5) + P = 3(2+P) solve and check
2(A+4) + 6A = 2(2 + 3A) solve and check
Answer:
hello, friend(✿◡‿◡)
Step-by-step explanation:
-7Q + 6 + 5Q = 15 - 7
Q=-1
3 (P+5) + P = 3(2+P)
P=-3
2(A+4) + 6A = 2(2 + 3A)
A=-2
Which graph shows the solution to the system of linear inequalities? 2x -3y ≤ 12 y < -3
First solve for y in [tex]2x - 3y \le 12[/tex] to get [tex]y \ge \frac{2}{3}x-4[/tex]. The inequality sign flips because we divided both sides by a negative value.
To graph [tex]y \ge \frac{2}{3}x-4[/tex] we need to graph the boundary line y = (2/3)x - 4. This line has a y intercept of (0,-4) and another point on the line is (6,0).
Draw a solid line through (0,-4) and (6,0). The boundary line is solid because of the "or equal to" part of the inequality sign. The last part is to shade above the boundary line because of the "greater than" sign in [tex]y \ge \frac{2}{3}x-4[/tex].
---------------
As for graphing y < -3, we draw a horizontal dashed line through -3 on the y axis. The line is dashed because there is no "or equal to" here. We do not include boundary points as part of the solution set. Shade below this dashed line due to the "less than" sign.
---------------
After doing both of these things on the same xy grid, you'll get something that looks like choice C. I'm assuming choice C has a dashed line for the red region.
Answer: Choice CThe graph is image 2. (last option)
We first draw the lines 2x - 3y = 12 and y=-3. Image 1.
For 2x - 3y ≤ 12
or, 2x - 12 ≤ 3y
or, 3y ≥ 2x - 12
or, y ≥ (2x - 12)/3
we shade upwards.
For y < - 3 we shade below.
So the graph is image 2.
Learn more: https://brainly.com/question/8806877
The surface area of a solid is 10 square feet. The dimensions of a similar solid are
three times as great as the first. The surface area of the new solid in square feet
is...
PLEASE urgent
Answer:
90 ft²
Step-by-step explanation:
Given the sides of similar figures in the ratio a : b, then
ratio of areas = a² : b²
Here ratio of sides = 1 : 3 , thus
ratio of areas = 1² : 3² = 1 : 9
That is the surface area of the new solid is 9 times the first
SA = 9 × 10 = 90 ft²
The total surface area of the new solid in square feet is 90 square feet
Let the solid be a cube.
The surface area of a cube = 6L²
L is the length o the cube;
If the surface area of a solid is 10 square feet, then;
10 = 6L²
L² = 10/6
L = √10/6
If the dimensions of a similar solid are three times as great as the first, then;
New length Ln = 3√10/6
Total surface area of the new solid = 6Ln²
Total surface area of the new solid = 6(3√10/6)²
Total surface area of the new solid = 6(9*10/6)
Total surface area of the new solid = 6(90/6)
Total surface area of the new solid = 90 square feet
This shows that the total surface area of the new solid in square feet is 90 square feet
Learn more here: https://brainly.com/question/23756628
Ronald bought a car for 2,500. The value of the car depreciates by 6 percent each year. What type of function is this ?
Answer:
Exponential
Step-by-step explanation:
The liner function represents that there is a constant change in the original value of the asset
While on the other hand the ex[onential function refers to that function in which there is an increase or decreased in the value of the asset that contains the current value of the asset
Hence, the given situation denotes the exponential function
If f(x)=k (square root)2+x, and f^-^1 (-15)=7, what is the value of k
There's a bit of ambiguity in your question...
We know that [tex]f^{-1}(-15)=7[/tex], which means [tex]f(7)=-15[/tex].
I see three possible interpretations:
• If [tex]f(x)=k\sqrt2+x[/tex], then
[tex]f(7)=-15=k\sqrt2+7\implies k\sqrt2=-22\implies k=-\dfrac{22}{\sqrt2}=11\sqrt2[/tex]
• If [tex]f(x)=k\sqrt{2+x}[/tex], then
[tex]f(7)=-15=k\sqrt{2+7}\implies -15=3k\implies k=-5[/tex]
• If [tex]f(x)=\sqrt[k]{2+x}[/tex], then
[tex]f(7)=-15=\sqrt[k]{2+7}\implies-15=9^{1/k}\implies\dfrac1k=\log_9(-15)[/tex]
which has no real-valued solution.
I suspect the second interpretation is what you meant to write.
In a standard normal distribution, what is the probability of a z-score being less than 2.55?
Answer:
The probability is 0.0053861
Step-by-step explanation:
To answer this question, the best thing to do is to put the wordings in a mathematical expression.
Thus what we have is;
P(z < 2.55)
Now since we have the mathematical expression, the next thing to do here is to use the standard normal distribution table.
From the standard normal distribution table, we can get the probability value that equals the given z-score value
Mathematically this is;
P(z<2.55) = 0.0053861
Compare 1/11 to 11/20 using least to greatest
Answer:
0.09
0.55
Step-by-step explanation:
to write least to greatest firstly, start comparing both number
so the answer will be=0.09,0.55
it least to greatest or in assending order.
In first half of a basketball game one team scored 45 points. This was 5/9 of their score for the whole game. How many points did the team score in the second half?
please help thx :)
Answer:
36
Step-by-step explanation:
45*(9/5)=81(The whole score)
81-45=36(the second half score)
Answer:
36
Step-by-step explanation:
Because you multiply 9*9=81, and then 81-45=36, Because 9*5=45, so the answer is 36.
The canvas of a painting has an area of 64 ft2. What length of frame is needed for the border of the painting?
Answer:
8
Step-by-step explanation:
Assuming, the canvas has the shape of a square. By the square area formula we can derive its side:
[tex]S=l^{2}\\64=l^{2}\\l=\sqrt{64}\\ l=8\: ft[/tex]
Then Each side of the painting measures 8 feet, the length of frame must have 8 feet long, and the width is decided by the framer.
Answer:
The answer is C: 32 ft
Step-by-step explanation:
If you take the square root of the area of 64 ft ^2, you get 8. then it asks what is the length needed for the frame as in the entire frame. So you just have to multiply 8 by 4 which is the number of sides. Also, I got this right on the edg quiz.
Question 4 of 8
Consider the recursive function of an arithmetic sequence below.
f(1) = 3
f(n) = f(n − 1) + 4, for n = 2, 3, 4,...
What is the 6th term of the sequence?
19
23
27
22
Submit
Answer:
[tex]\large \boxed{\sf \ \ 23 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]a_1=f(1)=3\\\\a_2=f(1)+4=3+4=7\\\\a_3=f(3)=a_2+4=7+4=11\\\\a_4=a_3+4=11+4=15\\\\a_5=a_4+4=15+4=19\\\\a_6=a_5+4=19+4=23[/tex]
So the answer is 23.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The Greenpoint factory produced two-fifths of the Consolidated Brick Company’s bricks in 1991. If the Greenpoint factory produced 1,400 tons of bricks in 1991, what was the Consolidated Brick Company’s total output that year, in tons?
Answer:
3500 tons
Step-by-step explanation:
The Greenpoint factory produced 2/5 of the bricks that the Consolidate Brick Company produced in 1991.
Let the amount of bricks produced by the Greenpoint factory be g and the amount of bricks produced by the Consolidated brick company be c.
Therefore:
g = 2/5 * c = 2c/5
That year, the Greenpoint factory produced 1400 tons of bricks. This implies that:
1400 = 2c/5
To find the amount that the Consolidated Brick Company produced, solve for c:
1400 = 2c/5
1400 * 5 = 2c
7000 = 2c
c = 7000 / 2 = 3500 tons
The Consolidated Brick Company had a total production output of 3500 tons in 1991.
Find the ordered pair $(s,t)$ that satisfieFor a certain value of $k,$ the system \begin{align*} 3a + 4b &= 7,\\ 6a + 4b &= k- 4b \end{align*}has infinitely many solutions $(a,b).$ What is $k$?s the system \begin{align*} \dfrac{s}{2} + 5t &= 3,\\ 3t - 6s &= 9. \end{align*}
Answer:
Step-by-step explanation:
Of the books in the Hogwarts Library, 1/4 came from Hermione and 8 came from Luna. Of the rest, 14 were Ron’s, 1/2 were Ginny’s. How many books are there in the library?
Will mark brainlist
Answer:
88
Step-by-step explanation:
The key to this question is combining the two fractional pieces we know about. Namely, Hermione has 1/4 of the books and Ginny has 1/2 of them. This means that between the two of them, they account for 3/4 of the library.
So what does that mean? Well, it means that the books Ron and Hermione have (22 in total) account for the remaining 1/4 of the library. So then the whole library is [tex]4*22=88[/tex].
If approximately 10% of people are left-handed, how many lefties would you expect in a high school graduating class of 424
Answer:
42
Step-by-step explanation:
P(left) = 0.10
Expected number of lefties among high school grads of 424
= 424 * 0.10
= 42 (to the nearest person)
Answer:
you do 20% of 424
1 0% of 424 =42.4
you could round it to 42
Complete the table for the given rule.
1
Rule: y =-
4
y
13
4
2
Answer:
x y
1/4 0
13/4 3
2 7/4
Step-by-step explanation:
To complete the table we just need to replace the value of x and get y as:
for x = 1/4
[tex]y=\frac{1}{4}-\frac{1}{4}=0\\[/tex]
for x=13/4
[tex]y=\frac{13}{4}-\frac{1}{4}=\frac{12}{4}=3[/tex]
for x=2
[tex]y=2-\frac{1}{4}=\frac{7}{4}[/tex]
So, the complete table is:
x y
1/4 0
13/4 3
2 7/4
figure out if the equation is inverse or direct
Answer:
A. Inverse variation
B. Direct variation
C. Direct variation
D. Inverse variation
Hope this helps you
Jacob had a six-sided number cube. Each side was labeled with one number, from 1
through 6. What is the probability that Jacob rolls a prime number?
Round to the nearest tenth.
Answer:
1 out of 6 because you have only one chance to get 4.
Step-by-step explanation:
Answer:
50% chance
Step-by-step explanation:
A prime number is a number that a natural number greater than 1 that is not a product of two smaller natural numbers. And the only prime numbers between 1 and 6 are 2,3, and 5. This is 3 numbers. So he has a chance of 3/6 =.5=50%
The shortest side of a triangle is 12cm and the area of the triangle is 8 square cm. A similar triangle has an area of 18 square cm. Calculate the shortest side of this triangle
Answer:
27cm
Step-by-step explanation:
Given the following :
Triangle A:
Shortest side = 12cm
Area of triangle = 8cm^2
Triangle B:
shortest side =?
AREA of triangle = 18cm^2
If triangle A and B are similar :.
Area A / Area B = Length A / length B
8cm^2 / 18 = 12 / length B
Cross multiply :
8cm * Length B = 18 × 12
Length B = 216 / 8
Length B = 27
Therefore, the shortest of the other triangle IS 27cm
Answer:
its A C and E hope this helps
Step-by-step explanation:
Which expressions are equivalent to -6n+(-12)+4n−6n+(−12)+4nminus, 6, n, plus, left parenthesis, minus, 12, right parenthesis, plus, 4, n ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 4(n-3) -6n4(n−3)−6n4, left parenthesis, n, minus, 3, right parenthesis, minus, 6, n (Choice B) B 2(2n-6)2(2n−6)2, left parenthesis, 2, n, minus, 6, right parenthesis (Choice C) C None of the above
Answer:
The correct option is;
Choice A 4·(n - 3) - 6·n
Step-by-step explanation:
The given expression is
Which gives;-6·n+(-12)+4·n
- 12 + 4·n-6·n = -2·n - 12 = - (2·n + 12)
The options given are Choice A and/or Choice B;
(Choice A) 4·(n - 3) - 6·n
Which can be simplified as follows;
4·(n - 3) - 6·n = 4·n - 12 - 6·n
Which gives;
4·n - 12 - 6·n = 4·n - 6·n- 12 = -2·n - 12 = -(2·n + 12)
Therefore, 4·(n - 3) - 6·n is equivalent to -6·n+(-12)+4·n
For choice B, we have;
2·(2·n - 6) which gives;
2·(2·n - 6) = 4·n - 12
Therefore, 2·(2·n - 6) is not equivalent to -6·n+(-12)+4·n
Which gives the correct option as Choice A.
4(n-3)-6n
Khan academy I got this right
The book cost (in dollars) for one semester's books are given below for a sample of five college students. Calculate the sample variance of the book costs. 200, 130, 400, 500, 345 Group of answer choices
Answer:
17,960
Step-by-step explanation:
Given the following data, book cost (in dollars) = 200, 130, 400, 500, 345.
First of all, we will find the mean of the given data.
[tex]Mean = \frac{200+ 130+ 400+500+ 345}{5}\\Mean =\frac{1575} {5 }\\Mean = 315[/tex]
Or
Mean = (200+130+400+500+345)/5
Mean = 1575/5 = 315.
Second step is to subtract the mean from each book cost;
(200-315) + (130-315) + (400-315) + (500-315) + (345-315)
(-115)+(-185)+85+185+30
Next you square the above deviation;
[tex](-115)^2+(-185)^2+85^2+185^2+30^2\\13225+34225+7225+34225+900\\= 89800[/tex]
Then, divide the above by the average which is 5 in this case.
[tex]Variance = \frac{89800}{5}\\\\Variance = 17960[/tex]
Hence, the value of the variance is 17,960.
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. h(x) = 5x – 5 h(x) = 5x + 5
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
If Marguerite rents for 1 week, it will cost her the same at either company
h(x) = 5x - 5
Step-by-step explanation:
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5
Answer: Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. In one week there are 7 days, therefore in x weeks the cost of rentals are given below:
For company A: f(x) = 15(7x)
For company B: g(x) = 100x + 5
h(x) = f(x) – g(x) represents the difference between the two rate structures.
h(x) = f(x) - g(x) = 15(7x) - (100x + 5)
h(x) = 105x - 100x - 5
h(x) = 5x - 5
If Marguerite rents for 2 weeks:
The cost for company A = 15(7x) = 15(7 × 2) = $210
The cost for company B = 100x + 5 = 100(2) + 5 = 200 + 5 = $205
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
If Marguerite rents for 1 weeks:
The cost for company A = 15(7x) = 15(7 × 1) = $105
The cost for company B = 100x + 5 = 100(1) + 5 = 100 + 5 = $105
If Marguerite rents for 1 week, it will cost her the same at either company
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
h(x) = 5x + 5
those are the answers on edge
Step-by-step explanation:
 Shelby baked 48 cookies with 6 scoops of flower. how many scoops of flour does Shelby need in order to bake 64 cookies? Solve using unit rates.
Answer:
8 scoops of flour
Step-by-step explanation:
It asks for you to solve using unit rates so we need to find out the rate of how much flour you need to bake a single cookie since the question is about how many scoops of flour Shelby needs to bake 64 cookies.
So first, do 6/48, which is 1/8.
It takes 1/8 scoop of flour to bake one cookie.
Unit rate: 1/8 scoop of flour per cookies.
Now, we can multiply 1/8 by 64 since 64 is the number of cookies Shelby needs and 1/8 is the amount of flour for one single cookies. 1/8 * 64 = 8.
Shelby needs 8 scoops of flour to bake 64 cookies
The angle measurements in the diagram are represented by the following expressions.
Answer:
143°Step-by-step explanation:
<A and <B are corresponding angles
< A = < B
plugging the values
[tex]7x + 24 = 3x + 92[/tex]
Move variable to L.H.S and change its sign
[tex]7x - 3x + 24 = 92[/tex]
Move constant to R.H.S and change its sign
[tex]7x - 3x = 92 - 24[/tex]
Calculate
[tex]4x = 68[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{68}{4} [/tex]
Calculate
[tex]x = 17[/tex]
Replacing value
<A = [tex]7x + 24[/tex]
[tex] = 7 \times 17 + 24[/tex]
[tex] = 119 + 24[/tex]
[tex] = 143[/tex]
hope this helps...
Find the value of x for the triangle.
37
37
45°
45°
Answer:
[tex]x=37\,\sqrt{2}[/tex]
Step-by-step explanation:
Notice you are dealing with a right angle triangle, since one of the angles measure [tex]90^o[/tex]. Now, what you are asked to find is the hypotenuse of that triangle, given an angle of [tex]45^o[/tex] and the opposite side: 37 units. Then, we can use for example the sine function which relates opposite, and hypotenuse:
[tex]sin(45^o)=\frac{opposite}{hyp} \\hyp=\frac{opposite}{sin(45^o)} \\hyp=\frac{37}{\sqrt{2}/2}\\hyp=37\,\sqrt{2}[/tex]